(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 729095, 34985]*) (*NotebookOutlinePosition[ 730038, 35016]*) (* CellTagsIndexPosition[ 729994, 35012]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Math 325: Differential Equations\tSolutions to Assignment 3\t\tFall \ 1997\ \>", "Subsection"], Cell[CellGroupData[{ Cell["Initialization", "Subsubsection", CellMargins->{{Inherited, 126}, {Inherited, Inherited}}, Evaluatable->False, PageBreakWithin->Automatic, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell["<{{18, 126}, {Inherited, Inherited}}, PageBreakWithin->Automatic, InitializationCell->True, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell["Problem 1", "Subsubsection"], Cell[TextData[{ "Using eigenvalues and eigenvectors, express the general solution of the \ system ", StyleBox["X'[t] == A.X[t]", "Input"], " in terms of real-valued functions for each of the matrices ", StyleBox["A", "Input"], " below. Check that your solutions are correct by comparing ", StyleBox["X'[t]", "Input"], " and ", StyleBox["A.X[t]", "Input"], ". Superimpose several plots for each using ", StyleBox["ParametricPlot3D[]", "Input"], " or ", StyleBox["ParametricPlot3D[]", "Input"], ".\n\n", StyleBox["a", FontSlant->"Italic"], ") ", StyleBox["A = {{ 3, 2},\n {-1, 1}};", "Input"], "\n\n", StyleBox["b", FontSlant->"Italic"], ") ", StyleBox["A = {{1,-1, 4},\n {3, 2,-1},\n {2, 1,-1}};", "Input"], "\n \n", StyleBox["c", FontSlant->"Italic"], ") ", StyleBox[ "A = {{-14,18, 8},\n { -6, 8, 2},\n { -5, 7, 3}};", "Input"] }], "Text"], Cell["Solution", "Subsubsection"], Cell[TextData[{ StyleBox["a", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[StyleBox["A = {{-3, -2},\n { 1, -1}};", "Input"]], "Input"], Cell[CellGroupData[{ Cell["Eigensystem[A]", "Input"], Cell[BoxData[ \({{\(-2\) - I, \(-2\) + I}, {{\(-1\) - I, 1}, {\(-1\) + I, 1}}}\)], "Output"] }, Open ]], Cell["A complex-valued solution is:", "Text"], Cell["Z[t_] = {-1+I,1}E^((-2+I)t);", "Input"], Cell[TextData[{ "The real and imaginary parts of ", StyleBox["Z[t]", "Input"], " give two indepenedent real-valued solutions:" }], "Text"], Cell[CellGroupData[{ Cell["X1[t_] = Re[Z[t]]//ComplexExpand", "Input"], Cell[BoxData[ \({\(-E\^\(\(-2\)\ t\)\)\ Cos[t] - E\^\(\(-2\)\ t\)\ Sin[t], E\^\(\(-2\)\ t\)\ Cos[t]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["X2[t_] = Im[Z[t]]//ComplexExpand", "Input"], Cell[BoxData[ \({E\^\(\(-2\)\ t\)\ Cos[t] - E\^\(\(-2\)\ t\)\ Sin[t], E\^\(\(-2\)\ t\)\ Sin[t]}\)], "Output"] }, Open ]], Cell["The general solution is", "Text"], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t]", "Input"], Cell[BoxData[ \({c1\ \((\(-E\^\(\(-2\)\ t\)\)\ Cos[t] - E\^\(\(-2\)\ t\)\ Sin[t])\) + c2\ \((E\^\(\(-2\)\ t\)\ Cos[t] - E\^\(\(-2\)\ t\)\ Sin[t])\), c1\ E\^\(\(-2\)\ t\)\ Cos[t] + c2\ E\^\(\(-2\)\ t\)\ Sin[t]}\)], "Output"] }, Open ]], Cell["The general solution is", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Simplify", "Input"], Cell[BoxData[ \({E\^\(\(-2\)\ t\)\ \(( \((c1 - 3\ c2)\)\ Cos[t] + \((3\ c1 + c2)\)\ Sin[t])\), \(-E\^\(\(-2\)\ t\)\)\ \((\((2\ c1 - c2)\)\ Cos[t] + \((c1 + 2\ c2)\)\ Sin[t])\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t]//Simplify", "Input"], Cell[BoxData[ \({E\^\(\(-2\)\ t\)\ \(( \((c1 - 3\ c2)\)\ Cos[t] + \((3\ c1 + c2)\)\ Sin[t])\), \(-E\^\(\(-2\)\ t\)\)\ \((\((2\ c1 - c2)\)\ Cos[t] + \((c1 + 2\ c2)\)\ Sin[t])\)}\)], "Output"] }, Open ]], Cell["Now we plot several solutions.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["solns = Flatten[Table[X[t],{c1,-1,1},{c2,-1,1}],1];", "Input", AspectRatioFixed->True], Cell[TextData[{ "The output of ", StyleBox["Table[]", "Input"], " is a doubly-nested list; ", StyleBox["Flatten[..,1]", "Input"], " removes the outer layer leaving a list of vector functions. For example, \ the first on the list would be ", StyleBox["X[t]", "Input"], " when both constants are ", StyleBox["-1", "Input"], ":" }], "Text"], Cell[CellGroupData[{ Cell["solns[[1]]", "Input"], Cell[BoxData[ \({2\ E\^\(\(-2\)\ t\)\ Sin[t], \(-E\^\(\(-2\)\ t\)\)\ Cos[t] - E\^\(\(-2\)\ t\)\ Sin[t]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["ParametricPlot[Evaluate[solns], {t,-1,1}]", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.100694 0.309017 0.0612676 [ [.09723 .29652 -6 -9 ] [.09723 .29652 6 0 ] [.29861 .29652 -6 -9 ] [.29861 .29652 6 0 ] [.70139 .29652 -3 -9 ] [.70139 .29652 3 0 ] [.90277 .29652 -3 -9 ] [.90277 .29652 3 0 ] [.4875 .06395 -12 -4.5 ] [.4875 .06395 0 4.5 ] [.4875 .18648 -12 -4.5 ] [.4875 .18648 0 4.5 ] [.4875 .43155 -6 -4.5 ] [.4875 .43155 0 4.5 ] [.4875 .55409 -6 -4.5 ] [.4875 .55409 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .09723 .30902 m .09723 .31527 L s [(-4)] .09723 .29652 0 1 Mshowa .29861 .30902 m .29861 .31527 L s [(-2)] .29861 .29652 0 1 Mshowa .70139 .30902 m .70139 .31527 L s [(2)] .70139 .29652 0 1 Mshowa .90277 .30902 m .90277 .31527 L s [(4)] .90277 .29652 0 1 Mshowa .125 Mabswid .14757 .30902 m .14757 .31277 L s .19792 .30902 m .19792 .31277 L s .24827 .30902 m .24827 .31277 L s .34896 .30902 m .34896 .31277 L s .39931 .30902 m .39931 .31277 L s .44965 .30902 m .44965 .31277 L s .55035 .30902 m .55035 .31277 L s .60069 .30902 m .60069 .31277 L s .65104 .30902 m .65104 .31277 L s .75173 .30902 m .75173 .31277 L s .80208 .30902 m .80208 .31277 L s .85243 .30902 m .85243 .31277 L s .04688 .30902 m .04688 .31277 L s .95312 .30902 m .95312 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 .06395 m .50625 .06395 L s [(-4)] .4875 .06395 1 0 Mshowa .5 .18648 m .50625 .18648 L s [(-2)] .4875 .18648 1 0 Mshowa .5 .43155 m .50625 .43155 L s [(2)] .4875 .43155 1 0 Mshowa .5 .55409 m .50625 .55409 L s [(4)] .4875 .55409 1 0 Mshowa .125 Mabswid .5 .09458 m .50375 .09458 L s .5 .12521 m .50375 .12521 L s .5 .15585 m .50375 .15585 L s .5 .21712 m .50375 .21712 L s .5 .24775 m .50375 .24775 L s .5 .27838 m .50375 .27838 L s .5 .33965 m .50375 .33965 L s .5 .37028 m .50375 .37028 L s .5 .40092 m .50375 .40092 L s .5 .46219 m .50375 .46219 L s .5 .49282 m .50375 .49282 L s .5 .52345 m .50375 .52345 L s .5 .03331 m .50375 .03331 L s .5 .00268 m .50375 .00268 L s .5 .58472 m .50375 .58472 L s .5 .61535 m .50375 .61535 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid 0 .27492 m .02649 .27025 L .14509 .25301 L .23714 .24275 L .27954 .23923 L .29731 .23803 L .31508 .23702 L .33044 .23631 L .33823 .23602 L .34636 .23576 L .35358 .23557 L .35999 .23544 L .36301 .23539 L .36626 .23535 L .36928 .23532 L .37205 .23529 L .37374 .23529 L .37465 .23528 L .3755 .23528 L .37699 .23527 L .37862 .23527 L .37953 .23527 L .38038 .23527 L .38197 .23528 L .38285 .23528 L .38367 .23528 L .3855 .2353 L .3883 .23532 L .39134 .23535 L .39447 .2354 L .39736 .23545 L .40741 .23572 L .4128 .23592 L .4176 .23612 L .43577 .23723 L .44507 .23802 L .45313 .23885 L .46797 .2408 L .47964 .24281 L .49089 .24526 L .49972 .24767 L .51363 .25277 L .51882 .25532 L .52351 .25815 L .52732 .26102 L .53004 .26362 L .53219 .26626 L .53368 .2687 L .53426 .26992 L .53475 .2712 L Mistroke .5351 .27238 L .53534 .27344 L .53544 .27402 L .53552 .27463 L .53558 .27515 L .5356 .27544 L .53561 .27571 L .53562 .27586 L .53562 .27602 L .53563 .2761 L .53563 .27617 L .53563 .27631 L .53563 .27645 L .53563 .27657 L .53563 .27671 L .53563 .27686 L .53562 .27701 L .53562 .27717 L .5356 .27749 L .53558 .27779 L .53556 .27806 L .5355 .27862 L .53541 .27921 L .53521 .28027 L .53495 .28128 L .53468 .28219 L .53397 .28404 L .53303 .28596 L .53083 .28942 L .52843 .29237 L .52572 .29512 L .5231 .29743 L .52293 .29756 L Mfstroke .27592 .06442 m .33061 .06927 L .38095 .07549 L .42509 .08272 L .4663 .09148 L .4997 .10052 L .52534 .10912 L .5653 .12707 L .57997 .13599 L .59276 .14563 L .60229 .15473 L .60992 .16419 L .61259 .16835 L .61501 .17276 L .61826 .18058 L .6195 .18479 L .62001 .18699 L .62045 .18931 L .62077 .19151 L .62098 .19349 L .62106 .19444 L .62112 .19546 L .62114 .19592 L .62116 .19642 L .62118 .19684 L .62119 .19729 L .6212 .1978 L .6212 .19827 L .6212 .19851 L .6212 .19878 L .6212 .19906 L .62119 .19932 L .62118 .1998 L .62117 .20024 L .62115 .20072 L .62113 .20123 L .62102 .20291 L .62094 .20386 L .62085 .20474 L .62031 .20847 L .61992 .21052 L .6195 .21236 L .61753 .21903 L .61473 .22589 L .60771 .23831 L .5997 .24894 L .59139 .25798 L .58233 .26642 L .5737 .27346 L .56488 .27991 L Mistroke .55688 .28521 L .54975 .28954 L .5428 .29344 L .53677 .29658 L .53106 .29934 L .5262 .30153 L .5221 .30325 L .51883 .30454 L Mfstroke 1 .06757 m .97795 .08484 L .92108 .12484 L .86981 .15773 L .81954 .18738 L .77556 .21135 L .73741 .23071 L .70116 .24785 L .67036 .26145 L .64172 .27324 L .61783 .2824 L .59798 .28949 L .57987 .2955 L .56507 .30003 L .55183 .30374 L .5412 .30644 L .53268 .30838 L .52519 .30987 L .5193 .31087 L .51473 .31151 L s 0 .43819 m .05304 .41699 L .12822 .38899 L .19675 .36528 L .25285 .34734 L .29867 .33384 L .33969 .32279 L .37263 .3148 L .39902 .30907 L .42224 .30469 L .4405 .30178 L .4562 .29979 L .46281 .29914 L .46828 .29871 L .47303 .29842 L .47547 .29831 L .47755 .29824 L .47858 .29822 L .47914 .29821 L .47965 .2982 L .48011 .29819 L .48053 .29819 L .48098 .29818 L .48123 .29818 L .48146 .29818 L .48169 .29818 L .48194 .29818 L .48207 .29818 L .4822 .29818 L .48244 .29818 L .48267 .29818 L .4829 .29818 L .4831 .29818 L .48332 .29818 L .4838 .29819 L .48431 .29819 L .4852 .29821 L .48608 .29823 L .48687 .29826 L .48855 .29834 L .48993 .29842 L .4913 .29852 L .49362 .29876 L .49553 .29903 L .49736 .29935 L .49879 .29968 L .50016 .30006 L .50123 .30043 L .50289 .30119 L .50355 .30161 L Mistroke .50404 .30198 L .5041 .30204 L Mfstroke .5 .30902 m .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L .5 .30902 L s 1 .17984 m .94696 .20104 L .87178 .22905 L .80325 .25276 L .74715 .2707 L .70133 .2842 L .66031 .29524 L .62737 .30324 L .60098 .30896 L .57776 .31335 L .5595 .31625 L .5438 .31824 L .53719 .31889 L .53172 .31932 L .52697 .31961 L .52453 .31972 L .52245 .31979 L .52142 .31982 L .52086 .31983 L .52035 .31984 L .51989 .31984 L .51947 .31985 L .51902 .31985 L .51877 .31985 L .51854 .31986 L .51831 .31986 L .51806 .31986 L .51793 .31986 L .5178 .31986 L .51756 .31986 L .51733 .31986 L .5171 .31986 L .5169 .31985 L .51668 .31985 L .5162 .31985 L .51569 .31984 L .5148 .31982 L .51392 .3198 L .51313 .31977 L .51145 .3197 L .51007 .31961 L .5087 .31951 L .50638 .31927 L .50447 .31901 L .50264 .31868 L .50121 .31836 L .49984 .31797 L .49877 .3176 L .49711 .31684 L .49645 .31643 L Mistroke .49596 .31605 L .4959 .31599 L Mfstroke 0 .55046 m .02205 .5332 L .07892 .4932 L .13019 .46031 L .18046 .43065 L .22444 .40668 L .26259 .38733 L .29884 .37018 L .32964 .35659 L .35828 .3448 L .38217 .33564 L .40202 .32854 L .42013 .32254 L .43493 .31801 L .44817 .3143 L .4588 .3116 L .46732 .30966 L .47481 .30816 L .4807 .30716 L .48527 .30652 L s .72408 .55362 m .66939 .54876 L .61905 .54254 L .57491 .53531 L .5337 .52655 L .5003 .51751 L .47466 .50892 L .4347 .49096 L .42003 .48204 L .40724 .4724 L .39771 .46331 L .39008 .45385 L .38741 .44969 L .38499 .44527 L .38174 .43746 L .3805 .43324 L .37999 .43104 L .37955 .42872 L .37923 .42652 L .37902 .42454 L .37894 .4236 L .37888 .42258 L .37886 .42211 L .37884 .42162 L .37882 .4212 L .37881 .42074 L .3788 .42023 L .3788 .41976 L .3788 .41952 L .3788 .41925 L .3788 .41897 L .37881 .41871 L .37882 .41823 L .37883 .41779 L .37885 .41731 L .37887 .41681 L .37898 .41512 L .37906 .41417 L .37915 .4133 L .37969 .40956 L .38008 .40751 L .3805 .40567 L .38247 .39901 L .38527 .39214 L .39229 .37972 L .4003 .36909 L .40861 .36005 L .41767 .35162 L .4263 .34457 L .43512 .33812 L Mistroke .44312 .33283 L .45025 .32849 L .4572 .3246 L .46323 .32146 L .46894 .31869 L .4738 .31651 L .4779 .31478 L .48117 .3135 L Mfstroke 1 .34312 m .97351 .34778 L .85491 .36502 L .76286 .37529 L .72046 .37881 L .70269 .38 L .68492 .38101 L .66956 .38172 L .66177 .38202 L .65364 .38228 L .64642 .38246 L .64001 .38259 L .63699 .38264 L .63374 .38269 L .63072 .38272 L .62795 .38274 L .62626 .38275 L .62535 .38275 L .6245 .38276 L .62301 .38276 L .62138 .38276 L .62047 .38276 L .61962 .38276 L .61803 .38276 L .61715 .38275 L .61633 .38275 L .6145 .38274 L .6117 .38271 L .60866 .38268 L .60553 .38263 L .60264 .38258 L .59259 .38231 L .5872 .38212 L .5824 .38191 L .56423 .3808 L .55493 .38001 L .54687 .37918 L .53203 .37723 L .52036 .37523 L .50911 .37278 L .50028 .37037 L .48637 .36527 L .48118 .36271 L .47649 .35989 L .47268 .35701 L .46996 .35441 L .46781 .35178 L .46632 .34933 L .46574 .34811 L .46525 .34684 L Mistroke .4649 .34565 L .46466 .34459 L .46456 .34401 L .46448 .3434 L .46442 .34288 L .4644 .34259 L .46439 .34232 L .46438 .34217 L .46438 .34201 L .46437 .34194 L .46437 .34186 L .46437 .34172 L .46437 .34159 L .46437 .34146 L .46437 .34132 L .46437 .34117 L .46438 .34103 L .46438 .34087 L .4644 .34054 L .46442 .34025 L .46444 .33997 L .4645 .33941 L .46459 .33882 L .46479 .33776 L .46505 .33675 L .46532 .33584 L .46603 .334 L .46697 .33207 L .46917 .32861 L .47157 .32566 L .47428 .32291 L .4769 .32061 L .47707 .32047 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[ooonIgYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00?l0VOl0I_l0CXf=SLcCXf=SLcII03=VoalO7eiN GYfMWMcLg02Z020000S`000ol0 002>0000S`000ol0002>0000S`000ol0002>0000S`000ol0002>0000S`000ol0002>0000S`000ol0 002>0000S`000ol0002>0000S`02ohl0002?0003o`0008h0002?0003o`0008h0002?0003o`0008h0 002?0003o`0008h0002?0003o`0008h0002?0003o`0008h0002700?o1@000ol0002>0000R0000ol0 00040003o`0008h0001?00Wo:005o`030?oo00;o1@03ohh0001H00co8P000ol0o`060003o`0008/0 0_l10000I007oa/000?o0?l01P000ol0002:0003o`000040001[00Ko5P02o`H000?o0000R@000ol0 00020000L@07oaL000?o0000R0000ol000030000N005oa8000?o0000Q`000ol000040000O@04o`h0 00?o0000Q@02o`L0002100?o2`000ol000240003o`0000L0002400Go1P000ol0002200;o2P0008T0 1Ol00`3oo`220003o`0000X0002>00?oP002o`d0002?0003o`3o00;oO0000ol0000=0000S`000ol0 000200;oN@000ol0000>0000S`000ol0000400;oM@02oa40002?0003o`0000H00oma0003o`000140 002?0003o`0000T00_m]00;o500008l000?o00002`02ofX000?o0000500008l00_l>00?oI@02oaL0 002?0003o`0001000_mR0003o`0001L0002?0003o`0001800_mN00;o6P0008l000?o00005002oe/0 00?o00006P0008l000?o00005P000ol0001F00;o7@0008l000?o00005`000ol0001D0003o`0001d0 002?0003o`0001P000?o0000D@02ob00002?0003o`0001P000?o0000D0000ol0000P0000S`000ol0 000I0003o`0004d00_lS0000S`02oa/000?o0000B`000ol0000S0000S`000ol0000J0003o`0004T0 0_lV0000S`000ol0000K0003o`0004H00_lX0000S`000ol0000L0003o`0004<00_lZ0000S`000ol0 000M0003o`0004000_l/0000S`000ol0000N0003o`0003h000?o0000;00008l000?o00007P000ol0 000l00;o;`0008H01?l50003o`0001l000?o0000>@02obh00_l10000Q`000ol000050003o`0001l0 00?o0000=`02obd00ol30000P005o`<000?o00001003oal000?o0000=@02obd00_l60000R@000ol0 00030003o`0001l00_ld00;o;003o`P000260004o`00o`D000?o000080000ol0000a0003o`0002X0 0_l;0000Q`02o`H000?o000080000ol0000_00;o:P03o`d0002?0003o`00020000?o0000;@02obX0 0_l@0000S`000ol0000P0003o`0002`000?o00009`03oa80002?0003o`0001l000?o0000:`02obL0 0olE0000S`000ol0000O0003o`0002T00_lV00?o600008l000?o00007`000ol0000W00;o9P02oa/0 002?00;o80000ol0000U00;o9@03oad0002?0003o`0001l000?o000090000ol0000R00?o800008l0 00?o00007P000ol0000S00;o8P03ob<0002?0003o`0001h000?o00008@02ob800_lV0000S`000ol0 000M0003o`0002000_lQ00?o:00005P09ol@0003o`0001d000?o00007P02ob000ol[0000BP0>obL0 1_l:0003o`0001`000?o00007@02oal00ol^0000@00:oc/01ol30003o`0001`000?o00006`02oal0 0_la0000=`09od`01OlL0003o`0001X00_lN00?o<`0002h02OmH0004o`3ooaP00_lK00;o7@03ocH0 000V00SoH@001Ol0003o01H000?o00006003oa`00oli00007`07ofT000?o00000P03oa8000?o0000 5P03oa`00oll00006007og0000?o00001@000ol0000?0003o`0001<00olL00?o?`0001401omg0003 o`0000H000?o00003@000ol0000B00;o7003od80000:00OoOP000ol0000600;o3002oa<00_lK00?o A@0000@01_lD00?o=@04ocD000?o00001`000ol000090003o`0001400_l<00Co2@04obT00olL0000 1?lK0003o`0003D000?o0000=@000ol000070003o`0000P000?o00003`03o`l000?o00001P03obh0 00?o00006`0001L01Ol00`3oo`02obl01Ol30003o`0003@00_l80003o`0000L000?o00003@03oa<0 00?o00000P03obl01?lL00007@000ol0o`0i0003o`0003<000?o00001`000ol0000500;o3@03oaL0 1?lb0003o`3o01d0000M0003o`3o03H000Co003o=@000ol0000600;o1003o``00olG00Co=@000ol0 o`0M00007P02ocL00_lf0003o`0000H000?o00000P000ol0000:00?o5P04o`030?oo03L00_lM0000 S`000ol000050003o`00008000?o00002003oaD01?mM0000S`000ol000040003o`0000?o2003oa@0 1?mQ0000P00@o`H000?o0?l02003oa801OmU0000O004o`l00_l400?o1`02oa001OmZ0000MP06o`d0 0ol30003o`00008000?o00000`05o`l00om_0000oolPo`40000=0003o`0000`000?o00002`000ol0 000<0003o`0000/000?o00002`000ol0000<0003o`0000H00ol20003o`0000`01?l50003o`000080 00Co00000ol70003o`0000<01_l30003o`0000/000?o000030000ol0000;0003o`0000/000?o0000 30000ol0000;0003o`0000`000?o0000300001`000?o0000=P000ol0000A00Co4@04o`D00ol400;o 3P05obH000?o0000=P000ol0000K0000I005oa401?l700;o00<0o`001@0?oh80001O00Go4`03o`T0 0_l30003o`0000@000?o0000SP0005/01?lE00?o2`000ol000020003o`0000D000?o0000SP0005L0 1?lG00;o3002o`@000?o00001P000ol0002>0000D`04oaP00ol<00;o1@02o`P000?o0000SP000500 0olH00Co3@02o`L000?o00001`000ol0002>0000C@03oaP00ol@0003o`0000L000?o00001`02ohl0 001:00?o6003oa400_l:0003o`0000L000?o0000R@04o`40001600Co6@02oa<000?o00002P000ol0 00070003o`0008801ol50000@`03oa/00_lD0003o`0000/00_l80003o`0007/01ol<0000@003oa`0 0_lF0003o`0000`000?o00001P000ol0001d00Oo4`0003d00olM00;o5`000ol0000>0003o`0000D0 00?o0000K@07oaX0000j00?o7P02oaL00_lB00?o10000ol0001V00Oo8@0003L00olN00?o60000ol0 000E00;o0P000ol0001O00Oo:00003@00olO00;o6P000ol0000H00?oF009obl0000a00?o8002oa`0 00?o00006P06odX02Olh0000;P03ob000olM0003o`0001/000?o00000`03oc`02om10000;002ob40 0_lO0003o`0001`000?o00001P09obH03Om<0000:@03ob000olQ0003o`0001`000?o00003`0VoeT0 000V00?o8@02ob<000?o00007@000ol0002>00009002ob800_lU0003o`0001d000?o0000SP000240 0olR00;o9P000ol0000N0003o`0008h0000N00?o90000ol0000V0003o`0001h000?o0000SP0001/0 0olU00;o:0000ol0000O00;oS`0001T00_lV00;o:P000ol0000O0003o`0008h0000F00?o9P02ob`0 00?o00007`000ol0002>00004`03obL00_l^0003o`0001l000?o0000SP0001000olY0003o`0002d0 00?o000080000ol0002>00003P02obX00_l`0003o`00020000?o0000SP0000/00olZ00;o0000ol0000H0003o`0000@00on>000000@0oooo ;@02ocX000?o00006@000ol000030003o`0008h000000ol0000/00;o?0000ol0000F0004o`00o`D0 00?o0000SP0002d00_ln0003o`0001L00_l60003o`0008h0000/0003o`0003l000?o00007P000ol0 002>0000:P02od<000?o00007@000ol0002>0000:002odH000?o000070000ol0002>00009P02odP0 00?o000070000ol0002>00009002od/000?o00006`000ol0002>00008`000ol0001<0003o`0001X0 0_n?00008@02odl000?o00006P000ol0002>000080000ol0001@0003o`0001T000?o0000SP0001h0 0_mD00;o6@000ol0002>00007@000ol0001F0003o`0001H000?o0000SP0001/00_mJ0003o`0001D0 00?o0000SP0001X000?o0000F`02oaD000?o0000SP0001P00_mP00;o4`000ol0002>00005`000ol0 001R00;o4@000ol0002>00005@02ofL00ol>00;oS`0001@000?o0000JP02o``000?o0000SP000180 0_m_00;o2P000ol0002>00004@000ol0001a00?o1`000ol0002>00003`02ogL00_l50003o`0008h0 000>0003o`0007T00ol20003o`0008h0000=0003o`0007d00on@00002`02oh801?n=00002P000ol0 002200;o0P05ohP0000800;oQ@000ol0000600CoQ00000L000?o0000Q@000ol0000:00CoP00000D0 0_n80003o`0000h00omm000010000ol000280003o`0001401Omh00000`000ol000290003o`0001H0 1oma00000P000ol0002:0003o`0001d01omZ000000<0o`00Q003o`D000?o00009007of<000000ol0 00250003o`0000@000?o0000:`0;oeP0002600Co1@03ocH02?m@0000QP000ol0o`060003o`0008h0 00260003o`3o00H000?o0000SP0008L00_l60003o`0008h0002?0003o`0008h0002?0003o`0008h0 002?0003o`0008h0002?0003o`0008h0002?0003o`0008h0002?00;oS`0008l000?o0000SP0008l0 00?o0000SP0008l000?o0000SP0008l000?o0000SP0008l000?o0000SP0008l000?o0000SP0008l0 00?o0000SP0008l000?o0000SP0008l00_n?0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-4.97786, -5.04378, 0.0346889, 0.0570116}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["The solutions are stable spirals that flow into the origin.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["b", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[StyleBox[ "A = {{1,-1, 4},\n {3, 2,-1},\n {2, 1,-1}};", "Input"]], "Input"], Cell[CellGroupData[{ Cell["Eigensystem[A]", "Input"], Cell[BoxData[ \({{\(-2\), 1, 3}, {{\(-1\), 1, 1}, {\(-1\), 4, 1}, {1, 2, 1}}}\)], "Output"] }, Open ]], Cell["Fundamental solutions are:", "Text"], Cell["\<\ X1[t_] = {-1,1,1}E^(-2t); X2[t_] = {-1,4,1}E^t; X3[t_] = {1,2,1}E^(3t);\ \>", "Input"], Cell["The general solution is", "Text"], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t] + c3 X3[t]", "Input"], Cell[BoxData[ \({\(-c1\)\ E\^\(\(-2\)\ t\) - c2\ E\^t + c3\ E\^\(3\ t\), c1\ E\^\(\(-2\)\ t\) + 4\ c2\ E\^t + 2\ c3\ E\^\(3\ t\), c1\ E\^\(\(-2\)\ t\) + c2\ E\^t + c3\ E\^\(3\ t\)}\)], "Output"] }, Open ]], Cell["Check:", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Simplify", "Input"], Cell[BoxData[ \({2\ c1\ E\^\(\(-2\)\ t\) - c2\ E\^t + 3\ c3\ E\^\(3\ t\), \(-2\)\ c1\ E\^\(\(-2\)\ t\) + 4\ c2\ E\^t + 6\ c3\ E\^\(3\ t\), \(-2\)\ c1\ E\^\(\(-2\)\ t\) + c2\ E\^t + 3\ c3\ E\^\(3\ t\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t]//Simplify", "Input"], Cell[BoxData[ \({2\ c1\ E\^\(\(-2\)\ t\) - c2\ E\^t + 3\ c3\ E\^\(3\ t\), \(-2\)\ c1\ E\^\(\(-2\)\ t\) + 4\ c2\ E\^t + 6\ c3\ E\^\(3\ t\), \(-2\)\ c1\ E\^\(\(-2\)\ t\) + c2\ E\^t + 3\ c3\ E\^\(3\ t\)}\)], "Output"] }, Open ]], Cell["Plots:", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ solns = Flatten[Table[X[t],{c1,-1,1},{c2,-1,1},{c3,-1,1}],2];\ \>", "Input", AspectRatioFixed->True], Cell[TextData[{ "In this case, ", StyleBox["Table[]", "Input"], " creates a triply-nested list; ", StyleBox["Flatten[..,2]", "Input"], " removes the outer two layers." }], "Text"], Cell[CellGroupData[{ Cell["ParametricPlot3D[Evaluate[solns], {t,-1,1}]", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.11058 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D /Courier findfont 10 scalefont setfont % Scaling calculations -0.0655946 1.20798 0 1.20798 [ [.10637 .1608 -17.3292 -9 ] [.10637 .1608 .67075 0 ] [.28233 .09024 -5.52981 -9 ] [.28233 .09024 .47019 0 ] [.4672 .01613 -10.5664 -9 ] [.4672 .01613 1.4336 0 ] [.04455 .7089 -18 -3.02544 ] [.04455 .7089 0 5.97456 ] [.16737 .81436 -18 -3.11661 ] [.16737 .81436 0 5.88339 ] [.2795 .91063 -6 -3.19716 ] [.2795 .91063 0 5.80284 ] [.38227 .99887 -12 -3.26885 ] [.38227 .99887 0 5.73115 ] [.47681 1.08003 -12 -3.33306 ] [.47681 1.08003 0 5.66694 ] [.03323 .25863 -18 -2.73598 ] [.03323 .25863 0 6.26402 ] [.01422 .41845 -6 -2.83339 ] [.01422 .41845 0 6.16661 ] [-0.0063 .59106 -12 -2.93919 ] [-0.0063 .59106 0 6.06081 ] [ 0 0 0 0 ] [ 1 1.11058 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .05392 .19694 m .54679 0 L s .11663 .17188 m .12176 .17742 L s [(-10)] .10637 .1608 .92547 1 Mshowa .29207 .10178 m .29693 .10755 L s [(0)] .28233 .09024 .84327 1 Mshowa .47634 .02815 m .48092 .03416 L s [(10)] .4672 .01613 .76107 1 Mshowa .125 Mabswid .15104 .15813 m .15409 .16149 L s .18578 .14425 m .1888 .14763 L s .22087 .13023 m .22385 .13364 L s .25629 .11608 m .25925 .11951 L s .32819 .08735 m .33108 .09084 L s .36468 .07277 m .36753 .07629 L s .40153 .05804 m .40435 .06159 L s .43875 .04317 m .44153 .04675 L s .08254 .1855 m .08565 .1888 L s .51432 .01298 m .51702 .01661 L s .25 Mabswid 0 .65354 m .53135 1.11058 L s .05889 .7042 m .06607 .70185 L s [(-20)] .04455 .7089 1 -0.32768 Mshowa .1818 .80992 m .18902 .8077 L s [(-10)] .16737 .81436 1 -0.30742 Mshowa .29401 .90643 m .30126 .90433 L s [(0)] .2795 .91063 1 -0.28952 Mshowa .39684 .99488 m .40412 .99289 L s [(10)] .38227 .99887 1 -0.27359 Mshowa .49143 1.07624 m .49874 1.07435 L s [(20)] .47681 1.08003 1 -0.25932 Mshowa .125 Mabswid .08441 .72615 m .08872 .72475 L s .10944 .74768 m .11376 .7463 L s .13401 .76881 m .13833 .76745 L s .15813 .78956 m .16245 .78821 L s .20505 .82992 m .20939 .8286 L s .22789 .84956 m .23223 .84826 L s .25032 .86885 m .25466 .86757 L s .27235 .88781 m .2767 .88653 L s .31528 .92473 m .31964 .92349 L s .3362 .94272 m .34055 .94149 L s .35675 .9604 m .36112 .95918 L s .37696 .97779 m .38133 .97658 L s .41638 1.01169 m .42076 1.01051 L s .43561 1.02823 m .43998 1.02706 L s .45452 1.04449 m .4589 1.04333 L s .47312 1.0605 m .4775 1.05935 L s .03289 .68184 m .03719 .68041 L s .00638 .65903 m .01068 .65759 L s .50945 1.09174 m .51383 1.09061 L s .52718 1.10699 m .53157 1.10588 L s .25 Mabswid .05392 .19694 m 0 .65354 L s .04729 .25312 m .05432 .25037 L s [(-10)] .03323 .25863 1 -0.39201 Mshowa .02838 .41321 m .03546 .41058 L s [(0)] .01422 .41845 1 -0.37036 Mshowa .00796 .58611 m .0151 .58364 L s [(10)] -0.0063 .59106 1 -0.34685 Mshowa .125 Mabswid .04362 .28418 m .04784 .28254 L s .0399 .31571 m .04413 .31409 L s .03612 .34772 m .04035 .34611 L s .03228 .38021 m .03652 .37862 L s .02443 .44671 m .02868 .44516 L s .02041 .48075 m .02467 .47921 L s .01632 .51531 m .02059 .51379 L s .01218 .55043 m .01645 .54893 L s .0509 .22252 m .05511 .22085 L s .00368 .62237 m .00797 .6209 L s .25 Mabswid .05392 .19694 m 0 .65354 L s 0 .65354 m .53135 1.11058 L s .53135 1.11058 m .53193 .69704 L s .53193 .69704 m .05392 .19694 L s .54679 0 m .95979 .56521 L s .95979 .56521 m 1 .99183 L s 1 .99183 m .5478 .46859 L s .5478 .46859 m .54679 0 L s .05392 .19694 m 0 .65354 L s 0 .65354 m .5478 .46859 L s .5478 .46859 m .54679 0 L s .54679 0 m .05392 .19694 L s .53193 .69704 m .95979 .56521 L s .95979 .56521 m 1 .99183 L s 1 .99183 m .53135 1.11058 L s .53135 1.11058 m .53193 .69704 L s 0 0 m 1 0 L 1 1.11058 L 0 1.11058 L closepath clip newpath .5 Mabswid .85616 .97159 m .83827 .95503 L s .86201 .96783 m .84047 .9474 L s .86778 .96414 m .86511 .96156 L s .84268 .93975 m .86511 .96156 L s .81723 .93554 m .83827 .95503 L s .81955 .92744 m .84047 .9474 L s .82187 .91934 m .84268 .93975 L s .7977 .91739 m .81723 .93554 L s .80013 .90881 m .81955 .92744 L s .80257 .90022 m .82187 .91934 L s .77955 .9005 m .7977 .91739 L s .78211 .89141 m .80013 .90881 L s .78467 .88231 m .80257 .90022 L s .76269 .88479 m .77955 .9005 L s .76538 .87516 m .78211 .89141 L s .76807 .86552 m .78467 .88231 L s .74703 .87017 m .76269 .88479 L s .58923 .76874 m .59066 .77271 L s .59036 .76441 m .59172 .76862 L s .59148 .76007 m .59279 .76452 L s .74986 .85998 m .76538 .87516 L s .58784 .76487 m .58923 .76874 L s .58903 .7603 m .59036 .76441 L s .73248 .85659 m .74703 .87017 L s .75269 .84977 m .76807 .86552 L s .59021 .75572 m .59148 .76007 L s .58648 .76113 m .58784 .76487 L s .58773 .75629 m .58903 .7603 L s .73546 .8458 m .74986 .85998 L s .58898 .75145 m .59021 .75572 L s .58514 .75749 m .58648 .76113 L s .71896 .84396 m .73248 .85659 L s .58646 .75238 m .58773 .75629 L s .73844 .83499 m .75269 .84977 L s .58779 .74726 m .58898 .75145 L s .58383 .75397 m .58514 .75749 L s .72209 .83254 m .73546 .8458 L s .58523 .74857 m .58646 .75238 L s .7064 .83223 m .71896 .84396 L s .58255 .75056 m .58383 .75397 L s .58663 .74316 m .58779 .74726 L s .72523 .82109 m .73844 .83499 L s .58402 .74485 m .58523 .74857 L s .70969 .82014 m .72209 .83254 L s .58129 .74726 m .58255 .75056 L s .5855 .73913 m .58663 .74316 L s .69472 .82134 m .7064 .83223 L s .58285 .74122 m .58402 .74485 L s .58006 .74406 m .58129 .74726 L s .71299 .80803 m .72523 .82109 L s .58441 .73518 m .5855 .73913 L s .69818 .80855 m .70969 .82014 L s .5817 .73768 m .58285 .74122 L s .68386 .81124 m .69472 .82134 L s .57885 .74098 m .58006 .74406 L s .58335 .7313 m .58441 .73518 L s .58059 .73424 m .5817 .73768 L s .70166 .79573 m .71299 .80803 L s .57766 .738 m .57885 .74098 L s .68751 .79771 m .69818 .80855 L s .67375 .80187 m .68386 .81124 L s .58233 .72749 m .58335 .7313 L s .5795 .73087 m .58059 .73424 L s .5765 .73512 m .57766 .738 L s .58133 .72374 m .58233 .72749 L s .96647 .97674 m .94042 .95481 L s .69116 .78414 m .70166 .79573 L s .57843 .7276 m .5795 .73087 L s .66435 .7932 m .67375 .80187 L s .67759 .78756 m .68751 .79771 L s .57535 .73235 m .5765 .73512 L s .97143 .97383 m .94219 .94886 L s .97634 .97096 m .94397 .94291 L s .58038 .72006 m .58133 .72374 L s .5774 .7244 m .57843 .7276 L s .57423 .72969 m .57535 .73235 L s .65559 .78517 m .66435 .7932 L s .6684 .77805 m .67759 .78756 L s .68145 .7732 m .69116 .78414 L s .57945 .71643 m .58038 .72006 L s .57639 .72128 m .5774 .7244 L s .57312 .72713 m .57423 .72969 L s .90975 .92905 m .94042 .95481 L s .64744 .77775 m .65559 .78517 L s .91161 .92274 m .94219 .94886 L s .57204 .72467 m .57312 .72713 L s .57855 .71286 m .57945 .71643 L s .57541 .71825 m .57639 .72128 L s .65986 .76915 m .6684 .77805 L s .67246 .76287 m .68145 .7732 L s .91347 .91643 m .94397 .94291 L s .57097 .72231 m .57204 .72467 L s .63984 .7709 m .64744 .77775 L s .57445 .71528 m .57541 .71825 L s .57769 .70935 m .57855 .71286 L s .65193 .76081 m .65986 .76915 L s .56991 .72006 m .57097 .72231 L s .57351 .7124 m .57445 .71528 L s .66414 .75309 m .67246 .76287 L s .88133 .90523 m .90975 .92905 L s .57686 .70588 m .57769 .70935 L s .63275 .76459 m .63984 .7709 L s .48972 .85856 m .49307 .84742 L s .56888 .71791 m .56991 .72006 L s .48795 .85708 m .49114 .84581 L s .48617 .85561 m .48921 .84421 L s .88327 .89854 m .91161 .92274 L s .5726 .70958 m .57351 .7124 L s .64458 .75299 m .65193 .76081 L s .57606 .70246 m .57686 .70588 L s .62614 .75879 m .63275 .76459 L s .56785 .71586 m .56888 .71791 L s .88522 .89185 m .91347 .91643 L s .65644 .74382 m .66414 .75309 L s .49307 .84742 m .49628 .83691 L s .57171 .70684 m .5726 .70958 L s .49114 .84581 m .49419 .83516 L s .48921 .84421 m .4921 .83342 L s .57529 .69909 m .57606 .70246 L s .56684 .71391 m .56785 .71586 L s .63774 .74566 m .64458 .75299 L s .61996 .75347 m .62614 .75879 L s .855 .88322 m .88133 .90523 L s .57085 .70417 m .57171 .70684 L s .49628 .83691 m .49937 .827 L s .56584 .71207 m .56684 .71391 L s .49419 .83516 m .4971 .8251 L s .57455 .69575 m .57529 .69909 L s .64933 .73502 m .65644 .74382 L s .4921 .83342 m .49483 .82321 L s .61418 .7486 m .61996 .75347 L s .85704 .87614 m .88327 .89854 L s .57 .70156 m .57085 .70417 L s .6314 .73878 m .63774 .74566 L s .56485 .71033 m .56584 .71207 L s .49937 .827 m .50234 .81767 L s .57385 .69245 m .57455 .69575 L s .4971 .8251 m .49988 .81561 L s .85909 .86904 m .88522 .89185 L s .49483 .82321 m .49741 .81355 L s .60877 .74417 m .61418 .7486 L s .56387 .7087 m .56485 .71033 L s .56918 .69902 m .57 .70156 L s .64275 .72666 m .64933 .73502 L s .6255 .73231 m .6314 .73878 L s .50234 .81767 m .5052 .80888 L s .57317 .68918 m .57385 .69245 L s .5629 .70717 m .56387 .7087 L s .83062 .86291 m .855 .88322 L s .49988 .81561 m .50253 .80665 L s .60371 .74014 m .60877 .74417 L s .56838 .69655 m .56918 .69902 L s .49741 .81355 m .49986 .80441 L s .56194 .70574 m .5629 .70717 L s .5052 .80888 m .50797 .80063 L s .63668 .71869 m .64275 .72666 L s .57253 .68594 m .57317 .68918 L s .62003 .72624 m .6255 .73231 L s .83276 .8554 m .85704 .87614 L s .59895 .73651 m .60371 .74014 L s .5676 .69414 m .56838 .69655 L s .50253 .80665 m .50507 .7982 L s .49986 .80441 m .50217 .79577 L s .56099 .70443 m .56194 .70574 L s .50797 .80063 m .51064 .79288 L s .59449 .73325 m .59895 .73651 L s .57191 .68273 m .57253 .68594 L s .83491 .84788 m .85909 .86904 L s .56683 .69178 m .5676 .69414 L s .50507 .7982 m .5075 .79024 L s .56004 .70322 m .56099 .70443 L s .61494 .72054 m .62003 .72624 L s .63107 .71107 m .63668 .71869 L s .50217 .79577 m .50435 .7876 L s .80804 .84416 m .83062 .86291 L s .51064 .79288 m .51323 .78561 L s .59029 .73034 m .59449 .73325 L s .5591 .70212 m .56004 .70322 L s .56609 .68949 m .56683 .69178 L s .48208 .83729 m .48523 .82547 L s .57133 .67953 m .57191 .68273 L s .48029 .8358 m .48329 .82385 L s .5075 .79024 m .50982 .78274 L s .47851 .83431 m .48135 .82223 L s .6102 .71517 m .61494 .72054 L s .50435 .7876 m .5064 .77988 L s .55816 .70113 m .5591 .70212 L s .58633 .72778 m .59029 .73034 L s .51323 .78561 m .51574 .7788 L s .81029 .83621 m .83276 .8554 L s .56537 .68726 m .56609 .68949 L s .62589 .70379 m .63107 .71107 L s .50982 .78274 m .51204 .77569 L s .57078 .67636 m .57133 .67953 L s .55722 .70025 m .55816 .70113 L s .58259 .72555 m .58633 .72778 L s .5064 .77988 m .50833 .77258 L s .51574 .7788 m .51818 .77244 L s .60581 .71012 m .6102 .71517 L s .48523 .82547 m .48824 .81427 L s .56466 .68509 m .56537 .68726 L s .81254 .82824 m .83491 .84788 L s .55628 .69949 m .55722 .70025 L s .48329 .82385 m .48613 .81251 L s .51204 .77569 m .51416 .76906 L s .57906 .72364 m .58259 .72555 L s .78715 .82688 m .80804 .84416 L s .48135 .82223 m .48402 .81075 L s .57025 .67319 m .57078 .67636 L s .51818 .77244 m .52056 .7665 L s .50833 .77258 m .51015 .76569 L s .55534 .69884 m .55628 .69949 L s .62113 .6968 m .62589 .70379 L s .56398 .68297 m .56466 .68509 L s .51416 .76906 m .5162 .76284 L s .57571 .72204 m .57906 .72364 L s .60171 .70536 m .60581 .71012 L s .52056 .7665 m .52288 .76098 L s .5544 .69832 m .55534 .69884 L s .51015 .76569 m .51184 .75917 L s .56976 .67004 m .57025 .67319 L s .78951 .81846 m .81029 .83621 L s .57252 .72075 m .57571 .72204 L s .48824 .81427 m .49111 .80366 L s .56331 .6809 m .56398 .68297 L s .5162 .76284 m .51816 .757 L s .52288 .76098 m .52516 .75585 L s .55346 .69792 m .5544 .69832 L s .48613 .81251 m .48883 .80175 L s .48402 .81075 m .48654 .79983 L s .56949 .71975 m .57252 .72075 L s .59791 .70088 m .60171 .70536 L s .51184 .75917 m .51343 .75302 L s .61673 .69008 m .62113 .6968 L s .55251 .69764 m .55346 .69792 L s .51816 .757 m .52003 .75153 L s .52516 .75585 m .52739 .75109 L s .56266 .67889 m .56331 .6809 L s .56931 .66689 m .56976 .67004 L s .5666 .71904 m .56949 .71975 L s .7678 .81095 m .78715 .82688 L s .79187 .81002 m .81254 .82824 L s .55155 .69749 m .55251 .69764 L s .52739 .75109 m .52959 .74671 L s .51343 .75302 m .5149 .74721 L s .52003 .75153 m .52183 .74641 L s .56383 .71861 m .5666 .71904 L s .49111 .80366 m .49387 .7936 L s .59437 .69666 m .59791 .70088 L s .55059 .69748 m .55155 .69749 L s .56202 .67693 m .56266 .67889 L s .52959 .74671 m .53177 .74267 L s .56117 .71847 m .56383 .71861 L s .48883 .80175 m .49139 .79152 L s .52183 .74641 m .52356 .74162 L s .56888 .66375 m .56931 .66689 L s .5149 .74721 m .51627 .74172 L s .61269 .6836 m .61673 .69008 L s .53177 .74267 m .53392 .73898 L s .54962 .69759 m .55059 .69748 L s .48654 .79983 m .48891 .78945 L s .5586 .7186 m .56117 .71847 L s .77028 .80204 m .78951 .81846 L s .52356 .74162 m .52523 .73715 L s .53392 .73898 m .53606 .73562 L s .5614 .67502 m .56202 .67693 L s .55613 .71902 m .5586 .7186 L s .54864 .69785 m .54962 .69759 L s .51627 .74172 m .51753 .73653 L s .59107 .69267 m .59437 .69666 L s .53606 .73562 m .5382 .73258 L s .55372 .71971 m .55613 .71902 L s .52523 .73715 m .52683 .73299 L s .54764 .69825 m .54864 .69785 L s .5382 .73258 m .54034 .72985 L s .55139 .72069 m .55372 .71971 L s .56848 .6606 m .56888 .66375 L s .54034 .72985 m .5425 .72743 L s .54911 .72194 m .55139 .72069 L s .51753 .73653 m .51868 .73163 L s .5425 .72743 m .54467 .72531 L s .49387 .7936 m .49651 .78408 L s .54687 .72348 m .54911 .72194 L s .54664 .6988 m .54764 .69825 L s .54467 .72531 m .54687 .72348 L s .52683 .73299 m .52837 .72912 L s .5608 .67316 m .5614 .67502 L s .7499 .79629 m .7678 .81095 L s .60898 .67733 m .61269 .6836 L s .49139 .79152 m .49382 .78182 L s .54561 .69951 m .54664 .6988 L s .52837 .72912 m .52986 .72553 L s .51868 .73163 m .51973 .727 L s .588 .68891 m .59107 .69267 L s .77276 .79311 m .79187 .81002 L s .48891 .78945 m .49113 .77957 L s .54457 .70037 m .54561 .69951 L s .52986 .72553 m .5313 .72221 L s .56812 .65744 m .56848 .6606 L s .54351 .70139 m .54457 .70037 L s .56021 .67134 m .5608 .67316 L s .51973 .727 m .52067 .72262 L s .5313 .72221 m .53269 .71914 L s .54242 .70259 m .54351 .70139 L s .53269 .71914 m .53403 .71632 L s .54131 .70396 m .54242 .70259 L s .53403 .71632 m .53533 .71373 L s .52067 .72262 m .52151 .71848 L s .54018 .70552 m .54131 .70396 L s .53533 .71373 m .5366 .71136 L s .53902 .70726 m .54018 .70552 L s .58514 .68536 m .588 .68891 L s .49651 .78408 m .49905 .77507 L s .5366 .71136 m .53782 .70921 L s .53782 .70921 m .53902 .70726 L s .7525 .78686 m .77028 .80204 L s .55964 .66958 m .56021 .67134 L s .60557 .67126 m .60898 .67733 L s .52151 .71848 m .52224 .71455 L s .56779 .65427 m .56812 .65744 L s .49382 .78182 m .49613 .77261 L s .52224 .71455 m .52286 .71083 L s .49113 .77957 m .49321 .77016 L s .73334 .78281 m .7499 .79629 L s .52286 .71083 m .52337 .70731 L s .55908 .66786 m .55964 .66958 L s .58247 .682 m .58514 .68536 L s .47435 .81577 m .4773 .80327 L s .52337 .70731 m .52378 .70395 L s .47255 .81427 m .47534 .80163 L s .48463 .63896 m .47929 .63473 L s .48949 .64288 m .48463 .63896 L s .49389 .64654 m .48949 .64288 L s .47929 .63473 m .47343 .63016 L s .49788 .64996 m .49389 .64654 L s .47343 .63016 m .46699 .62521 L s .50148 .65316 m .49788 .64996 L s .5675 .65108 m .56779 .65427 L s .52378 .70395 m .52406 .70076 L s .50473 .65619 m .50148 .65316 L s .46699 .62521 m .45993 .61984 L s .47076 .81277 m .47339 .8 L s .50765 .65907 m .50473 .65619 L s .49905 .77507 m .50149 .76654 L s .75511 .7774 m .77276 .79311 L s .45993 .61984 m .4522 .614 L s .51026 .66182 m .50765 .65907 L s .52406 .70076 m .52423 .69771 L s .60245 .66535 m .60557 .67126 L s .5126 .66446 m .51026 .66182 L s .55854 .66618 m .55908 .66786 L s .51466 .66701 m .5126 .66446 L s .4522 .614 m .44373 .60763 L s .52423 .69771 m .52428 .69479 L s .51649 .6695 m .51466 .66701 L s .49613 .77261 m .49832 .76388 L s .52428 .69479 m .5242 .69198 L s .51808 .67195 m .51649 .6695 L s .57999 .67882 m .58247 .682 L s .51946 .67436 m .51808 .67195 L s .5242 .69198 m .52398 .68928 L s .44373 .60763 m .43448 .6007 L s .52065 .67678 m .51946 .67436 L s .52398 .68928 m .52363 .68667 L s .52165 .67919 m .52065 .67678 L s .52363 .68667 m .52313 .68413 L s .52247 .68164 m .52165 .67919 L s .52313 .68413 m .52247 .68164 L s .49321 .77016 m .49515 .76121 L s .43448 .6007 m .42436 .59312 L s .73607 .77282 m .7525 .78686 L s .55801 .66455 m .55854 .66618 L s .56723 .64787 m .5675 .65108 L s .42436 .59312 m .41331 .58485 L s .71801 .77041 m .73334 .78281 L s .57767 .67581 m .57999 .67882 L s .50149 .76654 m .50384 .75847 L s .5996 .65959 m .60245 .66535 L s .41331 .58485 m .40124 .57582 L s .5575 .66296 m .55801 .66455 L s .4773 .80327 m .48009 .79136 L s .49832 .76388 m .5004 .75558 L s .56701 .64464 m .56723 .64787 L s .47534 .80163 m .47798 .78959 L s .57551 .67296 m .57767 .67581 L s .40124 .57582 m .38807 .56594 L s .49515 .76121 m .49696 .75269 L s .47339 .8 m .47586 .78781 L s .55699 .66141 m .5575 .66296 L s .73881 .76281 m .75511 .7774 L s .46374 .60421 m .45579 .59918 L s .47102 .60872 m .46374 .60421 L s .47769 .61277 m .47102 .60872 L s .45579 .59918 m .44713 .59359 L s .48381 .61638 m .47769 .61277 L s .50384 .75847 m .5061 .75086 L s .44713 .59359 m .43768 .58738 L s .48941 .61959 m .48381 .61638 L s .38807 .56594 m .37369 .55513 L s .597 .65395 m .5996 .65959 L s .49453 .62244 m .48941 .61959 L s .72088 .75985 m .73607 .77282 L s .43768 .58738 m .42739 .5805 L s .57349 .67026 m .57551 .67296 L s .55651 .6599 m .55699 .66141 L s .56681 .64137 m .56701 .64464 L s .49923 .62497 m .49453 .62244 L s .70382 .75904 m .71801 .77041 L s .5004 .75558 m .50237 .74772 L s .42739 .5805 m .41616 .57288 L s .50352 .62719 m .49923 .62497 L s .50745 .62914 m .50352 .62719 L s .41616 .57288 m .40393 .56446 L s .37369 .55513 m .358 .54331 L s .49696 .75269 m .49864 .74457 L s .55603 .65843 m .55651 .6599 L s .5716 .6677 m .57349 .67026 L s .51104 .63084 m .50745 .62914 L s .48009 .79136 m .48276 .78002 L s .5061 .75086 m .50829 .74366 L s .40393 .56446 m .3906 .55517 L s .56666 .63805 m .56681 .64137 L s .51432 .63231 m .51104 .63084 L s .47798 .78959 m .48046 .7781 L s .59463 .64841 m .597 .65395 L s .55557 .657 m .55603 .65843 L s .51731 .63357 m .51432 .63231 L s .47586 .78781 m .47816 .77617 L s .50237 .74772 m .50424 .74025 L s .358 .54331 m .34089 .53038 L s .56984 .66526 m .5716 .6677 L s .3906 .55517 m .37608 .54491 L s .72376 .74926 m .73881 .76281 L s .52004 .63464 m .51731 .63357 L s .6907 .7486 m .70382 .75904 L s .70684 .74786 m .72088 .75985 L s .55511 .6556 m .55557 .657 L s .49864 .74457 m .50019 .73684 L s .56654 .6347 m .56666 .63805 L s .45053 .57951 m .4409 .57403 L s .4594 .58433 m .45053 .57951 L s .46755 .58854 m .4594 .58433 L s .52253 .63554 m .52004 .63464 L s .4409 .57403 m .43042 .56784 L s .47506 .59218 m .46755 .58854 L s .50829 .74366 m .51041 .73687 L s .37608 .54491 m .36025 .53361 L s .43042 .56784 m .41902 .56088 L s .56819 .66295 m .56984 .66526 L s .48197 .59531 m .47506 .59218 L s .52479 .63628 m .52253 .63554 L s .59249 .64296 m .59463 .64841 L s .48833 .59796 m .48197 .59531 L s .34089 .53038 m .32223 .51622 L s .41902 .56088 m .40663 .55308 L s .55467 .65424 m .55511 .6556 L s .50424 .74025 m .50602 .73317 L s .4942 .60015 m .48833 .59796 L s .52686 .63689 m .52479 .63628 L s .40663 .55308 m .39315 .54437 L s .56665 .66076 m .56819 .66295 L s .48276 .78002 m .48529 .76923 L s .36025 .53361 m .34301 .52117 L s .56646 .63129 m .56654 .6347 L s .4996 .60193 m .4942 .60015 L s .55425 .65292 m .55467 .65424 L s .52874 .63736 m .52686 .63689 L s .50019 .73684 m .50162 .72946 L s .48046 .7781 m .4828 .76713 L s .51041 .73687 m .51247 .73047 L s .39315 .54437 m .37848 .53467 L s .67855 .73905 m .6907 .7486 L s .50459 .60331 m .4996 .60193 L s .47816 .77617 m .4803 .76504 L s .53044 .63771 m .52874 .63736 L s .70987 .73666 m .72376 .74926 L s .56521 .65867 m .56665 .66076 L s .69388 .73678 m .70684 .74786 L s .32223 .51622 m .30188 .50073 L s .55383 .65163 m .55425 .65292 L s .59056 .63757 m .59249 .64296 L s .50919 .60433 m .50459 .60331 L s .50602 .73317 m .5077 .72645 L s .37848 .53467 m .36251 .5239 L s .53199 .63796 m .53044 .63771 L s .34301 .52117 m .32422 .50749 L s .56641 .62783 m .56646 .63129 L s .51344 .60501 m .50919 .60433 L s .55342 .65037 m .55383 .65163 L s .56386 .65668 m .56521 .65867 L s .53339 .63812 m .53199 .63796 L s .51247 .73047 m .51447 .72444 L s .50162 .72946 m .50293 .72243 L s .36251 .5239 m .34514 .51196 L s .53466 .63819 m .53339 .63812 L s .51737 .60536 m .51344 .60501 L s .66731 .73031 m .67855 .73905 L s .55302 .64915 m .55342 .65037 L s .56259 .65478 m .56386 .65668 L s .48529 .76923 m .48771 .75895 L s .5077 .72645 m .5093 .72008 L s .58883 .63223 m .59056 .63757 L s .30188 .50073 m .27969 .48377 L s .56641 .6243 m .56641 .62783 L s .32422 .50749 m .30375 .49244 L s .53581 .63818 m .53466 .63819 L s .52101 .60541 m .51737 .60536 L s .4828 .76713 m .485 .75667 L s .68189 .72655 m .69388 .73678 L s .51447 .72444 m .51643 .71877 L s .55264 .64796 m .55302 .64915 L s .34514 .51196 m .32622 .49874 L s .69706 .72493 m .70987 .73666 L s .53684 .6381 m .53581 .63818 L s .56141 .65298 m .56259 .65478 L s .50293 .72243 m .50412 .71571 L s .4803 .76504 m .48229 .75439 L s .52439 .60517 m .52101 .60541 L s .55226 .6468 m .55264 .64796 L s .53778 .63796 m .53684 .6381 L s .5093 .72008 m .51081 .71403 L s .56645 .6207 m .56641 .6243 L s .6569 .72234 m .66731 .73031 L s .5603 .65125 m .56141 .65298 L s .58729 .62691 m .58883 .63223 L s .51643 .71877 m .51834 .71344 L s .53862 .63777 m .53778 .63796 L s .30375 .49244 m .28145 .4759 L s .52752 .60466 m .52439 .60517 L s .5519 .64567 m .55226 .6468 L s .32622 .49874 m .30563 .48413 L s .27969 .48377 m .25548 .46521 L s .50412 .71571 m .5052 .70929 L s .55925 .64961 m .5603 .65125 L s .53937 .63752 m .53862 .63777 L s .67083 .7171 m .68189 .72655 L s .48771 .75895 m .49001 .74915 L s .55154 .64457 m .5519 .64567 L s .53044 .60388 m .52752 .60466 L s .51081 .71403 m .51225 .7083 L s .56653 .61703 m .56645 .6207 L s .54005 .63723 m .53937 .63752 L s .485 .75667 m .48707 .74668 L s .51834 .71344 m .52022 .70844 L s .55827 .64804 m .55925 .64961 L s .64727 .71507 m .6569 .72234 L s .68524 .71402 m .69706 .72493 L s .55119 .6435 m .55154 .64457 L s .54065 .63691 m .54005 .63723 L s .58592 .62161 m .58729 .62691 L s .48229 .75439 m .48413 .74421 L s .53316 .60286 m .53044 .60388 L s .30563 .48413 m .28321 .46801 L s .5052 .70929 m .50616 .70315 L s .55735 .64654 m .55827 .64804 L s .28145 .4759 m .25714 .45773 L s .55086 .64246 m .55119 .6435 L s .54118 .63654 m .54065 .63691 L s .51225 .7083 m .51361 .70286 L s .52022 .70844 m .52207 .70376 L s .56665 .61326 m .56653 .61703 L s .54166 .63615 m .54118 .63654 L s .6606 .70837 m .67083 .7171 L s .53569 .60159 m .53316 .60286 L s .55648 .6451 m .55735 .64654 L s .55053 .64144 m .55086 .64246 L s .25548 .46521 m .22909 .44489 L s .63835 .70847 m .64727 .71507 L s .54208 .63573 m .54166 .63615 L s .49001 .74915 m .49221 .73983 L s .58473 .61629 m .58592 .62161 L s .50616 .70315 m .507 .69727 L s .55021 .64045 m .55053 .64144 L s .55567 .64373 m .55648 .6451 L s .52207 .70376 m .52391 .69939 L s .51361 .70286 m .51491 .69771 L s .67435 .70385 m .68524 .71402 L s .53807 .60009 m .53569 .60159 L s .54245 .63529 m .54208 .63573 L s .48707 .74668 m .48902 .73714 L s .56682 .60941 m .56665 .61326 L s .28321 .46801 m .25879 .45024 L s .54989 .63949 m .55021 .64045 L s .5549 .64241 m .55567 .64373 L s .63009 .70248 m .63835 .70847 L s .54277 .63483 m .54245 .63529 L s .48413 .74421 m .48582 .73446 L s .25714 .45773 m .23064 .43778 L s .52391 .69939 m .52573 .69532 L s .65117 .7003 m .6606 .70837 L s .54959 .63855 m .54989 .63949 L s .54031 .59836 m .53807 .60009 L s .507 .69727 m .50774 .69164 L s .55418 .64115 m .5549 .64241 L s .51491 .69771 m .51613 .69282 L s .54306 .63436 m .54277 .63483 L s .58369 .61095 m .58473 .61629 L s .54929 .63764 m .54959 .63855 L s .5433 .63387 m .54306 .63436 L s .56704 .60545 m .56682 .60941 L s .5535 .63994 m .55418 .64115 L s .62243 .69707 m .63009 .70248 L s .52573 .69532 m .52754 .69153 L s .22909 .44489 m .2003 .42264 L s .54241 .59641 m .54031 .59836 L s .54901 .63675 m .54929 .63764 L s .49221 .73983 m .49431 .73095 L s .66431 .69436 m .67435 .70385 L s .54351 .63336 m .5433 .63387 L s .51613 .69282 m .5173 .68818 L s .55285 .63879 m .5535 .63994 L s .50774 .69164 m .50835 .68623 L s .25879 .45024 m .23219 .43066 L s .64245 .69286 m .65117 .7003 L s .54368 .63285 m .54351 .63336 L s .54873 .63588 m .54901 .63675 L s .48902 .73714 m .49085 .72803 L s .52754 .69153 m .52936 .68802 L s .61533 .6922 m .62243 .69707 L s .55224 .63767 m .55285 .63879 L s .5673 .60137 m .56704 .60545 L s .54383 .63233 m .54368 .63285 L s .5444 .59424 m .54241 .59641 L s .58282 .60557 m .58369 .61095 L s .54845 .63504 m .54873 .63588 L s .48582 .73446 m .48738 .72511 L s .5173 .68818 m .5184 .68378 L s .55167 .6366 m .55224 .63767 L s .52936 .68802 m .53119 .68478 L s .23064 .43778 m .20176 .41588 L s .54395 .63181 m .54383 .63233 L s .50835 .68623 m .50885 .68103 L s .54819 .63421 m .54845 .63504 L s .60874 .68784 m .61533 .6922 L s .54405 .63128 m .54395 .63181 L s .55113 .63558 m .55167 .6366 L s .65507 .68549 m .66431 .69436 L s .6344 .68599 m .64245 .69286 L s .5463 .59185 m .5444 .59424 L s .54793 .63341 m .54819 .63421 L s .53119 .68478 m .53305 .68181 L s .5184 .68378 m .51944 .67961 L s .49431 .73095 m .49633 .72249 L s .54413 .63075 m .54405 .63128 L s .56762 .59718 m .5673 .60137 L s .55061 .63459 m .55113 .63558 L s .54767 .63264 m .54793 .63341 L s .60263 .68394 m .60874 .68784 L s .50885 .68103 m .50924 .67603 L s .58209 .60013 m .58282 .60557 L s .54418 .63022 m .54413 .63075 L s .53305 .68181 m .53492 .6791 L s .17359 .40192 m .2003 .42264 L s .55013 .63364 m .55061 .63459 L s .49085 .72803 m .49256 .71932 L s .23219 .43066 m .20321 .40912 L s .54743 .63188 m .54767 .63264 L s .51944 .67961 m .52043 .67566 L s .5481 .58924 m .5463 .59185 L s .54422 .62969 m .54418 .63022 L s .59695 .6805 m .60263 .68394 L s .54967 .63273 m .55013 .63364 L s .62697 .67964 m .6344 .68599 L s .54719 .63114 m .54743 .63188 L s .53492 .6791 m .53684 .67665 L s .48738 .72511 m .4888 .71615 L s .54424 .62916 m .54422 .62969 L s .50924 .67603 m .50951 .67119 L s .56798 .59286 m .56762 .59718 L s .64656 .67721 m .65507 .68549 L s .54923 .63185 m .54967 .63273 L s .54696 .63042 m .54719 .63114 L s .52043 .67566 m .52137 .67191 L s .54425 .62863 m .54424 .62916 L s .53684 .67665 m .5388 .67445 L s .59168 .67747 m .59695 .6805 L s .54983 .58642 m .5481 .58924 L s .54881 .631 m .54923 .63185 L s .58151 .59462 m .58209 .60013 L s .54673 .62972 m .54696 .63042 L s .20176 .41588 m .17027 .39186 L s .54425 .62811 m .54425 .62863 L s .49633 .72249 m .49825 .71444 L s .5388 .67445 m .54082 .6725 L s .58677 .67483 m .59168 .67747 L s .62012 .67379 m .62697 .67964 L s .54651 .62904 m .54673 .62972 L s .54842 .63019 m .54881 .631 L s .54423 .62759 m .54425 .62811 L s .50951 .67119 m .50965 .66652 L s .52137 .67191 m .52226 .66836 L s .54082 .6725 m .54291 .67079 L s .54629 .62837 m .54651 .62904 L s .58219 .67258 m .58677 .67483 L s .49256 .71932 m .49417 .711 L s .5442 .62707 m .54423 .62759 L s .54805 .6294 m .54842 .63019 L s .5684 .5884 m .56798 .59286 L s .5515 .58338 m .54983 .58642 L s .54291 .67079 m .54507 .66934 L s .63873 .66944 m .64656 .67721 L s .54609 .62773 m .54629 .62837 L s .54417 .62656 m .5442 .62707 L s .54769 .62864 m .54805 .6294 L s .57793 .67067 m .58219 .67258 L s .52226 .66836 m .52311 .66499 L s .54507 .66934 m .54732 .66813 L s .4888 .71615 m .49009 .70755 L s .20321 .40912 m .17163 .38542 L s .50965 .66652 m .50968 .662 L s .61379 .66838 m .62012 .67379 L s .54412 .62606 m .54417 .62656 L s .54588 .6271 m .54609 .62773 L s .57395 .6691 m .57793 .67067 L s .58107 .58901 m .58151 .59462 L s .54732 .66813 m .54968 .66717 L s .57023 .66786 m .57395 .6691 L s .54407 .62556 m .54412 .62606 L s .54968 .66717 m .55215 .66647 L s .52311 .66499 m .52391 .6618 L s .56674 .66692 m .57023 .66786 L s .55215 .66647 m .55474 .66602 L s .55311 .58012 m .5515 .58338 L s .56347 .66627 m .56674 .66692 L s .55474 .66602 m .55749 .66583 L s .49825 .71444 m .50011 .70677 L s .56888 .58379 m .5684 .5884 L s .56039 .66592 m .56347 .66627 L s .55749 .66583 m .56039 .66592 L s .50968 .662 m .50958 .6576 L s .60795 .66339 m .61379 .66838 L s .52391 .6618 m .52466 .65878 L s .63154 .66216 m .63873 .66944 L s .49417 .711 m .49568 .70303 L s .58076 .5833 m .58107 .58901 L s .16832 .39036 m .17027 .39186 L s .52466 .65878 m .52538 .65591 L s .55468 .57664 m .55311 .58012 L s .50958 .6576 m .50934 .65332 L s .60256 .65879 m .60795 .66339 L s .49009 .70755 m .49124 .69929 L s .56941 .57901 m .56888 .58379 L s .52538 .65591 m .52607 .65319 L s .62492 .65531 m .63154 .66216 L s .50011 .70677 m .50189 .69947 L s .50934 .65332 m .50898 .64913 L s .59758 .65454 m .60256 .65879 L s .52607 .65319 m .52671 .65061 L s .55622 .57294 m .55468 .57664 L s .16312 .37898 m .17163 .38542 L s .58059 .57745 m .58076 .5833 L s .49568 .70303 m .49708 .69541 L s .52671 .65061 m .52732 .64817 L s .57001 .57407 m .56941 .57901 L s .50898 .64913 m .50847 .64502 L s .59299 .65062 m .59758 .65454 L s .61885 .64885 m .62492 .65531 L s .52732 .64817 m .5279 .64585 L s .49124 .69929 m .49227 .69134 L s .55774 .569 m .55622 .57294 L s .50847 .64502 m .50782 .64098 L s .58875 .647 m .59299 .65062 L s .50189 .69947 m .50361 .69252 L s .5279 .64585 m .52845 .64366 L s .58055 .57146 m .58059 .57745 L s .52845 .64366 m .52898 .64158 L s .57067 .56893 m .57001 .57407 L s .58484 .64366 m .58875 .647 L s .61328 .64276 m .61885 .64885 L s .50782 .64098 m .50701 .63699 L s .49708 .69541 m .49839 .6881 L s .52898 .64158 m .52947 .63961 L s .55924 .56482 m .55774 .569 L s .58124 .64058 m .58484 .64366 L s .52947 .63961 m .52994 .63774 L s .49227 .69134 m .49317 .68369 L s .50701 .63699 m .50604 .63304 L s .52994 .63774 m .53038 .63597 L s .50361 .69252 m .50527 .6859 L s .60818 .63699 m .61328 .64276 L s .57791 .63774 m .58124 .64058 L s .57139 .5636 m .57067 .56893 L s .58064 .56531 m .58055 .57146 L s .53038 .63597 m .5308 .63429 L s .56073 .5604 m .55924 .56482 L s .50604 .63304 m .5049 .6291 L s .57484 .63512 m .57791 .63774 L s .5308 .63429 m .5312 .6327 L s .49839 .6881 m .49961 .6811 L s .5312 .6327 m .53158 .63119 L s .57201 .6327 m .57484 .63512 L s .60351 .63151 m .60818 .63699 L s .53158 .63119 m .53194 .62977 L s .5049 .6291 m .50357 .62516 L s .5694 .63047 m .57201 .6327 L s .53194 .62977 m .53228 .62841 L s .57219 .55805 m .57139 .5636 L s .49317 .68369 m .49394 .67631 L s .50527 .6859 m .50689 .6796 L s .56222 .55572 m .56073 .5604 L s .58086 .55898 m .58064 .56531 L s .53228 .62841 m .5326 .62713 L s .56699 .62841 m .5694 .63047 L s .5326 .62713 m .5329 .62592 L s .50357 .62516 m .50206 .62121 L s .59924 .62629 m .60351 .63151 L s .56477 .62651 m .56699 .62841 L s .5329 .62592 m .53319 .62476 L s .49961 .6811 m .50074 .67439 L s .53319 .62476 m .53346 .62367 L s .56272 .62476 m .56477 .62651 L s .53346 .62367 m .53372 .62264 L s .50206 .62121 m .50034 .61722 L s .56083 .62315 m .56272 .62476 L s .53372 .62264 m .53397 .62166 L s .56373 .55078 m .56222 .55572 L s .57306 .55227 m .57219 .55805 L s .59534 .6213 m .59924 .62629 L s .53397 .62166 m .5342 .62073 L s .50689 .6796 m .50847 .6736 L s .55908 .62166 m .56083 .62315 L s .5812 .55245 m .58086 .55898 L s .5342 .62073 m .53442 .61985 L s .49394 .67631 m .49459 .66919 L s .55747 .62028 m .55908 .62166 L s .53442 .61985 m .53463 .61902 L s .50034 .61722 m .49841 .61318 L s .53463 .61902 m .53483 .61823 L s .55599 .61902 m .55747 .62028 L s .53483 .61823 m .53502 .61748 L s .55462 .61785 m .55599 .61902 L s .53502 .61748 m .53519 .61677 L s .59179 .61651 m .59534 .6213 L s .53519 .61677 m .53536 .6161 L s .50074 .67439 m .5018 .66795 L s .55336 .61677 m .55462 .61785 L s .53536 .6161 m .53552 .61546 L s .56525 .54556 m .56373 .55078 L s .49841 .61318 m .49624 .60906 L s .55219 .61578 m .55336 .61677 L s .53552 .61546 m .53567 .61486 L s .574 .54625 m .57306 .55227 L s .53567 .61486 m .53582 .61429 L s .55112 .61486 m .55219 .61578 L s .53582 .61429 m .53595 .61375 L s .55013 .61401 m .55112 .61486 L s .53595 .61375 m .53608 .61324 L s .50847 .6736 m .51 .6679 L s .53608 .61324 m .5362 .61275 L s .54922 .61323 m .55013 .61401 L s .58167 .54569 m .5812 .55245 L s .58857 .61191 m .59179 .61651 L s .5362 .61275 m .53632 .61229 L s .54838 .61251 m .54922 .61323 L s .53632 .61229 m .53643 .61185 L s .49459 .66919 m .49512 .6623 L s .53643 .61185 m .53653 .61144 L s .49624 .60906 m .49383 .60485 L s .5476 .61185 m .54838 .61251 L s .53653 .61144 m .53663 .61105 L s .54688 .61124 m .5476 .61185 L s .53663 .61105 m .53672 .61068 L s .53672 .61068 m .53681 .61032 L s .54622 .61067 m .54688 .61124 L s .53681 .61032 m .53689 .60999 L s .54561 .61015 m .54622 .61067 L s .53689 .60999 m .53697 .60968 L s .53697 .60968 m .53705 .60938 L s .54505 .60967 m .54561 .61015 L s .53705 .60938 m .53712 .60909 L s .54453 .60923 m .54505 .60967 L s .53712 .60909 m .53719 .60883 L s .5668 .54006 m .56525 .54556 L s .53719 .60883 m .53725 .60857 L s .54406 .60882 m .54453 .60923 L s .5018 .66795 m .50277 .66176 L s .53725 .60857 m .53731 .60833 L s .58564 .60745 m .58857 .61191 L s .54362 .60845 m .54406 .60882 L s .54321 .6081 m .54362 .60845 L s .49383 .60485 m .49115 .60053 L s .54283 .60778 m .54321 .6081 L s .54249 .60749 m .54283 .60778 L s .57503 .53998 m .574 .54625 L s .54217 .60721 m .54249 .60749 L s .54188 .60696 m .54217 .60721 L s .54161 .60673 m .54188 .60696 L s .54136 .60652 m .54161 .60673 L s .51 .6679 m .51152 .66248 L s .54113 .60632 m .54136 .60652 L s .54091 .60614 m .54113 .60632 L s .54072 .60597 m .54091 .60614 L s .54054 .60582 m .54072 .60597 L s .54037 .60568 m .54054 .60582 L s .54022 .60555 m .54037 .60568 L s .58227 .5387 m .58167 .54569 L s .583 .60313 m .58564 .60745 L s .5384 .60399 m .5384 .60399 L s .49115 .60053 m .48818 .59607 L s .49512 .6623 m .49552 .65562 L s .53658 .60244 m .53642 .60231 L s .53642 .60231 m .53626 .60216 L s .53626 .60216 m .53608 .60201 L s .53608 .60201 m .53588 .60184 L s .53588 .60184 m .53567 .60166 L s .53567 .60166 m .53544 .60146 L s .53544 .60146 m .53519 .60125 L s .56838 .53425 m .5668 .54006 L s .53519 .60125 m .53492 .60102 L s .53492 .60102 m .53462 .60077 L s .53462 .60077 m .5343 .60049 L s .5343 .60049 m .53396 .6002 L s .50277 .66176 m .50366 .65582 L s .53396 .6002 m .53358 .59988 L s .53358 .59988 m .53317 .59953 L s .58061 .59891 m .583 .60313 L s .53317 .59953 m .53273 .59915 L s .53955 .59941 m .53949 .59965 L s .53273 .59915 m .53225 .59875 L s .48818 .59607 m .48491 .59145 L s .53961 .59915 m .53955 .59941 L s .57614 .53342 m .57503 .53998 L s .53225 .59875 m .53174 .5983 L s .53968 .59888 m .53961 .59915 L s .51152 .66248 m .51301 .65733 L s .53975 .5986 m .53968 .59888 L s .53174 .5983 m .53117 .59782 L s .53982 .5983 m .53975 .5986 L s .53117 .59782 m .53056 .5973 L s .5399 .59798 m .53982 .5983 L s .53999 .59765 m .5399 .59798 L s .53056 .5973 m .5299 .59673 L s .54007 .5973 m .53999 .59765 L s .5299 .59673 m .52918 .59612 L s .54017 .59693 m .54007 .5973 L s .54027 .59653 m .54017 .59693 L s .52918 .59612 m .5284 .59546 L s .54037 .59612 m .54027 .59653 L s .5284 .59546 m .52756 .59473 L s .57847 .59478 m .58061 .59891 L s .54048 .59568 m .54037 .59612 L s .58299 .53145 m .58227 .5387 L s .5406 .59522 m .54048 .59568 L s .52756 .59473 m .52664 .59395 L s .54072 .59473 m .5406 .59522 L s .48491 .59145 m .48131 .58664 L s .49552 .65562 m .4958 .64915 L s .52664 .59395 m .52565 .5931 L s .54085 .59422 m .54072 .59473 L s .57001 .52814 m .56838 .53425 L s .54098 .59367 m .54085 .59422 L s .52565 .5931 m .52457 .59218 L s .54113 .5931 m .54098 .59367 L s .52457 .59218 m .5234 .59118 L s .54128 .59249 m .54113 .5931 L s .50366 .65582 m .50449 .65009 L s .54144 .59185 m .54128 .59249 L s .5234 .59118 m .52213 .5901 L s .57656 .59072 m .57847 .59478 L s .51301 .65733 m .51449 .65243 L s .54161 .59118 m .54144 .59185 L s .52213 .5901 m .52076 .58893 L s .57734 .52657 m .57614 .53342 L s .54179 .59047 m .54161 .59118 L s .48131 .58664 m .47735 .58162 L s .54198 .58971 m .54179 .59047 L s .52076 .58893 m .51927 .58765 L s .54217 .58892 m .54198 .58971 L s .51927 .58765 m .51765 .58627 L s .54238 .58808 m .54217 .58892 L s .57486 .58671 m .57656 .59072 L s .54261 .5872 m .54238 .58808 L s .51765 .58627 m .51589 .58477 L s .58384 .52391 m .58299 .53145 L s .54284 .58626 m .54261 .5872 L s .4958 .64915 m .49595 .64285 L s .51589 .58477 m .51399 .58315 L s .57168 .52169 m .57001 .52814 L s .54309 .58528 m .54284 .58626 L s .47735 .58162 m .473 .57636 L s .50449 .65009 m .50524 .64458 L s .51449 .65243 m .51596 .64779 L s .54335 .58424 m .54309 .58528 L s .51399 .58315 m .51192 .58138 L s .57337 .58273 m .57486 .58671 L s .54362 .58314 m .54335 .58424 L s .51192 .58138 m .50968 .57947 L s .54392 .58198 m .54362 .58314 L s .57863 .51941 m .57734 .52657 L s .54422 .58075 m .54392 .58198 L s .50968 .57947 m .50725 .57739 L s .473 .57636 m .46824 .57082 L s .57207 .57875 m .57337 .58273 L s .54455 .57946 m .54422 .58075 L s .50725 .57739 m .50462 .57514 L s .54489 .57809 m .54455 .57946 L s .49595 .64285 m .49598 .63672 L s .51596 .64779 m .51743 .6434 L s .57341 .5149 m .57168 .52169 L s .58483 .51607 m .58384 .52391 L s .50524 .64458 m .50592 .63927 L s .54525 .57665 m .54489 .57809 L s .50462 .57514 m .50176 .5727 L s .57095 .57477 m .57207 .57875 L s .54563 .57512 m .54525 .57665 L s .46824 .57082 m .46304 .56498 L s .50176 .5727 m .49865 .57005 L s .54604 .57352 m .54563 .57512 L s .58001 .51191 m .57863 .51941 L s .54646 .57182 m .54604 .57352 L s .49865 .57005 m .49528 .56717 L s .56999 .57077 m .57095 .57477 L s .51743 .6434 m .51892 .63923 L s .54691 .57003 m .54646 .57182 L s .49598 .63672 m .49588 .63073 L s .50592 .63927 m .50655 .63414 L s .49528 .56717 m .49163 .56405 L s .46304 .56498 m .45735 .5588 L s .5752 .50775 m .57341 .5149 L s .54738 .56813 m .54691 .57003 L s .5692 .56673 m .56999 .57077 L s .58595 .5079 m .58483 .51607 L s .54789 .56613 m .54738 .56813 L s .49163 .56405 m .48767 .56066 L s .51892 .63923 m .52042 .6353 L s .54841 .56402 m .54789 .56613 L s .5815 .50406 m .58001 .51191 L s .56856 .56263 m .5692 .56673 L s .45735 .5588 m .45113 .55224 L s .48767 .56066 m .48336 .55699 L s .50655 .63414 m .50711 .62919 L s .54897 .5618 m .54841 .56402 L s .49588 .63073 m .49564 .62488 L s .54956 .55944 m .54897 .5618 L s .57706 .50021 m .5752 .50775 L s .48336 .55699 m .4787 .553 L s .56808 .55845 m .56856 .56263 L s .52042 .6353 m .52196 .6316 L s .5872 .49937 m .58595 .5079 L s .55019 .55696 m .54956 .55944 L s .45113 .55224 m .44435 .54526 L s .91689 .83093 m .90859 .8246 L s .4787 .553 m .47363 .54868 L s .56773 .55419 m .56808 .55845 L s .50711 .62919 m .50761 .6244 L s .55084 .55433 m .55019 .55696 L s .5831 .49582 m .5815 .50406 L s .49564 .62488 m .49527 .61913 L s .87765 .80123 m .90859 .8246 L s .52196 .6316 m .52353 .62811 L s .55154 .55156 m .55084 .55433 L s .47363 .54868 m .46813 .54398 L s .56752 .54982 m .56773 .55419 L s .579 .49228 m .57706 .50021 L s .44435 .54526 m .43695 .53782 L s .55227 .54863 m .55154 .55156 L s .50761 .6244 m .50805 .61976 L s .5886 .49047 m .5872 .49937 L s .46813 .54398 m .46216 .53888 L s .91232 .81984 m .91041 .81837 L s .56744 .54533 m .56752 .54982 L s .52353 .62811 m .52514 .62484 L s .55305 .54554 m .55227 .54863 L s .87956 .79463 m .91041 .81837 L s .49527 .61913 m .49476 .61348 L s .58481 .48719 m .5831 .49582 L s .43695 .53782 m .42889 .52987 L s .55387 .54228 m .55305 .54554 L s .46216 .53888 m .45569 .53335 L s .56749 .5407 m .56744 .54533 L s .51616 .54136 m .51304 .541 L s .51909 .54144 m .51616 .54136 L s .52186 .54125 m .51909 .54144 L s .51304 .541 m .50973 .54034 L s .50805 .61976 m .50844 .61526 L s .58103 .48391 m .579 .49228 L s .52449 .54079 m .52186 .54125 L s .53265 .58218 m .5326 .58167 L s .50973 .54034 m .5062 .53938 L s .52514 .62484 m .52682 .62178 L s .52698 .54007 m .52449 .54079 L s .5062 .53938 m .50242 .53811 L s .55473 .53883 m .55387 .54228 L s .52936 .53909 m .52698 .54007 L s .53082 .58061 m .53062 .57997 L s .5326 .58167 m .53255 .58115 L s .50242 .53811 m .49839 .53651 L s .53164 .53785 m .52936 .53909 L s .52899 .57905 m .52863 .57827 L s .49476 .61348 m .49411 .6079 L s .49839 .53651 m .49406 .53456 L s .53062 .57997 m .5304 .57931 L s .53255 .58115 m .53252 .58062 L s .45569 .53335 m .44865 .52734 L s .56766 .53591 m .56749 .5407 L s .84908 .77986 m .87765 .80123 L s .59014 .48115 m .5886 .49047 L s .90766 .80853 m .88146 .78801 L s .53383 .53635 m .53164 .53785 L s .55564 .53518 m .55473 .53883 L s .49406 .53456 m .48941 .53225 L s .52863 .57827 m .52825 .57746 L s .53252 .58062 m .53249 .58009 L s .5304 .57931 m .53018 .57863 L s .42889 .52987 m .4201 .52135 L s .53594 .5346 m .53383 .53635 L s .52682 .62178 m .52856 .61894 L s .50844 .61526 m .50877 .61089 L s .52825 .57746 m .52784 .57663 L s .53249 .58009 m .53247 .57956 L s .58664 .47813 m .58481 .48719 L s .48941 .53225 m .48441 .52955 L s .53018 .57863 m .52995 .57793 L s .53799 .5326 m .53594 .5346 L s .55661 .53134 m .55564 .53518 L s .56796 .53095 m .56766 .53591 L s .53247 .57956 m .53246 .57902 L s .52784 .57663 m .52742 .57576 L s .52995 .57793 m .52972 .57721 L s .44865 .52734 m .44102 .52083 L s .48441 .52955 m .47904 .52644 L s .53997 .53034 m .53799 .5326 L s .58315 .4751 m .58103 .48391 L s .53246 .57902 m .53247 .57848 L s .85107 .77286 m .87956 .79463 L s .52972 .57721 m .52948 .57647 L s .49411 .6079 m .49331 .60239 L s .52742 .57576 m .52697 .57486 L s .52856 .61894 m .53038 .61631 L s .47904 .52644 m .47325 .5229 L s .54192 .52781 m .53997 .53034 L s .53247 .57848 m .53249 .57793 L s .55763 .52727 m .55661 .53134 L s .52948 .57647 m .52924 .57571 L s .52697 .57486 m .5265 .57392 L s .4201 .52135 m .41053 .51223 L s .50877 .61089 m .50905 .60665 L s .56838 .5258 m .56796 .53095 L s .53249 .57793 m .53253 .57738 L s .59182 .47141 m .59014 .48115 L s .54383 .52502 m .54192 .52781 L s .52924 .57571 m .52898 .57493 L s .44102 .52083 m .43273 .51375 L s .5265 .57392 m .526 .57294 L s .47325 .5229 m .467 .51889 L s .53253 .57738 m .53258 .57683 L s .53038 .61631 m .5323 .6139 L s .5587 .52298 m .55763 .52727 L s .52898 .57493 m .52872 .57413 L s .82271 .76033 m .84908 .77986 L s .5886 .46861 m .58664 .47813 L s .526 .57294 m .52547 .57193 L s .85307 .76585 m .88146 .78801 L s .54571 .52196 m .54383 .52502 L s .53258 .57683 m .53266 .57629 L s .49331 .60239 m .49236 .59692 L s .56892 .52044 m .56838 .5258 L s .467 .51889 m .46026 .5144 L s .52872 .57413 m .52846 .5733 L s .52547 .57193 m .52492 .57087 L s .50905 .60665 m .50929 .60251 L s .53266 .57629 m .53275 .57574 L s .58537 .46581 m .58315 .4751 L s .55984 .51844 m .5587 .52298 L s .54757 .51862 m .54571 .52196 L s .52846 .5733 m .52818 .57246 L s .5323 .6139 m .53432 .6117 L s .43273 .51375 m .42373 .50606 L s .41053 .51223 m .40011 .50242 L s .52492 .57087 m .52433 .56977 L s .53275 .57574 m .53288 .5752 L s .46026 .5144 m .45298 .50937 L s .52818 .57246 m .5279 .57158 L s .56958 .51486 m .56892 .52044 L s .53288 .5752 m .53302 .57466 L s .82479 .75292 m .85107 .77286 L s .54943 .51499 m .54757 .51862 L s .52433 .56977 m .5237 .56862 L s .56104 .51365 m .55984 .51844 L s .59366 .46119 m .59182 .47141 L s .5279 .57158 m .52761 .57069 L s .49236 .59692 m .49124 .59147 L s .53432 .6117 m .53645 .60972 L s .53302 .57466 m .5332 .57413 L s .50929 .60251 m .50947 .59848 L s .5237 .56862 m .52304 .56743 L s .45298 .50937 m .4451 .50378 L s .55129 .51107 m .54943 .51499 L s .59069 .45861 m .5886 .46861 L s .52761 .57069 m .52731 .56977 L s .5332 .57413 m .53341 .5736 L s .42373 .50606 m .41396 .49771 L s .79837 .74252 m .82271 .76033 L s .57036 .50902 m .56958 .51486 L s .52304 .56743 m .52234 .56618 L s .56231 .50859 m .56104 .51365 L s .53341 .5736 m .53366 .57309 L s .40011 .50242 m .38876 .49187 L s .58771 .45603 m .58537 .46581 L s .52731 .56977 m .52701 .56882 L s .53645 .60972 m .53873 .60796 L s .82688 .7455 m .85307 .76585 L s .55315 .50685 m .55129 .51107 L s .4451 .50378 m .43659 .49758 L s .52234 .56618 m .52159 .56488 L s .50947 .59848 m .50961 .59455 L s .53366 .57309 m .53394 .57259 L s .52701 .56882 m .52669 .56785 L s .49124 .59147 m .48996 .58604 L s .53394 .57259 m .53427 .57211 L s .56365 .50324 m .56231 .50859 L s .52159 .56488 m .5208 .56351 L s .57125 .50293 m .57036 .50902 L s .53873 .60796 m .54115 .60644 L s .52669 .56785 m .52637 .56685 L s .41396 .49771 m .40335 .48865 L s .55503 .50231 m .55315 .50685 L s .80055 .73468 m .82479 .75292 L s .59566 .45048 m .59366 .46119 L s .53427 .57211 m .53464 .57165 L s .43659 .49758 m .42738 .49072 L s .5208 .56351 m .51996 .56209 L s .52637 .56685 m .52603 .56582 L s .77591 .7263 m .79837 .74252 L s .50961 .59455 m .5097 .5907 L s .59292 .4481 m .59069 .45861 L s .53464 .57165 m .53507 .57121 L s .54115 .60644 m .54374 .60515 L s .38876 .49187 m .37641 .48051 L s .56507 .49758 m .56365 .50324 L s .55694 .49744 m .55503 .50231 L s .51996 .56209 m .51907 .5606 L s .52603 .56582 m .52569 .56477 L s .57227 .49654 m .57125 .50293 L s .48996 .58604 m .4885 .5806 L s .59017 .44571 m .58771 .45603 L s .53507 .57121 m .53555 .57079 L s .42738 .49072 m .4174 .48316 L s .80274 .72683 m .82688 .7455 L s .52569 .56477 m .52534 .56368 L s .51907 .5606 m .51812 .55905 L s .54374 .60515 m .54652 .6041 L s .40335 .48865 m .39182 .4788 L s .53555 .57079 m .5361 .57041 L s .5097 .5907 m .50975 .58693 L s .55888 .49224 m .55694 .49744 L s .56656 .49161 m .56507 .49758 L s .5361 .57041 m .53671 .57006 L s .52534 .56368 m .52498 .56257 L s .77821 .718 m .80055 .73468 L s .51812 .55905 m .5171 .55742 L s .57341 .48985 m .57227 .49654 L s .75521 .71155 m .77591 .7263 L s .54652 .6041 m .5495 .60331 L s .59783 .43924 m .59566 .45048 L s .4885 .5806 m .48685 .57513 L s .53671 .57006 m .5374 .56975 L s .52498 .56257 m .52461 .56142 L s .37641 .48051 m .36297 .46826 L s .4174 .48316 m .4066 .47484 L s .5171 .55742 m .51602 .55571 L s .56085 .48668 m .55888 .49224 L s .5953 .43704 m .59292 .4481 L s .5374 .56975 m .53817 .56949 L s .50975 .58693 m .50975 .58323 L s .56815 .4853 m .56656 .49161 L s .5495 .60331 m .55271 .60279 L s .52461 .56142 m .52423 .56024 L s .59276 .43483 m .59017 .44571 L s .39182 .4788 m .3793 .46811 L s .53817 .56949 m .53903 .56927 L s .51602 .55571 m .51487 .55391 L s .57468 .48283 m .57341 .48985 L s .7805 .70969 m .80274 .72683 L s .73612 .69815 m .75521 .71155 L s .52423 .56024 m .52383 .55903 L s .55271 .60279 m .55617 .60254 L s .75761 .70277 m .77821 .718 L s .53903 .56927 m .53998 .56911 L s .56288 .48074 m .56085 .48668 L s .48685 .57513 m .485 .56962 L s .51487 .55391 m .51364 .55203 L s .4066 .47484 m .39489 .4657 L s .50975 .58323 m .50972 .57959 L s .56982 .47863 m .56815 .4853 L s .53998 .56911 m .54104 .56902 L s .52383 .55903 m .52343 .55778 L s .55617 .60254 m .55991 .60259 L s .60017 .42744 m .59783 .43924 L s .57607 .47546 m .57468 .48283 L s .51364 .55203 m .51233 .55005 L s .54104 .56902 m .54222 .56899 L s .36297 .46826 m .34833 .45504 L s .71853 .68602 m .73612 .69815 L s .52343 .55778 m .52301 .5565 L s .56496 .47442 m .56288 .48074 L s .3793 .46811 m .36569 .45649 L s .59783 .4254 m .5953 .43704 L s .55991 .60259 m .56395 .60295 L s .54222 .56899 m .54352 .56904 L s .73864 .68887 m .75761 .70277 L s .50972 .57959 m .50964 .57601 L s .76002 .69398 m .7805 .70969 L s .485 .56962 m .48294 .56404 L s .57159 .47158 m .56982 .47863 L s .59549 .42336 m .59276 .43483 L s .51233 .55005 m .51093 .54798 L s .52301 .5565 m .52259 .55518 L s .39489 .4657 m .38219 .45567 L s .56395 .60295 m .56832 .60364 L s .54352 .56904 m .54496 .56919 L s .70232 .67504 m .71853 .68602 L s .57759 .46771 m .57607 .47546 L s .5671 .4677 m .56496 .47442 L s .54496 .56919 m .54655 .56943 L s .51093 .54798 m .50943 .54579 L s .52259 .55518 m .52215 .55383 L s .56832 .60364 m .57305 .60469 L s .50964 .57601 m .50952 .57248 L s .72118 .6762 m .73864 .68887 L s .54655 .56943 m .5483 .56978 L s .68738 .66514 m .70232 .67504 L s .57345 .46413 m .57159 .47158 L s .57305 .60469 m .57818 .60611 L s .48294 .56404 m .48066 .55838 L s .52215 .55383 m .5217 .55244 L s .74117 .67957 m .76002 .69398 L s .36569 .45649 m .3509 .44386 L s .50943 .54579 m .50782 .54349 L s .34833 .45504 m .33241 .44075 L s .5483 .56978 m .55023 .57025 L s .60269 .41503 m .60017 .42744 L s .57818 .60611 m .58375 .60793 L s .38219 .45567 m .36842 .44468 L s .67362 .65624 m .68738 .66514 L s .56932 .46054 m .5671 .4677 L s .60053 .41315 m .59783 .4254 L s .57924 .45956 m .57759 .46771 L s .55023 .57025 m .55236 .57085 L s .5217 .55244 m .52123 .55101 L s .58375 .60793 m .58978 .61019 L s .50952 .57248 m .50937 .569 L s .7051 .66466 m .72118 .6762 L s .59837 .41126 m .59549 .42336 L s .50782 .54349 m .50611 .54107 L s .66095 .64825 m .67362 .65624 L s .55236 .57085 m .55469 .5716 L s .58978 .61019 m .59633 .6129 L s .57543 .45625 m .57345 .46413 L s .52123 .55101 m .52076 .54954 L s .64929 .64112 m .66095 .64825 L s .72383 .66637 m .74117 .67957 L s .59633 .6129 m .60344 .61612 L s .48066 .55838 m .47814 .55262 L s .55469 .5716 m .55725 .57251 L s .60344 .61612 m .61116 .61987 L s .50611 .54107 m .50427 .53851 L s .63854 .63477 m .64929 .64112 L s .6903 .65417 m .7051 .66466 L s .57161 .45294 m .56932 .46054 L s .61116 .61987 m .61955 .62419 L s .62865 .62914 m .63854 .63477 L s .55725 .57251 m .56007 .5736 L s .61955 .62419 m .62865 .62914 L s .50937 .569 m .50917 .56555 L s .58104 .45098 m .57924 .45956 L s .52076 .54954 m .52027 .54802 L s .3509 .44386 m .33483 .43013 L s .36842 .44468 m .35347 .43265 L s .56007 .5736 m .56315 .57488 L s .33241 .44075 m .31508 .4253 L s .67669 .64465 m .6903 .65417 L s .50427 .53851 m .5023 .53582 L s .70788 .65427 m .72383 .66637 L s .57752 .44792 m .57543 .45625 L s .60539 .40198 m .60269 .41503 L s .56315 .57488 m .56653 .57638 L s .52027 .54802 m .51976 .54647 L s .47814 .55262 m .47537 .54673 L s .6034 .40024 m .60053 .41315 L s .56653 .57638 m .57023 .57812 L s .50917 .56555 m .50894 .56214 L s .66418 .63601 m .67669 .64465 L s .57399 .44487 m .57161 .45294 L s .60141 .39849 m .59837 .41126 L s .57023 .57812 m .57428 .58012 L s .5023 .53582 m .50018 .53297 L s .51976 .54647 m .51925 .54487 L s .58297 .44194 m .58104 .45098 L s .69323 .64318 m .70788 .65427 L s .65268 .62818 m .66418 .63601 L s .57428 .58012 m .57872 .5824 L s .57872 .5824 m .58356 .58499 L s .64211 .6211 m .65268 .62818 L s .57972 .43912 m .57752 .44792 L s .35347 .43265 m .33725 .41948 L s .58356 .58499 m .58885 .58793 L s .50894 .56214 m .50867 .55875 L s .51925 .54487 m .51871 .54322 L s .50018 .53297 m .49792 .52996 L s .6324 .61471 m .64211 .6211 L s .33483 .43013 m .31736 .41521 L s .58885 .58793 m .59463 .59124 L s .47537 .54673 m .47232 .5407 L s .67977 .63303 m .69323 .64318 L s .59463 .59124 m .60093 .59495 L s .62349 .60895 m .6324 .61471 L s .57647 .4363 m .57399 .44487 L s .60093 .59495 m .60781 .59912 L s .61531 .60377 m .62349 .60895 L s .60781 .59912 m .61531 .60377 L s .31508 .4253 m .29622 .40857 L s .51871 .54322 m .51817 .54153 L s .6083 .38824 m .60539 .40198 L s .58505 .43242 m .58297 .44194 L s .66741 .62373 m .67977 .63303 L s .49792 .52996 m .49548 .52678 L s .60646 .38663 m .6034 .40024 L s .50867 .55875 m .50836 .55538 L s .58205 .42981 m .57972 .43912 L s .60462 .38502 m .60141 .39849 L s .51817 .54153 m .5176 .53979 L s .65608 .61521 m .66741 .62373 L s .47232 .5407 m .46899 .53449 L s .57906 .42721 m .57647 .4363 L s .49548 .52678 m .49287 .52342 L s .33725 .41948 m .31964 .4051 L s .64568 .60739 m .65608 .61521 L s .50836 .55538 m .50802 .55203 L s .5176 .53979 m .51702 .53801 L s .31736 .41521 m .29836 .39898 L s .63616 .60023 m .64568 .60739 L s .58729 .42238 m .58505 .43242 L s .55485 .52381 m .5557 .52633 L s .55417 .52124 m .55485 .52381 L s .55365 .51861 m .55417 .52124 L s .5557 .52633 m .55673 .52883 L s .55328 .51591 m .55365 .51861 L s .55673 .52883 m .55795 .53131 L s .55306 .51311 m .55328 .51591 L s .55795 .53131 m .55938 .53381 L s .62745 .59366 m .63616 .60023 L s .55298 .51021 m .55306 .51311 L s .55938 .53381 m .56103 .53633 L s .49287 .52342 m .49006 .51985 L s .56103 .53633 m .56291 .53889 L s .55303 .50718 m .55298 .51021 L s .58452 .41997 m .58205 .42981 L s .56291 .53889 m .56505 .54153 L s .55321 .50401 m .55303 .50718 L s .61948 .58762 m .62745 .59366 L s .56505 .54153 m .56746 .54425 L s .51702 .53801 m .51643 .53617 L s .56746 .54425 m .57017 .54708 L s .46899 .53449 m .46535 .52808 L s .55351 .50068 m .55321 .50401 L s .57017 .54708 m .57319 .55004 L s .6122 .58206 m .61948 .58762 L s .29622 .40857 m .27568 .39045 L s .58175 .41756 m .57906 .42721 L s .57319 .55004 m .57655 .55317 L s .60555 .57694 m .6122 .58206 L s .57655 .55317 m .58028 .55648 L s .55393 .49719 m .55351 .50068 L s .50802 .55203 m .50764 .54868 L s .58028 .55648 m .5844 .56001 L s .59949 .57222 m .60555 .57694 L s .5844 .56001 m .58895 .56379 L s .59397 .56785 m .59949 .57222 L s .58895 .56379 m .59397 .56785 L s .55446 .4935 m .55393 .49719 L s .49006 .51985 m .48705 .51608 L s .51643 .53617 m .51582 .53428 L s .55511 .48961 m .55446 .4935 L s .31964 .4051 m .30051 .38938 L s .58968 .41179 m .58729 .42238 L s .55588 .48551 m .55511 .48961 L s .58713 .40956 m .58452 .41997 L s .50764 .54868 m .50722 .54534 L s .55675 .48116 m .55588 .48551 L s .46535 .52808 m .46137 .52146 L s .51582 .53428 m .51519 .53233 L s .29836 .39898 m .2777 .38134 L s .53899 .49507 m .53775 .49708 L s .54026 .49284 m .53899 .49507 L s .53775 .49708 m .53655 .49888 L s .54157 .49038 m .54026 .49284 L s .58458 .40734 m .58175 .41756 L s .48705 .51608 m .4838 .51207 L s .53655 .49888 m .53538 .50048 L s .54292 .48769 m .54157 .49038 L s .53538 .50048 m .53423 .50189 L s .55774 .47656 m .55675 .48116 L s .54431 .48474 m .54292 .48769 L s .53423 .50189 m .5331 .5031 L s .54575 .48153 m .54431 .48474 L s .5331 .5031 m .532 .50414 L s .54724 .47805 m .54575 .48153 L s .55884 .47168 m .55774 .47656 L s .51519 .53233 m .51454 .53033 L s .532 .50414 m .53092 .50501 L s .50722 .54534 m .50677 .542 L s .54879 .47428 m .54724 .47805 L s .53092 .50501 m .52986 .5057 L s .59225 .40061 m .58968 .41179 L s .27568 .39045 m .25333 .37081 L s .4838 .51207 m .48031 .50782 L s .56004 .46652 m .55884 .47168 L s .5504 .47021 m .54879 .47428 L s .52986 .5057 m .52881 .50623 L s .58989 .39855 m .58713 .40956 L s .46137 .52146 m .45703 .51458 L s .30051 .38938 m .27972 .37221 L s .51454 .53033 m .51387 .52828 L s .55206 .46582 m .5504 .47021 L s .52961 .48007 m .52729 .48166 L s .53189 .47817 m .52961 .48007 L s .53414 .47596 m .53189 .47817 L s .52881 .50623 m .52777 .50661 L s .52729 .48166 m .52492 .48294 L s .58753 .3965 m .58458 .40734 L s .53638 .47343 m .53414 .47596 L s .56137 .46103 m .56004 .46652 L s .52492 .48294 m .52249 .48393 L s .5386 .47058 m .53638 .47343 L s .50677 .542 m .50629 .53865 L s .52249 .48393 m .52 .48462 L s .54082 .46739 m .5386 .47058 L s .52777 .50661 m .52675 .50683 L s .5538 .46111 m .55206 .46582 L s .52 .48462 m .51742 .48502 L s .54304 .46385 m .54082 .46739 L s .48031 .50782 m .47655 .5033 L s .5628 .45522 m .56137 .46103 L s .52675 .50683 m .52573 .5069 L s .51742 .48502 m .51475 .48511 L s .51387 .52828 m .51319 .52616 L s .54528 .45996 m .54304 .46385 L s .55561 .45605 m .5538 .46111 L s .2777 .38134 m .25523 .36214 L s .51475 .48511 m .51198 .48491 L s .59498 .38881 m .59225 .40061 L s .52573 .5069 m .52473 .50683 L s .54755 .4557 m .54528 .45996 L s .45703 .51458 m .45231 .50742 L s .56436 .44905 m .5628 .45522 L s .50629 .53865 m .50577 .53529 L s .55749 .45062 m .55561 .45605 L s .59281 .38691 m .58989 .39855 L s .51198 .48491 m .50908 .48441 L s .54984 .45105 m .54755 .4557 L s .51319 .52616 m .51248 .52399 L s .52473 .50683 m .52373 .50662 L s .47655 .5033 m .47251 .4985 L s .59063 .38501 m .58753 .3965 L s .50908 .48441 m .50605 .4836 L s .55945 .4448 m .55749 .45062 L s .56603 .44251 m .56436 .44905 L s .55217 .44601 m .54984 .45105 L s .52373 .50662 m .52273 .50627 L s .25333 .37081 m .22899 .34949 L s .27972 .37221 m .25712 .35347 L s .50605 .4836 m .50288 .48248 L s .50577 .53529 m .50521 .53191 L s .51248 .52399 m .51176 .52175 L s .55455 .44055 m .55217 .44601 L s .56151 .43858 m .55945 .4448 L s .52273 .50627 m .52174 .50579 L s .45231 .50742 m .44718 .49995 L s .56783 .43556 m .56603 .44251 L s .47251 .4985 m .46815 .49339 L s .50288 .48248 m .49954 .48104 L s .5979 .37635 m .59498 .38881 L s .5959 .37459 m .59281 .38691 L s .52174 .50579 m .52075 .50517 L s .55698 .43466 m .55455 .44055 L s .56365 .43194 m .56151 .43858 L s .51176 .52175 m .51101 .51945 L s .59389 .37283 m .59063 .38501 L s .49954 .48104 m .49602 .47928 L s .25523 .36214 m .23077 .34126 L s .50521 .53191 m .50462 .52851 L s .56975 .42819 m .56783 .43556 L s .52075 .50517 m .51975 .50442 L s .55948 .42831 m .55698 .43466 L s .46815 .49339 m .46345 .48795 L s .49602 .47928 m .49229 .47718 L s .5659 .42484 m .56365 .43194 L s .51101 .51945 m .51025 .51708 L s .44718 .49995 m .44159 .49213 L s .51975 .50442 m .51876 .50355 L s .5718 .42036 m .56975 .42819 L s .56205 .4215 m .55948 .42831 L s .50462 .52851 m .504 .52509 L s .60102 .36318 m .5979 .37635 L s .25712 .35347 m .23255 .33301 L s .49229 .47718 m .48835 .47474 L s .56825 .41727 m .5659 .42484 L s .59916 .36156 m .5959 .37459 L s .51876 .50355 m .51776 .50255 L s .22899 .34949 m .20248 .32636 L s .51025 .51708 m .50946 .51465 L s .59731 .35993 m .59389 .37283 L s .46345 .48795 m .45838 .48216 L s .5647 .41419 m .56205 .4215 L s .57399 .41205 m .5718 .42036 L s .48835 .47474 m .48416 .47193 L s .51776 .50255 m .51676 .50143 L s .504 .52509 m .50334 .52164 L s .57072 .4092 m .56825 .41727 L s .44159 .49213 m .43552 .48393 L s .50946 .51465 m .50865 .51214 L s .23077 .34126 m .20415 .31852 L s .56744 .40635 m .5647 .41419 L s .48416 .47193 m .47971 .46875 L s .51676 .50143 m .51575 .50018 L s .57632 .40324 m .57399 .41205 L s .45838 .48216 m .45292 .47598 L s .5733 .40061 m .57072 .4092 L s .50334 .52164 m .50265 .51815 L s .50865 .51214 m .50781 .50957 L s .51575 .50018 m .51474 .49882 L s .47971 .46875 m .47496 .46518 L s .57028 .39798 m .56744 .40635 L s .23255 .33301 m .20583 .31068 L s .5788 .39389 m .57632 .40324 L s .43552 .48393 m .42892 .47531 L s .45292 .47598 m .44702 .46938 L s .51474 .49882 m .51371 .49733 L s .57601 .39146 m .5733 .40061 L s .50781 .50957 m .50695 .50692 L s .20248 .32636 m .1736 .30123 L s .50265 .51815 m .50192 .51463 L s .47496 .46518 m .4699 .46119 L s .57322 .38903 m .57028 .39798 L s .51371 .49733 m .51268 .49573 L s .58143 .38396 m .5788 .39389 L s .57886 .38172 m .57601 .39146 L s .50695 .50692 m .50607 .50419 L s .4699 .46119 m .46448 .45677 L s .20415 .31852 m .17517 .29377 L s .44702 .46938 m .44066 .46234 L s .50192 .51463 m .50115 .51106 L s .42892 .47531 m .42176 .46622 L s .57628 .37947 m .57322 .38903 L s .51268 .49573 m .51163 .494 L s .58422 .37343 m .58143 .38396 L s .50607 .50419 m .50516 .50139 L s .46448 .45677 m .45869 .4519 L s .58185 .37136 m .57886 .38172 L s .20583 .31068 m .17674 .2863 L s .51163 .494 m .51058 .49216 L s .50115 .51106 m .50035 .50744 L s .57947 .36928 m .57628 .37947 L s .44066 .46234 m .43379 .45482 L s .42176 .46622 m .41399 .45663 L s .50516 .50139 m .50423 .4985 L s .51058 .49216 m .5095 .4902 L s .45869 .4519 m .45248 .44654 L s .58718 .36225 m .58422 .37343 L s .1736 .30123 m .14214 .27391 L s .58499 .36034 m .58185 .37136 L s .50035 .50744 m .49951 .50377 L s .5828 .35842 m .57947 .36928 L s .5095 .4902 m .50841 .48812 L s .43379 .45482 m .42636 .44678 L s .50423 .4985 m .50327 .49553 L s .17517 .29377 m .14361 .26681 L s .45248 .44654 m .44582 .44067 L s .59032 .3504 m .58718 .36225 L s .41399 .45663 m .40556 .44648 L s .49951 .50377 m .49864 .50005 L s .5883 .34863 m .58499 .36034 L s .50841 .48812 m .50731 .48592 L s .58628 .34686 m .5828 .35842 L s .50327 .49553 m .50228 .49248 L s .17674 .2863 m .14508 .25971 L s .44582 .44067 m .43867 .43425 L s .42636 .44678 m .41834 .43817 L s .50731 .48592 m .50619 .4836 L s .49864 .50005 m .49773 .49626 L s .59365 .33782 m .59032 .3504 L s .59178 .33618 m .5883 .34863 L s .50228 .49248 m .50126 .48934 L s .58992 .33455 m .58628 .34686 L s .40556 .44648 m .3964 .43571 L s .14214 .27391 m .10784 .2442 L s .50619 .4836 m .50504 .48116 L s .43867 .43425 m .43098 .42726 L s .49773 .49626 m .49678 .49241 L s .41834 .43817 m .40967 .42895 L s .50126 .48934 m .50021 .4861 L s .14361 .26681 m .10922 .23744 L s .50504 .48116 m .50388 .47861 L s .43098 .42726 m .42271 .41964 L s .49678 .49241 m .49579 .48849 L s .14508 .25971 m .11059 .23067 L s .3964 .43571 m .38647 .42428 L s .50021 .4861 m .49913 .48277 L s .50388 .47861 m .5027 .47593 L s .40967 .42895 m .40029 .41907 L s .49579 .48849 m .49477 .48449 L s .49913 .48277 m .49802 .47935 L s .42271 .41964 m .41379 .41137 L s .5027 .47593 m .50149 .47312 L s .0711 .21242 m .10784 .2442 L s .38647 .42428 m .37569 .41213 L s .40029 .41907 m .39014 .40848 L s .49802 .47935 m .49688 .47583 L s .49477 .48449 m .4937 .48042 L s .50149 .47312 m .50026 .4702 L s .07604 .20911 m .10922 .23744 L s .41379 .41137 m .40419 .40238 L s .08104 .20575 m .11059 .23067 L s .50026 .4702 m .499 .46714 L s .49688 .47583 m .49571 .4722 L s .4937 .48042 m .4926 .47626 L s .37569 .41213 m .364 .39917 L s .39014 .40848 m .37916 .39712 L s .40419 .40238 m .39382 .39263 L s .499 .46714 m .49771 .46396 L s .49571 .4722 m .4945 .46846 L s .4926 .47626 m .49145 .47202 L s .49771 .46396 m .4964 .46065 L s .37916 .39712 m .36727 .38492 L s .39382 .39263 m .38264 .38207 L s .4945 .46846 m .49325 .46462 L s .364 .39917 m .3513 .38535 L s .49145 .47202 m .49027 .46769 L s .4964 .46065 m .49505 .45721 L s .49325 .46462 m .49197 .46067 L s .49027 .46769 m .48904 .46325 L s .38264 .38207 m .37056 .37062 L s .36727 .38492 m .3544 .37181 L s .49505 .45721 m .49368 .45364 L s .3513 .38535 m .33753 .37058 L s .49197 .46067 m .49065 .45659 L s .48904 .46325 m .48776 .45872 L s .49368 .45364 m .49227 .44993 L s .37056 .37062 m .3575 .35823 L s .49065 .45659 m .48929 .4524 L s .3544 .37181 m .34045 .35771 L s .48776 .45872 m .48644 .45408 L s .33753 .37058 m .32258 .35478 L s .49227 .44993 m .49083 .44608 L s .48929 .4524 m .4879 .44809 L s .3575 .35823 m .34337 .34481 L s .48644 .45408 m .48508 .44933 L s .49083 .44608 m .48935 .44208 L s .34045 .35771 m .32533 .34255 L s .4879 .44809 m .48646 .44364 L s .32258 .35478 m .30635 .33785 L s .48508 .44933 m .48367 .44446 L s .48935 .44208 m .48784 .43795 L s .34337 .34481 m .32809 .33028 L s .48646 .44364 m .48498 .43907 L s .32533 .34255 m .30894 .32622 L s .48784 .43795 m .48628 .43367 L s .48367 .44446 m .48221 .43948 L s .30635 .33785 m .28872 .31969 L s .48498 .43907 m .48345 .43436 L s .32809 .33028 m .31154 .31456 L s .48628 .43367 m .48469 .42923 L s .48221 .43948 m .48071 .43437 L s .30894 .32622 m .29116 .30863 L s .48345 .43436 m .48188 .42951 L s .48469 .42923 m .48305 .42464 L s .48071 .43437 m .47915 .42912 L s .28872 .31969 m .26957 .30018 L s .31154 .31456 m .29361 .29755 L s .48188 .42951 m .48026 .42451 L s .48305 .42464 m .48137 .41989 L s .29116 .30863 m .27188 .28967 L s .29361 .29755 m .27418 .27913 L s .26957 .30018 m .24877 .27921 L s .27188 .28967 m .25094 .26921 L s .27418 .27913 m .25311 .25919 L s .24877 .27921 m .22617 .25665 L s .25094 .26921 m .2282 .24713 L s .25311 .25919 m .23025 .23759 L s .22617 .25665 m .20159 .23234 L s .2282 .24713 m .2035 .22327 L s .23025 .23759 m .20542 .2142 L s .20159 .23234 m .17486 .20612 L s .17785 .19863 m .2035 .22327 L s .18413 .19418 m .20542 .2142 L s .17167 .20301 m .17486 .20612 L s .25 Mabswid .54679 0 m .95979 .56521 L s .95979 .56521 m 1 .99183 L s 1 .99183 m .5478 .46859 L s .5478 .46859 m .54679 0 L s .05392 .19694 m 0 .65354 L s 0 .65354 m .5478 .46859 L s .5478 .46859 m .54679 0 L s .54679 0 m .05392 .19694 L s .05392 .19694 m .54679 0 L s .11663 .17188 m .12176 .17742 L s [(-10)] .10637 .1608 .92547 1 Mshowa .29207 .10178 m .29693 .10755 L s [(0)] .28233 .09024 .84327 1 Mshowa .47634 .02815 m .48092 .03416 L s [(10)] .4672 .01613 .76107 1 Mshowa .125 Mabswid .15104 .15813 m .15409 .16149 L s .18578 .14425 m .1888 .14763 L s .22087 .13023 m .22385 .13364 L s .25629 .11608 m .25925 .11951 L s .32819 .08735 m .33108 .09084 L s .36468 .07277 m .36753 .07629 L s .40153 .05804 m .40435 .06159 L s .43875 .04317 m .44153 .04675 L s .08254 .1855 m .08565 .1888 L s .51432 .01298 m .51702 .01661 L s .25 Mabswid 0 .65354 m .53135 1.11058 L s .05889 .7042 m .06607 .70185 L s [(-20)] .04455 .7089 1 -0.32768 Mshowa .1818 .80992 m .18902 .8077 L s [(-10)] .16737 .81436 1 -0.30742 Mshowa .29401 .90643 m .30126 .90433 L s [(0)] .2795 .91063 1 -0.28952 Mshowa .39684 .99488 m .40412 .99289 L s [(10)] .38227 .99887 1 -0.27359 Mshowa .49143 1.07624 m .49874 1.07435 L s [(20)] .47681 1.08003 1 -0.25932 Mshowa .125 Mabswid .08441 .72615 m .08872 .72475 L s .10944 .74768 m .11376 .7463 L s .13401 .76881 m .13833 .76745 L s .15813 .78956 m .16245 .78821 L s .20505 .82992 m .20939 .8286 L s .22789 .84956 m .23223 .84826 L s .25032 .86885 m .25466 .86757 L s .27235 .88781 m .2767 .88653 L s .31528 .92473 m .31964 .92349 L s .3362 .94272 m .34055 .94149 L s .35675 .9604 m .36112 .95918 L s .37696 .97779 m .38133 .97658 L s .41638 1.01169 m .42076 1.01051 L s .43561 1.02823 m .43998 1.02706 L s .45452 1.04449 m .4589 1.04333 L s .47312 1.0605 m .4775 1.05935 L s .03289 .68184 m .03719 .68041 L s .00638 .65903 m .01068 .65759 L s .50945 1.09174 m .51383 1.09061 L s .52718 1.10699 m .53157 1.10588 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{262.375, 291.125}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc0005o`000?l0K00008800ol@0003o`00008000?o0000J@000800 0_l00`3o000@0003o`00008000?o0000J@0007d00ol40003o`0000h000?o00000`000ol0001X0000 N`02oaP000?o000010000ol0001W0000N003oaX000?o00001@000ol0001V0000MP02o`8000?o0000 60000ol000050003o`0006H0001c00?o7`000ol000060003o`0006D0001a00;o8P000ol000070003 o`0006@0001^00Co8`000ol000080003o`0006<0001?00;o6`02o`<000?o00008@000ol000080003 o`0006<0001>0004o`00oaL00olY0003o`0000T000?o0000HP0004h000Co003o5@02ob`000?o0000 2P000ol0001Q0000CP001?l00?lB00?o00<0o`00:`000ol0000:0003o`000640001>0004o`00oa00 0_la0003o`0000/000?o0000H00004l00_l>00?o<`000ol0000<0003o`0005l0001M00;o=P000ol0 000=0003o`0005h0001J00?o0P000ol0000c0003o`0000d000?o0000GP0005L00olk0003o`0000h0 00?o0000G@0005D00_ln0003o`0000l000?o0000G00005801Oln0003o`00010000?o0000F`000500 0_l50003o`0003/000?o000040000ol0001K0000C@03odD000?o00004@000ol0001J0000B`03odL0 00?o00004P000ol0001I0000B003o`8000?o0000A@000ol0000B0003o`0005T0001600;oC@000ol0 000C0003o`0005P0001300?oC`000ol0000D0003o`0005L0000M00?o1002oa/00_l00`3oo`1?0003 o`0001D000?o0000EP0001h000?o00000P001?l00?lG00?oE0000ol0000E0003o`0005H0000G00Go 0P000ol000020004o`00oaD00_mG0003o`0001H000?o0000E@0001h000?o00000P001?l00?lB00?o F@000ol0000G0003o`0005@0000N0003o`00008000Co003o4002o`<000?o0000EP000ol0000H0003 o`0005<0000M00;o1@02o`h00omN0003o`0001P000?o0000D`0003800_mQ0003o`0001T000?o0000 DP0002l01OmQ0003o`0001X000?o0000D@0002d00_mV0003o`0001/000?o0000D00002X00omX0003 o`0001/000?o0000D00002P00omZ0003o`0001`000?o0000C`0002D00ol30003o`0006L000?o0000 7@000ol0001>00008`02og0000?o00007@000ol0001>00008003og8000?o00007P000ol0001=0000 7P02o`8000?o0000L0000ol0000O0003o`0004`0000K00?o7@000ol0001G0003o`00020000?o0000 B`0001X000?o00007`000ol0001F0003o`00020000?o0000B`0001X000?o000070001Ol0003o05L0 00?o00008@000ol0001:00006P02o`D00_lE0003o`3o00<000?o0000E0000ol0000R0003o`0004T0 000J0003o`3o00<00_l00`3o000D0003o`3o00<000?o0000D`000ol0000S0003o`0004P0000J0005 o`00o`000_l0103o0?lE0003o`3o00<000?o0000DP000ol0000S0003o`0004P0000I0003o`000080 00So003o0?l0oaD000?o0?l00`000ol0001A0003o`0002@000?o0000A`0001T00ol30008o`00o`3o 0?lE0003o`3o00<000?o0000D0000ol0000U0003o`0004H0000I0003o`0000@000So003o0?l0oaD0 00Co0?oo0P000ol0001?0003o`0002D000?o0000AP0001T000?o00001@001ol00?l0o`000_lD0004 o`00o`8000?o0000CP000ol0000V0003o`0004D0000I0003o`0000H000Ko003o0?l20003o`000180 00Co003o0P000ol0001=0003o`0002L000?o0000A00001T000?o00001`001Ol00?l000;o00<0o`00 4`001?l00?l20003o`0004`000?o0000:0000ol0001300006@000ol000080004o`00o`8000?o0?l0 50001?l00?l20003o`0004/000?o0000:0000ol0001300006@000ol000090003o`0000;o00@0o`3o 50001?l00?l20003o`0004X000?o0000:@000ol0001200006@03o`X000Ko0000o`03oa@000Co003o 0P000ol000190003o`0002X000?o0000@@0001P00_l=0005o`000?l00P02oa@000Co003o0P000ol0 00180003o`0002/000?o0000@00000X00ol400;o1@000ol0000=0005o`000?l00P02oa@000Co003o 0P000ol000170003o`0002/000?o0000@00000/000?o00000P001?l00?l40003o`0000h000Go0000 o`0200?o4`001?l00?l20003o`0004H000?o0000;0000ol0000o00001005o`8000?o00000P001?l0 0?l40003o`0000l000Go0000o`020003o`3o01<000Co003o0P000ol000150003o`0002d000?o0000 ?P0000/000?o00000P001?l00?l40003o`00010000Go0000o`020003o`3o01<000Co003o0P000ol0 00140003o`0002d000?o0000?P0000/000?o00000P001?l00?l40003o`00014000Co00000_l00`3o 0002oa8000Co003o0P000ol000130003o`0002h000?o0000?@0000X00_l500;o1@000ol0000B0003 o`00008000?o0?l00P000ol0000@0004o`00o`8000?o0000@P000ol0000_0003o`0003`0000H00;o 50000ol000020003o`3o008000?o000040001?l00?l200;o@P000ol0000`0003o`0003/0000H0003 o`0001@000?o00000P000ol0o`0200;o4@001?l00?l30003o`0003l000?o0000<0000ol0000k0000 5`000ol0000F0003o`00008000?o0?l00`000ol0000?0004o`00o`<000?o0000?P000ol0000a0003 o`0003X0000G0003o`0001L000?o00000P001?l0ool20003o`0000l000Co003o0`000ol0000m0003 o`00038000?o0000>@0001L000?o000060000ol000020004o`00o`8000?o00003`001?l00?l30003 o`0003`000?o0000<`000ol0000h00005`000ol0000H0003o`0000<00_l01@3o003o014000Co003o 0`000ol0000k0003o`0003<000?o0000>00001L000?o00006@000ol000040006o`3oo`3o4@001?l0 0?l30003o`0003X000?o0000=0000ol0000g00005`000ol0000J0003o`0000@000Go003o0002oa00 00?o00000_l20003o`0003T000?o0000=@000ol0000f00005`02oa`000?o000010001?l00?l20003 o`0000h000Go0000o`020003o`0003P000?o0000=@000ol0000f00005`000ol0000L0003o`0000@0 00Co003o0P000ol0000>0005o`000?l00P000ol0000g0003o`0003H000?o0000=@0001H000?o0000 7P000ol000040004o`00o`8000?o00003P001Ol0003o008000?o0000=P000ol0000g0003o`0003@0 000F0003o`0001l000?o00001002o`050?l00?l040001Ol0003o008000?o0000=@000ol0000h0003 o`0003<0000F0003o`00020000?o00001@000ol0o`020003o`0000h000Go0000o`020003o`0003@0 00?o0000>0000ol0000c00005P000ol0000Q0003o`0000D000?o0?l00P02o`l000Go0000o`020003 o`0003<000?o00001`000ol0000_0003o`000380000F0003o`00028000?o00001@000ol0o`030003 o`0000d000Go0000o`020003o`00038000?o00001`02oc4000?o0000<@0001H000?o00008`000ol0 00050004o`3oo`8000?o00003@001Ol0003o008000?o0000<@000ol000060003o`3o038000?o0000 <00001H00_lU0003o`0000D000Co003o0P000ol0000=0004o`00o`<00_la0003o`0000H00_lc0003 o`000300000F0003o`0002D000?o00001@02o`050?l00?l03`001?l00?l40003o`0002h000?o0000 1P02oc@000?o0000;`0001H000?o00009P000ol000060003o`3o008000?o00003@001?l00?l40003 o`0002d000?o00001@000ol0o`0e0003o`0002h0000E0003o`0002P000?o00001P000ol0o`020003 o`0000d000?o00000_l30003o`0002`000?o00001@03ocD000?o0000;P0001D000?o0000:@000ol0 00060006o`3oo`3o3`001Ol0003o00<000?o0000:`000ol0000500?o00<0ool0<`000ol0000]0000 5@000ol0000Z0003o`0000H000Ko003o0?l?0005o`000?l00`000ol0000Z0003o`0000D00ol00`3o o`0d0003o`0002`0000E0003o`0002/000?o00001P001_l00?l0o`l000Go0000o`030003o`0002T0 00?o00001@02o`040?ooocD000?o0000:`0001D000?o0000;0000ol000060005o`00o`000_l=0005 o`000?l010000ol0000X0003o`0000D00_l00`3oo`0f0003o`0002/0000E00;o7P02o`h000?o0000 1P001?l00?l20003o`0000/000Go0000o`040003o`0002L000?o00001003o`030?oo03L000?o0000 :P0001D000?o00007`000ol0000<0003o`0000H000?o00000_l00`3oo`0<0005o`000?l010000ol0 000V0003o`0000@00_l0103ooolh0003o`0002T0000E0003o`0002000_l=0003o`0000H000Go0000 o`020003o`0000X000Go0000o`040003o`0002D000?o00000`001?l0o`03o`030?l003H000?o0000 :00001D000?o00007`02o`030?l000`000?o00001P001Ol0003o008000?o00002P001Ol0003o00@0 00?o000090000ol0000300;o0P03o`030?oo03H000?o0000:00001@000?o00008P000ol0o`0=0003 o`0000H000Go0000o`020003o`0000X000Go0000o`040003o`0002<000?o00000`02o`8000?o0?l0 0olg0003o`0002L0000D0003o`0002<000?o0?l03@000ol000060004o`0000;o00<0o`002`001Ol0 003o00@000?o00008P000ol0000200?o0P02o`030?oo03T000?o00009P0001@000?o00008@02o`04 0?ooo``000?o00001`000ol000020003o`3o00`000Go0000o`0400;o8P000ol0000200?o0P02o`03 0?oo03T000?o00009P0001@000?o00008`000ol00002o``000?o00001`000ol000020004o`3oo`/0 00Go0000o`050003o`0001l000?o00000P03o`030?oo00;o00<0o`00>@000ol0000U00005003ob@0 0_l0103oool;0003o`0000L00_l30003o`0000;o2P001Ol0003o00D000?o00007P000ol0000200;o 0P02o`030?oo03`000?o0000900001@000?o00009P000ol0o`02o`/000?o000020001Ol0003o00<0 00?o000020001Ol0003o00D000?o00007@001?l00003o`050?l0o`000_lm0003o`0002<0000=00;o 1@000ol0000W0003o`0000?o2P000ol000080005o`000?l00`000ol000080005o`000?l01@000ol0 000;0003o`0000h000Co00000ol01@3oool000;o?@000ol0000S000030001?l00?l40003o`0002P0 0_l00`3o0002o`T000?o000020001Ol0003o00<000?o000020001Ol0003o00D000?o00002P000ol0 000>0005o`00o`000_l01@3oool000;o?P000ol0000R000030001?l00?l30003o`0002/000?o0?l0 0P000ol000070003o`0000P000Go0000o`030003o`0000L000?o00000P000ol000030003o`0000T0 0_l?0003o`0000?o0P001?l0o`02ocl000?o00008@0000`000Co003o0`000ol0000/0003o`3o0080 0_l80003o`0000P000Co00000_l20003o`0000L000?o00000P000ol000030003o`0000P00_l?0003 o`0000?o0P02o`040?oood0000?o0000800000`000Co003o0`000ol0000]0003o`3o00<000?o0000 1P000ol000080003o`00008000Co003o2@000ol000020003o`0000<000?o00001`03o`h000Co0?l0 0_l01@3oool000;o@@000ol0000P00003@02o`@000?o0000;P001?l0ool20003o`0000H000?o0000 20000ol000020004o`00o`T000?o00000P000ol000030003o`0000L00_l>0007o`3oo`3o0003o`03 0?oo048000?o00007`0001<000?o0000;`001?l00?l20003o`0000H000?o00002002o`<00_l00`3o 00080003o`00008000?o00000`000ol0000600;o3P02o`060?oo0?l00ol00`3o00120003o`0001h0 000C00;o<@02o`050?oo0?l020000ol000090003o`00008000Co0?oo20000ol000020003o`0000<0 0_l600?o3@02o`040?oo00;o00<0ool00_m40003o`0001d0000C0003o`00038000Go003o0002o`L0 00?o00002@000ol000020003o`0000;o1`000ol000020003o`0000@000?o00000`03o`d000Ko0?l0 o`03o`040?oood@000?o00007@0001<000?o0000<`001?l00?l20003o`0000D000?o00002@02o`<0 00Go0000o`070003o`00008000?o00000`000ol0000400;o3@001_l0o`3o00?o00@0o`3oA@000ol0 000L00004`000ol0000d0003o`0000;o00<0ool01P000ol0000:0005o`000?l00`000ol000040003 o`00008000?o00001002o`@00ol;00;o00<0o`000_l0103oo`02odL000?o00006`00018000?o0000 =P001Ol0003o008000?o000010000ol0000:0005o`000?l00`000ol000040003o`00008000?o0000 1@001?l00003o`/00ol00`3o0002o`030?oo00;oA`000ol0000K00004P000ol0000g00;o0P02o`03 0?oo00D000?o00002P001Ol0003o00<00_l50003o`00008000?o00001@02o`800ol900Co00<0o`00 0ol0103ooom80003o`0001X0000B0003o`0003T000Go0000o`020003o`0000<000?o00002P001Ol0 003o00@000?o00000P000ol000030003o`0000H000?o0?l00_l700?o00H0o`00o`03o`040?ooodT0 00?o00006@00018000?o0000>P02o`800_l00`3oo`040003o`0000X000Go0000o`0400;o0`000ol0 00030003o`0000H01Ol300Go0P03o`030?l000;o00@0o`3oBP000ol0000H00004P02ocd000Go0000 o`020003o`00008000?o00002P001?l00002o`@000Go0000o`050003o`0000H00_l00`3oo`02o`80 0_l30004o`3o00;o00<0o`000_m;0003o`0001P0000B0003o`0003d00_l20003o`0000;o0`000ol0 000:0003o`00008000?o00000P001Ol0003o00D000?o00001P05o`040?ooo`<000?o00001Ol0103o oom<0003o`0001L0000B0003o`0003l000Co003o0`001Ol0003o00`000?o00000P000ol000020004 o`00o`H000?o00000P05o`040?l0o`H000?o00001Ol0103ooom=0003o`0001H0000B0003o`000400 0_l00`3oo`020005o`000?l030000ol000020003o`00008000Co003o1@000ol0o`02o`<01Ol60004 o`0000Go00@0ooooCP000ol0000E00004P000ol000120004o`00o`8000Go0000o`0<0003o`000080 00?o00000P001?l00?l300?o1P001Ol0o`3o00H000Go003o0002o`030?l000?oCP000ol0000E0000 4@000ol0001400;o00@0o`000_l00`3o000<0003o`00008000?o00000P02o`040?ooo`<000?o0000 1002o`030?oo00@000Co00000_l00`3o0002o`030?oo04l000?o00005000014000?o0000AP000ol0 o`0300?o3@02o`<000Co00001?l60003o`0000<00_l200;o0P000ol0000200;o00<0o`000ol00`3o 001?0003o`0001<0000A0003o`0004L000Co0?oo0`02o`h000Co00000ol300;o1P000ol000020003 o`3o00800ol50006o`3o0?l00omA0003o`0001<0000A0003o`0004P000?o00000_l200;o3P03o`03 0?l000@00_l60007o`000?l0o`0:0006o`3o0?l00omB0003o`000180000A00;oBP02o`8000Go0000 o`0:00Co1002o`@00ol50005o`00o`000_l800;o00<0o`000_l0103ooomB0003o`000140000A0003 o`0004/000Co003o0`000ol0000400?o10000ol000030005o`000?l00P000ol000030006o`00o`3o 2002o`030?l000?o00@0o`3oDP000ol0000@00004@000ol0001<0004o`00o`<00_l0103oool80003 o`0000<000Go0000o`0200;o0`001_l00?l0o`L000?o00000_l01P3oool0o`8000?o0000C`000ol0 000@00004@000ol0001=0004o`00o`800ol<0003o`0000<00_l20005o`000?l00`001Ol0o`3o00H0 00Go0000o`020005o`3o0?l00P000ol0001@0003o`0000l0000A0003o`0004h01Ol200;o30000ol0 00040003o`3o00@00_l0103oool20003o`0000800_l30008o`00o`3o0?l30003o`00050000?o0000 3P00010000?o0000CP04o`030?oo00800ol;0003o`0000@000?o0?l01@04o`8000Co00000_l400;o 00H0o`3o0?l40003o`00050000?o00003@00010000?o0000B`03o`@000?o00000_l0103o0?l;00;o 1@000ol0o`0700So1@001Ol0ool000;o1P000ol0001?0003o`0000d0000@0003o`0004P00ol800;o 0P03o`030?oo00/000?o00000`02o`P000Co0?oo1`000ol00002o`030?oo00L000?o0000C`000ol0 000<00004002odH00ol=0004o`0000;o0P02o`X000?o00000`02o`L00_l00`3o00060003o`0000?o 00<0o`001`000ol0001?0003o`0000/0000@0003o`0004800olA0004o`0000;o0`02o`T000?o0000 10000ol0000400;o00<0o`001P000ol00005o`T000?o0000CP000ol0000;000040000ol0000o00?o 5@001?l00002o`@000?o00001P000ol0000400;o1@000ol0o`02o`D00_l00`3o0002o`030?l000T0 00?o0000CP000ol0000:000040000ol0000m00;o6@000ol000020003o`0000800_l700;o10000ol0 o`040003o`3o00;o1@001Ol00?l000;o00<0ool02@000ol0001?0003o`0000T0000@0003o`0003X0 0olL0003o`0000800_l40003o`0000H000?o00000P000ol0o`030003o`0000;o1@001Ol00?l000;o 00@0o`3o2@000ol0001=00?o2P0000l000?o0000>003ob000_l300;o10000ol000050003o`000080 00Co003o0P001?l00002o`030?oo00;o00D0o`00o`020003o`0000;o20000ol0001900?o0P000ol0 000800003`000ol0000e00?o9@001?l00003o`<000?o00001@001Ol0003o00<000?o0?l00`04o`03 0?oo00?o00D0o`00o`040003o`0000H000?o0000A@03o`D000?o0000200000l000?o00000003o`0000P0000?0003o`0002T00olg0003o`3o00800_l500;o00@0o`3o10001?l0ool400?o 10001_l0ool0o`L00_l50003o`0003D00olC0003o`0000L00000103oool400;o1@000ol0000V00?o >`03o`<000?o00001003o`030?l0008000?o00000_l300;o1@001?l0ool200;o1`000ol000030003 o`0003400olF0003o`0000L000020003o`00008000Co003o10000ol0000S00?o@002o`<000?o0000 1@03o`<000?o00000P02o`030?oo00D000Co0?oo1002o`H000?o00000`000ol0000]00?o6@000ol0 000700000P000ol000020004o`00o`@000?o00008003od@000?o00000P02o`H01?l00`3o000400?o 1P001?l00?l600;o1@000ol000030003o`0002P01?lL0003o`0000L000020003o`00008000Co003o 0`000ol0000N00?oB0000ol0000300;o1@000ol0000Bo`030?oo00L00_l40003o`0000<000?o0000 9003ob0000?o00001`00008000?o00000P001?l00?l30003o`0001/00om<00;o1@000ol000030004 o`00o`H00ol50003o`3o00;o2@000ol0000200;o10000ol0000P00?o8`000ol00007000000<0ool0 1@02o`@000?o00006003oe000_l500;o0`02o`030?l000@00_l00`3oo`030003o`0000801Ol60003 o`0000<000?o00000P000ol0000L00?o9P000ol0000700003P000ol0000E00?oE002o`H000?o0000 0_l00`3o00030003o`3o00<00_l00`3o00030003o`3o00800_l500;o10001Ol0003o01/00olY0003 o`0000L0000>00;o4`03oeP00ol500Co00<0o`000`03o`@00ol40004o`00o`<00_l500;o0`001Ol0 003o01H01?l/0003o`0000L0000>0003o`0000l00omL0003o`3o00H01?l30003o`3o008000Co0000 0_l40004o`00o`D00_l50004o`0000;o0P000ol0000@00?o<0000ol0000700003P000ol0000<00?o H0000ol0o`050004o`3oo`<000?o0?l00P02o`<00_l40004o`00o`H000?o00000`02o`<00_l00`3o 000=00?o<`000ol0000700003P000ol0000900?oI0000ol0o`040003o`3o00Co0P000ol00002o`<0 0ol30005o`000?l01P000ol000040003o`00008000?o0?l02P03ocL000?o00001P0000h000?o0000 1P03ofP000?o0?l00`001?l00?l200Wo0P001?l00?l20003o`00008000?o00001003o`@00_l30003 o`3o00H00olj0003o`0000H0000=0003o`0000@00om/0003o`3o008000Co0?oo0P000ol0o`0400;o 0`001_l00?l0o`@000?o00001`02o`@000So0000o`3o00Co?@000ol0000600003@001?l00003og00 00Ko0?l0o`02o`050?l00?l01@02o`8000Oo0000o`3o00@000?o000020000ol0000200;o0P03od40 00?o00001P0000d01?md0005o`3oo`000_l01@3o003o00D00ol00`3o000300;o1@000ol0000800;o 0`03o`8000?o0000?`000ol0000600003@02ogL000?o0?l00ol00`3o0002o`D00ol00`3o000400;o 1@000ol0000900?o0P02o`800_lo0003o`0000H0000?00;oMP02o`040?ooo`8000?o00001@04o`H0 00?o00001002o`H00ol00`3oo`040003o`0000;o?P000ol0000600003`02ogL000?o0?l00_l20003 o`0000D000Co0?oo1`02o`H000?o0?l00ol60003o`00008000?o00000_lm0003o`0000H0000A0003 o`0007@01Ol20003o`0000@01Ol70003o`3o00@00ol;00;o0`02o`040?oooc/000?o00001P000180 00?o0000L`04o`030?oo00D00_l20004o`3oo`H000?o00001?l20003o`0000/000?o00000P001Ol0 o`3o03X000?o00001P0001<000?o0000LP02o`030?l000;o1002o`<000Co0?l00_l500?o00<0o`00 0`000ol0000;0003o`00008000Go0?l0o`0j0003o`0000D0000D00;oL@001?l0o`02o`030?l00080 00?o00000`000ol00002o`030?oo00?o00D0o`00o`050003o`0000/00_l300;o0P000ol0000g0003 o`0000D0000E00;oL0001_l0o`3o00?o00<0ool01@02o`030?oo00;o0P001?l00?l300;o10000ol0 000<00;o0`000ol00002ocL000?o00001@0001L000?o0000K@000ol0o`02o`800_l00`3o000600?o 0P001?l00002o`030?l000<000?o00000P02o`h00_l20005o`000?l0=P000ol00005000060000ol0 001/0003o`3o00;o00<0o`000_l500Co00<0o`000P000ol0000200?o10000ol000030003o`0000d0 00?o00000_l20003o`0003<000?o00001@0001T000?o0000J`000ol0o`02o`030?l000;o0P03o`@0 0_l40003o`0000<000?o00000`000ol000030003o`0000d000?o00000ol00`3oo`0c0003o`0000D0 000J0003o`0006X00_l0203oo`3o0?l00_l200;o0`02o`@000?o00001002o`@000?o00000P000ol0 000>00;o00@0o`3o0P000ol0000`0003o`0000D0000K0003o`3o06T00ol02@3o0?l0o`3o0003o`07 0?oo0?l0o`040003o`0000<000?o0?l01002o`<000?o00003`001?l0o`02o`030?l0030000?o0000 1@0001`00_mY00Co00<0o`000_l0103o0?l40003o`0000;o1@000ol000030003o`3o00D000Co0000 0_l@00;o0`000ol0o`0`0003o`0000D0000=00Co0`02o`P000?o0000IP04o`030?l000;o00@0oooo 1@001?l0ool60003o`00008000Co003o1@000ol000020003o`0000h00_l30004o`3oobh000?o0000 1@0000h000?o00000P001?l00?l80003o`0006D01?l0103o0?l200;o1P04o`H000?o00000`02o`03 0?l000@000?o00000P000ol0000>00;o0`001?l00?l]0003o`0000D0000700Go0`001Ol0003o0080 00?o00001`000ol0001S0003o`3o00;o00@0oooo0P000ol0000300Oo1P000ol000040003o`3o00;o 0`02o`<000?o00003`02o`800_l00`3oo`0/0003o`0000@0000@0004o`00o`8000?o000020000ol0 001R00?o00@0ool00_l20004o`0000?o00<0ool00ol700;o10000ol000020003o`00008000Go0000 o`0A00;o0`001?l00?l[0003o`0000@0000=0004o`00o`8000Co003o2`02of800ol0103oo`02o`03 0?oo00800_l500?o2@000ol000020003o`00008000?o00000P001Ol0003o01400ol20003o`0000;o :@000ol0000400003P02o`@00_l=00;oH@04o`060?oo0?l00_l00`3oo`0600Go1`000ol000030003 o`0000800_l30005o`000?l04@000ol0o`020005o`000?l0:0000ol0000400009@000ol0001M0003 o`3o00?o00D0o`3o0003o`T00ol00`3o000600;o10000ol000030005o`000?l00`000ol0000>0003 o`0000;o00<0ool00P000ol0000U0003o`0000@0000V0003o`0005`00ol0103oo`02o`030?l000;o 2@03o`800_l70005o`000?l01P001Ol0003o00<000?o00003P001Ol0003o008000Co003o9P000ol0 000400009`000ol0001K00?o00@0ool00_l0103o0?l;00;o10000ol000040003o`00008000?o0000 10001Ol0003o00<000?o00003P001?l00002o`050?l00?l09@000ol000040000:002oe/00ol01@3o ool000;o00<0ool02`02o`D000?o000010000ol000020003o`0000@000Go0000o`030003o`0000h0 00?o00000P000ol0o`0200;o8`000ol000040000:002oe/00_l200;o0P02o`030?oo00/00ol500;o 1@000ol000020003o`0000@00_l200;o0P02o`l000?o00000P000ol0o`030003o`00020000?o0000 100002X00_mI00;o00T0o`3o0?l0o`000_l<00;o1`000ol000030003o`00008000?o00001@001Ol0 003o00<000?o00003@000ol000020004o`3oo`8000?o00007`000ol000040000;0000ol0001F00;o 00D0oooo0002o`040?l0o``00_l80003o`0000<000?o00000P000ol0000500;o0P001Ol0003o00l0 00?o00000P001?l00?l20003o`0001h000?o0000100002d000?o0000E003o`050?ooo`000_l0103o 0?l<00?o20000ol000030003o`00008000?o00001P001?l00?l30003o`0000`000?o00000`02o`05 0?oo0?l080000ol000030000;P000ol0001C00;o0P02o`030?l000;o0P000ol0000;00;o2@02o`@0 00Go0000o`090004o`00o`<000?o000030000ol000040005o`00o`000_lN0003o`0000<0000^00;o E002o`050?l0o`000_l01@3o003o00d00_l;0003o`00008000Go0000o`0900;o00<0o`000P000ol0 000<0003o`0000@000Co003o0P000ol0000K0003o`0000<0000`0003o`0005400_l01@3oool000?o 0`000ol0000;0003o`0000/000?o00000P001Ol0003o00X000Co0?oo0P000ol0000<0003o`0000@0 00?o00000_l00`3o000K0003o`0000<0000a0003o`0005000_l01@3oool000?o0`000ol0000J0003 o`00008000Co003o2`000ol00002o`030?oo00d000?o000010001_l0003o00;o6P000ol000030000 0004o`3o00;o1`000ol0000D0003o`000040001=0003o`00044000?o0000<`001Ol0003o0080 00?o00003P001_l0ool0o`L000?o00004`000ol000010000CP000ol000100003o`0003@000Go0000 o`020003o`0000h000Ko003o0?l60003o`0001<000?o00000@0004l00_m00003o`0003D000Go0000 o`020003o`0000h000Ko003o0?l60003o`00018000?o00000@0005400_ln0003o`0003H00_l20004 o`00oa0000Ko003o0?l60003o`0001800Ol10040001B0003o`0003`000?o0000>0001?l00?l20003 o`0000h000Go003o0002o`D000?o00004@01o`400@0005<000?o0000>`000ol0000i0003o`3o00<0 00?o00003P001?l00?l20003o`0000<000?o00004001o`400@0005@000?o0000>P000ol0000j0003 o`3o00<000?o00003P000ol00002o`030?l000@000?o00003`01o`400@0005D000Co0?oo>0000ol0 000k0003o`3o00<000?o00003P001ol0003o0?l01@000ol0000>007o0@010000CP02o`H00_li0003 o`0003`000?o0?l00`000ol0000>00;o0P000ol0o`040003o`0000h00Ol10040001=0004o`00o`L0 00?o0000=P000ol0000m0004o`3oo`8000?o00003`001_l00?l0o`@000?o00003@01o`400@0004d0 00Co003o20000ol0000e0003o`0003h000Co003o0P000ol0000?0005o`00o`000_l30003o`0000`0 0Ol10040001=0004o`00o`T000?o0000=0000ol0000o00;o00D0o`00o`0A00;o00D0o`00o`030003 o`0000/00Ol10040001=0004o`00o`X00_ld0003o`00044000?o0?l00P000ol0000@0006o`3oo`3o 0`000ol0000:007o0@010000CP02o``000?o00000003o`0003D01?li0000 P@000ol0000=0003o`0003401?lm0000PP02o`d000?o0000;@04od4000240003o`0000X000?o0000 :@04odD000250003o`0000T000?o00009P03odT000260003o`0000P000?o00008P04od`0001h00Co 0`02o`H00ol70003o`0001h01?m@0000N@000ol000020004o`00o`H000?o00001P000ol0000J00Co E00007X000Go0000o`020003o`0000D000?o00001@000ol0000F00CoF00007/000Co003o0P000ol0 000600;o1@000ol0000B00CoG00007P000Co003o0P001?l00?l900;o10000ol0000>00CoH00007T0 0_l400;o30001Ol0003o00d00omT0000SP001?l00?l900CoI`0008l000?o0?l01@04of/0002@00;o 00<0ool00_m_0000T@02og<0003o00L0003o00L0003o00L0003o00L00000\ \>"], ImageRangeCache->{{{0, 261.375}, {290.125, 0}} -> {0.00899487, -0.0332612, 0.00334056, 0.00334056}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics3D \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ StyleBox["c", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[StyleBox[ "A = {{-14,18, 8},\n { -6, 8, 2},\n { -5, 7, 3}};", "Input"]], "Input"], Cell[CellGroupData[{ Cell["Eigensystem[A]", "Input"], Cell[BoxData[ \({{\(-3\), \(-2\)\ I, 2\ I}, {{4, 2, 1}, {2 - I, 1 - I, 1}, {2 + I, 1 + I, 1}}}\)], "Output"] }, Open ]], Cell["We get a real-valued solution and a complex-valued solution:", "Text"], Cell["\<\ X1[t_] = {4,2,1}E^(-3t); Z[t_] = {2+I,1+I,1}E^(2I*t);\ \>", "Input"], Cell[TextData[{ "The real and imaginary parts of ", StyleBox["Z[t]", "Input"], " give two indepenedent real-valued solutions:" }], "Text"], Cell[CellGroupData[{ Cell["X2[t_] = Re[Z[t]]//ComplexExpand", "Input"], Cell[BoxData[ \({2\ Cos[2\ t] - Sin[2\ t], Cos[2\ t] - Sin[2\ t], Cos[2\ t]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["X3[t_] = Im[Z[t]]//ComplexExpand", "Input"], Cell[BoxData[ \({Cos[2\ t] + 2\ Sin[2\ t], Cos[2\ t] + Sin[2\ t], Sin[2\ t]}\)], "Output"] }, Open ]], Cell["The general solution is", "Text"], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t] + c3 X3[t]", "Input"], Cell[BoxData[ \({4\ c1\ E\^\(\(-3\)\ t\) + c2\ \((2\ Cos[2\ t] - Sin[2\ t])\) + c3\ \((Cos[2\ t] + 2\ Sin[2\ t])\), 2\ c1\ E\^\(\(-3\)\ t\) + c2\ \((Cos[2\ t] - Sin[2\ t])\) + c3\ \((Cos[2\ t] + Sin[2\ t])\), c1\ E\^\(\(-3\)\ t\) + c2\ Cos[2\ t] + c3\ Sin[2\ t]}\)], "Output"] }, Open ]], Cell["Check:", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Simplify", "Input"], Cell[BoxData[ \({\(-12\)\ c1\ E\^\(\(-3\)\ t\) - 2\ \((c2 - 2\ c3)\)\ Cos[2\ t] - 2\ \((2\ c2 + c3)\)\ Sin[2\ t], \(-6\)\ c1\ E\^\(\(-3\)\ t\) - 2\ \((c2 - c3)\)\ Cos[2\ t] - 2\ \((c2 + c3)\)\ Sin[2\ t], \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 2\ c3\ Cos[2\ t] - 2\ c2\ Sin[2\ t]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t]//Simplify", "Input"], Cell[BoxData[ \({\(-12\)\ c1\ E\^\(\(-3\)\ t\) - 2\ \((c2 - 2\ c3)\)\ Cos[2\ t] - 2\ \((2\ c2 + c3)\)\ Sin[2\ t], \(-6\)\ c1\ E\^\(\(-3\)\ t\) - 2\ \((c2 - c3)\)\ Cos[2\ t] - 2\ \((c2 + c3)\)\ Sin[2\ t], \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 2\ c3\ Cos[2\ t] - 2\ c2\ Sin[2\ t]}\)], "Output"] }, Open ]], Cell["Plots:", "Text"], Cell["\<\ solns = Flatten[Table[X[t],{c1,-1,1},{c2,-1,1},{c3,-1,1}],2];\ \>", "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ ParametricPlot3D[Evaluate[solns], {t,-Pi/2,Pi/2}, ViewPoint->{1.323, -2.716, -1.525}, PlotRange->{{-5,5},{-5,5},{-2,2}}]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .71183 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D /Courier findfont 10 scalefont setfont % Scaling calculations 5.55112e-17 1.06248 -0.228606 1.06248 [ [.0928 .54549 -5.43049 0 ] [.0928 .54549 6.56951 9 ] [.22157 .58196 -5.59455 0 ] [.22157 .58196 6.40545 9 ] [.35688 .62027 -2.88489 0 ] [.35688 .62027 3.11511 9 ] [.49924 .66057 -2.97869 0 ] [.49924 .66057 3.02131 9 ] [.64924 .70302 -3.07934 0 ] [.64924 .70302 2.92066 9 ] [.04608 .20021 -6.58636 -9 ] [.04608 .20021 5.41364 0 ] [.13423 .14476 -6.47453 -9 ] [.13423 .14476 5.52547 0 ] [.21426 .09441 -3.18755 -9 ] [.21426 .09441 2.81245 0 ] [.28725 .04849 -3.14307 -9 ] [.28725 .04849 2.85693 0 ] [.35409 .00645 -3.10303 -9 ] [.35409 .00645 2.89697 0 ] [-0.01294 .24032 -12 -5.5382 ] [-0.01294 .24032 0 3.4618 ] [-0.00526 .31093 -12 -5.59885 ] [-0.00526 .31093 0 3.40115 ] [.0022 .37955 -6 -5.65761 ] [.0022 .37955 0 3.34239 ] [.00946 .44624 -6 -5.71457 ] [.00946 .44624 0 3.28543 ] [.01652 .5111 -6 -5.7698 ] [.01652 .5111 0 3.2302 ] [ 0 0 0 0 ] [ 1 .71183 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .0293 .51471 m .72787 .71183 L s .09154 .53227 m .09092 .52566 L s [(-4)] .0928 .54549 -0.09492 -1 Mshowa .22067 .56871 m .22022 .56208 L s [(-2)] .22157 .58196 -0.06758 -1 Mshowa .35637 .607 m .35611 .60037 L s [(0)] .35688 .62027 -0.03837 -1 Mshowa .49915 .64729 m .4991 .64065 L s [(2)] .49924 .66057 -0.0071 -1 Mshowa .64959 .68974 m .64976 .6831 L s [(4)] .64924 .70302 .02645 -1 Mshowa .125 Mabswid .12324 .54122 m .12289 .53725 L s .15532 .55027 m .15499 .5463 L s .18779 .55943 m .18749 .55546 L s .25396 .5781 m .25372 .57413 L s .28767 .58761 m .28745 .58364 L s .3218 .59725 m .32162 .59327 L s .39138 .61688 m .39125 .6129 L s .42684 .62689 m .42675 .6229 L s .46276 .63702 m .4627 .63304 L s .53602 .65769 m .53602 .65371 L s .57337 .66824 m .57341 .66425 L s .61123 .67892 m .6113 .67493 L s .06023 .52344 m .05983 .51947 L s .68847 .70071 m .68861 .69673 L s .25 Mabswid 0 .24331 m .38581 0 L s .04738 .21343 m .04802 .22004 L s [(-4)] .04608 .20021 .09773 1 Mshowa .13528 .158 m .1358 .16462 L s [(-2)] .13423 .14476 .07909 1 Mshowa .21509 .10766 m .21551 .11429 L s [(0)] .21426 .09441 .06252 1 Mshowa .28788 .06176 m .2882 .06839 L s [(2)] .28725 .04849 .04769 1 Mshowa .35455 .01972 m .35477 .02636 L s [(4)] .35409 .00645 .03434 1 Mshowa .125 Mabswid .07018 .19905 m .07054 .20302 L s .09241 .18503 m .09276 .189 L s .11411 .17135 m .11444 .17532 L s .15594 .14496 m .15624 .14894 L s .17612 .13224 m .1764 .13621 L s .19583 .11981 m .1961 .12378 L s .23391 .0958 m .23414 .09977 L s .25231 .08419 m .25252 .08817 L s .27029 .07285 m .2705 .07683 L s .30509 .0509 m .30527 .05489 L s .32193 .04029 m .3221 .04427 L s .33841 .02989 m .33856 .03387 L s .02399 .22818 m .0244 .23214 L s .37034 .00976 m .37047 .01374 L s .25 Mabswid 0 .24331 m .0293 .51471 L s 0 .24331 m .00647 .2448 L s [(-2)] -0.01294 .24032 1 .23071 Mshowa .00764 .31408 m .01409 .31566 L s [(-1)] -0.00526 .31093 1 .24419 Mshowa .01506 .38286 m .02149 .38451 L s [(0)] .0022 .37955 1 .25725 Mshowa .02228 .4497 m .02869 .45143 L s [(1)] .00946 .44624 1 .2699 Mshowa .0293 .51471 m .03569 .51651 L s [(2)] .01652 .5111 1 .28218 Mshowa .125 Mabswid .00155 .25763 m .00543 .25853 L s .00308 .27186 m .00696 .27278 L s .00461 .28602 m .00849 .28694 L s .00613 .30009 m .01 .30103 L s .00914 .328 m .01301 .32895 L s .01064 .34183 m .0145 .34279 L s .01212 .35558 m .01598 .35656 L s .0136 .36926 m .01746 .37024 L s .01652 .39638 m .02038 .39738 L s .01797 .40982 m .02183 .41083 L s .01942 .42319 m .02327 .42421 L s .02085 .43648 m .0247 .43751 L s .0237 .46285 m .02754 .4639 L s .02511 .47592 m .02895 .47698 L s .02651 .48892 m .03035 .48999 L s .02791 .50185 m .03175 .50292 L s .25 Mabswid 0 .24331 m .0293 .51471 L s .0293 .51471 m .39225 .22867 L s .39225 .22867 m .38581 0 L s .38581 0 m 0 .24331 L s .74101 .41427 m 1 .10458 L s 1 .10458 m .97704 .35242 L s .97704 .35242 m .72787 .71183 L s .72787 .71183 m .74101 .41427 L s 0 .24331 m .0293 .51471 L s .0293 .51471 m .72787 .71183 L s .72787 .71183 m .74101 .41427 L s .74101 .41427 m 0 .24331 L s .38581 0 m 1 .10458 L s 1 .10458 m .97704 .35242 L s .97704 .35242 m .39225 .22867 L s .39225 .22867 m .38581 0 L s 0 0 m 1 0 L 1 .71183 L 0 .71183 L closepath clip newpath .5 Mabswid .93071 .41004 m .92821 .41007 L s .92821 .41007 m .90473 .41028 L s .90473 .41028 m .88153 .41031 L s .81239 .35315 m .81397 .35894 L s .80958 .34715 m .81239 .35315 L s .81397 .35894 m .81422 .36446 L s .80565 .341 m .80958 .34715 L s .81422 .36446 m .81305 .36966 L s .80074 .33476 m .80565 .341 L s .81305 .36966 m .81041 .3745 L s .94155 .34954 m .94155 .34954 L s .94155 .34954 m .91706 .34754 L s .88153 .41031 m .85842 .41009 L s .79502 .3285 m .80074 .33476 L s .81041 .3745 m .80625 .37892 L s .78071 .34423 m .78657 .35085 L s .78823 .35666 m .79089 .36264 L s .78376 .35031 m .78823 .35666 L s .78622 .35353 m .78979 .3597 L s .78086 .347 m .78622 .35353 L s .78979 .3597 m .79154 .36548 L s .91706 .34754 m .89624 .34648 L s .77752 .34361 m .78376 .35031 L s .79089 .36264 m .79173 .36821 L s .78868 .3223 m .79502 .3285 L s .77317 .33733 m .78071 .34423 L s .77375 .34015 m .78086 .347 L s .77433 .34299 m .78096 .34976 L s .79154 .36548 m .79146 .37082 L s .76955 .33662 m .77752 .34361 L s .76592 .33591 m .77433 .34299 L s .79173 .36821 m .79073 .37331 L s .76493 .33303 m .77375 .34015 L s .80625 .37892 m .80054 .38289 L s .89624 .34648 m .8785 .34622 L s .76401 .33019 m .77317 .33733 L s .79146 .37082 m .78955 .37568 L s .75989 .32939 m .76955 .33662 L s .78191 .31622 m .78868 .3223 L s .75577 .32858 m .76592 .33591 L s .8785 .34622 m .86328 .34664 L s .79073 .37331 m .78792 .37792 L s .75445 .32569 m .76493 .33303 L s .7533 .32287 m .76401 .33019 L s .7653 .35494 m .76998 .36129 L s .7584 .34811 m .7653 .35494 L s .76998 .36129 m .77247 .36713 L s .78955 .37568 m .78583 .38004 L s .74925 .34083 m .7584 .34811 L s .86328 .34664 m .85012 .3476 L s .74861 .32196 m .75989 .32939 L s .80054 .38289 m .79328 .38636 L s .85842 .41009 m .83524 .40957 L s .74392 .32104 m .75577 .32858 L s .77247 .36713 m .77283 .37244 L s .73781 .33313 m .74925 .34083 L s .85012 .3476 m .83857 .34901 L s .78792 .37792 m .78329 .38201 L s .77496 .31035 m .78191 .31622 L s .74238 .31818 m .75445 .32569 L s .74111 .31542 m .7533 .32287 L s .83857 .34901 m .82827 .35076 L s .78583 .38004 m .7803 .38385 L s .77283 .37244 m .77109 .37718 L s .73578 .31437 m .74861 .32196 L s .72406 .32504 m .73781 .33313 L s .82827 .35076 m .81887 .35275 L s .73045 .31333 m .74392 .32104 L s .79328 .38636 m .78445 .38932 L s .78329 .38201 m .77687 .38555 L s .72881 .31054 m .74238 .31818 L s .76809 .30477 m .77496 .31035 L s .81887 .35275 m .81009 .35492 L s .92496 .41572 m .9172 .41468 L s .77109 .37718 m .76731 .38134 L s .72755 .30789 m .74111 .31542 L s .70796 .31659 m .72406 .32504 L s .7803 .38385 m .77301 .38711 L s .72148 .3067 m .73578 .31437 L s .81009 .35492 m .80167 .35717 L s .9172 .41468 m .878 .40933 L s .71541 .3055 m .73045 .31333 L s .83524 .40957 m .81187 .40868 L s .77687 .38555 m .76871 .38852 L s .80167 .35717 m .79339 .35944 L s .78445 .38932 m .77408 .39172 L s .76731 .38134 m .76156 .38489 L s .71381 .30283 m .72881 .31054 L s .7616 .29957 m .76809 .30477 L s .68949 .30781 m .70796 .31659 L s .71271 .30033 m .72755 .30789 L s .77301 .38711 m .76399 .38977 L s .79339 .35944 m .78507 .36167 L s .70581 .29897 m .72148 .3067 L s .6989 .29761 m .71541 .3055 L s .76156 .38489 m .75389 .38782 L s .76871 .38852 m .75886 .39088 L s .75582 .29484 m .7616 .29957 L s .78507 .36167 m .77654 .36379 L s .69748 .2951 m .71381 .30283 L s .77408 .39172 m .76221 .39355 L s .66862 .29873 m .68949 .30781 L s .69671 .2928 m .71271 .30033 L s .76399 .38977 m .75331 .39183 L s .77654 .36379 m .76767 .36576 L s .68885 .29125 m .70581 .29897 L s .81187 .40868 m .78824 .40739 L s .878 .40933 m .84117 .40416 L s .68099 .2897 m .6989 .29761 L s .75389 .38782 m .7444 .39011 L s .75109 .29068 m .75582 .29484 L s .75886 .39088 m .74736 .39262 L s .67993 .28741 m .69748 .2951 L s .76767 .36576 m .75836 .36752 L s .76221 .39355 m .74887 .39477 L s .64529 .28937 m .66862 .29873 L s .67968 .28535 m .69671 .2928 L s .75331 .39183 m .74102 .39326 L s .67074 .28358 m .68885 .29125 L s .74784 .2872 m .75109 .29068 L s .75836 .36752 m .74852 .36905 L s .7444 .39011 m .73316 .39174 L s .72098 .33949 m .72277 .34375 L s .71805 .33502 m .72098 .33949 L s .72277 .34375 m .7234 .34775 L s .66178 .28182 m .68099 .2897 L s .71404 .33036 m .71805 .33502 L s .7234 .34775 m .72282 .35147 L s .70901 .32555 m .71404 .33036 L s .74736 .39262 m .7343 .39374 L s .71365 .34002 m .71586 .34435 L s .71014 .33542 m .71365 .34002 L s .71492 .34222 m .71648 .3464 L s .71206 .33775 m .71492 .34222 L s .70792 .33304 m .71206 .33775 L s .71586 .34435 m .71677 .34838 L s .66128 .27979 m .67993 .28741 L s .70537 .3306 m .71014 .33542 L s .72282 .35147 m .72104 .35487 L s .71648 .3464 m .71673 .35028 L s .78824 .40739 m .76429 .40566 L s .70252 .32811 m .70792 .33304 L s .70301 .32064 m .70901 .32555 L s .71677 .34838 m .71637 .3521 L s .69937 .32557 m .70537 .3306 L s .92939 .38026 m .89362 .37328 L s .61946 .27975 m .64529 .28937 L s .74887 .39477 m .73413 .39539 L s .70706 .34069 m .70956 .34506 L s .70313 .33601 m .70706 .34069 L s .71673 .35028 m .71567 .35382 L s .74852 .36905 m .73808 .37029 L s .69591 .32299 m .70252 .32811 L s .69777 .33106 m .70313 .33601 L s .70956 .34506 m .71064 .3491 L s .66176 .27804 m .67968 .28535 L s .74649 .2845 m .74784 .2872 L s .72104 .35487 m .71803 .35793 L s .71637 .3521 m .71465 .35546 L s .69216 .32037 m .69937 .32557 L s .69099 .32585 m .69777 .33106 L s .69615 .31566 m .70301 .32064 L s .84117 .40416 m .80639 .39911 L s .71064 .3491 m .7103 .35278 L s .74102 .39326 m .7272 .39405 L s .71567 .35382 m .7133 .35701 L s .68813 .31773 m .69591 .32299 L s .65157 .27603 m .67074 .28358 L s .6828 .32043 m .69099 .32585 L s .71465 .35546 m .71163 .35846 L s .7103 .35278 m .70857 .35609 L s .68382 .31505 m .69216 .32037 L s .73316 .39174 m .72027 .39272 L s .71803 .35793 m .71381 .36062 L s .6885 .31067 m .69615 .31566 L s .64137 .27402 m .66178 .28182 L s .7133 .35701 m .70964 .35981 L s .67923 .31235 m .68813 .31773 L s .67323 .31481 m .6828 .32043 L s .73808 .37029 m .72701 .37122 L s .70857 .35609 m .70548 .359 L s .7343 .39374 m .71975 .39421 L s .71163 .35846 m .70733 .36106 L s .63643 .35359 m .64751 .36054 L s .62114 .3456 m .63643 .35359 L s .74753 .2827 m .74649 .2845 L s .67437 .30963 m .68382 .31505 L s .60126 .33654 m .62114 .3456 L s .64163 .27231 m .66128 .27979 L s .71381 .36062 m .70838 .36292 L s .64751 .36054 m .65473 .3665 L s .68018 .30569 m .6885 .31067 L s .70964 .35981 m .70471 .36221 L s .89362 .37328 m .8509 .36495 L s .66926 .30689 m .67923 .31235 L s .57639 .32637 m .60126 .33654 L s .66228 .30903 m .67323 .31481 L s .73413 .39539 m .71806 .39537 L s .64309 .27093 m .66176 .27804 L s .70548 .359 m .70104 .3615 L s .59107 .2699 m .61946 .27975 L s .9145 .44263 m .9145 .44263 L s .9145 .44263 m .85575 .43133 L s .70733 .36106 m .70178 .36325 L s .65473 .3665 m .65838 .37149 L s .6639 .30415 m .67437 .30963 L s .76429 .40566 m .73999 .40346 L s .7272 .39405 m .71195 .3942 L s .70838 .36292 m .70177 .36482 L s .63148 .26864 m .65157 .27603 L s .72701 .37122 m .71527 .37181 L s .6713 .30079 m .68018 .30569 L s .70471 .36221 m .69854 .36419 L s .54604 .31501 m .57639 .32637 L s .7515 .28191 m .74753 .2827 L s .72027 .39272 m .70583 .39302 L s .6583 .3014 m .66926 .30689 L s .64999 .30312 m .66228 .30903 L s .70104 .3615 m .6953 .36356 L s .61987 .26635 m .64137 .27402 L s .65838 .37149 m .65877 .37554 L s .80639 .39911 m .77341 .3941 L s .70178 .36325 m .695 .36502 L s .65247 .29865 m .6639 .30415 L s .71975 .39421 m .70381 .39403 L s .65587 .34034 m .66138 .34512 L s .64805 .33502 m .65587 .34034 L s .63779 .32915 m .64805 .33502 L s .70177 .36482 m .69402 .36629 L s .62114 .26502 m .64163 .27231 L s .66138 .34512 m .66471 .34935 L s .662 .29601 m .6713 .30079 L s .69854 .36419 m .69117 .36574 L s .62492 .32273 m .63779 .32915 L s .63637 .2971 m .64999 .30312 L s .64641 .29591 m .6583 .3014 L s .75898 .28228 m .7515 .28191 L s .6953 .36356 m .68831 .36519 L s .50971 .30241 m .54604 .31501 L s .66471 .34935 m .66599 .35305 L s .71527 .37181 m .70286 .37203 L s .62383 .26408 m .64309 .27093 L s .71806 .39537 m .70075 .39473 L s .8509 .36495 m .81316 .3576 L s .65877 .37554 m .65617 .37869 L s .695 .36502 m .68705 .36635 L s .60929 .31575 m .62492 .32273 L s .93973 .32202 m .91787 .31684 L s .56004 .25983 m .59107 .2699 L s .64015 .29317 m .65247 .29865 L s .66599 .35305 m .66535 .3562 L s .71195 .3942 m .69535 .39369 L s .61061 .26147 m .63148 .26864 L s .65241 .2914 m .662 .29601 L s .70583 .39302 m .68995 .39265 L s .77061 .28393 m .75898 .28228 L s .69117 .36574 m .68264 .36684 L s .91787 .31684 m .87362 .30641 L s .63369 .29045 m .64641 .29591 L s .62147 .29101 m .63637 .2971 L s .73999 .40346 m .71534 .40078 L s .5907 .30821 m .60929 .31575 L s .66535 .3562 m .6629 .35881 L s .59738 .25885 m .61987 .26635 L s .70286 .37203 m .68977 .37188 L s .68705 .36635 m .67797 .36722 L s .65617 .37869 m .65083 .38094 L s .46679 .28849 m .50971 .30241 L s .70381 .39403 m .68658 .39319 L s .62703 .28775 m .64015 .29317 L s .78708 .28701 m .77061 .28393 L s .59992 .25798 m .62114 .26502 L s .64269 .287 m .65241 .2914 L s .87362 .30641 m .83772 .29808 L s .77341 .3941 m .74202 .38908 L s .56895 .30008 m .5907 .30821 L s .6629 .35881 m .65875 .36087 L s .68264 .36684 m .67302 .36749 L s .81316 .3576 m .77982 .3511 L s .60414 .25753 m .62383 .26408 L s .80918 .29167 m .78708 .28701 L s .6202 .28507 m .63369 .29045 L s .6053 .28487 m .62147 .29101 L s .83772 .29808 m .80918 .29167 L s .70075 .39473 m .68229 .39345 L s .69535 .39369 m .67752 .39254 L s .85575 .43133 m .80077 .42028 L s .61646 .28306 m .6299 .28831 L s .67797 .36722 m .66782 .36764 L s .58909 .25456 m .61061 .26147 L s .6132 .28241 m .62703 .28775 L s .52627 .24955 m .56004 .25983 L s .68995 .39265 m .67275 .39162 L s .65875 .36087 m .65302 .3624 L s .68977 .37188 m .67604 .37133 L s .60994 .28177 m .62417 .28718 L s .65083 .38094 m .643 .38233 L s .63302 .28288 m .64269 .287 L s .5438 .29136 m .56895 .30008 L s .67302 .36749 m .66237 .36767 L s .57401 .25158 m .59738 .25885 L s .60604 .2798 m .6202 .28507 L s .4166 .27313 m .46679 .28849 L s .71534 .40078 m .69038 .39759 L s .5879 .27872 m .6053 .28487 L s .68658 .39319 m .66818 .39171 L s .91678 .41745 m .87831 .4089 L s .77982 .3511 m .75039 .34536 L s .57813 .25122 m .59992 .25798 L s .65302 .3624 m .64582 .36339 L s .60246 .27794 m .61646 .28306 L s .66782 .36764 m .65667 .36759 L s .59875 .27721 m .6132 .28241 L s .58421 .25135 m .60414 .25753 L s .62357 .27908 m .63302 .28288 L s .59504 .27648 m .60994 .28177 L s .74202 .38908 m .71204 .38402 L s .51498 .282 m .5438 .29136 L s .67604 .37133 m .66168 .37038 L s .68229 .39345 m .66278 .39154 L s .643 .38233 m .63292 .38288 L s .66237 .36767 m .65075 .36739 L s .67752 .39254 m .65857 .39073 L s .59132 .27467 m .60604 .2798 L s .56706 .24796 m .58909 .25456 L s .67275 .39162 m .65436 .38992 L s .56928 .27257 m .5879 .27872 L s .64582 .36339 m .63727 .36385 L s .75039 .34536 m .72441 .34029 L s .588 .27301 m .60246 .27794 L s .48964 .23906 m .52627 .24955 L s .65667 .36759 m .6446 .36708 L s .61456 .27566 m .62357 .27908 L s .58377 .27218 m .59875 .27721 L s .54989 .24457 m .57401 .25158 L s .57955 .27135 m .59504 .27648 L s .35836 .25623 m .4166 .27313 L s .66818 .39171 m .64872 .38959 L s .66168 .37038 m .64676 .36902 L s .55591 .2448 m .57813 .25122 L s .48219 .27198 m .51498 .282 L s .87831 .4089 m .81516 .39438 L s .69038 .39759 m .66513 .3939 L s .65075 .36739 m .63824 .36665 L s .57613 .26974 m .59132 .27467 L s .63292 .38288 m .62081 .38261 L s .63727 .36385 m .62749 .36378 L s .56423 .2456 m .58421 .25135 L s .92708 .36308 m .88335 .35221 L s .72441 .34029 m .70148 .33582 L s .54947 .26644 m .56928 .27257 L s .80077 .42028 m .74926 .40942 L s .60619 .27267 m .61456 .27566 L s .66278 .39154 m .64235 .389 L s .57319 .2683 m .588 .27301 L s .71204 .38402 m .68334 .37887 L s .6446 .36708 m .63168 .36611 L s .65857 .39073 m .63863 .38829 L s .56838 .26735 m .58377 .27218 L s .54469 .24173 m .56706 .24796 L s .65436 .38992 m .63491 .38758 L s .56358 .2664 m .57955 .27135 L s .70148 .33582 m .68126 .33188 L s .63824 .36665 m .62493 .36545 L s .64676 .36902 m .63131 .36724 L s .62749 .36378 m .61659 .3632 L s .56057 .26502 m .57613 .26974 L s .44507 .26125 m .48219 .27198 L s .5987 .27017 m .60619 .27267 L s .52512 .23786 m .54989 .24457 L s .64872 .38959 m .62833 .38683 L s .45001 .22836 m .48964 .23906 L s .62081 .38261 m .6069 .38156 L s .52848 .26036 m .54947 .26644 L s .55815 .26384 m .57319 .2683 L s .53343 .23877 m .55591 .2448 L s .88335 .35221 m .82372 .337 L s .63168 .36611 m .61801 .36468 L s .54439 .24032 m .56423 .2456 L s .55268 .26276 m .56838 .26735 L s .68126 .33188 m .66343 .3284 L s .66513 .3939 m .63967 .3897 L s .29118 .23763 m .35836 .25623 L s .54721 .26168 m .56358 .2664 L s .64235 .389 m .62112 .38585 L s .61659 .3632 m .60469 .36211 L s .68334 .37887 m .65582 .37362 L s .62493 .36545 m .61092 .36379 L s .59236 .26822 m .5987 .27017 L s .63863 .38829 m .61783 .38522 L s .54475 .26057 m .56057 .26502 L s .63131 .36724 m .61541 .36506 L s .63491 .38758 m .61455 .38459 L s .66343 .3284 m .6477 .32534 L s .52213 .23591 m .54469 .24173 L s .54301 .25967 m .55815 .26384 L s .81516 .39438 m .75805 .38074 L s .61801 .36468 m .60367 .3628 L s .50631 .25434 m .52848 .26036 L s .40322 .24975 m .44507 .26125 L s .53678 .25844 m .55268 .26276 L s .6069 .38156 m .59141 .37974 L s .6477 .32534 m .63384 .32264 L s .53055 .25722 m .54721 .26168 L s .58741 .26688 m .59236 .26822 L s .49983 .2315 m .52512 .23786 L s .62833 .38683 m .60716 .38346 L s .74926 .40942 m .70096 .3987 L s .60469 .36211 m .59192 .36053 L s .51082 .23317 m .53343 .23877 L s .52489 .23557 m .54439 .24032 L s .82372 .337 m .77271 .32362 L s .61092 .36379 m .59628 .36169 L s .63384 .32264 m .62162 .32025 L s .52879 .2564 m .54475 .26057 L s .61541 .36506 m .59912 .36248 L s .40719 .21743 m .45001 .22836 L s .63967 .3897 m .61406 .385 L s .65582 .37362 m .6294 .36824 L s .62112 .38585 m .59922 .3821 L s .52788 .25583 m .54301 .25967 L s .62162 .32025 m .61085 .31815 L s .58418 .26622 m .58741 .26688 L s .61783 .38522 m .59632 .38155 L s .60367 .3628 m .58877 .36048 L s .52079 .25443 m .53678 .25844 L s .61455 .38459 m .59342 .38099 L s .49953 .23055 m .52213 .23591 L s .48297 .2484 m .50631 .25434 L s .61085 .31815 m .60136 .3163 L s .5137 .25303 m .53055 .25722 L s .214 .21717 m .29118 .23763 L s .91445 .40488 m .84836 .38807 L s .59192 .36053 m .5784 .35848 L s .59141 .37974 m .57456 .3772 L s .59628 .36169 m .58114 .35916 L s .60136 .3163 m .593 .31467 L s .35616 .23741 m .40322 .24975 L s .5128 .25255 m .52879 .2564 L s .58296 .26628 m .58418 .26622 L s .77271 .32362 m .72949 .31196 L s .59912 .36248 m .58254 .3595 L s .60716 .38346 m .58535 .37949 L s .593 .31467 m .58563 .31324 L s .47411 .22552 m .49983 .2315 L s .50596 .2314 m .52489 .23557 L s .48827 .22805 m .51082 .23317 L s .5129 .25234 m .52788 .25583 L s .58563 .31324 m .57914 .31197 L s .58877 .36048 m .57341 .35774 L s .75805 .38074 m .7065 .36792 L s .50483 .25075 m .52079 .25443 L s .57914 .31197 m .57342 .31086 L s .6294 .36824 m .60403 .36272 L s .5841 .26715 m .58296 .26628 L s .49675 .24916 m .5137 .25303 L s .5784 .35848 m .56426 .35597 L s .61406 .385 m .58842 .37982 L s .57342 .31086 m .56839 .30988 L s .45843 .24254 m .48297 .2484 L s .59632 .38155 m .57425 .37729 L s .70096 .3987 m .65565 .38809 L s .56839 .30988 m .56395 .30901 L s .58114 .35916 m .56559 .35621 L s .72949 .31196 m .6933 .30188 L s .47706 .22568 m .49953 .23055 L s .49689 .24905 m .5128 .25255 L s .56395 .30901 m .56004 .30825 L s .36094 .20624 m .40719 .21743 L s .57456 .3772 m .55656 .37396 L s .56004 .30825 m .5566 .30758 L s .58254 .3595 m .56576 .35615 L s .58797 .26889 m .5841 .26715 L s .5566 .30758 m .55357 .30699 L s .49819 .24925 m .5129 .25234 L s .55357 .30699 m .55091 .30647 L s .55091 .30647 m .54856 .30601 L s .57341 .35774 m .55769 .35459 L s .54856 .30601 m .54649 .30561 L s .489 .24743 m .50483 .25075 L s .54649 .30561 m .54466 .30525 L s .58535 .37949 m .56305 .37495 L s .4878 .22786 m .50596 .2314 L s .6933 .30188 m .66342 .29327 L s .54466 .30525 m .54306 .30494 L s .59497 .27157 m .58797 .26889 L s .54306 .30494 m .54165 .30466 L s .30335 .22415 m .35616 .23741 L s .44245 .32519 m .457 .32998 L s .42334 .31923 m .44245 .32519 L s .54165 .30466 m .5404 .30442 L s .46593 .22344 m .48827 .22805 L s .56426 .35597 m .54962 .35303 L s .44809 .21994 m .47411 .22552 L s .5404 .30442 m .53931 .30421 L s .39907 .312 m .42334 .31923 L s .53931 .30421 m .53834 .30402 L s .47981 .24562 m .49675 .24916 L s .457 .32998 m .46751 .3337 L s .53834 .30402 m .53749 .30385 L s .53749 .30385 m .53675 .30371 L s .53675 .30371 m .53609 .30358 L s .53609 .30358 m .53551 .30347 L s .53551 .30347 m .535 .30337 L s .84836 .38807 m .77299 .36809 L s .535 .30337 m .53455 .30328 L s .53455 .30328 m .53415 .3032 L s .60403 .36272 m .57968 .35707 L s .56559 .35621 m .54974 .35287 L s .36899 .30339 m .39907 .312 L s .60553 .27526 m .59497 .27157 L s .53124 .30263 m .53124 .30263 L s .46751 .3337 m .47445 .33641 L s .66342 .29327 m .63923 .28603 L s .48118 .24592 m .49689 .24905 L s .43267 .23676 m .45843 .24254 L s .52793 .30199 m .52833 .30207 L s .52748 .3019 m .52793 .30199 L s .52697 .3018 m .52748 .3019 L s .14535 .19967 m .214 .21717 L s .52639 .30169 m .52697 .3018 L s .52573 .30156 m .52639 .30169 L s .52498 .30141 m .52573 .30156 L s .52413 .30125 m .52498 .30141 L s .52317 .30106 m .52413 .30125 L s .62011 .28005 m .60553 .27526 L s .56576 .35615 m .54885 .35243 L s .52207 .30085 m .52317 .30106 L s .63923 .28603 m .62011 .28005 L s .52082 .3006 m .52207 .30085 L s .58842 .37982 m .56283 .37416 L s .48389 .24657 m .49819 .24925 L s .57425 .37729 m .55176 .37247 L s .51941 .30033 m .52082 .3006 L s .7065 .36792 m .66005 .35584 L s .5178 .30001 m .51941 .30033 L s .47445 .33641 m .47825 .3382 L s .51597 .29966 m .5178 .30001 L s .33235 .29328 m .36899 .30339 L s .55656 .37396 m .53762 .37006 L s .45488 .22134 m .47706 .22568 L s .5139 .29925 m .51597 .29966 L s .55769 .35459 m .54174 .35106 L s .51154 .29879 m .5139 .29925 L s .47343 .24451 m .489 .24743 L s .50886 .29827 m .51154 .29879 L s .50582 .29768 m .50886 .29827 L s .54962 .35303 m .53462 .34968 L s .50236 .297 m .50582 .29768 L s .47825 .3382 m .47931 .33913 L s .46296 .24244 m .47981 .24562 L s .49843 .29624 m .50236 .297 L s .47066 .225 m .4878 .22786 L s .65565 .38809 m .61319 .37757 L s .49397 .29537 m .49843 .29624 L s .54974 .35287 m .5337 .34915 L s .56305 .37495 m .54042 .36986 L s .28833 .28152 m .33235 .29328 L s .44729 .22005 m .46885 .22402 L s .46578 .2432 m .48118 .24592 L s .4889 .29438 m .49397 .29537 L s .311 .19476 m .36094 .20624 L s .44396 .21939 m .46593 .22344 L s .57968 .35707 m .55635 .35128 L s .44062 .21873 m .463 .22286 L s .48313 .29326 m .4889 .29438 L s .42187 .21481 m .44809 .21994 L s .47014 .24434 m .48389 .24657 L s .54885 .35243 m .53194 .34838 L s .47931 .33913 m .47799 .33927 L s .40562 .23106 m .43267 .23676 L s .47658 .29198 m .48313 .29326 L s .54174 .35106 m .52566 .34716 L s .24414 .20986 m .30335 .22415 L s .45823 .24199 m .47343 .24451 L s .46914 .29053 m .47658 .29198 L s .53462 .34968 m .51937 .34595 L s .55176 .37247 m .52903 .36712 L s .53762 .37006 m .51797 .36555 L s .56283 .37416 m .53742 .36807 L s .46068 .28888 m .46914 .29053 L s .43316 .21758 m .45488 .22134 L s .44631 .23964 m .46296 .24244 L s .23596 .26794 m .28833 .28152 L s .47799 .33927 m .47461 .33867 L s .5337 .34915 m .5176 .34509 L s .66005 .35584 m .61834 .34447 L s .45106 .287 m .46068 .28888 L s .45081 .24089 m .46578 .2432 L s .45477 .22286 m .47066 .225 L s .45707 .24257 m .47014 .24434 L s .77299 .36809 m .70643 .34966 L s .53194 .34838 m .51511 .344 L s .44012 .28487 m .45106 .287 L s .55635 .35128 m .53403 .34537 L s .54042 .36986 m .51763 .36426 L s .42632 .21667 m .44729 .22005 L s .52566 .34716 m .50957 .34294 L s .44351 .23991 m .45823 .24199 L s .42252 .21592 m .44396 .21939 L s .47461 .33867 m .4695 .3374 L s .42769 .28245 m .44012 .28487 L s .51937 .34595 m .50402 .34187 L s .41872 .21517 m .44062 .21873 L s .37722 .22544 m .40562 .23106 L s .39554 .21013 m .42187 .21481 L s .61319 .37757 m .57344 .36713 L s .42995 .23723 m .44631 .23964 L s .5176 .34509 m .50155 .3407 L s .41355 .27969 m .42769 .28245 L s .43637 .23903 m .45081 .24089 L s .17416 .25236 m .23596 .26794 L s .51797 .36555 m .49779 .36046 L s .52903 .36712 m .50622 .36129 L s .44481 .24131 m .45707 .24257 L s .25703 .18295 m .311 .19476 L s .41206 .21441 m .43316 .21758 L s .53742 .36807 m .51232 .36156 L s .4695 .3374 m .46293 .3355 L s .51511 .344 m .49847 .33935 L s .39747 .27655 m .41355 .27969 L s .44038 .2215 m .45477 .22286 L s .50957 .34294 m .49358 .3384 L s .61834 .34447 m .58102 .33374 L s .53403 .34537 m .51275 .33934 L s .42939 .23827 m .44351 .23991 L s .17778 .19441 m .24414 .20986 L s .50402 .34187 m .48869 .33746 L s .51763 .36426 m .49483 .3582 L s .37917 .27299 m .39747 .27655 L s .40611 .21392 m .42632 .21667 L s .41394 .23523 m .42995 .23723 L s .50155 .3407 m .48567 .33603 L s .40178 .21306 m .42252 .21592 L s .46293 .3355 m .45518 .33305 L s .42258 .23762 m .43637 .23903 L s .34736 .21986 m .37722 .22544 L s .43351 .24055 m .44481 .24131 L s .39745 .21221 m .41872 .21517 L s .49847 .33935 m .48214 .33443 L s .70643 .34966 m .64804 .33269 L s .36918 .20593 m .39554 .21013 L s .35836 .26893 m .37917 .27299 L s .49358 .3384 m .47783 .33359 L s .49779 .36046 m .47732 .35483 L s .41596 .2371 m .42939 .23827 L s .1284 .24111 m .17416 .25236 L s .50622 .36129 m .48349 .355 L s .48869 .33746 m .47351 .33276 L s .51275 .33934 m .49254 .33323 L s .42773 .22094 m .44038 .2215 L s .57344 .36713 m .53631 .35676 L s .39172 .21188 m .41206 .21441 L s .51232 .36156 m .48765 .35467 L s .45518 .33305 m .44649 .33008 L s .58102 .33374 m .5478 .32365 L s .48567 .33603 m .47007 .3311 L s .42331 .24033 m .43351 .24055 L s .39838 .23363 m .41394 .23523 L s .40954 .23669 m .42258 .23762 L s .33467 .26431 m .35836 .26893 L s .48214 .33443 m .46623 .32928 L s .38683 .21183 m .40611 .21392 L s .49483 .3582 m .4722 .3517 L s .47783 .33359 m .46242 .32855 L s .3819 .21085 m .40178 .21306 L s .40334 .2364 m .41596 .2371 L s .31591 .21432 m .34736 .21986 L s .47351 .33276 m .45861 .32781 L s .37697 .20988 m .39745 .21221 L s .44649 .33008 m .4371 .32665 L s .19862 .17072 m .25703 .18295 L s .49254 .33323 m .47343 .32704 L s .3077 .25905 m .33467 .26431 L s .47732 .35483 m .45674 .34873 L s .41433 .24065 m .42331 .24033 L s .4171 .22124 m .42773 .22094 L s .47007 .3311 m .45488 .32595 L s .39735 .23623 m .40954 .23669 L s .34286 .20221 m .36918 .20593 L s .1369 .1852 m .17778 .19441 L s .5478 .32365 m .51841 .31415 L s .48349 .355 m .46101 .3483 L s .38333 .23246 m .39838 .23363 L s .37233 .20999 m .39172 .21188 L s .64804 .33269 m .5972 .31711 L s .46623 .32928 m .45083 .32395 L s .48765 .35467 m .46355 .34744 L s .46242 .32855 m .44747 .3233 L s .4371 .32665 m .42723 .32282 L s .39161 .23618 m .40334 .2364 L s .53631 .35676 m .50174 .34649 L s .45861 .32781 m .44411 .32265 L s .27699 .25307 m .3077 .25905 L s .40672 .24152 m .41433 .24065 L s .47343 .32704 m .45546 .3208 L s .36864 .21041 m .38683 .21183 L s .4722 .3517 m .44991 .34482 L s .45488 .32595 m .4402 .32061 L s .36302 .2093 m .3819 .21085 L s .38611 .23625 m .39735 .23623 L s .40874 .22242 m .4171 .22124 L s .3574 .20819 m .37697 .20988 L s .36884 .2317 m .38333 .23246 L s .51841 .31415 m .49262 .30524 L s .28269 .20876 m .31591 .21432 L s .45083 .32395 m .43605 .31846 L s .42723 .32282 m .41709 .31864 L s .45674 .34873 m .43626 .34219 L s .44747 .3233 m .43309 .31789 L s .38087 .23644 m .39161 .23618 L s .44411 .32265 m .43013 .31731 L s .40061 .24297 m .40672 .24152 L s .46101 .3483 m .43895 .34125 L s .24201 .24625 m .27699 .25307 L s .35401 .20877 m .37233 .20999 L s .45546 .3208 m .43869 .31456 L s .31664 .19898 m .34286 .20221 L s .5972 .31711 m .55335 .30286 L s .4402 .32061 m .42615 .31513 L s .46355 .34744 m .44017 .33992 L s .3759 .23676 m .38611 .23625 L s .49262 .30524 m .47022 .29691 L s .41709 .31864 m .40687 .31417 L s .40293 .22452 m .40874 .22242 L s .35496 .23135 m .36884 .2317 L s .39612 .24499 m .40061 .24297 L s .3517 .20968 m .36864 .21041 L s .50174 .34649 m .46967 .33632 L s .43309 .31789 m .41939 .31235 L s .44991 .34482 m .42813 .3376 L s .3712 .23719 m .38087 .23644 L s .13528 .158 m .19862 .17072 L s .3453 .20842 m .36302 .2093 L s .24624 .31388 m .26878 .31866 L s .21693 .30731 m .24624 .31388 L s .3389 .20716 m .3574 .20819 L s .17983 .29876 m .21693 .30731 L s .43869 .31456 m .42316 .30832 L s .42615 .31513 m .41283 .30955 L s .26878 .31866 m .28544 .32184 L s .43626 .34219 m .41607 .33528 L s .20215 .23847 m .24201 .24625 L s .36679 .23775 m .3759 .23676 L s .3934 .24758 m .39612 .24499 L s .47022 .29691 m .45101 .28915 L s .2475 .20315 m .28269 .20876 L s .13376 .28803 m .17983 .29876 L s .40687 .31417 m .39676 .30945 L s .43895 .34125 m .41748 .33388 L s .28544 .32184 m .29706 .32357 L s .41939 .31235 m .40648 .30673 L s .33692 .20824 m .35401 .20877 L s .55335 .30286 m .51599 .28988 L s .39995 .22758 m .40293 .22452 L s .36268 .23842 m .3712 .23719 L s .34172 .2314 m .35496 .23135 L s .44017 .33992 m .41765 .33214 L s .39258 .25076 m .3934 .24758 L s .36226 .23988 m .36977 .23833 L s .45101 .28915 m .43481 .28195 L s .29057 .19624 m .31664 .19898 L s .42316 .30832 m .40892 .30214 L s .41283 .30955 m .40036 .3039 L s .11084 .28268 m .13376 .28803 L s .35888 .23921 m .36679 .23775 L s .29706 .32357 m .30437 .32398 L s .33616 .20967 m .3517 .20968 L s .39676 .30945 m .38692 .30453 L s .35549 .23855 m .36382 .23716 L s .42813 .3376 m .40702 .3301 L s .32887 .20823 m .3453 .20842 L s .39378 .25452 m .39258 .25076 L s .40648 .30673 m .39446 .30107 L s .46967 .33632 m .44009 .32628 L s .43481 .28195 m .42148 .27532 L s .35538 .24012 m .36268 .23842 L s .40011 .23162 m .39995 .22758 L s .15669 .22961 m .20215 .23847 L s .32159 .20679 m .3389 .20716 L s .41607 .33528 m .39637 .32805 L s .32914 .23183 m .34172 .2314 L s .39714 .25885 m .39378 .25452 L s .51599 .28988 m .48465 .27814 L s .35605 .2419 m .36226 .23988 L s .30437 .32398 m .30802 .32321 L s .40036 .3039 m .38881 .29824 L s .40892 .30214 m .39602 .29603 L s .42148 .27532 m .41085 .26926 L s .35221 .24115 m .35888 .23921 L s .38692 .30453 m .37751 .29948 L s .40278 .26377 m .39714 .25885 L s .41748 .33388 m .39676 .32626 L s .34836 .24039 m .35549 .23855 L s .41085 .26926 m .40278 .26377 L s .32119 .20839 m .33692 .20824 L s .39446 .30107 m .38342 .29541 L s .34936 .24228 m .35538 .24012 L s .21007 .19742 m .2475 .20315 L s .4037 .23667 m .40011 .23162 L s .41765 .33214 m .39613 .32418 L s .35121 .24439 m .35605 .2419 L s .39602 .29603 m .38451 .29005 L s .38881 .29824 m .37829 .29259 L s .32217 .21037 m .33616 .20967 L s .30802 .32321 m .30862 .32139 L s .48465 .27814 m .45887 .26759 L s .34684 .24353 m .35221 .24115 L s .37751 .29948 m .36867 .29433 L s .31723 .23264 m .32914 .23183 L s .40702 .3301 m .38674 .32237 L s .34246 .24268 m .34836 .24039 L s .31387 .20873 m .32887 .20823 L s .26464 .19397 m .29057 .19624 L s .38342 .29541 m .37344 .28979 L s .41103 .24277 m .4037 .23667 L s .34465 .24489 m .34936 .24228 L s .13528 .158 m .13528 .158 L s .44009 .32628 m .41298 .31639 L s .34778 .24733 m .35121 .24439 L s .39637 .32805 m .37734 .32055 L s .30557 .20709 m .32159 .20679 L s .38451 .29005 m .37442 .28422 L s .45887 .26759 m .43826 .2582 L s .37829 .29259 m .36888 .28702 L s .11835 .22214 m .15669 .22961 L s .34281 .24636 m .34684 .24353 L s .36867 .29433 m .36054 .28915 L s .42244 .24993 m .41103 .24277 L s .33783 .24538 m .34246 .24268 L s .39676 .32626 m .37696 .31843 L s .43826 .2582 m .42244 .24993 L s .37344 .28979 m .36461 .28426 L s .30862 .32139 m .30672 .31863 L s .34131 .24793 m .34465 .24489 L s .30695 .20924 m .32119 .20839 L s .34581 .2507 m .34778 .24733 L s .30596 .23378 m .31723 .23264 L s .37442 .28422 m .36579 .27859 L s .36888 .28702 m .36065 .28155 L s .34016 .2496 m .34281 .24636 L s .39613 .32418 m .37574 .31606 L s .36054 .28915 m .35323 .28398 L s .3345 .24849 m .33783 .24538 L s .30986 .21178 m .32217 .21037 L s .36461 .28426 m .35699 .27886 L s .34534 .25449 m .34581 .2507 L s .33936 .25137 m .34131 .24793 L s .36579 .27859 m .35865 .27318 L s .38674 .32237 m .36746 .31447 L s .36065 .28155 m .35366 .27623 L s .33891 .25323 m .34016 .2496 L s .30042 .20992 m .31387 .20873 L s .34637 .25865 m .34534 .25449 L s .17008 .19151 m .21007 .19742 L s .35323 .28398 m .34686 .27887 L s .35865 .27318 m .35303 .26803 L s .35699 .27886 m .35065 .27363 L s .33882 .25518 m .33936 .25137 L s .33248 .25197 m .3345 .24849 L s .30672 .31863 m .30282 .31505 L s .37734 .32055 m .35917 .31287 L s .34894 .26318 m .34637 .25865 L s .35303 .26803 m .34894 .26318 L s .35366 .27623 m .34797 .27109 L s .29531 .23523 m .30596 .23378 L s .33907 .25723 m .33891 .25323 L s .29097 .20806 m .30557 .20709 L s .41298 .31639 m .38834 .3067 L s .35065 .27363 m .34562 .26861 L s .33968 .25935 m .33882 .25518 L s .34686 .27887 m .34151 .27386 L s .34797 .27109 m .34362 .26619 L s .23885 .19215 m .26464 .19397 L s .34065 .26156 m .33907 .25723 L s .33177 .2558 m .33248 .25197 L s .34562 .26861 m .34196 .26384 L s .37696 .31843 m .35824 .31047 L s .34196 .26384 m .33968 .25935 L s .34362 .26619 m .34065 .26156 L s .29431 .21078 m .30695 .20924 L s .34151 .27386 m .33727 .26901 L s .33235 .25994 m .33177 .2558 L s .33727 .26901 m .3342 .26436 L s .37574 .31606 m .35663 .30787 L s .3342 .26436 m .33235 .25994 L s .29937 .21392 m .30986 .21178 L s .28521 .23695 m .29531 .23523 L s .30282 .31505 m .29737 .31075 L s .36746 .31447 m .34932 .30645 L s .28862 .2118 m .30042 .20992 L s .35917 .31287 m .342 .30504 L s .38834 .3067 m .36616 .29724 L s .27787 .20968 m .29097 .20806 L s .27558 .23889 m .28521 .23695 L s .35824 .31047 m .34073 .30242 L s .28338 .21299 m .29431 .21078 L s .29737 .31075 m .2908 .30583 L s .2908 .21676 m .29937 .21392 L s .35663 .30787 m .33892 .29964 L s .12715 .18532 m .17008 .19151 L s .21316 .19075 m .23885 .19215 L s .34932 .30645 m .33247 .29839 L s .26632 .24102 m .27558 .23889 L s .27858 .21435 m .28862 .2118 L s .342 .30504 m .32602 .29714 L s .36616 .29724 m .34646 .28804 L s .26635 .21195 m .27787 .20968 L s .34073 .30242 m .32457 .29436 L s .25729 .24327 m .26632 .24102 L s .2908 .30583 m .28349 .3004 L s .27424 .21588 m .28338 .21299 L s .28428 .2203 m .2908 .21676 L s .33892 .29964 m .32274 .29144 L s .33247 .29839 m .31705 .29034 L s .24833 .24558 m .25729 .24327 L s .27038 .21756 m .27858 .21435 L s .32602 .29714 m .31136 .28924 L s .34646 .28804 m .32925 .27917 L s .28349 .3004 m .27578 .29455 L s .32457 .29436 m .30991 .28634 L s .27989 .22451 m .28428 .2203 L s .25646 .21483 m .26635 .21195 L s .23924 .24788 m .24833 .24558 L s .26699 .21941 m .27424 .21588 L s .1875 .18974 m .21316 .19075 L s .32274 .29144 m .30819 .28333 L s .11862 .18412 m .12715 .18532 L s .22979 .25011 m .23924 .24788 L s .31705 .29034 m .30317 .28236 L s .26408 .22141 m .27038 .21756 L s .32925 .27917 m .31452 .27064 L s .31136 .28924 m .29815 .28139 L s .27773 .22938 m .27989 .22451 L s .21971 .25216 m .22979 .25011 L s .27578 .29455 m .26801 .28837 L s .30991 .28634 m .29685 .27842 L s .26167 .22356 m .26699 .21941 L s .24825 .2183 m .25646 .21483 L s .30819 .28333 m .29538 .27538 L s .20868 .25396 m .21971 .25216 L s .31452 .27064 m .30227 .26252 L s .30317 .28236 m .29096 .27452 L s .27785 .23489 m .27773 .22938 L s .25975 .22586 m .26408 .22141 L s .19634 .25541 m .20868 .25396 L s .29815 .28139 m .28653 .27366 L s .29685 .27842 m .2855 .27067 L s .26801 .28837 m .26045 .28195 L s .25834 .22831 m .26167 .22356 L s .18228 .25639 m .19634 .25541 L s .30227 .26252 m .2925 .25484 L s .28032 .24099 m .27785 .23489 L s .29538 .27538 m .2844 .26763 L s .16176 .18906 m .1875 .18974 L s .24175 .22233 m .24825 .2183 L s .29096 .27452 m .2805 .26687 L s .16603 .25679 m .18228 .25639 L s .2925 .25484 m .2852 .24765 L s .25742 .23089 m .25975 .22586 L s .2852 .24765 m .28032 .24099 L s .28653 .27366 m .2766 .26612 L s .2855 .27067 m .27596 .26314 L s .25701 .2336 m .25834 .22831 L s .14705 .25648 m .16603 .25679 L s .2844 .26763 m .27532 .26015 L s .26045 .28195 m .25338 .27538 L s .2805 .26687 m .27189 .25948 L s .25711 .23645 m .25742 .23089 L s .2766 .26612 m .26845 .25881 L s .12474 .25532 m .14705 .25648 L s .23696 .22688 m .24175 .22233 L s .27596 .26314 m .26829 .2559 L s .25772 .23942 m .25701 .2336 L s .27532 .26015 m .26821 .253 L s .27189 .25948 m .26519 .25241 L s .25883 .2425 m .25711 .23645 L s .26829 .2559 m .26257 .24901 L s .26845 .25881 m .26216 .25182 L s .25338 .27538 m .24702 .26875 L s .26045 .2457 m .25772 .23942 L s .26519 .25241 m .26045 .2457 L s .09842 .25315 m .12474 .25532 L s .26257 .24901 m .25883 .2425 L s .23386 .2319 m .23696 .22688 L s .24702 .26875 m .24159 .26214 L s .13578 .18866 m .16176 .18906 L s .09842 .25315 m .09842 .25315 L s .23241 .23734 m .23386 .2319 L s .24159 .26214 m .23727 .25562 L s .23256 .24315 m .23241 .23734 L s .23727 .25562 m .23421 .24927 L s .23421 .24927 m .23256 .24315 L s .10937 .18846 m .13578 .18866 L s .10655 .18845 m .10937 .18846 L s .25 Mabswid .74101 .41427 m 1 .10458 L s 1 .10458 m .97704 .35242 L s .97704 .35242 m .72787 .71183 L s .72787 .71183 m .74101 .41427 L s 0 .24331 m .0293 .51471 L s .0293 .51471 m .72787 .71183 L s .72787 .71183 m .74101 .41427 L s .74101 .41427 m 0 .24331 L s .0293 .51471 m .72787 .71183 L s .09154 .53227 m .09092 .52566 L s [(-4)] .0928 .54549 -0.09492 -1 Mshowa .22067 .56871 m .22022 .56208 L s [(-2)] .22157 .58196 -0.06758 -1 Mshowa .35637 .607 m .35611 .60037 L s [(0)] .35688 .62027 -0.03837 -1 Mshowa .49915 .64729 m .4991 .64065 L s [(2)] .49924 .66057 -0.0071 -1 Mshowa .64959 .68974 m .64976 .6831 L s [(4)] .64924 .70302 .02645 -1 Mshowa .125 Mabswid .12324 .54122 m .12289 .53725 L s .15532 .55027 m .15499 .5463 L s .18779 .55943 m .18749 .55546 L s .25396 .5781 m .25372 .57413 L s .28767 .58761 m .28745 .58364 L s .3218 .59725 m .32162 .59327 L s .39138 .61688 m .39125 .6129 L s .42684 .62689 m .42675 .6229 L s .46276 .63702 m .4627 .63304 L s .53602 .65769 m .53602 .65371 L s .57337 .66824 m .57341 .66425 L s .61123 .67892 m .6113 .67493 L s .06023 .52344 m .05983 .51947 L s .68847 .70071 m .68861 .69673 L s .25 Mabswid 0 .24331 m .38581 0 L s .04738 .21343 m .04802 .22004 L s [(-4)] .04608 .20021 .09773 1 Mshowa .13528 .158 m .1358 .16462 L s [(-2)] .13423 .14476 .07909 1 Mshowa .21509 .10766 m .21551 .11429 L s [(0)] .21426 .09441 .06252 1 Mshowa .28788 .06176 m .2882 .06839 L s [(2)] .28725 .04849 .04769 1 Mshowa .35455 .01972 m .35477 .02636 L s [(4)] .35409 .00645 .03434 1 Mshowa .125 Mabswid .07018 .19905 m .07054 .20302 L s .09241 .18503 m .09276 .189 L s .11411 .17135 m .11444 .17532 L s .15594 .14496 m .15624 .14894 L s .17612 .13224 m .1764 .13621 L s .19583 .11981 m .1961 .12378 L s .23391 .0958 m .23414 .09977 L s .25231 .08419 m .25252 .08817 L s .27029 .07285 m .2705 .07683 L s .30509 .0509 m .30527 .05489 L s .32193 .04029 m .3221 .04427 L s .33841 .02989 m .33856 .03387 L s .02399 .22818 m .0244 .23214 L s .37034 .00976 m .37047 .01374 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{323, 229.875}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[ooonIgYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00?l0VOl0I_l0CXf=SLcCXf=SLcII03=VoalO7eiN GYfMWMcLg02Z0200;o0P000ol000070003o`0002/01_n90000J0000ol0 000<00;o3@000ol0000a00KoP`0006T000?o00002@02o`030?l000`000?o0000=`06ogd0001V0004 o`00o`X000?o00003`000ol0000m00KoM`0006L00_l900;o4P000ol0001300KoL@0007000_l00`3o 000A0003o`0004T01_m[0000K`000ol0000D0003o`0004l01_mU0000K@02oaL000?o0000E@06oel0 001/0003o`3o01L000?o0000F`06oeT0001Z00;o6P000ol0001Q00KoD`0006P00_lM0003o`0006H0 1_m=0000I`02oah000?o0000K006odL0001U00;o00<0o`007@000ol0001b00Ko@@0005400_lA0003 o`00020000?o0000N006oc/0001@0004o`00o`h00_lS0003o`0007h01_le0000D0001?l00?l<00;o 00<0o`008P000ol0002400Ko;`00050000Co003o2`000ol0000U0003o`0008X01_lY0000D0001?l0 0?l900;o:0000ol0002@00Ko8`0005400_l90003o`3o02P000?o0000UP06oad0001J00;o:`000ol0 002L00Ko5`0005P00_l]0003o`000:801_lA0000E`02obh000?o0000Z006o`/0001E00;o00<0o`00 ;@000ol0002^00Ko1@0005@000?o0000<0000ol0002d00?o0P0005800_lc0003o`000;H00Ol10040 001@00?o=0000ol0002e00;o0P0004l000Co003o=0000ol0002d0003o`3o0080001=00;o>0000ol0 002c0004o`00o`80000j00Co3@02ocX000?o0000/P001Ol0003o0080000k0003o`0000`000?o0?l0 >P000ol0002a0005o`000?l00`0003@01Ol30003o`0000T00_lm0003o`000;4000Go0000o`030000 ?@000ol000070003o`0003d000?o0000/0000ol000020003o`000040000j0004o`00o`L00_m00003 o`000:l000?o00000`000ol000010000>`02o`H00_l00`3o000o0003o`000:h000?o000010000ol0 00010000@P000ol000120003o`000:d000?o00001@000ol000010000@002odD000?o0000[0000ol0 00060003o`000040000o00;oAP000ol0002[0003o`0000L000?o00000@0003d00_l00`3o00150003 o`000:/000?o00001`000ol000010000>`02odX000?o0000ZP000ol000080003o`000040000j0003 o`0004X000?o0000Z@000ol000090003o`000040000h00KoB@000ol0002X0003o`0000T000?o0000 0P0003L000Co003o0`07od8000?o0000Y`000ol0000:0003o`000080000e00;o0`000ol0000800Ko ?0000ol0002V0003o`0000/000?o00000P0003<00_lF00Go=`000ol0002V0003o`0000/000?o0000 0P00038000?o0?l06`05oc8000?o0000Y@000ol0000<0003o`000080000P00?o3@02o`8000?o0000 7P04obl000?o0000X`000ol0000=0003o`000080000Q0003o`0000/000?o00009`05obX000?o0000 XP000ol0000>0003o`000080000I00Go00<0ool00_l:00;o1P03obH01?lV0003o`000:4000?o0000 3`000ol0000200007`000ol0o`0900?o2P06ob@01?lR0003o`000:0000?o000040000ol000020000 7`000ol0o`080004o`00o`<09_l?00Co7P000ol0002P0003o`00010000?o00000P0002000_l600;o 600:o`/03ol400Co6P000ol0002O0003o`00014000?o00000P0002L000?o00007005o`030?oo00Oo 4@0=oaD000?o0000WP000ol0000A0003o`0000<0000U00;o5P03o`/01Ol500Go500:oa0000?o0000 W@000ol0000B0003o`0000<0000S00;o00<0o`006004o``01Ol500Ko5P08o`X000?o0000W0000ol0 000C0003o`0000<0000R0003o`0001l01Ol<00Go1P05o`L04?l00`3oo`07o`8000?o0000V`000ol0 000D0003o`0000<0000P00;o9`04o`d01?l602SoVP000ol0000D0003o`0000<0000O0003o`0002/0 1?l=00Ko0P04o`030?oo00Co4P0=oiD000?o00005@000ol0000300007@03oc401?l900Wo00@0oooo 1@07oa4000?o00003?n=0003o`0001H000?o00000`0001/00_l30003o`0003800ol300?o0`03o`03 0?oo00;o3P06o`/000?o0000100>ohH000?o00005`000ol0000300006P000ol0000H00Co7`03o`D0 0_l50003o`3o00;o4@05o`H000Co00005On10003o`0001P000?o00000`0001P00_lO00Ko6P000ol0 o`03o`030?l000@000?o00000`04oa801?l20004o`00o`T00ol700OoN`000ol0000I0003o`0000<0 000800Co2`02obH01OlE0003o`0000<00ol30003o`0000P01?lB00Go3@04o`P01ome0003o`0001T0 00?o0000100000T000?o00002@02o`030?l002X01Ol?0003o`0000@000?o00001?l602Go2`04o`L0 2?ma0003o`0001T000?o0000100000801Ol30003o`0000H00_ld00Co2`000ol000040003o`0000<0 1ol<00Co0P0Io`T01?l700WoJ`000ol0000J0003o`0000@0000;0003o`0000@000?o0000>005o`D0 00?o00001@000ol0000200;o0P04o`h02?l20003o`0000H000?o00003?l800Co1`0:ofD000?o0000 6`000ol00004000020001?l00?l500?o9003oaL01_l600Ko0P000ol0000300Co2006o`801Ol500Ko 1`0;o`H01?l700WoH@000ol0000L0003o`0000@0000900;o1P000ol0o`04ob<01OlG00Oo0P000ol0 00030003o`0000L01Ol20005o`3o0?l01@001?l00005o`H000?o00002`09o`D00ol800SoG@000ol0 000M0003o`0000@0000A0003o`0000@01OlS00Go4@05o`<01Ol400;o3004o`030?l000@000?o0000 1@000ol0o`03o`<00_l?00Wo1004o`P01omI0003o`0001h000?o00001000014000?o00002@04o`h0 1OlA00Co2@04o`8000?o00001@08o`030?l000/000?o0?l01?l00`3oo`080003o`0000<00ol200;o 4@0:o`<01?l700OoEP000ol0000N0003o`0000@0000A0003o`0000d01?l?01ko1`000ol0000500?o 1005o`T000Go0?l0o`0200Co1`000ol0000600?o00<0o`004P0;o`<00ol800KoDP000ol0000O0003 o`0000@0000A00?o4@05ob<01?l80003o`0000H00ol700Go1@001ol0o`3o0?l01003o`D000?o0000 2004oaL02?l300Co1`06odh000?o000080000ol0000400004P000ol0000E00Co8`03o`H000?o0000 1`02o`L000Co00001?l0103o0?l20003o`0000H01?l20003o`0000X01?lI00Oo0`03o`P01Om:0003 o`00024000?o00001000018000?o00006@04ob801?l30003o`0000L00_l70003o`0000@01ol<00Go 3@05oaP02Ol0103oool800GoAP000ol0000Q0003o`0000D0000B0003o`0001d01OlQ00Go2@03o`H0 00?o00001@0;o`T01?l=00;o00@0oooo600?o`H01Om20003o`00028000?o00001@0001800_lS00Co 8@04o`L01?l500;o1@000ol00002o`8000Co00001_l600Co3003o`030?oo00;o5`03o`030?oo00So 1P05od0000?o00008P000ol0000500004P000ol0000V00Co7`000ol0o`02o`D01Ol500Go00@0ool0 0_l20003o`0000H01Ol400Co3003o`800olG00?o00<0ool02?l500Ko?0000ol0000S0003o`0000D0 000B0003o`0002X01OlK0004o`0000Co0`04o`H00ol30004o`00o`8000?o00002P05o`030?oo00?o 3003o`800olG00;o00<0ool00ol00`3oo`05o`<01_lh0003o`0002@000?o00001@00018000?o0000 7P03o`h01?lH0003o`0000@02Ol30004o`0000;o0P000ol00002o`030?l000l01Ol0103oool<00?o 0P04oaD00ol200Co00<0ool01ol00`3oo`04oa@01olI0003o`0002D000?o00001@0001800_lR00?o 3`04oaD000?o00001`08o`H000?o00000_l00`3oo`04oa401?l0103oool<00?o0`03oaD00_l200Co 0P04o`802OlB0003o`0000@01?lD0003o`0002H000?o00001@00018000?o0?l09004o`l01?lB00;o 2`06o`D00_l200;o00D0oooo0002oa802?l<00?o0`03oa@00ol00`3oo`02o`801Ol400Oo3`000ol0 000800Ko3@000ol0000W0003o`0000D0000C0003o`0002L01Ol>00Go3`000ol000080003o`3o00Ko 1002o`8000Co00000_l00`3oo`0C00;o00<0ool01?l;00?o0`02oaD00_l200Co00<0ool01Ol400Go 3P02o`h01Ol80003o`0002L000?o00001@0001<000?o0000;005o`h01?l<0003o`0000H000?o0000 0P08o`<00_l00`3oo`0200;o0P02oa<000?o00000`05o`X00ol200?o5003o`800ol200?o00@0oooo 0`08o`/00_lA00Go0P000ol0000X0003o`0000D0000C0003o`0003401?l>00Co2@000ol0000300;o 1P06o`040?ooo`800_l00`3oo`0200;o0P02oa800ol500So1`03o`800_lE00?o0P02o`800ol200?o 0P04o`801Ol80003o`0001<01OlX0003o`0000D0000;00?o1@02ocH01?l>00Go1@02o`8000?o0000 2006o`800ol00`3oo`02o`<00_l200;o4`03o`D00ol00`3oo`04o`D00_l200?o5@05o`801?l300?o 00<0ool00_l500Go10000ol0000B0003o`0000801OlR0003o`0000H0000<0003o`0000@000?o0000 >@03oa001?l300;o3P04o`@00ol00`3oo`02o`040?ooo`800_lD00?o1@03o`<01_l200?o0P03oaD0 1Ol200?o1007o`P01?l00`3o000A0003o`0000P01OlM0003o`0000H0000500Go0P000ol000040003 o`0003`01?l@00Go4005o`@01ol00`3oo`02o`030?oo01D00ol500?o1P08o`801?lC00Go0P03o`H0 1Ol:00Go3P000ol0000>00?o6P000ol00006000030000ol000040003o`0004001Ol<00;o00<0ool0 0ol?00Go1P04o`800ol0103ooolE00?o1@03o`T01_l200?o4P001?l00?l200Co1`04o`/01ol80003 o`0001800olG0003o`0000H0000<0003o`0000@00om500Go1P000ol000040003o`3o00?o3@05o`L0 1?l200;o0P02oaH00ol500?o2P09oa400_l00`3oo`020003o`3o00L01_l:0003o`0000801Ol30003 o`0001D00olD0003o`0000H0000;00;o1P000ol0001:00Ko20000ol0000200Co2`05o`P02?l0103o oolF00?o1@03o`X00ol00`3oo`02oa4000?o0?l00_l00`3o0002o`L01ol80003o`0000H01OlI00Ko 3P000ol00006000050000ol0001=0003o`3o00Co10000ol0000500Go1`06o`T02?l00`3oo`0G00?o 1@03o`X02ol<00;o00@0ool00_l0103oool600Co00@0oooo1P000ol000060004o`0000Co6`03o`/0 00?o00001P0001@000?o0000B`02o`L01?l=00Co1P06o`P000?o0?l02OlG00?o1@03o`/01Ol200Go 2@001?l00?l20004o`0000;o1P03o`<01?l30003o`0000@000?o00001P05ob@000?o00001P0001@0 0_m;0003o`0001`01?l500Ko1P03o`030?oo00So5`03o`D00_l<00Co1@05o`D000Ko003o0?l50003 o`0000D00ol500Go10000ol0000<00Go7`000ol00006000050000ol000190003o`0002401?l400Ko 1P0>oaL00ol40003o`0000d01?l600Go00L0ool0o`3o00D000?o00001P02o`P00ol00`3o000C00Go 6P000ol00006000050000ol0001700;o:005o`801Ol900Co00<0ool01_lF00Co00<0ool03P02o`04 0?ooo`P01_l00`3o000400;o1`02o`T01OlG00Co5P000ol00006000050000ol000160003o`0002d0 1?l00`3oo`02o`T01Ol00`3oo`08oaD01_l=0004o`0000?o20000ol0o`03o`H00_l600;o2002o`<0 1?lG00Go40000ol0000700005002odH000?o000000Ko1`04o`H02_l>0003o`0000<0 1Ol700Go0`04o`L000?o00000`06o`030?oo00?o6003oa8000?o0000200001D000?o0000?0000ol0 001A00Oo1`04o`L02_l:00Go1@04o`801Ol800Co10001?l00004o`H000?o00001_lE00?o3P000ol0 000900005@000ol0000k0003o`0005H02?l600Co2@0@o`X02?l=00Wo0P000ol000040003o`0000H0 1OlC00;o30000ol0000900003P02o`D000?o0000>P000ol0001K00So1P04o`d04ol0103oo`04o`T0 1Ol200Co0`000ol000040003o`0000/01OlK0003o`0000X0000=0004o`00o`@00_li00;oHP08o`H0 1?l=00Co00<0ool06Ol800;o00<0ool00_l50003o`0001401?lF0003o`0000/0000=0004o`00o`@0 00?o0000=`000ol0001V00So1P04o`d01_lA00Co2@02o`<000?o0?l01?lH00Go40000ol0000<0000 3@001?l00?l40003o`0003H000?o0000K@07o`D01?l900;o1006o`l01?l400;o0`02o`@01?lK00Go 2`000ol0000<00003@001?l00?l50003o`0003@000?o0000LP0Eo``01Ol>00Go0P03o`@000?o0000 0P04oa`00_l80003o`0000d0000>00;o1P03oc800_mj013o4@07o`P01ol400;o2@04ob4000?o0000 3P0001H000?o0000<@000ol0002000ko5008o`030?oo00;o0P05o`h01?lM0003o`0000h0000F0003 o`00030000?o0000QP0?o``04ol300Co3P04oaP000?o00003`0001H000?o0000;P02ohd0:ol600Co 3P04oa<000?o0000400001H00_l^0003o`0009403_l>0003o`0000P02?l200Go3@04o`l000?o0000 400001H000?o0000;0000ol0002G00Co1008o`H000?o00004@05o`801Ol<00Co2P000ol0000A0000 5P000ol0000[0003o`0009`01?l5017o4@06o`030?oo00?o2`02o`L000?o00004P0001H000?o0000 :@02oj<01Ol300Go2@0?o`P01Ol00`3oo`02o`l000?o00004`0001L00_lX0003o`000:P01?l200Ko 500Po`030?l001@0000G0003o`0002H000?o0000[@02o`H01OlU00Oo0`000ol0000D00005`000ol0 000T00;o/@000ol0000900Go9002o`040?l0oaL0000G0003o`0002<000?o0000/@000ol0000>00Ko 8`000ol0000E00005`02ob<000?o0000/P000ol0000D00Go7@000ol0000F00005`000ol0000Q0003 o`000;<000?o00006@05oaL000?o00005`0001L000?o00007`02okH000?o00007P05oa8000?o0000 5`0000l00ol50003o`0001h000?o0000]P000ol0000S00Go30000ol0000H000040000ol0000400?o 7@000ol0002g0003o`0002P01?l70003o`0001T0000@0003o`0000D000?o00006P02okX000?o0000 ;005o`030?oo01/0000@0003o`0000D000?o00006@000ol0002j0003o`0003400_lL000040000ol0 00050003o`0001P000?o0000^`000ol0000a0003o`0001/0000?00;o1`03oaL000?o0000_0000ol0 000`0003o`0001`0000H0003o`0001D00_nn0003o`00034000?o0000700001P000?o000050000ol0 002n0003o`00030000?o00007@0001P000?o00004`000ol0002o0003o`0002l000?o00007P0001P0 0_lC0003o`000<0000?o0000;`000ol0000N000060000ol0000@00;o``000ol0000^0003o`0001l0 000I0003o`0000h000?o0000``000ol0000]0003o`000200000I0003o`0000d000?o0000a0000ol0 000]0003o`000200000I00;o3002olL000?o0000;0000ol0000Q00006@000ol0000:0003o`000`0005T000?o00007004o`03 0?l006l000?o00004`000ol0000l0000EP001?l00?lR00?oK`000ol0000C0003o`0003`0001G00;o 9P04of/000?o00004P000ol0000m0000P`03o`8000?o0000H`000ol0000A0003o`0003h0002600Co I0000ol0000A0003o`0003h0002:00?oH@000ol0000@0003o`0003l0002=00Co00<0o`00FP000ol0 000?0003o`000400002A00?oFP000ol0000>0003o`000440001l00;o5P04oeH000?o00003P000ol0 00110000N`001?l00?lI00?o0P000ol0001>0003o`0000d000?o0000@P0007/000Co003o7004odl0 00?o000030000ol000130000N`001?l00?lN0003o`3o00;oC0000ol0000<0003o`0004<0001k0004 o`00ob<01?l20003o`0004<000?o00002`000ol000140000O002obP00om50003o`0000X000?o0000 A@000:P01Om10003o`0000X000?o0000A@000:d00oln0003o`0000T000?o0000AP000;001?lj0003 o`0000P000?o0000A`000;<01?lg0003o`0000P000?o0000A`000;L01?lc0003o`0000L000?o0000 B0000;/01Ol^0003o`0000H000?o0000B@000;l00ol/0003o`0000D000?o0000BP000:H01?lH00Co :0000ol000050003o`0004X0002W0003o`0001`00ol00`3o000R0003o`0000@000?o0000B`000:P0 00?o00007P04ob0000?o000010000ol0001<0000Z@000ol0000Q00?o1P000ol0000D0003o`0000@0 00?o0000C0000:H000Co003o9P04o`8000?o000050000ol000030003o`0004d0002W00;o:`03oaH0 00?o00000P000ol0001>0000e`04oa8000?o00000P000ol0001>0000f`03o`l000Go0000o`1A0000 gP05o`X000Co003oDP000>800ol80003o`3o05<0003U00Co10000ol0o`1C0000j@03o`030?oo05@0 003E00?o5002oeD0003F0003o`0006X0003D00CoJ`000=@000?o0?l0K0000=@000?o0?l0K0000=D0 0_m/0000o`140000\ \>"], ImageRangeCache->{{{0, 322}, {228.875, 0}} -> {-0.0546985, 0.193249, 0.00310902, 0.00310902}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics3D \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Problem 2", "Subsubsection"], Cell[TextData[{ "For each of the matrices ", StyleBox["A", "Input"], " below, find the fundamental matrix ", StyleBox["Phi[t]", "Input"], " such that ", StyleBox["Phi[0]", "Input"], " is the identity matrix for the system ", StyleBox["X'[t] == A.X[t]", "Input"], ". Verify that ", StyleBox["Phi'[t]==A.Phi[t]", "Input"], ". Then use ", StyleBox["Phi[t]", "Input"], " to find a solution satisfying the given initial condition.\n\n", StyleBox["a)", FontSlant->"Italic"], StyleBox[" A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Input", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-7,-8, 2},\n { 9,11,-3},\n { 9, 8, 0}}", "Input"], StyleBox[";\n X[0]=={3,-1,1};", FontFamily->"Courier", FontWeight->"Bold"], "\n\n", StyleBox["b)", FontSlant->"Italic"], StyleBox[" A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Input", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-4,-2,-1},\n { 2, 6,-3},\n { 2, 4,-1}}", "Input"], StyleBox[";\n X[0]=={1,1,-2};\n \n", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["c)", FontSlant->"Italic"], StyleBox[" A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Input", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ "{{ 5, 3,-1},\n {-16,-6,-1},\n { -4,-3, 2}}", "Input"], StyleBox[";\n X[0]=={1,1,1}; \n \n", FontFamily->"Courier", FontWeight->"Bold"] }], "Text"], Cell["Solution", "Subsubsection"], Cell[TextData[{ StyleBox["a", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[{ StyleBox["A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Inpute", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-7,-8, 2},\n { 9,11,-3},\n { 9, 8, 0}}", "Inpute"], StyleBox[";", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[CellGroupData[{ Cell["Eigensystem[A]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{\(-1\), 2, 3}, {{\(-1\), 1, 1}, {\(-2\), 3, 3}, {\(-2\), 3, 2}}}\)], "Output"] }, Open ]], Cell["Fundamental solutions:", "Text"], Cell["\<\ X1[t_] = {-1,1,1}E^(-t); X2[t_] = {-2,3,3}E^(2t); X3[t_] = {-2,3,2}E^(3t);\ \>", "Input"], Cell[TextData[{ "A fundamental matrix has columns given by ", StyleBox["X1[t]", "Input"], ", ", StyleBox["X2[t]", "Input"], ", and ", StyleBox["X2[t]", "Input"], ". We use ", StyleBox["Transpose[]", "Input"], " to covert these vectors from rows into columns." }], "Text"], Cell[CellGroupData[{ Cell["\<\ Psi[t_] = Transpose[{X1[t], X2[t], X3[t]}]; Psi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(-E\^\(-t\)\), \(\(-2\)\ E\^\(2\ t\)\), \(\(-2\)\ E\^\(3\ t\)\)}, {\(E\^\(-t\)\), \(3\ E\^\(2\ t\)\), \(3\ E\^\(3\ t\)\)}, {\(E\^\(-t\)\), \(3\ E\^\(2\ t\)\), \(2\ E\^\(3\ t\)\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[TextData[{ "To get a fundamental matrix ", StyleBox["Phi[t]", "Input"], " such that ", StyleBox["Phi[0]", "Input"], " is the identity matrix, we multiply ", StyleBox["Psi[t]", "Input"], " on the right by the inverse of ", StyleBox["Psi[0]", "Input"], "." }], "Text"], Cell[CellGroupData[{ Cell["\<\ Phi[t_] = Psi[t].Inverse[Psi[0]]; Phi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(3\ E\^\(-t\) - 2\ E\^\(2\ t\)\), \(2\ E\^\(-t\) - 2\ E\^\(3\ t\)\), \(\(-2\)\ E\^\(2\ t\) + 2\ E\^\(3\ t\)\)}, {\(\(-3\)\ E\^\(-t\) + 3\ E\^\(2\ t\)\), \(\(-2\)\ E\^\(-t\) + 3\ E\^\(3\ t\)\), \(3\ E\^\(2\ t\) - 3\ E\^\(3\ t\)\)}, {\(\(-3\)\ E\^\(-t\) + 3\ E\^\(2\ t\)\), \(\(-2\)\ E\^\(-t\) + 2\ E\^\(3\ t\)\), \(3\ E\^\(2\ t\) - 2\ E\^\(3\ t\)\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Phi[0]//MatrixForm", "Input", AspectRatioFixed->True], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {"1", "0", "0"}, {"0", "1", "0"}, {"0", "0", "1"} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[TextData[{ "Let's check that ", StyleBox["Phi[t]", FontFamily->"Courier", FontWeight->"Bold"], " satisfies the equation:" }], "Text"], Cell[CellGroupData[{ Cell["Phi'[t]//Simplify//MatrixForm", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(\(-E\^\(-t\)\)\ \((3 + 4\ E\^\(3\ t\))\)\), \(\(-2\)\ E\^\(-t\)\ \((1 + 3\ E\^\(4\ t\))\)\), \(2\ E\^\(2\ t\)\ \((\(-2\) + 3\ E\^t)\)\)}, {\(3\ E\^\(-t\) + 6\ E\^\(2\ t\)\), \(E\^\(-t\)\ \((2 + 9\ E\^\(4\ t\))\)\), \(\(-3\)\ E\^\(2\ t\)\ \((\(-2\) + 3\ E\^t)\)\)}, {\(3\ E\^\(-t\) + 6\ E\^\(2\ t\)\), \(2\ E\^\(-t\) + 6\ E\^\(3\ t\)\), \(\(-6\)\ E\^\(2\ t\)\ \((\(-1\) + E\^t)\)\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.Phi[t]//Simplify//MatrixForm", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(\(-E\^\(-t\)\)\ \((3 + 4\ E\^\(3\ t\))\)\), \(\(-2\)\ E\^\(-t\)\ \((1 + 3\ E\^\(4\ t\))\)\), \(2\ E\^\(2\ t\)\ \((\(-2\) + 3\ E\^t)\)\)}, {\(3\ E\^\(-t\) + 6\ E\^\(2\ t\)\), \(E\^\(-t\)\ \((2 + 9\ E\^\(4\ t\))\)\), \(\(-3\)\ E\^\(2\ t\)\ \((\(-2\) + 3\ E\^t)\)\)}, {\(3\ E\^\(-t\) + 6\ E\^\(2\ t\)\), \(2\ E\^\(-t\) + 6\ E\^\(3\ t\)\), \(\(-6\)\ E\^\(2\ t\)\ \((\(-1\) + E\^t)\)\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell["\<\ The solution satisfying the given initial condition is simply:\ \>", "Text"], Cell[CellGroupData[{ Cell[TextData[{ "X[t_] = Phi[t].", StyleBox["{3,-1,1}", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[BoxData[ \({\(-2\)\ E\^\(-t\) - 2\ E\^\(2\ t\) + 4\ E\^\(3\ t\) + 3\ \((3\ E\^\(-t\) - 2\ E\^\(2\ t\))\), 2\ E\^\(-t\) + 3\ E\^\(2\ t\) - 6\ E\^\(3\ t\) + 3\ \((\(-3\)\ E\^\(-t\) + 3\ E\^\(2\ t\))\), 2\ E\^\(-t\) + 3\ E\^\(2\ t\) - 4\ E\^\(3\ t\) + 3\ \((\(-3\)\ E\^\(-t\) + 3\ E\^\(2\ t\))\)}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["b", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[{ StyleBox["A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Inpute", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-4,-2,-1},\n { 2, 6,-3},\n { 2, 4,-1}}", "Inpute"], StyleBox[";\n", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[CellGroupData[{ Cell["Eigensystem[A]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{\(-3\), 2, 2}, {{\(-3\), 1, 1}, {\(-1\), 2, 2}, {0, 0, 0}}}\)], "Output"] }, Open ]], Cell["We get two fundamental solutions from this:", "Text"], Cell[TextData[{ "X1[t_] = {-3,1,1}E^(-3t);\nX2[t_] = ", StyleBox["{-1,2,2}", FontFamily->"Courier", FontWeight->"Bold"], "E^(2t);" }], "Input"], Cell[TextData[{ "The eigenvalue ", StyleBox["2", "Input"], " is repeated and ", StyleBox["Eigensystem[]", FontFamily->"Courier", FontWeight->"Bold"], " finds only one non-trivial eigenvector, ", StyleBox["{-1,2,2}", FontFamily->"Courier", FontWeight->"Bold"], ". A generalized eigenvector is found by solving" }], "Text"], Cell[CellGroupData[{ Cell[TextData[{ "Solve[(A - 2*IdentityMatrix[3]).{w1,w2,w3} == {", StyleBox["-1,2,2", FontFamily->"Courier", FontWeight->"Bold"], "}]" }], "Input", AspectRatioFixed->True], Cell[BoxData[ \(Solve::"svars" \( : \ \) "Equations may not give solutions for all \"solve\" variables."\)], "Message"], Cell[BoxData[ \({{w1 \[Rule] \(-\(w3\/2\)\), w2 \[Rule] 1\/2 + w3}}\)], "Output"] }, Open ]], Cell[TextData[{ "For example, ", StyleBox["{w1,w2,w3} = {-1,5/2,2}", "Input"], ", from which we can derive a third independent solution:" }], "Text"], Cell[TextData[{ "X3[t_] = ", StyleBox["{-1,2,2}", FontFamily->"Courier", FontWeight->"Bold"], " t*E^(2t) + ", StyleBox["{-1,5/2,2}", "Input"], " E^(2t);" }], "Input"], Cell["The general solution is:", "Text"], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t] + c3 X3[t]", "Input"], Cell[BoxData[ \({\(-3\)\ c1\ E\^\(\(-3\)\ t\) - c2\ E\^\(2\ t\) + c3\ \((\(-E\^\(2\ t\)\) - E\^\(2\ t\)\ t)\), c1\ E\^\(\(-3\)\ t\) + 2\ c2\ E\^\(2\ t\) + c3\ \((\(5\ E\^\(2\ t\)\)\/2 + 2\ E\^\(2\ t\)\ t)\), c1\ E\^\(\(-3\)\ t\) + 2\ c2\ E\^\(2\ t\) + c3\ \((2\ E\^\(2\ t\) + 2\ E\^\(2\ t\)\ t)\)}\)], "Output"] }, Open ]], Cell["Check:", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Expand", "Input"], Cell[BoxData[ \({9\ c1\ E\^\(\(-3\)\ t\) - 2\ c2\ E\^\(2\ t\) - 3\ c3\ E\^\(2\ t\) - 2\ c3\ E\^\(2\ t\)\ t, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 7\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 6\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t]//Expand", "Input"], Cell[BoxData[ \({9\ c1\ E\^\(\(-3\)\ t\) - 2\ c2\ E\^\(2\ t\) - 3\ c3\ E\^\(2\ t\) - 2\ c3\ E\^\(2\ t\)\ t, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 7\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 6\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t}\)], "Output"] }, Open ]], Cell["Fundamental matrix:", "Text"], Cell[CellGroupData[{ Cell["\<\ Psi[t_] = Transpose[{X1[t], X2[t], X3[t]}]; Psi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(\(-3\)\ E\^\(\(-3\)\ t\)\), \(-E\^\(2\ t\)\), \(\(-E\^\(2\ t\)\) - E\^\(2\ t\)\ t\)}, {\(E\^\(\(-3\)\ t\)\), \(2\ E\^\(2\ t\)\), \(\(5\ E\^\(2\ t\)\)\/2 + 2\ E\^\(2\ t\)\ t\)}, {\(E\^\(\(-3\)\ t\)\), \(2\ E\^\(2\ t\)\), \(2\ E\^\(2\ t\) + 2\ E\^\(2\ t\)\ t\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Phi[t_] = Psi[t].Inverse[Psi[0]]; Phi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(\(6\ E\^\(\(-3\)\ t\)\)\/5 - E\^\(2\ t\)\/5\), \(2\ E\^\(2\ t\) + 2\ \((\(-E\^\(2\ t\)\) - E\^\(2\ t\)\ t)\)\), \(\(3\ E\^\(\(-3\)\ t\)\)\/5 - \(13\ E\^\(2\ t\)\)\/5 - 2\ \((\(-E\^\(2\ t\)\) - E\^\(2\ t\)\ t)\)\)}, {\(\(-\(2\/5\)\)\ E\^\(\(-3\)\ t\) + \(2\ E\^\(2\ t\)\)\/5\), \(\(-4\)\ E\^\(2\ t\) + 2\ \((\(5\ E\^\(2\ t\)\)\/2 + 2\ E\^\(2\ t\)\ t)\)\), \(\(-\(1\/5\)\)\ E\^\(\(-3\)\ t\) + \(26\ E\^\(2\ t\)\)\/5 - 2\ \((\(5\ E\^\(2\ t\)\)\/2 + 2\ E\^\(2\ t\)\ t)\)\)}, {\(\(-\(2\/5\)\)\ E\^\(\(-3\)\ t\) + \(2\ E\^\(2\ t\)\)\/5\), \(\(-4\)\ E\^\(2\ t\) + 2\ \((2\ E\^\(2\ t\) + 2\ E\^\(2\ t\)\ t)\)\), \(\(-\(1\/5\)\)\ E\^\(\(-3\)\ t\) + \(26\ E\^\(2\ t\)\)\/5 - 2\ \((2\ E\^\(2\ t\) + 2\ E\^\(2\ t\)\ t)\)\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell["The solution satisfying the given initial condition is:", "Text"], Cell[CellGroupData[{ Cell[TextData[{ "X[t_] = Phi[t].", StyleBox["{1,1,-2}//Simplify", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[BoxData[ \({\(-E\^\(2\ t\)\)\ \((\(-1\) + 6\ t)\), E\^\(2\ t\)\ \((1 + 12\ t)\), 2\ E\^\(2\ t\)\ \((\(-1\) + 6\ t)\)}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["c", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[{ StyleBox["A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Inputer", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{ 5, 3,-1},\n {-16,-6,-1},\n { -4,-3, 2}}", "Inputer"], StyleBox[";", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[CellGroupData[{ Cell["Eigensystem[A]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{\(-3\)\ I, 3\ I, 1}, {{\(-1\), 2 + I, 1}, {\(-1\), 2 - I, 1}, {\(-1\), 2, 2}}}\)], "Output"] }, Open ]], Cell["\<\ X1[t_] = {-1,2,2}E^t; Z[t_] = {-1,2-I,1}E^(3I*t);\ \>", "Input"], Cell[CellGroupData[{ Cell["X2[t_] = Re[Z[t]]//ComplexExpand", "Input"], Cell[BoxData[ \({\(-Cos[3\ t]\), 2\ Cos[3\ t] + Sin[3\ t], Cos[3\ t]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["X3[t_] = Im[Z[t]]//ComplexExpand", "Input"], Cell[BoxData[ \({\(-Sin[3\ t]\), \(-Cos[3\ t]\) + 2\ Sin[3\ t], Sin[3\ t]}\)], "Output"] }, Open ]], Cell["General solution:", "Text"], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t] + c3 X3[t]", "Input"], Cell[BoxData[ \({\(-c1\)\ E\^t - c2\ Cos[3\ t] - c3\ Sin[3\ t], 2\ c1\ E\^t + c2\ \((2\ Cos[3\ t] + Sin[3\ t])\) + c3\ \((\(-Cos[3\ t]\) + 2\ Sin[3\ t])\), 2\ c1\ E\^t + c2\ Cos[3\ t] + c3\ Sin[3\ t]}\)], "Output"] }, Open ]], Cell["Check:", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Simplify", "Input"], Cell[BoxData[ \({\(-c1\)\ E\^t - 3\ c3\ Cos[3\ t] + 3\ c2\ Sin[3\ t], 2\ c1\ E\^t + 3\ \((c2 + 2\ c3)\)\ Cos[3\ t] + \((\(-6\)\ c2 + 3\ c3)\)\ Sin[3\ t], 2\ c1\ E\^t + 3\ c3\ Cos[3\ t] - 3\ c2\ Sin[3\ t]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t]//Simplify", "Input"], Cell[BoxData[ \({\(-c1\)\ E\^t - 3\ c3\ Cos[3\ t] + 3\ c2\ Sin[3\ t], 2\ c1\ E\^t + 3\ \((c2 + 2\ c3)\)\ Cos[3\ t] + \((\(-6\)\ c2 + 3\ c3)\)\ Sin[3\ t], 2\ c1\ E\^t + 3\ c3\ Cos[3\ t] - 3\ c2\ Sin[3\ t]}\)], "Output"] }, Open ]], Cell["Fundamental matrix:", "Text"], Cell[CellGroupData[{ Cell["\<\ Psi[t_] = Transpose[{X1[t], X2[t], X3[t]}]; Psi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(-E\^t\), \(-Cos[3\ t]\), \(-Sin[3\ t]\)}, {\(2\ E\^t\), \(2\ Cos[3\ t] + Sin[3\ t]\), \(\(-Cos[3\ t]\) + 2\ Sin[3\ t]\)}, {\(2\ E\^t\), \(Cos[3\ t]\), \(Sin[3\ t]\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Phi[t_] = Psi[t].Inverse[Psi[0]]//Simplify; Phi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(\(-E\^t\) + 2\ Cos[3\ t] + 2\ Sin[3\ t]\), \(Sin[3\ t]\), \(\(-E\^t\) + Cos[3\ t]\)}, {\(\(-2\)\ \((\(-E\^t\) + Cos[3\ t] + 3\ Sin[3\ t])\)\), \(Cos[3\ t] - 2\ Sin[3\ t]\), \(2\ E\^t - 2\ Cos[3\ t] - Sin[3\ t]\)}, {\(\(-2\)\ \((\(-E\^t\) + Cos[3\ t] + Sin[3\ t])\)\), \(-Sin[3\ t]\), \(2\ E\^t - Cos[3\ t]\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell["The solution satisfying the given initial condition is:", "Text"], Cell[CellGroupData[{ Cell[TextData[{ "X[t_] = Phi[t].", StyleBox["{1,1,1}//Simplify", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[BoxData[ \({\(-2\)\ E\^t + 3\ Cos[3\ t] + 3\ Sin[3\ t], 4\ E\^t - 3\ Cos[3\ t] - 9\ Sin[3\ t], 4\ E\^t - 3\ Cos[3\ t] - 3\ Sin[3\ t]}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Problem 3", "Subsubsection"], Cell[TextData[{ "Use the method of variation of parameters to find the general solution of \ the system ", StyleBox["X'[t] == A.X[t] + G[t]", "Input"], " for each of the matrices ", StyleBox["A", "Input"], " and vector functions ", StyleBox["G[t]", "Input"], " below. Check that your solution is correct by comparing ", StyleBox["X'[t]", "Input"], " and ", StyleBox["A.X[t]+G[t]", "Input"], ". Then find the solution that satisfies the given initial condition.\n\n", StyleBox["a)", FontSlant->"Italic"], StyleBox[" ", FontFamily->"Courier", FontWeight->"Bold"], "(see ", StyleBox["Problem 2", FontWeight->"Bold"], StyleBox["a", FontSlant->"Italic"], ")", StyleBox["\n A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Input", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-7,-8, 2},\n { 9,11,-3},\n { 9, 8, 0}}", "Input"], StyleBox[";\n G[t_] = {t^2,t,1};\n X[0]=={3,-1,1};", FontFamily->"Courier", FontWeight->"Bold"], "\n\n", StyleBox["b) ", FontSlant->"Italic"], "(see ", StyleBox["Problem 2", FontWeight->"Bold"], StyleBox["b", FontSlant->"Italic"], ")", StyleBox["\n", FontSlant->"Italic"], StyleBox[" A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Input", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-4,-2,-1},\n { 2, 6,-3},\n { 2, 4,-1}}", "Input"], StyleBox[";\n G[t_] = {1,Cos[t],Sin[t]};\n X[0]=={1,1,-2};\n \n", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["c)", FontSlant->"Italic"], StyleBox[" ", FontFamily->"Courier", FontWeight->"Bold"], "(see ", StyleBox["Problem 2", FontWeight->"Bold"], StyleBox["c", FontSlant->"Italic"], ")\n", StyleBox[" ", "Input"], StyleBox["A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Input", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[ "{{ 5, 3,-1},\n {-16,-6,-1},\n { -4,-3, 2}}", "Input"], StyleBox[";\n G[t_] = {E^t,1,E^(-t)};\n X[0]=={1,1,1};", FontFamily->"Courier", FontWeight->"Bold"] }], "Text"], Cell["Solution", "Subsubsection"], Cell[TextData[{ StyleBox["a", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[{ StyleBox["A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Input", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-7,-8, 2},\n { 9,11,-3},\n { 9, 8, 0}}", "Input"], StyleBox[";\nG[t_] = {t^2,t,1};\n", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[TextData[{ "A solution to the associated homogeneous problem, ", StyleBox["X'[t] == A.X[t]", FontFamily->"Courier", FontWeight->"Bold"], ", was found in ", StyleBox["Problem 3", FontWeight->"Bold"], StyleBox["a", FontSlant->"Italic"], " :" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ X1[t_] = {-1,1,1}E^(-t); X2[t_] = {-2,3,3}E^(2t); X3[t_] = {-2,3,2}E^(3t); Psi[t_] = Transpose[{X1[t], X2[t], X3[t]}]; IPsi[t_] = Inverse[Psi[t]]; IPsi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(\(-3\)\ E\^t\), \(\(-2\)\ E\^t\), "0"}, {\(E\^\(\(-2\)\ t\)\), "0", \(E\^\(\(-2\)\ t\)\)}, {"0", \(E\^\(\(-3\)\ t\)\), \(-E\^\(\(-3\)\ t\)\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[TextData[{ "A particular solution to the non-homogeneous problem is given by\n", StyleBox["Y[t_] = ", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["Ps", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["i[t].U[t]", FontFamily->"Courier", FontWeight->"Bold"], " where ", StyleBox["U[t]", FontFamily->"Courier", FontWeight->"Bold"], " satisfies ", StyleBox["U'[t] == I", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["Ps", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["i[t].G[t]", FontFamily->"Courier", FontWeight->"Bold"], "." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["IPsi[t].G[t]", "Input"], Cell[BoxData[ \({\(-2\)\ E\^t\ t - 3\ E\^t\ t\^2, E\^\(\(-2\)\ t\) + E\^\(\(-2\)\ t\)\ t\^2, \(-E\^\(\(-3\)\ t\)\) + E\^\(\(-3\)\ t\)\ t}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["U[t_] = Integrate[IPsi[t].G[t], t]//Simplify", "Input"], Cell[BoxData[ \({E\^t\ \((\(-4\) + 4\ t - 3\ t\^2)\), \(-\(1\/4\)\)\ E\^\(\(-2\)\ t\)\ \((3 + 2\ t + 2\ t\^2)\), \(-\(1\/9\)\)\ E\^\(\(-3\)\ t\)\ \((\(-2\) + 3\ t)\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Y[t_] = Psi[t].U[t]//Simplify", "Input"], Cell[BoxData[ \({91\/18 - \(7\ t\)\/3 + 4\ t\^2, 1\/12\ \((\(-67\) + 18\ t - 54\ t\^2)\), 1\/36\ \((\(-209\) + 66\ t - 162\ t\^2)\)}\)], "Output"] }, Open ]], Cell["The general solution to the given system is then", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t] + c3 X3[t] + Y[t]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({91\/18 - c1\ E\^\(-t\) - 2\ c2\ E\^\(2\ t\) - 2\ c3\ E\^\(3\ t\) - \(7\ t\)\/3 + 4\ t\^2, c1\ E\^\(-t\) + 3\ c2\ E\^\(2\ t\) + 3\ c3\ E\^\(3\ t\) + 1\/12\ \((\(-67\) + 18\ t - 54\ t\^2)\), c1\ E\^\(-t\) + 3\ c2\ E\^\(2\ t\) + 2\ c3\ E\^\(3\ t\) + 1\/36\ \((\(-209\) + 66\ t - 162\ t\^2)\)}\)], "Output"] }, Open ]], Cell["Check:", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Simplify", "Input"], Cell[BoxData[ \({\(-\(7\/3\)\) + c1\ E\^\(-t\) - 4\ c2\ E\^\(2\ t\) - 6\ c3\ E\^\(3\ t\) + 8\ t, 3\/2 - c1\ E\^\(-t\) + 6\ c2\ E\^\(2\ t\) + 9\ c3\ E\^\(3\ t\) - 9\ t, 11\/6 - c1\ E\^\(-t\) + 6\ c2\ E\^\(2\ t\) + 6\ c3\ E\^\(3\ t\) - 9\ t} \)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t] + G[t]//Simplify", "Input"], Cell[BoxData[ \({\(-\(7\/3\)\) + c1\ E\^\(-t\) - 4\ c2\ E\^\(2\ t\) - 6\ c3\ E\^\(3\ t\) + 8\ t, 3\/2 - c1\ E\^\(-t\) + 6\ c2\ E\^\(2\ t\) + 9\ c3\ E\^\(3\ t\) - 9\ t, 11\/6 - c1\ E\^\(-t\) + 6\ c2\ E\^\(2\ t\) + 6\ c3\ E\^\(3\ t\) - 9\ t} \)], "Output"] }, Open ]], Cell[TextData[{ "We now solve for the constants ", StyleBox["c1", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["c2", FontFamily->"Courier", FontWeight->"Bold"], " that satisfy the given initial condition." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[{ "cs = Solve[", StyleBox["X[0]=={3,-1,1}", FontFamily->"Courier", FontWeight->"Bold"], "]" }], "Input", AspectRatioFixed->True], Cell[BoxData[ \({{c1 \[Rule] \(-3\), c2 \[Rule] 19\/4, c3 \[Rule] \(-\(20\/9\)\)}}\)], "Output"] }, Open ]], Cell["The solution to the initial value problem is thus", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["X[t_] = X[t] /. First[cs] //Simplify", "Input", AspectRatioFixed->True], Cell[BoxData[ \({91\/18 + 3\ E\^\(-t\) - \(19\ E\^\(2\ t\)\)\/2 + \(40\ E\^\(3\ t\)\)\/9 - \(7\ t\)\/3 + 4\ t\^2, 1\/12\ \(( \(-67\) - 36\ E\^\(-t\) + 171\ E\^\(2\ t\) - 80\ E\^\(3\ t\) + 18\ t - 54\ t\^2)\), \(-\(209\/36\)\) - 3\ E\^\(-t\) + \(57\ E\^\(2\ t\)\)\/4 - \(40\ E\^\(3\ t\)\)\/9 + \(11\ t\)\/6 - \(9\ t\^2\)\/2}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["b", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[{ StyleBox["A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Inpute", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{-4,-2,-1},\n { 2, 6,-3},\n { 2, 4,-1}}", "Inpute"], StyleBox[";\nG[t_] = {1,Cos[t],Sin[t]};", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[TextData[{ "A solution to the associated homogeneous problem, ", StyleBox["X'[t] == A.X[t]", FontFamily->"Courier", FontWeight->"Bold"], ", was found in ", StyleBox["Problem 3", FontWeight->"Bold"], StyleBox["b", FontSlant->"Italic"], " :" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[{ "X1[t_] = {-3,1,1}E^(-3t);\nX2[t_] = ", StyleBox["{-1,2,2}", FontFamily->"Courier", FontWeight->"Bold"], "E^(2t);\nX3[t_] = ", StyleBox["{-1,2,2}", FontFamily->"Courier", FontWeight->"Bold"], " t*E^(2t) + ", StyleBox["{-1,5/2,2}", "Input"], " E^(2t);\nPsi[t_] = Transpose[{X1[t], X2[t], X3[t]}];\nIPsi[t_] = \ Inverse[Psi[t]]//Simplify;\nIPsi[t]//MatrixForm" }], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(-\(\(2\ E\^\(3\ t\)\)\/5\)\), "0", \(-\(E\^\(3\ t\)\/5\)\)}, {\(E\^\(\(-2\)\ t\)\/5\), \(\(-2\)\ E\^\(\(-2\)\ t\)\ \((1 + t)\)\), \(1\/5\ E\^\(\(-2\)\ t\)\ \((13 + 10\ t)\)\)}, {"0", \(2\ E\^\(\(-2\)\ t\)\), \(\(-2\)\ E\^\(\(-2\)\ t\)\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[TextData[{ "A particular solution is ", StyleBox["Y[t_] = Psi[t].U[t]", FontFamily->"Courier", FontWeight->"Bold"], " where ", StyleBox["U'[t] == IPsi[t].G[t]", FontFamily->"Courier", FontWeight->"Bold"], "." }], "Text"], Cell[CellGroupData[{ Cell[TextData[StyleBox["IPsi[t].G[t]//Simplify", FontFamily->"Courier", FontWeight->"Bold"]], "Input"], Cell[BoxData[ \({\(-\(1\/5\)\)\ E\^\(3\ t\)\ \((2 + Sin[t])\), \(-\(1\/5\)\)\ E\^\(\(-2\)\ t\)\ \(( \(-1\) + 10\ \((1 + t)\)\ Cos[t] - \((13 + 10\ t)\)\ Sin[t])\), 2\ E\^\(\(-2\)\ t\)\ \((Cos[t] - Sin[t])\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["U[t_] = Integrate[IPsi[t].G[t]//Simplify, t]//Simplify", "Input"], Cell[BoxData[ \({1\/150\ E\^\(3\ t\)\ \((\(-20\) + 3\ Cos[t] - 9\ Sin[t])\), 1\/10\ E\^\(\(-2\)\ t\)\ \(( \(-1\) + \((2 + 4\ t)\)\ Cos[t] - 4\ \((5 + 3\ t)\)\ Sin[t])\), \(-\(2\/5\)\)\ E\^\(\(-2\)\ t\)\ \((Cos[t] - 3\ Sin[t])\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Y[t_] = Psi[t].U[t]//Simplify", "Input"], Cell[BoxData[ \({1\/50\ \((25 + 7\ Cos[t] + 49\ Sin[t])\), \(-\(1\/3\)\) - \(29\ Cos[t]\)\/50 - \(53\ Sin[t]\)\/50, 1\/150\ \((\(-50\) - 57\ Cos[t] - 249\ Sin[t])\)}\)], "Output"] }, Open ]], Cell["The general solution to the given system is then", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t] + c3 X3[t] + Y[t]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({\(-3\)\ c1\ E\^\(\(-3\)\ t\) - c2\ E\^\(2\ t\) + c3\ \((\(-E\^\(2\ t\)\) - E\^\(2\ t\)\ t)\) + 1\/50\ \((25 + 7\ Cos[t] + 49\ Sin[t])\), \(-\(1\/3\)\) + c1\ E\^\(\(-3\)\ t\) + 2\ c2\ E\^\(2\ t\) + c3\ \((\(5\ E\^\(2\ t\)\)\/2 + 2\ E\^\(2\ t\)\ t)\) - \(29\ Cos[t]\)\/50 - \(53\ Sin[t]\)\/50, c1\ E\^\(\(-3\)\ t\) + 2\ c2\ E\^\(2\ t\) + c3\ \((2\ E\^\(2\ t\) + 2\ E\^\(2\ t\)\ t)\) + 1\/150\ \((\(-50\) - 57\ Cos[t] - 249\ Sin[t])\)}\)], "Output"] }, Open ]], Cell["Check:", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Simplify", "Input"], Cell[BoxData[ \({9\ c1\ E\^\(\(-3\)\ t\) - 2\ c2\ E\^\(2\ t\) - 3\ c3\ E\^\(2\ t\) - 2\ c3\ E\^\(2\ t\)\ t + \(49\ Cos[t]\)\/50 - \(7\ Sin[t]\)\/50, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 7\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t - \(53\ Cos[t]\)\/50 + \(29\ Sin[t]\)\/50, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 6\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t - \(83\ Cos[t]\)\/50 + \(19\ Sin[t]\)\/50}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t] + G[t]//Simplify", "Input"], Cell[BoxData[ \({9\ c1\ E\^\(\(-3\)\ t\) - 2\ c2\ E\^\(2\ t\) - 3\ c3\ E\^\(2\ t\) - 2\ c3\ E\^\(2\ t\)\ t + \(49\ Cos[t]\)\/50 - \(7\ Sin[t]\)\/50, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 7\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t - \(53\ Cos[t]\)\/50 + \(29\ Sin[t]\)\/50, \(-3\)\ c1\ E\^\(\(-3\)\ t\) + 4\ c2\ E\^\(2\ t\) + 6\ c3\ E\^\(2\ t\) + 4\ c3\ E\^\(2\ t\)\ t - \(83\ Cos[t]\)\/50 + \(19\ Sin[t]\)\/50}\)], "Output"] }, Open ]], Cell[TextData[{ "We now solve for the constants ", StyleBox["c1", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["c2", FontFamily->"Courier", FontWeight->"Bold"], " that satisfy the given initial condition." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[{ "cs = Solve[", StyleBox["X[0]=={1,1,-2}", FontFamily->"Courier", FontWeight->"Bold"], "]" }], "Input", AspectRatioFixed->True], Cell[BoxData[ \({{c1 \[Rule] 17\/150, c2 \[Rule] \(-\(71\/10\)\), c3 \[Rule] 32\/5}}\)], "Output"] }, Open ]], Cell["The solution to the initial value problem is thus", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["X[t_] = X[t] /. First[cs] //Simplify", "Input", AspectRatioFixed->True], Cell[BoxData[ \({1\/50\ \((25 - 17\ E\^\(\(-3\)\ t\) + 35\ E\^\(2\ t\) - 320\ E\^\(2\ t\)\ t + 7\ Cos[t] + 49\ Sin[t])\), 1\/150\ \(( \(-50\) + 17\ E\^\(\(-3\)\ t\) + 270\ E\^\(2\ t\) + 1920\ E\^\(2\ t\)\ t - 87\ Cos[t] - 159\ Sin[t])\), 1\/150\ \(( \(-50\) + 17\ E\^\(\(-3\)\ t\) - 210\ E\^\(2\ t\) + 1920\ E\^\(2\ t\)\ t - 57\ Cos[t] - 249\ Sin[t])\)}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["c", FontSlant->"Italic"], ")" }], "Text"], Cell[TextData[{ StyleBox["A =", FontFamily->"Courier", FontWeight->"Bold"], StyleBox[" ", "Inpute", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["{{ 5, 3,-1},\n {-16,-6,-1},\n { -4,-3, 2}}", "Inpute"], StyleBox[";\nG[t_] = {E^t,1,E^(-t)};\n", FontFamily->"Courier", FontWeight->"Bold"] }], "Input"], Cell[TextData[{ "A solution to the associated homogeneous problem, ", StyleBox["X'[t] == A.X[t]", FontFamily->"Courier", FontWeight->"Bold"], ", was found in ", StyleBox["Problem 3", FontWeight->"Bold"], StyleBox["c", FontSlant->"Italic"], " :" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ X1[t_] = {-1,2,2}E^t; X2[t_] = {-Cos[3 t],2 Cos[3 t]+Sin[3 t],Cos[3 t]}; X3[t_] = {-Sin[3 t],-Cos[3 t]+2 Sin[3 t],Sin[3 t]}; Psi[t_] = Transpose[{X1[t], X2[t], X3[t]}]; IPsi[t_] = Inverse[Psi[t]]//Simplify; IPsi[t]//MatrixForm\ \>", "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(E\^\(-t\)\), "0", \(E\^\(-t\)\)}, {\(\(-2\)\ Cos[3\ t] + 2\ Sin[3\ t]\), \(Sin[3\ t]\), \(-Cos[3\ t]\)}, {\(\(-2\)\ \((Cos[3\ t] + Sin[3\ t])\)\), \(-Cos[3\ t]\), \(-Sin[3\ t]\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["IPsi[t].G[t]//Simplify", "Input"], Cell[BoxData[ \({1 + E\^\(\(-2\)\ t\), \((\(-E\^\(-t\)\) - 2\ E\^t)\)\ Cos[3\ t] + \((1 + 2\ E\^t)\)\ Sin[3\ t], \(-Cos[3\ t]\) - E\^\(-t\)\ Sin[3\ t] - 2\ E\^t\ \((Cos[3\ t] + Sin[3\ t])\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["U[t_] = Integrate[IPsi[t].G[t]//Simplify, t]//Simplify", "Input"], Cell[BoxData[ \({\(-\(1\/2\)\)\ E\^\(\(-2\)\ t\) + t, \(-\(1\/30\)\)\ E\^\(-t\)\ \(( \((\(-3\) + 10\ E\^t + 24\ E\^\(2\ t\))\)\ Cos[3\ t] + 3\ \((3 + 4\ E\^\(2\ t\))\)\ Sin[3\ t])\), 1\/30\ E\^\(-t\)\ \(( 3\ \((3 + 4\ E\^\(2\ t\))\)\ Cos[3\ t] - \((\(-3\) + 10\ E\^t + 24\ E\^\(2\ t\))\)\ Sin[3\ t])\)}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Y[t_] = Psi[t].U[t]//Simplify", "Input"], Cell[BoxData[ \({1\/3 + \(2\ E\^\(-t\)\)\/5 + \(4\ E\^t\)\/5 - E\^t\ t, \(-\(2\/3\)\) - \(11\ E\^\(-t\)\)\/10 - 2\ E\^t + 2\ E\^t\ t, \(-\(1\/3\)\) - \(9\ E\^\(-t\)\)\/10 - \(4\ E\^t\)\/5 + 2\ E\^t\ t}\)], "Output"] }, Open ]], Cell["The general solution to the given system is then", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["X[t_] = c1 X1[t] + c2 X2[t] + c3 X3[t] + Y[t]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({1\/3 + \(2\ E\^\(-t\)\)\/5 + \(4\ E\^t\)\/5 - c1\ E\^t - E\^t\ t - c2\ Cos[3\ t] - c3\ Sin[3\ t], \(-\(2\/3\)\) - \(11\ E\^\(-t\)\)\/10 - 2\ E\^t + 2\ c1\ E\^t + 2\ E\^t\ t + c2\ \((2\ Cos[3\ t] + Sin[3\ t])\) + c3\ \((\(-Cos[3\ t]\) + 2\ Sin[3\ t])\), \(-\(1\/3\)\) - \(9\ E\^\(-t\)\)\/10 - \(4\ E\^t\)\/5 + 2\ c1\ E\^t + 2\ E\^t\ t + c2\ Cos[3\ t] + c3\ Sin[3\ t]}\)], "Output"] }, Open ]], Cell["Check:", "Text"], Cell[CellGroupData[{ Cell["X'[t]//Simplify", "Input"], Cell[BoxData[ \({\(-\(\(2\ E\^\(-t\)\)\/5\)\) - E\^t\/5 - c1\ E\^t - E\^t\ t - 3\ c3\ Cos[3\ t] + 3\ c2\ Sin[3\ t], \(11\ E\^\(-t\)\)\/10 + 2\ c1\ E\^t + 2\ E\^t\ t + 3\ \((c2 + 2\ c3)\)\ Cos[3\ t] + \((\(-6\)\ c2 + 3\ c3)\)\ Sin[3\ t], \(9\ E\^\(-t\)\)\/10 + \(6\ E\^t\)\/5 + 2\ c1\ E\^t + 2\ E\^t\ t + 3\ c3\ Cos[3\ t] - 3\ c2\ Sin[3\ t]}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["A.X[t] + G[t]//Simplify", "Input"], Cell[BoxData[ \({\(-\(\(2\ E\^\(-t\)\)\/5\)\) - E\^t\/5 - c1\ E\^t - E\^t\ t - 3\ c3\ Cos[3\ t] + 3\ c2\ Sin[3\ t], \(11\ E\^\(-t\)\)\/10 + 2\ c1\ E\^t + 2\ E\^t\ t + 3\ \((c2 + 2\ c3)\)\ Cos[3\ t] + \((\(-6\)\ c2 + 3\ c3)\)\ Sin[3\ t], \(9\ E\^\(-t\)\)\/10 + \(6\ E\^t\)\/5 + 2\ c1\ E\^t + 2\ E\^t\ t + 3\ c3\ Cos[3\ t] - 3\ c2\ Sin[3\ t]}\)], "Output"] }, Open ]], Cell[TextData[{ "We now solve for the constants ", StyleBox["c1", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["c2", FontFamily->"Courier", FontWeight->"Bold"], " that satisfy the given initial condition." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[{ "cs = Solve[", StyleBox["X[0]=={1,1,1}", FontFamily->"Courier", FontWeight->"Bold"], "]" }], "Input", AspectRatioFixed->True], Cell[BoxData[ \({{c1 \[Rule] 5\/2, c2 \[Rule] \(-\(59\/30\)\), c3 \[Rule] \(-\(37\/10\)\)}}\)], "Output"] }, Open ]], Cell["The solution to the initial value problem is thus", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["X[t_] = X[t] /. First[cs] //Simplify", "Input", AspectRatioFixed->True], Cell[BoxData[ \({1\/30\ \((10 + 12\ E\^\(-t\) - 51\ E\^t - 30\ E\^t\ t + 59\ Cos[3\ t] + 111\ Sin[3\ t])\), 1\/30\ \(( \(-20\) - 33\ E\^\(-t\) + 90\ E\^t + 60\ E\^t\ t - 7\ Cos[3\ t] - 281\ Sin[3\ t])\), 1\/30\ \(( \(-10\) - 27\ E\^\(-t\) + 126\ E\^t + 60\ E\^t\ t - 59\ Cos[3\ t] - 111\ Sin[3\ t])\)}\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Problem 4", "Subsubsection"], Cell[TextData[{ "Consider the autonomous system:\n", StyleBox[" x'[t] == 1 - x[t]y[t]\n y'[t] == x[t] - y[t]^3\n", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["a)", FontSlant->"Italic"], " Find all critical points of this system. At each critical point, \ calculate the corresponding linear system and find the eigenvalues of the \ coefficient matrix. Then identify the type and stability of the critical \ point.\n", StyleBox["b)", FontSlant->"Italic"], " Plot the vector field using ", StyleBox["PlotVectorField[]", FontFamily->"Courier", FontWeight->"Bold"], " with the options ", StyleBox["ScaleFunction->(Log[50#+1]&)", FontFamily->"Courier", FontWeight->"Bold"], " (this makes the arrows bigger near the critical points) and ", StyleBox["Frame->True", FontFamily->"Courier", FontWeight->"Bold"], ". Use the vector field plot to choose a representative sample of several \ initial points ", StyleBox["{x0,y0}", FontFamily->"Courier", FontWeight->"Bold"], ". Use ", StyleBox["NDSolve[]", FontFamily->"Courier", FontWeight->"Bold"], " to obtain numerical solutions through these points and plot the \ corresponding trajectories on a single graph. Indicate what happens to the \ trajectories for increasing ", StyleBox["t", FontFamily->"Courier", FontWeight->"Bold"], "." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Solution", "Subsubsection", CellMargins->{{Inherited, 126}, {Inherited, Inherited}}, Evaluatable->False, PageBreakWithin->Automatic, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell["\<\ F[x_, y_] = 1 - x y; G[x_, y_] = x - y^3;\ \>", "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["a)", FontSlant->"Italic"], " Find the critical points:" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["cp = Solve[{F[x,y] == 0, G[x,y] == 0}]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{x \[Rule] \(-1\), y \[Rule] \(-1\)}, {x \[Rule] \(-I\), y \[Rule] I}, {x \[Rule] I, y \[Rule] \(-I\)}, {x \[Rule] 1, y \[Rule] 1}}\)], "Output"] }, Open ]], Cell[TextData[{ "The critical points are thus ", StyleBox["{-1,-1}", FontFamily->"Courier", FontWeight->"Bold"], ", and ", StyleBox["{1,1}", FontFamily->"Courier", FontWeight->"Bold"], ". To analyze them we need to examine the matrix of partial derivative \ evaluated at each." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ A = {{D[F[x,y],x], D[F[x,y],y]}, {D[G[x,y],x], D[G[x,y],y]}}; A//MatrixForm\ \>", "Input", AspectRatioFixed->True], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(-y\), \(-x\)}, {"1", \(\(-3\)\ y\^2\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[TextData[{ "At the critical point ", StyleBox["{-1,-1}", FontFamily->"Courier", FontWeight->"Bold"], ":" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ A1 = A /. cp[[1]]; A1//MatrixForm\ \>", "Input", AspectRatioFixed->True], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {"1", "1"}, {"1", \(-3\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Eigensystem[A1]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{\(-1\) - \@5, \(-1\) + \@5}, {{2 - \@5, 1}, {2 + \@5, 1}}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["N[%]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{\(-3.2360679774997898`\), 1.2360679774997898`}, {{\(-0.236067977499789805`\), 1.`}, { 4.2360679774997898`, 1.`}}}\)], "Output"] }, Open ]], Cell[TextData[{ "Since the eigenvalues have opposite signs, the point ", StyleBox["{-1,-1}", FontFamily->"Courier", FontWeight->"Bold"], " is unstable saddle point.\nAt the point ", StyleBox["{1,1}", FontFamily->"Courier", FontWeight->"Bold"], ":" }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ A2 = A /. cp[[4]]; A2//MatrixForm\ \>", "Input", AspectRatioFixed->True], Cell[BoxData[ TagBox[ RowBox[{"(", GridBox[{ {\(-1\), \(-1\)}, {"1", \(-3\)} }], ")"}], (MatrixForm[ #]&)]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Eigensystem[A2]", "Input", AspectRatioFixed->True], Cell[BoxData[ \({{\(-2\), \(-2\)}, {{1, 1}, {0, 0}}}\)], "Output"] }, Open ]], Cell[TextData[{ "Since there is only one independent eigenvector, the point ", StyleBox["{1,1}", FontFamily->"Courier", FontWeight->"Bold"], " is a node (proper or improper) or a spiral point. It is asymtotically \ stable since both eigenvalues are negative." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox["b)", FontSlant->"Italic"]], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["?PlotVectorField", "Input", AspectRatioFixed->True], Cell[BoxData[ \("PlotVectorField[f, {x, x0, x1, (xu)}, {y, y0, y1, (yu)}, (options)] \ produces a vector field plot of the two-dimensional vector function f."\)], "Print"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ v = PlotVectorField[{F[x,y],G[x,y]},{x,-2,2},{y,-2,2}, ScaleFunction->(Log[50#+1]&), Frame->True]\ \>", "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .91776 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.501983 0.218514 0.45888 0.218514 [ [.06495 -0.0125 -6 -9 ] [.06495 -0.0125 6 0 ] [.28347 -0.0125 -6 -9 ] [.28347 -0.0125 6 0 ] [.50198 -0.0125 -3 -9 ] [.50198 -0.0125 3 0 ] [.7205 -0.0125 -3 -9 ] [.7205 -0.0125 3 0 ] [.93901 -0.0125 -3 -9 ] [.93901 -0.0125 3 0 ] [ 0 0 -0.125 0 ] [-0.0125 .02185 -12 -4.5 ] [-0.0125 .02185 0 4.5 ] [-0.0125 .24037 -12 -4.5 ] [-0.0125 .24037 0 4.5 ] [-0.0125 .45888 -6 -4.5 ] [-0.0125 .45888 0 4.5 ] [-0.0125 .67739 -6 -4.5 ] [-0.0125 .67739 0 4.5 ] [-0.0125 .89591 -6 -4.5 ] [-0.0125 .89591 0 4.5 ] [ 0 0 -0.125 0 ] [ 0 .91776 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 .91776 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .06495 0 m .06495 .00625 L s [(-2)] .06495 -0.0125 0 1 Mshowa .28347 0 m .28347 .00625 L s [(-1)] .28347 -0.0125 0 1 Mshowa .50198 0 m .50198 .00625 L s [(0)] .50198 -0.0125 0 1 Mshowa .7205 0 m .7205 .00625 L s [(1)] .7205 -0.0125 0 1 Mshowa .93901 0 m .93901 .00625 L s [(2)] .93901 -0.0125 0 1 Mshowa .125 Mabswid .10866 0 m .10866 .00375 L s .15236 0 m .15236 .00375 L s .19606 0 m .19606 .00375 L s .23977 0 m .23977 .00375 L s .32717 0 m .32717 .00375 L s .37087 0 m .37087 .00375 L s .41458 0 m .41458 .00375 L s .45828 0 m .45828 .00375 L s .54569 0 m .54569 .00375 L s .58939 0 m .58939 .00375 L s .63309 0 m .63309 .00375 L s .67679 0 m .67679 .00375 L s .7642 0 m .7642 .00375 L s .8079 0 m .8079 .00375 L s .85161 0 m .85161 .00375 L s .89531 0 m .89531 .00375 L s .02125 0 m .02125 .00375 L s .98271 0 m .98271 .00375 L s .25 Mabswid 0 0 m 1 0 L s 0 .02185 m .00625 .02185 L s [(-2)] -0.0125 .02185 1 0 Mshowa 0 .24037 m .00625 .24037 L s [(-1)] -0.0125 .24037 1 0 Mshowa 0 .45888 m .00625 .45888 L s [(0)] -0.0125 .45888 1 0 Mshowa 0 .67739 m .00625 .67739 L s [(1)] -0.0125 .67739 1 0 Mshowa 0 .89591 m .00625 .89591 L s [(2)] -0.0125 .89591 1 0 Mshowa .125 Mabswid 0 .06555 m .00375 .06555 L s 0 .10926 m .00375 .10926 L s 0 .15296 m .00375 .15296 L s 0 .19666 m .00375 .19666 L s 0 .28407 m .00375 .28407 L s 0 .32777 m .00375 .32777 L s 0 .37147 m .00375 .37147 L s 0 .41518 m .00375 .41518 L s 0 .50258 m .00375 .50258 L s 0 .54629 m .00375 .54629 L s 0 .58999 m .00375 .58999 L s 0 .63369 m .00375 .63369 L s 0 .7211 m .00375 .7211 L s 0 .7648 m .00375 .7648 L s 0 .8085 m .00375 .8085 L s 0 .85221 m .00375 .85221 L s .25 Mabswid 0 0 m 0 .91776 L s .06495 .91151 m .06495 .91776 L s .28347 .91151 m .28347 .91776 L s .50198 .91151 m .50198 .91776 L s .7205 .91151 m .7205 .91776 L s .93901 .91151 m .93901 .91776 L s .125 Mabswid .10866 .91401 m .10866 .91776 L s .15236 .91401 m .15236 .91776 L s .19606 .91401 m .19606 .91776 L s .23977 .91401 m .23977 .91776 L s .32717 .91401 m .32717 .91776 L s .37087 .91401 m .37087 .91776 L s .41458 .91401 m .41458 .91776 L s .45828 .91401 m .45828 .91776 L s .54569 .91401 m .54569 .91776 L s .58939 .91401 m .58939 .91776 L s .63309 .91401 m .63309 .91776 L s .67679 .91401 m .67679 .91776 L s .7642 .91401 m .7642 .91776 L s .8079 .91401 m .8079 .91776 L s .85161 .91401 m .85161 .91776 L s .89531 .91401 m .89531 .91776 L s .02125 .91401 m .02125 .91776 L s .98271 .91401 m .98271 .91776 L s .25 Mabswid 0 .91776 m 1 .91776 L s .99375 .02185 m 1 .02185 L s .99375 .24037 m 1 .24037 L s .99375 .45888 m 1 .45888 L s .99375 .67739 m 1 .67739 L s .99375 .89591 m 1 .89591 L s .125 Mabswid .99625 .06555 m 1 .06555 L s .99625 .10926 m 1 .10926 L s .99625 .15296 m 1 .15296 L s .99625 .19666 m 1 .19666 L s .99625 .28407 m 1 .28407 L s .99625 .32777 m 1 .32777 L s .99625 .37147 m 1 .37147 L s .99625 .41518 m 1 .41518 L s .99625 .50258 m 1 .50258 L s .99625 .54629 m 1 .54629 L s .99625 .58999 m 1 .58999 L s .99625 .63369 m 1 .63369 L s .99625 .7211 m 1 .7211 L s .99625 .7648 m 1 .7648 L s .99625 .8085 m 1 .8085 L s .99625 .85221 m 1 .85221 L s .25 Mabswid 1 0 m 1 .91776 L s % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto fill -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto -0.02 0.005 lineto stroke } ifelse grestore } def % End of user PostScript .0001 w .06495 .02185 m .03928 .0732 L s % Start of user PostScript -2. -2. -2.11748 -1.76503 MAarrowhead1 % End of user PostScript .06495 .08428 m .03245 .12494 L s % Start of user PostScript -2. -1.71429 -2.14873 -1.52824 MAarrowhead1 % End of user PostScript .06495 .14672 m .02381 .167 L s % Start of user PostScript -2. -1.42857 -2.18829 -1.33575 MAarrowhead1 % End of user PostScript .06495 .20915 m .02595 .19376 L s % Start of user PostScript -2. -1.14286 -2.1785 -1.21329 MAarrowhead1 % End of user PostScript .06495 .27158 m .04507 .23344 L s % Start of user PostScript -2. -0.857143 -2.091 -1.03171 MAarrowhead1 % End of user PostScript .06495 .33401 m .06145 .28955 L s % Start of user PostScript -2. -0.571429 -2.01603 -0.774938 MAarrowhead1 % End of user PostScript .06495 .39645 m .07463 .35184 L s % Start of user PostScript -2. -0.285714 -1.95574 -0.489851 MAarrowhead1 % End of user PostScript .06495 .45888 m .08581 .41718 L s % Start of user PostScript -2. 0 -1.90458 -0.190842 MAarrowhead1 % End of user PostScript .06495 .52131 m .09437 .48344 L s % Start of user PostScript -2. 0.285714 -1.86539 0.11239 MAarrowhead1 % End of user PostScript .06495 .58375 m .09974 .54825 L s % Start of user PostScript -2. 0.571429 -1.8408 0.408984 MAarrowhead1 % End of user PostScript .06495 .64618 m .10213 .61016 L s % Start of user PostScript -2. 0.857143 -1.82986 0.6923 MAarrowhead1 % End of user PostScript .06495 .70861 m .10203 .6692 L s % Start of user PostScript -2. 1.14286 -1.83035 0.962515 MAarrowhead1 % End of user PostScript .06495 .77104 m .09996 .72643 L s % Start of user PostScript -2. 1.42857 -1.8398 1.22442 MAarrowhead1 % End of user PostScript .06495 .83348 m .09665 .7831 L s % Start of user PostScript -2. 1.71429 -1.85494 1.48375 MAarrowhead1 % End of user PostScript .06495 .89591 m .09288 .84007 L s % Start of user PostScript -2. 2. -1.87222 1.74445 MAarrowhead1 % End of user PostScript .12739 .02185 m .10668 .07544 L s % Start of user PostScript -1.71429 -2. -1.80904 -1.75476 MAarrowhead1 % End of user PostScript .12739 .08428 m .10121 .12915 L s % Start of user PostScript -1.71429 -1.71429 -1.83406 -1.50896 MAarrowhead1 % End of user PostScript .12739 .14672 m .09279 .1754 L s % Start of user PostScript -1.71429 -1.42857 -1.87262 -1.29732 MAarrowhead1 % End of user PostScript .12739 .20915 m .08974 .20045 L s % Start of user PostScript -1.71429 -1.14286 -1.88658 -1.18266 MAarrowhead1 % End of user PostScript .12739 .27158 m .11134 .2345 L s % Start of user PostScript -1.71429 -0.857143 -1.78774 -1.02686 MAarrowhead1 % End of user PostScript .12739 .33401 m .12796 .29111 L s % Start of user PostScript -1.71429 -0.571429 -1.71166 -0.767767 MAarrowhead1 % End of user PostScript .12739 .39645 m .14019 .35402 L s % Start of user PostScript -1.71429 -0.285714 -1.6557 -0.479893 MAarrowhead1 % End of user PostScript .12739 .45888 m .15029 .41961 L s % Start of user PostScript -1.71429 0 -1.60946 -0.179694 MAarrowhead1 % End of user PostScript .12739 .52131 m .15788 .48574 L s % Start of user PostScript -1.71429 0.285714 -1.57473 0.12294 MAarrowhead1 % End of user PostScript .12739 .58375 m .16246 .55006 L s % Start of user PostScript -1.71429 0.571429 -1.55376 0.41729 MAarrowhead1 % End of user PostScript .12739 .64618 m .16419 .61124 L s % Start of user PostScript -1.71429 0.857143 -1.54587 0.697273 MAarrowhead1 % End of user PostScript .12739 .70861 m .16345 .66953 L s % Start of user PostScript -1.71429 1.14286 -1.54925 0.964004 MAarrowhead1 % End of user PostScript .12739 .77104 m .1608 .72619 L s % Start of user PostScript -1.71429 1.42857 -1.56138 1.22332 MAarrowhead1 % End of user PostScript .12739 .83348 m .15707 .78259 L s % Start of user PostScript -1.71429 1.71429 -1.57845 1.48142 MAarrowhead1 % End of user PostScript .12739 .89591 m .1531 .83951 L s % Start of user PostScript -1.71429 2. -1.59663 1.74192 MAarrowhead1 % End of user PostScript .18982 .02185 m .17416 .07726 L s % Start of user PostScript -1.42857 -2. -1.50023 -1.74643 MAarrowhead1 % End of user PostScript .18982 .08428 m .17043 .13259 L s % Start of user PostScript -1.42857 -1.71429 -1.51731 -1.49324 MAarrowhead1 % End of user PostScript .18982 .14672 m .16425 .18324 L s % Start of user PostScript -1.42857 -1.42857 -1.54558 -1.26142 MAarrowhead1 % End of user PostScript .18982 .20915 m .15556 .21262 L s % Start of user PostScript -1.42857 -1.14286 -1.58536 -1.12696 MAarrowhead1 % End of user PostScript .18982 .27158 m .17981 .23597 L s % Start of user PostScript -1.42857 -0.857143 -1.47437 -1.02011 MAarrowhead1 % End of user PostScript .18982 .33401 m .19582 .29346 L s % Start of user PostScript -1.42857 -0.571429 -1.40112 -0.757028 MAarrowhead1 % End of user PostScript .18982 .39645 m .20647 .35692 L s % Start of user PostScript -1.42857 -0.285714 -1.35239 -0.466594 MAarrowhead1 % End of user PostScript .18982 .45888 m .21516 .42267 L s % Start of user PostScript -1.42857 0 -1.31259 -0.165693 MAarrowhead1 % End of user PostScript .18982 .52131 m .2216 .48855 L s % Start of user PostScript -1.42857 0.285714 -1.28315 0.135773 MAarrowhead1 % End of user PostScript .18982 .58375 m .22527 .55222 L s % Start of user PostScript -1.42857 0.571429 -1.26634 0.427161 MAarrowhead1 % End of user PostScript .18982 .64618 m .22623 .61249 L s % Start of user PostScript -1.42857 0.857143 -1.26196 0.702979 MAarrowhead1 % End of user PostScript .18982 .70861 m .22474 .66987 L s % Start of user PostScript -1.42857 1.14286 -1.26878 0.965549 MAarrowhead1 % End of user PostScript .18982 .77104 m .22141 .72591 L s % Start of user PostScript -1.42857 1.42857 -1.28399 1.22202 MAarrowhead1 % End of user PostScript .18982 .83348 m .21724 .78206 L s % Start of user PostScript -1.42857 1.71429 -1.30307 1.47898 MAarrowhead1 % End of user PostScript .18982 .89591 m .21311 .83897 L s % Start of user PostScript -1.42857 2. -1.32198 1.73944 MAarrowhead1 % End of user PostScript .25225 .02185 m .2416 .07865 L s % Start of user PostScript -1.14286 -2. -1.1916 -1.74006 MAarrowhead1 % End of user PostScript .25225 .08428 m .23973 .13512 L s % Start of user PostScript -1.14286 -1.71429 -1.20014 -1.48166 MAarrowhead1 % End of user PostScript .25225 .14672 m .23715 .18904 L s % Start of user PostScript -1.14286 -1.42857 -1.21199 -1.23488 MAarrowhead1 % End of user PostScript .25225 .20915 m .23154 .23282 L s % Start of user PostScript -1.14286 -1.14286 -1.23765 -1.03452 MAarrowhead1 % End of user PostScript .25225 .27158 m .25354 .23921 L s % Start of user PostScript -1.14286 -0.857143 -1.13696 -1.00529 MAarrowhead1 % End of user PostScript .25225 .33401 m .26554 .29739 L s % Start of user PostScript -1.14286 -0.571429 -1.08205 -0.739023 MAarrowhead1 % End of user PostScript .25225 .39645 m .27359 .36099 L s % Start of user PostScript -1.14286 -0.285714 -1.04523 -0.448002 MAarrowhead1 % End of user PostScript .25225 .45888 m .28047 .42663 L s % Start of user PostScript -1.14286 0 -1.01373 -0.14757 MAarrowhead1 % End of user PostScript .25225 .52131 m .28554 .49205 L s % Start of user PostScript -1.14286 0.285714 -0.990527 0.151798 MAarrowhead1 % End of user PostScript .25225 .58375 m .28818 .55485 L s % Start of user PostScript -1.14286 0.571429 -0.978425 0.439187 MAarrowhead1 % End of user PostScript .25225 .64618 m .28824 .61395 L s % Start of user PostScript -1.14286 0.857143 -0.978144 0.709653 MAarrowhead1 % End of user PostScript .25225 .70861 m .28585 .67022 L s % Start of user PostScript -1.14286 1.14286 -0.98911 0.967146 MAarrowhead1 % End of user PostScript .25225 .77104 m .28174 .72558 L s % Start of user PostScript -1.14286 1.42857 -1.00789 1.22052 MAarrowhead1 % End of user PostScript .25225 .83348 m .27713 .78151 L s % Start of user PostScript -1.14286 1.71429 -1.029 1.47647 MAarrowhead1 % End of user PostScript .25225 .89591 m .2729 .83846 L s % Start of user PostScript -1.14286 2. -1.04837 1.73708 MAarrowhead1 % End of user PostScript .31469 .02185 m .30891 .07963 L s % Start of user PostScript -0.857143 -2. -0.883586 -1.73556 MAarrowhead1 % End of user PostScript .31469 .08428 m .30879 .13677 L s % Start of user PostScript -0.857143 -1.71429 -0.884112 -1.47408 MAarrowhead1 % End of user PostScript .31469 .14672 m .30971 .19232 L s % Start of user PostScript -0.857143 -1.42857 -0.879904 -1.21988 MAarrowhead1 % End of user PostScript .31469 .20915 m .31579 .24357 L s % Start of user PostScript -0.857143 -1.14286 -0.852085 -0.985349 MAarrowhead1 % End of user PostScript .31469 .27158 m .33653 .25286 L s % Start of user PostScript -0.857143 -0.857143 -0.757171 -0.942833 MAarrowhead1 % End of user PostScript .31469 .33401 m .33717 .30446 L s % Start of user PostScript -0.857143 -0.571429 -0.75423 -0.706686 MAarrowhead1 % End of user PostScript .31469 .39645 m .34149 .36685 L s % Start of user PostScript -0.857143 -0.285714 -0.734477 -0.421168 MAarrowhead1 % End of user PostScript .31469 .45888 m .34617 .4319 L s % Start of user PostScript -0.857143 0 -0.713076 -0.123486 MAarrowhead1 % End of user PostScript .31469 .52131 m .3497 .49655 L s % Start of user PostScript -0.857143 0.285714 -0.696903 0.172383 MAarrowhead1 % End of user PostScript .31469 .58375 m .35122 .55815 L s % Start of user PostScript -0.857143 0.571429 -0.689951 0.454296 MAarrowhead1 % End of user PostScript .31469 .64618 m .35024 .6157 L s % Start of user PostScript -0.857143 0.857143 -0.69441 0.717658 MAarrowhead1 % End of user PostScript .31469 .70861 m .34673 .67057 L s % Start of user PostScript -0.857143 1.14286 -0.7105 0.968786 MAarrowhead1 % End of user PostScript .31469 .77104 m .34171 .72521 L s % Start of user PostScript -0.857143 1.42857 -0.733452 1.2188 MAarrowhead1 % End of user PostScript .31469 .83348 m .33668 .78097 L s % Start of user PostScript -0.857143 1.71429 -0.756485 1.47399 MAarrowhead1 % End of user PostScript .31469 .89591 m .33244 .83799 L s % Start of user PostScript -0.857143 2. -0.775911 1.73493 MAarrowhead1 % End of user PostScript .37712 .02185 m .37599 .08025 L s % Start of user PostScript -0.571429 -2. -0.576568 -1.73274 MAarrowhead1 % End of user PostScript .37712 .08428 m .37736 .13769 L s % Start of user PostScript -0.571429 -1.71429 -0.570312 -1.46988 MAarrowhead1 % End of user PostScript .37712 .14672 m .3808 .19369 L s % Start of user PostScript -0.571429 -1.42857 -0.554585 -1.21362 MAarrowhead1 % End of user PostScript .37712 .20915 m .39074 .24531 L s % Start of user PostScript -0.571429 -1.14286 -0.509109 -0.97737 MAarrowhead1 % End of user PostScript .37712 .27158 m .40931 .27526 L s % Start of user PostScript -0.571429 -0.857143 -0.424122 -0.840308 MAarrowhead1 % End of user PostScript .37712 .33401 m .40867 .31598 L s % Start of user PostScript -0.571429 -0.571429 -0.42703 -0.653942 MAarrowhead1 % End of user PostScript .37712 .39645 m .40957 .37519 L s % Start of user PostScript -0.571429 -0.285714 -0.422917 -0.382997 MAarrowhead1 % End of user PostScript .37712 .45888 m .41199 .43896 L s % Start of user PostScript -0.571429 0 -0.411856 -0.0911845 MAarrowhead1 % End of user PostScript .37712 .52131 m .41397 .50247 L s % Start of user PostScript -0.571429 0.285714 -0.402802 0.199499 MAarrowhead1 % End of user PostScript .37712 .58375 m .41437 .56246 L s % Start of user PostScript -0.571429 0.571429 -0.400943 0.474009 MAarrowhead1 % End of user PostScript .37712 .64618 m .41223 .61787 L s % Start of user PostScript -0.571429 0.857143 -0.410744 0.727589 MAarrowhead1 % End of user PostScript .37712 .70861 m .40729 .67094 L s % Start of user PostScript -0.571429 1.14286 -0.433357 0.97045 MAarrowhead1 % End of user PostScript .37712 .77104 m .40121 .72479 L s % Start of user PostScript -0.571429 1.42857 -0.461165 1.21689 MAarrowhead1 % End of user PostScript .37712 .83348 m .39583 .78046 L s % Start of user PostScript -0.571429 1.71429 -0.485803 1.47166 MAarrowhead1 % End of user PostScript .37712 .89591 m .3917 .83759 L s % Start of user PostScript -0.571429 2. -0.504705 1.73311 MAarrowhead1 % End of user PostScript .43955 .02185 m .44281 .08056 L s % Start of user PostScript -0.285714 -2. -0.270789 -1.73135 MAarrowhead1 % End of user PostScript .43955 .08428 m .44532 .13805 L s % Start of user PostScript -0.285714 -1.71429 -0.259299 -1.46825 MAarrowhead1 % End of user PostScript .43955 .14672 m .45019 .19399 L s % Start of user PostScript -0.285714 -1.42857 -0.237029 -1.21225 MAarrowhead1 % End of user PostScript .43955 .20915 m .45998 .24577 L s % Start of user PostScript -0.285714 -1.14286 -0.192213 -0.975284 MAarrowhead1 % End of user PostScript .43955 .27158 m .47321 .28692 L s % Start of user PostScript -0.285714 -0.857143 -0.131667 -0.786959 MAarrowhead1 % End of user PostScript .43955 .33401 m .47643 .32965 L s % Start of user PostScript -0.285714 -0.571429 -0.116937 -0.591423 MAarrowhead1 % End of user PostScript .43955 .39645 m .47642 .38591 L s % Start of user PostScript -0.285714 -0.285714 -0.116972 -0.333926 MAarrowhead1 % End of user PostScript .43955 .45888 m .47721 .44812 L s % Start of user PostScript -0.285714 0 -0.113348 -0.0492475 MAarrowhead1 % End of user PostScript .43955 .52131 m .47795 .51034 L s % Start of user PostScript -0.285714 0.285714 -0.110003 0.235511 MAarrowhead1 % End of user PostScript .43955 .58375 m .47754 .56832 L s % Start of user PostScript -0.285714 0.571429 -0.111878 0.500848 MAarrowhead1 % End of user PostScript .43955 .64618 m .47421 .62069 L s % Start of user PostScript -0.285714 0.857143 -0.127118 0.740517 MAarrowhead1 % End of user PostScript .43955 .70861 m .46738 .6713 L s % Start of user PostScript -0.285714 1.14286 -0.158352 0.972107 MAarrowhead1 % End of user PostScript .43955 .77104 m .46009 .72436 L s % Start of user PostScript -0.285714 1.42857 -0.191728 1.21491 MAarrowhead1 % End of user PostScript .43955 .83348 m .45451 .78003 L s % Start of user PostScript -0.285714 1.71429 -0.217264 1.46969 MAarrowhead1 % End of user PostScript .43955 .89591 m .45067 .8373 L s % Start of user PostScript -0.285714 2. -0.234843 1.73177 MAarrowhead1 % End of user PostScript .50198 .02185 m .50933 .08061 L s % Start of user PostScript 0 -2. 0.0336113 -1.73111 MAarrowhead1 % End of user PostScript .50198 .08428 m .51265 .13801 L s % Start of user PostScript 0 -1.71429 0.0488083 -1.46839 MAarrowhead1 % End of user PostScript .50198 .14672 m .51813 .19379 L s % Start of user PostScript 0 -1.42857 0.0738917 -1.21314 MAarrowhead1 % End of user PostScript .50198 .20915 m .52674 .24611 L s % Start of user PostScript 0 -1.14286 0.113311 -0.973716 MAarrowhead1 % End of user PostScript .50198 .27158 m .53618 .29312 L s % Start of user PostScript 0 -0.857143 0.156486 -0.758597 MAarrowhead1 % End of user PostScript .50198 .33401 m .54028 .34116 L s % Start of user PostScript 0 -0.571429 0.175259 -0.538727 MAarrowhead1 % End of user PostScript .50198 .39645 m .54077 .39735 L s % Start of user PostScript 0 -0.285714 0.17749 -0.281575 MAarrowhead1 % End of user PostScript .50198 .45888 m .54078 .45888 L s % Start of user PostScript 0 0 0.177526 0 MAarrowhead1 % End of user PostScript .50198 .52131 m .54077 .52041 L s % Start of user PostScript 0 0.285714 0.17749 0.281575 MAarrowhead1 % End of user PostScript .50198 .58375 m .54028 .5766 L s % Start of user PostScript 0 0.571429 0.175259 0.538727 MAarrowhead1 % End of user PostScript .50198 .64618 m .53618 .62464 L s % Start of user PostScript 0 0.857143 0.156486 0.758597 MAarrowhead1 % End of user PostScript .50198 .70861 m .52674 .67165 L s % Start of user PostScript 0 1.14286 0.113311 0.973716 MAarrowhead1 % End of user PostScript .50198 .77104 m .51813 .72397 L s % Start of user PostScript 0 1.42857 0.0738917 1.21314 MAarrowhead1 % End of user PostScript .50198 .83348 m .51265 .77975 L s % Start of user PostScript 0 1.71429 0.0488083 1.46839 MAarrowhead1 % End of user PostScript .50198 .89591 m .50933 .83715 L s % Start of user PostScript 0 2. 0.0336113 1.73111 MAarrowhead1 % End of user PostScript .56442 .02185 m .57553 .08046 L s % Start of user PostScript 0.285714 -2. 0.336585 -1.73177 MAarrowhead1 % End of user PostScript .56442 .08428 m .57937 .13773 L s % Start of user PostScript 0.285714 -1.71429 0.354165 -1.46969 MAarrowhead1 % End of user PostScript .56442 .14672 m .58495 .1934 L s % Start of user PostScript 0.285714 -1.42857 0.379701 -1.21491 MAarrowhead1 % End of user PostScript .56442 .20915 m .59225 .24646 L s % Start of user PostScript 0.285714 -1.14286 0.413077 -0.972107 MAarrowhead1 % End of user PostScript .56442 .27158 m .59907 .29707 L s % Start of user PostScript 0.285714 -0.857143 0.444311 -0.740517 MAarrowhead1 % End of user PostScript .56442 .33401 m .6024 .34944 L s % Start of user PostScript 0.285714 -0.571429 0.459551 -0.500848 MAarrowhead1 % End of user PostScript .56442 .39645 m .60281 .40742 L s % Start of user PostScript 0.285714 -0.285714 0.461425 -0.235511 MAarrowhead1 % End of user PostScript .56442 .45888 m .60208 .46964 L s % Start of user PostScript 0.285714 0 0.45808 0.0492475 MAarrowhead1 % End of user PostScript .56442 .52131 m .60129 .53185 L s % Start of user PostScript 0.285714 0.285714 0.454456 0.333926 MAarrowhead1 % End of user PostScript .56442 .58375 m .6013 .58811 L s % Start of user PostScript 0.285714 0.571429 0.454492 0.591423 MAarrowhead1 % End of user PostScript .56442 .64618 m .59808 .63084 L s % Start of user PostScript 0.285714 0.857143 0.439762 0.786959 MAarrowhead1 % End of user PostScript .56442 .70861 m .58485 .67199 L s % Start of user PostScript 0.285714 1.14286 0.379215 0.975284 MAarrowhead1 % End of user PostScript .56442 .77104 m .57505 .72377 L s % Start of user PostScript 0.285714 1.42857 0.3344 1.21225 MAarrowhead1 % End of user PostScript .56442 .83348 m .57019 .77971 L s % Start of user PostScript 0.285714 1.71429 0.312129 1.46825 MAarrowhead1 % End of user PostScript .56442 .89591 m .56768 .8372 L s % Start of user PostScript 0.285714 2. 0.300639 1.73135 MAarrowhead1 % End of user PostScript .62685 .02185 m .64143 .08017 L s % Start of user PostScript 0.571429 -2. 0.638152 -1.73311 MAarrowhead1 % End of user PostScript .62685 .08428 m .64556 .1373 L s % Start of user PostScript 0.571429 -1.71429 0.657054 -1.47166 MAarrowhead1 % End of user PostScript .62685 .14672 m .65094 .19297 L s % Start of user PostScript 0.571429 -1.42857 0.681692 -1.21689 MAarrowhead1 % End of user PostScript .62685 .20915 m .65702 .24682 L s % Start of user PostScript 0.571429 -1.14286 0.709501 -0.97045 MAarrowhead1 % End of user PostScript .62685 .27158 m .66196 .29989 L s % Start of user PostScript 0.571429 -0.857143 0.732113 -0.727589 MAarrowhead1 % End of user PostScript .62685 .33401 m .6641 .3553 L s % Start of user PostScript 0.571429 -0.571429 0.741914 -0.474009 MAarrowhead1 % End of user PostScript .62685 .39645 m .6637 .41529 L s % Start of user PostScript 0.571429 -0.285714 0.740055 -0.199499 MAarrowhead1 % End of user PostScript .62685 .45888 m .66172 .47881 L s % Start of user PostScript 0.571429 0 0.731002 0.0911845 MAarrowhead1 % End of user PostScript .62685 .52131 m .6593 .54257 L s % Start of user PostScript 0.571429 0.285714 0.71994 0.382997 MAarrowhead1 % End of user PostScript .62685 .58375 m .6584 .60178 L s % Start of user PostScript 0.571429 0.571429 0.715828 0.653942 MAarrowhead1 % End of user PostScript .62685 .64618 m .65904 .6425 L s % Start of user PostScript 0.571429 0.857143 0.718735 0.840308 MAarrowhead1 % End of user PostScript .62685 .70861 m .64047 .67245 L s % Start of user PostScript 0.571429 1.14286 0.633748 0.97737 MAarrowhead1 % End of user PostScript .62685 .77104 m .63053 .72407 L s % Start of user PostScript 0.571429 1.42857 0.588272 1.21362 MAarrowhead1 % End of user PostScript .62685 .83348 m .62709 .78007 L s % Start of user PostScript 0.571429 1.71429 0.572545 1.46988 MAarrowhead1 % End of user PostScript .62685 .89591 m .62573 .83751 L s % Start of user PostScript 0.571429 2. 0.566289 1.73274 MAarrowhead1 % End of user PostScript .68928 .02185 m .70703 .07977 L s % Start of user PostScript 0.857143 -2. 0.938375 -1.73493 MAarrowhead1 % End of user PostScript .68928 .08428 m .71128 .13679 L s % Start of user PostScript 0.857143 -1.71429 0.957801 -1.47399 MAarrowhead1 % End of user PostScript .68928 .14672 m .71631 .19256 L s % Start of user PostScript 0.857143 -1.42857 0.980834 -1.2188 MAarrowhead1 % End of user PostScript .68928 .20915 m .72132 .24719 L s % Start of user PostScript 0.857143 -1.14286 1.00379 -0.968786 MAarrowhead1 % End of user PostScript .68928 .27158 m .72484 .30206 L s % Start of user PostScript 0.857143 -0.857143 1.01988 -0.717658 MAarrowhead1 % End of user PostScript .68928 .33401 m .72581 .35961 L s % Start of user PostScript 0.857143 -0.571429 1.02433 -0.454296 MAarrowhead1 % End of user PostScript .68928 .39645 m .7243 .42121 L s % Start of user PostScript 0.857143 -0.285714 1.01738 -0.172383 MAarrowhead1 % End of user PostScript .68928 .45888 m .72076 .48586 L s % Start of user PostScript 0.857143 0 1.00121 0.123486 MAarrowhead1 % End of user PostScript .68928 .52131 m .71609 .55091 L s % Start of user PostScript 0.857143 0.285714 0.979809 0.421168 MAarrowhead1 % End of user PostScript .68928 .58375 m .71177 .6133 L s % Start of user PostScript 0.857143 0.571429 0.960056 0.706686 MAarrowhead1 % End of user PostScript .68928 .64618 m .71113 .6649 L s % Start of user PostScript 0.857143 0.857143 0.957115 0.942833 MAarrowhead1 % End of user PostScript .68928 .70861 m .69039 .67419 L s % Start of user PostScript 0.857143 1.14286 0.8622 0.985349 MAarrowhead1 % End of user PostScript .68928 .77104 m .68431 .72544 L s % Start of user PostScript 0.857143 1.42857 0.834382 1.21988 MAarrowhead1 % End of user PostScript .68928 .83348 m .68339 .78099 L s % Start of user PostScript 0.857143 1.71429 0.830174 1.47408 MAarrowhead1 % End of user PostScript .68928 .89591 m .6835 .83813 L s % Start of user PostScript 0.857143 2. 0.830699 1.73556 MAarrowhead1 % End of user PostScript .75171 .02185 m .77236 .0793 L s % Start of user PostScript 1.14286 -2. 1.23734 -1.73708 MAarrowhead1 % End of user PostScript .75171 .08428 m .77659 .13625 L s % Start of user PostScript 1.14286 -1.71429 1.25672 -1.47647 MAarrowhead1 % End of user PostScript .75171 .14672 m .78121 .19218 L s % Start of user PostScript 1.14286 -1.42857 1.27782 -1.22052 MAarrowhead1 % End of user PostScript .75171 .20915 m .78531 .24754 L s % Start of user PostScript 1.14286 -1.14286 1.2966 -0.967146 MAarrowhead1 % End of user PostScript .75171 .27158 m .78771 .30381 L s % Start of user PostScript 1.14286 -0.857143 1.30757 -0.709653 MAarrowhead1 % End of user PostScript .75171 .33401 m .78764 .36291 L s % Start of user PostScript 1.14286 -0.571429 1.30729 -0.439187 MAarrowhead1 % End of user PostScript .75171 .39645 m .785 .42571 L s % Start of user PostScript 1.14286 -0.285714 1.29519 -0.151798 MAarrowhead1 % End of user PostScript .75171 .45888 m .77993 .49113 L s % Start of user PostScript 1.14286 0 1.27198 0.14757 MAarrowhead1 % End of user PostScript .75171 .52131 m .77305 .55678 L s % Start of user PostScript 1.14286 0.285714 1.24048 0.448002 MAarrowhead1 % End of user PostScript .75171 .58375 m .765 .62037 L s % Start of user PostScript 1.14286 0.571429 1.20366 0.739023 MAarrowhead1 % End of user PostScript .75171 .64618 m .753 .67855 L s % Start of user PostScript 1.14286 0.857143 1.14875 1.00529 MAarrowhead1 % End of user PostScript .75171 .70861 m .731 .68494 L s % Start of user PostScript 1.14286 1.14286 1.04807 1.03452 MAarrowhead1 % End of user PostScript .75171 .77104 m .73661 .72872 L s % Start of user PostScript 1.14286 1.42857 1.07373 1.23488 MAarrowhead1 % End of user PostScript .75171 .83348 m .7392 .78264 L s % Start of user PostScript 1.14286 1.71429 1.08557 1.48166 MAarrowhead1 % End of user PostScript .75171 .89591 m .74106 .83911 L s % Start of user PostScript 1.14286 2. 1.09412 1.74006 MAarrowhead1 % End of user PostScript .81415 .02185 m .83744 .07879 L s % Start of user PostScript 1.42857 -2. 1.53516 -1.73944 MAarrowhead1 % End of user PostScript .81415 .08428 m .84157 .1357 L s % Start of user PostScript 1.42857 -1.71429 1.55408 -1.47898 MAarrowhead1 % End of user PostScript .81415 .14672 m .84574 .19185 L s % Start of user PostScript 1.42857 -1.42857 1.57315 -1.22202 MAarrowhead1 % End of user PostScript .81415 .20915 m .84906 .24789 L s % Start of user PostScript 1.42857 -1.14286 1.58836 -0.965549 MAarrowhead1 % End of user PostScript .81415 .27158 m .85055 .30527 L s % Start of user PostScript 1.42857 -0.857143 1.59518 -0.702979 MAarrowhead1 % End of user PostScript .81415 .33401 m .8496 .36554 L s % Start of user PostScript 1.42857 -0.571429 1.59081 -0.427161 MAarrowhead1 % End of user PostScript .81415 .39645 m .84592 .42921 L s % Start of user PostScript 1.42857 -0.285714 1.574 -0.135773 MAarrowhead1 % End of user PostScript .81415 .45888 m .83949 .49509 L s % Start of user PostScript 1.42857 0 1.54456 0.165693 MAarrowhead1 % End of user PostScript .81415 .52131 m .83079 .56084 L s % Start of user PostScript 1.42857 0.285714 1.50475 0.466594 MAarrowhead1 % End of user PostScript .81415 .58375 m .82014 .6243 L s % Start of user PostScript 1.42857 0.571429 1.45602 0.757028 MAarrowhead1 % End of user PostScript .81415 .64618 m .80414 .68179 L s % Start of user PostScript 1.42857 0.857143 1.38277 1.02011 MAarrowhead1 % End of user PostScript .81415 .70861 m .77989 .70514 L s % Start of user PostScript 1.42857 1.14286 1.27179 1.12696 MAarrowhead1 % End of user PostScript .81415 .77104 m .78858 .73452 L s % Start of user PostScript 1.42857 1.42857 1.31156 1.26142 MAarrowhead1 % End of user PostScript .81415 .83348 m .79476 .78518 L s % Start of user PostScript 1.42857 1.71429 1.33983 1.49324 MAarrowhead1 % End of user PostScript .81415 .89591 m .79849 .8405 L s % Start of user PostScript 1.42857 2. 1.35691 1.74643 MAarrowhead1 % End of user PostScript .87658 .02185 m .90229 .07825 L s % Start of user PostScript 1.71429 -2. 1.83194 -1.74192 MAarrowhead1 % End of user PostScript .87658 .08428 m .90626 .13517 L s % Start of user PostScript 1.71429 -1.71429 1.85013 -1.48142 MAarrowhead1 % End of user PostScript .87658 .14672 m .90999 .19157 L s % Start of user PostScript 1.71429 -1.42857 1.86719 -1.22332 MAarrowhead1 % End of user PostScript .87658 .20915 m .91264 .24823 L s % Start of user PostScript 1.71429 -1.14286 1.87932 -0.964004 MAarrowhead1 % End of user PostScript .87658 .27158 m .91338 .30652 L s % Start of user PostScript 1.71429 -0.857143 1.88271 -0.697273 MAarrowhead1 % End of user PostScript .87658 .33401 m .91166 .3677 L s % Start of user PostScript 1.71429 -0.571429 1.87481 -0.41729 MAarrowhead1 % End of user PostScript .87658 .39645 m .90708 .43202 L s % Start of user PostScript 1.71429 -0.285714 1.85385 -0.12294 MAarrowhead1 % End of user PostScript .87658 .45888 m .89948 .49815 L s % Start of user PostScript 1.71429 0 1.81911 0.179694 MAarrowhead1 % End of user PostScript .87658 .52131 m .88938 .56374 L s % Start of user PostScript 1.71429 0.285714 1.77287 0.479893 MAarrowhead1 % End of user PostScript .87658 .58375 m .87715 .62665 L s % Start of user PostScript 1.71429 0.571429 1.71691 0.767767 MAarrowhead1 % End of user PostScript .87658 .64618 m .86053 .68326 L s % Start of user PostScript 1.71429 0.857143 1.64083 1.02686 MAarrowhead1 % End of user PostScript .87658 .70861 m .83893 .71731 L s % Start of user PostScript 1.71429 1.14286 1.54199 1.18266 MAarrowhead1 % End of user PostScript .87658 .77104 m .84198 .74236 L s % Start of user PostScript 1.71429 1.42857 1.55595 1.29732 MAarrowhead1 % End of user PostScript .87658 .83348 m .85041 .78861 L s % Start of user PostScript 1.71429 1.71429 1.59451 1.50896 MAarrowhead1 % End of user PostScript .87658 .89591 m .85587 .84232 L s % Start of user PostScript 1.71429 2. 1.61953 1.75476 MAarrowhead1 % End of user PostScript .93901 .02185 m .96693 .07769 L s % Start of user PostScript 2. -2. 2.12778 -1.74445 MAarrowhead1 % End of user PostScript .93901 .08428 m .97071 .13466 L s % Start of user PostScript 2. -1.71429 2.14506 -1.48375 MAarrowhead1 % End of user PostScript .93901 .14672 m .97402 .19133 L s % Start of user PostScript 2. -1.42857 2.1602 -1.22442 MAarrowhead1 % End of user PostScript .93901 .20915 m .97608 .24856 L s % Start of user PostScript 2. -1.14286 2.16965 -0.962515 MAarrowhead1 % End of user PostScript .93901 .27158 m .97619 .3076 L s % Start of user PostScript 2. -0.857143 2.17014 -0.6923 MAarrowhead1 % End of user PostScript .93901 .33401 m .9738 .36951 L s % Start of user PostScript 2. -0.571429 2.1592 -0.408984 MAarrowhead1 % End of user PostScript .93901 .39645 m .96843 .43432 L s % Start of user PostScript 2. -0.285714 2.13461 -0.11239 MAarrowhead1 % End of user PostScript .93901 .45888 m .95986 .50058 L s % Start of user PostScript 2. 0 2.09542 0.190842 MAarrowhead1 % End of user PostScript .93901 .52131 m .94868 .56592 L s % Start of user PostScript 2. 0.285714 2.04426 0.489851 MAarrowhead1 % End of user PostScript .93901 .58375 m .93551 .62822 L s % Start of user PostScript 2. 0.571429 1.98397 0.774938 MAarrowhead1 % End of user PostScript .93901 .64618 m .91913 .68432 L s % Start of user PostScript 2. 0.857143 1.909 1.03171 MAarrowhead1 % End of user PostScript .93901 .70861 m .90001 .724 L s % Start of user PostScript 2. 1.14286 1.8215 1.21329 MAarrowhead1 % End of user PostScript .93901 .77104 m .89787 .75076 L s % Start of user PostScript 2. 1.42857 1.81171 1.33575 MAarrowhead1 % End of user PostScript .93901 .83348 m .90651 .79282 L s % Start of user PostScript 2. 1.71429 1.85127 1.52824 MAarrowhead1 % End of user PostScript .93901 .89591 m .91334 .84456 L s % Start of user PostScript 2. 2. 1.88252 1.76503 MAarrowhead1 % End of user PostScript 0 0 m 1 0 L 1 .91776 L 0 .91776 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 258}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc@000ol0000>00008@001?l00?lg0003o`0003<000Co003o =`000ol0000f0004o`00oa00000R00;o=`02ocH00_lg00;o>@02oa40003o01/0003o01/0003o01/0 003o01/0000?0?oo2ol100003`000ol000020003o`0000T000?o00002@000ol000080003o`0000T0 00?o000020000ol000090003o`0000T000?o000020000ol000090003o`0000T000?o000020000ol0 00090003o`0000P000?o00002@000ol000090003o`0000P000?o00002@000ol000080003o`0000T0 00?o00002@000ol000080003o`0000T000Go0000o`0100003`000ol0000>0003o`0003L000?o0000 =`000ol0000g0003o`0003L000?o00003@01o`40000?0003o`000?l01`01o`40000700Co10000ol0 003o00L00Ol1000020000ol000040003o`000?l01`01o`4000000`3oo`03o`<000?o00000`02o`l0 00?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000h000?o00003@000ol0 000>0003o`0000d000?o00003P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000`0 0_l100002P000ol000020003o`0000h000?o00003P000ol0000=0003o`0000h000?o00003@000ol0 000>0003o`0000h000?o00003@000ol0000>0003o`0000d000?o00003P000ol0000=0003o`0000h0 00?o00003P000ol0000=0003o`0000d00Ol100001`001?l00?l40003o`0000d000?o00003P000ol0 000>0003o`0000h000?o00003@000ol0000>0003o`0000h000?o00003@000ol0000>0003o`0000d0 00?o00003`000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000`00Ol100002002o`D0 00?o00003@000ol0000>0003o`0000d000?o00003P000ol0000>0003o`0000h000?o00003P000ol0 000=0003o`0000h000?o00003P000ol0000>0003o`0000d000?o00003P000ol0000>0003o`0000d0 00?o00003001o`40000?0003o`0000`000?o00003P000ol0000>0003o`0000h000?o00003P000ol0 000>0003o`0000h000?o00003@000ol0000?0003o`0000d000?o00003P000ol0000=0003o`0000h0 00?o00003P000ol0000>0003o`0000/00Ol100003`000ol0000<0003o`0000h000?o00003P000ol0 000>0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00003P000ol0000=0003o`0000l0 00?o00003@000ol0000>0003o`0000h000?o00003@000ol0000;007o0@0000l000?o00002`000ol0 000?0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00003P000ol0000>0003o`0000h0 00?o00003@000ol0000?0003o`0000d000?o00003P000ol0000>0003o`0000h000?o00002P01o`40 000?0003o`0000/000?o00003P000ol0000>0003o`0000l000?o00003P000ol0000>0003o`0000h0 00?o00003P000ol0000>0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00003P000ol0 000=0003o`0000X00Ol100003`000ol0000800?o4@000ol0000>0003o`0000h000?o00003P000ol0 000?0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00003`000ol0000=0003o`0000h0 00?o00003P000ol0000>0003o`0000T00Ol100003`000ol0000800?o3`02o`l00ol@0003o`0000h0 00?o00003`000ol0000>0003o`0000h000?o00003`000ol0000=0003o`0000l000?o00003@000ol0 000>0003o`0000h000?o00003`000ol00008007o0@0000l000?o00002004o`h00ol>00Co3P03o`h0 1?l=00Co3`02o`l00ol?00;o3P03o`l00_l?00;o3`02o`l00_l?00;o2@01o`40000?0003o`0000P0 0ol?00?o3P04o`h00ol>00Co3@04o`h00ol>00Co3@04o`h00ol>00?o3P03o`h00ol>00?o3P03o`T0 0Ol100003`02o`P00ol?00?o3`03o`l00_l?00?o3`03o`h00ol>00Co3@04o`h00ol>00?o3P03o`h0 0ol>00?o3`03o`L00_l100003`000ol0000700;o4002oa000_l@00;o4002o`l00ol>00?o3`03o`h0 0ol?00;o3`03o`h00ol>00?o3P03o`l00_l8007o0@0000l000?o00001`000ol0000?0003o`0000l0 0_l@00;o4002o`l00_l@0003o`0000h00_l@00;o3`02oa000_l?00;o3`02o`l00_l@0003o`0000H0 0Ol100003`000ol0000[0003o`0000l000?o00003`000ol0000?0003o`0000h000?o00003P02oa00 0_l?00;o4@000ol0000>0003o`0000h000?o00003P000ol0000?0003o`0000D00Ol100003`000ol0 001Q0003o`0000h000?o00003`000ol0000?0003o`0000h000?o0000G001o`40000?0003o`0000h0 00?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000h000?o00003@000ol0 000>0003o`0000d000?o00003P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000d0 0Ol100003`000ol0000>0003o`0000h000?o00003@000ol0000>0003o`0000d000?o00003P000ol0 000>0003o`0000d000?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000h0 00?o00003@000ol0000=007o0@0000l000?o00003@000ol0000>0003o`0000d000?o00003`000ol0 000=0003o`0000h000?o00003P000ol0000=0003o`0000h000?o00003P000ol0000>0003o`0000d0 00?o00003P000ol0000>0003o`0000d000?o00003001o`40000?0003o`0000`000?o00003`000ol0 000=0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00003P000ol0000>0003o`0000d0 00?o00003P000ol0000=0003o`0000h000?o00003P000ol0000>0003o`0000/00Ol100003`000ol0 000;0003o`0000l000?o00003P000ol0000>0003o`0000h000?o00003P000ol0000>0003o`0000h0 00?o00003P000ol0000=0003o`0000l000?o00003@000ol0000>0003o`0000h000?o00003@000ol0 000;007o0@0000l000?o00002P000ol0000?0003o`0000h000?o00003`000ol0000>0003o`0000h0 00?o00003P000ol0000>0003o`0000h000?o00003P000ol0000>0003o`0000d000?o00003P000ol0 000>0003o`0000h000?o00002P01o`40000?00;o2@02o`l00_l00`3o000?0003o`0000h000?o0000 3`000ol0000>0003o`0000h000?o00003P000ol0000?0003o`0000d000?o00003P000ol0000>0003 o`0000h000?o00003P000ol0000>0003o`0000P00_l100003`000ol0000800?o3P03o`l00_lA0003 o`0000l000?o00003P000ol0000>0003o`0000h000?o00003`000ol0000=0003o`0000l000?o0000 3P000ol0000>0003o`0000h000?o00003P000ol00008007o0@0000l000?o00001`02oa001?l>00?o 3P04o`h01?l?0003o`0000l000?o00003P000ol0000>00;o3`03o`h00ol>00?o3P03o`h00ol>00?o 2001o`40000?0003o`0000H000?o00004003o`l00ol>00Co3P04o`h00ol>00Co3P03o`h00ol>00Co 3@04o`h00ol>00?o3P03o`h00ol8007o0@0000l000?o00001@000ol0000@00?o4002o`l00ol?00?o 3`03o`h01?l>00?o3P03o`h01?l=00Co3P03o`h00ol>00?o3`03o`L00Ol100003`000ol0000H00;o 4002oa000_l@00?o3`03o`l00ol?00;o3`02o`l00ol>00?o3`03o`h00ol>00?o3`02o`L00Ol10000 3`000ol0000H0003o`0000l00_l@00;o4@02oa0000?o00003P02oa000_l@00;o3`02o`l00ol?00;o 3`02o`l00_l@0003o`0000D00Ol100003`000ol0000Z0003o`0000l000?o000040000ol0000?0003 o`0000h00_l@00;o4002o`l00_l@00;o40000ol0000>0003o`0000h000?o00003`000ol00004007o 0@0000l000?o0000C`000ol0000?0003o`0000l000?o00003`000ol0000?0003o`0000h000?o0000 3`000ol00019007o0@0000l000?o0000o`07007o0@0000l000?o00003@02o`l00_l?0003o`0000h0 00?o00003@000ol0000>0003o`0000h000?o00003@000ol0000>0003o`0000d000?o00003P000ol0 000=0003o`0000h000?o00003P000ol0000=0003o`0000d00Ol100003`000ol0000;00;o40000ol0 000?0003o`0000h000?o00003@000ol0000>0003o`0000h000?o00003@000ol0000>0003o`0000d0 00?o00003P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000d00Ol100003`02o`P0 00Co0?oo4@000ol0000?0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00003@000ol0 000?0003o`0000d000?o00003P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000/0 0_l100003`000ol0000600?o4P000ol0000?0003o`0000l000?o00003P000ol0000>0003o`0000h0 00?o00003P000ol0000>0003o`0000d000?o00003P000ol0000>0003o`0000h000?o00003P000ol0 000=0003o`0000/00Ol100003`000ol0000500Co4002oa8000?o00003`000ol0000>0003o`0000h0 00?o00003`000ol0000=0003o`0000h000?o00003P000ol0000>0003o`0000d000?o00003P000ol0 000>0003o`0000h000?o00002P01o`40000?0003o`0000@01Ol?00;o4003oa4000?o00003`000ol0 000>0003o`0000l000?o00003@000ol0000?0003o`0000d000?o00003`000ol0000=0003o`0000h0 00?o00003P000ol0000=0003o`0000X00Ol100003`000ol0000300?o4@04o`l01?l>00?o4@000ol0 000>0003o`0000l000?o00003P000ol0000>0003o`0000h000?o00003P000ol0000>0003o`0000h0 00?o00003P000ol0000=0003o`0000T00Ol100003`000ol0000F00?o4003oa001?l>00Co4002o`l0 0_l?00?o3`02o`l00_l?00;o3P000ol0o`0>0003o`3o00h000?o0?l03P000ol0o`08007o0@0000l0 00?o00005@000ol0000A00;o4@04o`h01?l>00Co3P03o`h01?l>00?o3P03o`l00_l?00;o3`02o`l0 0_l?00;o2001o`40000?0003o`0002T000?o00004003o`l00ol?00Co3P03o`h01?l>00?o3P04o`d0 1?l=00Co3@04o`d01?l=00Co1`01o`40000?0003o`0002P000?o00004@02oa400_l@00?o3`02o`l0 0ol?00;o3`03o`l00_l?00;o3`02o`l00_l?00;o1`01o`40000?0003o`0003`00_lA00;o4002oa00 0_l@00;o4002o`l00_l@0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00001@01o`40 000?0003o`0003`000?o000040000ol0000?00;o4002oa000_l@00;o4002oa0000?o00003P000ol0 000>0003o`0000h000?o00003P000ol00004007o0@0000l000?o00001004oeX000?o00003`000ol0 000?0003o`0000l000?o00003`000ol0001I007o0@0000l00_l700Co3P03onX00_l100003`000ol0 000700Co2P06on/00Ol100003`000ol000080003o`0000?o2@07o``00_oJ007o0@0000l000?o0000 3P000ol000090004o`0000;o1`09oa0000?o00003@000ol0000>0003o`0000h000?o00003@000ol0 000>0003o`0000d000?o00003P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000d0 0Ol100003`000ol0000V00Oo40000ol0o`0@0003o`0000h000?o00003P000ol0000=0003o`0000h0 00?o00003@000ol0000>0003o`0000d000?o00003P000ol0000>0003o`0000h000?o00003001o`40 000?0003o`0002X00ol@00;o4@000ol0000?0003o`0000h000?o00003@000ol0000>0003o`0000d0 00?o00003P000ol0000=0003o`0000h000?o00003P000ol0000>0003o`0000/00Ol100003`000ol0 000l00Co40000ol0000?0003o`0000h000?o00003P000ol0000>0003o`0000d000?o00003P000ol0 000=0003o`0000h000?o00003P000ol0000>0003o`0000X00Ol100003`000ol0000k00?o4@04oa00 0_l?00?o3@000ol0000>0003o`0000h000?o00003P000ol0000=0003o`0000h000?o00003P000ol0 000>0003o`0000T00Ol100003`000ol0000k0003o`0001401?l>00Co3`03o`h00ol>00?o3P000ol0 o`0>0003o`3o00d000Co003o3@001?l00?l=0004o`00o`d000?o00002001o`40000700?o1@000ol0 00090003o`0002h000?o00004`03o`l00ol>00Co3P03o`h00ol>00?o3P03o`h00ol>00?o3P03o`h0 0_l8007o0@0000P000?o000010000ol000090003o`0000h000?o000040000ol0000P00;o4@03o`h0 0ol?00?o3P03o`d01?l=00Co3@04o`d01?l=00Co3003o`P00Ol1000000<0ool00ol20003o`0000@0 0_l:00;o3`02oa4000?o000040000ol0000=00;o4P02o`l00ol?00;o3`02o`l00_l?00;o3`02o`l0 0_l?00;o3P02o`H00_l1000020000ol000040003o`0000T00ol>00?o4002oa4000?o00003P000ol0 000A0003o`0000h00_l@0003o`0000h000?o00003P000ol0000>0003o`0000h000?o00003P000ol0 000>0003o`0000h000?o00001001o`4000080003o`0000@000?o00002P03o`h00ol?00;o4@000ol0 000d0003o`0000l000?o00003P000ol0000>0003o`0000h000?o00003P000ol0000>0003o`0000h0 00?o00003P000ol00003007o0@0000L00_l60003o`0000X00_l?00Co3P02oa000olC00;o[`01o`40 000?0003o`0000X000?o0?l03P03o`l00ol?00?o4@04ojl00Ol100003`000ol0000<0003o`0000h0 00?o00003P000ol0000>00?o4004ok000Ol100003`000ol0000=0003o`0000h000?o00003@000ol0 000?0003o`0000h01?na007o0@0000l000?o00003@000ol0000>0003o`0000h000?o00003P000ol0 000>00Co/@01o`40000?0003o`0000h000?o00003P000ol0000=0003o`0000h000?o00003@001?l0 0?l=00Oo2P02o`h00_l?00;o3P02o`l000?o00003@02o`l00_l?0003o`0000d000?o00003@01o`40 000?0003o`0006@01ol900Co30000ol0000>0003o`0000d000?o00003@000ol0000>0003o`0000h0 00?o000030000ol0000>0003o`0000`00Ol100003`000ol0001T00?o3`03o``00ol>0003o`0000d0 00?o00003@000ol0000>0003o`0000h000?o000030000ol0000>0003o`0000/00Ol100003`000ol0 001e00Go3@02o`h00_l>0003o`0000d000?o00003P000ol0000>0003o`0000`000?o00003P000ol0 000:007o0@0000l00_mf00Ko2`04o`h00_l>00;o3P000ol0o`0>0003o`3o00h000?o000030000ol0 000>0003o`0000P00_l100003`000ol0000=0003o`0007P00ol<00Co3P02o`h00_l?00;o3`02o`d0 00?o0?l03P000ol0o`08007o0@0000l000?o00003@000ol0000?0003o`0000l000?o0000E`000ol0 000;00?o3004o``01?l=00Co3P02o`h00_l?00;o2001o`40000?0003o`0000d00_l@0003o`0000l0 00?o00003`000ol0001F0003o`0000/00ol=00?o3P03o``01?l=00?o3@04o`L00Ol100003`000ol0 000=00;o3`02oa000_lA0003o`0006L000?o000030000ol0000>0003o`0000`00ol>00;o3P03o`H0 0Ol100003`000ol0000<00?o3`03o`l00_l@00;o4P000ol0001T0003o`0000h000?o00003P000ol0 000<0003o`0000h000?o00001001o`40000?0003o`0000`01?l>00?o3`02o`l00olA00;oV0000ol0 000>0003o`0000<00Ol100003`000ol0000<00;o3`04o`h00ol?00?o4002ok000Ol100003`000ol0 000>0003o`0000h000?o00003P02o`h01?l?00?o4P02oi`00Ol100003`000ol0000>0003o`0000h0 00?o00003P000ol0000>0003o`3o00h01?l?00CoW@01o`40000?0003o`0000h000?o00003P000ol0 000>0003o`0000h000?o00003`02o`l01?nN007o0@0000l00_l?0003o`0000h000?o00003@000ol0 000?0003o`0000h000?o00003P04o`l01?n;00;o0@0000l000?o00003P000ol0000>0003o`0000d0 00?o00003P000ol0000>0003o`0000h000Co003o4006ohX00Ol100003`000ol0000>0003o`0000h0 00?o00003@000ol0000>0003o`0000d000?o00003P000ol0000>00So2004o`030?oo00X00_l>00;o 3`02o`h00_l?00;o3`000ol0000=0003o`0000d00Ol100003`000ol0001f0003o`0000d01_l900Go 2`02o`l000?o00003@000ol0000>0003o`0000d000?o00003@000ol0000<007o0@0000l000?o0000 Q`06o`/01?l;0003o`3o00d00_l>0003o`0000h000?o00003@000ol0000=0003o`0000/00Ol10000 3`000ol0002G00Ko2`03o`h00_l=0004o`00o`d000?o00003@000ol0000=0003o`0000X00Ol10000 3`000ol0002K00?o2P04o`d00ol=00?o3P02o`h000?o0?l03@000ol00009007o0@0000l000?o0000 4@000ol0000>0003o`0008D00ol;00Go3004o`h000?o00003@02o`h000?o0?l02001o`40000?0003 o`00014000?o00003P000ol0000?0003o`0007H000?o00002`03o`d00ol<00?o3@04o`h00_l8007o 0@0000l000?o00004002o`l00_l@00;o40000ol0001f0003o`0000`000?o00003002o`h00ol<00Co 1`01o`40000?0003o`0000l00ol>00?o3`03oa0000?o0000QP000ol0000=0003o`0000d000?o0000 3002o`L00Ol100003`000ol0000?00?o3P03o`h01?l?00;o4@02oiH000?o00003@000ol00004007o 0@0000l00_l?00Co3@04o`d01?l?00;o4004oj`00_l100003`000ol0000@0003o`0000h00_l?00;o 3P03o`l01?lA00;oV`01o`40000?0003o`0000l000?o00003P000ol0000>0003o`3o00l00_l>00Co 3`04oi`00Ol100003`000ol0000?0003o`0000h000?o00003P000ol0000>0003o`0000l00ol=00Go W@01o`40000?0003o`0000l000?o00003P000ol0000>0003o`0000h000?o00003P000ol0o`0?00?o 3P06ohX00Ol100003`000ol0000?0003o`0000h000?o00003@000ol0000>0003o`0000h000?o0000 3P02o`030?l000h01?l=00;oO@01o`40000?0003o`0000h000?o00003P000ol0000>0003o`0000h0 00?o00003@000ol0000>0003o`0000l01Ol>00GoNP01o`40000?0003o`0000h000?o00003P000ol0 000=0003o`0000h000?o00003@000ol0000>0003o`0000h00_l30003o`0000P02ol600Co00<0ool0 2@02o`l00_l>00;o3`000ol0000>0003o`0000d000?o00003@01o`40000?0003o`0008L00ol=00Ko 2002o`8000?o00002P000ol0000=0003o`0000d000?o00003@000ol0000=0003o`0000d00Ol10000 3`000ol0002G00Oo2@04o``00_l00`3o000;0003o`0000d000?o00003@000ol0000=0003o`0000`0 0Ol100003`000ol0002X00Co3@02o`d00ol=0003o`0000d000?o00003@000ol0000;007o0@0000l0 00?o0000ZP03o`/01?l=00;o3P03o`d000?o0?l03@000ol0000:007o0@0000l00_lE0003o`0009H0 00?o00002P03o`/01?l=00?o3P02o`h00ol800;o0@0000l000?o00004`02oa0000?o0000U@000ol0 000:00?o3P02o``01?l=00?o2@01o`40000?0003o`0001800_l@00;o3`02oiH000?o000030000ol0 000<00?o3@03o`P00Ol100003`000ol0000A00?o3`02o`l00ol?00;oU@000ol0000=0003o`0000`0 0_l8007o0@0000l000?o00004004o`h00ol>00?o3`03oa000_nD0003o`0000`000?o00001P01o`40 000?0003o`00018000?o00003004o`d01?l>00?o3P05oj@000?o00001@01o`40000?0003o`000140 00?o00003P02o`l00ol=00Co3@05o`l00onK007o0@0000l000?o000040000ol0000?0003o`0000d0 00?o0?l03`02o`h01?l=00GoW001o`40000?0003o`00010000?o00003P000ol0000>0003o`0000h0 00?o00003@001?l00?l>00Co4004ohT00Ol100002002o`D000?o00003`000ol0000>0003o`0000h0 00?o00003P000ol0000=0003o`0000l000Co0?oo3P05oh/00Ol100001`001?l00?l40003o`0000l0 00?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>00;o0P000ol0000;00Go3P04og/0 0Ol100001`001?l00?l400;o3`000ol0000>0003o`0000d000?o00003P000ol0000=0003o`0000h0 00?o00003P02o`<000?o0000200;o`H00ol200;o2@02o`l00_l>0003o`0000h000?o00003P000ol0 000=0003o`0000`00_l100001`001?l00?l40003o`0008L01?l;00Ko2@02o`l000?o00002`000ol0 000>0003o`0000h000?o00003@000ol0000=007o0@0000L000Co003o10000ol000270003o`0000d0 1_l:00Co30000ol0000;0003o`0000h000?o00003P000ol0000=0003o`0000`00Ol100002002o`D0 00?o0000U`07o`X01?l<00;o30000ol0000>0003o`0000d000?o00003@000ol0000<007o0@0000l0 00?o0000Y`06o`/00_l=0003o`3o00d000?o00003P000ol0000=0003o`0000/00Ol100003`000ol0 002[00?o2@04o`d00_l>00?o3@000ol0o`0=0003o`0000/00Ol100003`000ol0002i00?o2`04o`d0 0ol>00;o3P02o`/00Ol100003`000ol0000E00;o3`02oi@000?o00002P03o`d00ol<00Co3003o`/0 0Ol100003`000ol0000D00?o3@04o`l00_nB0003o`0000`00_l=00?o3@03o`X00Ol100003`000ol0 000C00?o3@04o`h01?l?00;oPP000ol0000<0003o`0000`00_l>00;o2P01o`40000?0003o`000180 1?l<00Co3P04o`d01?l@00;oP@000ol0000<00;o3P000ol00008007o0@0000l000?o00004`03o`d0 0ol=00Co3@04o`h01?nB0003o`0000d000?o00001`01o`40000?00;o4`000ol0o`0>00;o3`03o`d0 0ol>00Co3`04oiT00_l100003`000ol0000B0003o`0000h000?o00003@000ol0o`0>00;o3`03o`d0 1OnL007o0@0000l000?o00004@000ol0000>0003o`0000d000?o00003P000ol0000>0003o`3o00l0 0ol=00OoR@01o`40000?0003o`00010000?o00003P000ol0000=0003o`0000h000?o00003@02oa00 0_l00`3o000=00Go3004og/00Ol100003`000ol0000?0003o`0000h000?o00003@000ol0000>0003 o`0000d000?o00003P02oa001Ol>00KoN@01o`40000?0003o`0000h000?o00003P000ol0000=0003 o`0000h000?o00003@000ol0000>0003o`0000h00_l30003o`0000P02Ol800?o0P02o`T00_l?0003 o`0000d000?o00003P000ol0000>0003o`0000d000?o00003@01o`40000?0003o`0008L000?o0000 3005o`X00_l00`3o000:0003o`0000d000?o00003P000ol0000>0003o`0000d000?o00003@01o`40 000?0003o`0009L01Ol;00?o2`000ol0000=0003o`0000h000?o00003@000ol0000=0003o`0000d0 0Ol100003`000ol0002K00;o2P04o`/000?o0?l03@000ol0000=0003o`0000h000?o00003@000ol0 000<007o0@0000l000?o0000Y`05o`/00_l=00?o3@000ol0000>0003o`0000d000?o00003001o`40 000?0003o`000:/00_l900Co3003o`h00ol=0003o`0000d000?o00003001o`40000?00;o^@03o``0 0ol<00Co3004o`d00ol;00;o0@0000l000?o00005P02o`l00_nA0003o`0000/00_l<00Co3004o``0 1?l<007o0@0000l000?o00005@03o`d01?l?00;oP@000ol0000;0003o`0000/00ol=00?o3004o``0 0Ol100003`000ol0000D00?o3@04o`h01?l>00;oP0000ol0000;00;o3P02o`d00ol<007o0@0000l0 00?o00004`03o`d01?l>00Co3005o`l00_mn0003o`0000`00_l>00;o3001o`40000?0003o`0001<0 0ol>00?o3@04o``01Ol=00Co3`03ogd000?o00003002o``00Ol100003`000ol0000B0003o`3o00h0 00?o0?l03@05o``01?l=00Co3@04o`l01?ml0003o`0000X00Ol100003`000ol0000A0003o`0000h0 00?o00003@001Ol0003o00`000Co003o3@04o`h00ol=00GoR`01o`40000?0003o`00010000?o0000 3P000ol0000=0003o`0000h000?o00003@02o`8000?o00002`02o`030?l000d00ol>00KoN@01o`40 000?0003o`0000l000?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>00;o3`03o`03 0?l000`01_mk007o0@0000l000?o00003P000ol0000>0003o`0000d000?o00003P000ol0000=0003 o`0000h000?o00003P000ol0000=00?o0P02o`X02?l800;o3`000ol0000=0003o`0000h000?o0000 3P000ol0000=0003o`0000d00Ol100003`000ol000270003o`0000d01_l800;o00<0o`002P000ol0 000=0003o`0000h000?o00003P000ol0000=0003o`0000d00Ol100003`02oiP00ol=00?o2`000ol0 000=0003o`0000d000?o00003P000ol0000=0003o`0000`00_l100003`000ol0002W00Co2`000ol0 o`0<0003o`0000d000?o00003P000ol0000=0003o`0000d00Ol100003`000ol0002V00Ko2`02o``0 00?o00003P000ol0000=0003o`0000d000?o00003@01o`40000?0003o`000:X00ol900Co3002o`h0 00?o00003@000ol0000=0003o`0000d00Ol100003`000ol0002h00;o2`03o``01?l<00Co3P000ol0 000=007o0@0000l000?o00005`02oj0000?o00002@03o``01?l<00Co3004o`h00Ol100003`000ol0 000E00Co3P02o`l00_l>00;oL0000ol0000900?o3003o`d00ol<00Co3P01o`40000?0003o`0001@0 1?l=00Co3@04o``01?l?00;o3P02oe`00_l=00;o3@03o``00ol?007o0@0000l000?o00004`04o`d0 1?l=00Co3004o`d01Ol<00Co3`02od`000?o00002`02o`d00_l>00;o3`01o`40000?0003o`0001@0 0ol=00?o3@04o``01?l=00Go3004o`d01?l?00;oB`000ol0000<0003o`0000`00_l?007o0@0000l0 00?o00004`000ol0o`0>00;o3P04o`d00ol>00?o3004o`d01?l=00CoF`000ol0000<0003o`0000h0 0Ol100003`000ol0000B0003o`0000h000?o00003@001?l00?l=0003o`3o00d00_l00`3o000<00Co 3@03o`d01?l?00CoJ@01o`40000?00;o4P000ol0000>0003o`0000d000?o00003P000ol0000=0003 o`0000h000Co003o3@000ol0o`0>00?o3@05ofX00_l100003`000ol0000@0003o`0000h000?o0000 3@000ol0000>0003o`0000d000?o00003P000ol0000>0003o`0000d00_l00`3o000=00?o3@04oe`0 0Ol100003`000ol0000?0003o`0000h000?o00003@000ol0000>0003o`0000d000?o00003P000ol0 000>0003o`0000d000?o00003P02o`030?l000d01omI007o0@0000l000?o00003P000ol0000>0003 o`0000d000?o00003P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000h000?o0000 3@08o`T00ol=0003o`0000h000?o00003P000ol0000=0003o`0000d00Ol100003`000ol0002W0003 o`0000`000?o00002`000ol0000>0003o`0000h000?o00003@000ol0000=007o0@0000l000?o0000 ]@03o``000?o00003@000ol0000>0003o`0000d000?o00003P01o`40000?0003o`000;L00_l:00Co 3@000ol0000>0003o`0000d000?o00003P01o`40000?0003o`000;T000?o00001`04o`/00ol=00?o 3`000ol0000?007o0@0000l000?o0000^P000ol0000700?o2`04o``01?l<00?o4@01o`40000700?o 1@000ol0000G00;o3P02o`l00_l>00;o3P02o`l000?o0000F002o``01?l<00Co3004oa000Ol10000 20000ol000040003o`0001D01?l=00?o3@04o``01?l=00?o3P02o`h00_l>00;o3P000ol0000<0003 o`0000X000?o00003@02o``00ol=00?o3@03oa400Ol1000020000ol0000400;o5@04o`d00ol=00Co 3004o`d00ol>00;o3P03o`d00ol=00;o3P000ol0000:0003o`0000h000?o00002P02o`d00ol=00?o 4@02o`4000080003o`0000@000?o00004`04o`d01?l<00Co3004o`d00ol>00?o3@03o`d00ol=00?o 3@02o``000?o00006`000ol0000<00;o3P02oa<00Ol1000020000ol000040003o`0001@00ol>00?o 3@03o`d00ol<00Co3@04o``01?l<00Co3003o`d00_l=0003o`0000P00_lP0003o`0000d000?o0000 4P01o`40000700;o1P000ol0000C0003o`3o00h000?o0?l03@000ol0o`0>00;o3P02o`h000?o0?l0 3P03o`d00ol;00Co3003o``00ol900?oA001o`40000?0003o`00018000?o00003P000ol0000=0003 o`0000h000?o00003@000ol0000>0003o`0000d000?o0?l03@000ol0o`0=0003o`3o00d00_l<00?o 2P03od<00Ol100003`000ol0000A0003o`0000h000?o00003@000ol0000>0003o`0000d000?o0000 3P000ol0000>0003o`0000d000?o00003@000ol0000=0003o`0000/00ol:00Co@P01o`40000?0003 o`00010000?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000h000?o0000 3@000ol0000=0003o`0000d000?o00003@000ol0000900?o@`01o`40000?0003o`0000l000?o0000 3P000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000h000?o00003@000ol0000>0003 o`0000d000?o00003@000ol0000:0003o`3o00/00old007o0@0000l000?o00003P000ol0000>0003 o`0000d000?o00003P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000h000?o0000 3@000ol0000>0003o`0000d000?o00001@0:o`T00_l300?o3P02o`l00Ol100003`000ol0003@00;o 3006o``000?o00000_lA007o0@0000l000?o0000g@05o`d01?lC007o0@0000l000?o0000g006o``0 1?lD007o0@0000l00_o^00Go4`02o`40000?0003o`0001L000?o00003@02o`h00_l?0003o`0000d0 00?o000030000ol0000=0003o`0000`000?o00003@000ol0000;0003o`0000`000?o0000=P03oaL0 0Ol100003`000ol0000F00;o3P03o`d00ol>00;o3P02o`h000?o00003@000ol0000<0003o`0000d0 00?o00002`000ol0000<0003o`0000X000?o0000@`01o`40000?0003o`0001D00_l>00?o3@03o`h0 0_l>00;o3P02o`h00_l=00;o3P02o`d000?o000030000ol0000:0003o`0000/000?o0000=@01o`40 000?0003o`0001@00ol=00?o3@04o`d00ol=00?o3@02o`h00_l=00?o3@03o``00ol<00?o2`02o``0 0_lf007o0@0000l000?o00004`04o``01?l<00Go3004o``01?l<00?o3@03o``01?l<00Co3003o``0 0ol<00;o3002o`/00_lX007o0@0000l000?o00005002o`l000?o00003@02o`h00_l>00;o3P02o`h0 0_l=0003o`3o00h00_l<00?o3003o``00ol;00?o2P04obH00Ol100003`000ol0000C0003o`0000h0 00?o00003@000ol0000=0003o`0000d000?o00003@000ol0000>0003o`0000`000?o00003P000ol0 000<0003o`0000`000?o00002`02o``01?l:00Co9@01o`40000?0003o`00018000?o00003P000ol0 000=0003o`0000h000?o00003@000ol0000=0003o`0000d000?o00003@000ol0000=0003o`0000`0 00?o00003P000ol0000;0003o`0000/00_l<00Co2@04oaL00Ol100003`000ol0000A0003o`0000h0 00?o00003@000ol0000>0003o`0000d000?o00003@000ol0000>0003o`0000`000?o00003P000ol0 000<0003o`0000h000?o00002`000ol0000=0003o`0000X01?l:00Go5001o`40000?0003o`000140 00?o00003P000ol0000=0003o`0000d000?o00003@000ol0000>0003o`0000d000?o00003@000ol0 000>0003o`0000`000?o00003P000ol0000<0003o`0000d000?o00002P001?l00?l:00Co5001o`40 000?00;o4@000ol0000>0003o`0000d000?o00003P000ol0000=0003o`0000d000?o00003P000ol0 000=0003o`0000h000?o000030000ol0000>0003o`0000`000?o00003@000ol0000>0003o`0000P0 00?o00000_lA00;o0@0000l000?o00003`000ol0000>0003o`0000d000?o00003P000ol0000=0003 o`0000h000?o00003P000ol0000<0003o`0000h000?o00003@000ol0000>0003o`0000`000?o0000 3P000ol0000>0003o`0000`00_l@007o0@0000l000?o00003P000ol0000>0003o`0000d000?o0000 3P000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>0003 o`0000d000?o00003P000ol0000>0003o`0000d000?o00003@01o`40000?0003o`000?l01`01o`40 000?0003o`0007H000?o000030000ol0000<0003o`0000`000?o0000H001o`40000?0003o`0001H0 00?o00003P000ol0000=0003o`0000`000?o00003@000ol0000=0003o`0000d000?o000030000ol0 000<0003o`0000`000?o000030000ol0000<0003o`0004800Ol100003`000ol0000E00;o3`02o`h0 0_l>0003o`0000d000?o00003@000ol0000<00;o3@02o`d00_l>00;o3@000ol0000<0003o`0000`0 00?o0000<`01o`40000?0003o`0001@00ol>00;o3P02o`h00_l>00;o3P02o`d00ol=00;o3@02o`h0 0_l=00;o3@02o`d000?o000030000ol0000T007o0@0000l000?o00004`04o`d00ol=00?o3@02o`h0 0_l>00;o3P02o`h00_l=00?o3003o`d00_l=00?o3002o`d000?o00003002oaH00Ol100003`000ol0 000B00Co3@04o``01?l<00?o3@03o`d00ol=00?o3@03o``01?l<00Co3002o`d00ol=00;o3002o`d0 0olE007o0@0000l000?o00004`03o`h00_l>00;o3P02o`h00_l>00;o3`000ol0000<00;o3004o``0 1?l<00?o3004o``00ol<00;o3@03oa@00Ol100003`000ol0000C0003o`3o00h000?o00003@000ol0 000=0003o`0000d000?o00003@000ol0000=0003o`0000d000?o00003@000ol0000<0003o`0000d0 00?o00002`02o`h00_l=00?o3004oa<00Ol100003`02oa<000?o00003P000ol0000=0003o`0000d0 00?o00003@000ol0000>0003o`0000d000?o000030000ol0000=0003o`0000d000?o00003@000ol0 000<0003o`0000d000?o00002`000ol0o`0<00?o4`02o`40000?0003o`00018000?o00003P000ol0 000=0003o`0000d000?o00003@000ol0000=0003o`0000h000?o000030000ol0000=0003o`0000d0 00?o00003@000ol0000=0003o`0000d000?o000030000ol0000;00;o5001o`40000?0003o`000140 00?o00003P000ol0000=0003o`0000d000?o00003@000ol0000>0003o`0000d000?o00003@000ol0 000=0003o`0000d000?o00003@000ol0000=0003o`0000d000?o00003@000ol0000<0003o`000140 0Ol100003`000ol0000A0003o`0000h000?o00003@000ol0000=0003o`0000d000?o00003P000ol0 000=0003o`0000d000?o00003@000ol0000=0003o`0000d000?o00003@000ol0000=0003o`0000d0 00?o00003@000ol0000@007o0@0000l000?o000040000ol0000>0003o`0000d000?o00003@000ol0 000=0003o`0000h000?o00003P000ol0000=0003o`0000d000?o00003@000ol0000>0003o`0000`0 00?o00003P000ol0000=0003o`0000`000?o00004001o`40000?0003o`0000l000?o00003P000ol0 000=0003o`0000h000?o00003@000ol0000>0003o`0000h000?o000030000ol0000>0003o`0000d0 00?o00003P000ol0000<0003o`0000h000?o00003P000ol0000<0003o`0000l00Ol100003`000ol0 000?0003o`0000h000?o00003@000ol0000>0003o`0000d000?o00003P000ol0000=0003o`0000d0 00?o00003P000ol0000=0003o`0000h000?o00003@000ol0000=0003o`0000h000?o00003@000ol0 000>007o0@0000l000?o00003P000ol0000>0003o`0000d000?o00003P000ol0000=0003o`0000h0 00?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000d000?o00003P000ol0 000>0003o`0000d000?o00003@01o`40000?0003o`0001D000?o00003@000ol0000=0003o`0000d0 00?o00003@000ol0000=0003o`0000`000?o00003@000ol0000=0003o`0000`000?o000030000ol0 000=0003o`0000`000?o000000;o3P02o`h0 0_l>00;o3@02o`h00_l>00;o3P000ol0000<00;o3P02o`d00_l=0003o`0000`000?o00005001o`40 000?0003o`0001<00ol=00?o3@03o`d00ol=00?o3@03o`d00ol=00?o3@03o``00ol=00;o3P02o`d0 0ol<00;o3@02oaD00Ol100003`02oa@00_l>00;o3P03o`d00ol=00?o3@03o`d00ol=00?o3@03o``0 0ol=00;o3@03o`d00ol=00;o3@02oa<00_l100003`000ol0000B00?o3@03o`d01?l<00Co3004o``0 1?l<00Co3004o``01?l<00?o3@03o``01?l<00Co3003o``00olC007o0@0000l000?o00004P000ol0 o`0>00;o3P000ol0o`0=0003o`0000d000?o00003P000ol0000<0003o`0000d000?o00003P000ol0 000<0003o`0000d000?o00002`03o`d00_l>00;o3@04oa800Ol100003`000ol0000B0003o`0000d0 00?o00003@000ol0000>0003o`0000d000?o00003@000ol0000=0003o`0000d000?o00003P000ol0 000<0003o`0000d000?o00003@000ol0000=0003o`0000`000?o000030000ol0000B007o0@0000l0 00?o00004@000ol0000>0003o`0000d000?o00003@000ol0000=0003o`0000h000?o00003@000ol0 000=0003o`0000d000?o00003@000ol0000=0003o`0000d000?o00003@000ol0000=0003o`0000`0 00?o00004@01o`40000?0003o`00014000?o00003P000ol0000=0003o`0000d000?o00003@000ol0 000>0003o`0000d000?o00003@000ol0000=0003o`0000d000?o00003@000ol0000=0003o`0000d0 00?o00003@000ol0000=0003o`0001000Ol100003`000ol0000A0003o`0000d000?o00003@000ol0 000>0003o`0000d000?o00003@000ol0000>0003o`0000d000?o00003@000ol0000=0003o`0000d0 00?o00003@000ol0000>0003o`0000d000?o000030000ol0000@007o0@0000l000?o000040000ol0 000>0003o`0000d000?o00003@000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000d0 00?o00003@000ol0000=0003o`0000d000?o00003P000ol0000=0003o`0000d000?o00003`01o`40 000?0003o`00010000?o00003@000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000d0 00?o00003@000ol0000>0003o`0000d000?o00003P000ol0000=0003o`0000d000?o00003P000ol0 000<0003o`0000l00Ol100001`04o`@000?o00003`000ol0000>0003o`0000d000?o00003P000ol0 000=0003o`0000h000?o00003@000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000d0 00?o00003@000ol0000>0003o`0000d000?o00003P01o`4000080003o`0000@000?o00003`000ol0 000>0003o`0000d000?o00003@000ol0000=0003o`0000h000?o00003P000ol0000=0003o`0000h0 00?o00003@000ol0000>0003o`0000d000?o00003P000ol0000=0003o`0000d000?o00003P01o`40 00090003o`0000<00_l?0003o`0000h000?o00003@000ol0000>0003o`0000d000?o00003P000ol0 000>0003o`0000d000?o00003P000ol0000=0003o`0000h000?o00003@000ol0000>0003o`0000h0 00?o00003@000ol0000<00;o0@0000X000?o00000P000ol0003o00L00Ol100001`001?l00?l40003 o`000?l01`01o`40000800;o1@000ol0003o00L00Ol100003`000ol0000>0003o`0003L000?o0000 =`000ol0000g0003o`0003L000?o00003@01o`40000?0003o`00008000?o00002@000ol000090003 o`0000P000?o00002@000ol000080003o`0000T000?o00002@000ol000080003o`0000T000?o0000 2@000ol000080003o`0000T000?o000020000ol000090003o`0000T000?o000020000ol000090003 o`0000P000?o00002@000ol000090003o`0000P000?o00002@001Ol0003o0040000?0?oo2ol10000 \ \>"], ImageRangeCache->{{{0, 281}, {257, 0}} -> {-2.56129, -2.32064, 0.0172333, 0.0172333}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "From the vector field plot, it appears that initial points chosen around \ the edge of the above rectangle will produce a representative set of \ trajectories. Both ", StyleBox["First[]", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["Flatten[]", FontFamily->"Courier", FontWeight->"Bold"], " are present below only to get rid of extra braces. ", StyleBox["Evaluate[]", FontFamily->"Courier", FontWeight->"Bold"], " keeps ", StyleBox["Mathematica", FontSlant->"Italic"], " from complaining about not being able to compile the functions." }], "Text"], Cell["\<\ solns1 = Flatten[Table[{x[t],y[t]} /. First[NDSolve[ {x'[t] == 1 - x[t]y[t], y'[t] == x[t] - y[t]^3, x[0] == i, y[0] == j}, {x[t],y[t]},{t,0,10}]], {i,-2,2,4}, {j,-2,2,.5}],1];\ \>", "Input"], Cell["\<\ solns2 = Flatten[Table[{x[t],y[t]} /. First[NDSolve[ {x'[t] == 1 - x[t]y[t], y'[t] == x[t] - y[t]^3, x[0] == i, y[0] == j}, {x[t],y[t]},{t,0,10}]], {i,-2,2,.5}, {j,-2,2,4}],1];\ \>", "Input"], Cell[CellGroupData[{ Cell["\<\ p = ParametricPlot[Evaluate[Union[solns1,solns2]],{t,0,10}, PlotRange->{{-4,4},{-4,4}}]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.125 0.309017 0.0772542 [ [0 .29652 -6 -9 ] [0 .29652 6 0 ] [.125 .29652 -6 -9 ] [.125 .29652 6 0 ] [.25 .29652 -6 -9 ] [.25 .29652 6 0 ] [.375 .29652 -6 -9 ] [.375 .29652 6 0 ] [.625 .29652 -3 -9 ] [.625 .29652 3 0 ] [.75 .29652 -3 -9 ] [.75 .29652 3 0 ] [.875 .29652 -3 -9 ] [.875 .29652 3 0 ] [1 .29652 -3 -9 ] [1 .29652 3 0 ] [.4875 0 -12 -4.5 ] [.4875 0 0 4.5 ] [.4875 .07725 -12 -4.5 ] [.4875 .07725 0 4.5 ] [.4875 .15451 -12 -4.5 ] [.4875 .15451 0 4.5 ] [.4875 .23176 -12 -4.5 ] [.4875 .23176 0 4.5 ] [.4875 .38627 -6 -4.5 ] [.4875 .38627 0 4.5 ] [.4875 .46353 -6 -4.5 ] [.4875 .46353 0 4.5 ] [.4875 .54078 -6 -4.5 ] [.4875 .54078 0 4.5 ] [.4875 .61803 -6 -4.5 ] [.4875 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .30902 m 0 .31527 L s [(-4)] 0 .29652 0 1 Mshowa .125 .30902 m .125 .31527 L s [(-3)] .125 .29652 0 1 Mshowa .25 .30902 m .25 .31527 L s [(-2)] .25 .29652 0 1 Mshowa .375 .30902 m .375 .31527 L s [(-1)] .375 .29652 0 1 Mshowa .625 .30902 m .625 .31527 L s [(1)] .625 .29652 0 1 Mshowa .75 .30902 m .75 .31527 L s [(2)] .75 .29652 0 1 Mshowa .875 .30902 m .875 .31527 L s [(3)] .875 .29652 0 1 Mshowa 1 .30902 m 1 .31527 L s [(4)] 1 .29652 0 1 Mshowa .125 Mabswid .025 .30902 m .025 .31277 L s .05 .30902 m .05 .31277 L s .075 .30902 m .075 .31277 L s .1 .30902 m .1 .31277 L s .15 .30902 m .15 .31277 L s .175 .30902 m .175 .31277 L s .2 .30902 m .2 .31277 L s .225 .30902 m .225 .31277 L s .275 .30902 m .275 .31277 L s .3 .30902 m .3 .31277 L s .325 .30902 m .325 .31277 L s .35 .30902 m .35 .31277 L s .4 .30902 m .4 .31277 L s .425 .30902 m .425 .31277 L s .45 .30902 m .45 .31277 L s .475 .30902 m .475 .31277 L s .525 .30902 m .525 .31277 L s .55 .30902 m .55 .31277 L s .575 .30902 m .575 .31277 L s .6 .30902 m .6 .31277 L s .65 .30902 m .65 .31277 L s .675 .30902 m .675 .31277 L s .7 .30902 m .7 .31277 L s .725 .30902 m .725 .31277 L s .775 .30902 m .775 .31277 L s .8 .30902 m .8 .31277 L s .825 .30902 m .825 .31277 L s .85 .30902 m .85 .31277 L s .9 .30902 m .9 .31277 L s .925 .30902 m .925 .31277 L s .95 .30902 m .95 .31277 L s .975 .30902 m .975 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 0 m .50625 0 L s [(-4)] .4875 0 1 0 Mshowa .5 .07725 m .50625 .07725 L s [(-3)] .4875 .07725 1 0 Mshowa .5 .15451 m .50625 .15451 L s [(-2)] .4875 .15451 1 0 Mshowa .5 .23176 m .50625 .23176 L s [(-1)] .4875 .23176 1 0 Mshowa .5 .38627 m .50625 .38627 L s [(1)] .4875 .38627 1 0 Mshowa .5 .46353 m .50625 .46353 L s [(2)] .4875 .46353 1 0 Mshowa .5 .54078 m .50625 .54078 L s [(3)] .4875 .54078 1 0 Mshowa .5 .61803 m .50625 .61803 L s [(4)] .4875 .61803 1 0 Mshowa .125 Mabswid .5 .01545 m .50375 .01545 L s .5 .0309 m .50375 .0309 L s .5 .04635 m .50375 .04635 L s .5 .0618 m .50375 .0618 L s .5 .09271 m .50375 .09271 L s .5 .10816 m .50375 .10816 L s .5 .12361 m .50375 .12361 L s .5 .13906 m .50375 .13906 L s .5 .16996 m .50375 .16996 L s .5 .18541 m .50375 .18541 L s .5 .20086 m .50375 .20086 L s .5 .21631 m .50375 .21631 L s .5 .24721 m .50375 .24721 L s .5 .26266 m .50375 .26266 L s .5 .27812 m .50375 .27812 L s .5 .29357 m .50375 .29357 L s .5 .32447 m .50375 .32447 L s .5 .33992 m .50375 .33992 L s .5 .35537 m .50375 .35537 L s .5 .37082 m .50375 .37082 L s .5 .40172 m .50375 .40172 L s .5 .41717 m .50375 .41717 L s .5 .43262 m .50375 .43262 L s .5 .44807 m .50375 .44807 L s .5 .47898 m .50375 .47898 L s .5 .49443 m .50375 .49443 L s .5 .50988 m .50375 .50988 L s .5 .52533 m .50375 .52533 L s .5 .55623 m .50375 .55623 L s .5 .57168 m .50375 .57168 L s .5 .58713 m .50375 .58713 L s .5 .60258 m .50375 .60258 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .25 .15451 m .24134 .16402 L .23239 .17176 L .21668 .18156 L .20718 .18577 L .19817 .18886 L .19 .19107 L .18101 .19295 L .17207 .19438 L .16198 .19555 L .15679 .19601 L .15112 .1964 L .14568 .1967 L .14062 .19691 L .13554 .19706 L .13075 .19715 L .1254 .19721 L .11958 .19722 L .11393 .19719 L .10851 .19712 L .10355 .19702 L .09808 .19689 L .08513 .19648 L .0725 .19597 L .0416 .1944 L s .0416 .1944 m 0 .19183 L s .25 .19314 m .24409 .19541 L .23772 .1974 L .23216 .19881 L .22603 .20006 L .21868 .20122 L .21156 .20204 L .20814 .20235 L .20445 .20263 L .20101 .20284 L .1977 .203 L .19394 .20315 L .19045 .20324 L .18663 .20332 L .18239 .20335 L .17864 .20336 L .17457 .20333 L .17066 .20328 L .16706 .20321 L .16236 .20309 L .15795 .20295 L .14765 .20256 L .12774 .20155 L s .12774 .20155 m 0 .19271 L s .25 .23176 m .24345 .22817 L .23653 .22513 L .22724 .22185 L .21775 .21914 L .19504 .21422 L .16525 .20953 L .12821 .20502 L .07841 .20002 L s .07841 .20002 m 0 .19358 L s .3125 .15451 m .30679 .16484 L .30099 .17333 L .2911 .1843 L .28526 .18916 L .27982 .19285 L .26971 .19803 L .26451 .20002 L .25894 .20174 L .25407 .20296 L .24874 .20403 L .24291 .20494 L .23733 .2056 L .23386 .20592 L .2305 .20617 L .22743 .20636 L .22406 .20652 L .22225 .20658 L .22058 .20664 L .21723 .20672 L .21415 .20676 L .21083 .20678 L .20909 .20678 L .20721 .20677 L .20375 .20673 L .20162 .2067 L .19957 .20666 L .19567 .20656 L .18848 .20632 L .18159 .20603 L .16502 .20515 L .07304 .19847 L s .07304 .19847 m 0 .19301 L s .25 .27039 m .24996 .26861 L .24987 .26701 L .24969 .26517 L .24944 .26346 L .24884 .26046 L .24793 .25728 L .24663 .25388 L .24491 .2504 L .24095 .24447 L .23567 .23883 L .22961 .234 L .22173 .22919 L .21176 .22456 L .20019 .22043 L .18565 .21642 L .15365 .2101 L .11465 .20468 L .07013 .19984 L s .07013 .19984 m 0 .19394 L s .25 .30902 m .25552 .30156 L .25965 .29477 L .26313 .28747 L .26461 .28345 L .26567 .27985 L .26611 .27803 L .2665 .27613 L .26678 .27449 L .26701 .27275 L .26718 .27089 L .26728 .26918 L .26731 .26814 L .26731 .26716 L .26729 .26628 L .26726 .26534 L .26713 .26362 L .26696 .26208 L .26669 .26032 L .26637 .2587 L .26563 .25586 L .26459 .25288 L .26316 .24974 L .26157 .24692 L .25935 .24371 L .257 .24092 L .25128 .23564 L .24374 .23059 L .23615 .22675 L .22665 .22301 L .2165 .21986 L .20585 .21715 L .1813 .21237 L .14814 .20759 L .05587 .19805 L s .05587 .19805 m 0 .19364 L s .375 .15451 m .36952 .1749 L .36524 .18705 L .36081 .1969 L .3572 .20324 L .3539 .20786 L .35051 .21164 L .34705 .21462 L .34383 .21674 L .34055 .21836 L .33687 .21967 L .33498 .22017 L .33291 .22061 L .33091 .22095 L .32903 .22119 L .32714 .22138 L .32533 .22151 L .32427 .22156 L .3233 .2216 L .32276 .22162 L .32216 .22164 L .3216 .22165 L .32107 .22166 L .3201 .22167 L .31901 .22167 L .31794 .22166 L .31733 .22166 L .31677 .22165 L .31576 .22163 L .31465 .22159 L .31257 .22152 L .30798 .22129 L .3034 .22098 L .29177 .22001 L .26193 .21701 L .17159 .20782 L s .17159 .20782 m 0 .19335 L s .25 .34764 m .28886 .31909 L .30242 .3064 L .31347 .29367 L .32161 .28155 L .32676 .27111 L .32887 .26521 L .32964 .26245 L .33019 .26 L .33058 .25785 L .33073 .25678 L .33086 .25566 L .33092 .25508 L .33096 .25456 L .33103 .25355 L .33105 .25299 L .33106 .25239 L .33107 .25183 L .33106 .25132 L .33103 .25036 L .33101 .24988 L .33097 .24936 L .33088 .24846 L .33078 .24764 L .33046 .24585 L .33023 .24489 L .32999 .24404 L .32948 .24256 L .32881 .24103 L .32733 .23846 L .32556 .23622 L .32331 .23409 L .32111 .23244 L .31837 .23078 L .31515 .22921 L .31136 .2277 L .30352 .2253 L .29345 .223 L .28025 .22066 L .24947 .2164 L .20312 .21115 L .0389 .19618 L s .0389 .19618 m 0 .1933 L s .75 .38627 m .74378 .38968 L .73784 .39225 L .7313 .39446 L .72438 .39621 L .72096 .39689 L .71731 .39749 L .71416 .39791 L .71088 .39826 L .70801 .3985 L .70651 .3986 L .70491 .39869 L .70347 .39876 L .70217 .39881 L .70088 .39885 L .69967 .39887 L .69894 .39888 L .69815 .39889 L .69673 .3989 L .69538 .39889 L .69415 .39888 L .69284 .39885 L .69142 .39881 L .68864 .39871 L .68629 .39858 L .68385 .39843 L .67967 .39809 L .67054 .39708 L .66347 .39606 L .64505 .39241 L .63557 .38992 L .63028 .38827 L .62767 .38736 L .62637 .38686 L .62566 .38657 L .62533 .38642 L .62515 .38634 L .62507 .38631 L .62504 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .6875 .46353 m .66953 .4328 L .65738 .41681 L .64338 .40183 L .63129 .39119 L .62737 .3881 L .62594 .387 L .62535 .38655 L .62513 .38638 L .62505 .38631 L .62502 .38629 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke Mfstroke .75 .34764 m .74996 .34942 L .74987 .35103 L .74969 .35286 L .74945 .35456 L .74887 .35754 L .74802 .36067 L .74682 .364 L .74529 .36735 L .74193 .37291 L .73776 .37797 L .73337 .38207 L .72816 .38585 L .72228 .38913 L .71627 .39168 L .70973 .39373 L .70678 .39445 L .70368 .39509 L .69826 .39594 L .6956 .39624 L .69279 .39649 L .69153 .39657 L .69021 .39665 L .68909 .39671 L .68791 .39675 L .68677 .39678 L .68574 .39681 L .68473 .39682 L .68378 .39682 L .68269 .39682 L .6817 .39681 L .68062 .39679 L .68008 .39678 L .6795 .39676 L .67758 .3967 L .67555 .3966 L .67166 .39634 L .6683 .39604 L .66537 .39572 L .65394 .39405 L .64576 .39242 L .64028 .39113 L .63282 .38906 L .62905 .38784 L .62698 .38709 L .62598 .3867 L .62549 .3865 L .62523 .38638 L .62511 .38633 L .62505 .3863 L Mistroke .62502 .38628 L .62501 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .75 .30902 m .75549 .31664 L .75947 .32387 L .76124 .32805 L .76253 .33186 L .7631 .33396 L .76362 .33624 L .764 .33839 L .76426 .34036 L .76444 .34225 L .76454 .34427 L .76455 .34616 L .76449 .34787 L .76434 .34985 L .76422 .35097 L .76408 .35199 L .76377 .35385 L .76335 .35581 L .76216 .35994 L .7607 .36367 L .75717 .37016 L .75249 .37624 L .74672 .38174 L .74133 .38566 L .7351 .38919 L .72821 .39216 L .72082 .3945 L .71728 .39536 L .71397 .39604 L .71083 .39658 L .70794 .397 L .70516 .39732 L .70266 .39755 L .69995 .39775 L .69846 .39784 L .6971 .3979 L .69587 .39794 L .69458 .39798 L .69386 .39799 L .69317 .398 L .69191 .39802 L .6906 .39802 L .6894 .39801 L .68879 .398 L .68811 .39799 L .68677 .39796 L .68562 .39792 L .68454 .39788 L .68256 .39779 L .67832 .39752 L Mistroke .67487 .39723 L .67135 .39687 L .65881 .39512 L .64903 .39325 L .63706 .39032 L .63111 .38854 L .62813 .38752 L .62652 .38692 L .62575 .3866 L .62537 .38644 L .62518 .38636 L .62509 .38631 L .62504 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .75 .46353 m .72207 .43504 L .70169 .42014 L .67559 .40595 L .64807 .39481 L .63625 .39059 L .63066 .38856 L .62771 .38742 L .62632 .38686 L .62566 .38657 L .62531 .38642 L .62515 .38634 L .62507 .38631 L .62503 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L s .75 .27039 m .77157 .28609 L .78186 .2954 L .78969 .3041 L .79624 .31353 L .79903 .3188 L .80112 .32381 L .80189 .32607 L .80258 .32846 L .80308 .33053 L .80351 .33275 L .80386 .33513 L .80407 .33735 L .80415 .33869 L .80419 .33997 L .80417 .34236 L .80411 .34361 L .80401 .34495 L .80372 .34738 L .80332 .34971 L .80285 .35182 L .80143 .35654 L .79942 .36133 L .79501 .36881 L .78887 .37613 L .78107 .38288 L .77179 .38872 L .76256 .39297 L .75401 .39589 L .74596 .39794 L .74162 .3988 L .7376 .39946 L .73072 .40032 L .72716 .40064 L .72343 .4009 L .72151 .401 L .71975 .40107 L .71785 .40113 L .7168 .40116 L .71586 .40118 L .71487 .40119 L .71396 .4012 L .71298 .40121 L .71195 .40121 L .71024 .4012 L .70928 .40118 L .70839 .40117 L .70674 .40113 L .7052 .40109 L .70237 .40097 L Mistroke .69943 .40082 L .69633 .40063 L .68546 .39965 L .67698 .3986 L .66191 .39615 L .64403 .39225 L .63495 .38976 L .62993 .38816 L .62747 .38729 L .62626 .38682 L .62561 .38654 L .6253 .38641 L .62514 .38634 L .62506 .3863 L .62503 .38629 L .62501 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .625 .46353 m .61683 .43054 L .61259 .41338 L .61144 .40785 L .611 .40537 L .61068 .4033 L .61046 .40158 L .61037 .40074 L .6103 .39991 L .61025 .39924 L .6102 .39854 L .61018 .39794 L .61016 .3974 L .61016 .39708 L .61015 .39674 L .61016 .39617 L .61017 .39583 L .61018 .39552 L .61019 .39525 L .61021 .39496 L .61024 .39445 L .61029 .39394 L .61041 .39308 L .61054 .39233 L .61068 .39169 L .61107 .39041 L .61132 .3898 L .61157 .38928 L .61207 .38843 L .61264 .38768 L .61329 .38702 L .61435 .38624 L .61494 .38591 L .6155 .38567 L .61603 .38548 L .61657 .38533 L .61715 .38521 L .61742 .38516 L .61766 .38513 L .61789 .3851 L .61813 .38508 L .61834 .38506 L .61853 .38505 L .61864 .38505 L .61874 .38504 L .61884 .38504 L .6189 .38504 L .61896 .38504 L .61906 .38504 L .61912 .38504 L Mistroke .61918 .38504 L .61928 .38504 L .61938 .38504 L .61948 .38504 L .61957 .38505 L .61976 .38506 L .61993 .38506 L .6201 .38508 L .62069 .38513 L .62126 .38521 L .6218 .3853 L .62261 .38548 L .62379 .38581 L .62439 .38602 L .62469 .38614 L .62485 .3862 L .62493 .38624 L .62497 .38625 L .62498 .38626 L .62499 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .5 .46353 m .50288 .45076 L .50584 .44013 L .51092 .42594 L .51661 .41409 L .52153 .40619 L .52645 .39983 L .53157 .39446 L .54037 .38745 L .54476 .38478 L .54942 .38242 L .55378 .3806 L .5583 .37908 L .56235 .378 L .56592 .37724 L .56937 .37668 L .57252 .3763 L .57419 .37615 L .57572 .37604 L .57707 .37597 L .57782 .37594 L .5785 .37591 L .57923 .3759 L .57991 .37588 L .58064 .37588 L .58105 .37588 L .58141 .37588 L .58215 .37588 L .58256 .37589 L .58294 .3759 L .58363 .37592 L .58435 .37594 L .58552 .37599 L .58675 .37606 L .58892 .37622 L .59137 .37646 L .59351 .37673 L .6012 .37807 L .60484 .37891 L .6078 .3797 L .61606 .3824 L .62072 .38428 L .62295 .38527 L .62401 .38577 L .62454 .38604 L .62479 .38616 L .6249 .38622 L .62495 .38625 L .62498 .38626 L .62499 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .5625 .46353 m .56253 .45686 L .56262 .45154 L .56277 .44611 L .56296 .44156 L .56316 .43777 L .56338 .43458 L .56396 .42825 L .56463 .42288 L .56545 .41787 L .56639 .41337 L .56731 .40984 L .56931 .40392 L .57159 .39899 L .57376 .39539 L .57586 .39262 L .57814 .39018 L .58056 .38808 L .58483 .38532 L .58737 .38411 L .58969 .38323 L .59169 .38262 L .59381 .38212 L .5957 .38178 L .59739 .38155 L .5983 .38146 L .59911 .3814 L .59955 .38137 L .60002 .38134 L .60046 .38132 L .60086 .38131 L .60121 .3813 L .60157 .38129 L .60197 .38129 L .60233 .38129 L .60268 .38129 L .60306 .38129 L .60345 .3813 L .60381 .38131 L .60446 .38133 L .60504 .38136 L .60629 .38145 L .60755 .38156 L .6088 .38171 L .61087 .38201 L .61475 .38279 L .61948 .38412 L .62225 .3851 L .62363 .38565 L .62435 .38597 L Mistroke .62469 .38612 L .62485 .3862 L .62493 .38624 L .62497 .38625 L .62499 .38626 L .62499 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .4375 .46353 m .44867 .43869 L .4577 .4236 L .46729 .41094 L .47522 .40242 L .48978 .39025 L .50358 .38186 L .51624 .3763 L .5229 .37406 L .52878 .37245 L .53414 .37126 L .53897 .3704 L .54383 .36974 L .54633 .36948 L .54897 .36926 L .55126 .36911 L .5525 .36905 L .55365 .369 L .55472 .36897 L .55528 .36896 L .55586 .36894 L .55689 .36893 L .55783 .36892 L .55893 .36892 L .55954 .36893 L .56009 .36893 L .56116 .36895 L .56216 .36898 L .56331 .36902 L .56436 .36906 L .5667 .36919 L .57018 .36946 L .57385 .36985 L .58076 .37085 L .58683 .37202 L .59183 .3732 L .60122 .37595 L .61301 .38042 L .61907 .3832 L .62228 .38481 L .62373 .38558 L .62444 .38596 L .62475 .38613 L .62488 .38621 L .62495 .38624 L .62498 .38626 L .62499 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .375 .46353 m .39144 .43725 L .40432 .42125 L .42837 .39854 L .4476 .38522 L .46536 .37581 L .48277 .36888 L .49068 .36643 L .49766 .36461 L .51002 .36214 L .5162 .36127 L .51947 .36091 L .52252 .36063 L .52521 .36042 L .5281 .36026 L .52936 .3602 L .53068 .36015 L .53193 .36012 L .53305 .36009 L .53445 .36007 L .53574 .36007 L .53713 .36007 L .53783 .36007 L .53859 .36008 L .53987 .36011 L .54122 .36015 L .54363 .36024 L .54599 .36037 L .5485 .36054 L .55296 .36094 L .55714 .36143 L .56087 .36196 L .57589 .36498 L .58329 .36702 L .58946 .36901 L .607 .3762 L .61691 .38138 L .62142 .38402 L .62339 .38525 L .62432 .38584 L .62471 .38608 L .62488 .38619 L .62495 .38624 L .62498 .38626 L .62499 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .75 .23176 m .7835 .25215 L .8149 .27308 L .82805 .28369 L .83971 .29527 L .84439 .30099 L .84819 .30646 L .85127 .3118 L .8536 .31684 L .85554 .32242 L .8563 .32539 L .85692 .32858 L .85714 .33017 L .85732 .33191 L .85744 .33355 L .85749 .33506 L .85747 .33792 L .85738 .33951 L .85725 .34094 L .85687 .34376 L .85637 .34632 L .85566 .34911 L .85474 .35201 L .85278 .35679 L .8501 .36185 L .8423 .37225 L .83699 .37747 L .83168 .3818 L .82038 .38902 L .8089 .39439 L .7984 .39806 L .78679 .40104 L .78104 .40217 L .77493 .40316 L .76975 .40383 L .7642 .4044 L .75914 .40479 L .75455 .40505 L .75206 .40515 L .74982 .40522 L .74729 .40528 L .74493 .40531 L .74292 .40533 L .74082 .40532 L .73906 .40531 L .73714 .40528 L .73511 .40524 L .73297 .40518 L .72919 .40505 L .72499 .40484 L Mistroke .7207 .40458 L .71339 .40403 L .69876 .4025 L .67794 .39948 L .65154 .39419 L .63856 .39085 L .63203 .38887 L .62846 .38765 L .62672 .387 L .62587 .38666 L .62542 .38646 L .6252 .38637 L .62509 .38632 L .62504 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .25 .4249 m .32234 .37551 L .37032 .35049 L .40961 .33362 L .42614 .32777 L .44031 .3235 L .45271 .32041 L .46581 .31786 L .47289 .31681 L .47938 .31606 L .48554 .31552 L .48864 .31533 L .4904 .31524 L .49204 .31516 L .49376 .3151 L .49532 .31506 L .49704 .31503 L .49799 .31502 L .49888 .31501 L .5005 .31501 L .502 .31502 L .50363 .31504 L .50536 .31508 L .5068 .31512 L .50834 .31518 L .51113 .31531 L .51443 .31552 L .51744 .31576 L .52407 .31645 L .53124 .31744 L .54407 .31991 L .55561 .32292 L .56784 .32701 L .57996 .3321 L .59016 .33735 L .60673 .34841 L .61945 .36028 L .6265 .36952 L .6289 .37376 L .63031 .37701 L .63079 .3784 L .63114 .37974 L .63126 .3803 L .63135 .38085 L .63141 .38129 L .63144 .38153 L .63145 .38175 L .63147 .38195 L .63148 .38216 L .63148 .38235 L Mistroke .63148 .38251 L .63148 .3827 L .63147 .38287 L .63146 .38306 L .63145 .38323 L .63141 .38352 L .63137 .38377 L .63131 .38403 L .63124 .38428 L .63108 .38475 L .6309 .38511 L .63067 .38547 L .63044 .38575 L .63001 .38613 L .62976 .3863 L .62953 .38642 L .6293 .38653 L .62905 .38662 L .62884 .38667 L .62862 .38672 L .62839 .38676 L .62826 .38678 L .62815 .38679 L .62804 .3868 L .62795 .38681 L .6279 .38681 L .62785 .38681 L .6278 .38681 L .62775 .38681 L .6277 .38681 L .62766 .38681 L .62762 .38681 L .62758 .38681 L .62753 .38681 L .62751 .38681 L .62748 .38681 L .6274 .38681 L .62732 .38681 L .62724 .3868 L .6271 .38679 L .62694 .38677 L .62679 .38675 L .62654 .38671 L .62613 .38663 L .62584 .38656 L .62543 .38644 L .62521 .38636 L .6251 .38632 L .62505 .38629 L .62502 .38628 L Mistroke .62501 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .25 .46353 m .29703 .41645 L .33297 .39041 L .38405 .36211 L .40517 .35282 L .42516 .34535 L .44223 .34011 L .45699 .33649 L .47169 .33381 L .47919 .33282 L .48296 .33242 L .48698 .33206 L .49047 .33182 L .49363 .33165 L .49514 .33159 L .49678 .33153 L .49833 .33149 L .49976 .33146 L .50063 .33145 L .50157 .33144 L .50326 .33143 L .50491 .33144 L .50642 .33146 L .50805 .33149 L .50983 .33155 L .51168 .33162 L .5134 .3317 L .51669 .3319 L .51971 .33213 L .52646 .33283 L .5323 .33362 L .53837 .33465 L .54856 .33684 L .55924 .33982 L .57837 .3471 L .59521 .35604 L .60729 .36446 L .61592 .37199 L .62358 .38074 L .6251 .38314 L .62556 .38404 L .62581 .38468 L .62589 .38492 L .62595 .38516 L .62597 .38526 L .62599 .38536 L .62599 .38541 L .626 .38546 L .626 .3855 L .62601 .38554 L Mistroke .62601 .38556 L .62601 .38558 L .62601 .38562 L .62601 .38565 L .62601 .38568 L .62601 .38569 L .62601 .38571 L .62601 .38573 L .62601 .38575 L .626 .38577 L .626 .3858 L .62599 .38586 L .62598 .3859 L .62596 .38598 L .62594 .38605 L .62591 .38611 L .62587 .38616 L .62583 .3862 L .62576 .38626 L .62572 .38628 L .62569 .3863 L .62565 .38632 L .62561 .38633 L .62558 .38634 L .62555 .38634 L .62553 .38635 L .62551 .38635 L .62549 .38635 L .62548 .38635 L .62546 .38635 L .62545 .38636 L .62544 .38636 L .62543 .38636 L .62543 .38636 L .62542 .38636 L .62542 .38636 L .62541 .38636 L .6254 .38636 L .62539 .38636 L .62539 .38636 L .62538 .38636 L .62538 .38636 L .62536 .38635 L .62535 .38635 L .62534 .38635 L .62531 .38635 L .62527 .38634 L .62523 .38634 L .62512 .38631 L .62506 .3863 L Mistroke .62503 .38628 L .62502 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .75 .19314 m .83726 .25127 L .87091 .27505 L .88548 .28844 L .89561 .30085 L .89965 .30747 L .90141 .31099 L .90299 .31473 L .90413 .318 L .90512 .32162 L .90578 .32491 L .90619 .328 L .90641 .33128 L .90641 .33439 L .90623 .33716 L .90585 .34018 L .90523 .34342 L .90432 .34684 L .90208 .35288 L .89847 .35977 L .89349 .36684 L .88827 .37267 L .88202 .37837 L .86853 .38773 L .85482 .39458 L .84064 .39977 L .82757 .40325 L .8204 .40474 L .81269 .40604 L .80615 .40693 L .79907 .40768 L .79272 .4082 L .7869 .40854 L .78376 .40868 L .78092 .40878 L .77785 .40886 L .77467 .40891 L .77214 .40893 L .76948 .40894 L .767 .40892 L .76478 .40889 L .76221 .40885 L .75947 .40878 L .75462 .40861 L .74968 .40839 L .74456 .40809 L .73582 .40747 L .71816 .40575 L .69055 .40196 L .65793 .39575 L Mistroke .64193 .39181 L .63386 .38946 L .6294 .38799 L .62721 .38719 L .62605 .38673 L .62551 .3865 L .62525 .38639 L .62512 .38633 L .62506 .3863 L .62503 .38628 L .62501 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .625 .15451 m .64293 .18124 L .65916 .19833 L .69475 .22536 L .75918 .26443 L .78643 .28384 L .79732 .29366 L .80563 .30297 L .81293 .31395 L .81575 .31983 L .8169 .32284 L .81792 .32609 L .81861 .32883 L .81909 .33133 L .81945 .33384 L .81966 .33621 L .81973 .33754 L .81976 .33895 L .8197 .34148 L .8196 .34303 L .81946 .34447 L .81929 .34576 L .81908 .34715 L .81859 .34958 L .81803 .35177 L .81642 .3566 L .81448 .36091 L .81229 .36484 L .80625 .37297 L .79822 .38063 L .78934 .38683 L .7792 .39204 L .77028 .39546 L .76041 .39825 L .75144 .40007 L .74703 .40075 L .7423 .40133 L .73834 .40172 L .73421 .40202 L .73224 .40214 L .73041 .40223 L .72865 .4023 L .72704 .40235 L .72516 .40239 L .72418 .40241 L .72313 .40242 L .72205 .40243 L .72102 .40243 L .71913 .40242 L .71739 .4024 L Mistroke .7158 .40237 L .71409 .40233 L .71229 .40227 L .70833 .4021 L .70475 .4019 L .69843 .40142 L .6877 .40032 L .67799 .39903 L .66414 .3967 L .64586 .39275 L .63558 .38996 L .63044 .38834 L .62764 .38735 L .6263 .38683 L .62565 .38656 L .62531 .38642 L .62515 .38634 L .62507 .38631 L .62503 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .6875 .15451 m .77598 .23123 L .81379 .25456 L .84684 .27808 L .86043 .29075 L .86999 .30254 L .87356 .3083 L .87664 .31462 L .87778 .31753 L .87878 .32063 L .87952 .32348 L .88007 .32619 L .88032 .32779 L .88053 .32953 L .88074 .33258 L .88078 .3343 L .88075 .33613 L .88065 .33786 L .88051 .33941 L .88009 .34244 L .87976 .34413 L .87941 .34568 L .87764 .35145 L .87633 .35463 L .87492 .35754 L .87107 .36393 L .86652 .36981 L .86088 .37565 L .84965 .38447 L .83804 .39115 L .82452 .39685 L .81746 .39916 L .80985 .40123 L .80325 .40271 L .79727 .40383 L .7858 .40545 L .77989 .40605 L .77358 .40652 L .77047 .4067 L .7672 .40684 L .76563 .4069 L .76416 .40695 L .76144 .40701 L .75896 .40705 L .75633 .40706 L .75389 .40706 L .7517 .40704 L .74917 .407 L .74776 .40697 L .74646 .40694 L Mistroke .74167 .40678 L .73679 .40656 L .73254 .40631 L .72356 .40565 L .70923 .40422 L .69762 .40275 L .66324 .39684 L .64428 .39242 L .63489 .38978 L .63016 .38825 L .62754 .38732 L .62627 .38682 L .6256 .38654 L .62529 .38641 L .62514 .38634 L .62507 .3863 L .62503 .38629 L .62502 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .5 .15451 m .50301 .16732 L .50637 .17806 L .51274 .19264 L .51681 .19959 L .52078 .20522 L .52847 .21403 L .54509 .22769 L .56439 .23917 L .60517 .25839 L .64859 .27897 L .66591 .28882 L .68259 .30029 L .69094 .30729 L .69765 .31396 L .70311 .32048 L .70789 .32757 L .71142 .3345 L .71369 .34077 L .71447 .34376 L .7148 .34532 L .71509 .34696 L .71529 .34839 L .71545 .34994 L .71555 .35134 L .71561 .35263 L .71562 .35423 L .7156 .35513 L .71557 .35595 L .71547 .35744 L .7153 .359 L .7151 .36036 L .71487 .36162 L .71422 .36441 L .7133 .36728 L .71229 .36977 L .70949 .37489 L .70662 .37869 L .70319 .38217 L .7 .38471 L .6964 .38702 L .69207 .38919 L .68797 .39076 L .68403 .39191 L .68048 .39269 L .67707 .39325 L .67522 .39348 L .67356 .39364 L .67206 .39376 L .67127 .39381 L Mistroke .67045 .39385 L .66967 .39389 L .66897 .39391 L .66828 .39393 L .66764 .39394 L .66689 .39395 L .66609 .39396 L .66569 .39395 L .66527 .39395 L .66451 .39394 L .66377 .39393 L .66307 .39391 L .6618 .39386 L .66035 .39378 L .65905 .3937 L .65626 .39347 L .65191 .39298 L .64834 .39245 L .64177 .39123 L .63386 .38929 L .62941 .38794 L .62722 .38717 L .62613 .38676 L .62554 .38652 L .62527 .38639 L .62512 .38633 L .62506 .3863 L .62503 .38629 L .62501 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .4375 .15451 m .43753 .16117 L .43762 .16649 L .43778 .17192 L .43798 .17648 L .43821 .18028 L .43846 .18348 L .43913 .18984 L .43953 .19274 L .43993 .19525 L .44097 .20033 L .4421 .20459 L .44345 .20857 L .44488 .21195 L .44657 .2152 L .44995 .22025 L .45361 .22434 L .4573 .22761 L .46702 .23396 L .47706 .23873 L .50357 .24812 L .565 .26693 L .59644 .27818 L .61417 .28568 L .63009 .29354 L .64589 .30292 L .65865 .31232 L .67001 .32316 L .67483 .32903 L .67907 .33535 L .6819 .34067 L .68313 .34347 L .68425 .34647 L .68508 .34917 L .68569 .35161 L .68614 .35391 L .68633 .35513 L .68647 .35627 L .6866 .35759 L .68668 .35877 L .68672 .36003 L .68673 .36073 L .68672 .36137 L .68669 .36242 L .68662 .36356 L .68651 .36472 L .68638 .36578 L .68596 .36815 L .68544 .3702 L .68471 .37243 L Mistroke .68388 .37442 L .68209 .37773 L .6802 .38034 L .67781 .3829 L .67539 .38492 L .6709 .38765 L .66834 .38878 L .66601 .38959 L .66366 .39024 L .6612 .39075 L .66004 .39095 L .65896 .3911 L .657 .39131 L .65591 .39139 L .65532 .39142 L .65477 .39145 L .65428 .39147 L .65383 .39149 L .65334 .3915 L .65282 .3915 L .6523 .39151 L .65182 .39151 L .65155 .3915 L .65131 .3915 L .65103 .3915 L .65077 .39149 L .65026 .39148 L .64979 .39146 L .64876 .39141 L .6479 .39136 L .64715 .39131 L .64552 .39117 L .64285 .39085 L .6379 .39003 L .63448 .38928 L .63174 .38858 L .62839 .38756 L .62671 .38697 L .62588 .38665 L .62543 .38646 L .62521 .38637 L .6251 .38632 L .62505 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke Mfstroke .75 .4249 m .68521 .40358 L .65404 .39537 L .6398 .39137 L .63272 .38915 L .62882 .3878 L .62692 .38708 L .62591 .38668 L .62544 .38647 L .62522 .38637 L .6251 .38632 L .62505 .3863 L .62502 .38628 L .62501 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L s .3125 .46353 m .33416 .4358 L .35076 .41886 L .38096 .39454 L .42557 .36924 L .44483 .36144 L .46066 .35637 L .46889 .35421 L .47748 .35231 L .48524 .35091 L .49228 .3499 L .49837 .34923 L .50144 .34896 L .50475 .34873 L .5066 .34862 L .5083 .34854 L .51006 .34847 L .51163 .34843 L .51318 .34839 L .51462 .34837 L .51614 .34836 L .51698 .34836 L .51776 .34837 L .51924 .34838 L .52081 .34841 L .52229 .34845 L .52362 .3485 L .52685 .34865 L .52987 .34884 L .53574 .34936 L .54192 .35011 L .55174 .35175 L .56184 .35404 L .5797 .35969 L .5929 .36533 L .60371 .37103 L .61642 .37926 L .62174 .38335 L .6238 .38509 L .62462 .38584 L .62489 .38612 L .62498 .38622 L .62499 .38624 L .625 .38626 L .625 .38626 L .625 .38626 L .625 .38626 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mistroke .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .5625 .15451 m .66503 .25145 L .71376 .27949 L .72519 .28751 L .73608 .29639 L .74483 .30502 L .7515 .31323 L .75672 .32165 L .75885 .32614 L .76063 .33091 L .76123 .3329 L .76177 .33504 L .76216 .33689 L .7625 .3389 L .76267 .34011 L .76279 .34123 L .76289 .3423 L .76296 .34343 L .76301 .34559 L .76298 .34752 L .76286 .34941 L .76266 .35138 L .76241 .35305 L .76208 .35485 L .76107 .35877 L .75982 .3623 L .75688 .36831 L .75288 .37413 L .74759 .37978 L .74213 .3842 L .73571 .38816 L .72865 .39145 L .72249 .3936 L .71676 .39513 L .71063 .39634 L .70727 .39684 L .70426 .39719 L .70148 .39745 L .699 .39763 L .69766 .39771 L .69622 .39777 L .69488 .39782 L .69366 .39786 L .69255 .39788 L .69152 .39789 L .69041 .39789 L .68923 .39789 L .68802 .39788 L .68688 .39785 L .68588 .39783 L Mistroke .6848 .3978 L .68234 .39769 L .68018 .39757 L .67562 .39724 L .66825 .39646 L .66184 .39558 L .65674 .39473 L .6476 .39292 L .63673 .39023 L .63116 .38856 L .62806 .3875 L .62654 .38692 L .62573 .3866 L .62535 .38643 L .62517 .38635 L .62508 .38631 L .62504 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .75 .15451 m .85592 .23722 L .89694 .26417 L .91479 .27857 L .92805 .29232 L .93347 .29964 L .9381 .30767 L .93971 .31123 L .94113 .31502 L .94209 .31827 L .9429 .32185 L .94345 .32547 L .9437 .32877 L .94374 .33059 L .94371 .33258 L .94343 .33618 L .94293 .33952 L .94215 .34305 L .94116 .34635 L .94008 .34931 L .93634 .35695 L .93186 .36368 L .9259 .37066 L .91856 .37748 L .90427 .38749 L .89603 .39197 L .88666 .3962 L .87766 .39958 L .86922 .40224 L .86127 .40435 L .85251 .40629 L .83758 .40878 L .82958 .40975 L .82224 .41044 L .81434 .41098 L .81046 .41119 L .80627 .41135 L .80275 .41146 L .79904 .41154 L .7956 .41157 L .79252 .41159 L .79066 .41158 L .7887 .41157 L .78525 .41153 L .78336 .41149 L .78161 .41145 L .77769 .41134 L .77134 .41109 L .76479 .41076 L .75295 .40996 L Mistroke .74284 .40909 L .72278 .4069 L .69469 .40287 L .66117 .39652 L .64302 .39212 L .63414 .38956 L .6297 .3881 L .62729 .38722 L .62613 .38677 L .62557 .38653 L .62527 .3864 L .62513 .38633 L .62506 .3863 L .62503 .38629 L .62501 .38628 L .62501 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke .25 .38627 m .34846 .32917 L .40624 .29612 L .41737 .29053 L .42894 .28543 L .43886 .28177 L .44973 .2786 L .45565 .27725 L .46121 .27621 L .46661 .27542 L .46941 .27508 L .47245 .27477 L .47522 .27455 L .47778 .27438 L .48038 .27424 L .48287 .27415 L .48428 .27411 L .48579 .27409 L .48722 .27407 L .48853 .27407 L .49007 .27408 L .49095 .27409 L .49176 .2741 L .49325 .27413 L .49484 .27417 L .49814 .2743 L .5013 .27447 L .50732 .27492 L .51395 .27559 L .52131 .27653 L .53495 .27878 L .54795 .28153 L .57613 .28949 L .59209 .29538 L .60659 .30184 L .62003 .30907 L .63285 .31757 L .64323 .32623 L .65102 .33449 L .65753 .34359 L .66021 .34853 L .66218 .35307 L .66352 .35713 L .66436 .3607 L .66466 .3625 L .6648 .3635 L .66489 .3644 L .66496 .36534 L .66502 .36632 L .66504 .36721 L Mistroke .66503 .36804 L .66501 .36892 L .66498 .3694 L .66495 .36984 L .66488 .37063 L .66478 .37145 L .66456 .37281 L .66426 .37423 L .66385 .37567 L .66334 .3771 L .66226 .37943 L .66098 .38144 L .65965 .38308 L .65695 .38549 L .65547 .38646 L .65382 .38733 L .65222 .38801 L .65052 .38857 L .64898 .38896 L .64761 .38923 L .64634 .38941 L .64572 .38948 L .64506 .38955 L .64435 .3896 L .64404 .38961 L .64371 .38963 L .64341 .38964 L .64309 .38965 L .64281 .38966 L .64254 .38966 L .64222 .38966 L .64191 .38966 L .64164 .38966 L .64135 .38965 L .6412 .38965 L .64103 .38964 L .64071 .38963 L .64013 .38961 L .63915 .38954 L .63814 .38946 L .63648 .38927 L .6349 .38903 L .6334 .38875 L .63098 .38822 L .62805 .3874 L .62656 .3869 L .62575 .38659 L .62537 .38644 L .62518 .38636 L .62508 .38631 L Mistroke .62504 .38629 L .62502 .38628 L .62501 .38628 L .625 .38627 L .625 .38627 L .625 .38627 L .625 .38627 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc00;o3`000ol0000=00;o3`02odP0001;0003o`0000h0 00?o00003@000ol0000>0003o`0000P000?o00000`000ol0000?0003o`0000`000?o00003`000ol0 000>0003o`0004D0001:0003o`0000h000?o00003P000ol0000>0003o`0000D000Co003o1@000ol0 000@0003o`0000`000?o00003`000ol0000>0003o`0004@0001800;o40000ol0000>0003o`0000l0 00?o00001P02o`H000?o00004@000ol0000;0003o`00010000?o00003P000ol000130000A`000ol0 000@0003o`0000h000?o00003`000ol0000>0003o`00018000?o00002`000ol0000@0003o`0000h0 0_m30000A@02oa8000?o00003`000ol0000?0003o`0000h00_lD0003o`0000/000?o00004002oa00 00?o0000@00004<00_lC0003o`00010000?o00003`000ol0000>00;o5@000ol0000:0003o`000180 00?o00003P000ol0000o0000@@02oa@000?o00004@000ol0000?0003o`0000h00_lF0003o`0000X0 00?o00004P000ol0000>00;o?`0003l00_lE0003o`00014000?o000040000ol0000>0003o`3o01H0 00?o00002P000ol0000B0003o`0000l000?o0000?00003`00olE00;o50000ol0000@0003o`0000h0 00?o0?l05`000ol0000:0003o`00018000?o00003`000ol0000k00002@0:obD01?l?0003o`0000@0 0_lF0003o`00010000?o00003P001?l00?lG0003o`0000X000?o00004P02o`<00_l;0003o`0003X0 000>02[o3`04o`H000?o00005@000ol0000B0003o`0000d000Co003o60000ol0000:0003o`0001<0 00?o00000P000ol0000900;o>P0001D06_lC00Go2002oaP000?o00004P000ol0000=0005o`000?l0 60000ol0000:00;o50000ol0000200;o2`000ol0000g00007`0So`L01_lI0003o`0001<000?o0000 3@000ol000020003o`0001H000?o00002`000ol0000B0003o`0000<000?o00002@000ol0000f0000 :`0Noah000?o000050000ol0000=0003o`00008000?o00005`000ol0000;0003o`00018000?o0000 0`000ol000090003o`0003D0000`01Ko80000ol0000F0003o`0000`000?o00000`000ol0000G0003 o`0000/00_lC00;o1002o`X00_le0000=`0:o`802olG0003o`0001L000?o000030000ol0000400;o 60000ol0000<0003o`00018000?o00000`000ol000090003o`000380000m00So1P0>o`T00olK0003 o`0000/000?o00001P000ol0000F0003o`0000`000?o00004P000ol0000300;o2P000ol0000a0000 @0000ol0000200?o2P0@oah000?o00000P03o`H000?o00001`000ol0000F0003o`0000`000?o0000 4P000ol000040003o`0000P00_la0000@@03o`<00ol?00?o9@03o`8000?o00001@000ol0000800;o 5`000ol0000<00;o4`000ol0000400;o2P000ol0000^0000A002o`<00ol@00;o8@06o`030?l000H0 0_l;00;o5P000ol0000=00;o2`02o`D00_l60003o`0000P000?o0000;@0004H000?o00000P000ol0 000@00;o9@02o`L000?o00003002oaD000?o00003P000ol0000:0003o`0000@000?o00001002o`T0 00?o0000;00004L000?o00000P000ol0000@00;o9@03o`D000?o00003P02oa@000?o00003P02o`/0 0_l500;o1P000ol0000700;o;00004P000?o00000P000ol0000@0003o`0002800_l200?o0P000ol0 000@00;o4`000ol0000?00;o2`000ol000040003o`0000@000?o000020000ol0000Y0000B@000ol0 00020003o`0000l00_lZ00?o50000ol0000A0003o`00010000?o00002@02o`D000?o00001002o`T0 0_lY0000BP001?l00002oa4000?o0000:P03oa<00_lB0003o`0001000_l;0003o`0000<00_l60003 o`0000P00_lW0000BP000ol000020003o`0000l000?o0000:P000ol00003oa800_lA00;o4P02o`X0 0_l50003o`0000@00_l:0003o`0002@0001;0005o`000?l04@000ol0000Z0003o`0000<01?l@0003 o`0001000_lB0003o`0000T000?o00000`02o`H000?o00002002ob@0001;0003o`00008000?o0000 3@000ol0000[0003o`0000L00ol>00;o4P02oa400_l:00;o1@000ol0000400;o2P000ol0000Q0000 B`000ol000020003o`0000d000?o0000:`000ol0000:00?o3@03oa400_lA00;o2P02o`@00_l60003 o`0000P00_lQ0000B`000ol000020003o`0000d000?o0000:`000ol0000=00?o3@02oa4000?o0000 40000ol000090003o`0000<000?o00001002o`X000?o00007P0000/00olM00?o7@06o`l000?o0000 2P03oah000?o00004003o`T01Ol@00;o2P04o`<00_l:00;o1002o`H00ol80003o`0001@00ol60000 30000ol0000O0003o`0001`000Co003o3`000ol0000;0003o`0001804ol>00?o1`001?l00003o`l0 0_l90004o`00o`@00_l:0003o`0000<000?o000010000ol0o`080003o`0001@000?o00001@0000@0 1Ol00`3oo`02oaL01Ol40003o`0001D01Ol300;o3`000ol0000500Go0P000ol0000>00Co2`000ol0 000500Co3@02o`D000?o00001002o`l00_l80003o`0000;o10000ol000080003o`0000<000?o0000 1002o`T000?o00004@04o`H0000:0003o`3o01l00_lQ0003o`0000`000?o00003@000ol0000;00?o 3`000ol0000900?o3003o`8000?o00001P02o`l000?o00001P001Ol0003o00@000?o000020000ol0 00030003o`0000800ol90003o`00014000?o0?l01`0000X000?o0?l08@000ol0000K0004o`00o`h0 00?o00003@000ol0000900;o4P000ol0000<00Co2`03o`X000?o00003@000ol000020004o`00o`@0 00Go0000o`0;0003o`0000<000?o00000`02o`T000?o000040000ol0o`0700002`02oah00olO00?o 3@000ol0000=00;o2003oa@000?o00004004o`P00ol:00;o3P000ol0000200;o1P001Ol0003o00/0 00?o00000`000ol0o`02o`8000?o00001`000ol0000@00;o1`0004h000?o00002`000ol0000G0003 o`0001D000?o00005003o`P00_l:0003o`0000`000?o00002P001?l00002o`X000?o00000`000ol0 00030003o`0000P000?o0000600004h000?o00002P000ol0000F00;o60000ol0000G00;o2002o`T0 00?o000030000ol000090003o`0000<000?o00001`000ol000040003o`0000<000?o000020000ol0 000G0000C@000ol0000:0003o`0001D00_lJ0003o`0001T00_l800;o20000ol0000<0003o`0000T0 00?o00000`000ol000070003o`0000@000?o00000`000ol000080003o`0001H0001<0003o`0000X0 00?o00005002oa`000?o00006`000ol000070003o`0000H000?o000030000ol000090003o`000080 00?o000020000ol000030003o`0000@000?o00001`000ol0000F00002@3oo`_o1`0000T000?o0000 0`000ol000040003o`0000@000?o00000`000ol000040003o`0000@000?o00000`000ol000040003 o`0000@000?o00000`000ol000040003o`0000800_l60003o`0000@000?o00000`02o`D000?o0000 10000ol000030003o`0000@000?o000010000ol000030003o`0000@000?o00000`000ol000040003 o`0000@00_l40004o`00o`<000?o00000`02o`D000?o000010000ol000030003o`0000<00_l30004 o`00o`D00_l50003o`0000@000?o00000`001Ol0003o008000?o000010000ol000030003o`0000D0 00090003o`0001h000?o00007P000ol000080003o`0001400olF01Ko5P000ol0o`070003o`0000H0 00?o00002`02o`X000?o00000P000ol000070003o`0000<00_l500;o2@000ol0000<0003o`0000D0 001D00;o4P02oaH00ol;0003o`0000P00olF0003o`0000D000?o00001P000ol0000;00;o2P001Ol0 003o00T000?o000010000ol000040003o`0000L000?o0000500005<000?o00004002oa@01?l>0003 o`0000/00olD0003o`0000D000?o00001P000ol0000;0003o`0000P000?o00000P000ol000070003 o`0000<000?o000010000ol000070003o`0001@0001A00;o4@02oa<00olB0003o`0000h01?lA0003 o`0000D000?o00001P000ol0000:00;o2P001Ol0003o00T000?o00000`000ol000040003o`0000L0 00?o00005000050000?o00003`02oa<00_l>00oo3@000ol0000?0003o`0000@000?o00001P000ol0 000;0003o`0000P000Go0000o`090003o`0000@000?o00000`000ol000070003o`0001@0001?0003 o`0000l000?o00004@02o`T01ol70003o`0000D01ol70003o`0000l000?o000010000ol000060003 o`0000X000?o000020001Ol0003o00T000?o000010000ol000030003o`0000L000?o0000500004d0 0_l@00;o4@03o`P00ol>0003o`0000`00_l600;o3`000ol000050003o`0000D000?o00002P02o`T0 00Go0000o`090003o`0000<00_l50003o`0000L000?o0000500004`000?o00003P02oa000ol900;o 4@000ol0000>00?o1@03o`d000?o000010000ol000050003o`0000X00_l90005o`000?l02@000ol0 00030003o`0000@000?o00001`000ol0000D0000B`000ol0000=00;o3`03o`X00_lC0003o`3o00Co 3@02o`H000?o00002`000ol000030003o`0000H000?o00001P000ol00002o`T000Go0000o`090003 o`0000<000?o000010000ol000070003o`0001@0001J0003o`0000d00_l:00?o3P09o`D02Ol600?o 0`000ol0000;0003o`0000@000?o00001@000ol000060003o`0000;o2@001Ol0003o00T000?o0000 0`000ol000040003o`0000H000?o00005@0005P00_l>00;o2@03o`h00ol70003o`0000d01?l50005 o`000?l03@000ol000030003o`0000D000?o00001P001?l00?l:0005o`000?l02@000ol000020003 o`0000@000?o00001`000ol0000E0000EP02o`h00_l800?o3P03o`X000?o00004@03o`<000Go0000 o`0<0003o`0000<000?o00001@000ol000060004o`00o`T000Go0000o`090003o`0000<000?o0000 0`000ol000070003o`0001H0001E0003o`0000`00_l800;o3P03o`d04ol40005o`000?l00`000ol0 00090003o`0000<000?o00001@000ol000050003o`0000;o2@001Ol0003o00P000?o000010000ol0 00030003o`0000L000?o00005P0005<00_l>0003o`0000H00_l=00?o3005oa801?l01P3oool0o`<0 00?o000020000ol000030003o`0000@000?o00001P000ol00002o`T000Co003o2@000ol000030003 o`0000<000?o00001`000ol0000G0000D@02o`h00_l80003o`0000/00_l=00;o10000ol0000700oo 0P000ol0o`030003o`0000L000?o00000`000ol000040003o`0000H000Co003o2@001Ol0003o00P0 00?o00000`000ol000040003o`0000H000?o0000600004l00_l>00;o2002o``00_l<00?o1P000ol0 000200Go3@06o`030?l0008000?o00001P000ol0000200;o1@000ol000060003o`0000;o20001Ol0 003o00P000?o00000`000ol0000300;o20000ol0000I0000CP000ol0000<00;o2002o`d000?o0000 2P05o`H000?o0?l00_l;013o0P000ol000060003o`00008000?o00000`000ol0000500;o0P02o`P0 00Go0000o`080003o`0000800_l400;o2002oa`0001<00;o3P000ol0000600;o3@02o`/00_l30003 o`0000D00_l:00Co2009o`030?oo00H00_l30003o`0000<000?o00001@001Ol0003o00T000?o0000 0_l700;o10000ol000030003o`0000L000?o0000700004/000?o00003002o`P000?o00002`02o`/0 0_l50003o`0000@00ol90003o`0000P00ol500Go1P02o`<00_l50003o`0000<00_l200Co1P02o`80 00?o00001P000ol0000200;o1@000ol000070003o`0001d0001I0003o`0000H00_l=0003o`0000X0 00?o00001@000ol000030003o`3o00T000?o000020000ol0000500;o0P09o`800_l400?o1@000ol0 0002o`030?l000D00_l200;o1`02o`@000?o00000`02o`P00_lP0000E`02o`L00_l=00;o2`02o`P0 00Co00000_l20003o`0000H000?o000020000ol000060003o`0000802_l00`3oo`03o`D01_l00`3o o`0400?o0P02o`L00_l400;o1@000ol0000600;o8P0005H000?o00001P000ol0000;00;o30000ol0 000700;o0P000ol000020003o`0000D000?o000020000ol000070003o`0000@000?o00005ol400;o 0P03o`L00_l300?o1003o`H00olT0000E002o`P000?o00002`000ol0000;0003o`0000/000?o0000 0`000ol000040003o`0000P000?o000020000ol000050004o`0001go1@05o`030?oo00;o0`04o`L0 0_lW0000D`000ol0000600;o3@000ol0000;0003o`0000/000?o000010000ol000030003o`0000T0 00?o000020000ol000060003o`0000<00_l2013o0`08o`801?l300Co1P05obT0001B0003o`0000H0 00?o00002`02o`d000?o00002`000ol000050003o`00008000?o00002P000ol000080003o`0000H0 00?o00001@02o`<00ol00`3oo`0Ko`@01_l^0000D002o`P000?o00002`000ol0000<0003o`0000/0 00?o00001P000ol000020003o`0000T000?o00002@000ol000070003o`0000H00ol300?o1P0Ioc@0 001?0003o`0000L000?o00002`000ol0000<0003o`0000/000?o00001`001Ol0003o00`000?o0000 2@000ol000080003o`0000P00_l400?oD00004d00_l800;o3@000ol0000<0003o`0000/000?o0000 20001Ol0003o00`000?o00002@000ol000090003o`0000T00_l500?oC@0004`000?o00001`000ol0 000<0003o`0000`000?o00002`000ol000090004o`00o`d000?o00002P000ol000080003o`0000/0 00?o00001@03odX0001;0003o`0000L000?o000030000ol0000=0003o`0000/000?o00002@000ol0 o`0>0003o`0000X000?o00002@000ol0000;0003o`0000L000?o0000A`0005@000?o000030000ol0 000=0003o`0000/000?o00002P000ol0o`0=0003o`0000`000?o00002@000ol0000;0003o`000500 001C0003o`0000`000?o00003@000ol0000<0003o`0000X000?o0?l03@000ol0000<0003o`0000X0 00?o00002`000ol0001?0000DP000ol0000<0003o`0000d000?o000030000ol0000;00;o3P000ol0 000<0003o`0000X000?o000030000ol0001>0000D@000ol0000=0003o`0000d000?o000030000ol0 000;00;o3P000ol0000=0003o`0000X000?o000030000ol0001=0000D0000ol0000=0003o`0000d0 00?o000030000ol0000<00;o3P000ol0000=0003o`0000/000?o000030000ol0001<0000C`000ol0 000=0003o`0000d000?o00003@000ol0000<0003o`0000d000?o00003@000ol0000;0003o`0000d0 00?o0000B`0004h000?o00003@000ol0000=0003o`0000d000?o00003@000ol0000=0003o`0000d0 00?o000030000ol0000=0003o`0004X0001=0003o`0000h000?o00003@000ol0000=0003o`0000@0 1?l50003o`0000d000?o00003@000ol0000<0003o`0000h000?o0000B@0004`000?o00003P000ol0 000=0003o`0000h000?o00001@000ol000050003o`0000d000?o00003P000ol0000<0003o`0000h0 00?o0000B00004/000?o00003P000ol0000=0003o`0000h000?o00001`000ol0000400;o3P000ol0 000>0003o`0000d000?o00003P000ol000170000R0000ol000030003o`0008T000250004o`00o`D0 00?o0000R@0008H00_l60003o`0008T0002>0003o`0008T0002>0003o`0008T0002>0003o`0008T0 002>0003o`0008T0002>0003o`0008T0002>0003o`0008T0002>0003o`0008T0002>0003o`0008T0 002>0003o`0008T0002>0003o`0008T0002>0003o`0008T0002>0003o`0008T0002>0003o`0008T0 002>0003o`0008T0002500?o1P000ol000290000R0000ol000030003o`0008T000280003o`0000<0 0_n:0000QP02o`H000?o0000R@0008P000?o00000`000ol000290000Q@03o`H000?o0000R@0008h0 00?o0000R@0008h000?o0000R@0008h000?o0000R@0008h000?o0000R@0008h000?o0000R@0008h0 00?o0000R@0008h000?o0000R@0008h000?o0000R@0008h000?o0000R@0008h000?o0000R@0008h0 00?o0000R@0008h000?o0000R@0008h000?o0000R@0008h000?o0000R@0008h000?o0000R@0008H0 0ol50003o`0008T000270003o`0000@000?o0000R@0008D01?l500;oRP0008D000?o0?l0TP0008D0 00?o0?l0TP0008H00_nB0000o`0K0000\ \>"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-4.28103, -4.21956, 0.0301481, 0.0487807}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Closed]], Cell[TextData[{ "It appears that the trajectories near and to the left of the saddle point \ at ", StyleBox["{-1,-1}", FontFamily->"Courier", FontWeight->"Bold"], " go off to infinity asymptotically along the same curve towards the left. \ Trajectories to the right of the saddle point seem to spiral into the \ critical point at ", StyleBox["{1,1}", FontFamily->"Courier", FontWeight->"Bold"], "." }], "Text"], Cell[OutputFormData["\<\ Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output"], Cell[CellGroupData[{ Cell["Show[p,v,PlotRange->{{-2,2},{-2,2}}]", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.25 0.309017 0.154508 [ [0 .29652 -6 -9 ] [0 .29652 6 0 ] [.125 .29652 -12 -9 ] [.125 .29652 12 0 ] [.25 .29652 -6 -9 ] [.25 .29652 6 0 ] [.375 .29652 -12 -9 ] [.375 .29652 12 0 ] [.625 .29652 -9 -9 ] [.625 .29652 9 0 ] [.75 .29652 -3 -9 ] [.75 .29652 3 0 ] [.875 .29652 -9 -9 ] [.875 .29652 9 0 ] [1 .29652 -3 -9 ] [1 .29652 3 0 ] [.4875 0 -12 -4.5 ] [.4875 0 0 4.5 ] [.4875 .07725 -24 -4.5 ] [.4875 .07725 0 4.5 ] [.4875 .15451 -12 -4.5 ] [.4875 .15451 0 4.5 ] [.4875 .23176 -24 -4.5 ] [.4875 .23176 0 4.5 ] [.4875 .38627 -18 -4.5 ] [.4875 .38627 0 4.5 ] [.4875 .46353 -6 -4.5 ] [.4875 .46353 0 4.5 ] [.4875 .54078 -18 -4.5 ] [.4875 .54078 0 4.5 ] [.4875 .61803 -6 -4.5 ] [.4875 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash 0 .30902 m 0 .31527 L s [(-2)] 0 .29652 0 1 Mshowa .125 .30902 m .125 .31527 L s [(-1.5)] .125 .29652 0 1 Mshowa .25 .30902 m .25 .31527 L s [(-1)] .25 .29652 0 1 Mshowa .375 .30902 m .375 .31527 L s [(-0.5)] .375 .29652 0 1 Mshowa .625 .30902 m .625 .31527 L s [(0.5)] .625 .29652 0 1 Mshowa .75 .30902 m .75 .31527 L s [(1)] .75 .29652 0 1 Mshowa .875 .30902 m .875 .31527 L s [(1.5)] .875 .29652 0 1 Mshowa 1 .30902 m 1 .31527 L s [(2)] 1 .29652 0 1 Mshowa .125 Mabswid .025 .30902 m .025 .31277 L s .05 .30902 m .05 .31277 L s .075 .30902 m .075 .31277 L s .1 .30902 m .1 .31277 L s .15 .30902 m .15 .31277 L s .175 .30902 m .175 .31277 L s .2 .30902 m .2 .31277 L s .225 .30902 m .225 .31277 L s .275 .30902 m .275 .31277 L s .3 .30902 m .3 .31277 L s .325 .30902 m .325 .31277 L s .35 .30902 m .35 .31277 L s .4 .30902 m .4 .31277 L s .425 .30902 m .425 .31277 L s .45 .30902 m .45 .31277 L s .475 .30902 m .475 .31277 L s .525 .30902 m .525 .31277 L s .55 .30902 m .55 .31277 L s .575 .30902 m .575 .31277 L s .6 .30902 m .6 .31277 L s .65 .30902 m .65 .31277 L s .675 .30902 m .675 .31277 L s .7 .30902 m .7 .31277 L s .725 .30902 m .725 .31277 L s .775 .30902 m .775 .31277 L s .8 .30902 m .8 .31277 L s .825 .30902 m .825 .31277 L s .85 .30902 m .85 .31277 L s .9 .30902 m .9 .31277 L s .925 .30902 m .925 .31277 L s .95 .30902 m .95 .31277 L s .975 .30902 m .975 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 0 m .50625 0 L s [(-2)] .4875 0 1 0 Mshowa .5 .07725 m .50625 .07725 L s [(-1.5)] .4875 .07725 1 0 Mshowa .5 .15451 m .50625 .15451 L s [(-1)] .4875 .15451 1 0 Mshowa .5 .23176 m .50625 .23176 L s [(-0.5)] .4875 .23176 1 0 Mshowa .5 .38627 m .50625 .38627 L s [(0.5)] .4875 .38627 1 0 Mshowa .5 .46353 m .50625 .46353 L s [(1)] .4875 .46353 1 0 Mshowa .5 .54078 m .50625 .54078 L s [(1.5)] .4875 .54078 1 0 Mshowa .5 .61803 m .50625 .61803 L s [(2)] .4875 .61803 1 0 Mshowa .125 Mabswid .5 .01545 m .50375 .01545 L s .5 .0309 m .50375 .0309 L s .5 .04635 m .50375 .04635 L s .5 .0618 m .50375 .0618 L s .5 .09271 m .50375 .09271 L s .5 .10816 m .50375 .10816 L s .5 .12361 m .50375 .12361 L s .5 .13906 m .50375 .13906 L s .5 .16996 m .50375 .16996 L s .5 .18541 m .50375 .18541 L s .5 .20086 m .50375 .20086 L s .5 .21631 m .50375 .21631 L s .5 .24721 m .50375 .24721 L s .5 .26266 m .50375 .26266 L s .5 .27812 m .50375 .27812 L s .5 .29357 m .50375 .29357 L s .5 .32447 m .50375 .32447 L s .5 .33992 m .50375 .33992 L s .5 .35537 m .50375 .35537 L s .5 .37082 m .50375 .37082 L s .5 .40172 m .50375 .40172 L s .5 .41717 m .50375 .41717 L s .5 .43262 m .50375 .43262 L s .5 .44807 m .50375 .44807 L s .5 .47898 m .50375 .47898 L s .5 .49443 m .50375 .49443 L s .5 .50988 m .50375 .50988 L s .5 .52533 m .50375 .52533 L s .5 .55623 m .50375 .55623 L s .5 .57168 m .50375 .57168 L s .5 .58713 m .50375 .58713 L s .5 .60258 m .50375 .60258 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto fill -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto -0.02 0.005 lineto stroke } ifelse grestore } def % End of user PostScript .5 Mabswid .125 0 m .11357 .02067 L .10198 .03764 L .08219 .05957 L .07052 .0693 L .05964 .07668 L .03942 .08705 L .02902 .09102 L .01788 .09446 L .00813 .0969 L s .00813 .0969 m 0 .09854 L s 0 .30902 m .01103 .29411 L .0193 .28052 L .02626 .26591 L .02922 .25788 L .03134 .25068 L .03222 .24705 L .033 .24323 L .03355 .23996 L .03402 .23648 L .03437 .23277 L .03456 .22934 L .03461 .22726 L .03462 .2253 L .03459 .22355 L .03451 .22165 L .03427 .21822 L .03392 .21514 L .03339 .21163 L .03274 .20838 L .03125 .2027 L .02917 .19674 L .02633 .19045 L .02315 .18481 L .0187 .1784 L .01401 .17282 L .00256 .16227 L s .00256 .16227 m 0 .16055 L s .25 0 m .23905 .04079 L .23049 .06509 L .22163 .08479 L .21439 .09745 L .2078 .1067 L .20103 .11426 L .19411 .12022 L .18766 .12446 L .1811 .12771 L .17375 .13032 L .16997 .13133 L .16582 .13221 L .16181 .13288 L .15806 .13337 L .15427 .13374 L .15067 .134 L .14855 .13411 L .1466 .13419 L .14551 .13423 L .14432 .13426 L .1432 .13428 L .14214 .1343 L .14019 .13432 L .13802 .13432 L .13588 .13431 L .13466 .1343 L .13354 .13428 L .13152 .13423 L .12929 .13417 L .12514 .13402 L .11597 .13356 L .10679 .13295 L .08354 .13101 L .02387 .125 L s .02387 .125 m 0 .12257 L s 0 .38627 m .07771 .32916 L .10484 .30378 L .12694 .27831 L .14321 .25408 L .15351 .23321 L .15774 .2214 L .15927 .21589 L .16039 .21098 L .16116 .20669 L .16147 .20455 L .16173 .2023 L .16184 .20114 L .16193 .2001 L .16205 .19807 L .1621 .19696 L .16213 .19577 L .16214 .19465 L .16213 .19362 L .16207 .1917 L .16201 .19074 L .16194 .18971 L .16177 .18791 L .16156 .18627 L .16092 .18269 L .16046 .18077 L .15997 .17906 L .15895 .1761 L .15763 .17304 L .15466 .16791 L .15111 .16343 L .14663 .15916 L .14222 .15585 L .13674 .15254 L .1303 .14939 L .12271 .14638 L .10704 .14158 L .0869 .13699 L .06051 .1323 L s .06051 .1323 m 0 .12392 L s 1 .46353 m .98756 .47035 L .97568 .47548 L .9626 .47989 L .94876 .4834 L .94192 .48476 L .93462 .48595 L .92831 .4868 L .92177 .4875 L .91601 .48799 L .91301 .48819 L .90983 .48837 L .90695 .48851 L .90435 .4886 L .90177 .48868 L .89935 .48873 L .89787 .48875 L .89629 .48877 L .89347 .48878 L .89076 .48876 L .8883 .48873 L .88567 .48868 L .88284 .48861 L .87727 .48839 L .87257 .48815 L .8677 .48784 L .85935 .48717 L .84107 .48515 L .82694 .4831 L .7901 .4758 L .77115 .47082 L .76056 .46753 L .75533 .46569 L .75273 .4647 L .75132 .46412 L .75065 .46383 L .7503 .46367 L .75014 .4636 L .75007 .46356 L .75003 .46354 L .75002 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mistroke .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .875 .61803 m .83906 .55658 L .81475 .5246 L .78675 .49465 L .76258 .47337 L .75474 .46719 L .75187 .46498 L .7507 .46408 L .75026 .46374 L .7501 .46361 L .75004 .46356 L .75001 .46354 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mistroke .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mistroke .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mistroke Mfstroke 1 .38627 m .99993 .38983 L .99974 .39304 L .99938 .39669 L .99891 .40011 L .99774 .40606 L .99603 .41233 L .99365 .41897 L .99058 .42569 L .98385 .43681 L .97552 .44693 L .96673 .45512 L .95632 .46268 L .94456 .46924 L .93254 .47433 L .91945 .47844 L .91356 .47988 L .90736 .48116 L .89651 .48285 L .8912 .48346 L .88559 .48396 L .88306 .48413 L .88043 .48429 L .87819 .48439 L .87581 .48448 L .87354 .48455 L .87149 .48459 L .86946 .48462 L .86756 .48463 L .86538 .48462 L .86339 .48461 L .86124 .48457 L .86017 .48454 L .859 .48451 L .85516 .48438 L .8511 .48418 L .84333 .48366 L .8366 .48306 L .83074 .48243 L .80789 .47908 L .79152 .47583 L .78057 .47325 L .76564 .46911 L .75809 .46667 L .75396 .46517 L .75196 .46438 L .75099 .46397 L .75047 .46375 L .75023 .46364 L .7501 .46358 L Mistroke .75005 .46355 L .75002 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke 1 .44821 m .99345 .45445 L .98266 .4623 L .97019 .46936 L .95642 .47529 L .94163 .47998 L .93456 .48171 L .92795 .48307 L .92167 .48415 L .91588 .48498 L .91031 .48562 L .90532 .48609 L .8999 .48649 L .89692 .48666 L .8942 .48678 L .89175 .48687 L .88917 .48694 L .88771 .48697 L .88635 .48699 L .88382 .48702 L .88119 .48702 L .8788 .487 L .87757 .48698 L .87622 .48696 L .87354 .4869 L .87123 .48683 L .86908 .48675 L .86512 .48657 L .85663 .48603 L .84975 .48545 L .8427 .48473 L .81763 .48121 L .79807 .47747 L .77411 .47162 L .76222 .46806 L .75627 .46603 L .75304 .46482 L .75149 .46419 L .75075 .46387 L .75035 .46369 L .75017 .46361 L .75008 .46356 L .75004 .46354 L .75002 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mistroke .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke 1 .61803 m .94413 .56106 L .90337 .53126 L .85119 .50289 L .79614 .48061 L .7725 .47217 L .76132 .4681 L .75542 .46583 L .75264 .4647 L .75131 .46413 L .75062 .46382 L .7503 .46367 L .75014 .4636 L .75007 .46356 L .75003 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s 1 .4848 m .99191 .48685 L .98323 .48857 L .97521 .4899 L .96143 .49162 L .95433 .49227 L .94685 .49278 L .94302 .49298 L .93951 .49313 L .93571 .49325 L .93361 .4933 L .93171 .49334 L .92974 .49337 L .92793 .49338 L .92596 .49339 L .9239 .4934 L .92048 .49337 L .91856 .49335 L .91678 .49332 L .91347 .49325 L .91039 .49315 L .90474 .49293 L .89885 .49263 L .89266 .49224 L .87092 .49029 L .85395 .48818 L .82383 .48328 L .78805 .47548 L .7699 .47051 L .75986 .46731 L .75495 .46556 L .75252 .46461 L .75121 .46407 L .75059 .4638 L .75027 .46366 L .75013 .46359 L .75006 .46356 L .75003 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s .75 .61803 m .73365 .55206 L .72518 .51773 L .72288 .50669 L .722 .50172 L .72136 .49757 L .72092 .49413 L .72075 .49247 L .72059 .49079 L .72049 .48946 L .72041 .48807 L .72036 .48686 L .72032 .48578 L .72031 .48514 L .72031 .48447 L .72032 .48332 L .72033 .48264 L .72035 .48202 L .72038 .48148 L .72041 .4809 L .72049 .47988 L .72059 .47885 L .72081 .47715 L .72108 .47564 L .72137 .47436 L .72215 .47181 L .72264 .47059 L .72314 .46954 L .72414 .46784 L .72528 .46633 L .72658 .46501 L .72869 .46345 L .72989 .4628 L .731 .46232 L .73206 .46194 L .73315 .46164 L .7343 .4614 L .73483 .46131 L .73532 .46124 L .73577 .46119 L .73625 .46114 L .73668 .46111 L .73706 .46109 L .73728 .46108 L .73747 .46107 L .73769 .46107 L .7378 .46106 L .73791 .46106 L .73812 .46106 L .73824 .46106 L Mistroke .73835 .46106 L .73855 .46106 L .73876 .46107 L .73896 .46107 L .73913 .46108 L .73953 .46109 L .73986 .46111 L .74021 .46114 L .74138 .46125 L .74253 .4614 L .74361 .46159 L .74522 .46193 L .74759 .4626 L .74879 .46302 L .74939 .46326 L .74971 .46339 L .74986 .46346 L .74993 .46349 L .74997 .46351 L .74998 .46352 L .74999 .46352 L .75 .46352 L .75 .46352 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .5 .61803 m .50576 .5925 L .51168 .57124 L .52183 .54286 L .53322 .51917 L .54306 .50335 L .5529 .49064 L .56315 .4799 L .58074 .46589 L .58952 .46054 L .59883 .45582 L .60757 .45219 L .6166 .44915 L .6247 .44697 L .63183 .44546 L .63873 .44434 L .64505 .44358 L .64837 .44328 L .65144 .44306 L .65414 .44292 L .65564 .44286 L .65701 .44281 L .65847 .44277 L .65982 .44275 L .66128 .44274 L .66209 .44274 L .66283 .44274 L .6643 .44275 L .66512 .44276 L .66588 .44278 L .66726 .44281 L .6687 .44286 L .67104 .44296 L .67351 .4431 L .67784 .44342 L .68274 .44391 L .68702 .44444 L .70241 .44712 L .70969 .44881 L .7156 .45039 L .73211 .45579 L .74144 .45954 L .7459 .46153 L .74801 .46253 L .74909 .46306 L .74957 .4633 L .7498 .46342 L .74991 .46348 L .74996 .4635 L .74998 .46351 L Mistroke .74999 .46352 L .75 .46352 L .75 .46352 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .625 .61803 m .62507 .60471 L .62523 .59407 L .62554 .58321 L .62591 .57411 L .62633 .56653 L .62677 .56014 L .62791 .54749 L .62925 .53675 L .6309 .52672 L .63279 .51773 L .63463 .51065 L .63863 .49881 L .64318 .48896 L .64753 .48176 L .65172 .47622 L .65628 .47134 L .66112 .46715 L .66966 .46162 L .67474 .4592 L .67937 .45744 L .68338 .45623 L .68762 .45522 L .69139 .45454 L .69478 .45409 L .69659 .45391 L .69821 .45378 L .69909 .45372 L .70004 .45367 L .70092 .45363 L .70173 .4536 L .70241 .45358 L .70314 .45357 L .70393 .45356 L .70466 .45355 L .70536 .45356 L .70612 .45356 L .7069 .45358 L .70762 .4536 L .70892 .45365 L .71008 .45371 L .71258 .45387 L .71509 .45411 L .71761 .4544 L .72175 .45501 L .7295 .45657 L .73897 .45922 L .7445 .46117 L .74725 .46228 L .74871 .46292 L Mistroke .74938 .46323 L .7497 .46338 L .74986 .46346 L .74993 .46349 L .74997 .46351 L .74999 .46352 L .74999 .46352 L .75 .46352 L .75 .46352 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .375 .61803 m .39734 .56837 L .41541 .53819 L .43458 .51286 L .45045 .49583 L .47955 .47148 L .50716 .45471 L .53247 .44357 L .5458 .4391 L .55756 .43588 L .56827 .4335 L .57794 .43179 L .58766 .43047 L .59266 .42995 L .59794 .4295 L .60252 .42921 L .60499 .42909 L .6073 .42899 L .60944 .42892 L .61055 .4289 L .61172 .42887 L .61378 .42884 L .61565 .42883 L .61785 .42883 L .61907 .42884 L .62018 .42885 L .62231 .42889 L .62432 .42894 L .62662 .42902 L .62872 .42911 L .63339 .42937 L .64035 .42991 L .6477 .43068 L .66152 .43268 L .67366 .43503 L .68365 .43739 L .70243 .44288 L .72602 .45183 L .73814 .45738 L .74455 .4606 L .74746 .46214 L .74888 .46291 L .7495 .46324 L .74977 .46339 L .7499 .46347 L .74995 .4635 L .74998 .46351 L .74999 .46352 L .75 .46352 L .75 .46352 L Mistroke .75 .46352 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .25 .61803 m .28289 .56549 L .30864 .53347 L .35675 .48806 L .3952 .46142 L .43073 .44259 L .46554 .42875 L .48135 .42385 L .49532 .4202 L .52004 .41527 L .5324 .41353 L .53894 .4128 L .54504 .41223 L .55042 .41183 L .5562 .4115 L .55871 .41139 L .56137 .41129 L .56386 .41122 L .56609 .41117 L .56891 .41113 L .57147 .41111 L .57426 .41112 L .57566 .41113 L .57718 .41115 L .57973 .4112 L .58244 .41128 L .58727 .41146 L .59198 .41172 L .59701 .41206 L .60591 .41286 L .61427 .41384 L .62174 .41489 L .65179 .42095 L .66657 .42502 L .67893 .429 L .71401 .44339 L .73383 .45374 L .74283 .45903 L .74678 .46148 L .74864 .46265 L .74941 .46315 L .74976 .46337 L .7499 .46346 L .74996 .4635 L .74998 .46351 L .74999 .46352 L .75 .46352 L .75 .46352 L .75 .46353 L .75 .46353 L Mistroke .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke 1 .50142 m .99965 .50143 L .99457 .50154 L .98985 .50161 L .98584 .50163 L .98164 .50163 L .97811 .5016 L .97428 .50155 L .97023 .50147 L .96594 .50135 L .95838 .50108 L .94999 .50067 L .94139 .50015 L .92679 .49904 L .89751 .49599 L .85588 .48994 L .80308 .47937 L .77711 .47268 L .76407 .46873 L .75691 .46629 L .75344 .46498 L .75174 .4643 L .75083 .46391 L .75041 .46372 L .75019 .46362 L .75009 .46357 L .75004 .46355 L .75002 .46354 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s 0 .54078 m .14469 .442 L .24064 .39195 L .31921 .35823 L .35229 .34652 L .38062 .33798 L .40542 .3318 L .43161 .32671 L .44578 .3246 L .45875 .32309 L .47108 .32203 L .47728 .32164 L .48081 .32145 L .48409 .32131 L .48752 .32119 L .49063 .32111 L .49409 .32104 L .49598 .32102 L .49776 .321 L .50101 .321 L .50399 .32101 L .50726 .32106 L .51071 .32113 L .5136 .32122 L .51669 .32134 L .52226 .3216 L .52886 .32202 L .53487 .3225 L .54815 .32388 L .56248 .32587 L .58813 .33081 L .61123 .33683 L .63568 .345 L .65992 .35518 L .68032 .36568 L .71346 .3878 L .73891 .41154 L .753 .43002 L .7578 .4385 L .76063 .445 L .76157 .44779 L .76228 .45047 L .76252 .45158 L .7627 .45268 L .76282 .45357 L .76287 .45404 L .76291 .45448 L .76293 .45488 L .76295 .4553 L .76296 .45567 L Mistroke .76296 .45601 L .76296 .45639 L .76294 .45673 L .76292 .4571 L .76289 .45744 L .76282 .45802 L .76274 .45853 L .76263 .45904 L .76249 .45955 L .76216 .46048 L .7618 .46121 L .76135 .46192 L .76089 .46248 L .76002 .46325 L .75952 .46358 L .75906 .46383 L .75859 .46404 L .7581 .46421 L .75769 .46433 L .75724 .46443 L .75677 .46451 L .75652 .46455 L .7563 .46457 L .75609 .46459 L .7559 .4646 L .7558 .4646 L .75569 .46461 L .75559 .46461 L .7555 .46461 L .75541 .46461 L .75532 .46461 L .75524 .46461 L .75515 .46461 L .75506 .46461 L .75501 .46461 L .75496 .46461 L .75479 .4646 L .75464 .46459 L .75448 .46458 L .7542 .46456 L .75389 .46453 L .75358 .46449 L .75307 .46441 L .75225 .46425 L .75167 .4641 L .75087 .46386 L .75042 .4637 L .75021 .46362 L .7501 .46357 L .75005 .46355 L Mistroke .75002 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke 0 .61803 m .09405 .52389 L .16594 .47181 L .26809 .4152 L .31033 .39662 L .35031 .38169 L .38446 .3712 L .41397 .36397 L .44337 .35861 L .45838 .35662 L .46593 .35582 L .47397 .35511 L .48093 .35463 L .48726 .35428 L .49028 .35416 L .49356 .35404 L .49666 .35396 L .49952 .3539 L .50126 .35387 L .50314 .35386 L .50653 .35385 L .50982 .35386 L .51283 .3539 L .51609 .35397 L .51966 .35408 L .52336 .35422 L .5268 .35438 L .53338 .35478 L .53943 .35525 L .55292 .35663 L .56459 .35823 L .57675 .36028 L .59711 .36467 L .61848 .37063 L .65675 .38519 L .69042 .40307 L .71459 .41991 L .73183 .43497 L .74716 .45245 L .75021 .45726 L .75111 .45907 L .75162 .46033 L .75178 .46083 L .7519 .4613 L .75194 .46151 L .75197 .46171 L .75199 .46181 L .752 .4619 L .75201 .46199 L .75201 .46207 L Mistroke .75202 .46211 L .75202 .46215 L .75202 .46222 L .75202 .46228 L .75202 .46234 L .75202 .46237 L .75202 .46241 L .75202 .46244 L .75201 .46247 L .75201 .46253 L .752 .46259 L .75199 .4627 L .75197 .46279 L .75193 .46294 L .75188 .46308 L .75181 .4632 L .75174 .4633 L .75166 .46339 L .75153 .4635 L .75145 .46355 L .75138 .46358 L .7513 .46362 L .75123 .46364 L .75116 .46366 L .7511 .46367 L .75106 .46368 L .75102 .46368 L .75099 .46369 L .75095 .46369 L .75092 .46369 L .75089 .46369 L .75088 .46369 L .75086 .46369 L .75085 .46369 L .75085 .46369 L .75083 .46369 L .75082 .46369 L .7508 .46369 L .75079 .46369 L .75078 .46369 L .75076 .46369 L .75075 .46369 L .75073 .46369 L .7507 .46369 L .75068 .46369 L .75062 .46368 L .75053 .46367 L .75045 .46366 L .75024 .46361 L .75012 .46357 L Mistroke .75006 .46355 L .75003 .46354 L .75002 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke 1 .50778 m .99935 .50775 L .98912 .50717 L .97164 .50592 L .93632 .50248 L .88109 .4949 L .81587 .48248 L .78386 .47461 L .76772 .46991 L .7588 .46696 L .75443 .46537 L .7521 .46445 L .75102 .46399 L .7505 .46376 L .75023 .46364 L .75011 .46358 L .75005 .46355 L .75002 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s .75 0 m .78587 .05347 L .81833 .08763 L .88949 .14171 L s .88949 .14171 m 1 .20871 L s 1 .49156 m .99406 .49247 L .98461 .49364 L .97668 .49441 L .96842 .49503 L .96448 .49526 L .96081 .49544 L .95731 .49558 L .95407 .49568 L .95032 .49576 L .94836 .4958 L .94626 .49582 L .94409 .49584 L .94205 .49584 L .93826 .49583 L .93478 .49579 L .93161 .49573 L .92818 .49564 L .92459 .49553 L .91666 .49518 L .9095 .49477 L .89686 .49383 L .87539 .49163 L .85599 .48904 L .82829 .48439 L .79173 .47647 L .77115 .47091 L .76087 .46766 L .75529 .46569 L .7526 .46465 L .7513 .46411 L .75062 .46381 L .7503 .46367 L .75015 .4636 L .75007 .46356 L .75003 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s .875 0 m 0 0 rlineto s .875 0 m 1 .10839 L s 1 .50502 m .99833 .50499 L .99551 .50493 L .99292 .50487 L .98333 .50455 L .97359 .5041 L .96508 .5036 L .94712 .50228 L .91846 .49942 L .89524 .49648 L .82648 .48465 L .78856 .47583 L .76979 .47054 L .76031 .46749 L .75509 .46562 L .75254 .46463 L .7512 .46407 L .75058 .4638 L .75028 .46366 L .75013 .46359 L .75006 .46356 L .75003 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s .5 0 m .50603 .02561 L .51275 .04711 L .52548 .07627 L .53363 .09015 L .54155 .10142 L .55695 .11905 L .59018 .14636 L .62877 .16933 L .71034 .20777 L .79717 .24893 L .83182 .26861 L .86518 .29156 L .88188 .30557 L .8953 .3189 L .90622 .33193 L .91577 .34613 L .92284 .35999 L .92738 .37252 L .92894 .37851 L .9296 .38163 L .93017 .38491 L .93057 .38776 L .9309 .39086 L .93111 .39366 L .93122 .39624 L .93125 .39945 L .93121 .40124 L .93114 .40288 L .93093 .40586 L .9306 .40898 L .9302 .41171 L .92975 .41423 L .92843 .41981 L .92661 .42554 L .92459 .43052 L .91898 .44076 L .91324 .44836 L .90638 .45532 L .90001 .46041 L .89281 .46503 L .88414 .46936 L .87594 .4725 L .86805 .47481 L .86095 .47637 L .85415 .47748 L .85044 .47794 L .84713 .47826 L .84411 .4785 L .84255 .4786 L Mistroke .84091 .47869 L .83934 .47876 L .83795 .47881 L .83656 .47884 L .83527 .47887 L .83379 .47889 L .83218 .47889 L .83138 .47889 L .83053 .47889 L .82902 .47887 L .82753 .47884 L .82615 .4788 L .82361 .4787 L .8207 .47855 L .8181 .47839 L .81253 .47792 L .80383 .47694 L .79668 .47589 L .78354 .47345 L .76773 .46957 L .75882 .46686 L .75443 .46533 L .75226 .4645 L .75108 .46401 L .75053 .46377 L .75025 .46364 L .75012 .46358 L .75006 .46355 L .75003 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .375 0 m .37507 .01332 L .37524 .02397 L .37556 .03483 L .37597 .04394 L .37643 .05154 L .37692 .05795 L .37825 .07066 L .37905 .07646 L .37987 .08148 L .38193 .09164 L .3842 .10016 L .38691 .10812 L .38977 .11488 L .39314 .12139 L .3999 .13148 L .40721 .13966 L .4146 .14621 L .43404 .1589 L .45412 .16845 L .50714 .18721 L .63001 .22483 L .69288 .24734 L .72835 .26235 L .76019 .27806 L .79179 .29681 L .8173 .31563 L .84002 .33731 L .84966 .34904 L .85813 .36169 L .86379 .37232 L .86626 .37793 L .8685 .38392 L .87017 .38933 L .87139 .39421 L .87228 .39879 L .87266 .40124 L .87295 .40352 L .8732 .40616 L .87336 .40853 L .87344 .41104 L .87345 .41244 L .87344 .41372 L .87338 .41582 L .87324 .41809 L .87302 .42042 L .87276 .42255 L .87191 .42728 L .87089 .43138 L .86942 .43585 L Mistroke .86777 .43982 L .86417 .44644 L .86041 .45165 L .85561 .45679 L .85079 .46082 L .84181 .46629 L .83669 .46854 L .83203 .47017 L .82731 .47146 L .8224 .47249 L .82008 .47287 L .81792 .47317 L .814 .47359 L .81181 .47376 L .81063 .47383 L .80954 .47389 L .80855 .47393 L .80766 .47395 L .80667 .47398 L .80563 .47399 L .8046 .474 L .80365 .474 L .80311 .47399 L .80262 .47399 L .80207 .47398 L .80155 .47397 L .80051 .47394 L .79958 .47391 L .79751 .47381 L .7958 .47371 L .79429 .4736 L .79104 .47332 L .7857 .47269 L .7758 .47104 L .76896 .46955 L .76347 .46813 L .75677 .4661 L .75343 .46493 L .75176 .46428 L .75085 .46391 L .75042 .46372 L .7502 .46362 L .75009 .46357 L .75005 .46355 L .75002 .46354 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mistroke Mfstroke 1 .54078 m .87042 .49815 L .80808 .48173 L .77961 .47372 L .76543 .46928 L .75764 .46658 L .75384 .46515 L .75182 .46434 L .75088 .46393 L .75043 .46373 L .7502 .46362 L .7501 .46357 L .75005 .46355 L .75002 .46354 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s .125 .61803 m .16832 .56259 L .20152 .5287 L .26192 .48006 L .35114 .42945 L .38966 .41386 L .42132 .40372 L .43779 .3994 L .45496 .3956 L .47048 .3928 L .48456 .39078 L .49674 .38944 L .50288 .3889 L .50949 .38844 L .51319 .38823 L .51661 .38807 L .52011 .38793 L .52327 .38784 L .52635 .38777 L .52924 .38773 L .53227 .38771 L .53397 .38771 L .53553 .38772 L .53848 .38775 L .54162 .38781 L .54457 .38789 L .54724 .38798 L .55371 .38828 L .55975 .38867 L .57148 .3897 L .58383 .3912 L .60349 .39449 L .62369 .39907 L .6594 .41036 L .6858 .42165 L .70741 .43305 L .73284 .44951 L .74348 .45767 L .7476 .46116 L .74923 .46267 L .74977 .46322 L .74996 .46343 L .74999 .46347 L .75 .4635 L .75001 .4635 L .75001 .46351 L .75001 .46351 L .75001 .46351 L .75001 .46352 L .75001 .46352 L Mistroke .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46352 L .75001 .46353 L .75001 .46353 L .75001 .46353 L .75001 .46353 L .75001 .46353 L .75001 .46353 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mistroke .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .625 0 m .83005 .19388 L .92753 .24996 L .95038 .26599 L .97216 .28375 L .98966 .30102 L s .98966 .30102 m 1 .31374 L s 1 .4454 m .99519 .45054 L .98426 .45938 L .97142 .46731 L .9573 .47388 L .94497 .47819 L .93352 .48125 L .92126 .48366 L .91455 .48466 L .90853 .48537 L .90295 .48589 L .898 .48625 L .89531 .4864 L .89243 .48653 L .88975 .48663 L .88732 .48669 L .88509 .48674 L .88304 .48676 L .88082 .48677 L .87846 .48676 L .87603 .48673 L .87376 .48669 L .87175 .48664 L .86959 .48657 L .86467 .48637 L .86037 .48613 L .85123 .48546 L .83651 .48391 L .82368 .48214 L .81349 .48045 L .79521 .47683 L .77346 .47144 L .76232 .46809 L .75612 .46598 L .75308 .46483 L .75146 .46418 L .75071 .46385 L .75035 .46369 L .75016 .4636 L .75008 .46356 L .75004 .46354 L .75002 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s 1 .51039 m .98568 .50916 L .94557 .50478 L .88938 .49673 L .82234 .48402 L .78603 .47522 L .76827 .47009 L .75941 .46718 L .75458 .46543 L .75226 .46451 L .75114 .46404 L .75054 .46378 L .75026 .46365 L .75012 .46358 L .75006 .46355 L .75003 .46354 L .75001 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L s 0 .46353 m .19691 .34933 L .31248 .28323 L .33474 .27204 L .35788 .26184 L .37772 .25453 L .39946 .24819 L .41131 .24548 L .42242 .24341 L .43323 .24182 L .43883 .24115 L .44491 .24053 L .45045 .24007 L .45556 .23973 L .46076 .23947 L .46574 .23928 L .46856 .23921 L .47158 .23916 L .47444 .23913 L .47705 .23912 L .48015 .23914 L .4819 .23915 L .48351 .23918 L .4865 .23924 L .48968 .23933 L .49627 .23959 L .5026 .23993 L .51465 .24083 L .52789 .24216 L .54263 .24404 L .5699 .24855 L .59589 .25404 L .65226 .26996 L .68419 .28175 L .71318 .29466 L .74006 .30913 L .7657 .32613 L .78645 .34344 L .80205 .35996 L .81506 .37817 L .82043 .38804 L .82436 .39713 L .82703 .40524 L .82872 .41239 L .82933 .41597 L .82959 .41799 L .82978 .41979 L .82993 .42166 L .83003 .42363 L .83007 .42541 L Mistroke .83007 .42707 L .83001 .42882 L .82996 .42979 L .8299 .43067 L .82976 .43225 L .82957 .43388 L .82913 .43661 L .82851 .43945 L .82771 .44232 L .82669 .44518 L .82451 .44984 L .82197 .45387 L .81931 .45713 L .8139 .46196 L .81094 .46391 L .80764 .46565 L .80444 .467 L .80105 .46812 L .79796 .46891 L .79522 .46944 L .79268 .46981 L .79143 .46995 L .79011 .47007 L .78871 .47017 L .78808 .47021 L .78742 .47024 L .78683 .47026 L .78619 .47028 L .78562 .47029 L .78509 .4703 L .78443 .4703 L .78382 .4703 L .78327 .4703 L .78269 .47029 L .78239 .47028 L .78207 .47027 L .78141 .47025 L .78026 .4702 L .77829 .47007 L .77628 .4699 L .77296 .46951 L .7698 .46904 L .7668 .46849 L .76196 .46742 L .7561 .46578 L .75312 .46478 L .7515 .46417 L .75073 .46385 L .75036 .46369 L .75017 .46361 L Mistroke .75008 .46357 L .75004 .46355 L .75002 .46353 L .75001 .46353 L .75 .46353 L .75 .46353 L .75 .46353 L Mfstroke .0001 w 0 0 m 0 0 rlineto s % Start of user PostScript -2. -2. -2.11748 -1.76503 MAarrowhead1 % End of user PostScript 0 .04415 m 0 0 rlineto s % Start of user PostScript -2. -1.71429 -2.14873 -1.52824 MAarrowhead1 % End of user PostScript 0 .08829 m 0 0 rlineto s % Start of user PostScript -2. -1.42857 -2.18829 -1.33575 MAarrowhead1 % End of user PostScript 0 .13244 m 0 0 rlineto s % Start of user PostScript -2. -1.14286 -2.1785 -1.21329 MAarrowhead1 % End of user PostScript 0 .17658 m 0 0 rlineto s % Start of user PostScript -2. -0.857143 -2.091 -1.03171 MAarrowhead1 % End of user PostScript 0 .22073 m 0 0 rlineto s % Start of user PostScript -2. -0.571429 -2.01603 -0.774938 MAarrowhead1 % End of user PostScript 0 .26487 m .01106 .23333 L s % Start of user PostScript -2. -0.285714 -1.95574 -0.489851 MAarrowhead1 % End of user PostScript 0 .30902 m .02386 .27953 L s % Start of user PostScript -2. 0 -1.90458 -0.190842 MAarrowhead1 % End of user PostScript 0 .35316 m .03365 .32638 L s % Start of user PostScript -2. 0.285714 -1.86539 0.11239 MAarrowhead1 % End of user PostScript 0 .39731 m .0398 .37221 L s % Start of user PostScript -2. 0.571429 -1.8408 0.408984 MAarrowhead1 % End of user PostScript 0 .44145 m .04254 .41598 L s % Start of user PostScript -2. 0.857143 -1.82986 0.6923 MAarrowhead1 % End of user PostScript 0 .4856 m .04241 .45773 L s % Start of user PostScript -2. 1.14286 -1.83035 0.962515 MAarrowhead1 % End of user PostScript 0 .52974 m .04005 .4982 L s % Start of user PostScript -2. 1.42857 -1.8398 1.22442 MAarrowhead1 % End of user PostScript 0 .57389 m .03627 .53827 L s % Start of user PostScript -2. 1.71429 -1.85494 1.48375 MAarrowhead1 % End of user PostScript 0 .61803 m .03194 .57855 L s % Start of user PostScript -2. 2. -1.87222 1.74445 MAarrowhead1 % End of user PostScript .07143 0 m .04774 .03789 L s % Start of user PostScript -1.71429 -2. -1.80904 -1.75476 MAarrowhead1 % End of user PostScript .07143 .04415 m .04149 .07587 L s % Start of user PostScript -1.71429 -1.71429 -1.83406 -1.50896 MAarrowhead1 % End of user PostScript .07143 .08829 m .03185 .10857 L s % Start of user PostScript -1.71429 -1.42857 -1.87262 -1.29732 MAarrowhead1 % End of user PostScript .07143 .13244 m .02835 .12629 L s % Start of user PostScript -1.71429 -1.14286 -1.88658 -1.18266 MAarrowhead1 % End of user PostScript .07143 .17658 m .05307 .15036 L s % Start of user PostScript -1.71429 -0.857143 -1.78774 -1.02686 MAarrowhead1 % End of user PostScript .07143 .22073 m .07208 .19039 L s % Start of user PostScript -1.71429 -0.571429 -1.71166 -0.767767 MAarrowhead1 % End of user PostScript .07143 .26487 m .08608 .23487 L s % Start of user PostScript -1.71429 -0.285714 -1.6557 -0.479893 MAarrowhead1 % End of user PostScript .07143 .30902 m .09763 .28125 L s % Start of user PostScript -1.71429 0 -1.60946 -0.179694 MAarrowhead1 % End of user PostScript .07143 .35316 m .10632 .32801 L s % Start of user PostScript -1.71429 0.285714 -1.57473 0.12294 MAarrowhead1 % End of user PostScript .07143 .39731 m .11156 .37349 L s % Start of user PostScript -1.71429 0.571429 -1.55376 0.41729 MAarrowhead1 % End of user PostScript .07143 .44145 m .11353 .41675 L s % Start of user PostScript -1.71429 0.857143 -1.54587 0.697273 MAarrowhead1 % End of user PostScript .07143 .4856 m .11269 .45796 L s % Start of user PostScript -1.71429 1.14286 -1.54925 0.964004 MAarrowhead1 % End of user PostScript .07143 .52974 m .10966 .49803 L s % Start of user PostScript -1.71429 1.42857 -1.56138 1.22332 MAarrowhead1 % End of user PostScript .07143 .57389 m .10539 .53791 L s % Start of user PostScript -1.71429 1.71429 -1.57845 1.48142 MAarrowhead1 % End of user PostScript .07143 .61803 m .10084 .57816 L s % Start of user PostScript -1.71429 2. -1.59663 1.74192 MAarrowhead1 % End of user PostScript .14286 0 m .12494 .03918 L s % Start of user PostScript -1.42857 -2. -1.50023 -1.74643 MAarrowhead1 % End of user PostScript .14286 .04415 m .12067 .0783 L s % Start of user PostScript -1.42857 -1.71429 -1.51731 -1.49324 MAarrowhead1 % End of user PostScript .14286 .08829 m .1136 .11412 L s % Start of user PostScript -1.42857 -1.42857 -1.54558 -1.26142 MAarrowhead1 % End of user PostScript .14286 .13244 m .10366 .13489 L s % Start of user PostScript -1.42857 -1.14286 -1.58536 -1.12696 MAarrowhead1 % End of user PostScript .14286 .17658 m .13141 .1514 L s % Start of user PostScript -1.42857 -0.857143 -1.47437 -1.02011 MAarrowhead1 % End of user PostScript .14286 .22073 m .14972 .19205 L s % Start of user PostScript -1.42857 -0.571429 -1.40112 -0.757028 MAarrowhead1 % End of user PostScript .14286 .26487 m .1619 .23692 L s % Start of user PostScript -1.42857 -0.285714 -1.35239 -0.466594 MAarrowhead1 % End of user PostScript .14286 .30902 m .17185 .28342 L s % Start of user PostScript -1.42857 0 -1.31259 -0.165693 MAarrowhead1 % End of user PostScript .14286 .35316 m .17921 .33 L s % Start of user PostScript -1.42857 0.285714 -1.28315 0.135773 MAarrowhead1 % End of user PostScript .14286 .39731 m .18342 .37502 L s % Start of user PostScript -1.42857 0.571429 -1.26634 0.427161 MAarrowhead1 % End of user PostScript .14286 .44145 m .18451 .41763 L s % Start of user PostScript -1.42857 0.857143 -1.26196 0.702979 MAarrowhead1 % End of user PostScript .14286 .4856 m .1828 .4582 L s % Start of user PostScript -1.42857 1.14286 -1.26878 0.965549 MAarrowhead1 % End of user PostScript .14286 .52974 m .179 .49783 L s % Start of user PostScript -1.42857 1.42857 -1.28399 1.22202 MAarrowhead1 % End of user PostScript .14286 .57389 m .17423 .53753 L s % Start of user PostScript -1.42857 1.71429 -1.30307 1.47898 MAarrowhead1 % End of user PostScript .14286 .61803 m .16951 .57778 L s % Start of user PostScript -1.42857 2. -1.32198 1.73944 MAarrowhead1 % End of user PostScript .21429 0 m .2021 .04016 L s % Start of user PostScript -1.14286 -2. -1.1916 -1.74006 MAarrowhead1 % End of user PostScript .21429 .04415 m .19996 .08009 L s % Start of user PostScript -1.14286 -1.71429 -1.20014 -1.48166 MAarrowhead1 % End of user PostScript .21429 .08829 m .197 .11822 L s % Start of user PostScript -1.14286 -1.42857 -1.21199 -1.23488 MAarrowhead1 % End of user PostScript .21429 .13244 m .19059 .14917 L s % Start of user PostScript -1.14286 -1.14286 -1.23765 -1.03452 MAarrowhead1 % End of user PostScript .21429 .17658 m .21576 .15369 L s % Start of user PostScript -1.14286 -0.857143 -1.13696 -1.00529 MAarrowhead1 % End of user PostScript .21429 .22073 m .22949 .19483 L s % Start of user PostScript -1.14286 -0.571429 -1.08205 -0.739023 MAarrowhead1 % End of user PostScript .21429 .26487 m .23869 .2398 L s % Start of user PostScript -1.14286 -0.285714 -1.04523 -0.448002 MAarrowhead1 % End of user PostScript .21429 .30902 m .24657 .28622 L s % Start of user PostScript -1.14286 0 -1.01373 -0.14757 MAarrowhead1 % End of user PostScript .21429 .35316 m .25237 .33247 L s % Start of user PostScript -1.14286 0.285714 -0.990527 0.151798 MAarrowhead1 % End of user PostScript .21429 .39731 m .25539 .37688 L s % Start of user PostScript -1.14286 0.571429 -0.978425 0.439187 MAarrowhead1 % End of user PostScript .21429 .44145 m .25546 .41866 L s % Start of user PostScript -1.14286 0.857143 -0.978144 0.709653 MAarrowhead1 % End of user PostScript .21429 .4856 m .25272 .45845 L s % Start of user PostScript -1.14286 1.14286 -0.98911 0.967146 MAarrowhead1 % End of user PostScript .21429 .52974 m .24803 .4976 L s % Start of user PostScript -1.14286 1.42857 -1.00789 1.22052 MAarrowhead1 % End of user PostScript .21429 .57389 m .24275 .53714 L s % Start of user PostScript -1.14286 1.71429 -1.029 1.47647 MAarrowhead1 % End of user PostScript .21429 .61803 m .23791 .57741 L s % Start of user PostScript -1.14286 2. -1.04837 1.73708 MAarrowhead1 % End of user PostScript .28571 0 m .2791 .04086 L s % Start of user PostScript -0.857143 -2. -0.883586 -1.73556 MAarrowhead1 % End of user PostScript .28571 .04415 m .27897 .08126 L s % Start of user PostScript -0.857143 -1.71429 -0.884112 -1.47408 MAarrowhead1 % End of user PostScript .28571 .08829 m .28002 .12053 L s % Start of user PostScript -0.857143 -1.42857 -0.879904 -1.21988 MAarrowhead1 % End of user PostScript .28571 .13244 m .28698 .15677 L s % Start of user PostScript -0.857143 -1.14286 -0.852085 -0.985349 MAarrowhead1 % End of user PostScript .28571 .17658 m .31071 .16334 L s % Start of user PostScript -0.857143 -0.857143 -0.757171 -0.942833 MAarrowhead1 % End of user PostScript .28571 .22073 m .31144 .19983 L s % Start of user PostScript -0.857143 -0.571429 -0.75423 -0.706686 MAarrowhead1 % End of user PostScript .28571 .26487 m .31638 .24394 L s % Start of user PostScript -0.857143 -0.285714 -0.734477 -0.421168 MAarrowhead1 % End of user PostScript .28571 .30902 m .32173 .28994 L s % Start of user PostScript -0.857143 0 -0.713076 -0.123486 MAarrowhead1 % End of user PostScript .28571 .35316 m .32577 .33565 L s % Start of user PostScript -0.857143 0.285714 -0.696903 0.172383 MAarrowhead1 % End of user PostScript .28571 .39731 m .32751 .37921 L s % Start of user PostScript -0.857143 0.571429 -0.689951 0.454296 MAarrowhead1 % End of user PostScript .28571 .44145 m .3264 .4199 L s % Start of user PostScript -0.857143 0.857143 -0.69441 0.717658 MAarrowhead1 % End of user PostScript .28571 .4856 m .32238 .4587 L s % Start of user PostScript -0.857143 1.14286 -0.7105 0.968786 MAarrowhead1 % End of user PostScript .28571 .52974 m .31664 .49733 L s % Start of user PostScript -0.857143 1.42857 -0.733452 1.2188 MAarrowhead1 % End of user PostScript .28571 .57389 m .31088 .53676 L s % Start of user PostScript -0.857143 1.71429 -0.756485 1.47399 MAarrowhead1 % End of user PostScript .28571 .61803 m .30602 .57708 L s % Start of user PostScript -0.857143 2. -0.775911 1.73493 MAarrowhead1 % End of user PostScript .35714 0 m .35586 .04129 L s % Start of user PostScript -0.571429 -2. -0.576568 -1.73274 MAarrowhead1 % End of user PostScript .35714 .04415 m .35742 .08191 L s % Start of user PostScript -0.571429 -1.71429 -0.570312 -1.46988 MAarrowhead1 % End of user PostScript .35714 .08829 m .36135 .1215 L s % Start of user PostScript -0.571429 -1.42857 -0.554585 -1.21362 MAarrowhead1 % End of user PostScript .35714 .13244 m .37272 .158 L s % Start of user PostScript -0.571429 -1.14286 -0.509109 -0.97737 MAarrowhead1 % End of user PostScript .35714 .17658 m .39397 .17918 L s % Start of user PostScript -0.571429 -0.857143 -0.424122 -0.840308 MAarrowhead1 % End of user PostScript .35714 .22073 m .39324 .20798 L s % Start of user PostScript -0.571429 -0.571429 -0.42703 -0.653942 MAarrowhead1 % End of user PostScript .35714 .26487 m .39427 .24984 L s % Start of user PostScript -0.571429 -0.285714 -0.422917 -0.382997 MAarrowhead1 % End of user PostScript .35714 .30902 m .39704 .29493 L s % Start of user PostScript -0.571429 0 -0.411856 -0.0911845 MAarrowhead1 % End of user PostScript .35714 .35316 m .3993 .33984 L s % Start of user PostScript -0.571429 0.285714 -0.402802 0.199499 MAarrowhead1 % End of user PostScript .35714 .39731 m .39976 .38226 L s % Start of user PostScript -0.571429 0.571429 -0.400943 0.474009 MAarrowhead1 % End of user PostScript .35714 .44145 m .39731 .42144 L s % Start of user PostScript -0.571429 0.857143 -0.410744 0.727589 MAarrowhead1 % End of user PostScript .35714 .4856 m .39166 .45896 L s % Start of user PostScript -0.571429 1.14286 -0.433357 0.97045 MAarrowhead1 % End of user PostScript .35714 .52974 m .38471 .49704 L s % Start of user PostScript -0.571429 1.42857 -0.461165 1.21689 MAarrowhead1 % End of user PostScript .35714 .57389 m .37855 .5364 L s % Start of user PostScript -0.571429 1.71429 -0.485803 1.47166 MAarrowhead1 % End of user PostScript .35714 .61803 m .37382 .5768 L s % Start of user PostScript -0.571429 2. -0.504705 1.73311 MAarrowhead1 % End of user PostScript .42857 0 m .4323 .04151 L s % Start of user PostScript -0.285714 -2. -0.270789 -1.73135 MAarrowhead1 % End of user PostScript .42857 .04415 m .43518 .08216 L s % Start of user PostScript -0.285714 -1.71429 -0.259299 -1.46825 MAarrowhead1 % End of user PostScript .42857 .08829 m .44074 .12171 L s % Start of user PostScript -0.285714 -1.42857 -0.237029 -1.21225 MAarrowhead1 % End of user PostScript .42857 .13244 m .45195 .15833 L s % Start of user PostScript -0.285714 -1.14286 -0.192213 -0.975284 MAarrowhead1 % End of user PostScript .42857 .17658 m .46708 .18743 L s % Start of user PostScript -0.285714 -0.857143 -0.131667 -0.786959 MAarrowhead1 % End of user PostScript .42857 .22073 m .47077 .21764 L s % Start of user PostScript -0.285714 -0.571429 -0.116937 -0.591423 MAarrowhead1 % End of user PostScript .42857 .26487 m .47076 .25742 L s % Start of user PostScript -0.285714 -0.285714 -0.116972 -0.333926 MAarrowhead1 % End of user PostScript .42857 .30902 m .47166 .30141 L s % Start of user PostScript -0.285714 0 -0.113348 -0.0492475 MAarrowhead1 % End of user PostScript .42857 .35316 m .4725 .34541 L s % Start of user PostScript -0.285714 0.285714 -0.110003 0.235511 MAarrowhead1 % End of user PostScript .42857 .39731 m .47203 .3864 L s % Start of user PostScript -0.285714 0.571429 -0.111878 0.500848 MAarrowhead1 % End of user PostScript .42857 .44145 m .46822 .42343 L s % Start of user PostScript -0.285714 0.857143 -0.127118 0.740517 MAarrowhead1 % End of user PostScript .42857 .4856 m .46041 .45922 L s % Start of user PostScript -0.285714 1.14286 -0.158352 0.972107 MAarrowhead1 % End of user PostScript .42857 .52974 m .45207 .49673 L s % Start of user PostScript -0.285714 1.42857 -0.191728 1.21491 MAarrowhead1 % End of user PostScript .42857 .57389 m .44568 .5361 L s % Start of user PostScript -0.285714 1.71429 -0.217264 1.46969 MAarrowhead1 % End of user PostScript .42857 .61803 m .44129 .57659 L s % Start of user PostScript -0.285714 2. -0.234843 1.73177 MAarrowhead1 % End of user PostScript .5 0 m .5084 .04155 L s % Start of user PostScript 0 -2. 0.0336113 -1.73111 MAarrowhead1 % End of user PostScript .5 .04415 m .5122 .08214 L s % Start of user PostScript 0 -1.71429 0.0488083 -1.46839 MAarrowhead1 % End of user PostScript .5 .08829 m .51847 .12158 L s % Start of user PostScript 0 -1.42857 0.0738917 -1.21314 MAarrowhead1 % End of user PostScript .5 .13244 m .52833 .15857 L s % Start of user PostScript 0 -1.14286 0.113311 -0.973716 MAarrowhead1 % End of user PostScript .5 .17658 m .53912 .19181 L s % Start of user PostScript 0 -0.857143 0.156486 -0.758597 MAarrowhead1 % End of user PostScript .5 .22073 m .54381 .22578 L s % Start of user PostScript 0 -0.571429 0.175259 -0.538727 MAarrowhead1 % End of user PostScript .5 .26487 m .54437 .26551 L s % Start of user PostScript 0 -0.285714 0.17749 -0.281575 MAarrowhead1 % End of user PostScript .5 .30902 m .54438 .30902 L s % Start of user PostScript 0 0 0.177526 0 MAarrowhead1 % End of user PostScript .5 .35316 m .54437 .35252 L s % Start of user PostScript 0 0.285714 0.17749 0.281575 MAarrowhead1 % End of user PostScript .5 .39731 m .54381 .39225 L s % Start of user PostScript 0 0.571429 0.175259 0.538727 MAarrowhead1 % End of user PostScript .5 .44145 m .53912 .42623 L s % Start of user PostScript 0 0.857143 0.156486 0.758597 MAarrowhead1 % End of user PostScript .5 .4856 m .52833 .45946 L s % Start of user PostScript 0 1.14286 0.113311 0.973716 MAarrowhead1 % End of user PostScript .5 .52974 m .51847 .49646 L s % Start of user PostScript 0 1.42857 0.0738917 1.21314 MAarrowhead1 % End of user PostScript .5 .57389 m .5122 .5359 L s % Start of user PostScript 0 1.71429 0.0488083 1.46839 MAarrowhead1 % End of user PostScript .5 .61803 m .5084 .57649 L s % Start of user PostScript 0 2. 0.0336113 1.73111 MAarrowhead1 % End of user PostScript .57143 0 m .58415 .04144 L s % Start of user PostScript 0.285714 -2. 0.336585 -1.73177 MAarrowhead1 % End of user PostScript .57143 .04415 m .58854 .08194 L s % Start of user PostScript 0.285714 -1.71429 0.354165 -1.46969 MAarrowhead1 % End of user PostScript .57143 .08829 m .59493 .1213 L s % Start of user PostScript 0.285714 -1.42857 0.379701 -1.21491 MAarrowhead1 % End of user PostScript .57143 .13244 m .60327 .15882 L s % Start of user PostScript 0.285714 -1.14286 0.413077 -0.972107 MAarrowhead1 % End of user PostScript .57143 .17658 m .61108 .1946 L s % Start of user PostScript 0.285714 -0.857143 0.444311 -0.740517 MAarrowhead1 % End of user PostScript .57143 .22073 m .61489 .23163 L s % Start of user PostScript 0.285714 -0.571429 0.459551 -0.500848 MAarrowhead1 % End of user PostScript .57143 .26487 m .61536 .27263 L s % Start of user PostScript 0.285714 -0.285714 0.461425 -0.235511 MAarrowhead1 % End of user PostScript .57143 .30902 m .61452 .31663 L s % Start of user PostScript 0.285714 0 0.45808 0.0492475 MAarrowhead1 % End of user PostScript .57143 .35316 m .61361 .36061 L s % Start of user PostScript 0.285714 0.285714 0.454456 0.333926 MAarrowhead1 % End of user PostScript .57143 .39731 m .61362 .4004 L s % Start of user PostScript 0.285714 0.571429 0.454492 0.591423 MAarrowhead1 % End of user PostScript .57143 .44145 m .60994 .43061 L s % Start of user PostScript 0.285714 0.857143 0.439762 0.786959 MAarrowhead1 % End of user PostScript .57143 .4856 m .5948 .45971 L s % Start of user PostScript 0.285714 1.14286 0.379215 0.975284 MAarrowhead1 % End of user PostScript .57143 .52974 m .5836 .49632 L s % Start of user PostScript 0.285714 1.42857 0.3344 1.21225 MAarrowhead1 % End of user PostScript .57143 .57389 m .57803 .53587 L s % Start of user PostScript 0.285714 1.71429 0.312129 1.46825 MAarrowhead1 % End of user PostScript .57143 .61803 m .57516 .57653 L s % Start of user PostScript 0.285714 2. 0.300639 1.73135 MAarrowhead1 % End of user PostScript .64286 0 m .65954 .04124 L s % Start of user PostScript 0.571429 -2. 0.638152 -1.73311 MAarrowhead1 % End of user PostScript .64286 .04415 m .66426 .08163 L s % Start of user PostScript 0.571429 -1.71429 0.657054 -1.47166 MAarrowhead1 % End of user PostScript .64286 .08829 m .67042 .121 L s % Start of user PostScript 0.571429 -1.42857 0.681692 -1.21689 MAarrowhead1 % End of user PostScript .64286 .13244 m .67738 .15907 L s % Start of user PostScript 0.571429 -1.14286 0.709501 -0.97045 MAarrowhead1 % End of user PostScript .64286 .17658 m .68303 .1966 L s % Start of user PostScript 0.571429 -0.857143 0.732113 -0.727589 MAarrowhead1 % End of user PostScript .64286 .22073 m .68548 .23578 L s % Start of user PostScript 0.571429 -0.571429 0.741914 -0.474009 MAarrowhead1 % End of user PostScript .64286 .26487 m .68501 .27819 L s % Start of user PostScript 0.571429 -0.285714 0.740055 -0.199499 MAarrowhead1 % End of user PostScript .64286 .30902 m .68275 .32311 L s % Start of user PostScript 0.571429 0 0.731002 0.0911845 MAarrowhead1 % End of user PostScript .64286 .35316 m .67999 .36819 L s % Start of user PostScript 0.571429 0.285714 0.71994 0.382997 MAarrowhead1 % End of user PostScript .64286 .39731 m .67896 .41006 L s % Start of user PostScript 0.571429 0.571429 0.715828 0.653942 MAarrowhead1 % End of user PostScript .64286 .44145 m .67968 .43885 L s % Start of user PostScript 0.571429 0.857143 0.718735 0.840308 MAarrowhead1 % End of user PostScript .64286 .4856 m .65844 .46003 L s % Start of user PostScript 0.571429 1.14286 0.633748 0.97737 MAarrowhead1 % End of user PostScript .64286 .52974 m .64707 .49653 L s % Start of user PostScript 0.571429 1.42857 0.588272 1.21362 MAarrowhead1 % End of user PostScript .64286 .57389 m .64314 .53613 L s % Start of user PostScript 0.571429 1.71429 0.572545 1.46988 MAarrowhead1 % End of user PostScript .64286 .61803 m .64157 .57674 L s % Start of user PostScript 0.571429 2. 0.566289 1.73274 MAarrowhead1 % End of user PostScript .71429 0 m .73459 .04096 L s % Start of user PostScript 0.857143 -2. 0.938375 -1.73493 MAarrowhead1 % End of user PostScript .71429 .04415 m .73945 .08127 L s % Start of user PostScript 0.857143 -1.71429 0.957801 -1.47399 MAarrowhead1 % End of user PostScript .71429 .08829 m .74521 .1207 L s % Start of user PostScript 0.857143 -1.42857 0.980834 -1.2188 MAarrowhead1 % End of user PostScript .71429 .13244 m .75095 .15933 L s % Start of user PostScript 0.857143 -1.14286 1.00379 -0.968786 MAarrowhead1 % End of user PostScript .71429 .17658 m .75497 .19813 L s % Start of user PostScript 0.857143 -0.857143 1.01988 -0.717658 MAarrowhead1 % End of user PostScript .71429 .22073 m .75608 .23882 L s % Start of user PostScript 0.857143 -0.571429 1.02433 -0.454296 MAarrowhead1 % End of user PostScript .71429 .26487 m .75435 .28238 L s % Start of user PostScript 0.857143 -0.285714 1.01738 -0.172383 MAarrowhead1 % End of user PostScript .71429 .30902 m .7503 .3281 L s % Start of user PostScript 0.857143 0 1.00121 0.123486 MAarrowhead1 % End of user PostScript .71429 .35316 m .74495 .37409 L s % Start of user PostScript 0.857143 0.285714 0.979809 0.421168 MAarrowhead1 % End of user PostScript .71429 .39731 m .74001 .41821 L s % Start of user PostScript 0.857143 0.571429 0.960056 0.706686 MAarrowhead1 % End of user PostScript .71429 .44145 m .73928 .45469 L s % Start of user PostScript 0.857143 0.857143 0.957115 0.942833 MAarrowhead1 % End of user PostScript .71429 .4856 m .71555 .46126 L s % Start of user PostScript 0.857143 1.14286 0.8622 0.985349 MAarrowhead1 % End of user PostScript .71429 .52974 m .7086 .4975 L s % Start of user PostScript 0.857143 1.42857 0.834382 1.21988 MAarrowhead1 % End of user PostScript .71429 .57389 m .70754 .53677 L s % Start of user PostScript 0.857143 1.71429 0.830174 1.47408 MAarrowhead1 % End of user PostScript .71429 .61803 m .70767 .57718 L s % Start of user PostScript 0.857143 2. 0.830699 1.73556 MAarrowhead1 % End of user PostScript .78571 0 m .80934 .04062 L s % Start of user PostScript 1.14286 -2. 1.23734 -1.73708 MAarrowhead1 % End of user PostScript .78571 .04415 m .81418 .08089 L s % Start of user PostScript 1.14286 -1.71429 1.25672 -1.47647 MAarrowhead1 % End of user PostScript .78571 .08829 m .81946 .12044 L s % Start of user PostScript 1.14286 -1.42857 1.27782 -1.22052 MAarrowhead1 % End of user PostScript .78571 .13244 m .82415 .15958 L s % Start of user PostScript 1.14286 -1.14286 1.2966 -0.967146 MAarrowhead1 % End of user PostScript .78571 .17658 m .82689 .19937 L s % Start of user PostScript 1.14286 -0.857143 1.30757 -0.709653 MAarrowhead1 % End of user PostScript .78571 .22073 m .82682 .24116 L s % Start of user PostScript 1.14286 -0.571429 1.30729 -0.439187 MAarrowhead1 % End of user PostScript .78571 .26487 m .8238 .28556 L s % Start of user PostScript 1.14286 -0.285714 1.29519 -0.151798 MAarrowhead1 % End of user PostScript .78571 .30902 m .818 .33182 L s % Start of user PostScript 1.14286 0 1.27198 0.14757 MAarrowhead1 % End of user PostScript .78571 .35316 m .81012 .37824 L s % Start of user PostScript 1.14286 0.285714 1.24048 0.448002 MAarrowhead1 % End of user PostScript .78571 .39731 m .80092 .4232 L s % Start of user PostScript 1.14286 0.571429 1.20366 0.739023 MAarrowhead1 % End of user PostScript .78571 .44145 m .78719 .46434 L s % Start of user PostScript 1.14286 0.857143 1.14875 1.00529 MAarrowhead1 % End of user PostScript .78571 .4856 m .76202 .46886 L s % Start of user PostScript 1.14286 1.14286 1.04807 1.03452 MAarrowhead1 % End of user PostScript .78571 .52974 m .76843 .49982 L s % Start of user PostScript 1.14286 1.42857 1.07373 1.23488 MAarrowhead1 % End of user PostScript .78571 .57389 m .77139 .53795 L s % Start of user PostScript 1.14286 1.71429 1.08557 1.48166 MAarrowhead1 % End of user PostScript .78571 .61803 m .77353 .57787 L s % Start of user PostScript 1.14286 2. 1.09412 1.74006 MAarrowhead1 % End of user PostScript .85714 0 m .88379 .04026 L s % Start of user PostScript 1.42857 -2. 1.53516 -1.73944 MAarrowhead1 % End of user PostScript .85714 .04415 m .88852 .0805 L s % Start of user PostScript 1.42857 -1.71429 1.55408 -1.47898 MAarrowhead1 % End of user PostScript .85714 .08829 m .89329 .1202 L s % Start of user PostScript 1.42857 -1.42857 1.57315 -1.22202 MAarrowhead1 % End of user PostScript .85714 .13244 m .89709 .15983 L s % Start of user PostScript 1.42857 -1.14286 1.58836 -0.965549 MAarrowhead1 % End of user PostScript .85714 .17658 m .8988 .2004 L s % Start of user PostScript 1.42857 -0.857143 1.59518 -0.702979 MAarrowhead1 % End of user PostScript .85714 .22073 m .8977 .24302 L s % Start of user PostScript 1.42857 -0.571429 1.59081 -0.427161 MAarrowhead1 % End of user PostScript .85714 .26487 m .8935 .28804 L s % Start of user PostScript 1.42857 -0.285714 1.574 -0.135773 MAarrowhead1 % End of user PostScript .85714 .30902 m .88614 .33462 L s % Start of user PostScript 1.42857 0 1.54456 0.165693 MAarrowhead1 % End of user PostScript .85714 .35316 m .87619 .38111 L s % Start of user PostScript 1.42857 0.285714 1.50475 0.466594 MAarrowhead1 % End of user PostScript .85714 .39731 m .864 .42598 L s % Start of user PostScript 1.42857 0.571429 1.45602 0.757028 MAarrowhead1 % End of user PostScript .85714 .44145 m .84569 .46663 L s % Start of user PostScript 1.42857 0.857143 1.38277 1.02011 MAarrowhead1 % End of user PostScript .85714 .4856 m .81795 .48314 L s % Start of user PostScript 1.42857 1.14286 1.27179 1.12696 MAarrowhead1 % End of user PostScript .85714 .52974 m .82789 .50392 L s % Start of user PostScript 1.42857 1.42857 1.31156 1.26142 MAarrowhead1 % End of user PostScript .85714 .57389 m .83496 .53974 L s % Start of user PostScript 1.42857 1.71429 1.33983 1.49324 MAarrowhead1 % End of user PostScript .85714 .61803 m .83923 .57885 L s % Start of user PostScript 1.42857 2. 1.35691 1.74643 MAarrowhead1 % End of user PostScript .92857 0 m .95799 .03988 L s % Start of user PostScript 1.71429 -2. 1.83194 -1.74192 MAarrowhead1 % End of user PostScript .92857 .04415 m .96253 .08013 L s % Start of user PostScript 1.71429 -1.71429 1.85013 -1.48142 MAarrowhead1 % End of user PostScript .92857 .08829 m .9668 .12 L s % Start of user PostScript 1.71429 -1.42857 1.86719 -1.22332 MAarrowhead1 % End of user PostScript .92857 .13244 m .96983 .16007 L s % Start of user PostScript 1.71429 -1.14286 1.87932 -0.964004 MAarrowhead1 % End of user PostScript .92857 .17658 m .97068 .20128 L s % Start of user PostScript 1.71429 -0.857143 1.88271 -0.697273 MAarrowhead1 % End of user PostScript .92857 .22073 m .9687 .24454 L s % Start of user PostScript 1.71429 -0.571429 1.87481 -0.41729 MAarrowhead1 % End of user PostScript .92857 .26487 m .96346 .29002 L s % Start of user PostScript 1.71429 -0.285714 1.85385 -0.12294 MAarrowhead1 % End of user PostScript .92857 .30902 m .95478 .33678 L s % Start of user PostScript 1.71429 0 1.81911 0.179694 MAarrowhead1 % End of user PostScript .92857 .35316 m .94322 .38316 L s % Start of user PostScript 1.71429 0.285714 1.77287 0.479893 MAarrowhead1 % End of user PostScript .92857 .39731 m .92923 .42764 L s % Start of user PostScript 1.71429 0.571429 1.71691 0.767767 MAarrowhead1 % End of user PostScript .92857 .44145 m .91021 .46768 L s % Start of user PostScript 1.71429 0.857143 1.64083 1.02686 MAarrowhead1 % End of user PostScript .92857 .4856 m .8855 .49175 L s % Start of user PostScript 1.71429 1.14286 1.54199 1.18266 MAarrowhead1 % End of user PostScript .92857 .52974 m .88899 .50946 L s % Start of user PostScript 1.71429 1.42857 1.55595 1.29732 MAarrowhead1 % End of user PostScript .92857 .57389 m .89863 .54216 L s % Start of user PostScript 1.71429 1.71429 1.59451 1.50896 MAarrowhead1 % End of user PostScript .92857 .61803 m .90488 .58014 L s % Start of user PostScript 1.71429 2. 1.61953 1.75476 MAarrowhead1 % End of user PostScript 1 0 m 0 0 rlineto s % Start of user PostScript 2. -2. 2.12778 -1.74445 MAarrowhead1 % End of user PostScript 1 .04415 m 0 0 rlineto s 1 .04415 m 1 .04415 L s % Start of user PostScript 2. -1.71429 2.14506 -1.48375 MAarrowhead1 % End of user PostScript 1 .08829 m 0 0 rlineto s 1 .08829 m 1 .08829 L s % Start of user PostScript 2. -1.42857 2.1602 -1.22442 MAarrowhead1 % End of user PostScript 1 .13244 m 0 0 rlineto s 1 .13244 m 1 .13244 L s % Start of user PostScript 2. -1.14286 2.16965 -0.962515 MAarrowhead1 % End of user PostScript 1 .17658 m 0 0 rlineto s 1 .17658 m 1 .17658 L s % Start of user PostScript 2. -0.857143 2.17014 -0.6923 MAarrowhead1 % End of user PostScript 1 .22073 m 0 0 rlineto s 1 .22073 m 1 .22073 L s % Start of user PostScript 2. -0.571429 2.1592 -0.408984 MAarrowhead1 % End of user PostScript 1 .26487 m 0 0 rlineto s 1 .26487 m 1 .26487 L s % Start of user PostScript 2. -0.285714 2.13461 -0.11239 MAarrowhead1 % End of user PostScript 1 .30902 m 0 0 rlineto s 1 .30902 m 1 .30902 L s % Start of user PostScript 2. 0 2.09542 0.190842 MAarrowhead1 % End of user PostScript 1 .35316 m 0 0 rlineto s 1 .35316 m 1 .35316 L s % Start of user PostScript 2. 0.285714 2.04426 0.489851 MAarrowhead1 % End of user PostScript 1 .39731 m .99599 .42875 L s % Start of user PostScript 2. 0.571429 1.98397 0.774938 MAarrowhead1 % End of user PostScript 1 .44145 m .97725 .46843 L s % Start of user PostScript 2. 0.857143 1.909 1.03171 MAarrowhead1 % End of user PostScript 1 .4856 m .95537 .49648 L s % Start of user PostScript 2. 1.14286 1.8215 1.21329 MAarrowhead1 % End of user PostScript 1 .52974 m .95293 .5154 L s % Start of user PostScript 2. 1.42857 1.81171 1.33575 MAarrowhead1 % End of user PostScript 1 .57389 m .96282 .54514 L s % Start of user PostScript 2. 1.71429 1.85127 1.52824 MAarrowhead1 % End of user PostScript 1 .61803 m .97063 .58173 L s % Start of user PostScript 2. 2. 1.88252 1.76503 MAarrowhead1 % End of user PostScript % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc0003o`3o018000?o00001`000ol000060003o`000100 00?o000010000ol000090003o`0001P0000K0003o`0000/000?o00000P000ol0000@0003o`0000L0 00?o00001`000ol0000@0005o`000?l03P000ol000070004o`00o`D000?o000040000ol0000>0003 o`3o018000?o00001`000ol000060003o`00010000?o000010000ol000090003o`0001L0000J0003 o`0000/000?o00000`000ol0000@0003o`0000H000?o000020000ol0000@0005o`000?l03P000ol0 000800;o1P000ol0000@0003o`0000l00_lB0003o`0000P000?o00001P000ol0000@0003o`0000@0 00?o00002@000ol0000F00006P000ol0000;0003o`00008000?o00004@000ol000060003o`0000L0 00?o00004@001Ol0003o00h000?o00004002oa4000?o00004002oa8000?o00001`000ol000060003 o`00010000?o00001@000ol000090003o`0001D0000300;o4P03o`d000Co00000olA00;o2@000ol0 000500?o4`001Ol0003o00h000?o00004002oa8000?o000040000ol0000@0003o`0000P000?o0000 1P000ol0000@0003o`0000D000?o000020000ol0000E00000`03oa400ol=0004o`0000?o4@03o`L0 00?o00001P04oa001?l20003o`0000/00ol@00Co4004oa400_lA00?o20000ol0000600;o4@02o`H0 00?o00002003oa400_l100000P03oa400ol=0003o`0000800olA00?o1`000ol0000600Co4004o`80 00?o00002`03oa001?l@00Co4003oa001?l80003o`0000D00ol@00?o1`02o`P00ol@00?o0@000080 0_lB00;o3@000ol0000200?o4P02o`P000?o00001P03oa400ol30003o`0000`00_lA00?o4@03oa00 1?l@00?o2@000ol0000500?o4003o`P000?o00001P03oa400_l0008000?o00004@000ol0000<0003 o`0000800_lB00;o2@000ol0000700;o4P02o`<000?o00003002oa400olB00;o4@04oa000ol80003 o`0000H00_lA00;o2@000ol0000600;o4`0000030?l0018000?o000030000ol000030003o`000140 0_l80003o`0000P00_lB00;o0`000ol0000<00;o4@03oa800_lB00;o00<0o`003`02o`T000?o0000 1P000ol0000@0003o`0000P000?o00001P000ol0000A000090000ol0000G0003o`0000L000?o0000 20000ol0000A0003o`0000<000?o000030000ol0000?0003o`3o01<000?o00004@001?l00?l@0003 o`0000P000?o00001P000ol0000@0003o`0000P000?o00001P000ol0000@00002@000ol0000@0003 o`0000@000?o00002@000ol0000@0003o`0000<000?o00002P000ol0000@0003o`00008000?o0000 2`000ol0000@0004o`00o`h000?o000040000ol000060003o`0000L000?o00003P000ol0o`0B0003 o`00010000?o000040000ol0000500006`000ol000040003o`0000X000?o000040000ol000020003 o`0000/000?o000040000ol000020003o`0000/000?o000040001?l00?l>0003o`00010000?o0000 1`000ol000060003o`0000l00_lC0003o`00010000?o00005`0001X000?o000010000ol0000:0003 o`00010000?o00000`000ol0000;0003o`00010000?o00000P000ol0000;0003o`00010000Go0000 o`0>0003o`00010000?o00001`000ol000060003o`0000l00_lC0003o`0001000_lG00000P000ol0 000A0004o`00o`H000?o00002P000ol0000A0003o`0000<000?o00002P000ol0000A0003o`000080 00?o00002`000ol0000@00;o0P000ol0000<0003o`00014000?o00001`000ol000060003o`0000l0 0_lC0003o`0001000_lF00000P02oa800ol500;o2`03oa400_l50003o`0000T00olA00Co0`000ol0 000;00?o4003o`030?l000h00ol@0004o`3oo`L000?o00001@001?l00?l?00;o0P000ol0000>0003 o`3o01000_lE000000<0ool00_l@00Co10000ol0000;00?o4@03o`@000?o00002@04oa001?l30003 o`0000X01?l@00?o0P000ol0000<00?o4@03o`P00_l600?o4004oa400_lA00?o4@02o`000olB00;o 1002o`d00olB00?o10000ol0000900Co4@03o`<000?o00002@05o`800_l300?o1P03o`8000?o0000 3003oa001?l:0003o`0000<01?l@00Co3`04oa000ol@00?o000E0003o`00008000?o00003@02oa80 0ol40003o`0000X00olB00?o0`000ol0000:00Co0P02o`H000?o00000`03o`8000?o00003@02oa40 0ol;0003o`0000<00olA00?o4@03oa400_lA007o000D0004o`0000;o40000ol0000A00;o1@000ol0 000;00;o4P02o`@000?o00000`05o`800ol;0003o`0000<01?l20003o`0000d00_lA00?o2`000ol0 000300;o4P02oa<000?o00004002oa40000F00;o4@000ol0000B0003o`0000@000?o00002`02oa<0 00?o00000P000ol0000:00?o2003o`H000Co0?oo0P000ol0000=00;o4P02o``000?o00000`02oa80 0_lC0003o`0001000_l@00005002obh000?o000030000ol0000B0003o`0000<000?o00002@000ol0 o`080003o`0000H000Co003o0`000ol0000=0003o`00014000?o00002`000ol000030003o`000140 00?o00009P02o`h000090003o`0000H00_l700;o4@02oa8000?o0?l040000ol0000@0003o`0000<0 00?o00002003o`T01?l50003o`0000@000?o000020000ol0000@0003o`00010000?o0?l040000ol0 000600;o2002oa400_l;0003o`0000<000?o00001@0000;o3P02o`L00_lB0003o`0001800_lA0003 o`00010000?o00000`000ol0000:0003o`00010000?o00001@000ol000070003o`00010000?o0000 4@000ol0o`0@0003o`0000L000?o00001`000ol0000@0003o`0000T000?o00002P0000;o2`03o`D0 00Co0?oo4`000ol0000B0003o`3o014000?o000040000ol000030003o`0000/000?o00003`02o`L0 00?o00001`000ol0000@0003o`00014000?o0?l040000ol000070003o`0000L000?o000040000ol0 00090003o`0000T00003o`H01?l700?o4`02oa<00_l00`3o000@0003o`00014000?o000010000ol0 000:0003o`0000l00_l80003o`0000L000?o000040000ol0000A0003o`3o010000?o00001`000ol0 00070003o`00010000?o00002@000ol0000800000ol@00Co4`02oa<00olA00?o4@03o`D000?o0000 2P02oa0000Co0?oo1`000ol000070003o`3o010000?o0?l04@000ol0o`0@0003o`3o00L00_l80003 o`3o010000?o0?l02@000ol00006007o000B00Ko4@04oa400olB00?o4@03o`D000?o00002@03oa00 1?l70003o`0000P00_lA00;o4P03oa000_l90003o`0000H00_lA00;o2P000ol00005007o000A00?o 5003oa<00_lC00;o4`02o`D000?o00002@03oa001?l80003o`0000H01?l?00Co4005o`l00ol90003 o`0000@01?l?00Co2P000ol0000300;o000W0003o`0001@000?o00004P02oa<00_l60003o`0000T0 0ol?0003o`3o00;o20000ol0000700;o4@03oa401?l@00;o2@02o`H00ol@00?o3`02o`00?@000ol0 000C00;o4`02o`H000?o00002P02o`l000?o00000_l90003o`0000L000?o00004@000ol0000A0003 o`3o010000?o00002@000ol000050003o`00010000?o00003`0000?o>@000ol0000D0003o`0001<0 00?o00001@000ol0000:0003o`0000d000Go0000o`0:00;o20000ol0000A0003o`00014000?o0?l0 40000ol000090003o`0000D000?o000040000ol0000>00000ol600ko8`02ocD000?o00006P000ol0 000>0003o`00030000?o00006P000ol0000X000000<0ool02`0>o`d00_l=00;o>0000ol0000I0003 o`0000l000?o0000<002oa/00_lX00000P000ol000040003o`0000H07_l200Ko1`001?l0oolB0003 o`00010000?o000020000ol000050003o`00010000?o00003`02oa400_lA00;o3@001?l00002oa40 0_l40003o`0000X00_lA0003o`0000D0000E0003o`0000H01?l200ko3@02oa801?lA0003o`0000T0 00?o000010000ol0000@00;o4P000ol0000@0003o`00010000?o00002`000ol000020003o`000100 00?o00000P000ol0000;0003o`0001H0000R00?o0`03oa<00olB00Co4P02o`X000?o000010000ol0 o`0?0003o`3o018000?o00004002oa400_l<0003o`0000800_lA00;o0`000ol0000;00;o5P0002D0 0olE00Co4`03oa400ol;0003o`0000@00_l?0003o`0000;o4@03oa400_lA0003o`3o00X000?o0000 0`03oa000ol00`3oo`0=00?o4`0002P00olA00?o5@03oa800ol;00;o0`04o`D00ol60003o`3o00;o 4P02oa800_lA00;o2`000ol0000300?o4@02o`800_l=00;o4P0000<00_lB0003o`0001401?l<0003 o`0001H00_lD00;o3@02o`<00ol50003o`0000D000Co00000_l@00Go3`04o`l01?l;0004o`0000Go 3`04o`<000?o00002@04oa000Ol000<00olA00;o4`001?l00?lB0003o`00010000?o00004`000ol0 000=0004o`0000Go0P000ol0000500;o10000ol0000?00Go3`03oa000ol;0003o`0000<00ol>00Go 0`02o`T01Ol>00;o000400?o4@02oa800_l20003o`0000l000?o000040000ol0000D0003o`0000d0 0_l30003o`00008000?o00001@000ol000040003o`00014000?o0?l04@000ol0000@0003o`0000T0 00?o00001@000ol0000?00;o1002o`/00_l?00001004o`030?oo00d00olA00?o0P000ol0000=00;o 5`02ob800_l60003o`0000D000?o00006`02obl000?o00007P000ol0000I00001003o`@000?o0000 2P04oa400ol00`3o000>00?o4`04obD000?o00000P02o`L000?o00007@02obh000?o00007P02oaT0 00050003o`0000@000?o00002P02oa800_l30003o`0000`00olB00Co9`02o`/000?o00007`02obd0 00?o00007`02oaL0000=0003o`0000/000?o00003`02o`@000?o00002P04oa800olC00;o5@03o`P0 00?o00008@02ob`000?o00008002oaD000090003o`00008000?o00002`000ol0000@0005o`000?l0 3P000ol0000@0003o`3o01002Ol:00?o0P02o`@00ol500;o4002oa400ol@00;o4@02o`H000?o0000 2002oa400_l40003o`0000X000?o00001@0000h000?o00008P02ocL01_l<00Ko1@03o`8000?o0?l0 1?l=00;o0`000ol0000;00?o4002oa400_l50003o`0000T00_lA00;o0`02oa80000?0003o`000280 00?o0000=@03oa001_l700?o1004o`d01Ol>00Go3P02o`030?l000h00_l01@3o003o00`00_l00`3o 000>00;o0`02oa0000080003o`0000@000?o00008P000ol0001800Oo200:o`h01?l@00?o3`03oa00 0ol20003o`0000/00ol@00?o0P000ol0000=000020000ol000050003o`0000T000?o00004P001?l0 0?mI0004o`0000?o00@0oooo3@05o`h01_l=00Co3`04o`800_l;00Co4003o`800_l<007o000800;o 1`000ol000080003o`00018000Co003o4@000ol000150003o`0000@00olB00;o4@04o`d00ol>00Go 0`02o`T01Ol>00Go0`02o`T00_l000P00_l70003o`0000L00_lC00;o0P000ol0000>00;o4`02oc80 00?o00001`04obD00_l>0003o`0000l00_l40003o`0000X00_lA00;o10000ol0000800001`03o`L0 00?o00001`03oa400ol20003o`0000d00_lA00Go0003o`00010000?o000040000ol0000?00ko1P0;o`L01?l300;o 0`03o`@00ol@00;o1@02o`X00_lA00;o1@02o`X00_lA0003o`0000D0000B0003o`0001h000?o0000 @`001?l00?l300;o1P000ol000030003o`0000<01_l:00So0`03o`@00ol00`3oo`0<00?o0P05o`T0 0_l30003o`0000/00_l50003o`0000T00_lG00004P000ol0000M0003o`0003h01Ol01@3o003o00/0 00?o00000`02o`@00ol?00Oo1@03o`@01Ol=00Go0P02o`T01Ol>00Go00<0ool02`02o`030?l00140 0Ol000`000?o00000`000ol0000;0003o`0000l000?o0000A0001?l00?l800?o1P000ol0000T00?o 00<0ool01?l=00Go0`02o`T01?l@00?o0P02o`/00olA007o000<0003o`0000<000?o00002`000ol0 000?0003o`3o04@000Co003o1`07o`<000?o00009`03o`800ol<00Ko1002o`L01Ol>00Go0`02o`T0 1?l?00;o000;00;o1@000ol0000:0003o`0000l000Co0?oo4P02oc402_l00`3oo`02o`803OlS00?o 6P02o`T00_lA00;o10000ol0000800?o3@03o`002P02o`H000?o00002@02oa0000Co0?oo4@04oa<0 0_lG00Ko4`000ol0000700Ko8003oaT00_lQ00;o2`000ol0000=00002P02o`D000?o00002@03oa00 1?l@00Co4@04oa801_lI0003o`0000d01olL00;o6@02ob400_lI00002@03o`D000?o00002003oa00 1Ol?00Co4@04oa001_lL0003o`0001@01OlI00;o6@02ob4000?o00005P0000X000?o000010000ol0 000900;o40001?l0oolA00;o4@04oa001Ol@00Oo1`000ol0000I00?o6003oaP00_lP0003o`0001D0 000:0003o`0000@000?o00002@000ol0000>0003o`3o018000?o000040001?l00?l=00Co0P02o`l0 1ol90003o`0000<01?lE00?o6002oaP00_lO0003o`0001@000090003o`0000@000?o00002@000ol0 000?00;o4P000ol0000@0003o`0000d00_l00`3o00030003o`0000/00ol300;o2`00003o`0000D0000O0003o`0002P00_li01;o8@06o`d01?l30003o`0000T0 0_l30003o`0000X00_l40003o`0000T00_lB0003o`000040000N0003o`0002L00_lc00So2@000ol0 000600[o6`03o``01Ol30003o`0000L01?l30003o`0000P01?l40003o`0000P00_lA00;o0`000140 0_l900;o1P02ob000_l`00Go4@000ol0000@00?o:`02o`<00_l900?o0`000ol0000900?o10000ol0 00090003o`0000d01?l200003P04o`T000?o00000`04oa400ol<0003o`0000<00_lV00Go5P000ol0 000C00Go;@000ol000090005o`000?l030000ol000030003o`0000T000?o00003P03o`40000=00Co 2@000ol0000300Co3`06o`X00_l300Co4@03oa000olK0003o`0001P01?lZ00;o3P000ol0000:0003 o`00008000?o00002P000ol0000?007o0@0000d00ol800;o1P03oa001Ol900;o0`05o`l01?l>00So 6P000ol0000L00?o:@000ol0000<0003o`0000l000?o00007001o`0030000ol0o`080003o`0000D0 00?o0?l04@04o`T000?o00000`04oa000ol;00Co00<0ool00ol?00Co2@000ol0000O00;o:0000ol0 000;0003o`00010000?o0000700000/000?o000020000ol000050003o`0001000_l20003o`0000H0 0_l400;o0P000ol0000=00;o00<0o`002003o`@01?lA00Ko1`000ol0000300;o7003obD000?o0000 30000ol0000@0003o`0001/0000:0003o`0000L00_l70003o`00010000?o00002@02o`D000?o0000 4002o`X00ol400?o0P000ol0000=00Oo2@000ol0000300Go7003ob<000?o000030000ol0000?0003 o`0001/000090003o`0000L000?o00001P000ol0000@0003o`0000P00_l60003o`00010000?o0000 1`03o`H000?o00004003o`<000?o0?l05ol500Co0`02o`X00_l300;o3002oa400_l00`3o000=00;o 40000ol0o`0B0003o`0000D0000B0003o`0002@000?o00008@02oad01ol;0003o`0000<00ol400Oo 0P08o`T00ol0103oool<00;o00<0o`003P000ol0o`0>0003o`0000h000?o0?l06P0001000_lU00;o 8@03oa`00olB0003o`0001402ol;00Go3@03o`l00ol>0003o`3o00h000?o0?l00_lG00003`000ol0 000S00;o8@02oaT01_lE0003o`0001D01Ol=00Oo2P05o`d01?l>00?o3P000ol0o`02oa400_l40000 3P000ol0000R00;o8@02oaH01OlK0003o`0001X01?l=00;o00<0o`002`03o`h00ol=00Co3P04o`l0 1?l400003002o`@00_lA00;o2`000ol0000N00?o5@03ob0000?o00007P03o`h00_l=0003o`0000d0 0_l=00?o3P001?l0ool?00Co100000/000Co00001Ol>00Co2P02o`D00ol@00Co0`02oaD00ol?00;o 1002o`<00ol60003o`0002400_l>0003o`0001/00_l=00;o3P000ol00002o`l00ol400002P001?l0 0005o`h01?l900;o1004o`l01Ol300;o3004o`@00ol800Co1@001?l00?l300;o1P000ol000030003 o`0002<00ol<00;o70000ol0000;0003o`3o00d000?o00000_l@00;o100000T000Co00001Ol>00Co 2@000ol0000400?o4004o`040?ooo`/01Ol300?o2005o`L000Co003o2`000ol0000300;o9`02o``0 00?o00006P000ol0000:0003o`0000h000Co003o3P001?l00?l400002`02o`<000?o00002`02o`80 00?o00001P02o`D00_l00`3o000>00;o00<0ool00_l=00Co0P03o`X01?l90004o`00o`@01ol301So 5P02o`/00_lK0003o`0000X000?o00003@000ol0000?0003o`0000D0000:0003o`00010000?o0000 2@02o`D00_lA00;o0`02o``00ol200Co2P03o`8000?o000020001Ol00?l000go0`000ol0000300Ko 2@05oa<00_l;0003o`0001P000?o00002P000ol0000=0003o`0000l000?o00001@0000T000?o0000 40000ol0000800;o1P000ol0000@0004o`0000;o3@000ol0000200;o30000ol0000?00Co0P04o`03 0?oo00;o1@0:o`P03Ol600;o20000ol0000600;o00<0o`003P000ol000080003o`0000D000Go0000 o`0>00;o4@000ol0000500009P000ol0000K00;o4P02ob401Ol>0003o`0000<000?o00003`0;o`@0 1Ol400;o20000ol0o`0>0003o`0000P000?o00001@001Ol0003o00h00_lA0003o`0000D0000T00;o 7002oa400olP00?o4`000ol0000E00?o2003o`@01?l400;o1`03o`h00ol70003o`0000D000Go0000 o`0>00;o4@000ol0000500008P02oa`00_lA00;o8003oaH000?o00008`09o`D000?o00001002o`03 0?l000/01?l70003o`0000D00ol20003o`0000X01?l>00?o1`0002000_lL00;o4@02oal00olI0003 o`0000P04Ol=00?o00@0oooo1@02o`<01?l00`3o000;00?o20000ol0000400?o0P000ol0000:00Co 3P04o`H0000C00;o2P000ol0000J00;o4@02oah00olL0003o`0000So4@07o`T00ol80003o`000080 1?l=00?o1`000ol0000500;o0P000ol0000:00?o3`04o`H0000@00Co2@02o`H00ol?00Go4003o`l0 0_l<00?o7`03ob001?l800;o1`02o`D00_l=00;o1`000ol0000500;o0P000ol0000;00;o3`03o`L0 000?00Co2002o`D01?l>00Ko3`04o`h01?l;00;o1003oa000ol200Oo9P04o`H00_l70003o`0000@0 00?o00002`000ol000050003o`0000D00_l00`3o000=00;o3`03o`L0000>00Co1`02o`L00ol?00Go 3P05o`h01?l900?o0`04o`l02?l60003o`0000@01?lP00Co1002o`H000?o000010000ol0000B0003 o`0000H000?o0?l03P000ol0000>00?o1`0000d000Co003o1`000ol000060003o`3o01001?l?00Co 3P04o`P00_l600?o4005o`T000Co00001Ol=01Co1@02o`@00_l50003o`0000@000?o00004@000ol0 00080003o`0000/000?o00003`02o`P0000;00;o2@02o`L00_lA00;o0P000ol0000<00?o00<0o`00 3002o`8000?o00001@02o`H00_l00`3o000>00Go2`001?l00003o`X01Ol00`3oo`03o`h01_l00`3o o`0400;o10000ol000030003o`00014000?o000020000ol0000;0003o`0000h000?o0000200000X0 00?o00001`02o`L00_lA00;o4@03oa0000?o00002002o`H00_lA00Co00<0o`002`04o`030?l000L0 0ol300?o00<0ool04008o`040?ooo`<000Go0000o`060003o`00010000?o000020000ol0000:0003 o`0000h000?o00002@0000T000?o00001`000ol000060003o`0000l00_lB00;o4@000ol000080003 o`0000D000?o00003`03oa4000?o00001`04o`@00_l40003o`0000X02Ol400?o00<0ool01?l20003 o`0000<000?o000010000ol0000800;o1P001?l00?l=0003o`3o00h000Go0000o`0700004@02oaX0 00?o00004@000ol0000J00;o6002oa@000?o00001003oaP02Ol00`3oo`06o`030?oo00Ko0P000ol0 00030003o`0000801?l80003o`0000<00ol00`3o000<0004o`00o`d000?o00000P000ol000050000 3`02oaX00_lB00;o6`02oaP00_lF0004o`0000?o5P05oa802ol00`3o00030003o`0000801?l80003 o`0000<00ol00`3o000;00;o00<0o`002`02o`8000Co0?oo1`0000d00_lK0003o`0001000_lK00;o 6@000ol0000F0004o`3ooaL00_lF00go00<0o`000P000ol0000300?o1`000ol0000400Co30001?l0 ool<0003o`0000800ol8000030000ol0000400;o4`02oa400_lK00;o6@02oa000ol600;o5`02oa@0 1?l600So00D0o`00o`0500;o1`000ol0000500?o30000ol0o`03o`X000?o00000P04o`P0000:00;o 1005oa000ol@00?o4002o`T00_l500;o4@03o`l00_l20003o`0000<00ol500;o3`03oa0000?o0?l0 0_l:0004o`0000Oo00<0o`001002o`L000?o00001003o`/00_l200;o2`000ol0000200?o2P0000T0 00?o00000`05o`h01Ol>00Go3P04o`P00_l400Go3P04o`h01Ol20003o`00008000?o00000_l200Co 3P04o`l00ol=0003o`0000;o0`05o`H000?o00000`02o`L00_l:00;o10000ol0000800;o1003o`80 0_l700003`04o`l01?l>00Go3P04o`P000?o00000`05o`h01?l>00Go0`000ol00002o`<000?o0000 1?l=00Go3`03o`d00_l00`3o000600Ko1P03o`L00ol:0003o`0000<000?o00001`02o`@00ol30003 o`0000L0000>0004o`3oo`l01?l?00Co3`03o`L00_l600Co3`03oa000ol400?o1@000ol0o`03o``0 1_l?00?o3P04o`P02ol500Go2@04o`h00_l400?o0`02o`X0000<00;o0P000ol0000=00Co3`001?l0 0?l?0003o`3o00H00_l70004o`00o`l00ol@0003o`3o00@00_l70003o`0000?o2`001?l00003o`h0 1?l>00?o2P0@o`T01?l?00?o0`04o`030?oo00;o300000/000?o00004003oa000_lA00;o1`02o`P0 00?o00004002oa4000?o00001@000ol000060005o`3o0?l02`001ol0003o0?l04002o`h01?l<00Co 00<0ool04?l?00Co0`04o`040?oooa00000:0003o`0001000ol@00;o4@000ol000060003o`0000L0 00?o000040000ol0000@0003o`0000D000?o00001`02o`h000Co003o4P02o`l01?l=00?o0`0@o`L0 2?l200Ko00@0oooo4`0000T000?o00004002oa4000?o000040000ol000060003o`0000L000?o0000 40000ol0000@0003o`0000D000?o000020000ol0000<0004o`00oa800_lA0003o`3o00h00ol502Go 1P02o`<01?l700006`02oa4000?o00006@000ol0000J0003o`0001P000?o00002@000ol0000;0003 o`0001@000?o00004P000ol0000>0003o`0000H00ol00`3oo`0Do`/02Ol20003o`0000D0000J0003 o`0000l00_lJ00;o70000ol0000H0003o`0000X000?o00002`000ol0000D0003o`00018000?o0000 3`000ol0000800?o0`0Wo`P0000B00;o1002o`/00_l40003o`0000T00_l>0003o`0000;o4002o`L0 00?o00001P02oa000_l<0005o`000?l020000ol000060003o`0000/000Co003o3`001?l00?lA0003 o`0000/00ol400Co00<0ool05ol=00003`05o`<000?o00002@04o`800_l:00Co3@000ol0o`03o`h0 1?l60003o`0000D01?l?00?o30001Ol0003o00L000?o00001`000ol0000;0004o`00o`l000Co003o 30000ol000030003o`0000d00_l600?o100Io`L0000>00Go0P02o`/01?l20003o`0000T01?l=0003 o`3o00?o3P04o`H000?o00001@04o`l00ol=0003o`0000;o1P000ol0000700;o3@001?l0ool?00;o 0P000ol0000900;o1@000ol0000600;o1P02o`L00ol801;o1`0000h01?l20003o`0000X01?l20003 o`0000T01?l=0003o`3o00?o3P04o`H000?o00001@04o`l01?l=0004o`3oo`L000?o00001P02o`d0 00?o00000_l?00;o0P000ol0000900?o1@000ol0000500Co1P000ol0000300Oo3P09o`L0000>00Ko 3@06o`d00ol;00;o0`03o`l00ol50003o`0000L00ol>0003o`3o00;o3@04o`H000?o00001P03o`d0 00?o00000_l>00?o0P000ol0000:00?o1@000ol0000500Co1P02o`@01Ol0103ooolK00003@000ol0 0002o`h000?o00000_l>0003o`3o00/000?o00000P000ol0o`0@00;o1@000ol0000800;o3`001?l0 ool>0004o`3oo`D000?o00002002o`d000?o0?l00_l>00Co00<0o`002`04o`D000?o00001@03o`P0 0_l300Co1003o`@01_l>000030001Ol0003o00h000Go0000o`0>0003o`0000/000?o00000P000ol0 000@0003o`0000@000?o00002@000ol0000=0003o`3o010000?o0?l01@000ol000090003o`0000`0 00Co003o3`03o`8000?o00002P02o`P000?o00001@02o`X00_l200Co1P03o`<01?l>00002`000ol0 0002o`h000Go0000o`0>0003o`0000/000?o00000P000ol0000@0003o`0000@000?o00002@000ol0 000=0004o`00oa000_l60003o`0000P000?o000030001Ol0003o014000Go0000o`0=0003o`0000H0 00?o00001P000ol000090004o`00o`800_l700?o00@0ool00ol;00002P001?l00?l?0005o`000?l0 3P000ol0000;0003o`00008000?o000040000ol000040003o`0000T000?o00003@001?l00?lA00;o 1@000ol000090003o`0000`000Co003o4P001Ol0003o00d000?o00001P000ol000070003o`0000T0 0_l50003o`0000L00ol400?o200000T000Co0?oo3`001Ol0003o00h000?o00002`000ol000020003 o`00010000?o000010000ol000090003o`0000h00ol400;o0`03o`H000?o000010000ol000080003 o`0000d000Co003o4P001Ol0003o00h000?o00001P000ol000070003o`0000X00_l40003o`0000T0 0ol40003o`0000D0000:0003o`00018000?o00006P000ol0000L0003o`0000l000?o000020000ol0 o`0400?o1P000ol000030004o`00o`8000?o00002`000ol0000;0004o`00oa4000?o00000`000ol0 000E0003o`0001D000?o00004003o`T000090003o`0000D00_l;0003o`0000<00_l@00;o0`000ol0 000:00;o4002oa000_l90004o`00o`@000?o00001P000ol0000300;o00D0o`00o`0=0003o`0000/0 00Co003o4@000ol000030003o`0000P000?o00002P001?l00?lE0003o`0001800_l700004003o`X0 00?o00000P04o`l00ol20003o`0000X00ol?00;o4003o`T000Co003o0`02o`D00ol60006o`3oo`3o 3@02o``000Co00000_l@00;o10000ol000080003o`0000/000Co0?oo3`02o`@000?o00006P0000l0 0ol:0003o`0000801?l?00?o0P000ol0000:00?o3`03o`l01?l80005o`000?l00P03o`D000?o0000 1P04o`030?l000`00_l<0004o`0000;o4002o`D000?o00001`02o`d000Co0?oo3P04o`<00_l800;o 400000h01?l90003o`0000801?l?00Co00<0o`002`04o`h01?l>00Co20001?l00002o`800_l600Co 1@03o`8000?o00002`03o`/000?o00000ol?00?o1@000ol0000700?o30000ol0o`02o`h01?l40003 o`0000H01?l=00003P04o`P000?o00001003oa001?l>00?o3P03oa400_l80003o`0000@00ol?00?o 00<0o`003004o`/000?o00001?l>00Co10000ol0000700Co3005o`h01?l40003o`0000H01?l<0000 3@001?l00?l80003o`0000@000?o0?l040001?l0ool>0003o`3o00h000Co0?oo40000ol0o`070003 o`0000H00_l?00?o00<0o`003@000ol0o`0;0003o`0000Co3P03o`D000?o00001`03o`h00ol?00?o 1P000ol0000600?o300000`000?o00002@000ol000040003o`00010000Co003o3`000ol0000=0003 o`3o018000?o00001`000ol000050003o`0000l00_l20003o`0000`000?o00002`001Ol0003o0180 00?o000010000ol000080003o`0000`000Co003o3`000ol0o`060003o`0000H000?o0?l02`0000/0 00?o00002@000ol000040003o`00010000Go0000o`0>0003o`0000d000?o0?l04P000ol000070003 o`0000H000?o00003`02o`8000?o00002`000ol0000<0005o`000?l04P000ol000040003o`0000P0 00?o00003@000ol0o`0B0003o`0000@000?o00002002o`T0000:0003o`0000T000?o000010000ol0 000@0005o`000?l03P000ol0000>0003o`3o018000?o00001P000ol000070003o`0000l000Co003o 3P000ol0000<0005o`000?l04P000ol000040003o`0000T000?o00003@000ol0o`0B0003o`0000@0 00?o00002@000ol0000600002@000ol000090003o`0000@000?o000040001Ol0003o00h000?o0000 3P000ol0o`0B0003o`0000L000?o00001P000ol0000@0004o`00o`h000?o000030001Ol0003o0180 00?o000010000ol000090003o`0000d000Co003o4P000ol000040003o`0000T000?o00001@0001@0 00?o00003002o`d000Go0000o`0A0003o`0000L000?o00001@000ol0000?0003o`00008000?o0000 2P000ol0000=0004o`3oo`l000?o00002`001Ol0003o014000?o00001@000ol000060003o`000140 00?o00006P000ol0000@00004002o`030?l000d00ol=0003o`0000;o4002o`T000?o00001002oa40 00?o00000P000ol0000:0003o`0000d000?o0?l040000ol0000;0005o`000?l04@000ol000060003 o`0000D000?o00003`000ol0o`0>0003o`0000`000Co0?oo3P0000l01?l>00?o3@000ol00002oa00 0_l90003o`0000@00ol@00;o0`000ol0000:00;o3`03oa0000?o00002`001?l00002oa000_l70003 o`0000D00_l@0004o`00o`d00_l>00Co3@0000h01?l>00?o3@000ol00003o`l00ol80003o`0000@0 1?l?00;o10000ol0000900?o3`03o`l00ol<0003o`0000?o4002o`L000?o00001@03o`l00_l20003 o`0000/00_l>00Co300000d01?l>00Co30000ol00004o`h01?l80003o`0000<01?l?00?o0`000ol0 000:00?o3`03o`l00ol<0003o`0000?o3`03o`L000?o00001@03oa000_l00`3o000<00?o3P04o`/0 000>00?o40000ol0000;0004o`0000;o4@000ol000060003o`0000H00_l@00;o0`000ol0000900Co 3P04o`l00ol<0003o`0000Co3P04o`L000?o00001004o`l00ol00`3o000;00Co3P04o`X0000=00?o 40000ol0000;0007o`000?l0o`0@0003o`0000L000?o00001@000ol0o`0@0003o`00008000?o0000 2P000ol0o`0?00;o40000ol0000<0005o`000?l04003o`P000?o00001003oa000_l30003o`0000X0 0_l@00;o2`0000d000?o00003`000ol0000;0003o`00008000?o00003`000ol000070003o`0000H0 00?o000040001Ol0003o00d000?o00003`02oa0000?o000030001Ol0003o018000?o00001P000ol0 00060003o`0000l000Go0000o`0=0003o`0000l000?o00002@0000`000?o000040000ol0000;0005 o`000?l04P000ol000060003o`0000L000?o00003`000ol000020003o`0000/000?o00003`02oa00 00?o000030001Ol0003o018000?o00001P000ol000060003o`00010000Go0000o`0=0003o`0000l0 00?o0000200000/000?o000040000ol0000;0003o`00008000?o00003`000ol000070003o`0000H0 00?o000040001Ol0003o00h000?o00001P04o`D000?o00003`000ol0000<0005o`000?l04P000ol0 00060003o`0000H000?o000040001Ol0003o00h000?o00003`000ol0000700002P000ol0000@0003 o`0000/000?o00000P000ol0000@0003o`0000H000?o00001`000ol0000@0005o`000?l03@000ol0 00080003o`0000D000?o00003`000ol0000<0005o`000?l04P000ol000070003o`0000H000?o0000 3`000ol000020003o`0000/000?o000040000ol0000600002@000ol0000@0003o`0000/000?o0000 0P000ol0000@0003o`0000H000?o00001`000ol0000@0005o`000?l03P000ol000090003o`0000@0 0_l@0003o`0000`000Go0000o`0B0003o`0000L000?o00001P000ol0000@0003o`00008000?o0000 2`000ol0000@0003o`0000D000280003o`0008l000250004o`00oi40002600;oTP000?l06`000001 \ \>"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-2.14052, -2.10978, 0.0150741, 0.0243904}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]] }, Open ]], Cell["Problem 5", "Subsubsection"], Cell[TextData[{ "In this problem we consider the equations describing the motion of a \ pendulum, both damped and undamped. For each situation below convert the \ equation into a system of equations in ", StyleBox["x[t] = theta[t]", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["y[t] = theta'[t]", FontFamily->"Courier", FontWeight->"Bold"], ". Plot the corresponding vector field. Use ", StyleBox["NDSolve[]", FontFamily->"Courier", FontWeight->"Bold"], " to solve this system and plot on a single graph the trajectories \ corresponding to the given initial velocities ", StyleBox["b", FontFamily->"Courier", FontWeight->"Bold"], ". Based on these plots, describe what the pendulum is doing in each case. \ Experiment to see if you can find a value for the initial velocity ", StyleBox["b", FontFamily->"Courier", FontWeight->"Bold"], " such that the trajectory approaches the unstable equilibrium point ", StyleBox["{Pi,0}", FontFamily->"Courier", FontWeight->"Bold"], " corresponding to the pendulum being stationary in an upright position.\n\n\ ", StyleBox["a)", FontSlant->"Italic"], " The undamped pendulum:\n", StyleBox[ "\n theta''[t] + Sin[theta] == 0,\n theta[0] == 0, theta'[0] == b\n\n\ ", FontFamily->"Courier", FontWeight->"Bold"], "The initial velocities are ", StyleBox["b = 0.5", FontFamily->"Courier", FontWeight->"Bold"], " to ", StyleBox["3.0", FontFamily->"Courier", FontWeight->"Bold"], " in steps of ", StyleBox["0.5", FontFamily->"Courier", FontWeight->"Bold"], ".\n", StyleBox["\nb)", FontSlant->"Italic"], " The damped pendulum:\n", StyleBox[ "\n theta''[t] + 0.5 theta'[t] + Sin[theta] == 0,\n theta[0] == 0, \ theta'[0] == b\n\n", FontFamily->"Courier", FontWeight->"Bold"], "The initial velocities are ", StyleBox["b = 0.5", FontFamily->"Courier", FontWeight->"Bold"], " to ", StyleBox["6.0", FontFamily->"Courier", FontWeight->"Bold"], " in steps of ", StyleBox["0.5", FontFamily->"Courier", FontWeight->"Bold"], "." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Solution", "Subsubsection", CellMargins->{{Inherited, 126}, {Inherited, Inherited}}, Evaluatable->False, PageBreakWithin->Automatic, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[TextData[{ StyleBox["a)", FontSlant->"Italic"], " Since ", StyleBox["x'[t] == theta'[t] == y[t]", FontFamily->"Courier", FontWeight->"Bold"], ", and ", StyleBox["y'[t]==theta''[t]==-Sin[x[t]]", FontFamily->"Courier", FontWeight->"Bold"], ", the system is:\n\n", StyleBox[ " x'[t] == y[t], x[0] == 0\n y'[t] == -Sin[x[t]], y[0] == b", FontFamily->"Courier", FontWeight->"Bold"] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ PlotVectorField[{y,-Sin[x]},{x,-2,16},{y,-4,4}, ScaleFunction->(Log[50#+1]&),Frame->True]\ \>", "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .43279 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.151131 0.0498385 0.216288 0.0498385 [ [.15113 -0.0125 -3 -9 ] [.15113 -0.0125 3 0 ] [.40032 -0.0125 -3 -9 ] [.40032 -0.0125 3 0 ] [.64952 -0.0125 -6 -9 ] [.64952 -0.0125 6 0 ] [.89871 -0.0125 -6 -9 ] [.89871 -0.0125 6 0 ] [ 0 0 -0.125 0 ] [-0.0125 .01693 -12 -4.5 ] [-0.0125 .01693 0 4.5 ] [-0.0125 .11661 -12 -4.5 ] [-0.0125 .11661 0 4.5 ] [-0.0125 .21629 -6 -4.5 ] [-0.0125 .21629 0 4.5 ] [-0.0125 .31597 -6 -4.5 ] [-0.0125 .31597 0 4.5 ] [-0.0125 .41564 -6 -4.5 ] [-0.0125 .41564 0 4.5 ] [ 0 0 -0.125 0 ] [ 0 .43279 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 .43279 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .15113 0 m .15113 .00625 L s [(0)] .15113 -0.0125 0 1 Mshowa .40032 0 m .40032 .00625 L s [(5)] .40032 -0.0125 0 1 Mshowa .64952 0 m .64952 .00625 L s [(10)] .64952 -0.0125 0 1 Mshowa .89871 0 m .89871 .00625 L s [(15)] .89871 -0.0125 0 1 Mshowa .125 Mabswid .20097 0 m .20097 .00375 L s .25081 0 m .25081 .00375 L s .30065 0 m .30065 .00375 L s .35048 0 m .35048 .00375 L s .45016 0 m .45016 .00375 L s .5 0 m .5 .00375 L s .54984 0 m .54984 .00375 L s .59968 0 m .59968 .00375 L s .69935 0 m .69935 .00375 L s .74919 0 m .74919 .00375 L s .79903 0 m .79903 .00375 L s .84887 0 m .84887 .00375 L s .10129 0 m .10129 .00375 L s .05145 0 m .05145 .00375 L s .00162 0 m .00162 .00375 L s .94855 0 m .94855 .00375 L s .99838 0 m .99838 .00375 L s .25 Mabswid 0 0 m 1 0 L s 0 .01693 m .00625 .01693 L s [(-4)] -0.0125 .01693 1 0 Mshowa 0 .11661 m .00625 .11661 L s [(-2)] -0.0125 .11661 1 0 Mshowa 0 .21629 m .00625 .21629 L s [(0)] -0.0125 .21629 1 0 Mshowa 0 .31597 m .00625 .31597 L s [(2)] -0.0125 .31597 1 0 Mshowa 0 .41564 m .00625 .41564 L s [(4)] -0.0125 .41564 1 0 Mshowa .125 Mabswid 0 .04185 m .00375 .04185 L s 0 .06677 m .00375 .06677 L s 0 .09169 m .00375 .09169 L s 0 .14153 m .00375 .14153 L s 0 .16645 m .00375 .16645 L s 0 .19137 m .00375 .19137 L s 0 .24121 m .00375 .24121 L s 0 .26613 m .00375 .26613 L s 0 .29105 m .00375 .29105 L s 0 .34088 m .00375 .34088 L s 0 .3658 m .00375 .3658 L s 0 .39072 m .00375 .39072 L s .25 Mabswid 0 0 m 0 .43279 L s .15113 .42654 m .15113 .43279 L s .40032 .42654 m .40032 .43279 L s .64952 .42654 m .64952 .43279 L s .89871 .42654 m .89871 .43279 L s .125 Mabswid .20097 .42904 m .20097 .43279 L s .25081 .42904 m .25081 .43279 L s .30065 .42904 m .30065 .43279 L s .35048 .42904 m .35048 .43279 L s .45016 .42904 m .45016 .43279 L s .5 .42904 m .5 .43279 L s .54984 .42904 m .54984 .43279 L s .59968 .42904 m .59968 .43279 L s .69935 .42904 m .69935 .43279 L s .74919 .42904 m .74919 .43279 L s .79903 .42904 m .79903 .43279 L s .84887 .42904 m .84887 .43279 L s .10129 .42904 m .10129 .43279 L s .05145 .42904 m .05145 .43279 L s .00162 .42904 m .00162 .43279 L s .94855 .42904 m .94855 .43279 L s .99838 .42904 m .99838 .43279 L s .25 Mabswid 0 .43279 m 1 .43279 L s .99375 .01693 m 1 .01693 L s .99375 .11661 m 1 .11661 L s .99375 .21629 m 1 .21629 L s .99375 .31597 m 1 .31597 L s .99375 .41564 m 1 .41564 L s .125 Mabswid .99625 .04185 m 1 .04185 L s .99625 .06677 m 1 .06677 L s .99625 .09169 m 1 .09169 L s .99625 .14153 m 1 .14153 L s .99625 .16645 m 1 .16645 L s .99625 .19137 m 1 .19137 L s .99625 .24121 m 1 .24121 L s .99625 .26613 m 1 .26613 L s .99625 .29105 m 1 .29105 L s .99625 .34088 m 1 .34088 L s .99625 .3658 m 1 .3658 L s .99625 .39072 m 1 .39072 L s .25 Mabswid 1 0 m 1 .43279 L s % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto fill -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto -0.02 0.005 lineto stroke } ifelse grestore } def % End of user PostScript .0001 w .05145 .01693 m .02381 .02322 L s % Start of user PostScript -2. -4. -2.55468 -3.87391 MAarrowhead1 % End of user PostScript .05145 .04541 m .02776 .0517 L s % Start of user PostScript -2. -3.42857 -2.47544 -3.30248 MAarrowhead1 % End of user PostScript .05145 .07389 m .03171 .08018 L s % Start of user PostScript -2. -2.85714 -2.3962 -2.73105 MAarrowhead1 % End of user PostScript .05145 .10237 m .03566 .10866 L s % Start of user PostScript -2. -2.28571 -2.31696 -2.15962 MAarrowhead1 % End of user PostScript .05145 .13085 m .03961 .13713 L s % Start of user PostScript -2. -1.71429 -2.23772 -1.58819 MAarrowhead1 % End of user PostScript .05145 .15933 m .04356 .16561 L s % Start of user PostScript -2. -1.14286 -2.15848 -1.01677 MAarrowhead1 % End of user PostScript .05145 .18781 m .0475 .19409 L s % Start of user PostScript -2. -0.571429 -2.07924 -0.445337 MAarrowhead1 % End of user PostScript .05145 .21629 m .05145 .22257 L s % Start of user PostScript -2. 0 -2. 0.126092 MAarrowhead1 % End of user PostScript .05145 .24477 m .0554 .25105 L s % Start of user PostScript -2. 0.571429 -1.92076 0.69752 MAarrowhead1 % End of user PostScript .05145 .27325 m .05935 .27953 L s % Start of user PostScript -2. 1.14286 -1.84152 1.26895 MAarrowhead1 % End of user PostScript .05145 .30173 m .0633 .30801 L s % Start of user PostScript -2. 1.71429 -1.76228 1.84038 MAarrowhead1 % End of user PostScript .05145 .3302 m .06725 .33649 L s % Start of user PostScript -2. 2.28571 -1.68304 2.41181 MAarrowhead1 % End of user PostScript .05145 .35868 m .0712 .36497 L s % Start of user PostScript -2. 2.85714 -1.6038 2.98323 MAarrowhead1 % End of user PostScript .05145 .38716 m .07515 .39345 L s % Start of user PostScript -2. 3.42857 -1.52456 3.55466 MAarrowhead1 % End of user PostScript .05145 .41564 m .0791 .42193 L s % Start of user PostScript -2. 4. -1.44532 4.12609 MAarrowhead1 % End of user PostScript .11553 .01693 m .08789 .02146 L s % Start of user PostScript -0.714286 -4. -1.26896 -3.90916 MAarrowhead1 % End of user PostScript .11553 .04541 m .09184 .04994 L s % Start of user PostScript -0.714286 -3.42857 -1.18972 -3.33773 MAarrowhead1 % End of user PostScript .11553 .07389 m .09579 .07842 L s % Start of user PostScript -0.714286 -2.85714 -1.11048 -2.7663 MAarrowhead1 % End of user PostScript .11553 .10237 m .09974 .1069 L s % Start of user PostScript -0.714286 -2.28571 -1.03124 -2.19487 MAarrowhead1 % End of user PostScript .11553 .13085 m .10368 .13538 L s % Start of user PostScript -0.714286 -1.71429 -0.952005 -1.62345 MAarrowhead1 % End of user PostScript .11553 .15933 m .10763 .16386 L s % Start of user PostScript -0.714286 -1.14286 -0.872765 -1.05202 MAarrowhead1 % End of user PostScript .11553 .18781 m .11158 .19234 L s % Start of user PostScript -0.714286 -0.571429 -0.793525 -0.480589 MAarrowhead1 % End of user PostScript .11553 .21629 m .11553 .22082 L s % Start of user PostScript -0.714286 0 -0.714286 0.0908393 MAarrowhead1 % End of user PostScript .11553 .24477 m .11948 .24929 L s % Start of user PostScript -0.714286 0.571429 -0.635046 0.662268 MAarrowhead1 % End of user PostScript .11553 .27325 m .12343 .27777 L s % Start of user PostScript -0.714286 1.14286 -0.555806 1.2337 MAarrowhead1 % End of user PostScript .11553 .30173 m .12738 .30625 L s % Start of user PostScript -0.714286 1.71429 -0.476567 1.80513 MAarrowhead1 % End of user PostScript .11553 .3302 m .13133 .33473 L s % Start of user PostScript -0.714286 2.28571 -0.397327 2.37655 MAarrowhead1 % End of user PostScript .11553 .35868 m .13528 .36321 L s % Start of user PostScript -0.714286 2.85714 -0.318087 2.94798 MAarrowhead1 % End of user PostScript .11553 .38716 m .13923 .39169 L s % Start of user PostScript -0.714286 3.42857 -0.238848 3.51941 MAarrowhead1 % End of user PostScript .11553 .41564 m .14318 .42017 L s % Start of user PostScript -0.714286 4. -0.159608 4.09084 MAarrowhead1 % End of user PostScript .17961 .01693 m .15197 .0132 L s % Start of user PostScript 0.571429 -4. 0.0167507 -4.075 MAarrowhead1 % End of user PostScript .17961 .04541 m .15591 .04168 L s % Start of user PostScript 0.571429 -3.42857 0.0959904 -3.50357 MAarrowhead1 % End of user PostScript .17961 .07389 m .15986 .07015 L s % Start of user PostScript 0.571429 -2.85714 0.17523 -2.93214 MAarrowhead1 % End of user PostScript .17961 .10237 m .16381 .09863 L s % Start of user PostScript 0.571429 -2.28571 0.25447 -2.36071 MAarrowhead1 % End of user PostScript .17961 .13085 m .16776 .12711 L s % Start of user PostScript 0.571429 -1.71429 0.333709 -1.78928 MAarrowhead1 % End of user PostScript .17961 .15933 m .17171 .15559 L s % Start of user PostScript 0.571429 -1.14286 0.412949 -1.21785 MAarrowhead1 % End of user PostScript .17961 .18781 m .17566 .18407 L s % Start of user PostScript 0.571429 -0.571429 0.492189 -0.646426 MAarrowhead1 % End of user PostScript .17961 .21629 m .17961 .21255 L s % Start of user PostScript 0.571429 0 0.571429 -0.0749972 MAarrowhead1 % End of user PostScript .17961 .24477 m .18356 .24103 L s % Start of user PostScript 0.571429 0.571429 0.650668 0.496431 MAarrowhead1 % End of user PostScript .17961 .27325 m .18751 .26951 L s % Start of user PostScript 0.571429 1.14286 0.729908 1.06786 MAarrowhead1 % End of user PostScript .17961 .30173 m .19146 .29799 L s % Start of user PostScript 0.571429 1.71429 0.809148 1.63929 MAarrowhead1 % End of user PostScript .17961 .3302 m .19541 .32647 L s % Start of user PostScript 0.571429 2.28571 0.888387 2.21072 MAarrowhead1 % End of user PostScript .17961 .35868 m .19936 .35495 L s % Start of user PostScript 0.571429 2.85714 0.967627 2.78215 MAarrowhead1 % End of user PostScript .17961 .38716 m .2033 .38343 L s % Start of user PostScript 0.571429 3.42857 1.04687 3.35357 MAarrowhead1 % End of user PostScript .17961 .41564 m .20725 .4119 L s % Start of user PostScript 0.571429 4. 1.12611 3.925 MAarrowhead1 % End of user PostScript .24369 .01693 m .21604 .0103 L s % Start of user PostScript 1.85714 -4. 1.30246 -4.13302 MAarrowhead1 % End of user PostScript .24369 .04541 m .21999 .03878 L s % Start of user PostScript 1.85714 -3.42857 1.3817 -3.56159 MAarrowhead1 % End of user PostScript .24369 .07389 m .22394 .06726 L s % Start of user PostScript 1.85714 -2.85714 1.46094 -2.99017 MAarrowhead1 % End of user PostScript .24369 .10237 m .22789 .09574 L s % Start of user PostScript 1.85714 -2.28571 1.54018 -2.41874 MAarrowhead1 % End of user PostScript .24369 .13085 m .23184 .12422 L s % Start of user PostScript 1.85714 -1.71429 1.61942 -1.84731 MAarrowhead1 % End of user PostScript .24369 .15933 m .23579 .1527 L s % Start of user PostScript 1.85714 -1.14286 1.69866 -1.27588 MAarrowhead1 % End of user PostScript .24369 .18781 m .23974 .18118 L s % Start of user PostScript 1.85714 -0.571429 1.7779 -0.704452 MAarrowhead1 % End of user PostScript .24369 .21629 m .24369 .20966 L s % Start of user PostScript 1.85714 0 1.85714 -0.133023 MAarrowhead1 % End of user PostScript .24369 .24477 m .24764 .23814 L s % Start of user PostScript 1.85714 0.571429 1.93638 0.438405 MAarrowhead1 % End of user PostScript .24369 .27325 m .25159 .26662 L s % Start of user PostScript 1.85714 1.14286 2.01562 1.00983 MAarrowhead1 % End of user PostScript .24369 .30173 m .25554 .2951 L s % Start of user PostScript 1.85714 1.71429 2.09486 1.58126 MAarrowhead1 % End of user PostScript .24369 .3302 m .25948 .32357 L s % Start of user PostScript 1.85714 2.28571 2.1741 2.15269 MAarrowhead1 % End of user PostScript .24369 .35868 m .26343 .35205 L s % Start of user PostScript 1.85714 2.85714 2.25334 2.72412 MAarrowhead1 % End of user PostScript .24369 .38716 m .26738 .38053 L s % Start of user PostScript 1.85714 3.42857 2.33258 3.29555 MAarrowhead1 % End of user PostScript .24369 .41564 m .27133 .40901 L s % Start of user PostScript 1.85714 4. 2.41182 3.86698 MAarrowhead1 % End of user PostScript .30777 .01693 m .28012 .01694 L s % Start of user PostScript 3.14286 -4. 2.58818 -3.99982 MAarrowhead1 % End of user PostScript .30777 .04541 m .28407 .04542 L s % Start of user PostScript 3.14286 -3.42857 2.66742 -3.4284 MAarrowhead1 % End of user PostScript .30777 .07389 m .28802 .0739 L s % Start of user PostScript 3.14286 -2.85714 2.74666 -2.85697 MAarrowhead1 % End of user PostScript .30777 .10237 m .29197 .10238 L s % Start of user PostScript 3.14286 -2.28571 2.8259 -2.28554 MAarrowhead1 % End of user PostScript .30777 .13085 m .29592 .13086 L s % Start of user PostScript 3.14286 -1.71429 2.90514 -1.71411 MAarrowhead1 % End of user PostScript .30777 .15933 m .29987 .15934 L s % Start of user PostScript 3.14286 -1.14286 2.98438 -1.14268 MAarrowhead1 % End of user PostScript .30777 .18781 m .30382 .18782 L s % Start of user PostScript 3.14286 -0.571429 3.06362 -0.571253 MAarrowhead1 % End of user PostScript .30777 .21629 m .30777 .2163 L s % Start of user PostScript 3.14286 0 3.14286 0.000175346 MAarrowhead1 % End of user PostScript .30777 .24477 m .31172 .24478 L s % Start of user PostScript 3.14286 0.571429 3.2221 0.571604 MAarrowhead1 % End of user PostScript .30777 .27325 m .31566 .27326 L s % Start of user PostScript 3.14286 1.14286 3.30134 1.14303 MAarrowhead1 % End of user PostScript .30777 .30173 m .31961 .30173 L s % Start of user PostScript 3.14286 1.71429 3.38058 1.71446 MAarrowhead1 % End of user PostScript .30777 .3302 m .32356 .33021 L s % Start of user PostScript 3.14286 2.28571 3.45982 2.28589 MAarrowhead1 % End of user PostScript .30777 .35868 m .32751 .35869 L s % Start of user PostScript 3.14286 2.85714 3.53906 2.85732 MAarrowhead1 % End of user PostScript .30777 .38716 m .33146 .38717 L s % Start of user PostScript 3.14286 3.42857 3.6183 3.42875 MAarrowhead1 % End of user PostScript .30777 .41564 m .33541 .41565 L s % Start of user PostScript 3.14286 4. 3.69754 4.00018 MAarrowhead1 % End of user PostScript .37184 .01693 m .3442 .02357 L s % Start of user PostScript 4.42857 -4. 3.87389 -3.86688 MAarrowhead1 % End of user PostScript .37184 .04541 m .34815 .05205 L s % Start of user PostScript 4.42857 -3.42857 3.95313 -3.29545 MAarrowhead1 % End of user PostScript .37184 .07389 m .3521 .08053 L s % Start of user PostScript 4.42857 -2.85714 4.03237 -2.72402 MAarrowhead1 % End of user PostScript .37184 .10237 m .35605 .10901 L s % Start of user PostScript 4.42857 -2.28571 4.11161 -2.15259 MAarrowhead1 % End of user PostScript .37184 .13085 m .36 .13749 L s % Start of user PostScript 4.42857 -1.71429 4.19085 -1.58116 MAarrowhead1 % End of user PostScript .37184 .15933 m .36395 .16596 L s % Start of user PostScript 4.42857 -1.14286 4.27009 -1.00974 MAarrowhead1 % End of user PostScript .37184 .18781 m .36789 .19444 L s % Start of user PostScript 4.42857 -0.571429 4.34933 -0.438307 MAarrowhead1 % End of user PostScript .37184 .21629 m .37184 .22292 L s % Start of user PostScript 4.42857 0 4.42857 0.133122 MAarrowhead1 % End of user PostScript .37184 .24477 m .37579 .2514 L s % Start of user PostScript 4.42857 0.571429 4.50781 0.70455 MAarrowhead1 % End of user PostScript .37184 .27325 m .37974 .27988 L s % Start of user PostScript 4.42857 1.14286 4.58705 1.27598 MAarrowhead1 % End of user PostScript .37184 .30173 m .38369 .30836 L s % Start of user PostScript 4.42857 1.71429 4.66629 1.84741 MAarrowhead1 % End of user PostScript .37184 .3302 m .38764 .33684 L s % Start of user PostScript 4.42857 2.28571 4.74553 2.41884 MAarrowhead1 % End of user PostScript .37184 .35868 m .39159 .36532 L s % Start of user PostScript 4.42857 2.85714 4.82477 2.99026 MAarrowhead1 % End of user PostScript .37184 .38716 m .39554 .3938 L s % Start of user PostScript 4.42857 3.42857 4.90401 3.56169 MAarrowhead1 % End of user PostScript .37184 .41564 m .39949 .42228 L s % Start of user PostScript 4.42857 4. 4.98325 4.13312 MAarrowhead1 % End of user PostScript .43592 .01693 m .40828 .02066 L s % Start of user PostScript 5.71429 -4. 5.15961 -3.9253 MAarrowhead1 % End of user PostScript .43592 .04541 m .41223 .04914 L s % Start of user PostScript 5.71429 -3.42857 5.23885 -3.35387 MAarrowhead1 % End of user PostScript .43592 .07389 m .41618 .07762 L s % Start of user PostScript 5.71429 -2.85714 5.31809 -2.78244 MAarrowhead1 % End of user PostScript .43592 .10237 m .42013 .10609 L s % Start of user PostScript 5.71429 -2.28571 5.39733 -2.21101 MAarrowhead1 % End of user PostScript .43592 .13085 m .42407 .13457 L s % Start of user PostScript 5.71429 -1.71429 5.47657 -1.63958 MAarrowhead1 % End of user PostScript .43592 .15933 m .42802 .16305 L s % Start of user PostScript 5.71429 -1.14286 5.55581 -1.06816 MAarrowhead1 % End of user PostScript .43592 .18781 m .43197 .19153 L s % Start of user PostScript 5.71429 -0.571429 5.63505 -0.496727 MAarrowhead1 % End of user PostScript .43592 .21629 m .43592 .22001 L s % Start of user PostScript 5.71429 0 5.71429 0.074702 MAarrowhead1 % End of user PostScript .43592 .24477 m .43987 .24849 L s % Start of user PostScript 5.71429 0.571429 5.79353 0.646131 MAarrowhead1 % End of user PostScript .43592 .27325 m .44382 .27697 L s % Start of user PostScript 5.71429 1.14286 5.87277 1.21756 MAarrowhead1 % End of user PostScript .43592 .30173 m .44777 .30545 L s % Start of user PostScript 5.71429 1.71429 5.952 1.78899 MAarrowhead1 % End of user PostScript .43592 .3302 m .45172 .33393 L s % Start of user PostScript 5.71429 2.28571 6.03124 2.36042 MAarrowhead1 % End of user PostScript .43592 .35868 m .45567 .36241 L s % Start of user PostScript 5.71429 2.85714 6.11048 2.93184 MAarrowhead1 % End of user PostScript .43592 .38716 m .45962 .39089 L s % Start of user PostScript 5.71429 3.42857 6.18972 3.50327 MAarrowhead1 % End of user PostScript .43592 .41564 m .46357 .41936 L s % Start of user PostScript 5.71429 4. 6.26896 4.0747 MAarrowhead1 % End of user PostScript .5 .01693 m .47236 .01239 L s % Start of user PostScript 7. -4. 6.44532 -4.0911 MAarrowhead1 % End of user PostScript .5 .04541 m .4763 .04087 L s % Start of user PostScript 7. -3.42857 6.52456 -3.51968 MAarrowhead1 % End of user PostScript .5 .07389 m .48025 .06935 L s % Start of user PostScript 7. -2.85714 6.6038 -2.94825 MAarrowhead1 % End of user PostScript .5 .10237 m .4842 .09783 L s % Start of user PostScript 7. -2.28571 6.68304 -2.37682 MAarrowhead1 % End of user PostScript .5 .13085 m .48815 .12631 L s % Start of user PostScript 7. -1.71429 6.76228 -1.80539 MAarrowhead1 % End of user PostScript .5 .15933 m .4921 .15479 L s % Start of user PostScript 7. -1.14286 6.84152 -1.23396 MAarrowhead1 % End of user PostScript .5 .18781 m .49605 .18327 L s % Start of user PostScript 7. -0.571429 6.92076 -0.662533 MAarrowhead1 % End of user PostScript .5 .21629 m .5 .21175 L s % Start of user PostScript 7. 0 7. -0.091104 MAarrowhead1 % End of user PostScript .5 .24477 m .50395 .24023 L s % Start of user PostScript 7. 0.571429 7.07924 0.480325 MAarrowhead1 % End of user PostScript .5 .27325 m .5079 .26871 L s % Start of user PostScript 7. 1.14286 7.15848 1.05175 MAarrowhead1 % End of user PostScript .5 .30173 m .51185 .29718 L s % Start of user PostScript 7. 1.71429 7.23772 1.62318 MAarrowhead1 % End of user PostScript .5 .3302 m .5158 .32566 L s % Start of user PostScript 7. 2.28571 7.31696 2.19461 MAarrowhead1 % End of user PostScript .5 .35868 m .51975 .35414 L s % Start of user PostScript 7. 2.85714 7.3962 2.76604 MAarrowhead1 % End of user PostScript .5 .38716 m .5237 .38262 L s % Start of user PostScript 7. 3.42857 7.47544 3.33747 MAarrowhead1 % End of user PostScript .5 .41564 m .52764 .4111 L s % Start of user PostScript 7. 4. 7.55468 3.9089 MAarrowhead1 % End of user PostScript .56408 .01693 m .53643 .01066 L s % Start of user PostScript 8.28571 -4. 7.73104 -4.12595 MAarrowhead1 % End of user PostScript .56408 .04541 m .54038 .03914 L s % Start of user PostScript 8.28571 -3.42857 7.81028 -3.55452 MAarrowhead1 % End of user PostScript .56408 .07389 m .54433 .06762 L s % Start of user PostScript 8.28571 -2.85714 7.88952 -2.98309 MAarrowhead1 % End of user PostScript .56408 .10237 m .54828 .09609 L s % Start of user PostScript 8.28571 -2.28571 7.96876 -2.41166 MAarrowhead1 % End of user PostScript .56408 .13085 m .55223 .12457 L s % Start of user PostScript 8.28571 -1.71429 8.048 -1.84023 MAarrowhead1 % End of user PostScript .56408 .15933 m .55618 .15305 L s % Start of user PostScript 8.28571 -1.14286 8.12723 -1.2688 MAarrowhead1 % End of user PostScript .56408 .18781 m .56013 .18153 L s % Start of user PostScript 8.28571 -0.571429 8.20647 -0.697374 MAarrowhead1 % End of user PostScript .56408 .21629 m .56408 .21001 L s % Start of user PostScript 8.28571 0 8.28571 -0.125945 MAarrowhead1 % End of user PostScript .56408 .24477 m .56803 .23849 L s % Start of user PostScript 8.28571 0.571429 8.36495 0.445483 MAarrowhead1 % End of user PostScript .56408 .27325 m .57198 .26697 L s % Start of user PostScript 8.28571 1.14286 8.44419 1.01691 MAarrowhead1 % End of user PostScript .56408 .30173 m .57593 .29545 L s % Start of user PostScript 8.28571 1.71429 8.52343 1.58834 MAarrowhead1 % End of user PostScript .56408 .3302 m .57987 .32393 L s % Start of user PostScript 8.28571 2.28571 8.60267 2.15977 MAarrowhead1 % End of user PostScript .56408 .35868 m .58382 .35241 L s % Start of user PostScript 8.28571 2.85714 8.68191 2.7312 MAarrowhead1 % End of user PostScript .56408 .38716 m .58777 .38089 L s % Start of user PostScript 8.28571 3.42857 8.76115 3.30263 MAarrowhead1 % End of user PostScript .56408 .41564 m .59172 .40937 L s % Start of user PostScript 8.28571 4. 8.84039 3.87405 MAarrowhead1 % End of user PostScript .62816 .01693 m .60051 .01794 L s % Start of user PostScript 9.57143 -4. 9.01675 -3.97974 MAarrowhead1 % End of user PostScript .62816 .04541 m .60446 .04642 L s % Start of user PostScript 9.57143 -3.42857 9.09599 -3.40831 MAarrowhead1 % End of user PostScript .62816 .07389 m .60841 .0749 L s % Start of user PostScript 9.57143 -2.85714 9.17523 -2.83688 MAarrowhead1 % End of user PostScript .62816 .10237 m .61236 .10338 L s % Start of user PostScript 9.57143 -2.28571 9.25447 -2.26545 MAarrowhead1 % End of user PostScript .62816 .13085 m .61631 .13186 L s % Start of user PostScript 9.57143 -1.71429 9.33371 -1.69402 MAarrowhead1 % End of user PostScript .62816 .15933 m .62026 .16034 L s % Start of user PostScript 9.57143 -1.14286 9.41295 -1.12259 MAarrowhead1 % End of user PostScript .62816 .18781 m .62421 .18882 L s % Start of user PostScript 9.57143 -0.571429 9.49219 -0.551165 MAarrowhead1 % End of user PostScript .62816 .21629 m .62816 .2173 L s % Start of user PostScript 9.57143 0 9.57143 0.0202631 MAarrowhead1 % End of user PostScript .62816 .24477 m .63211 .24578 L s % Start of user PostScript 9.57143 0.571429 9.65067 0.591692 MAarrowhead1 % End of user PostScript .62816 .27325 m .63605 .27426 L s % Start of user PostScript 9.57143 1.14286 9.72991 1.16312 MAarrowhead1 % End of user PostScript .62816 .30173 m .64 .30274 L s % Start of user PostScript 9.57143 1.71429 9.80915 1.73455 MAarrowhead1 % End of user PostScript .62816 .3302 m .64395 .33121 L s % Start of user PostScript 9.57143 2.28571 9.88839 2.30598 MAarrowhead1 % End of user PostScript .62816 .35868 m .6479 .35969 L s % Start of user PostScript 9.57143 2.85714 9.96763 2.87741 MAarrowhead1 % End of user PostScript .62816 .38716 m .65185 .38817 L s % Start of user PostScript 9.57143 3.42857 10.0469 3.44883 MAarrowhead1 % End of user PostScript .62816 .41564 m .6558 .41665 L s % Start of user PostScript 9.57143 4. 10.1261 4.02026 MAarrowhead1 % End of user PostScript .69223 .01693 m .66459 .02378 L s % Start of user PostScript 10.8571 -4. 10.3025 -3.86266 MAarrowhead1 % End of user PostScript .69223 .04541 m .66854 .05226 L s % Start of user PostScript 10.8571 -3.42857 10.3817 -3.29123 MAarrowhead1 % End of user PostScript .69223 .07389 m .67249 .08074 L s % Start of user PostScript 10.8571 -2.85714 10.4609 -2.7198 MAarrowhead1 % End of user PostScript .69223 .10237 m .67644 .10922 L s % Start of user PostScript 10.8571 -2.28571 10.5402 -2.14837 MAarrowhead1 % End of user PostScript .69223 .13085 m .68039 .1377 L s % Start of user PostScript 10.8571 -1.71429 10.6194 -1.57694 MAarrowhead1 % End of user PostScript .69223 .15933 m .68434 .16617 L s % Start of user PostScript 10.8571 -1.14286 10.6987 -1.00551 MAarrowhead1 % End of user PostScript .69223 .18781 m .68828 .19465 L s % Start of user PostScript 10.8571 -0.571429 10.7779 -0.434086 MAarrowhead1 % End of user PostScript .69223 .21629 m .69223 .22313 L s % Start of user PostScript 10.8571 0 10.8571 0.137343 MAarrowhead1 % End of user PostScript .69223 .24477 m .69618 .25161 L s % Start of user PostScript 10.8571 0.571429 10.9364 0.708771 MAarrowhead1 % End of user PostScript .69223 .27325 m .70013 .28009 L s % Start of user PostScript 10.8571 1.14286 11.0156 1.2802 MAarrowhead1 % End of user PostScript .69223 .30173 m .70408 .30857 L s % Start of user PostScript 10.8571 1.71429 11.0949 1.85163 MAarrowhead1 % End of user PostScript .69223 .3302 m .70803 .33705 L s % Start of user PostScript 10.8571 2.28571 11.1741 2.42306 MAarrowhead1 % End of user PostScript .69223 .35868 m .71198 .36553 L s % Start of user PostScript 10.8571 2.85714 11.2533 2.99449 MAarrowhead1 % End of user PostScript .69223 .38716 m .71593 .39401 L s % Start of user PostScript 10.8571 3.42857 11.3326 3.56591 MAarrowhead1 % End of user PostScript .69223 .41564 m .71988 .42249 L s % Start of user PostScript 10.8571 4. 11.4118 4.13734 MAarrowhead1 % End of user PostScript .75631 .01693 m .72867 .01977 L s % Start of user PostScript 12.1429 -4. 11.5882 -3.94301 MAarrowhead1 % End of user PostScript .75631 .04541 m .73262 .04825 L s % Start of user PostScript 12.1429 -3.42857 11.6674 -3.37158 MAarrowhead1 % End of user PostScript .75631 .07389 m .73657 .07673 L s % Start of user PostScript 12.1429 -2.85714 11.7467 -2.80015 MAarrowhead1 % End of user PostScript .75631 .10237 m .74052 .10521 L s % Start of user PostScript 12.1429 -2.28571 11.8259 -2.22873 MAarrowhead1 % End of user PostScript .75631 .13085 m .74446 .13369 L s % Start of user PostScript 12.1429 -1.71429 11.9051 -1.6573 MAarrowhead1 % End of user PostScript .75631 .15933 m .74841 .16217 L s % Start of user PostScript 12.1429 -1.14286 11.9844 -1.08587 MAarrowhead1 % End of user PostScript .75631 .18781 m .75236 .19065 L s % Start of user PostScript 12.1429 -0.571429 12.0636 -0.51444 MAarrowhead1 % End of user PostScript .75631 .21629 m .75631 .21913 L s % Start of user PostScript 12.1429 0 12.1429 0.0569884 MAarrowhead1 % End of user PostScript .75631 .24477 m .76026 .24761 L s % Start of user PostScript 12.1429 0.571429 12.2221 0.628417 MAarrowhead1 % End of user PostScript .75631 .27325 m .76421 .27609 L s % Start of user PostScript 12.1429 1.14286 12.3013 1.19985 MAarrowhead1 % End of user PostScript .75631 .30173 m .76816 .30457 L s % Start of user PostScript 12.1429 1.71429 12.3806 1.77127 MAarrowhead1 % End of user PostScript .75631 .3302 m .77211 .33304 L s % Start of user PostScript 12.1429 2.28571 12.4598 2.3427 MAarrowhead1 % End of user PostScript .75631 .35868 m .77606 .36152 L s % Start of user PostScript 12.1429 2.85714 12.5391 2.91413 MAarrowhead1 % End of user PostScript .75631 .38716 m .78001 .39 L s % Start of user PostScript 12.1429 3.42857 12.6183 3.48556 MAarrowhead1 % End of user PostScript .75631 .41564 m .78396 .41848 L s % Start of user PostScript 12.1429 4. 12.6975 4.05699 MAarrowhead1 % End of user PostScript .82039 .01693 m .79275 .01169 L s % Start of user PostScript 13.4286 -4. 12.8739 -4.10529 MAarrowhead1 % End of user PostScript .82039 .04541 m .7967 .04017 L s % Start of user PostScript 13.4286 -3.42857 12.9531 -3.53386 MAarrowhead1 % End of user PostScript .82039 .07389 m .80064 .06865 L s % Start of user PostScript 13.4286 -2.85714 13.0324 -2.96243 MAarrowhead1 % End of user PostScript .82039 .10237 m .80459 .09712 L s % Start of user PostScript 13.4286 -2.28571 13.1116 -2.391 MAarrowhead1 % End of user PostScript .82039 .13085 m .80854 .1256 L s % Start of user PostScript 13.4286 -1.71429 13.1909 -1.81957 MAarrowhead1 % End of user PostScript .82039 .15933 m .81249 .15408 L s % Start of user PostScript 13.4286 -1.14286 13.2701 -1.24815 MAarrowhead1 % End of user PostScript .82039 .18781 m .81644 .18256 L s % Start of user PostScript 13.4286 -0.571429 13.3493 -0.676717 MAarrowhead1 % End of user PostScript .82039 .21629 m .82039 .21104 L s % Start of user PostScript 13.4286 0 13.4286 -0.105288 MAarrowhead1 % End of user PostScript .82039 .24477 m .82434 .23952 L s % Start of user PostScript 13.4286 0.571429 13.5078 0.46614 MAarrowhead1 % End of user PostScript .82039 .27325 m .82829 .268 L s % Start of user PostScript 13.4286 1.14286 13.5871 1.03757 MAarrowhead1 % End of user PostScript .82039 .30173 m .83224 .29648 L s % Start of user PostScript 13.4286 1.71429 13.6663 1.609 MAarrowhead1 % End of user PostScript .82039 .3302 m .83619 .32496 L s % Start of user PostScript 13.4286 2.28571 13.7455 2.18043 MAarrowhead1 % End of user PostScript .82039 .35868 m .84014 .35344 L s % Start of user PostScript 13.4286 2.85714 13.8248 2.75185 MAarrowhead1 % End of user PostScript .82039 .38716 m .84409 .38192 L s % Start of user PostScript 13.4286 3.42857 13.904 3.32328 MAarrowhead1 % End of user PostScript .82039 .41564 m .84803 .41039 L s % Start of user PostScript 13.4286 4. 13.9832 3.89471 MAarrowhead1 % End of user PostScript .88447 .01693 m .85682 .01114 L s % Start of user PostScript 14.7143 -4. 14.1596 -4.11621 MAarrowhead1 % End of user PostScript .88447 .04541 m .86077 .03962 L s % Start of user PostScript 14.7143 -3.42857 14.2388 -3.54478 MAarrowhead1 % End of user PostScript .88447 .07389 m .86472 .0681 L s % Start of user PostScript 14.7143 -2.85714 14.3181 -2.97335 MAarrowhead1 % End of user PostScript .88447 .10237 m .86867 .09658 L s % Start of user PostScript 14.7143 -2.28571 14.3973 -2.40192 MAarrowhead1 % End of user PostScript .88447 .13085 m .87262 .12506 L s % Start of user PostScript 14.7143 -1.71429 14.4766 -1.8305 MAarrowhead1 % End of user PostScript .88447 .15933 m .87657 .15354 L s % Start of user PostScript 14.7143 -1.14286 14.5558 -1.25907 MAarrowhead1 % End of user PostScript .88447 .18781 m .88052 .18202 L s % Start of user PostScript 14.7143 -0.571429 14.635 -0.687639 MAarrowhead1 % End of user PostScript .88447 .21629 m .88447 .2105 L s % Start of user PostScript 14.7143 0 14.7143 -0.11621 MAarrowhead1 % End of user PostScript .88447 .24477 m .88842 .23898 L s % Start of user PostScript 14.7143 0.571429 14.7935 0.455218 MAarrowhead1 % End of user PostScript .88447 .27325 m .89237 .26745 L s % Start of user PostScript 14.7143 1.14286 14.8728 1.02665 MAarrowhead1 % End of user PostScript .88447 .30173 m .89632 .29593 L s % Start of user PostScript 14.7143 1.71429 14.952 1.59808 MAarrowhead1 % End of user PostScript .88447 .3302 m .90026 .32441 L s % Start of user PostScript 14.7143 2.28571 15.0312 2.1695 MAarrowhead1 % End of user PostScript .88447 .35868 m .90421 .35289 L s % Start of user PostScript 14.7143 2.85714 15.1105 2.74093 MAarrowhead1 % End of user PostScript .88447 .38716 m .90816 .38137 L s % Start of user PostScript 14.7143 3.42857 15.1897 3.31236 MAarrowhead1 % End of user PostScript .88447 .41564 m .91211 .40985 L s % Start of user PostScript 14.7143 4. 15.269 3.88379 MAarrowhead1 % End of user PostScript .94855 .01693 m .9209 .01892 L s % Start of user PostScript 16. -4. 15.4453 -3.96008 MAarrowhead1 % End of user PostScript .94855 .04541 m .92485 .0474 L s % Start of user PostScript 16. -3.42857 15.5246 -3.38865 MAarrowhead1 % End of user PostScript .94855 .07389 m .9288 .07588 L s % Start of user PostScript 16. -2.85714 15.6038 -2.81722 MAarrowhead1 % End of user PostScript .94855 .10237 m .93275 .10436 L s % Start of user PostScript 16. -2.28571 15.683 -2.24579 MAarrowhead1 % End of user PostScript .94855 .13085 m .9367 .13284 L s % Start of user PostScript 16. -1.71429 15.7623 -1.67436 MAarrowhead1 % End of user PostScript .94855 .15933 m .94065 .16132 L s % Start of user PostScript 16. -1.14286 15.8415 -1.10293 MAarrowhead1 % End of user PostScript .94855 .18781 m .9446 .1898 L s % Start of user PostScript 16. -0.571429 15.9208 -0.531505 MAarrowhead1 % End of user PostScript .94855 .21629 m .94855 .21828 L s % Start of user PostScript 16. 0 16. 0.0399234 MAarrowhead1 % End of user PostScript .94855 .24477 m .9525 .24676 L s % Start of user PostScript 16. 0.571429 16.0792 0.611352 MAarrowhead1 % End of user PostScript .94855 .27325 m .95644 .27524 L s % Start of user PostScript 16. 1.14286 16.1585 1.18278 MAarrowhead1 % End of user PostScript .94855 .30173 m .96039 .30372 L s % Start of user PostScript 16. 1.71429 16.2377 1.75421 MAarrowhead1 % End of user PostScript .94855 .3302 m .96434 .33219 L s % Start of user PostScript 16. 2.28571 16.317 2.32564 MAarrowhead1 % End of user PostScript .94855 .35868 m .96829 .36067 L s % Start of user PostScript 16. 2.85714 16.3962 2.89707 MAarrowhead1 % End of user PostScript .94855 .38716 m .97224 .38915 L s % Start of user PostScript 16. 3.42857 16.4754 3.46849 MAarrowhead1 % End of user PostScript .94855 .41564 m .97619 .41763 L s % Start of user PostScript 16. 4. 16.5547 4.03992 MAarrowhead1 % End of user PostScript 0 0 m 1 0 L 1 .43279 L 0 .43279 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 122}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc@03o`@0 0_lf00?o0`03oah0000j0004o`00ocd000?o0000=`000ol000020004o`00ocH000?o00001@000ol0 000K0000>P001?l00?lm0003o`0003L000?o00000P001?l00?lf0003o`0000D000?o00006`0003X0 00Co003o>P03ocX000?o00000P001?l00?lf0003o`0000800olN0000>P001?l00?lj0003o`0003X0 00?o00000P001?l00?lf0003o`00008000?o00007P0003/00_lk00Co>002o`D00_lf00;o1004oad0 003o01/0003o01/0003o01/0003o01/0003o01/0000F0?co200001H000?o00002P000ol000090003 o`0000X000?o00002@000ol0000:0003o`0000T000?o00002P000ol000090003o`0000X000?o0000 2P000ol000090003o`0000X000?o00002@000ol0000:0003o`0000T000?o00002P000ol000090003 o`0000X000?o00002@000ol0000:0003o`0000H0000?00?o10000ol0000V00?o2P06och00ol:00Ko ?@03o`X01_lN0003o`0000H0000@0003o`0000<000?o00001`02o`h00_l:00Ko3004o`d00ol>00;o 3P02o`/01_l<00Co3@03o`d00_l?00;o2P06o``01?l=00?o3P000ol0000600002005o`030?oo00;o 1003o`@01ol900Oo2P06o``01?l800So2P06o`T01ol;00Ko2`02o`030?oo00P02?l:00Ko2@07o`X0 1_l<00Co2008o`X00ol800003P000ol0o`050003o`0000<01_l:00Ko3`000ol0000=0003o`0000`0 0_l;00Ko2@07o`h000?o00003@000ol0000=00;o2`05o`X01_l?0003o`0000d000?o00003002o`h0 00?o00001P0000h000?o0?l01@000ol0000700;oBP07odX01_m>0003o`0000H0000?00;o1@000ol0 003h0003o`0000H0000F0003o`000?P000?o00001P0001H000?o0000=004odd01?m_0003o`0000H0 000F00;o2002o`l00_l:00Ko3004o`d00ol>00;o3P02o`/01_l<00Co3@03o`d00_l?00;o2P06o`X0 1_l>00;o3002o`P0000F0003o`0000H01Ol:00Ko2`05o`d00ol900Oo2`05o`X01_l<00Go3004o`T0 1ol;00Go2P06o`/01Ol;00Go2P06o``000?o00001P0001H000?o00001@05o`X01_l?0003o`0000d0 00?o00003002o`/01_l900Oo3P000ol0000=0003o`0000d00_l;00Go2P06o`l000?o00003@000ol0 000800Ko3@000ol0000600005P000ol0000400KoBP07odX01_m=0003o`0000H0000F0003o`000?P0 00?o00001P0001H000?o0000n0000ol0000600005P02ooP00_l800005P000ol0000800;o3`02o`X0 1_l:00Ko3@03o`h00_l>00;o2`06o`X01_l=00?o3@02o`l00_l:00Ko2P06o`h00_l<0003o`0000H0 000F0003o`0000L01?l;00Go3004o``01?l:00Ko3004o`/01Ol=00Co3004o`X01_l<00Co2`05o``0 1?l<00Co2`05o``000?o00001P0001H000?o00001P05o`X01_l?0003o`0000d000?o00002P04o`/0 1Ol:00Oo3P000ol0000=0003o`0000d00_l;00Go2P06o`h000?o00003P000ol0000800Ko30000ol0 000600005P000ol0000500Ko?`000ol0000800KoB`03odl000?o00001P0001H000?o0000n0000ol0 000600005P000ol0003h0003o`0000H0000F00;on002o`P0000F0003o`0000T00_l>00;o2`06o`X0 1_l=00?o3@02o`l00_l;00Ko2P06o`h00_l=00;o3`02o`X01_l:00Ko3P02o`/000?o00001P0001H0 00?o00002003o``01?l=00Co3004o`X01_l<00?o3005o`d01?l<00Co2`05o``00ol<00Go3004o``0 1?l;00Go2`000ol0000600005P000ol0000700Go2P06o`h00_l=00;o3@04o`/01Ol:00Oo3@02o`h0 0_l;00Ko2`05o`X01_l=00;o3P02o`/01_l;0003o`0000H0000>00Co10000ol0000600?o8P000ol0 000<0003o`0000h000?o00002003ob8000?o00003@000ol0000=00;o2P03ob4000?o00003@000ol0 000J0003o`0000H0000?0003o`0000@000?o0000n0000ol0000600002005o`<000?o00000`03ooH0 0ol800004@000ol000020003o`000?P000?o00001P0000h000Co003o10000ol0000:00;o3P02oa/0 1?l?00?o3@02o`l00_l;00Co3004oa000_l=0003o`0000d00_l;00Co3004oa000_l:0003o`0000H0 000?00;o1@000ol0000900?o3@03o`/01_l<00Co2P06o``00ol<00Go3@04o`/01Ol;00Go3003o``0 1?l=00Co3004o`/01Ol:0003o`0000H0000F0003o`0000P01Ol;00Go3004o`d00ol<00Co2`05o`X0 1ol=00?o3003o`/01_l;00Go2P06o`d00ol=00?o2P06o`X000?o00001P0001H000?o00001`03o`d0 0olA0003o`0000d000?o00003P000ol0000800?o8P000ol0000<0003o`0000h00_l:00?o8@000ol0 000=0003o`0001T000?o00001P0001H00_oh00;o200001H000?o0000n0000ol0000600005P000ol0 000;0003o`0000h000?o0000?0000ol0000>0003o`0003d000?o0000B@000ol0000600005P000ol0 000;00;o3P02oa/00_lB00;o3@02o`h00_lL00;o4P02o`d000?o00003@02o`/00_l>00;o4P02o`T0 00?o00001P0001H000?o00002P04o``01?l:00Co3005o``01Ol<00Co3004o`/00ol=00Co3@05o``0 0ol<00Co2`05o`/01Ol<00Go2@000ol0000600005P000ol0000900?o3@03o`h01?l;00Go2P06o`/0 0ol=00Go3004o``01?l;00Ko2`02o`d01_l;00Go2`05o`X01_l90003o`0000H0000F00;o2@000ol0 000=0003o`0001000ol<00?o3`02o`X000?o00003@03oa000ol=00?o3`02o`X000?o00007`03o`d0 0olI00;o200001H000?o0000;0000ol0000<0003o`0003h000?o00003@000ol0000m0003o`0000d0 00?o00006@000ol0000600005P000ol0000;0003o`0000d000?o0000CP000ol000290003o`0000H0 000F0003o`0000/00_l>00;o?P02o`l00_lm00;o40000ol0000]00;o2@000ol0000600005P000ol0 000:00Co3004oa/000?o00007`03o`d01?lK0003o`0001000_l<00?o3`02o`/000?o00003@000ol0 000?00?o2@000ol0000600005P000ol0000:00;o3P02o`d00_l>00;o4@03o`/00_l>00?o3@02o`h0 00?o00003P04o``00ol>00Co2P02o`h00_l?00Go20000ol0000600005P000ol0000:0003o`0000d0 00?o00003005o``00_l=00Ko2`000ol0000=0003o`0000d00ol=00;o3P06o`X00ol>00?o3@02o`h0 0_l=00?o2`000ol0000600005P02o`X000?o00003@000ol0000>00Go2`03oa000_l:0003o`0000d0 00?o00003`03o`d00_lM00;o3P000ol0000>00?o3@03oaT00_l800005P000ol0000[00?o3004ocd0 1?l<00?o2`04o`d000?o00007P04o``01?l;00?o2`000ol0000600005P000ol0000I00?o40000ol0 000<0003o`0002/01?l?0003o`0000`000?o00002`04oad00ol?0003o`0000d000?o00002`03o`/0 00?o00001P0001H000?o00002@03o`d00olm00Co3004obd00ol<00Co3@03obd00ol;0003o`0000H0 000?00;o1@000ol0000900?o3@03oah000?o00007004o``00olO0003o`0000`00_l=00Co3@03oah0 00?o00003@000ol0000:0003o`0000H0000>0004o`00o`@000?o00002@03o`h000?o00003@000ol0 000=0003o`0001`00ol>00;o3`000ol0000=0003o`0000`00_l>00?o3P000ol0000=0003o`0000d0 00?o00003@000ol0000:0003o`0000H0000>0004o`00o`@00ol:0003o`0000d000?o00003@000ol0 000=0003o`0000d000?o00003@02o`h00_l?0003o`0000`00_l?0003o`0000`00_l?0003o`0000d0 00?o00003@000ol0000=0003o`0000P00ol800003P001?l00?l40003o`0000X000?o00003@000ol0 000=0003o`0000`00olN00;o3P000ol0000=00;o3P03oad00_l?0003o`0000d000?o00003@000ol0 000J0003o`0000H0000>0004o`00o`@000?o00002P000ol0000L00?o3@03oah000?o00007@03o`d0 0olN0003o`0001`00ol=00?o6`000ol0000600003`02o`D000?o0000:@03o`d00oln00?o3004ocd0 0ol=00?o6`000ol0000600005P000ol0000800;o3P02o`l00ol]00;o3P000ol0000=00Co;002o`d0 00?o00003`03o`d00ol;0003o`0000d000?o00001P0001H000?o00001`03o`d00olQ0003o`0001X0 0ol=00;o;@02o`l00ol=00;o;P02o`h000?o00001P0001H00_l900?o3P02o`l00_l>00;o2P04o`h0 0ol<00Co4002o`h00_l:00Go3@03o`/01?l@00;o3P02o`X01?l<00;o200001H000?o00002@02o`l0 00?o00003003o`d00ol:00Ko3@03o`d00_l>00Co3@03o`T01ol=00;o3@03o`h00ol=00?o3003o``0 00?o00001P0001H000?o00002P000ol0000>0003o`0000X00ol=00?o2`03oa400_l?0003o`0000X0 1?l=00?o7`000ol0000>0003o`0000X00ol=00?o40000ol000090003o`0000H0000F0003o`0000/0 00?o00006@03o`d01?lP0003o`0001T01?l=00Co80000ol0000I00Co3004oa`000?o00001P0001H0 00?o00009`03oa0000?o0000>`03o`l000?o0000?003o`d00olL0003o`0000H0000F0003o`0002P0 00?o0000CP000ol0001>0003o`0000d000?o00006`000ol0000600005P02o`X000?o00003002ocl0 00?o00003002od0000?o00003002obh00_l<00;o200001H000?o00002002o`h00ol?00?o3P02o`X0 1?l>0003o`0000`00ol@00;o3`02o`X01?l=00;o3P03oa000_l>00;o2`03o``000?o00001P0001H0 00?o00001`04o``01Ol;00Go3005o`X01_l;00?o3005o``01Ol<00Co2`06o`X01?l<00Go3004o``0 1Ol:00Go2`000ol0000600005P000ol0000900?o3`02o`X01?l<00Go2`04o`l00_l?00;o2P05o``0 1?l;00?o4003o`l00_l:00Co3005o`/01_l:0003o`0000H0000F0003o`0000`000?o00006@02o`h0 0ol<0003o`00018000?o00006@03o`d00olR0003o`0001P00ol>00?o70000ol0000600005P000ol0 000X0003o`0000h000?o0000?@000ol0000=0003o`0003d000?o00003P000ol0000K0003o`0000H0 000F0003o`000?P000?o00001P0001H00_oh00;o200001H000?o00002@02o`h00_l@00?o3@03o`X0 1?l=00;o3P02oa000ol>00?o2P02o`l00_l=00;o4@03o`d00ol:00;o3@000ol0000600005P000ol0 000900?o3@03o``01?l<00Co3006o`/00ol=00Co2`04o`d01?l<00Go3003o``01Ol;00Co3004o``0 1Ol:0003o`0000H0000F0003o`0000P01Ol;00Go2`03o`d00ol=00Co3005o`/01_l:00?o3P03o`d0 1_l:00Go2`06o`X00ol=00?o3@06o`T000?o00001P0000h01?l40003o`0000`00_l>00;o2`000ol0 000=0003o`0000`000?o00004@02oa/000?o00003P000ol0000<00?o4@02oa/000?o00003@000ol0 000K0003o`0000H0000?0003o`0000@000?o0000n0000ol00006000040000ol0000300?omP03o`P0 000A0003o`00008000?o0000n0000ol0000600003P001?l00?l40003o`0000X00_l=00;o8@03o`X0 0_l?00;o3P02oa000ol=00Co2P02o`l00_l=00;o4@03o`d00ol:00;o30000ol0000600003`02o`D0 00?o00002P03o``01?l<00Ko2P04o``01Ol<00?o3@04o`/01?l<00Go3005o``00ol<00Go2`04o``0 1?l<00Go2@000ol0000600005P000ol0000900Go2`05o`/01?l<00?o3@06o`X01Ol;00Ko2P03o`d0 0ol>00Ko2P05o`/01_l:00?o3@03o`d01_l80003o`0000H0000F0003o`0000d00_l:00Ko2P000ol0 000>0003o`0000`00olA00;o2P03o`h000?o00003@000ol0000=00?o4@02o`X00ol>0003o`0000d0 00?o00003003o`/000?o00001P0001H00_oh00;o200001H000?o0000n0000ol0000600005P000ol0 003h0003o`0000H0000F0003o`0003X01_l:00;o@@04o`X00_la00?o2P06o`X00_l;0003o`0000H0 000F0003o`0000X00_l>00;o3P06o`X01?l<00Go3002o`h00_l=00Ko2P05o``01Ol;00;o3P04o``0 1?l<00Co3005o`P000?o00001P0001H000?o00002P05o`/01Ol;00Co3003o`d01_l:00Go2`05o`/0 1?l<00?o3P06o`X01Ol;00Ko2P02o`h00ol=00Ko1`000ol0000600005P02o`/01_l:00Ko2P000ol0 000>0003o`0000`00ol=00Ko2P06o`/000?o00003@000ol0000=00?o3@06o`X00ol=0003o`0000h0 00?o00003003o`T00_l800005P000ol0003h0003o`0000H0000F0003o`000?P000?o00001P0001H0 00?o0000n0000ol0000600005P000ol0000[00Co3006ocX01?l<00Oo>P04o``01_lF0003o`0000H0 000F0003o`0000/00_l>00;o3P06o`X01?l<00Co3@02o`h00_l=00Ko2P05o``01?l<00;o3P02o`h0 1_l:00Co3004o`P000?o00001P0001H000?o00002P06o`X01_l:00Go2`04o``01ol900Go2`06o`/0 1?l<00?o3@07o`T01Ol;00Ko2P05o`/00ol=00Oo1P000ol0000600005P02o``01_l:00Ko2P000ol0 000>0003o`0000`00ol=00Go2`06o`/000?o00003@000ol0000=00?o3@05o`/01_l:0003o`0000d0 00?o00003@03o`P00_l800005P000ol0001O00;oC`02odH000?o00001P0001H000?o0000n0000ol0 000600005P000ol0003h0003o`0000H0000?00?o10000ol0000/00Co3006ocX01?l<00Oo>P04o``0 1?lG0003o`0000H0000@0003o`0000<000?o00003002o`h00_l>00Ko2P04o``01?l=00;o3P02o`d0 1_l:00Go3004o``00_l>00;o3P06o`X01_l:00Co1`000ol0000600003P04o`@00ol:00Ko2P07o`T0 1_l:00Co3008o`P01_l:00Oo2P05o`/01?l<00So2006o`X01ol900Ko2P06o`X02?l300?o200000h0 00?o0?l01@000ol0000<00Go2`06o`X000?o00003@000ol0000=00?o3@05o`/01_l;0003o`0000d0 00?o00003@03o`d01Ol;00Ko2P000ol0000=0003o`0000d00ol80003o`0000H0000>0003o`3o00D0 00?o00003006o`X00olm00Ko2P03och01_m50003o`0000H0000?00;o1@000ol0000:0003o`0000T0 00?o00002P000ol000090003o`0000X000?o00002@000ol0000:0003o`0000T000?o00002P000ol0 000:0003o`0000T000?o00002P000ol000090003o`0000X000?o00002@000ol0000:0003o`0000T0 00?o00002P000ol000090003o`0000X000?o00001P0001H0o?l80000\ \>"], ImageRangeCache->{{{0, 281}, {121, 0}} -> {-4.82766, -5.30985, 0.0799129, 0.0799129}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ solns = Table[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t], y'[t] == -Sin[x[t]], x[0] == 0, y[0] == b}, {x[t],y[t]}, {t,0,20}]], {b, 0.5, 3, 0.5}];\ \>", "Input", AspectRatioFixed->True], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[solns],{t,0,20},PlotRange->{{-2,16},{-2,4}},\ AspectRatio->1/3]\ \>", "Input", AspectRatioFixed->True], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .33333 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.111111 0.0555556 0.111111 0.0555556 [ [.25 .09861 -9 -9 ] [.25 .09861 9 0 ] [.38889 .09861 -3 -9 ] [.38889 .09861 3 0 ] [.52778 .09861 -9 -9 ] [.52778 .09861 9 0 ] [.66667 .09861 -6 -9 ] [.66667 .09861 6 0 ] [.80556 .09861 -12 -9 ] [.80556 .09861 12 0 ] [.94444 .09861 -6 -9 ] [.94444 .09861 6 0 ] [.09861 0 -12 -4.5 ] [.09861 0 0 4.5 ] [.09861 .05556 -12 -4.5 ] [.09861 .05556 0 4.5 ] [.09861 .16667 -6 -4.5 ] [.09861 .16667 0 4.5 ] [.09861 .22222 -6 -4.5 ] [.09861 .22222 0 4.5 ] [.09861 .27778 -6 -4.5 ] [.09861 .27778 0 4.5 ] [.09861 .33333 -6 -4.5 ] [.09861 .33333 0 4.5 ] [ 0 0 0 0 ] [ 1 .33333 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .25 .11111 m .25 .11736 L s [(2.5)] .25 .09861 0 1 Mshowa .38889 .11111 m .38889 .11736 L s [(5)] .38889 .09861 0 1 Mshowa .52778 .11111 m .52778 .11736 L s [(7.5)] .52778 .09861 0 1 Mshowa .66667 .11111 m .66667 .11736 L s [(10)] .66667 .09861 0 1 Mshowa .80556 .11111 m .80556 .11736 L s [(12.5)] .80556 .09861 0 1 Mshowa .94444 .11111 m .94444 .11736 L s [(15)] .94444 .09861 0 1 Mshowa .125 Mabswid .13889 .11111 m .13889 .11486 L s .16667 .11111 m .16667 .11486 L s .19444 .11111 m .19444 .11486 L s .22222 .11111 m .22222 .11486 L s .27778 .11111 m .27778 .11486 L s .30556 .11111 m .30556 .11486 L s .33333 .11111 m .33333 .11486 L s .36111 .11111 m .36111 .11486 L s .41667 .11111 m .41667 .11486 L s .44444 .11111 m .44444 .11486 L s .47222 .11111 m .47222 .11486 L s .5 .11111 m .5 .11486 L s .55556 .11111 m .55556 .11486 L s .58333 .11111 m .58333 .11486 L s .61111 .11111 m .61111 .11486 L s .63889 .11111 m .63889 .11486 L s .69444 .11111 m .69444 .11486 L s .72222 .11111 m .72222 .11486 L s .75 .11111 m .75 .11486 L s .77778 .11111 m .77778 .11486 L s .83333 .11111 m .83333 .11486 L s .86111 .11111 m .86111 .11486 L s .88889 .11111 m .88889 .11486 L s .91667 .11111 m .91667 .11486 L s .08333 .11111 m .08333 .11486 L s .05556 .11111 m .05556 .11486 L s .02778 .11111 m .02778 .11486 L s .97222 .11111 m .97222 .11486 L s .25 Mabswid 0 .11111 m 1 .11111 L s .11111 0 m .11736 0 L s [(-2)] .09861 0 1 0 Mshowa .11111 .05556 m .11736 .05556 L s [(-1)] .09861 .05556 1 0 Mshowa .11111 .16667 m .11736 .16667 L s [(1)] .09861 .16667 1 0 Mshowa .11111 .22222 m .11736 .22222 L s [(2)] .09861 .22222 1 0 Mshowa .11111 .27778 m .11736 .27778 L s [(3)] .09861 .27778 1 0 Mshowa .11111 .33333 m .11736 .33333 L s [(4)] .09861 .33333 1 0 Mshowa .125 Mabswid .11111 .01111 m .11486 .01111 L s .11111 .02222 m .11486 .02222 L s .11111 .03333 m .11486 .03333 L s .11111 .04444 m .11486 .04444 L s .11111 .06667 m .11486 .06667 L s .11111 .07778 m .11486 .07778 L s .11111 .08889 m .11486 .08889 L s .11111 .1 m .11486 .1 L s .11111 .12222 m .11486 .12222 L s .11111 .13333 m .11486 .13333 L s .11111 .14444 m .11486 .14444 L s .11111 .15556 m .11486 .15556 L s .11111 .17778 m .11486 .17778 L s .11111 .18889 m .11486 .18889 L s .11111 .2 m .11486 .2 L s .11111 .21111 m .11486 .21111 L s .11111 .23333 m .11486 .23333 L s .11111 .24444 m .11486 .24444 L s .11111 .25556 m .11486 .25556 L s .11111 .26667 m .11486 .26667 L s .11111 .28889 m .11486 .28889 L s .11111 .3 m .11486 .3 L s .11111 .31111 m .11486 .31111 L s .11111 .32222 m .11486 .32222 L s .25 Mabswid .11111 0 m .11111 .33333 L s 0 0 m 1 0 L 1 .33333 L 0 .33333 L closepath clip newpath .5 Mabswid .11111 .13889 m .1118 .13888 L .11242 .13886 L .11314 .13881 L .11382 .13876 L .11502 .13861 L .11632 .1384 L .11773 .13809 L .11921 .13768 L .1218 .13676 L .12436 .13554 L .12664 .13418 L .13127 .13033 L .13333 .12797 L .13503 .12554 L .13634 .12319 L .13747 .12058 L .13799 .11905 L .13838 .11764 L .1387 .11621 L .13893 .11485 L .13902 .11407 L .13907 .11365 L .1391 .11325 L .13915 .11254 L .13917 .11217 L .13918 .11177 L .13919 .11134 L .13919 .11087 L .13918 .11043 L .13916 .11002 L .13915 .10965 L .13912 .10925 L .13905 .10843 L .13898 .10774 L .13889 .10711 L .13863 .10568 L .13831 .1043 L .13789 .10284 L .13691 .10026 L .1358 .098 L .13425 .0955 L .13227 .09297 L .13016 .0908 L .12797 .08899 L .12559 .08738 L .12328 .08613 L .12058 .08499 L .11903 .08448 L .11757 .08409 L Mistroke .11614 .08379 L .11461 .08355 L .11372 .08346 L .11329 .08342 L .11289 .08339 L .11214 .08335 L .11175 .08334 L .11133 .08333 L .11062 .08334 L .10986 .08336 L .10914 .0834 L .10848 .08346 L .10772 .08354 L .10689 .08366 L .1054 .08393 L .10407 .08424 L .10265 .08465 L .10016 .08558 L .09733 .08697 L .09489 .08852 L .09043 .09243 L .08854 .09471 L .08676 .09741 L .08538 .1001 L .08436 .10276 L .08369 .10521 L .08341 .10662 L .08323 .10792 L .08315 .1086 L .08309 .10933 L .08306 .11003 L .08304 .11066 L .08304 .1114 L .08305 .11182 L .08306 .1122 L .0831 .11291 L .08312 .11327 L .08316 .11367 L .08334 .11517 L .08348 .116 L .08364 .11677 L .08401 .11828 L .08441 .11963 L .08539 .12214 L .08669 .12471 L .08971 .12898 L .09175 .13112 L .0942 .13319 L .0967 .13488 L .09919 .13621 L Mistroke .10164 .13723 L .10437 .13806 L .10596 .13841 L .10675 .13854 L .10749 .13865 L .10821 .13874 L .10887 .1388 L .1096 .13885 L .11 .13887 L .11037 .13888 L .11109 .13889 L .11149 .13889 L .11187 .13888 L .11263 .13885 L .11306 .13882 L .11344 .13879 L .11414 .13872 L .11489 .13863 L .11624 .13841 L .11781 .13807 L .11945 .13761 L .12232 .13654 L .12487 .13526 L .12708 .13388 L .1293 .13217 L .13152 .13007 L .1347 .12605 L .13611 .12365 L .13719 .12131 L .13813 .1186 L .13853 .11703 L .13881 .11557 L .139 .11429 L .13907 .11355 L .13913 .11286 L .13917 .11214 L .13918 .11147 L .13919 .11111 L .13918 .11071 L .13916 .10998 L .13912 .10927 L .13907 .1086 L .139 .108 L .13892 .10735 L .13868 .1059 L .13838 .10459 L .13768 .10222 L .1367 .0998 L .13539 .09727 L .13397 .09509 L Mistroke .13221 .0929 L .13006 .09072 L .12787 .08891 L .12568 .08744 L .1233 .08614 L .12102 .08516 L .11844 .08432 L .11699 .08396 L .11559 .0837 L .11496 .0836 L .11429 .08352 L .11371 .08346 L .11308 .0834 L .11234 .08336 L .11164 .08334 L .11095 .08333 L .11033 .08335 L .10963 .08337 L .10889 .08342 L .10819 .08349 L .10755 .08356 L .106 .08381 L .10454 .08412 L .10171 .08497 L .09875 .08623 L .09628 .0876 L .09411 .0891 L .09172 .09113 L .08974 .09321 L .08804 .0954 L .08644 .09797 L .08512 .1007 L .08458 .10213 L .08408 .1037 L .08369 .10521 L .08341 .10662 L .08322 .10797 L .08315 .10866 L .08312 .10905 L .08309 .10941 L .08306 .1101 L .08304 .11073 L .08304 .1114 L .08306 .11214 L .08309 .11278 L .08314 .11346 L .0832 .1141 L .08327 .11468 L .08352 .11618 L .08382 .11756 L Mistroke .08476 .1206 L .08588 .12318 L .08734 .12578 L .09071 .13008 L .09295 .1322 L .09518 .13391 L .09741 .1353 L .09997 .13657 L .1025 .13752 L .10491 .13819 L .10629 .13847 L .10757 .13866 L .10825 .13874 L .10899 .13881 L .10936 .13883 L .10976 .13886 L .11048 .13888 L .11117 .13889 L .11191 .13888 L .1126 .13885 L .11325 .13881 L .11383 .13875 L .11446 .13869 L .11574 .1385 L .11727 .1382 L .11866 .13784 L .1217 .1368 L .12439 .13552 L .1268 .13407 L .1311 .13051 L .13298 .12842 L .13479 .12592 L .1361 .12365 L .13727 .1211 L .13812 .1186 L .13844 .1174 L .13869 .11625 L .13881 .11559 L .13892 .11487 L .139 .11427 L .13907 .1136 L .13913 .11288 L .13915 .11249 L .13917 .11212 L .13918 .11146 L .13918 .11075 L .13917 .11009 L .13913 .10938 L .13908 .1087 L .13901 .10807 L Mistroke .13885 .10689 L .13862 .10564 L .13827 .10416 L .1378 .10258 L .1367 .0998 L .13535 .0972 L .13386 .09494 L .13215 .09284 L .13011 .09076 L .12591 .08758 L .12307 .08603 L .12023 .08487 L .11759 .0841 L .11607 .08378 L .11538 .08366 L .11465 .08356 L .11398 .08348 L .11325 .08342 L .11258 .08337 L .11195 .08335 L .11122 .08333 L .11055 .08334 L .11017 .08335 L .10977 .08337 L .10904 .08341 L .10841 .08347 L .10772 .08354 L .10632 .08375 L .10504 .08401 L .10385 .0843 L .10098 .08524 L .09846 .08637 L .0957 .08797 L .09327 .08976 L .08934 .09368 L .08752 .09617 L .08611 .09858 L .08503 .10094 L .08455 .10222 L .08411 .10358 L .08379 .1048 L .0835 .10615 L .0833 .10738 L .08323 .10793 L .08316 .10854 L .0831 .10925 L .08308 .10964 L .08306 .11001 L .08304 .11066 L .08304 .11137 L Mistroke .08305 .11176 L .08306 .11219 L .08308 .1126 L .0831 .11298 L .08316 .11369 L .08324 .11444 L .08347 .11594 L .08377 .11734 L .08451 .11991 L .08549 .12236 L .0866 .12454 L .08979 .12907 L .09166 .13103 L .09386 .13294 L .09593 .1344 L .09831 .13578 L .10126 .13709 L .10267 .13758 L .10418 .13801 L .10557 .13833 L .10631 .13847 L .10711 .1386 L .10785 .13869 L .10852 .13877 L .10917 .13882 L .10986 .13886 L .11058 .13888 L .11098 .13889 L .11136 .13889 L .11204 .13887 L .11277 .13884 L .11342 .13879 L .11403 .13873 L .1154 .13855 L .11687 .13828 L .1182 .13797 L .12113 .13702 L .12354 .13597 L .12603 .13457 L .13015 .13142 L .13191 .12966 L Mfstroke .11111 .16667 m .11248 .16665 L .11373 .1666 L .11517 .16652 L .11652 .1664 L .11893 .16611 L .12152 .16569 L .12435 .16507 L .12731 .16427 L .13249 .16244 L .13763 .16007 L .14219 .15743 L .15154 .15014 L .15574 .14574 L .15926 .14127 L .16202 .13701 L .1645 .1323 L .16661 .12705 L .16736 .12467 L .16803 .12207 L .16837 .12047 L .16864 .119 L .16885 .11761 L .16903 .11608 L .1691 .11542 L .16915 .11471 L .16923 .11342 L .16926 .11267 L .16928 .11195 L .16929 .11131 L .16929 .11061 L .16926 .10938 L .1692 .10825 L .16911 .10702 L .16899 .10572 L .16869 .10353 L .16825 .10115 L .16764 .09856 L .16683 .09582 L .16496 .09095 L .16225 .08559 L .15911 .08074 L .15586 .07662 L .15183 .07236 L .14319 .06544 L .13791 .0623 L .13268 .05986 L .12758 .05804 L .12279 .05679 L .1201 .05629 L Mistroke .11867 .05607 L .11715 .05588 L .11567 .05574 L .11434 .05565 L .11299 .05559 L .11173 .05556 L .11037 .05556 L .10891 .0556 L .10754 .05567 L .10629 .05577 L .10482 .05591 L .10324 .05612 L .10038 .0566 L .09741 .05726 L .09431 .05814 L .08889 .06013 L .08414 .0624 L .07989 .06488 L .07115 .07165 L .06743 .07541 L .0638 .0798 L .06074 .08431 L .05801 .08932 L .05596 .09418 L .05455 .09868 L .05403 .10087 L .05358 .10326 L .05341 .10436 L .05326 .10552 L .05314 .10661 L .05306 .10762 L .05299 .10884 L .05296 .10949 L .05294 .11018 L .05293 .11134 L .05296 .11261 L .05301 .11374 L .05309 .11496 L .05319 .11611 L .05332 .11717 L .05367 .11954 L .0542 .12212 L .05569 .12727 L .05746 .13172 L .05982 .13636 L .06525 .14428 L .06921 .14869 L .07327 .15246 L .07807 .15613 L .08378 .15964 L Mistroke .08907 .16217 L .09424 .16406 L .09711 .16488 L .09987 .16552 L .10141 .16582 L .1031 .16609 L .10464 .16629 L .10607 .16644 L .10751 .16655 L .10904 .16663 L .11058 .16666 L .11145 .16667 L .11227 .16665 L .11374 .1666 L .11508 .16652 L .11583 .16647 L .11663 .16639 L .11809 .16623 L .12081 .16582 L .12367 .16523 L .12872 .16383 L .13431 .16167 L .13931 .15915 L .14444 .15593 L .14961 .15189 L .15724 .14395 L .16067 .1392 L .16337 .13458 L .16543 .13018 L .16698 .12593 L .16767 .12355 L .16828 .12096 L .16871 .11858 L .169 .11639 L .16912 .11513 L .16921 .11392 L .16926 .11284 L .16929 .11167 L .16928 .11039 L .16927 .10968 L .16924 .10903 L .16917 .10778 L .16908 .10659 L .16896 .10548 L .16881 .1043 L .16846 .10221 L .16799 .09996 L .16735 .09752 L .1656 .09246 L .16313 .08718 L Mistroke .15717 .07819 L .15325 .07377 L .14921 .06999 L .14445 .0663 L .13876 .06276 L .13349 .0602 L .12834 .05827 L .12548 .05743 L .12271 .05678 L .12118 .05647 L .1195 .05619 L .11795 .05598 L .11652 .05582 L .11508 .0557 L .11356 .05561 L .11202 .05556 L .11115 .05556 L .11034 .05556 L .10887 .0556 L .10753 .05567 L .10679 .05572 L .10598 .05579 L .10452 .05595 L .1018 .05634 L .09894 .0569 L .09388 .05827 L .08829 .06039 L .08327 .06287 L .07812 .06606 L .07291 .07007 L .06524 .07796 L .06177 .08269 L .05904 .08729 L .05695 .09168 L .05536 .09591 L .05466 .09829 L .05403 .10088 L .05358 .10325 L .05327 .10545 L .05314 .10671 L .05304 .10791 L .05298 .10898 L .05294 .11016 L .05293 .11143 L .05294 .11214 L .05296 .11279 L .05302 .11404 L .05311 .11523 L .05322 .11634 L .05336 .11751 L Mistroke .05369 .11961 L .05414 .12185 L .05476 .1243 L .05646 .12936 L .05889 .13465 L .06477 .14367 L .06864 .14811 L .07264 .15191 L .07736 .15563 L .08302 .15922 L .08825 .16182 L .09339 .16379 L .0961 .16461 L .09899 .16533 L .10052 .16565 L .10221 .16595 L .10375 .16618 L .10518 .16635 L .10661 .16648 L .10813 .16659 L .10966 .16665 L .11053 .16666 L .11135 .16667 L .11282 .16664 L .11416 .16658 L .1149 .16654 L .1157 .16648 L .11716 .16634 L .11988 .16597 L .12275 .16544 L .12782 .16411 L .13343 .16205 L .13847 .15962 L .14365 .15647 L .14889 .1525 L .15663 .14469 L .16015 .13999 L .16293 .1354 L .16507 .13104 L .16669 .12681 L .16742 .12444 L .16808 .12186 L .16856 .11949 L .16889 .11729 L .16904 .11604 L .16914 .11484 L .16922 .11377 L .16927 .11259 L .16929 .11132 L .16929 .11061 L Mistroke .16927 .10997 L .16923 .10871 L .16916 .10753 L .16906 .10642 L .16893 .10525 L .16863 .10315 L .1682 .1009 L .16761 .09845 L .16596 .09339 L .1636 .08809 L .16082 .08325 L .15782 .07902 L .15438 .07496 L .15028 .07093 L .14191 .06461 L .13678 .06172 L .13171 .05947 L .12591 .05755 L .12257 .05675 L .12098 .05644 L .11947 .05619 L .11809 .056 L .11659 .05583 L .11522 .05571 L .11396 .05563 L .1126 .05558 L .11109 .05556 L .11034 .05556 L .10952 .05558 L .10806 .05564 L .1067 .05573 L .10521 .05587 L .10253 .05622 L .09993 .05669 L .09755 .05723 L .09169 .05902 L .08658 .06117 L .08098 .0642 L .07606 .06754 L .06784 .07496 L .06431 .07913 L .06096 .08396 L .05853 .08826 L .0564 .09301 L .05485 .09759 L .05383 .10183 L .05344 .10413 L .05327 .10544 L .05314 .10667 L .05304 .10797 L Mistroke .05297 .10916 L .05295 .10982 L .05294 .11054 L .05294 .11184 L .05297 .11306 L .05303 .11417 L .05313 .11545 L .05325 .11665 L .05355 .11878 L .05397 .12109 L .05456 .12358 L .05536 .1263 L .05745 .13171 L .05995 .13658 L .06274 .14096 L .06609 .14528 L .07022 .14969 L .07427 .15328 L .07895 .15673 L .08345 .15945 L .08869 .16201 L .09367 .16388 L .0985 .16522 L Mfstroke .11111 .19444 m .11317 .19442 L .11504 .19435 L .1172 .19422 L .11923 .19405 L .12284 .19362 L .12673 .19298 L .13097 .19207 L .13541 .19088 L .14319 .18821 L .15091 .18478 L .15779 .18104 L .172 .17106 L .18407 .15952 L .19281 .14839 L .19665 .14216 L .20004 .13534 L .20247 .12892 L .20338 .12581 L .20407 .12296 L .20461 .1201 L .20483 .11864 L .20502 .11708 L .20516 .11551 L .20526 .11405 L .2053 .11315 L .20533 .11231 L .20534 .11155 L .20534 .11072 L .20531 .10934 L .20524 .10782 L .20519 .10705 L .20512 .10623 L .20497 .10473 L .20456 .10184 L .20405 .09919 L .20274 .09416 L .20078 .08864 L .19516 .07751 L .19109 .07138 L .18663 .06564 L .17668 .05524 L .16378 .04499 L .15566 .03995 L .14756 .03586 L .1402 .0329 L .13202 .03041 L .12725 .02934 L .12489 .02892 L .12268 .02858 L Mistroke .12051 .02831 L .11855 .02811 L .11636 .02794 L .11515 .02788 L .11402 .02783 L .11188 .02778 L .11066 .02778 L .10953 .02779 L .10724 .02787 L .10596 .02794 L .1048 .02802 L .10272 .0282 L .10047 .02846 L .0964 .02908 L .09167 .03005 L .08674 .03136 L .07811 .03439 L .07038 .03791 L .06365 .04164 L .0499 .05143 L .03962 .0611 L .03082 .0718 L .02404 .08294 L .02123 .08918 L .01928 .09484 L .01858 .09741 L .01798 .10011 L .01771 .10153 L .01747 .10308 L .01728 .10451 L .01714 .10581 L .01703 .10714 L .01695 .10839 L .0169 .10971 L .01688 .11115 L .0169 .11241 L .01694 .11374 L .01701 .11488 L .01711 .11614 L .01726 .11755 L .01743 .11885 L .01792 .12183 L .01856 .12473 L .01941 .12783 L .0214 .13347 L .0237 .13861 L .0313 .15108 L .04103 .1626 L .0526 .17297 L .05979 .17814 L Mistroke .06702 .18253 L .07408 .1861 L .08081 .18888 L .08854 .19137 L .0929 .19245 L .09709 .19326 L .09924 .1936 L .10158 .1939 L .1038 .19412 L .10584 .19428 L .10769 .19437 L .10972 .19443 L .11184 .19444 L .11382 .1944 L .11493 .19436 L .11614 .19429 L .11833 .19413 L .12046 .19392 L .12242 .19368 L .12685 .19295 L .1315 .19194 L .13906 .18972 L .14593 .18708 L .16058 .17934 L .1737 .16963 L .1852 .15825 L .19302 .14808 L .19938 .13681 L .20189 .13064 L .20287 .12762 L .20363 .12484 L .20419 .12236 L .20468 .11964 L .20504 .1169 L .20517 .11541 L .20526 .11401 L .20532 .11251 L .20534 .11166 L .20534 .11087 L .20531 .10943 L .20528 .10862 L .20525 .1079 L .20515 .10651 L .205 .10502 L .20464 .10231 L .20404 .09911 L .2032 .09574 L .2012 .0897 L .19865 .08389 L .19581 .0786 L Mistroke .1876 .06682 L .17777 .05625 L .16661 .04699 L .15265 .03833 L .14499 .03475 L .13617 .03157 L .12841 .02958 L .12397 .02877 L .12185 .02847 L .11988 .02824 L .11804 .02807 L .11607 .02793 L .11388 .02782 L .1119 .02778 L .11002 .02778 L .10798 .02784 L .10606 .02793 L .1043 .02806 L .1021 .02827 L .10002 .02852 L .09615 .02912 L .09202 .02997 L .08758 .03112 L .07978 .03373 L .07282 .03671 L .05803 .04527 L .04451 .0562 L .03473 .06668 L .03044 .07235 L .02655 .07837 L .02367 .08368 L .02111 .08949 L .0193 .09476 L .01807 .09966 L .01752 .1027 L .01732 .10415 L .01717 .1055 L .01704 .10697 L .01698 .10775 L .01694 .10858 L .01691 .10945 L .01689 .11028 L .01688 .11103 L .01689 .11184 L .01693 .11335 L .017 .11473 L .01706 .11549 L .01713 .11631 L .01729 .1178 L .01771 .12069 L Mistroke .01824 .12335 L .01957 .12836 L .02156 .13386 L .02723 .14499 L .03578 .1568 L .04574 .16717 L .05966 .17805 L .06668 .18234 L .0749 .18647 L .08297 .18966 L .09081 .19196 L .09522 .19293 L .0993 .19361 L .10145 .19388 L .10381 .19412 L .105 .19422 L .10628 .1943 L .10857 .19441 L .11075 .19444 L .11275 .19443 L .11495 .19436 L .11605 .1943 L .11727 .19422 L .11931 .19404 L .12149 .1938 L .12541 .19322 L .12945 .19242 L .13324 .19149 L .14021 .18932 L .14758 .18635 L .15537 .18243 L .16972 .17289 L .18104 .16275 L .18977 .15264 L .19715 .14124 L .19998 .13548 L .20238 .12919 L .20388 .12381 L .20449 .1208 L .20472 .11938 L .2049 .11807 L .20504 .11686 L .20516 .11552 L .20525 .11418 L .20531 .11276 L .20534 .11151 L .20533 .11017 L .2053 .1089 L .20524 .10774 L .20513 .10625 L Mistroke .20498 .10485 L .20462 .10222 L .2041 .09939 L .20336 .09632 L .2016 .09078 L .1995 .08568 L .19287 .07393 L .18319 .06173 L .17232 .05143 L .16549 .04618 L .15851 .04161 L .15161 .03779 L .14373 .03423 L .13626 .0316 L .12916 .02974 L .12501 .02894 L .12117 .02839 L .11915 .02817 L .11693 .02798 L .11581 .02791 L .11461 .02785 L .11245 .02779 L .1104 .02778 L .10819 .02783 L .10609 .02793 L .10417 .02807 L .10243 .02823 L .10053 .02845 L .0967 .02903 L .0921 .02995 L .08795 .03101 L .07885 .03409 L .07077 .03771 L .0635 .04174 L .04566 .05513 L Mfstroke .11111 .22222 m .11385 .22219 L .11635 .2221 L .11922 .22193 L .12194 .2217 L .12675 .22112 L .13193 .22028 L .13759 .21908 L .14351 .21753 L .1539 .21409 L .17346 .20519 L .19274 .19356 L .24534 .15054 L .26819 .12849 L .2779 .11885 L .28239 .11437 L .28423 .11253 L .28501 .11175 L .28538 .11139 L .28554 .11124 L .28556 .11122 L .28559 .11121 L .2856 .1112 L .28561 .1112 L .28562 .11119 L .28562 .11119 L .28563 .11119 L .28563 .11119 L .28563 .11119 L .28564 .11119 L .28564 .11119 L .28564 .11119 L .28564 .11119 L .28564 .11119 L .28565 .11119 L .28565 .11119 L .28565 .11119 L .28565 .11119 L .28565 .11119 L .28565 .11119 L .28566 .11119 L .28566 .11119 L .28566 .11119 L .28567 .11119 L .28568 .1112 L .28569 .1112 L .28573 .11123 L .28578 .11127 L .28597 .11145 L .28644 .11191 L Mistroke .28747 .11294 L .28973 .11519 L .29524 .12069 L .30743 .13276 L .33711 .16075 L .36358 .18281 L .3784 .19346 L .39698 .20473 L .40645 .20948 L .41707 .21397 L .4275 .21745 L .43726 .21987 L .44308 .22091 L .44851 .22161 L .45135 .22187 L .45299 .22199 L .45449 .22208 L .45607 .22215 L .45778 .2222 L .46086 .22222 L .46357 .22217 L .46609 .22206 L .46885 .22188 L .4718 .22162 L .47488 .22125 L .47778 .22083 L .48317 .21985 L .49366 .21722 L .50483 .21337 L .52592 .20333 L .55761 .18217 L .60058 .14471 L .61953 .12625 L .61955 .12622 L Mfstroke .11111 .25 m .21383 .21799 L .23458 .20793 L .24518 .20336 L .25477 .19984 L .26005 .19822 L .26569 .19678 L .27074 .19576 L .27313 .19538 L .27536 .19508 L .27761 .19483 L .27967 .19466 L .28195 .19453 L .28321 .19448 L .28441 .19445 L .28555 .19444 L .28678 .19445 L .28898 .19451 L .29033 .19458 L .2916 .19466 L .29399 .19486 L .29608 .19509 L .29803 .19536 L .30251 .19612 L .3117 .19835 L .31987 .201 L .32894 .20452 L .37365 .226 L .39943 .23742 L .41502 .24287 L .42268 .24504 L .42997 .24676 L .43689 .24806 L .44329 .24898 L .44677 .24936 L .45044 .24966 L .45414 .24987 L .45623 .24994 L .45818 .24999 L .46007 .25 L .46212 .24999 L .46584 .24988 L .46945 .24969 L .47278 .24943 L .47637 .24906 L .48031 .24855 L .48822 .2472 L .49531 .24563 L .50293 .24359 L .51648 .23911 L Mistroke .54047 .22897 L .56614 .21637 L .58701 .20642 L .59658 .20245 L .60649 .199 L .61093 .19772 L .61555 .1966 L .61983 .19576 L .62369 .19517 L .62596 .1949 L .62809 .19471 L .63035 .19456 L .63162 .1945 L .63279 .19447 L .63474 .19444 L .63689 .19447 L .63914 .19456 L .64125 .1947 L .64361 .19492 L .6461 .19522 L .65058 .19593 L .65546 .19696 L .66085 .19838 L .68045 .20556 L .69985 .21466 L .72499 .22709 L .75067 .23826 L .7638 .24279 L .77645 .24619 L .78293 .24753 L .78994 .24867 L .79396 .24916 L .79778 .24953 L .80121 .24977 L .80496 .24993 L .8087 .25 L .81222 .24997 L .81607 .24983 L .81824 .24971 L .82022 .24957 L .82398 .24922 L .82809 .24873 L .83631 .24739 L .84343 .24586 L .85095 .24389 L .8642 .2396 L .9133 .21732 L .93545 .20669 L .94667 .20206 L .95672 .19864 L Mistroke .96537 .19644 L .97013 .19555 L .97446 .19496 L .97689 .19473 L .97915 .19457 L .98044 .19451 L .98162 .19447 L .98297 .19445 L .98425 .19445 L .98538 .19446 L .98657 .19449 L .98871 .19459 L .99102 .19476 L .99355 .19502 L .99798 .19564 L Mfstroke .99798 .19564 m 1 .19602 L s .11111 .27778 m .11523 .27773 L .11897 .27759 L .12328 .27733 L .12735 .27699 L .13456 .27614 L .14234 .2749 L .15973 .27099 L .17535 .26632 L .23533 .24451 L .24826 .24064 L .25525 .23891 L .26181 .23757 L .26547 .23695 L .26945 .23638 L .27309 .23597 L .27638 .23568 L .27978 .23548 L .28165 .2354 L .28341 .23536 L .28653 .23534 L .28992 .23541 L .29162 .23548 L .29345 .23558 L .29676 .23583 L .3007 .23624 L .30431 .23672 L .31221 .23809 L .31979 .2398 L .34879 .24898 L .37508 .25891 L .40547 .26929 L .4143 .2717 L .42372 .27389 L .43186 .27541 L .43656 .27612 L .44084 .27666 L .44491 .27708 L .44934 .27743 L .45178 .27757 L .45402 .27766 L .45845 .27777 L .46225 .27777 L .46643 .27766 L .47079 .27744 L .47486 .27713 L .47912 .27671 L .48374 .27613 L .49212 .27477 L .5076 .2713 L Mistroke .5252 .26607 L .54095 .26053 L .5735 .24828 L .58849 .2432 L .60182 .2395 L .60849 .23802 L .61465 .23693 L .62102 .23609 L .62438 .23576 L .62612 .23563 L .62797 .23552 L .62984 .23543 L .63156 .23538 L .63342 .23534 L .63546 .23534 L .63723 .23536 L .63912 .23542 L .64256 .23558 L .64595 .23584 L .64952 .23621 L .65593 .23712 L .66186 .23821 L .66825 .23965 L .67996 .2429 L .70782 .2527 L .73963 .26452 L .75736 .2701 L .76731 .27267 L .77673 .27467 L .78505 .27604 L .78936 .2766 L .79405 .27709 L .79672 .27731 L .7992 .27748 L .80157 .2776 L .80409 .2777 L .80845 .27778 L .81093 .27777 L .81326 .27773 L .81739 .27758 L .82174 .27731 L .82544 .27699 L .82949 .27656 L .83848 .27525 L .84678 .27366 L .86376 .26934 L .8816 .26356 L .91219 .25213 L .92564 .24718 L .9396 .24258 L Mistroke .95215 .2392 L .95822 .23789 L .96381 .23691 L .97002 .23609 L .97329 .23578 L .97496 .23565 L .97676 .23553 L .97995 .2354 L .98295 .23534 L .98586 .23535 L .98854 .23543 L .9918 .2356 L .99485 .23583 L .9982 .23617 L Mfstroke .9982 .23617 m 1 .2364 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{484.5, 161}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc0003o`0000`01?oo0940000^00?o40000ol0 000?00?oo`2?0000;@02oa8000?o00004@02ool0SP0002/00_lD0003o`0001<00_oo08`0000Y00?o 5@03oaD00_oo08X0000X00;o5`000ol0000F00;oo`2900009P02oaT000?o000060000ol0003o08H0 000U00;o3`03o`P000?o00006@000ol0003o08D0000T00;o4@000ol000070003o`0001X000?o0000 o`2400008`02o`/01Ol20003o`0000<02OlI0003o`000?l0P`0002800_lC00Oo0`000ol0000200Go 5002ool0Q00002400_lC00Co1`000ol0000600Co4P02ool0P`0002000_lB00Co2@000ol0000900;o 4P02ool0PP0001l000?o0?l04003o``000?o00002`02oa400_oo0840000N0003o`3o01000_l>00?o 3002oa400_oo0800000N00;o4002o`l000?o00003@02oa4000?o0000o`1n00007@02oa000_l@0003 o`0000h00_lA0003o`000?l0O@0001d000?o00003P000ol0000@0003o`00010000?o00003P02ool0 OP0001d000?o00003@000ol0000A0003o`0001000_l@0003o`000?l0O00001`000?o00003@02oa<0 0olA00;o3`02ool0O@0001/000?o00003P000ol0000B0003o`00018000?o00003P000ol0003o07/0 000J00;o3`000ol0000C0003o`0001<000?o00003P000ol0003o07X0000I00;o3`02oa002ol@00;o 3`02o`h01?l300;o0`03ocH00olg0003o`0000<00_l300?o<`03o`@00_l`00?o0`04o`<00_l300?o <003o`<00olU00006@000ol0000>0003o`0000h00_l40003o`0000800_l@00;o3`000ol0000=0003 o`0000<00_l60003o`0003H000?o0000=0000ol0000300;o1P000ol0000a0003o`00008000Co003o <0000ol000030003o`0000<00_l60003o`0002h000?o00001@000ol0000R000060000ol0000>0003 o`0000d00_l600?o1002o`h00_l?00;o3`000ol0000:0003o`0003H000?o0000=@000ol0000:0003 o`00034000?o00000P001?l00?l`0003o`0000@000?o00002P000ol0000^0003o`0000D000?o0000 8P0001P000?o00003P000ol0000<00;o1`000ol000060003o`0000`00_l?0003o`0000h000?o0000 1P03ocH00olh0003o`0000L00old0003o`00008000Co003o<0000ol000050003o`0000H00ola0003 o`0000800olU00005`02o`l00_l=00;o20000ol000070003o`0000/00_l?00;o30001?l00?l80003 o`0003H000?o0000>@000ol000060003o`0003@000?o00000P001?l00?l`0003o`00008000Co003o 20000ol0000a0003o`00008000?o00009@0001L000?o00003P000ol0000<0003o`0000L000?o0000 1`02o`d000?o00003P000ol0000;00;o2@04ocD01?le00Co2004oc800_l500;o<002o`D00_l900Co ;`02o`@01?lT00005`000ol0000>0003o`0000/000?o000020000ol000080003o`0000/00_l?0003 o`000?l0M`0001L000?o00003@02o``00_l:00?o2@000ol0000;0003o`0000d000?o0000o`1g0000 5`000ol0000=0003o`0000/000?o00002@000ol000090003o`0000/000?o00003@000ol0003o07L0 000G0003o`0000d000?o00002`000ol000090003o`0000T000?o00002`000ol0000=00;oo`1h0000 5P02o`l000?o00002`000ol000090003o`0000X000?o00002P000ol0000>0003o`000?l0MP0001H0 00?o00003P000ol0000:0003o`0000X000?o00002P000ol0000:0003o`0000h000?o0000o`1f0000 3`3oolOo3`0001H000?o00000P000ol0000900;o2`02o`/000?o00002P000ol0000900;o2`000ol0 00020003o`0000@000?o00002P000ol0000:0003o`0000;o1`000ol0000:0003o`0000T000?o0000 2P000ol0000:0003o`0000T000?o00002P000ol000090003o`0000X000?o00002@000ol0000:0003 o`0000X000?o00002@000ol0000:0003o`0000T000?o00002P000ol0000:0003o`0000T000?o0000 2P000ol000090003o`0000X000?o00002@000ol0000:0003o`0000X000?o00002@000ol0000J0000 5P000ol000020003o`0000T00_l;00;o2`000ol0000:0003o`0000T00_l;0003o`00008000?o0000 10000ol0000:0003o`0000X000?o0?l00P000ol000040003o`0000X000?o00002@000ol0000:0003 o`0000X000?o00002@000ol0000:0003o`0000T000?o00002P000ol000090003o`0000X000?o0000 2P000ol000090003o`0000X000?o00002@000ol0000:0003o`0000X000?o00002@000ol0000:0003 o`0000T000?o00002P000ol000090003o`0000X000?o00002P000ol000090003o`0001X0000G0003 o`0000d000?o00002`000ol000090003o`0000T00_l<0003o`0000h000?o00004@000ol0000;0005 o`000?l0;0000ol0000l0003o`0003`000?o0000?0000ol0000l0003o`0002H0000G0003o`0000d0 00?o00002`000ol000090003o`0000T000?o00002`000ol0000=00;o7`02o`D000?o0000o`1?0000 5`000ol0000=0003o`0000/000?o00002@03o`T000?o00002`000ol0000=0003o`0001d000?o0000 1P02ool0C`0001L000?o00003@02o`d000?o000020000ol0000800;o3@000ol0000=0003o`0001`0 00?o00002@000ol0003o04`0000G0003o`0000h000?o00002`000ol000080003o`0000P000?o0000 2`02o`l000?o00006`000ol0000;0003o`0008d000?o0000^P0001P000?o00003@000ol0000<0003 o`0000L000?o00001`000ol0000<0003o`0000d00_lL0003o`0000d000?o0000S0000ol0002j0000 60000ol0000=00;o3P000ol000060003o`0000H00_l>0003o`0000d000?o00006P000ol0000?0003 o`0008X000?o0000^`0001P00_l>00;o3`02o`H00ol500;o3P02o`h00_lK0003o`00014000?o0000 R0000ol0002l00006002o`l000?o00003P02o`D000?o00000`02oa0000?o00003@000ol0000I0003 o`0001<000?o0000QP000ol0002m00006@000ol0000=00;o4003o`<000?o00001?l@00;o3`000ol0 000H0003o`0001D000?o0000Q0000ol0002n00006@02o`l000?o00004@07oa800_l?00;o6@000ol0 000G0003o`00088000?o0000_`0001T00_l@0003o`0001<000?o00004`000ol0000>0003o`0001L0 00?o00006@000ol000200003o`000<00000J0003o`0000l000?o00004P03oa8000?o00003P02oaP0 00?o00006`000ol0001n0003o`000<40000K0003o`0000l000?o00004@000ol0000A00;o40000ol0 000F0003o`0001d000?o0000N`02ol@0000K00;o4@000ol0000@0003o`0001000_l@0003o`0001H0 00?o00007`000ol0001i0003o`000<@0000L00;o4@000ol0000?0003o`0000h00olA0003o`0001@0 0_lS0003o`0007L000?o0000a@0001d000?o00004002o`l000?o00003@03oa4000?o000050000ol0 000T0003o`0007D000?o0000aP0001h000?o00004002o`h00ol<00;o4P02oaD000?o00009P000ol0 001c0003o`00000009@02oa0000?o00001`000ol0000H00;o5@000ol0000f0003 o`0006800_oA00009P02o`l000?o00001`000ol0000G00;o5002ocX00_mQ0003o`000=40000X0003 o`0000/00_l90003o`0001D00_lE0003o`0003`000?o0000G@000ol0003B0000:@000ol0000E0003 o`0001@00_lE0003o`0003h000?o0000F`000ol0003C0000:P02oaD00olB00;o5P000ol000100003 o`0005T000?o0000e00002`000?o00004P000ol0000A00;o5P000ol000120003o`0005L000?o0000 e@0002d00olA0003o`0000l00olE00;oAP02oeD00_oH0000<003o`h000?o00003@03oaH000?o0000 B0000ol0001A0003o`000=P0000b00;o3@000ol0000:00Co5`000ol0001:00;oC`02om/0000c00Co 2P03o`L01OlH0003o`0004d000?o0000B`000ol0003K0000=P06o`D000?o00000`06oaX000?o0000 C`000ol0001800;ogP0003/03_lL00;o900=ob800_m600;o9@0P03obD05?lV00?o<`00044000?o0000;002och00omJ00;o@002oeX00olf0000@@000ol0 000Y00?o@`03oe@00om400?oE003ocT0001100?o9P03odT00om?00;oBP02odl00oll0000@@000ol0 000S00?oC`02odX00om>00?oB@03ocl000110003o`0002400_mD00?oA@02oe@00_m400?o@P000440 00?o00007P03oeT00olo00?oF003ocl00_m50000@@000ol0000K00?oG`02oc/00_mN00?o>@03odL0 001100?o6003of@00ole00?oH`04oc800om:0000@@000ol0000E00?oJP03obh01?mZ00?o;003odd0 00110003o`0001401?m`00Go9005og400_lV00CoD00003H00ol80003o`0000d01?mi00Co6P06ogP0 2?lK00?oE00003T000?o00001@000ol0000400WoP@06o`l01On600Co3P09oeL0000i0003o`0000D0 1on@00ooS`0>of00000g00;o20000ol0003o0:40000i0003o`0000D000?o0000o`2Q0000=P03o`P0 00?o0000o`2Q0000@@000ol0003o0:40001100?oo`2Q0000@@000ol0003o0:4000110003o`000?l0 X@00044000?o0000o`2Q0000@@000ol0003o0:40001100?oo`2Q0000@@000ol0003o0:4000110003 o`000?l0X@00044000?o0000o`2Q0000@@000ol0003o0:40001100?oo`2Q0000@@000ol0003o0:40 00110003o`000?l0X@00044000?o0000o`2Q0000@@000ol0003o0:40001100?oo`2Q0000@@000ol0 003o0:4000110003o`000?l0X@0003L00ol70003o`000?l0X@0003P000?o00001P000ol0003o0:40 000f00Co1`04ool0X00003H000?o0?l0o`2/0000=P000ol0o`3o0:`0000g00;oo`2/0000o`3U0000 \ \>"], ImageRangeCache->{{{0, 483.5}, {160, 0}} -> {-2.60596, -2.17883, 0.0397351, 0.0397351}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "The first three initial velocities start the pendulum swinging back and \ forth so that the same ", StyleBox["x", FontFamily->"Courier", FontWeight->"Bold"], " (", StyleBox["theta", FontFamily->"Courier", FontWeight->"Bold"], ") and ", StyleBox["y", FontFamily->"Courier", FontWeight->"Bold"], " (", StyleBox["theta'", FontFamily->"Courier", FontWeight->"Bold"], ") coordinates are repeated over and over. This translates into the three \ closed trajectories in the ", StyleBox["xy", FontFamily->"Courier", FontWeight->"Bold"], "-plane. The initial velocities ", StyleBox["2", FontFamily->"Courier", FontWeight->"Bold"], ", ", StyleBox["2.5", FontFamily->"Courier", FontWeight->"Bold"], ", and ", StyleBox["3.0", FontFamily->"Courier", FontWeight->"Bold"], " are enough to make the pendulum go all the way around, so that the angle \ (", StyleBox["x==theta", FontFamily->"Courier", FontWeight->"Bold"], ") is ever increasing. There is an initial velocity which lies on the \ boundary of these two types of behaviour: namely an initial velocity just \ enough to swing the pendulum from pointing down (", StyleBox["x==0", FontFamily->"Courier", FontWeight->"Bold"], ") to pointing up (", StyleBox["x==Pi", FontFamily->"Courier", FontWeight->"Bold"], "). The trajectory would approach the unstable equilibrium point ", StyleBox["{Pi,0}", FontFamily->"Courier", FontWeight->"Bold"], ". We know that an initial velocity of ", StyleBox["2", FontFamily->"Courier", FontWeight->"Bold"], " is too fast. Let's experiment with a smaller values to see if we can \ `shrink' the trajectory so that it stops at the point ", StyleBox["{Pi,0}", FontFamily->"Courier", FontWeight->"Bold"], "." }], "Text"], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]],x[0] == 0, y[0] == 1.99}, {x[t],y[t]},{t,0,20}]]],{t,0,20},AspectRatio->Automatic]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .67652 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.499997 0.161887 0.338256 0.161887 [ [.01433 .32576 -6 -9 ] [.01433 .32576 6 0 ] [.17622 .32576 -6 -9 ] [.17622 .32576 6 0 ] [.33811 .32576 -6 -9 ] [.33811 .32576 6 0 ] [.66188 .32576 -3 -9 ] [.66188 .32576 3 0 ] [.82377 .32576 -3 -9 ] [.82377 .32576 3 0 ] [.98566 .32576 -3 -9 ] [.98566 .32576 3 0 ] [.4875 .01448 -12 -4.5 ] [.4875 .01448 0 4.5 ] [.4875 .17637 -12 -4.5 ] [.4875 .17637 0 4.5 ] [.4875 .50014 -6 -4.5 ] [.4875 .50014 0 4.5 ] [.4875 .66203 -6 -4.5 ] [.4875 .66203 0 4.5 ] [ 0 0 0 0 ] [ 1 .67652 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .01433 .33826 m .01433 .34451 L s [(-3)] .01433 .32576 0 1 Mshowa .17622 .33826 m .17622 .34451 L s [(-2)] .17622 .32576 0 1 Mshowa .33811 .33826 m .33811 .34451 L s [(-1)] .33811 .32576 0 1 Mshowa .66188 .33826 m .66188 .34451 L s [(1)] .66188 .32576 0 1 Mshowa .82377 .33826 m .82377 .34451 L s [(2)] .82377 .32576 0 1 Mshowa .98566 .33826 m .98566 .34451 L s [(3)] .98566 .32576 0 1 Mshowa .125 Mabswid .04671 .33826 m .04671 .34201 L s .07909 .33826 m .07909 .34201 L s .11147 .33826 m .11147 .34201 L s .14384 .33826 m .14384 .34201 L s .2086 .33826 m .2086 .34201 L s .24098 .33826 m .24098 .34201 L s .27335 .33826 m .27335 .34201 L s .30573 .33826 m .30573 .34201 L s .37049 .33826 m .37049 .34201 L s .40286 .33826 m .40286 .34201 L s .43524 .33826 m .43524 .34201 L s .46762 .33826 m .46762 .34201 L s .53237 .33826 m .53237 .34201 L s .56475 .33826 m .56475 .34201 L s .59713 .33826 m .59713 .34201 L s .62951 .33826 m .62951 .34201 L s .69426 .33826 m .69426 .34201 L s .72664 .33826 m .72664 .34201 L s .75902 .33826 m .75902 .34201 L s .79139 .33826 m .79139 .34201 L s .85615 .33826 m .85615 .34201 L s .88853 .33826 m .88853 .34201 L s .9209 .33826 m .9209 .34201 L s .95328 .33826 m .95328 .34201 L s .25 Mabswid 0 .33826 m 1 .33826 L s .5 .01448 m .50625 .01448 L s [(-2)] .4875 .01448 1 0 Mshowa .5 .17637 m .50625 .17637 L s [(-1)] .4875 .17637 1 0 Mshowa .5 .50014 m .50625 .50014 L s [(1)] .4875 .50014 1 0 Mshowa .5 .66203 m .50625 .66203 L s [(2)] .4875 .66203 1 0 Mshowa .125 Mabswid .5 .04686 m .50375 .04686 L s .5 .07924 m .50375 .07924 L s .5 .11161 m .50375 .11161 L s .5 .14399 m .50375 .14399 L s .5 .20875 m .50375 .20875 L s .5 .24112 m .50375 .24112 L s .5 .2735 m .50375 .2735 L s .5 .30588 m .50375 .30588 L s .5 .37063 m .50375 .37063 L s .5 .40301 m .50375 .40301 L s .5 .43539 m .50375 .43539 L s .5 .46777 m .50375 .46777 L s .5 .53252 m .50375 .53252 L s .5 .5649 m .50375 .5649 L s .5 .59728 m .50375 .59728 L s .5 .62965 m .50375 .62965 L s .25 Mabswid .5 0 m .5 .67652 L s 0 0 m 1 0 L 1 .67652 L 0 .67652 L closepath clip newpath .5 Mabswid .5 .66041 m .50795 .66031 L .51518 .66005 L .52352 .65955 L .53139 .65888 L .54533 .65723 L .56037 .65477 L .57677 .6513 L .59395 .64681 L .62405 .63681 L .68075 .61096 L .73664 .57715 L .88852 .45104 L .92881 .41029 L .95232 .38395 L .96056 .37352 L .96718 .36393 L .97156 .35612 L .97315 .35257 L .97431 .34942 L .97526 .34605 L .97563 .34431 L .97578 .34343 L .97591 .34249 L .97601 .3417 L .97608 .34098 L .97613 .34026 L .97616 .33957 L .97619 .33878 L .97619 .33805 L .97618 .33724 L .97614 .33638 L .97607 .33552 L .976 .33472 L .97575 .33293 L .97545 .33133 L .97505 .32963 L .97391 .32594 L .9722 .32174 L .96776 .31352 L .96211 .3051 L .94256 .28122 L .86582 .20391 L .80411 .14987 L .75916 .11511 L .71016 .08236 L .65563 .053 L .6226 .03916 L .59118 .02892 L .57365 .02448 L Mistroke .55718 .02116 L .53894 .01845 L .52869 .01738 L .52417 .01701 L .51938 .01668 L .51512 .01645 L .51045 .01627 L .50222 .01611 L .49759 .01611 L .49263 .01618 L .48794 .01633 L .48368 .01651 L .47542 .01704 L .46646 .01784 L .45803 .01883 L .45026 .01993 L .41947 .02611 L .40247 .03075 L .38715 .03567 L .33176 .05908 L .27613 .09094 L .22522 .12671 L .10218 .23456 L .06492 .27295 L .04367 .29749 L .03641 .30718 L .0306 .31629 L .02858 .3201 L .02685 .32393 L .02562 .32732 L .02474 .33043 L .0244 .33207 L .02425 .33293 L .02411 .33384 L .02401 .3346 L .02393 .33543 L .02387 .33619 L .02384 .3369 L .02381 .33774 L .02381 .33862 L .02383 .33938 L .02387 .3402 L .02393 .3411 L .02403 .34205 L .02428 .34379 L .02459 .34542 L .02503 .34721 L .02607 .35052 L .02891 .35706 L .0334 .36484 L Mistroke .04024 .37459 L .06156 .39988 L .1448 .48239 L .2117 .53936 L .25648 .57247 L .31165 .60684 L .34516 .62388 L .3772 .63728 L .39317 .64285 L .41075 .64812 L .42748 .65228 L .44327 .65543 L .45951 .65787 L .46816 .65884 L .47744 .65962 L .48212 .65992 L .4872 .66016 L .49201 .66031 L .49646 .66039 L .50487 .66037 L .5138 .66012 L .52147 .6597 L .52973 .65904 L .53751 .65823 L .54462 .65733 L .56104 .65464 L .57815 .65098 L .61056 .64162 L .63903 .63085 L .69864 .601 L .78819 .53943 L .90803 .43177 L .95864 .37605 L .96571 .36621 L .97052 .35815 L .97249 .35411 L .9739 .35059 L .97507 .34681 L .97553 .34478 L .9757 .34386 L .97585 .34287 L .97597 .34195 L .97606 .3411 L .97612 .3403 L .97616 .33945 L .97618 .33868 L .97618 .33797 L .97617 .33719 L .97613 .33635 L .97606 .33546 L Mistroke .97596 .33449 L .97571 .33271 L .97537 .33096 L .97497 .32933 L .97404 .32631 L .9727 .32288 L .96891 .31545 L .95607 .29718 L .93248 .27014 L .93182 .26943 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 190}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc002ocH00_mC0000D@02ocX000?o0000=`02oe40001@0003o`0003X000?o0000>@000ol0001>0000 CP02ocd000?o0000>P02odh0001=0003o`0003d000?o0000?0000ol0001;0000B`02od0000?o0000 ?@02od/0001:0003o`00040000?o0000?`02odT000190003o`00044000?o0000@@000ol000160000 A`02od@000?o0000@P02odH000160003o`0004@00_m50003o`0004<0001400;oA`000ol0001500;o @`0004<000?o0000A`000ol000170003o`00040000120003o`0004P000?o0000B0000ol0000o0000 @002od/000?o0000B@02ocl0000o0003o`0004/000?o0000B`000ol0000l0000?P000ol0001<0003 o`0004`000?o0000>`0003d000?o0000C@000ol0001=0003o`0003X0000l0003o`0004h000?o0000 CP02ocX0000k0003o`0004l00_mA0003o`0003L0000i00;oDP000ol0001A0003o`0003H0000h0003 o`00058000?o0000DP02ocH0000g0003o`0005<000?o0000E0000ol0000c0000=P000ol0001D0003 o`0005D000?o0000`000ol0001?00;oCP000ol0o`0j0000?0000ol0001>0003o`0004`0 00?o0?l0>`0003d00_m>0003o`0004X01?ll0000?`000ol0001;0003o`0004T000?o0?l0?P000400 00?o0000BP000ol0001800?o?`0004400_m:0003o`0004L00_m10000@`000ol000170003o`0004H0 0_m20000A0000ol000160003o`0004@00_m40000A@02odH000?o0000@`02odD000170003o`0004<0 0_m30003o`0004D000180003o`00048000?o0000@002odP0001900;o@P000ol0000o00;oB@0004/0 00?o0000?`000ol0000n00;oBP0004`00_lo0003o`0003`00_m<0000CP02ocd000?o0000>`02odd0 001@0003o`0003X000?o0000>@02odl0001A00;o>P000ol0000h0003o`0004l0001C0003o`0003L0 00?o0000=P02oe80001D00;o=`02ocH000?o0000DP0005H00_le0003o`0003<00_mE0000F0000ol0 000b0003o`0003400_mG0000F@02oc8000?o0000;`02oeT0001K00;o<0000ol0000]00?oFP0005d0 0ol]0003o`0002/00omL0000H002ob/000?o0000:@03oeh0001R00;o:@000ol0000W00;oH@0006@0 0_lW0003o`0002D00_mS0000IP03ob@00_lS00?oI@0006T00_lR0003o`0002000omW0000J`02ob00 00?o00007@03ofX0001]00;o7P000ol0000K00?oK00006l01?lJ0003o`0001P00om_0000L`05oaD0 00?o00005@03og80001h00Co4@000ol0000@00GoM@0007`01Ol400Co10000ol0000<00GoN@000840 2_l20003o`0000coOP0008L000Co00001On:0000R0000ol000020003o`0008X000250004o`00o`@0 00?o0000RP0008H00_l50003o`0008X0002=0003o`0008X00000\ \>"], ImageRangeCache->{{{0, 281}, {189, 0}} -> {-3.14465, -2.10003, 0.0222225, 0.0222225}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]],x[0] == 0, y[0] == 1.9999}, {x[t],y[t]},{t,0,20}]]],{t,0,20},AspectRatio->Automatic]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .64068 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.499971 0.152554 0.320329 0.152554 [ [.04231 .30783 -6 -9 ] [.04231 .30783 6 0 ] [.19486 .30783 -6 -9 ] [.19486 .30783 6 0 ] [.34742 .30783 -6 -9 ] [.34742 .30783 6 0 ] [.65253 .30783 -3 -9 ] [.65253 .30783 3 0 ] [.80508 .30783 -3 -9 ] [.80508 .30783 3 0 ] [.95763 .30783 -3 -9 ] [.95763 .30783 3 0 ] [.48747 .01522 -12 -4.5 ] [.48747 .01522 0 4.5 ] [.48747 .16777 -12 -4.5 ] [.48747 .16777 0 4.5 ] [.48747 .47288 -6 -4.5 ] [.48747 .47288 0 4.5 ] [.48747 .62544 -6 -4.5 ] [.48747 .62544 0 4.5 ] [ 0 0 0 0 ] [ 1 .64068 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .04231 .32033 m .04231 .32658 L s [(-3)] .04231 .30783 0 1 Mshowa .19486 .32033 m .19486 .32658 L s [(-2)] .19486 .30783 0 1 Mshowa .34742 .32033 m .34742 .32658 L s [(-1)] .34742 .30783 0 1 Mshowa .65253 .32033 m .65253 .32658 L s [(1)] .65253 .30783 0 1 Mshowa .80508 .32033 m .80508 .32658 L s [(2)] .80508 .30783 0 1 Mshowa .95763 .32033 m .95763 .32658 L s [(3)] .95763 .30783 0 1 Mshowa .125 Mabswid .07282 .32033 m .07282 .32408 L s .10333 .32033 m .10333 .32408 L s .13384 .32033 m .13384 .32408 L s .16435 .32033 m .16435 .32408 L s .22537 .32033 m .22537 .32408 L s .25588 .32033 m .25588 .32408 L s .28639 .32033 m .28639 .32408 L s .31691 .32033 m .31691 .32408 L s .37793 .32033 m .37793 .32408 L s .40844 .32033 m .40844 .32408 L s .43895 .32033 m .43895 .32408 L s .46946 .32033 m .46946 .32408 L s .53048 .32033 m .53048 .32408 L s .56099 .32033 m .56099 .32408 L s .5915 .32033 m .5915 .32408 L s .62201 .32033 m .62201 .32408 L s .68304 .32033 m .68304 .32408 L s .71355 .32033 m .71355 .32408 L s .74406 .32033 m .74406 .32408 L s .77457 .32033 m .77457 .32408 L s .83559 .32033 m .83559 .32408 L s .8661 .32033 m .8661 .32408 L s .89661 .32033 m .89661 .32408 L s .92712 .32033 m .92712 .32408 L s .0118 .32033 m .0118 .32408 L s .98814 .32033 m .98814 .32408 L s .25 Mabswid 0 .32033 m 1 .32033 L s .49997 .01522 m .50622 .01522 L s [(-2)] .48747 .01522 1 0 Mshowa .49997 .16777 m .50622 .16777 L s [(-1)] .48747 .16777 1 0 Mshowa .49997 .47288 m .50622 .47288 L s [(1)] .48747 .47288 1 0 Mshowa .49997 .62544 m .50622 .62544 L s [(2)] .48747 .62544 1 0 Mshowa .125 Mabswid .49997 .04573 m .50372 .04573 L s .49997 .07624 m .50372 .07624 L s .49997 .10675 m .50372 .10675 L s .49997 .13726 m .50372 .13726 L s .49997 .19829 m .50372 .19829 L s .49997 .2288 m .50372 .2288 L s .49997 .25931 m .50372 .25931 L s .49997 .28982 m .50372 .28982 L s .49997 .35084 m .50372 .35084 L s .49997 .38135 m .50372 .38135 L s .49997 .41186 m .50372 .41186 L s .49997 .44237 m .50372 .44237 L s .49997 .50339 m .50372 .50339 L s .49997 .5339 m .50372 .5339 L s .49997 .56442 m .50372 .56442 L s .49997 .59493 m .50372 .59493 L s .25 Mabswid .49997 0 m .49997 .64068 L s 0 0 m 1 0 L 1 .64068 L 0 .64068 L closepath clip newpath .5 Mabswid .49997 .62542 m .5075 .62533 L .51435 .62508 L .52225 .62461 L .5297 .62398 L .5429 .62241 L .55714 .62008 L .57268 .6168 L .58894 .61254 L .61746 .60308 L .67116 .57864 L .72411 .54673 L .86854 .42857 L .93126 .36801 L .95786 .34147 L .97003 .32902 L .97303 .32574 L .97475 .32362 L .97532 .32278 L .97572 .32209 L .97588 .32173 L .97602 .32136 L .97607 .3212 L .97611 .32104 L .97614 .3209 L .97616 .32074 L .97617 .32066 L .97618 .32058 L .97619 .32051 L .97619 .32043 L .97619 .32035 L .97619 .32029 L .97619 .32022 L .97618 .32014 L .97618 .32006 L .97617 .31997 L .97614 .3198 L .97611 .31963 L .97607 .31948 L .97598 .31916 L .97586 .31887 L .9755 .31817 L .9743 .31644 L .97207 .31384 L .96297 .30436 L .94233 .28364 L .89796 .24007 L .85378 .19841 L .79442 .14664 L .75674 .11706 L Mistroke .70877 .08394 L .65738 .05495 L .63013 .04258 L .60407 .03282 L .57356 .02407 L .5572 .02059 L .5488 .01913 L .53976 .01783 L .53206 .01692 L .52503 .01626 L .51795 .01576 L .51124 .01544 L .50342 .01525 L .4962 .01526 L .48827 .01546 L .47987 .0159 L .4716 .01655 L .46404 .01735 L .44711 .0198 L .43232 .0227 L .41694 .02646 L .38503 .03663 L .35162 .0506 L .29643 .08065 L .25229 .11038 L .17411 .17334 L .08807 .25358 L .05087 .29038 L .03363 .30779 L .0267 .3152 L .02503 .31732 L .02455 .31806 L .02417 .31878 L .02403 .31915 L .02392 .31948 L .02389 .31964 L .02386 .31979 L .02383 .31994 L .02382 .32002 L .02382 .32006 L .02382 .32011 L .02381 .32019 L .02381 .32027 L .02381 .32032 L .02381 .32037 L .02381 .32045 L .02381 .3205 L .02382 .32055 L .02382 .32063 L .02383 .32072 L Mistroke .02385 .32082 L .02388 .32099 L .02392 .32117 L .02402 .3215 L .02417 .32187 L .02435 .32223 L .02489 .32313 L .02649 .32521 L .0328 .33202 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 180}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc@000ol0001?0000 CP02oc`000?o0000>P02odl0001=0003o`0003`000?o0000?0000ol0001<0000C0000ol0000m0003 o`0003d00_m<0000BP02od0000?o0000?`02odX000190003o`0004000_m20003o`0004L000180003 o`00044000?o0000@P02odL0001600;oA0000ol000140003o`0004@000150003o`0004@000?o0000 A@02od@000140003o`0004D000?o0000A`000ol000110000@P02odP000?o0000B0000ol000100000 @@000ol000180003o`0004T000?o0000?`00040000?o0000B@000ol0001:0003o`0003h0000o0003 o`0004X000?o0000B`000ol0000m0000?@02odd00_m=0003o`0003`0000l0003o`0004d000?o0000 C@000ol0000k0000>`000ol0001>0003o`0004h000?o0000>P0003T00_mA0003o`0004l00_lj0000 >0000ol0001A0003o`00054000?o0000=`0003L000?o0000DP000ol0001B0003o`0003H0000f0003 o`0004/00ol50003o`0005<000?o0000=@0003@00_m?0003o`0000@000?o0000E0000ol0000d0000 <`000ol0001800Go0P000ol0000400?oE@02oc@0000b0003o`00050000?o000010000ol0001G0003 o`000340000`00;oD`000ol000040003o`0005P000?o0000<00002l000?o0000DP02o`H000?o0000 F@000ol0000_0000;P000ol0001K0003o`0005X00_l_0000;@000ol0001L0003o`0005`000?o0000 ;00002`000?o0000G@000ol0001M0003o`0002/0000[0003o`0005h000?o0000GP000ol0000Z0000 :P000ol0001O0003o`0005l000?o0000:@0002T000?o0000H002of4000?o0000:00002P000?o0000 H@000ol0001Q0003o`0002L0000W0003o`00068000?o0000HP000ol0000V00009P000ol0001S0003 o`0006<000?o00009@0002@00_mV0003o`0006@000?o0000900002<000?o0000IP000ol0001U0003 o`0002<0000R0003o`0006L000?o0000IP000ol0000R00008@000ol0001X0003o`0006L000?o0000 8@00020000?o0000J@02ofT000?o0000800001l000?o0000JP000ol0001Y0003o`0001l0000N0003 o`0006/000?o0000JP000ol0000N00007@000ol0001/0003o`0006/000?o00007@0001`000?o0000 K@000ol0001/0003o`0001`0000K0003o`0006h000?o0000K@000ol0000K00006P000ol0001_0003 o`0006h000?o00006P0001T000?o0000L0000ol0001_0003o`0001T0000I0003o`00070000?o0000 L0000ol0000H000060000ol0001a00;oLP000ol0000G00005`000ol0001b0003o`00078000?o0000 5P0001H000?o0000L`000ol0001c0003o`0001D0000E0003o`0007@000?o0000M0000ol0000D0000 50000ol0001e0003o`0007D000?o00004`0001<000?o0000MP000ol0001f0003o`000180000B0003 o`0007L000?o0000M`000ol0000A00003@03o`030?l002D01?lV00?o9`000ol0000U00?o:004ob@0 00?o0?l00_l>000040000ol0000V0003o`0002L000?o00009P02obL000?o0000:0000ol0000U0005 o`000?l03@0000L01Ol300;o8@05o`<000?o00007`05o`8000?o00009P000ol0000V0003o`0002T0 00?o00009@001?l00?l=00003P02ob/000?o00009@000ol0000V0003o`0002H000?o0000:P000ol0 000U00;o3P0000d000Co003o9`001?l00?lW0003o`0002H000?o00009P000ol0000W0004o`00obP0 0_l=00003004obT00_lW00;o:0000ol0000U00;o:P02obL01?l=00002`000ol0001n0003o`0007h0 0_l;00002P000ol0001o0003o`00080000?o0000200000T000?o0000P0000ol000210003o`0000L0 00080003o`00084000?o0000P@000ol00007000000<0ool0oolFo`8000040003o`0000;o0`000ol0 00060003o`0000D000?o00001P000ol000050003o`0000H000?o00001@000ol000060003o`0000D0 00?o00001P000ol000050003o`0000H000?o00001@000ol000060003o`0000D000?o00001P000ol0 00050003o`0000H000?o00001@000ol000060003o`0000D000?o00001P000ol000050003o`0000H0 00?o00001@000ol000060003o`0000D000?o00001P000ol000050003o`0000H000?o00001@000ol0 00020005o`000?l01@0000T000Co003o:P000ol0000W0003o`0002P000?o00009`000ol0000X0003 o`0002L000Co00000_l900002P000ol0001o0003o`00080000?o0000200008`000?o0000O`000ol0 00090000S0000ol0001n0003o`0000X0002<0003o`0007`00_l=0000S0000ol0001k0003o`0000d0 002<00;oN`000ol0000>0000S0000ol0001i0003o`0000l0002<0003o`0007P000?o0000400008`0 00?o0000M`000ol0000A0000S0000ol0001f0003o`000180002<0003o`0007D000?o00004`0008`0 00?o0000M0000ol0000D0000S0000ol0001c0003o`0001D0002<0003o`00078000?o00005P0008`0 0_mb0003o`0001L0002<0003o`00070000?o0000600008`000?o0000K`000ol0000I0000S0000ol0 001^0003o`0001X0002<0003o`0006d000?o00006`0008`000?o0000K0000ol0000L0000S0000ol0 001[0003o`0001d0002<0003o`0006X000?o00007P0008`00_mZ0003o`0001l0002<0003o`0006P0 00?o0000800008`000?o0000I`000ol0000Q0000S0000ol0001V0003o`000280002<0003o`0006D0 00?o00008`0008`000?o0000H`02obH0002<0003o`00068000?o00009P0008`000?o0000H@000ol0 000W0000S0000ol0001P0003o`0002P0002<00;oG`02ob/0002<0003o`0005d000?o0000:`0008`0 00?o0000G0000ol0000/0000S0000ol0001K0003o`0002d0002<0003o`0005T00_l`0000S0000ol0 001H0003o`000300002400?o1@000ol0001G0003o`00034000250003o`0000@000?o0000EP000ol0 000b0000Q@000ol0000400?oE002ocD000250003o`0000@000?o0000D`000ol0000e0000Q@000ol0 00040003o`00058000?o0000=P0008@00_l60003o`00054000?o0000=`0008`000?o0000C`02ocX0 002<0003o`0004h000?o0000>P0008`000?o0000C@000ol0000k0000S0000ol0001<0003o`0003`0 002<0003o`0004/000?o0000?@0008`00_m:00;o@00008`000?o0000B0000ol000100000S0000ol0 00170003o`000440002<0003o`0004H000?o0000@P0008`000?o0000A002odD0002<0003o`0004<0 00?o0000A@0008`000?o0000@P000ol000160000S0000ol000110003o`0004L0002<00;o@002odX0 002<0003o`0003h000?o0000BP0008`000?o0000?@000ol0001;0000S0000ol0000l0003o`0004`0 002<0003o`0003X00_m?0000S0000ol0000i0003o`0004l0002<0003o`0003L00_mB0000S0000ol0 000f0003o`000580002<0003o`0003@00_mE0000S002oc<00_mG0000S0000ol0000a0003o`0005L0 002<0003o`0002l00_mJ0000S0000ol0000^0003o`0005X0002<0003o`0002`00_mM0000S0000ol0 000Z00;oG`0008`000?o0000:002of40002<0003o`0002D00omS0000S002ob@00_mV0000S0000ol0 000Q00;oJ00008`000?o00007`02ofX0002<0003o`0001`00om/0000S0000ol0000H00CoK`0008`0 00?o00005@03og<0002<0003o`0001800omf0000Q004o`@000?o00003`03ogT000250003o`0000@0 00?o00001`08og`000260003o`0000<02_n40000Q`000ol000020003o`0008/000240004o`00o`@0 00?o0000R`0008D00_l50003o`0008/0002<0003o`0008/00000\ \>"], ImageRangeCache->{{{0, 281}, {179, 0}} -> {-3.30575, -2.10591, 0.0235298, 0.0235298}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]],x[0] == 0, y[0] == 1.9999995}, {x[t],y[t]},{t,0,20}]]],{t,0,20},AspectRatio->Automatic]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.16919 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.303178 0.534998 0.303178 [ [.1754 .5225 -9 -9 ] [.1754 .5225 9 0 ] [.32699 .5225 -3 -9 ] [.32699 .5225 3 0 ] [.47858 .5225 -9 -9 ] [.47858 .5225 9 0 ] [.63017 .5225 -3 -9 ] [.63017 .5225 3 0 ] [.78175 .5225 -9 -9 ] [.78175 .5225 9 0 ] [.93334 .5225 -3 -9 ] [.93334 .5225 3 0 ] [.01131 .08023 -24 -4.5 ] [.01131 .08023 0 4.5 ] [.01131 .23182 -12 -4.5 ] [.01131 .23182 0 4.5 ] [.01131 .38341 -24 -4.5 ] [.01131 .38341 0 4.5 ] [.01131 .68659 -18 -4.5 ] [.01131 .68659 0 4.5 ] [.01131 .83818 -6 -4.5 ] [.01131 .83818 0 4.5 ] [.01131 .98977 -18 -4.5 ] [.01131 .98977 0 4.5 ] [.01131 1.14135 -6 -4.5 ] [.01131 1.14135 0 4.5 ] [ 0 0 0 0 ] [ 1 1.16919 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .1754 .535 m .1754 .54125 L s [(0.5)] .1754 .5225 0 1 Mshowa .32699 .535 m .32699 .54125 L s [(1)] .32699 .5225 0 1 Mshowa .47858 .535 m .47858 .54125 L s [(1.5)] .47858 .5225 0 1 Mshowa .63017 .535 m .63017 .54125 L s [(2)] .63017 .5225 0 1 Mshowa .78175 .535 m .78175 .54125 L s [(2.5)] .78175 .5225 0 1 Mshowa .93334 .535 m .93334 .54125 L s [(3)] .93334 .5225 0 1 Mshowa .125 Mabswid .05413 .535 m .05413 .53875 L s .08445 .535 m .08445 .53875 L s .11476 .535 m .11476 .53875 L s .14508 .535 m .14508 .53875 L s .20572 .535 m .20572 .53875 L s .23603 .535 m .23603 .53875 L s .26635 .535 m .26635 .53875 L s .29667 .535 m .29667 .53875 L s .35731 .535 m .35731 .53875 L s .38762 .535 m .38762 .53875 L s .41794 .535 m .41794 .53875 L s .44826 .535 m .44826 .53875 L s .50889 .535 m .50889 .53875 L s .53921 .535 m .53921 .53875 L s .56953 .535 m .56953 .53875 L s .59985 .535 m .59985 .53875 L s .66048 .535 m .66048 .53875 L s .6908 .535 m .6908 .53875 L s .72112 .535 m .72112 .53875 L s .75144 .535 m .75144 .53875 L s .81207 .535 m .81207 .53875 L s .84239 .535 m .84239 .53875 L s .87271 .535 m .87271 .53875 L s .90303 .535 m .90303 .53875 L s .96366 .535 m .96366 .53875 L s .99398 .535 m .99398 .53875 L s .25 Mabswid 0 .535 m 1 .535 L s .02381 .08023 m .03006 .08023 L s [(-1.5)] .01131 .08023 1 0 Mshowa .02381 .23182 m .03006 .23182 L s [(-1)] .01131 .23182 1 0 Mshowa .02381 .38341 m .03006 .38341 L s [(-0.5)] .01131 .38341 1 0 Mshowa .02381 .68659 m .03006 .68659 L s [(0.5)] .01131 .68659 1 0 Mshowa .02381 .83818 m .03006 .83818 L s [(1)] .01131 .83818 1 0 Mshowa .02381 .98977 m .03006 .98977 L s [(1.5)] .01131 .98977 1 0 Mshowa .02381 1.14135 m .03006 1.14135 L s [(2)] .01131 1.14135 1 0 Mshowa .125 Mabswid .02381 .11055 m .02756 .11055 L s .02381 .14087 m .02756 .14087 L s .02381 .17118 m .02756 .17118 L s .02381 .2015 m .02756 .2015 L s .02381 .26214 m .02756 .26214 L s .02381 .29246 m .02756 .29246 L s .02381 .32277 m .02756 .32277 L s .02381 .35309 m .02756 .35309 L s .02381 .41373 m .02756 .41373 L s .02381 .44404 m .02756 .44404 L s .02381 .47436 m .02756 .47436 L s .02381 .50468 m .02756 .50468 L s .02381 .56532 m .02756 .56532 L s .02381 .59563 m .02756 .59563 L s .02381 .62595 m .02756 .62595 L s .02381 .65627 m .02756 .65627 L s .02381 .7169 m .02756 .7169 L s .02381 .74722 m .02756 .74722 L s .02381 .77754 m .02756 .77754 L s .02381 .80786 m .02756 .80786 L s .02381 .86849 m .02756 .86849 L s .02381 .89881 m .02756 .89881 L s .02381 .92913 m .02756 .92913 L s .02381 .95945 m .02756 .95945 L s .02381 1.02008 m .02756 1.02008 L s .02381 1.0504 m .02756 1.0504 L s .02381 1.08072 m .02756 1.08072 L s .02381 1.11104 m .02756 1.11104 L s .02381 .04991 m .02756 .04991 L s .02381 .0196 m .02756 .0196 L s .25 Mabswid .02381 0 m .02381 1.16919 L s 0 0 m 1 0 L 1 1.16919 L 0 1.16919 L closepath clip newpath .5 Mabswid .02381 1.14135 m .03878 1.14117 L .05239 1.14068 L .06808 1.13974 L .08289 1.13848 L .10913 1.13536 L .13744 1.13074 L .16832 1.12422 L .20064 1.11575 L .2573 1.09695 L .36404 1.04838 L .46927 .98495 L .75632 .75015 L .88104 .62984 L .93401 .57722 L .95848 .55278 L .96854 .54272 L .97281 .53846 L .97479 .53647 L .97562 .53564 L .97599 .53526 L .97609 .53516 L .97614 .5351 L .97617 .53506 L .97618 .53504 L .97619 .53503 L .97619 .53502 L .97619 .53501 L .97619 .53501 L .97619 .53501 L .97619 .53501 L .97619 .535 L .97619 .535 L .97619 .535 L .97619 .535 L .97619 .535 L .97619 .535 L .97619 .53499 L .97619 .53499 L .97619 .53499 L .97619 .53499 L .97619 .53499 L .97619 .53498 L .97619 .53498 L .97619 .53498 L .97618 .53497 L .97618 .53495 L .97616 .53493 L .97615 .53491 L .9761 .53484 L Mistroke .97588 .53462 L .97541 .53414 L .97426 .53299 L .97169 .53042 L .96529 .52401 L .95076 .5095 L .91893 .47774 L .84093 .40078 L .67111 .24256 L .37556 .02784 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{211, 246}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc0003o`0006H000080003o`0000P00ol40003o`0004h00_mV000020000ol0 00080003o`0000@000?o0000D0000ol0001S00001`02o`X01?l30003o`00054000?o0000HP0001X0 00?o0000DP02of80000J0003o`0005@000?o0000G`0001X00_mF00;oG`0001X000?o0000E`000ol0 001L00006P000ol0001H0003o`0005/0000J0003o`0005T00_mK00006P000ol0001K0003o`0005P0 000J0003o`0005`000?o0000E`0001X00_mN00;oE`0001X000?o0000G`000ol0001D00006P000ol0 001P0003o`0005<0000J0003o`0006400_mC00006P000ol0001S0003o`000500000J00;oI@02oe00 000J0003o`0006H000?o0000C@0001X000?o0000I`000ol0001<00006P000ol0001X00;oC00001X0 00?o0000JP000ol0001900006P000ol0001[0003o`0004P0000J00;oK@02odP0000J0003o`0006h0 00?o0000A@0001X000?o0000K`000ol0001400006P000ol0001`00;oA00001<00ol40003o`000780 00?o0000@@0001@000?o00000`000ol0001c00;o@@0000d01Ol20003o`0000<00_mf0003o`0003h0 000D0003o`0000<000?o0000MP000ol0000m000050000ol000030003o`0007L00_lm00004`02o`D0 00?o0000N@000ol0000j00006P000ol0001j0003o`0003T0000J00;oO0000ol0000h00006P000ol0 001l0003o`0003L0000J0003o`0007d000?o0000=P0001X000?o0000OP000ol0000e00006P000ol0 001o0003o`0003@0000J0003o`00080000?o0000<`0001X00_n20003o`000380000J0003o`000880 0_lb00006P000ol000240003o`0002l0000J0003o`0008D000?o0000;P0001X000?o0000QP000ol0 000]00006P000ol000270003o`0002`0000J00;oR@000ol0000[00006P000ol000290003o`0002X0 000J0003o`0008X000?o0000:@0001X000?o0000R`000ol0000X00006P000ol0002<00;o:00001X0 0_n?0003o`0002D0000J0003o`0008l000?o0000900001X000?o0000T0000ol0000S00006P000ol0 002A0003o`000280000800;o1002o`<00ol40003o`00098000?o00008@0000L000Co003o0`02o`H0 00Go0000o`2E0003o`00020000000`3oo`03o`050?l00?l02`001?l00002oiD000?o00007`0000L0 00Co003o2003o`@000?o0000U@000ol0000N00001`001?l00?l80003o`0000@000?o0000UP000ol0 000M00002002o`T01?l30003o`0009L000?o0000700001X000?o0000U`000ol0000L00006P000ol0 002H0003o`0001/0000J00;oVP000ol0000J00006P000ol0002J0003o`0001T0000J0003o`0009/0 00?o0000600001X000?o0000W0000ol0000G00006P000ol0002M0003o`0001H0000J0003o`0009h0 00?o00005@0001X00_nP0003o`0001@0000J0003o`000:0000?o00004`0001X000?o0000X@000ol0 000B00006P000ol0002R0003o`000140000J0003o`000:<000?o0000400001X00_nU0003o`0000l0 000J0003o`000:D000?o00003P0001X000?o00004P02o`@00_l300?o5003oa<00ol400;o0`03oa@0 1?lB00Co0`02o`<00olD00?o3@0001X000?o00004@001?l00?l300;o1P000ol0000B0003o`0001<0 00?o00000`02o`H000?o00004P000ol0000C0003o`0000<00_l60003o`00018000?o0?l0300001X0 00?o00004@001?l00?l;0003o`00018000?o00004`000ol0000;0003o`0001<000?o00004`000ol0 000:0003o`0001<00_l<00006P000ol0000A0004o`00o`P00olE0003o`0001<000?o00002003oaL0 00?o00004`000ol0000600?o5@03o``0000J00;o4P001?l00?l80003o`0001D000?o00004`000ol0 00080003o`0001@000Co003o4P001?l00?l80003o`0001L00_l;00006P000ol0000B00;o2@04oa<0 0_lD00;o2P04oa@00_lD00;o2@04oa<00ol20003o`0000P0000J0003o`000:`000?o00001`0001X0 00?o0000[@000ol0000600006P000ol0002^0003o`0000D0000J0003o`000:l00_l500005@2no`00 6P000ol0000I0003o`0001X000?o00006@000ol0000J0003o`0001T000?o00006P000ol000040003 o`0000@0000J0003o`000:h000?o00001@0001X000?o0000[@000ol0000600006P000ol0002/0003 o`0000L0000J00;o[0000ol0000800006P000ol0002Z0003o`0000T0000J0003o`000:T000?o0000 2P0001X000?o0000Z0000ol0000;00006P000ol0002W0003o`0000`0000J0003o`000:H000?o0000 3@0001X00_nV0003o`0000h0000J0003o`000:@000?o00003`0001X000?o0000X`000ol0000@0000 6P000ol0002R0003o`000140000J0003o`000:4000?o00004P0001X000?o0000X0000ol0000C0000 6P02oj0000?o0000500001X000?o0000W@02oaL0000J0003o`0009`000?o00005`0001X000?o0000 V`000ol0000H00006P000ol0002J0003o`0001T0000J00;oVP000ol0000J00006P000ol0002H0003 o`0001/0000J0003o`0009L000?o0000700001X000?o0000UP000ol0000M00002002o`@00_l300?o 10000ol0002E0003o`0001h000070004o`00o`<00_l60005o`000?l0UP000ol0000O00001`001?l0 0?l;0004o`0000;oU0000ol0000P00001`001?l00?l800?o10000ol0002B0003o`00024000070004 o`00o`P000?o000010000ol0002A0003o`000280000800;o2@04o`<000?o0000T0000ol0000S0000 6P000ol0002?0003o`0002@0000J0003o`0008h000?o00009@0001X00_n>0003o`0002H0000J0003 o`0008`000?o00009`0001X000?o0000R`000ol0000X00006P000ol0002:0003o`0002T0000J0003 o`0008T000?o0000:P0001X000?o0000R0000ol0000[00006P02ohL00_l^00006P000ol000250003 o`0002h0000J0003o`0008@000?o0000;`0001X000?o0000P`000ol0000`00006P000ol0002100;o <`0001X00_n10003o`0003<0000J0003o`0007l000?o0000=00001X000?o0000OP000ol0000e0000 6P000ol0001m0003o`0003H0000J0003o`0007/00_li00006P000ol0001j0003o`0003T0000J00;o NP000ol0000j00006P000ol0001h0003o`0003/0000J0003o`0007H00_ln00006P000ol0001e0003 o`0003h0000C00?o10000ol0001d0003o`0003l0000D0003o`0000<000?o0000L`000ol000100000 50000ol0000300;oL`000ol00011000050000ol000030003o`0007000_m4000050000ol000030003 o`0006l000?o0000A00001<00_l50003o`0006h000?o0000A@0001X000?o0000K@000ol000160000 6P02of`00_m900006P000ol0001Z0003o`0004T0000J0003o`0006T000?o0000BP0001X000?o0000 J0000ol0001;00006P000ol0001V00;oCP0001X000?o0000I@000ol0001>00006P02ofD000?o0000 C`0001X000?o0000H`000ol0001@00006P000ol0001R0003o`000540000J0003o`0006000_mD0000 6P000ol0001O0003o`0005@0000J0003o`0005h000?o0000E@0001X00_mN0003o`0005H0000J0003 o`0005/00_mI00006P000ol0001J0003o`0005T0000J0003o`0005T000?o0000FP0001X000?o0000 F0000ol0001K00006P000ol0001G0003o`0005`0000J00;oEP02oel0000J0003o`0005@000?o0000 G`0001X000?o0000D`000ol0001P00001`03o`@00_l300?o10000ol0001B0003o`00064000080003 o`0000<00_l60005o`000?l0DP02of@000080003o`0000/000Co00000_m?00;oIP0000P000?o0000 2003o`@000?o0000C@000ol0001V000020000ol000080003o`0000@000?o0000B`02ofT0000700;o 2P04o`<000?o0000B@02of/0000J0003o`0004P000?o0000J`0001X000?o0000AP02ofh0000J00;o A@02og00000J0003o`0004<000?o0000L00001X000?o0000@@02og<0000J0003o`0003l00_me0000 6P000ol0000n0003o`0007D0000J0003o`0003`00_mh00006P02oc/00_mj00006P000ol0000g00?o O00001X000?o0000=@02ogl0000J0003o`0003<00_n100006P000ol0000a00;oP`0001X00_l`00;o Q@0001X000?o0000;003ohL0000J0003o`0002X00_n:00006P000ol0000X00;oS00001X000?o0000 9@03ohh0000J0003o`0002800onA00006P02ob000onD00006P000ol0000M00;oU`0001X000?o0000 6P03oiT0000J0003o`0001D01OnL00004`04o`<000?o00004005oj40000D0003o`0000<000?o0000 100"], ImageRangeCache->{{{0, 210}, {245, 0}} -> {-0.462034, -1.98419, 0.0175329, 0.0175329}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]],x[0] == 0, y[0] == 1.999999518}, {x[t],y[t]},{t,0,20}]]],{t,0,20},AspectRatio->Automatic]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .62802 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.299057 0.0149529 0.299057 [ [.17334 .00245 -9 -9 ] [.17334 .00245 9 0 ] [.32287 .00245 -3 -9 ] [.32287 .00245 3 0 ] [.4724 .00245 -9 -9 ] [.4724 .00245 9 0 ] [.62192 .00245 -3 -9 ] [.62192 .00245 3 0 ] [.77145 .00245 -9 -9 ] [.77145 .00245 9 0 ] [.92098 .00245 -3 -9 ] [.92098 .00245 3 0 ] [.01131 .16448 -18 -4.5 ] [.01131 .16448 0 4.5 ] [.01131 .31401 -6 -4.5 ] [.01131 .31401 0 4.5 ] [.01131 .46354 -18 -4.5 ] [.01131 .46354 0 4.5 ] [.01131 .61307 -6 -4.5 ] [.01131 .61307 0 4.5 ] [ 0 0 0 0 ] [ 1 .62802 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17334 .01495 m .17334 .0212 L s [(0.5)] .17334 .00245 0 1 Mshowa .32287 .01495 m .32287 .0212 L s [(1)] .32287 .00245 0 1 Mshowa .4724 .01495 m .4724 .0212 L s [(1.5)] .4724 .00245 0 1 Mshowa .62192 .01495 m .62192 .0212 L s [(2)] .62192 .00245 0 1 Mshowa .77145 .01495 m .77145 .0212 L s [(2.5)] .77145 .00245 0 1 Mshowa .92098 .01495 m .92098 .0212 L s [(3)] .92098 .00245 0 1 Mshowa .125 Mabswid .05372 .01495 m .05372 .0187 L s .08362 .01495 m .08362 .0187 L s .11353 .01495 m .11353 .0187 L s .14343 .01495 m .14343 .0187 L s .20324 .01495 m .20324 .0187 L s .23315 .01495 m .23315 .0187 L s .26306 .01495 m .26306 .0187 L s .29296 .01495 m .29296 .0187 L s .35277 .01495 m .35277 .0187 L s .38268 .01495 m .38268 .0187 L s .41258 .01495 m .41258 .0187 L s .44249 .01495 m .44249 .0187 L s .5023 .01495 m .5023 .0187 L s .53221 .01495 m .53221 .0187 L s .56211 .01495 m .56211 .0187 L s .59202 .01495 m .59202 .0187 L s .65183 .01495 m .65183 .0187 L s .68174 .01495 m .68174 .0187 L s .71164 .01495 m .71164 .0187 L s .74155 .01495 m .74155 .0187 L s .80136 .01495 m .80136 .0187 L s .83126 .01495 m .83126 .0187 L s .86117 .01495 m .86117 .0187 L s .89108 .01495 m .89108 .0187 L s .95089 .01495 m .95089 .0187 L s .98079 .01495 m .98079 .0187 L s .25 Mabswid 0 .01495 m 1 .01495 L s .02381 .16448 m .03006 .16448 L s [(0.5)] .01131 .16448 1 0 Mshowa .02381 .31401 m .03006 .31401 L s [(1)] .01131 .31401 1 0 Mshowa .02381 .46354 m .03006 .46354 L s [(1.5)] .01131 .46354 1 0 Mshowa .02381 .61307 m .03006 .61307 L s [(2)] .01131 .61307 1 0 Mshowa .125 Mabswid .02381 .04486 m .02756 .04486 L s .02381 .07476 m .02756 .07476 L s .02381 .10467 m .02756 .10467 L s .02381 .13458 m .02756 .13458 L s .02381 .19439 m .02756 .19439 L s .02381 .22429 m .02756 .22429 L s .02381 .2542 m .02756 .2542 L s .02381 .2841 m .02756 .2841 L s .02381 .34392 m .02756 .34392 L s .02381 .37382 m .02756 .37382 L s .02381 .40373 m .02756 .40373 L s .02381 .43363 m .02756 .43363 L s .02381 .49344 m .02756 .49344 L s .02381 .52335 m .02756 .52335 L s .02381 .55326 m .02756 .55326 L s .02381 .58316 m .02756 .58316 L s .25 Mabswid .02381 0 m .02381 .62802 L s 0 0 m 1 0 L 1 .62802 L 0 .62802 L closepath clip newpath .5 Mabswid .02381 .61307 m .03857 .61289 L .052 .6124 L .06748 .61147 L .08209 .61023 L .10797 .60716 L .13589 .6026 L .16635 .59616 L .19824 .58781 L .25413 .56927 L .35941 .52136 L .46322 .45879 L .74637 .22718 L .86939 .10851 L .92164 .0566 L .94578 .03249 L .95571 .02257 L .95991 .01837 L .96187 .01641 L .96269 .01559 L .96306 .01522 L .96321 .01507 L .96328 .015 L .96331 .01498 L .96331 .01497 L .96332 .01497 L .96332 .01497 L .96332 .01497 L .96332 .01496 L .96332 .01496 L .96332 .01496 L .96332 .01496 L .96332 .01496 L .96332 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01496 L .96333 .01497 L .96333 .01497 L Mistroke .96334 .01497 L .96336 .01499 L .96342 .01504 L .96353 .01516 L .96382 .01545 L .96448 .01611 L .96592 .01755 L .96948 .02111 L .97619 .02782 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{199, 124}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc00005@000ol0002M0003o`0000l0 000E00;oW@000ol0000@00005@000ol0002K0003o`000140000E0003o`0009X000?o00004P0001D0 00?o0000V@000ol0000C00005@000ol0002H0003o`0001@0000E0003o`0009L000?o00005@0001D0 0_nG0003o`0001H0000E0003o`0009@00_lI00005@000ol0002C0003o`0001T0000E0003o`000980 00?o00006P0001D000?o0000T@000ol0000K00005@02oi4000?o0000700001D000?o0000S`000ol0 000M00005@000ol0002>0003o`0001h0000E0003o`0008d000?o00007`0000<00_l400;o0`03o`@0 00?o0000S0000ol0000P00000P001?l00?l300;o1P001Ol0003o08d000?o00008@00008000Co003o 2`001?l00002oh/000?o00008P00008000Co003o2003o`@000?o0000R@000ol0000S00000P001?l0 0?l80003o`0000@000?o0000R0000ol0000T00000`02o`T01?l30003o`0008L000?o00009@0001D0 00?o0000QP000ol0000V00005@02ohH000?o00009`0001D000?o0000Q0000ol0000X00005@000ol0 00230003o`0002T0000E0003o`00088000?o0000:P0001D000?o0000P@000ol0000[00005@02oh40 00?o0000;00001D000?o0000OP02obl0000E0003o`0007d000?o0000;`0001D000?o0000O0000ol0 000`00005@000ol0001k0003o`000340000E0003o`0007T00_ld00005@02ogT000?o0000=00001D0 00?o0000M`000ol0000e00005@000ol0001f0003o`0003H0000E0003o`0007@00_li00005@000ol0 001c0003o`0003T0000E00;oL`000ol0000j00005@000ol0001a0003o`0003/0000E0003o`0006l0 0_ln00003P03o`@000?o0000KP000ol0000n00003`000ol000030003o`0006d000?o0000?`0000l0 00?o00000`02ofd000?o0000@00000l000?o00000`000ol0001Z00;o@`0000l000?o00000`000ol0 001Y0003o`0004<0000>00;o1@000ol0001X0003o`0004@0000E0003o`0006L000?o0000A@0001D0 00?o0000I@02odP0000E00;oI@000ol0001800005@000ol0001S0003o`0004T0000E0003o`000680 00?o0000BP0001D000?o0000H@000ol0001;00005@000ol0001O00;oCP0001D00_mO0003o`0004h0 000E0003o`0005d000?o0000C`0001D000?o0000G0000ol0001@00005@000ol0001J00;oD`0001D0 00?o0000F@000ol0001C00005@02oeT000?o0000E00001D000?o0000E`000ol0001E00005@000ol0 001E00;oF00001D000?o0000E0000ol0001H00005@000ol0001C0003o`0005T0000E0003o`000580 00?o0000FP0001D00_mA00;oG@0001D000?o0000C`000ol0001M00005@000ol0001>0003o`0005h0 000200?o1002o`<00ol40003o`0004d000?o0000G`0000<000?o00000`02o`H000Go0000o`1=00;o HP0000<000?o00002`001?l00002od/000?o0000HP0000<000?o00002003o`@000?o0000B002ofD0 00030003o`0000P000?o000010000ol0001600;oI`0000800_l:00Co0`000ol000150003o`0006L0 000E0003o`0004<00_mZ00005@000ol000120003o`0006X0000E00;o@@02ofd0000E0003o`0003l0 00?o0000K@0001D000?o0000?@02og00000E0003o`0003/00_mb00005@000ol0000j0003o`000780 000E00;o>@02ogD0000E0003o`0003D00omg00005@000ol0000c00;oNP0001D000?o0000<@02og`0 000E0003o`0002h00omn00005@02obd00_n100005@000ol0000Z00;oP`0001D000?o00009`03ohD0 000E0003o`0002@00on800005@000ol0000Q00?oR`0001D000?o00007P03ohh0000E00;o7003oi40 000E0003o`0001P00onD00005@000ol0000D00CoU`0000h01?l30003o`0000l01OnK00003`000ol0 00030003o`0000L02?nP000040000ol0000200[oZ000014000Go0000o`2a00003P001?l00?l30003 o`000:l0000?00;o10000ol0002_0000a`000001\ \>"], ImageRangeCache->{{{0, 198}, {123, 0}} -> {-0.402652, -0.20964, 0.0186469, 0.0186469}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "It looks like an initial velocity of ", StyleBox["1.999999518", FontFamily->"Courier", FontWeight->"Bold"], " is close to the critical value. Of course, numerical methods are being \ used, so we should be skeptical of any such numbers until we make a closer \ analysis of the error." }], "Text"], Cell[TextData[{ StyleBox["b)", FontSlant->"Italic"], " The system for the damped system is deriveed as in part ", StyleBox["a", FontSlant->"Italic"], ":\n\n", StyleBox[ " x'[t] == y[t], x[0] == 0\n y'[t] == -Sin[x[t]] - \ 0.5 y[t], y[0] == b", FontFamily->"Courier", FontWeight->"Bold"] }], "Text"], Cell[CellGroupData[{ Cell["\<\ PlotVectorField[{y,-Sin[x]-0.5y},{x,-2,10},{y,-2,6}, ScaleFunction->(Log[50#+1]&), Frame->True]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .6218 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.197501 0.0740242 0.162853 0.0740242 [ [.04945 -0.0125 -6 -9 ] [.04945 -0.0125 6 0 ] [.1975 -0.0125 -3 -9 ] [.1975 -0.0125 3 0 ] [.34555 -0.0125 -3 -9 ] [.34555 -0.0125 3 0 ] [.4936 -0.0125 -3 -9 ] [.4936 -0.0125 3 0 ] [.64165 -0.0125 -3 -9 ] [.64165 -0.0125 3 0 ] [.7897 -0.0125 -3 -9 ] [.7897 -0.0125 3 0 ] [.93774 -0.0125 -6 -9 ] [.93774 -0.0125 6 0 ] [ 0 0 -0.125 0 ] [-0.0125 .0148 -12 -4.5 ] [-0.0125 .0148 0 4.5 ] [-0.0125 .16285 -6 -4.5 ] [-0.0125 .16285 0 4.5 ] [-0.0125 .3109 -6 -4.5 ] [-0.0125 .3109 0 4.5 ] [-0.0125 .45895 -6 -4.5 ] [-0.0125 .45895 0 4.5 ] [-0.0125 .607 -6 -4.5 ] [-0.0125 .607 0 4.5 ] [ 0 0 -0.125 0 ] [ 0 .6218 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 .6218 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .04945 0 m .04945 .00625 L s [(-2)] .04945 -0.0125 0 1 Mshowa .1975 0 m .1975 .00625 L s [(0)] .1975 -0.0125 0 1 Mshowa .34555 0 m .34555 .00625 L s [(2)] .34555 -0.0125 0 1 Mshowa .4936 0 m .4936 .00625 L s [(4)] .4936 -0.0125 0 1 Mshowa .64165 0 m .64165 .00625 L s [(6)] .64165 -0.0125 0 1 Mshowa .7897 0 m .7897 .00625 L s [(8)] .7897 -0.0125 0 1 Mshowa .93774 0 m .93774 .00625 L s [(10)] .93774 -0.0125 0 1 Mshowa .125 Mabswid .08647 0 m .08647 .00375 L s .12348 0 m .12348 .00375 L s .16049 0 m .16049 .00375 L s .23451 0 m .23451 .00375 L s .27153 0 m .27153 .00375 L s .30854 0 m .30854 .00375 L s .38256 0 m .38256 .00375 L s .41957 0 m .41957 .00375 L s .45659 0 m .45659 .00375 L s .53061 0 m .53061 .00375 L s .56762 0 m .56762 .00375 L s .60463 0 m .60463 .00375 L s .67866 0 m .67866 .00375 L s .71567 0 m .71567 .00375 L s .75268 0 m .75268 .00375 L s .82671 0 m .82671 .00375 L s .86372 0 m .86372 .00375 L s .90073 0 m .90073 .00375 L s .01244 0 m .01244 .00375 L s .97476 0 m .97476 .00375 L s .25 Mabswid 0 0 m 1 0 L s 0 .0148 m .00625 .0148 L s [(-2)] -0.0125 .0148 1 0 Mshowa 0 .16285 m .00625 .16285 L s [(0)] -0.0125 .16285 1 0 Mshowa 0 .3109 m .00625 .3109 L s [(2)] -0.0125 .3109 1 0 Mshowa 0 .45895 m .00625 .45895 L s [(4)] -0.0125 .45895 1 0 Mshowa 0 .607 m .00625 .607 L s [(6)] -0.0125 .607 1 0 Mshowa .125 Mabswid 0 .05182 m .00375 .05182 L s 0 .08883 m .00375 .08883 L s 0 .12584 m .00375 .12584 L s 0 .19987 m .00375 .19987 L s 0 .23688 m .00375 .23688 L s 0 .27389 m .00375 .27389 L s 0 .34791 m .00375 .34791 L s 0 .38493 m .00375 .38493 L s 0 .42194 m .00375 .42194 L s 0 .49596 m .00375 .49596 L s 0 .53297 m .00375 .53297 L s 0 .56999 m .00375 .56999 L s .25 Mabswid 0 0 m 0 .6218 L s .04945 .61555 m .04945 .6218 L s .1975 .61555 m .1975 .6218 L s .34555 .61555 m .34555 .6218 L s .4936 .61555 m .4936 .6218 L s .64165 .61555 m .64165 .6218 L s .7897 .61555 m .7897 .6218 L s .93774 .61555 m .93774 .6218 L s .125 Mabswid .08647 .61805 m .08647 .6218 L s .12348 .61805 m .12348 .6218 L s .16049 .61805 m .16049 .6218 L s .23451 .61805 m .23451 .6218 L s .27153 .61805 m .27153 .6218 L s .30854 .61805 m .30854 .6218 L s .38256 .61805 m .38256 .6218 L s .41957 .61805 m .41957 .6218 L s .45659 .61805 m .45659 .6218 L s .53061 .61805 m .53061 .6218 L s .56762 .61805 m .56762 .6218 L s .60463 .61805 m .60463 .6218 L s .67866 .61805 m .67866 .6218 L s .71567 .61805 m .71567 .6218 L s .75268 .61805 m .75268 .6218 L s .82671 .61805 m .82671 .6218 L s .86372 .61805 m .86372 .6218 L s .90073 .61805 m .90073 .6218 L s .01244 .61805 m .01244 .6218 L s .97476 .61805 m .97476 .6218 L s .25 Mabswid 0 .6218 m 1 .6218 L s .99375 .0148 m 1 .0148 L s .99375 .16285 m 1 .16285 L s .99375 .3109 m 1 .3109 L s .99375 .45895 m 1 .45895 L s .99375 .607 m 1 .607 L s .125 Mabswid .99625 .05182 m 1 .05182 L s .99625 .08883 m 1 .08883 L s .99625 .12584 m 1 .12584 L s .99625 .19987 m 1 .19987 L s .99625 .23688 m 1 .23688 L s .99625 .27389 m 1 .27389 L s .99625 .34791 m 1 .34791 L s .99625 .38493 m 1 .38493 L s .99625 .42194 m 1 .42194 L s .99625 .49596 m 1 .49596 L s .99625 .53297 m 1 .53297 L s .99625 .56999 m 1 .56999 L s .25 Mabswid 1 0 m 1 .6218 L s % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto fill -0.02 0.005 moveto 0 0 lineto -0.02 -0.005 lineto -0.02 0.005 lineto stroke } ifelse grestore } def % End of user PostScript .0001 w .04945 .0148 m .02381 .03929 L s % Start of user PostScript -2. -2. -2.34642 -1.66929 MAarrowhead1 % End of user PostScript .04945 .0571 m .02719 .08241 L s % Start of user PostScript -2. -1.42857 -2.30075 -1.08677 MAarrowhead1 % End of user PostScript .04945 .0994 m .03245 .12594 L s % Start of user PostScript -2. -0.857143 -2.22964 -0.498704 MAarrowhead1 % End of user PostScript .04945 .1417 m .04189 .16954 L s % Start of user PostScript -2. -0.285714 -2.10213 0.0903688 MAarrowhead1 % End of user PostScript .04945 .184 m .05882 .20914 L s % Start of user PostScript -2. 0.285714 -1.87341 0.62529 MAarrowhead1 % End of user PostScript .04945 .2263 m .07398 .24006 L s % Start of user PostScript -2. 0.857143 -1.66872 1.04294 MAarrowhead1 % End of user PostScript .04945 .2686 m .07999 .27277 L s % Start of user PostScript -2. 1.42857 -1.58743 1.48489 MAarrowhead1 % End of user PostScript .04945 .3109 m .08257 .3094 L s % Start of user PostScript -2. 2. -1.55259 1.97971 MAarrowhead1 % End of user PostScript .04945 .3532 m .08409 .34813 L s % Start of user PostScript -2. 2.57143 -1.53203 2.50292 MAarrowhead1 % End of user PostScript .04945 .3955 m .08519 .38797 L s % Start of user PostScript -2. 3.14286 -1.51723 3.04115 MAarrowhead1 % End of user PostScript .04945 .4378 m .08606 .42846 L s % Start of user PostScript -2. 3.71429 -1.50542 3.58807 MAarrowhead1 % End of user PostScript .04945 .4801 m .0868 .46935 L s % Start of user PostScript -2. 4.28571 -1.49544 4.14049 MAarrowhead1 % End of user PostScript .04945 .5224 m .08745 .51051 L s % Start of user PostScript -2. 4.85714 -1.48672 4.69659 MAarrowhead1 % End of user PostScript .04945 .5647 m .08802 .55187 L s % Start of user PostScript -2. 5.42857 -1.47894 5.25532 MAarrowhead1 % End of user PostScript .04945 .607 m .08855 .59338 L s % Start of user PostScript -2. 6. -1.47188 5.81598 MAarrowhead1 % End of user PostScript .1129 .0148 m .08726 .03929 L s % Start of user PostScript -1.14286 -2. -1.48924 -1.66923 MAarrowhead1 % End of user PostScript .1129 .0571 m .09064 .08241 L s % Start of user PostScript -1.14286 -1.42857 -1.44356 -1.0867 MAarrowhead1 % End of user PostScript .1129 .0994 m .09591 .12594 L s % Start of user PostScript -1.14286 -0.857143 -1.37245 -0.49864 MAarrowhead1 % End of user PostScript .1129 .1417 m .10535 .16955 L s % Start of user PostScript -1.14286 -0.285714 -1.24495 0.0904244 MAarrowhead1 % End of user PostScript .1129 .184 m .12227 .20915 L s % Start of user PostScript -1.14286 0.285714 -1.01633 0.625372 MAarrowhead1 % End of user PostScript .1129 .2263 m .13742 .24007 L s % Start of user PostScript -1.14286 0.857143 -0.811646 1.0431 MAarrowhead1 % End of user PostScript .1129 .2686 m .14344 .27278 L s % Start of user PostScript -1.14286 1.42857 -0.730306 1.48504 MAarrowhead1 % End of user PostScript .1129 .3109 m .14602 .30941 L s % Start of user PostScript -1.14286 2. -0.695443 1.97983 MAarrowhead1 % End of user PostScript .1129 .3532 m .14754 .34814 L s % Start of user PostScript -1.14286 2.57143 -0.674872 2.50302 MAarrowhead1 % End of user PostScript .1129 .3955 m .14864 .38798 L s % Start of user PostScript -1.14286 3.14286 -0.660074 3.04123 MAarrowhead1 % End of user PostScript .1129 .4378 m .14951 .42846 L s % Start of user PostScript -1.14286 3.71429 -0.648261 3.58814 MAarrowhead1 % End of user PostScript .1129 .4801 m .15025 .46935 L s % Start of user PostScript -1.14286 4.28571 -0.638282 4.14054 MAarrowhead1 % End of user PostScript .1129 .5224 m .1509 .51052 L s % Start of user PostScript -1.14286 4.85714 -0.629564 4.69664 MAarrowhead1 % End of user PostScript .1129 .5647 m .15147 .55188 L s % Start of user PostScript -1.14286 5.42857 -0.621782 5.25537 MAarrowhead1 % End of user PostScript .1129 .607 m .152 .59338 L s % Start of user PostScript -1.14286 6. -0.614728 5.81602 MAarrowhead1 % End of user PostScript .17635 .0148 m .14741 .03335 L s % Start of user PostScript -0.285714 -2. -0.676629 -1.74945 MAarrowhead1 % End of user PostScript .17635 .0571 m .14997 .0755 L s % Start of user PostScript -0.285714 -1.42857 -0.642116 -1.18006 MAarrowhead1 % End of user PostScript .17635 .0994 m .15403 .11791 L s % Start of user PostScript -0.285714 -0.857143 -0.58729 -0.607192 MAarrowhead1 % End of user PostScript .17635 .1417 m .1632 .16125 L s % Start of user PostScript -0.285714 -0.285714 -0.463384 -0.0216178 MAarrowhead1 % End of user PostScript .17635 .184 m .19461 .19288 L s % Start of user PostScript -0.285714 0.285714 -0.0391092 0.405675 MAarrowhead1 % End of user PostScript .17635 .2263 m .20322 .2217 L s % Start of user PostScript -0.285714 0.857143 0.0772126 0.795016 MAarrowhead1 % End of user PostScript .17635 .2686 m .20609 .2596 L s % Start of user PostScript -0.285714 1.42857 0.115989 1.30697 MAarrowhead1 % End of user PostScript .17635 .3109 m .20795 .29955 L s % Start of user PostScript -0.285714 2. 0.141196 1.84671 MAarrowhead1 % End of user PostScript .17635 .3532 m .20937 .34031 L s % Start of user PostScript -0.285714 2.57143 0.160275 2.39732 MAarrowhead1 % End of user PostScript .17635 .3955 m .21051 .38149 L s % Start of user PostScript -0.285714 3.14286 0.175728 2.95352 MAarrowhead1 % End of user PostScript .17635 .4378 m .21147 .4229 L s % Start of user PostScript -0.285714 3.71429 0.188748 3.51306 MAarrowhead1 % End of user PostScript .17635 .4801 m .21231 .46449 L s % Start of user PostScript -0.285714 4.28571 0.200013 4.07479 MAarrowhead1 % End of user PostScript .17635 .5224 m .21304 .50618 L s % Start of user PostScript -0.285714 4.85714 0.209947 4.63807 MAarrowhead1 % End of user PostScript .17635 .5647 m .2137 .54796 L s % Start of user PostScript -0.285714 5.42857 0.218837 5.20249 MAarrowhead1 % End of user PostScript .17635 .607 m .2143 .58981 L s % Start of user PostScript -0.285714 6. 0.226884 5.76778 MAarrowhead1 % End of user PostScript .2398 .0148 m .20732 .02226 L s % Start of user PostScript 0.571429 -2. 0.132606 -1.89925 MAarrowhead1 % End of user PostScript .2398 .0571 m .20922 .06082 L s % Start of user PostScript 0.571429 -1.42857 0.158253 -1.37841 MAarrowhead1 % End of user PostScript .2398 .0994 m .21282 .09587 L s % Start of user PostScript 0.571429 -0.857143 0.206899 -0.904886 MAarrowhead1 % End of user PostScript .2398 .1417 m .22624 .12281 L s % Start of user PostScript 0.571429 -0.285714 0.388185 -0.540958 MAarrowhead1 % End of user PostScript .2398 .184 m .24988 .15989 L s % Start of user PostScript 0.571429 0.285714 0.707561 -0.0400395 MAarrowhead1 % End of user PostScript .2398 .2263 m .25971 .20378 L s % Start of user PostScript 0.571429 0.857143 0.840395 0.55295 MAarrowhead1 % End of user PostScript .2398 .2686 m .26443 .24696 L s % Start of user PostScript 0.571429 1.42857 0.904173 1.13623 MAarrowhead1 % End of user PostScript .2398 .3109 m .26737 .28966 L s % Start of user PostScript 0.571429 2. 0.943887 1.71305 MAarrowhead1 % End of user PostScript .2398 .3532 m .26947 .33213 L s % Start of user PostScript 0.571429 2.57143 0.972225 2.28673 MAarrowhead1 % End of user PostScript .2398 .3955 m .27109 .37447 L s % Start of user PostScript 0.571429 3.14286 0.994092 2.85879 MAarrowhead1 % End of user PostScript .2398 .4378 m .2724 .41675 L s % Start of user PostScript 0.571429 3.71429 1.01183 3.42996 MAarrowhead1 % End of user PostScript .2398 .4801 m .2735 .459 L s % Start of user PostScript 0.571429 4.28571 1.02671 4.00062 MAarrowhead1 % End of user PostScript .2398 .5224 m .27445 .50122 L s % Start of user PostScript 0.571429 4.85714 1.03952 4.57097 MAarrowhead1 % End of user PostScript .2398 .5647 m .27528 .54342 L s % Start of user PostScript 0.571429 5.42857 1.05075 5.14116 MAarrowhead1 % End of user PostScript .2398 .607 m .27602 .58562 L s % Start of user PostScript 0.571429 6. 1.06075 5.71123 MAarrowhead1 % End of user PostScript .30325 .0148 m .2701 .01497 L s % Start of user PostScript 1.42857 -2. 0.980805 -1.99774 MAarrowhead1 % End of user PostScript .30325 .0571 m .27292 .05125 L s % Start of user PostScript 1.42857 -1.42857 1.01887 -1.50762 MAarrowhead1 % End of user PostScript .30325 .0994 m .27948 .08384 L s % Start of user PostScript 1.42857 -0.857143 1.10751 -1.0674 MAarrowhead1 % End of user PostScript .30325 .1417 m .29448 .11569 L s % Start of user PostScript 1.42857 -0.285714 1.31005 -0.637087 MAarrowhead1 % End of user PostScript .30325 .184 m .31042 .15556 L s % Start of user PostScript 1.42857 0.285714 1.52549 -0.0985397 MAarrowhead1 % End of user PostScript .30325 .2263 m .3197 .19908 L s % Start of user PostScript 1.42857 0.857143 1.65082 0.489342 MAarrowhead1 % End of user PostScript .30325 .2686 m .32503 .24262 L s % Start of user PostScript 1.42857 1.42857 1.72277 1.07761 MAarrowhead1 % End of user PostScript .30325 .3109 m .32848 .2858 L s % Start of user PostScript 1.42857 2. 1.76946 1.66083 MAarrowhead1 % End of user PostScript .30325 .3532 m .33096 .32868 L s % Start of user PostScript 1.42857 2.57143 1.80286 2.24019 MAarrowhead1 % End of user PostScript .30325 .3955 m .33285 .37138 L s % Start of user PostScript 1.42857 3.14286 1.82844 2.81698 MAarrowhead1 % End of user PostScript .30325 .4378 m .33437 .41395 L s % Start of user PostScript 1.42857 3.71429 1.84898 3.39204 MAarrowhead1 % End of user PostScript .30325 .4801 m .33563 .45643 L s % Start of user PostScript 1.42857 4.28571 1.86604 3.96594 MAarrowhead1 % End of user PostScript .30325 .5224 m .33671 .49885 L s % Start of user PostScript 1.42857 4.85714 1.88058 4.53901 MAarrowhead1 % End of user PostScript .30325 .5647 m .33765 .54123 L s % Start of user PostScript 1.42857 5.42857 1.89323 5.11151 MAarrowhead1 % End of user PostScript .30325 .607 m .33847 .58358 L s % Start of user PostScript 1.42857 6. 1.9044 5.68358 MAarrowhead1 % End of user PostScript .3667 .0148 m .33375 .01884 L s % Start of user PostScript 2.28571 -2. 1.84055 -1.9455 MAarrowhead1 % End of user PostScript .3667 .0571 m .33595 .05622 L s % Start of user PostScript 2.28571 -1.42857 1.87034 -1.44045 MAarrowhead1 % End of user PostScript .3667 .0994 m .34088 .08957 L s % Start of user PostScript 2.28571 -0.857143 1.93691 -0.99004 MAarrowhead1 % End of user PostScript .3667 .1417 m .35592 .1186 L s % Start of user PostScript 2.28571 -0.285714 2.1401 -0.59776 MAarrowhead1 % End of user PostScript .3667 .184 m .37513 .15749 L s % Start of user PostScript 2.28571 0.285714 2.39966 -0.0724279 MAarrowhead1 % End of user PostScript .3667 .2263 m .38483 .20126 L s % Start of user PostScript 2.28571 0.857143 2.53069 0.518835 MAarrowhead1 % End of user PostScript .3667 .2686 m .38993 .24471 L s % Start of user PostScript 2.28571 1.42857 2.59948 1.10584 MAarrowhead1 % End of user PostScript .3667 .3109 m .39314 .2877 L s % Start of user PostScript 2.28571 2. 2.64291 1.68654 MAarrowhead1 % End of user PostScript .3667 .3532 m .39543 .3304 L s % Start of user PostScript 2.28571 2.57143 2.67381 2.26341 MAarrowhead1 % End of user PostScript .3667 .3955 m .39718 .37294 L s % Start of user PostScript 2.28571 3.14286 2.69751 2.83802 MAarrowhead1 % End of user PostScript .3667 .4378 m .3986 .41537 L s % Start of user PostScript 2.28571 3.71429 2.71661 3.41124 MAarrowhead1 % End of user PostScript .3667 .4801 m .39978 .45773 L s % Start of user PostScript 2.28571 4.28571 2.73254 3.98357 MAarrowhead1 % End of user PostScript .3667 .5224 m .40079 .50006 L s % Start of user PostScript 2.28571 4.85714 2.74618 4.55532 MAarrowhead1 % End of user PostScript .3667 .5647 m .40167 .54235 L s % Start of user PostScript 2.28571 5.42857 2.75808 5.12668 MAarrowhead1 % End of user PostScript .3667 .607 m .40245 .58463 L s % Start of user PostScript 2.28571 6. 2.76864 5.69776 MAarrowhead1 % End of user PostScript .43015 .0148 m .3998 .03 L s % Start of user PostScript 3.14286 -2. 2.73285 -1.79474 MAarrowhead1 % End of user PostScript .43015 .0571 m .40194 .07123 L s % Start of user PostScript 3.14286 -1.42857 2.76176 -1.23769 MAarrowhead1 % End of user PostScript .43015 .0994 m .40517 .11193 L s % Start of user PostScript 3.14286 -0.857143 2.80542 -0.687929 MAarrowhead1 % End of user PostScript .43015 .1417 m .41198 .15087 L s % Start of user PostScript 3.14286 -0.285714 2.89743 -0.161913 MAarrowhead1 % End of user PostScript .43015 .184 m .44836 .17498 L s % Start of user PostScript 3.14286 0.285714 3.38887 0.163797 MAarrowhead1 % End of user PostScript .43015 .2263 m .45515 .21384 L s % Start of user PostScript 3.14286 0.857143 3.48059 0.688776 MAarrowhead1 % End of user PostScript .43015 .2686 m .45837 .25451 L s % Start of user PostScript 3.14286 1.42857 3.52416 1.23826 MAarrowhead1 % End of user PostScript .43015 .3109 m .46051 .29574 L s % Start of user PostScript 3.14286 2. 3.55303 1.79517 MAarrowhead1 % End of user PostScript .43015 .3532 m .46211 .33724 L s % Start of user PostScript 3.14286 2.57143 3.57465 2.35574 MAarrowhead1 % End of user PostScript .43015 .3955 m .46339 .37889 L s % Start of user PostScript 3.14286 3.14286 3.59195 2.91849 MAarrowhead1 % End of user PostScript .43015 .4378 m .46446 .42066 L s % Start of user PostScript 3.14286 3.71429 3.60636 3.48269 MAarrowhead1 % End of user PostScript .43015 .4801 m .46537 .4625 L s % Start of user PostScript 3.14286 4.28571 3.61872 4.04792 MAarrowhead1 % End of user PostScript .43015 .5224 m .46617 .5044 L s % Start of user PostScript 3.14286 4.85714 3.62954 4.61393 MAarrowhead1 % End of user PostScript .43015 .5647 m .46689 .54634 L s % Start of user PostScript 3.14286 5.42857 3.63915 5.18054 MAarrowhead1 % End of user PostScript .43015 .607 m .46753 .58832 L s % Start of user PostScript 3.14286 6. 3.64781 5.74763 MAarrowhead1 % End of user PostScript .4936 .0148 m .46717 .03802 L s % Start of user PostScript 4. -2. 3.64292 -1.68634 MAarrowhead1 % End of user PostScript .4936 .0571 m .47038 .08101 L s % Start of user PostScript 4. -1.42857 3.68638 -1.10562 MAarrowhead1 % End of user PostScript .4936 .0994 m .47548 .12446 L s % Start of user PostScript 4. -0.857143 3.7552 -0.518602 MAarrowhead1 % End of user PostScript .4936 .1417 m .48517 .16823 L s % Start of user PostScript 4. -0.285714 3.88619 0.0726399 MAarrowhead1 % End of user PostScript .4936 .184 m .50436 .20713 L s % Start of user PostScript 4. 0.285714 4.14538 0.5981 MAarrowhead1 % End of user PostScript .4936 .2263 m .51941 .23619 L s % Start of user PostScript 4. 0.857143 4.34864 0.99065 MAarrowhead1 % End of user PostScript .4936 .2686 m .52435 .26952 L s % Start of user PostScript 4. 1.42857 4.41537 1.44093 MAarrowhead1 % End of user PostScript .4936 .3109 m .52655 .30689 L s % Start of user PostScript 4. 2. 4.4452 1.94586 MAarrowhead1 % End of user PostScript .4936 .3532 m .52796 .34613 L s % Start of user PostScript 4. 2.57143 4.46422 2.47594 MAarrowhead1 % End of user PostScript .4936 .3955 m .52903 .38632 L s % Start of user PostScript 4. 3.14286 4.47859 3.01881 MAarrowhead1 % End of user PostScript .4936 .4378 m .5299 .42705 L s % Start of user PostScript 4. 3.71429 4.49038 3.56901 MAarrowhead1 % End of user PostScript .4936 .4801 m .53065 .46812 L s % Start of user PostScript 4. 4.28571 4.50048 4.12385 MAarrowhead1 % End of user PostScript .4936 .5224 m .5313 .50942 L s % Start of user PostScript 4. 4.85714 4.50938 4.68182 MAarrowhead1 % End of user PostScript .4936 .5647 m .53189 .55089 L s % Start of user PostScript 4. 5.42857 4.51735 5.24202 MAarrowhead1 % End of user PostScript .4936 .607 m .53243 .59248 L s % Start of user PostScript 4. 6. 4.52458 5.80388 MAarrowhead1 % End of user PostScript .55705 .0148 m .53181 .03991 L s % Start of user PostScript 4.85714 -2. 4.51623 -1.66087 MAarrowhead1 % End of user PostScript .55705 .0571 m .53527 .08308 L s % Start of user PostScript 4.85714 -1.42857 4.56291 -1.07765 MAarrowhead1 % End of user PostScript .55705 .0994 m .54059 .12663 L s % Start of user PostScript 4.85714 -0.857143 4.63486 -0.489383 MAarrowhead1 % End of user PostScript .55705 .1417 m .54987 .17015 L s % Start of user PostScript 4.85714 -0.285714 4.7602 0.0985046 MAarrowhead1 % End of user PostScript .55705 .184 m .56582 .21001 L s % Start of user PostScript 4.85714 0.285714 4.9757 0.637037 MAarrowhead1 % End of user PostScript .55705 .2263 m .58082 .24186 L s % Start of user PostScript 4.85714 0.857143 5.17825 1.0673 MAarrowhead1 % End of user PostScript .55705 .2686 m .58738 .27445 L s % Start of user PostScript 4.85714 1.42857 5.26686 1.50752 MAarrowhead1 % End of user PostScript .55705 .3109 m .59019 .31073 L s % Start of user PostScript 4.85714 2. 5.30491 1.99766 MAarrowhead1 % End of user PostScript .55705 .3532 m .5918 .3492 L s % Start of user PostScript 4.85714 2.57143 5.32661 2.51736 MAarrowhead1 % End of user PostScript .55705 .3955 m .59292 .38886 L s % Start of user PostScript 4.85714 3.14286 5.3418 3.05312 MAarrowhead1 % End of user PostScript .55705 .4378 m .59381 .42921 L s % Start of user PostScript 4.85714 3.71429 5.35373 3.59829 MAarrowhead1 % End of user PostScript .55705 .4801 m .59455 .47001 L s % Start of user PostScript 4.85714 4.28571 5.3637 4.1494 MAarrowhead1 % End of user PostScript .55705 .5224 m .59519 .5111 L s % Start of user PostScript 4.85714 4.85714 5.37236 4.7045 MAarrowhead1 % End of user PostScript .55705 .5647 m .59576 .5524 L s % Start of user PostScript 4.85714 5.42857 5.38008 5.26243 MAarrowhead1 % End of user PostScript .55705 .607 m .59627 .59385 L s % Start of user PostScript 4.85714 6. 5.38705 5.82244 MAarrowhead1 % End of user PostScript .6205 .0148 m .59291 .03603 L s % Start of user PostScript 5.71429 -2. 5.34167 -1.71333 MAarrowhead1 % End of user PostScript .6205 .0571 m .59585 .07872 L s % Start of user PostScript 5.71429 -1.42857 5.38135 -1.13655 MAarrowhead1 % End of user PostScript .6205 .0994 m .60057 .12189 L s % Start of user PostScript 5.71429 -0.857143 5.44507 -0.553331 MAarrowhead1 % End of user PostScript .6205 .1417 m .6104 .16579 L s % Start of user PostScript 5.71429 -0.285714 5.57789 0.0396569 MAarrowhead1 % End of user PostScript .6205 .184 m .6341 .20284 L s % Start of user PostScript 5.71429 0.285714 5.89799 0.540224 MAarrowhead1 % End of user PostScript .6205 .2263 m .64749 .22977 L s % Start of user PostScript 5.71429 0.857143 6.0789 0.903992 MAarrowhead1 % End of user PostScript .6205 .2686 m .65108 .26484 L s % Start of user PostScript 5.71429 1.42857 6.1274 1.3778 MAarrowhead1 % End of user PostScript .6205 .3109 m .65297 .30341 L s % Start of user PostScript 5.71429 2. 6.15303 1.89881 MAarrowhead1 % End of user PostScript .6205 .3532 m .65432 .34337 L s % Start of user PostScript 5.71429 2.57143 6.17124 2.43868 MAarrowhead1 % End of user PostScript .6205 .3955 m .65539 .38403 L s % Start of user PostScript 5.71429 3.14286 6.1857 2.98795 MAarrowhead1 % End of user PostScript .6205 .4378 m .65629 .42509 L s % Start of user PostScript 5.71429 3.71429 6.19784 3.54264 MAarrowhead1 % End of user PostScript .6205 .4801 m .65707 .46641 L s % Start of user PostScript 5.71429 4.28571 6.20834 4.10079 MAarrowhead1 % End of user PostScript .6205 .5224 m .65776 .5079 L s % Start of user PostScript 5.71429 4.85714 6.21763 4.6613 MAarrowhead1 % End of user PostScript .6205 .5647 m .65837 .54952 L s % Start of user PostScript 5.71429 5.42857 6.22597 5.22351 MAarrowhead1 % End of user PostScript .6205 .607 m .65893 .59123 L s % Start of user PostScript 5.71429 6. 6.23353 5.787 MAarrowhead1 % End of user PostScript .68395 .0148 m .65234 .02612 L s % Start of user PostScript 6.57143 -2. 6.14439 -1.84718 MAarrowhead1 % End of user PostScript .68395 .0571 m .6542 .06606 L s % Start of user PostScript 6.57143 -1.42857 6.16958 -1.30761 MAarrowhead1 % End of user PostScript .68395 .0994 m .65707 .10393 L s % Start of user PostScript 6.57143 -0.857143 6.20838 -0.796022 MAarrowhead1 % End of user PostScript .68395 .1417 m .66573 .13269 L s % Start of user PostScript 6.57143 -0.285714 6.32538 -0.407496 MAarrowhead1 % End of user PostScript .68395 .184 m .69706 .1644 L s % Start of user PostScript 6.57143 0.285714 6.74861 0.0208457 MAarrowhead1 % End of user PostScript .68395 .2263 m .70625 .20776 L s % Start of user PostScript 6.57143 0.857143 6.87269 0.606602 MAarrowhead1 % End of user PostScript .68395 .2686 m .71031 .25017 L s % Start of user PostScript 6.57143 1.42857 6.92761 1.17961 MAarrowhead1 % End of user PostScript .68395 .3109 m .71287 .29233 L s % Start of user PostScript 6.57143 2. 6.96217 1.74909 MAarrowhead1 % End of user PostScript .68395 .3532 m .71473 .33441 L s % Start of user PostScript 6.57143 2.57143 6.98725 2.31755 MAarrowhead1 % End of user PostScript .68395 .3955 m .71618 .37647 L s % Start of user PostScript 6.57143 3.14286 7.00689 2.88574 MAarrowhead1 % End of user PostScript .68395 .4378 m .71737 .41853 L s % Start of user PostScript 6.57143 3.71429 7.023 3.45394 MAarrowhead1 % End of user PostScript .68395 .4801 m .71838 .4606 L s % Start of user PostScript 6.57143 4.28571 7.03664 4.02225 MAarrowhead1 % End of user PostScript .68395 .5224 m .71926 .50268 L s % Start of user PostScript 6.57143 4.85714 7.04848 4.5907 MAarrowhead1 % End of user PostScript .68395 .5647 m .72003 .54477 L s % Start of user PostScript 6.57143 5.42857 7.05892 5.1593 MAarrowhead1 % End of user PostScript .68395 .607 m .72072 .58687 L s % Start of user PostScript 6.57143 6. 7.06826 5.72805 MAarrowhead1 % End of user PostScript .7474 .0148 m .71428 .01628 L s % Start of user PostScript 7.42857 -2. 6.98115 -1.98006 MAarrowhead1 % End of user PostScript .7474 .0571 m .71686 .0529 L s % Start of user PostScript 7.42857 -1.42857 7.01605 -1.48534 MAarrowhead1 % End of user PostScript .7474 .0994 m .72289 .08561 L s % Start of user PostScript 7.42857 -0.857143 7.09749 -1.04344 MAarrowhead1 % End of user PostScript .7474 .1417 m .73804 .11655 L s % Start of user PostScript 7.42857 -0.285714 7.30215 -0.625534 MAarrowhead1 % End of user PostScript .7474 .184 m .75495 .15615 L s % Start of user PostScript 7.42857 0.285714 7.53059 -0.0905352 MAarrowhead1 % End of user PostScript .7474 .2263 m .76438 .19976 L s % Start of user PostScript 7.42857 0.857143 7.65807 0.498514 MAarrowhead1 % End of user PostScript .7474 .2686 m .76965 .24329 L s % Start of user PostScript 7.42857 1.42857 7.72919 1.08658 MAarrowhead1 % End of user PostScript .7474 .3109 m .77303 .28641 L s % Start of user PostScript 7.42857 2. 7.77488 1.66912 MAarrowhead1 % End of user PostScript .7474 .3532 m .77544 .32924 L s % Start of user PostScript 7.42857 2.57143 7.80749 2.24775 MAarrowhead1 % End of user PostScript .7474 .3955 m .77729 .37189 L s % Start of user PostScript 7.42857 3.14286 7.83245 2.82386 MAarrowhead1 % End of user PostScript .7474 .4378 m .77878 .41441 L s % Start of user PostScript 7.42857 3.71429 7.85251 3.39835 MAarrowhead1 % End of user PostScript .7474 .4801 m .78001 .45686 L s % Start of user PostScript 7.42857 4.28571 7.8692 3.97175 MAarrowhead1 % End of user PostScript .7474 .5224 m .78107 .49925 L s % Start of user PostScript 7.42857 4.85714 7.88344 4.54441 MAarrowhead1 % End of user PostScript .7474 .5647 m .78198 .5416 L s % Start of user PostScript 7.42857 5.42857 7.89583 5.11654 MAarrowhead1 % End of user PostScript .7474 .607 m .7828 .58392 L s % Start of user PostScript 7.42857 6. 7.9068 5.68829 MAarrowhead1 % End of user PostScript .81084 .0148 m .77773 .01632 L s % Start of user PostScript 8.28571 -2. 7.83831 -1.97947 MAarrowhead1 % End of user PostScript .81084 .0571 m .7803 .05296 L s % Start of user PostScript 8.28571 -1.42857 7.87312 -1.48459 MAarrowhead1 % End of user PostScript .81084 .0994 m .78631 .08568 L s % Start of user PostScript 8.28571 -0.857143 7.95431 -1.0426 MAarrowhead1 % End of user PostScript .81084 .1417 m .80147 .11658 L s % Start of user PostScript 8.28571 -0.285714 8.15901 -0.625125 MAarrowhead1 % End of user PostScript .81084 .184 m .81841 .15617 L s % Start of user PostScript 8.28571 0.285714 8.38791 -0.0902569 MAarrowhead1 % End of user PostScript .81084 .2263 m .82785 .19978 L s % Start of user PostScript 8.28571 0.857143 8.51546 0.498831 MAarrowhead1 % End of user PostScript .81084 .2686 m .83311 .24331 L s % Start of user PostScript 8.28571 1.42857 8.58655 1.08689 MAarrowhead1 % End of user PostScript .81084 .3109 m .83649 .28643 L s % Start of user PostScript 8.28571 2. 8.63221 1.6694 MAarrowhead1 % End of user PostScript .81084 .3532 m .83891 .32926 L s % Start of user PostScript 8.28571 2.57143 8.66478 2.248 MAarrowhead1 % End of user PostScript .81084 .3955 m .84075 .3719 L s % Start of user PostScript 8.28571 3.14286 8.68973 2.8241 MAarrowhead1 % End of user PostScript .81084 .4378 m .84224 .41443 L s % Start of user PostScript 8.28571 3.71429 8.70977 3.39856 MAarrowhead1 % End of user PostScript .81084 .4801 m .84347 .45687 L s % Start of user PostScript 8.28571 4.28571 8.72644 3.97195 MAarrowhead1 % End of user PostScript .81084 .5224 m .84452 .49926 L s % Start of user PostScript 8.28571 4.85714 8.74067 4.54459 MAarrowhead1 % End of user PostScript .81084 .5647 m .84544 .54161 L s % Start of user PostScript 8.28571 5.42857 8.75306 5.11671 MAarrowhead1 % End of user PostScript .81084 .607 m .84625 .58394 L s % Start of user PostScript 8.28571 6. 8.76402 5.68845 MAarrowhead1 % End of user PostScript .87429 .0148 m .84271 .0262 L s % Start of user PostScript 9.14286 -2. 8.71614 -1.846 MAarrowhead1 % End of user PostScript .87429 .0571 m .84457 .06618 L s % Start of user PostScript 9.14286 -1.42857 8.74137 -1.30601 MAarrowhead1 % End of user PostScript .87429 .0994 m .84744 .10411 L s % Start of user PostScript 9.14286 -0.857143 8.78012 -0.793508 MAarrowhead1 % End of user PostScript .87429 .1417 m .85598 .13303 L s % Start of user PostScript 9.14286 -0.285714 8.89543 -0.40292 MAarrowhead1 % End of user PostScript .87429 .184 m .8875 .16454 L s % Start of user PostScript 9.14286 0.285714 9.32127 0.0227864 MAarrowhead1 % End of user PostScript .87429 .2263 m .89665 .20787 L s % Start of user PostScript 9.14286 0.857143 9.44491 0.60808 MAarrowhead1 % End of user PostScript .87429 .2686 m .9007 .25026 L s % Start of user PostScript 9.14286 1.42857 9.49959 1.18073 MAarrowhead1 % End of user PostScript .87429 .3109 m .90325 .2924 L s % Start of user PostScript 9.14286 2. 9.53403 1.75 MAarrowhead1 % End of user PostScript .87429 .3532 m .9051 .33446 L s % Start of user PostScript 9.14286 2.57143 9.55903 2.31832 MAarrowhead1 % End of user PostScript .87429 .3955 m .90655 .37652 L s % Start of user PostScript 9.14286 3.14286 9.57861 2.88641 MAarrowhead1 % End of user PostScript .87429 .4378 m .90774 .41857 L s % Start of user PostScript 9.14286 3.71429 9.59468 3.45453 MAarrowhead1 % End of user PostScript .87429 .4801 m .90875 .46064 L s % Start of user PostScript 9.14286 4.28571 9.6083 4.02278 MAarrowhead1 % End of user PostScript .87429 .5224 m .90962 .50271 L s % Start of user PostScript 9.14286 4.85714 9.62011 4.59118 MAarrowhead1 % End of user PostScript .87429 .5647 m .91039 .5448 L s % Start of user PostScript 9.14286 5.42857 9.63054 5.15974 MAarrowhead1 % End of user PostScript .87429 .607 m .91108 .5869 L s % Start of user PostScript 9.14286 6. 9.63986 5.72845 MAarrowhead1 % End of user PostScript .93774 .0148 m .91019 .03608 L s % Start of user PostScript 10. -2. 9.62777 -1.71263 MAarrowhead1 % End of user PostScript .93774 .0571 m .91313 .07878 L s % Start of user PostScript 10. -1.42857 9.66754 -1.13574 MAarrowhead1 % End of user PostScript .93774 .0994 m .91786 .12196 L s % Start of user PostScript 10. -0.857143 9.73141 -0.55238 MAarrowhead1 % End of user PostScript .93774 .1417 m .9277 .16586 L s % Start of user PostScript 10. -0.285714 9.86426 0.0406095 MAarrowhead1 % End of user PostScript .93774 .184 m .95126 .20298 L s % Start of user PostScript 10. 0.285714 10.1826 0.542048 MAarrowhead1 % End of user PostScript .93774 .2263 m .96472 .22994 L s % Start of user PostScript 10. 0.857143 10.3644 0.906224 MAarrowhead1 % End of user PostScript .93774 .2686 m .96833 .26496 L s % Start of user PostScript 10. 1.42857 10.4133 1.37932 MAarrowhead1 % End of user PostScript .93774 .3109 m .97024 .30349 L s % Start of user PostScript 10. 2. 10.4389 1.89993 MAarrowhead1 % End of user PostScript .93774 .3532 m .97158 .34344 L s % Start of user PostScript 10. 2.57143 10.4572 2.43957 MAarrowhead1 % End of user PostScript .93774 .3955 m .97265 .38409 L s % Start of user PostScript 10. 3.14286 10.4716 2.98869 MAarrowhead1 % End of user PostScript .93774 .4378 m .97355 .42514 L s % Start of user PostScript 10. 3.71429 10.4837 3.54327 MAarrowhead1 % End of user PostScript .93774 .4801 m .97433 .46645 L s % Start of user PostScript 10. 4.28571 10.4942 4.10134 MAarrowhead1 % End of user PostScript .93774 .5224 m .97501 .50794 L s % Start of user PostScript 10. 4.85714 10.5035 4.66179 MAarrowhead1 % End of user PostScript .93774 .5647 m .97563 .54955 L s % Start of user PostScript 10. 5.42857 10.5118 5.22395 MAarrowhead1 % End of user PostScript .93774 .607 m .97619 .59126 L s % Start of user PostScript 10. 6. 10.5194 5.7874 MAarrowhead1 % End of user PostScript 0 0 m 1 0 L 1 .6218 L 0 .6218 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{231, 143}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLcL0003W00007@04oaT00_lL00Co6`03oa`0 0_lM00;o6@03o`@00_l>00007P000ol0000H0004o`00oa`000?o000070000ol0000J0004o`00oa/0 00Co003o6@000ol000020004o`00o`d0000G00Go0`000ol0000G0004o`00oad000?o00006@04oa/0 00Co003o6`001?l00?lI0003o`00008000Co003o3@00020000?o00005P001?l00?lN0003o`0001P0 00?o0?l07003oad00_lJ0003o`00008000Co003o3@0001d000Co003o60001?l00?lK0004o`00oaX0 00?o0?l070000ol0000L0004o`00oaT000?o00000P001?l00?l=00007P02oaX00_lM00;o7002oad0 0olL00;o6@02o`D00_l>0000i`000>L0003W0000i`000180d?l500002P04o`@000Co003o1P000ol0 00050003o`0000D000?o000010000ol000050003o`0000D000?o000010000ol000050003o`0000D0 00?o000010000ol000050003o`0000D000?o000010000ol000050003o`0000D000?o000010000ol0 00050003o`0000D000?o000010000ol000050003o`0000D000?o00001@000ol000040003o`0000D0 00?o00001@000ol000040003o`00008000?o00000`0000/000?o000010000ol0000g00?o2`02od`0 0ol:00?o:@000ol0000300001005o`<000?o00000`02o`P000?o00002P000ol0000:00;o2005o`D0 2?l600Oo2`02o``000?o00002P02o`/00_l800;o00<0ool01@08o`D02?l90004o`3oo``00_l:00;o 1@0000d000?o00000P000ol000060003o`0000X000?o000020000ol0o`0800Co2`02o`P01Ol;00?o 2`000ol0o`0<0003o`0000T00_l900Co2P02o``00_l:00?o2`000ol0o`0=0003o`0000<0000:0004 o`00o`@000?o00001002o`/00_l;00;o2005oaP00_l:00Co2`02o``000?o00002P000ol0000700Go 8`04o`/00_l>0003o`0000<0000;00;o1@000ol0000400?o2P03o`T01?l_00;o3@04o`X00ol:00?o 1`03obD00_l=00Co3@000ol0000300004P000ol0000300;o2`02o`X00_m100;o2`02o`/00_m000;o 3`000ol0000300004P000ol000020003o`0000X000?o0000C0000ol0000:0003o`0000X000?o0000 ?`000ol0000?0003o`0000<0000B0003o`000<`000?o00000`00018000?o0000c0000ol000030000 4P02ob`00_l900Go2P03odX01Ol800Go:0000ol0000300004P000ol000070003o`0000X000?o0000 2P02o`H01ol800Go1P07o`T01?l<0003o`0000/000?o00002@02o`P00_l00`3oo`0800Go2005o`T0 1?l<00;o2`000ol0000300004P000ol000050003o`3o00X000?o0?l02P02o`L01_l<0003o`0000T0 0_l:00?o30000ol0o`0<0003o`0000P00_l900Co30000ol0000:0003o`0000L01?l<00;o3@000ol0 000300004P000ol0000500;o2`02o`X00ol`00Go2`02o`/00_l;00;o2005ob801Ol;00?o3@000ol0 000300004P000ol0000400?o2P03o`T00_la00?o3@03o`/00_l:0003o`0003h00_l?0003o`0000<0 000B0003o`0000@000?o00002P000ol000080003o`00044000?o00002P000ol000090003o`0003h0 00?o00003`000ol0000300004P000ol000030003o`0000X000?o00009002obH000?o00002P000ol0 001M0003o`0000<0000B0003o`0003L01?mH00?o2P03obT000?o00000`0001800_li00Co2005od/0 1?l900Co9`000ol0000300004P000ol0000Y00Go2`03o`X00olo00;o2`03o`X00ol;00;o6P000ol0 000300004P000ol000070003o`0000X000?o000020001?l0ool800Go2P000ol0o`0:0003o`3o00T0 1?l<0003o`0000/000?o00002P000ol0000500Ko2P000ol0o`0:0003o`3o00P01Ol<00;o2`000ol0 000300004P000ol0000500?o2P03o`X00_l<0003o`0002801?l;00?o2P02o`030?l000T00_l700Ko 8P05o`/00_l=0003o`0000<0000B0003o`0000D00ol:00?o2@04obl00_l>00?o2P03o`/00_lo00?o 30000ol0000300004P000ol0000500;o2`02o`X00_lJ0003o`0002@00_l;00;o2`000ol0000H0003 o`0000X000?o00005P02o`h000?o00000`00018000?o00001002o`/00_l:0003o`0001X000?o0000 2P000ol0000F00;o2`02o`/000?o00006@000ol0000:0003o`0001D000?o00003P000ol000030000 4P02o`D000?o00002P000ol0000H00;o3002o`/00_lG0003o`0000X000?o00009P02o`/00_lW0003 o`0000<0000B0003o`0002`00ol;00;o2`03odd000?o00002P02obH000?o00000`00018000?o0000 ;@03o`X00ol;00?o?003o`d00_l;00?o2003oaX000?o00000`00018000?o00001`000ol0000:0003 o`0000/000?o00002003o``000?o00002@02o`/00_l<0003o`0000/000?o00002P000ol0000800?o 2`02o`/00_l;00?o30000ol000090003o`0000<0000B0003o`0000L000?o00002P000ol0000900?o 2`000ol0000R00Go2`000ol0000;0003o`0000P00ol;0003o`0002D000?o00002@03o`/000?o0000 0`00018000?o00001P02o`/00_l;00?o;`03o`d00ol:00;o2`03ocl00ol;0003o`0000<0000;00;o 1@000ol0000600?o2P03o`X00_lK0003o`0002800ol:00?o2P03oa/000?o00002P000ol0000D00;o 30000ol0000300002P001?l00?l40003o`0000H00ol:00?o2@02oa0000?o00002@000ol0000;0003 o`0001@00_l;00?o2P02oa`000?o00002P000ol0000C00;o3@000ol0000300002P001?l00?l400;o 1`02o`/00_l:0003o`0000l000?o00002002o`d000?o00005002o`/00_l;0003o`0000h00_l:00;o 2`02o`d000?o00001@000ol0000;00;o1@0000X000Co003o10000ol000060003o`0000X000?o0000 6P02o`X00_l<00;o5P000ol0000:0003o`0001X00ol900;o3002o``00_lF0003o`0000<0000:0004 o`00o`@000?o0000;`02o`X00ol;00?o3003oc000ol900?o2`03o`/00olF0003o`0000<0000;00;o 1@000ol0000R0003o`0000T00ol;00;o3002o`X01?l`00Co2P02o`/000?o0?l02P03oaL000?o0000 0`00018000?o00001`000ol0000:0003o`0000/00_l;00;o2`000ol0000:0003o`0000X00ol:0003 o`0000/000?o00002P02o`/00_l;0003o`0000X000?o00002P000ol0o`0;00;o2P000ol000030000 4P000ol0000700?o2P03o`X01?lb0003o`0000T00ol;00;o2P03ocl00ol:0003o`0000<0000B0003 o`0000L00ol:00?o3@02ocd00ol:00?o3002ocl00_l:0003o`0000<0000B0003o`0000L00ol:00?o :0000ol0000R00;o2P03o`d000?o0000?P02o`T000?o00000`0001800_l900;o2`02oa/00_l:00;o 3@000ol0000E00;o2P02o`h000?o00005`02o``000?o00005P000ol000070003o`0000<0000B0003 o`0000T000?o00002P000ol0000H00?o2@03o``00_lH0003o`0000P00_lL00;o2004o`/00_l<00;o 50000ol0000300004P000ol0000`00?o2@03o``00_l<00?o5P000ol0000H00Co1`04o`/00_l;00Co 50000ol0000300004P000ol0000_00Co2P02o`/00ol:00Co<@04o`T00ol:00?o2P04oaD000?o0000 0`00018000?o00008`05o`P00_l;00;o2`02o`/00olU00;o2`03o`X00_l;00;o2`03o`/00_l90003 o`0000<0000B0003o`0000L00ol:00Co2P04o`T000?o00002P000ol0000:0003o`0000X000?o0?l0 2P04o`X00ol:00Go20000ol0o`0:0003o`0000X000?o00002P000ol0o`0;00Go1`000ol000030000 4P000ol0000900;o2`03o`X000?o0000?`04o`T00_l;00Go?@05o`H000?o00000`0001800_l900Co 2@05od/01Ol700CoE`000ol0000300004P000ol0000;00;o3002obD000?o0000<@02oeH000?o0000 0`00018000?o0000<`02o`X00_l<00;oC@02o`/00_lQ0003o`0000<0000B0003o`0003401?l900?o 2P04od000_l900Co2@04o``00_lC0003o`0000<0000B0003o`0003001?l900?o2P04o``00ol`00Co 2004o`T01?l;00?o50000ol0000300004P000ol0000S00Ko1`03o`/00_l;00?o2P04oc001?l:00;o 2`02o`/00olE0003o`0000<0000B0003o`0000X00_l;00;o2P04o`T00_l;0003o`0000X000?o0?l0 2P04o`/00ol:00;o2`05o`L000?o0?l02P000ol0000:0003o`0000X000?o0?l03005o`D000?o0000 0`00018000?o00001`07o`H01ol700?o2P000ol0000:0003o`0000X000?o00002P001?l00?l900So 1P06o`L01Ol80003o`0000X000?o00002P000ol0000:0003o`0000/01Ol70003o`0000<0000B00;o 2P06o`P01Om:00;o2`05o`P000?o0000?`000ol000070003o`0000<0000B0003o`000<`000?o0000 0`00018000?o0000@002oe/000?o0000;0000ol0000300004P000ol0000c00;o2P03o``00_m<00;o 3002ob0000?o00000`00018000?o0000L00000\ \>"], ImageRangeCache->{{{0, 230}, {142, 0}} -> {-3.87438, -2.95506, 0.0651282, 0.0651282}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell["\<\ solns = Table[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t], y'[t] == -Sin[x[t]] - 0.5 y[t], x[0] == 0, y[0] == b}, {x[t],y[t]}, {t,0,20}]], {b, 0.0, 6.0, 0.5}];\ \>", "Input"], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[solns],{t,0,20},PlotRange->{{-1,10},{-2,7}}]\ \ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0909091 0.0909091 0.137341 0.0686704 [ [.27273 .12484 -3 -9 ] [.27273 .12484 3 0 ] [.45455 .12484 -3 -9 ] [.45455 .12484 3 0 ] [.63636 .12484 -3 -9 ] [.63636 .12484 3 0 ] [.81818 .12484 -3 -9 ] [.81818 .12484 3 0 ] [1 .12484 -6 -9 ] [1 .12484 6 0 ] [.07841 0 -12 -4.5 ] [.07841 0 0 4.5 ] [.07841 .27468 -6 -4.5 ] [.07841 .27468 0 4.5 ] [.07841 .41202 -6 -4.5 ] [.07841 .41202 0 4.5 ] [.07841 .54936 -6 -4.5 ] [.07841 .54936 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .27273 .13734 m .27273 .14359 L s [(2)] .27273 .12484 0 1 Mshowa .45455 .13734 m .45455 .14359 L s [(4)] .45455 .12484 0 1 Mshowa .63636 .13734 m .63636 .14359 L s [(6)] .63636 .12484 0 1 Mshowa .81818 .13734 m .81818 .14359 L s [(8)] .81818 .12484 0 1 Mshowa 1 .13734 m 1 .14359 L s [(10)] 1 .12484 0 1 Mshowa .125 Mabswid .13636 .13734 m .13636 .14109 L s .18182 .13734 m .18182 .14109 L s .22727 .13734 m .22727 .14109 L s .31818 .13734 m .31818 .14109 L s .36364 .13734 m .36364 .14109 L s .40909 .13734 m .40909 .14109 L s .5 .13734 m .5 .14109 L s .54545 .13734 m .54545 .14109 L s .59091 .13734 m .59091 .14109 L s .68182 .13734 m .68182 .14109 L s .72727 .13734 m .72727 .14109 L s .77273 .13734 m .77273 .14109 L s .86364 .13734 m .86364 .14109 L s .90909 .13734 m .90909 .14109 L s .95455 .13734 m .95455 .14109 L s .04545 .13734 m .04545 .14109 L s .25 Mabswid 0 .13734 m 1 .13734 L s .09091 0 m .09716 0 L s [(-2)] .07841 0 1 0 Mshowa .09091 .27468 m .09716 .27468 L s [(2)] .07841 .27468 1 0 Mshowa .09091 .41202 m .09716 .41202 L s [(4)] .07841 .41202 1 0 Mshowa .09091 .54936 m .09716 .54936 L s [(6)] .07841 .54936 1 0 Mshowa .125 Mabswid .09091 .03434 m .09466 .03434 L s .09091 .06867 m .09466 .06867 L s .09091 .10301 m .09466 .10301 L s .09091 .17168 m .09466 .17168 L s .09091 .20601 m .09466 .20601 L s .09091 .24035 m .09466 .24035 L s .09091 .30902 m .09466 .30902 L s .09091 .34335 m .09466 .34335 L s .09091 .37769 m .09466 .37769 L s .09091 .44636 m .09466 .44636 L s .09091 .48069 m .09466 .48069 L s .09091 .51503 m .09466 .51503 L s .09091 .5837 m .09466 .5837 L s .25 Mabswid .09091 0 m .09091 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .09091 .13734 m .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L .09091 .13734 L s .09091 .17168 m .09904 .16802 L .10678 .16321 L .11337 .1576 L .11803 .15211 L .12004 .14894 L .1215 .14598 L .12245 .14337 L .12283 .14193 L .1231 .14062 L .1232 .13996 L .12328 .13925 L .12334 .13859 L .12337 .13799 L .12338 .13763 L .12338 .1373 L .12338 .13694 L .12337 .13656 L .12335 .1362 L .12332 .13587 L .12326 .13524 L .12317 .1346 L .12304 .13392 L .12276 .13275 L .12235 .13153 L .12181 .13026 L .12063 .12823 L .11925 .12651 L .11782 .12512 L .11608 .1238 L .114 .12259 L .11163 .12156 L .10948 .12089 L .10823 .1206 L .10703 .12038 L .10588 .12021 L .10532 .12015 L .1048 .12011 L .10417 .12006 L .10361 .12004 L .10299 .12002 L .10265 .12001 L .10233 .12001 L .10173 .12002 L .10118 .12004 L .10057 .12007 L .09991 .12011 L .09923 .12017 L .09858 .12025 L .09738 .12042 L Mistroke .09525 .12083 L .09332 .12133 L .08921 .12283 L .08723 .1238 L .08524 .12496 L .08213 .12728 L .07974 .12973 L .07814 .13203 L .07752 .13323 L .07725 .13389 L .07704 .13451 L .07687 .13507 L .07674 .13568 L .07669 .13594 L .07665 .13621 L .07662 .13645 L .0766 .1367 L .07658 .137 L .07658 .13727 L .07658 .13755 L .07658 .13771 L .07659 .13786 L .07661 .13812 L .07664 .13836 L .07668 .13863 L .07673 .13888 L .07686 .13943 L .07703 .13992 L .07724 .14043 L .07751 .14095 L .07807 .14177 L .07866 .14244 L .07945 .14312 L .08029 .14367 L .08112 .14409 L .08193 .14441 L .08285 .14469 L .08334 .14479 L .08387 .14489 L .08437 .14495 L .08465 .14498 L .08491 .145 L .08519 .14502 L .08545 .14503 L .08559 .14503 L .08574 .14503 L .08602 .14503 L .08626 .14503 L .08652 .14502 L .08679 .145 L Mistroke .08704 .14498 L .0875 .14493 L .08798 .14486 L .08853 .14477 L .08913 .14464 L .09019 .14434 L .09117 .14399 L .09203 .14361 L .09373 .14264 L .09506 .14158 L .09599 .14057 L .0964 .14 L .09671 .13946 L .09695 .13893 L .09705 .13864 L .09713 .13837 L .09719 .13812 L .09721 .13799 L .09723 .13786 L .09725 .13775 L .09726 .13762 L .09727 .13751 L .09727 .13741 L .09727 .13729 L .09727 .13716 L .09726 .13709 L .09726 .13702 L .09724 .1369 L .09722 .13678 L .0972 .13666 L .09715 .13646 L .09708 .13622 L .097 .13601 L .09675 .13558 L .0965 .13525 L .09619 .13493 L .09585 .13467 L .09552 .13447 L .0951 .13428 L .09487 .13419 L .09462 .13411 L .09437 .13405 L .09414 .13401 L .09391 .13397 L .09369 .13395 L .09358 .13394 L .09346 .13393 L .09335 .13393 L .09324 .13392 L .09312 .13392 L Mistroke .09306 .13392 L .09299 .13393 L .09288 .13393 L .09276 .13394 L .09264 .13395 L .09252 .13396 L .0923 .13399 L .09203 .13403 L .0918 .13408 L .09139 .13418 L .09097 .13432 L .09025 .13464 L .08953 .13507 L .089 .13552 L .08876 .13578 L .08854 .13606 L .08837 .13633 L .08825 .13658 L .08817 .13681 L .08813 .13693 L .08811 .13705 L .0881 .13711 L .08809 .13717 L .08809 .1372 L .08809 .13723 L .08809 .13726 L .08808 .13729 L .08808 .13735 L .08808 .1374 L .08809 .13746 L .08809 .13749 L .08809 .13752 L .0881 .13758 L .08811 .13763 L .08814 .13774 L .08817 .13784 L .08821 .13795 L .08832 .13813 L .08844 .13829 L .08857 .13841 L .08873 .13853 L .08889 .13863 L .08905 .1387 L .08925 .13877 L .08936 .1388 L .08947 .13882 L .08958 .13884 L .08967 .13885 L .08973 .13885 L .08975 .13886 L Mistroke .08978 .13886 L .08984 .13886 L .08989 .13886 L .08994 .13886 L .08997 .13886 L .09 .13886 L .09005 .13886 L .0901 .13885 L .09019 .13884 L .09029 .13883 L .09039 .13882 L .0905 .13879 L .0907 .13874 L .09088 .13869 L .09106 .13861 L .09135 .13846 L .09162 .13827 L .09185 .13805 L .09194 .13794 L .09201 .13783 L .09207 .13773 L .09211 .13763 L .09213 .13758 L .09214 .13753 L .09215 .13748 L .09216 .13745 L .09216 .13742 L .09216 .1374 L .09216 .13737 L .09216 .13735 L .09216 .13732 L .09216 .13731 L .09216 .1373 L .09216 .13728 L .09216 .13727 L .09216 .13725 L .09215 .13722 L .09214 .13718 L .09213 .13714 L .09212 .1371 L .0921 .13706 L .09206 .13699 L .09201 .13693 L .09195 .13687 L .09189 .13682 L .09181 .13677 L .09172 .13673 L .09168 .13671 L .09163 .1367 L .09158 .13669 L Mistroke .09153 .13668 L .0915 .13668 L .09148 .13667 L .09146 .13667 L .09143 .13667 L .09141 .13667 L .09139 .13667 L .09137 .13667 L .09134 .13667 L .09132 .13667 L .0913 .13667 L .09128 .13667 L .09127 .13667 L .09124 .13667 L .0912 .13668 L .09115 .13668 L .09107 .1367 L .09099 .13672 L .0909 .13675 L .09081 .13679 L .09067 .13687 L .09055 .13696 L .0905 .13701 L .09046 .13706 L .09043 .13711 L .0904 .13716 L .09038 .1372 L .09037 .13724 L .09036 .13727 L .09036 .13729 L .09035 .1373 L .09035 .13731 L .09035 .13731 L .09035 .13732 L .09035 .13733 L .09035 .13734 L .09035 .13736 L .09035 .13737 L .09035 .13738 L .09035 .13738 L .09036 .13739 L .09036 .13741 L .09037 .13743 L .09037 .13745 L .09039 .13749 L .09042 .13752 L .09044 .13755 L .09047 .13757 L .0905 .13759 L .09054 .13761 L Mistroke .09056 .13762 L .09058 .13762 L .0906 .13763 L .09062 .13763 L .09064 .13764 L .09065 .13764 L .09066 .13764 L .09067 .13764 L .09068 .13764 L .09069 .13764 L .0907 .13764 L .09071 .13764 L .09072 .13764 L .09073 .13764 L .09074 .13764 L .09075 .13764 L .09076 .13764 L .09078 .13764 L .09079 .13763 L .09082 .13763 L .09085 .13762 L .09089 .13761 L .09096 .13758 L .091 .13756 L .09103 .13754 L .09106 .13752 L Mfstroke .09091 .20601 m .10717 .1987 L .12266 .18912 L .13587 .17803 L .14526 .16729 L .14936 .16115 L .15237 .15543 L .15438 .15041 L .15524 .14764 L .15584 .14513 L .15609 .14385 L .15631 .14249 L .15647 .14122 L .15658 .14008 L .15662 .13939 L .15666 .13875 L .15668 .13806 L .15668 .13732 L .15668 .13663 L .15666 .13598 L .15659 .13478 L .15654 .13418 L .15647 .13353 L .15629 .13223 L .15608 .13104 L .15584 .12995 L .15517 .12756 L .15425 .12511 L .15215 .12107 L .1497 .11767 L .14651 .11432 L .14261 .11122 L .13887 .10892 L .13509 .10711 L .1307 .1055 L .12833 .10482 L .12575 .10422 L .12334 .10377 L .12112 .10346 L .12005 .10334 L .11888 .10323 L .11778 .10315 L .11675 .10309 L .11556 .10305 L .11444 .10303 L .11322 .10303 L .11253 .10304 L .1119 .10305 L .11064 .10311 L .10993 .10315 L Mistroke .10927 .10319 L .10679 .10342 L .10554 .10357 L .1042 .10376 L .10179 .10418 L .09737 .10518 L .09242 .10669 L .0881 .10838 L .08074 .11218 L .07488 .11629 L .06971 .12118 L .06742 .12402 L .06571 .12661 L .06444 .12904 L .06388 .13036 L .06344 .13158 L .06311 .13269 L .06287 .13369 L .06267 .13478 L .06259 .13535 L .06253 .13594 L .06249 .13653 L .06247 .13706 L .06247 .13736 L .06247 .13767 L .06249 .13823 L .06253 .13876 L .06259 .1393 L .06266 .13976 L .06275 .14025 L .06301 .14134 L .06338 .14246 L .0638 .14346 L .06426 .14434 L .0653 .14591 L .06662 .14741 L .06791 .14853 L .06948 .14962 L .07131 .15059 L .07232 .15102 L .07342 .15142 L .07441 .15171 L .07552 .15198 L .07654 .15218 L .0775 .15233 L .078 .15239 L .07856 .15244 L .07912 .15249 L .07943 .15251 L .07972 .15252 L Mistroke .08025 .15254 L .08073 .15254 L .081 .15254 L .08129 .15254 L .08182 .15252 L .08234 .1525 L .08281 .15247 L .08335 .15243 L .08385 .15237 L .08572 .15211 L .08676 .1519 L .08784 .15165 L .08972 .1511 L .09184 .15031 L .09365 .14948 L .09662 .14771 L .09926 .14558 L .10023 .14458 L .10114 .14347 L .10241 .14145 L .10289 .14037 L .10321 .13937 L .10334 .13882 L .10338 .13855 L .10342 .13831 L .10345 .13805 L .10346 .13792 L .10347 .13777 L .10348 .13762 L .10348 .13748 L .10348 .13722 L .10347 .13698 L .10347 .13685 L .10346 .13672 L .10343 .13648 L .10339 .13622 L .10329 .13575 L .10318 .13535 L .10301 .13489 L .1028 .13442 L .1023 .13363 L .1017 .13292 L .10104 .13233 L .10038 .13188 L .09962 .13147 L .09872 .13111 L .09825 .13097 L .09772 .13084 L .09727 .13075 L .09701 .13071 L Mistroke .09677 .13067 L .09655 .13065 L .0963 .13063 L .09607 .13061 L .09587 .1306 L .09563 .13059 L .09541 .13059 L .09521 .13059 L .09499 .1306 L .09476 .13061 L .09463 .13061 L .09451 .13062 L .09406 .13066 L .09364 .13071 L .0932 .13079 L .09241 .13095 L .0915 .13121 L .09058 .13154 L .08909 .13228 L .08786 .13311 L .08681 .13409 L .08639 .13458 L .08607 .13505 L .08581 .1355 L .08562 .13593 L .08547 .13637 L .08541 .13661 L .08538 .13673 L .08536 .13685 L .08535 .13698 L .08534 .13709 L .08533 .13716 L .08533 .13721 L .08533 .13728 L .08533 .13734 L .08533 .13745 L .08533 .13755 L .08534 .13765 L .08536 .13776 L .08537 .13786 L .08539 .13794 L .08543 .13813 L .08549 .1383 L .08554 .13845 L .08571 .13878 L .08593 .1391 L .08622 .1394 L .08652 .13965 L .08682 .13984 L .08717 .14001 L Mistroke .08758 .14015 L .08779 .14021 L .08802 .14026 L .08823 .14029 L .08834 .14031 L .08845 .14032 L .08855 .14033 L .08866 .14033 L .08876 .14034 L .08885 .14034 L .08895 .14034 L .08905 .14034 L .08914 .14034 L .08924 .14033 L .08934 .14032 L .08945 .14031 L .08965 .14029 L .08985 .14026 L .09004 .14023 L .09038 .14014 L .09077 .14002 L .09112 .13989 L .09182 .13953 L .09236 .13914 L .09277 .13875 L .0931 .1383 L .09322 .13805 L .09327 .13795 L .09331 .13783 L .09334 .13773 L .09336 .13763 L .09337 .13757 L .09338 .13752 L .09338 .13747 L .09339 .13742 L .09339 .13737 L .09339 .13733 L .09339 .13728 L .09339 .13724 L .09338 .1372 L .09338 .13715 L .09337 .13711 L .09336 .13707 L .09334 .13698 L .09331 .1369 L .09328 .13681 L .09324 .13673 L .09314 .13658 L .09301 .13644 L .09288 .13633 L Mistroke .09273 .13624 L .09258 .13616 L .09244 .13611 L .09226 .13606 L .09215 .13604 L .0921 .13603 L .09206 .13602 L .09201 .13602 L .09197 .13602 L .09192 .13601 L .0919 .13601 L .09188 .13601 L .09183 .13601 L .09178 .13601 L .09174 .13601 L .09171 .13601 L .09168 .13601 L .09164 .13601 L .0916 .13602 L .0915 .13603 L .09141 .13604 L .09132 .13606 L .09114 .1361 L .091 .13614 L .09083 .1362 L .09066 .13628 L .09038 .13645 L .09017 .13663 L .08999 .13683 L .08993 .13693 L .08987 .13705 L .08985 .1371 L .08984 .13715 L .08982 .13719 L .08982 .13724 L .08981 .13726 L .08981 .13729 L .08981 .1373 L .08981 .13731 L .08981 .13732 L .08981 .13734 L .08981 .13736 L .08981 .13738 L .08981 .13739 L .08981 .1374 L .08981 .13742 L .08982 .13744 L .08982 .13746 L .08983 .1375 L .08984 .13753 L Mistroke .08985 .13757 L .08989 .13764 L .08994 .1377 L .09 .13776 L .09006 .13781 L .09013 .13785 L .0902 .13788 L .09023 .13789 L .09028 .1379 L .09031 .13791 L .09035 .13792 L .09039 .13793 L .09043 .13793 L .09045 .13793 L .09047 .13793 L .09049 .13793 L .09051 .13793 L .09053 .13793 L .09055 .13793 L .09056 .13793 L .09058 .13793 L .0906 .13793 L .09062 .13793 L .09065 .13792 L .09069 .13792 L .09072 .13791 L .09078 .1379 L .09086 .13788 L .09092 .13786 L .09105 .1378 L .09115 .13773 L Mfstroke .09091 .24035 m .11529 .22938 L .13854 .2151 L .15842 .19879 L .1727 .18328 L .17903 .17453 L .1838 .16646 L .18711 .15942 L .18969 .15205 L .19062 .14835 L .19104 .14626 L .19134 .14438 L .19159 .14241 L .19169 .14135 L .19176 .14034 L .19181 .13942 L .19184 .13857 L .19186 .13764 L .19185 .13666 L .19183 .13576 L .19179 .13493 L .19174 .13403 L .19166 .13309 L .19148 .13152 L .19122 .12983 L .19057 .12677 L .18978 .12399 L .18753 .11849 L .18593 .11555 L .18425 .11293 L .18076 .10851 L .17627 .10405 L .16709 .09744 L .16141 .09445 L .15574 .09207 L .14969 .0901 L .14282 .08846 L .13928 .08784 L .13731 .08756 L .13544 .08733 L .1337 .08716 L .1318 .087 L .13007 .0869 L .12847 .08683 L .12697 .08679 L .12536 .08677 L .12384 .08678 L .12245 .08681 L .12083 .08687 L .11906 .08697 L Mistroke .1174 .08709 L .11586 .08723 L .1125 .08761 L .10949 .08806 L .10285 .08938 L .09644 .09113 L .08997 .09339 L .0793 .09835 L .06939 .10471 L .06461 .10862 L .06066 .11245 L .05752 .11607 L .05466 .12002 L .05273 .1233 L .05106 .12686 L .05039 .12868 L .0498 .13062 L .04954 .13167 L .04934 .13262 L .04918 .13358 L .04906 .13446 L .04898 .13522 L .04892 .13602 L .0489 .13647 L .04889 .13689 L .04888 .13767 L .04891 .13849 L .04896 .13924 L .04904 .14004 L .04916 .14088 L .04947 .14238 L .04985 .14376 L .05081 .14621 L .05148 .1475 L .05218 .14864 L .05402 .15103 L .05572 .15273 L .05783 .1544 L .06024 .1559 L .06268 .15708 L .06532 .15806 L .06833 .15886 L .06989 .15916 L .07076 .15929 L .07158 .1594 L .07235 .15948 L .07319 .15955 L .07395 .1596 L .07466 .15963 L .07532 .15965 L Mistroke .07603 .15966 L .0767 .15965 L .07731 .15964 L .07803 .15961 L .0788 .15956 L .07954 .15951 L .08022 .15944 L .0817 .15927 L .08303 .15906 L .08595 .15846 L .08876 .15767 L .09161 .15665 L .09629 .15443 L .10062 .1516 L .10271 .14986 L .10442 .14815 L .10578 .14653 L .10701 .14477 L .10784 .1433 L .10854 .1417 L .10883 .14083 L .10905 .14002 L .10922 .13918 L .10929 .13872 L .10931 .13852 L .10934 .1383 L .10936 .13794 L .10937 .13761 L .10938 .1374 L .10938 .13721 L .10937 .13686 L .10934 .1365 L .10931 .13617 L .10926 .13581 L .1092 .13544 L .10904 .13477 L .10885 .13416 L .10838 .13308 L .10773 .13201 L .10687 .13096 L .106 .13016 L .10497 .12942 L .10391 .12883 L .10289 .12839 L .10165 .12798 L .101 .12782 L .10028 .12768 L .09966 .12758 L .09931 .12754 L .09898 .1275 L Mistroke .09868 .12748 L .09834 .12746 L .09804 .12745 L .09776 .12744 L .09743 .12744 L .09707 .12744 L .09674 .12745 L .09643 .12747 L .09608 .12749 L .09569 .12753 L .09499 .12761 L .09426 .12773 L .0935 .12788 L .09217 .12822 L .09084 .12867 L .08969 .12916 L .08736 .13047 L .08566 .1318 L .08488 .13258 L .08428 .1333 L .08381 .13397 L .0834 .1347 L .08322 .1351 L .08307 .13546 L .08295 .13582 L .08286 .13616 L .0828 .13644 L .08276 .13674 L .08274 .1369 L .08273 .13707 L .08272 .13721 L .08272 .13736 L .08272 .13752 L .08273 .13766 L .08275 .13782 L .08276 .13798 L .08281 .13824 L .08288 .13852 L .08297 .13878 L .08308 .13906 L .08332 .13952 L .08369 .14002 L .08409 .14042 L .08456 .14079 L .08513 .14111 L .0857 .14136 L .08627 .14153 L .08658 .1416 L .08687 .14165 L .08719 .1417 L Mistroke .08735 .14171 L .08745 .14172 L .08753 .14173 L .08769 .14173 L .08784 .14174 L .08799 .14174 L .08808 .14174 L .08816 .14174 L .0883 .14173 L .08845 .14173 L .0886 .14172 L .08875 .1417 L .08903 .14167 L .08931 .14163 L .08982 .14153 L .09035 .14139 L .0909 .1412 L .09194 .14073 L .09276 .1402 L .09315 .13989 L .09351 .13953 L .09381 .13919 L .09404 .13887 L .09423 .13854 L .09436 .13825 L .09442 .1381 L .09447 .13793 L .09449 .13784 L .09451 .13776 L .09452 .13768 L .09453 .1376 L .09454 .13752 L .09454 .13745 L .09455 .13738 L .09455 .13731 L .09455 .13728 L .09454 .13724 L .09454 .13717 L .09454 .13713 L .09453 .13709 L .09452 .13702 L .09449 .13687 L .09445 .13675 L .0944 .13661 L .09434 .13648 L .09421 .13626 L .09406 .13609 L .09387 .13591 L .09366 .13577 L .09345 .13565 L Mistroke .09325 .13557 L .09302 .13549 L .09288 .13546 L .09276 .13543 L .09264 .13541 L .0925 .1354 L .09243 .13539 L .09239 .13539 L .09235 .13539 L .09228 .13539 L .09222 .13539 L .09216 .13539 L .09209 .13539 L .09204 .13539 L .09198 .13539 L .09192 .1354 L .09185 .1354 L .09172 .13542 L .09159 .13544 L .09144 .13547 L .09116 .13554 L .0909 .13563 L .09068 .13572 L .09024 .13596 L .0899 .13623 L .08965 .13648 L .08954 .13662 L .08946 .13676 L .08939 .13689 L .08934 .13703 L .08932 .13711 L .08931 .13715 L .08931 .13718 L .0893 .13722 L .0893 .13725 L .08929 .13728 L .08929 .1373 L .08929 .13731 L .08929 .13735 L .08929 .13736 L .08929 .13738 L .0893 .13741 L .0893 .13743 L .0893 .13745 L .0893 .13748 L .08931 .13751 L .08932 .13756 L .08934 .13762 L .08937 .13769 L .08942 .13779 L Mistroke .08949 .13788 L .08956 .13795 L .08966 .13802 L .08975 .13808 L .08985 .13812 L .08994 .13815 L .09005 .13818 L .09011 .13819 L .09014 .1382 L .09017 .1382 L .0902 .1382 L .09022 .13821 L .09025 .13821 L .09028 .13821 L .09031 .13821 L .09033 .13821 L .09035 .13821 L .09038 .13821 L .09041 .13821 L .09043 .13821 L .09046 .1382 L .09051 .1382 L .09057 .13819 L .09063 .13818 L .09074 .13816 L .09086 .13812 L .09107 .13803 L .0911 .13802 L Mfstroke .09091 .27468 m .12342 .26007 L .15444 .24119 L .18107 .22004 L .20043 .20044 L .20922 .18961 L .21603 .17977 L .22102 .17119 L .22511 .1625 L .22676 .15816 L .22822 .15352 L .22924 .14941 L .22992 .14565 L .23022 .14344 L .23033 .14236 L .23041 .14136 L .23052 .13952 L .23055 .13856 L .23056 .13754 L .23056 .13645 L .23052 .13527 L .23047 .13417 L .23039 .13317 L .2302 .13128 L .22992 .12932 L .22923 .12591 L .22836 .12277 L .22617 .1171 L .22303 .1113 L .21876 .10535 L .21434 .10048 L .20897 .09564 L .19778 .08786 L .18397 .08104 L .17549 .07795 L .16735 .07563 L .15995 .07402 L .15564 .07329 L .15168 .07275 L .14745 .07232 L .14511 .07213 L .1429 .072 L .14085 .07191 L .13896 .07185 L .13688 .07183 L .13468 .07183 L .13247 .07187 L .13007 .07196 L .12781 .07209 L .12572 .07224 L Mistroke .12178 .07261 L .11761 .07314 L .11275 .07394 L .10824 .07485 L .1 .07695 L .08582 .08205 L .07843 .08553 L .07209 .08905 L .0601 .0974 L .05105 .10581 L .04361 .11529 L .04059 .12057 L .03855 .12527 L .03779 .12753 L .03723 .12961 L .03677 .13174 L .03659 .13285 L .03644 .13404 L .03636 .13498 L .03629 .136 L .03626 .13705 L .03627 .13801 L .0363 .13891 L .03636 .13971 L .03645 .14062 L .03657 .14147 L .03692 .14338 L .03715 .14432 L .03744 .14533 L .03873 .14863 L .03964 .15038 L .04076 .15217 L .04313 .15513 L .04594 .15779 L .04886 .15993 L .05238 .16191 L .05641 .16361 L .05816 .16418 L .06009 .16472 L .06178 .16511 L .06366 .16546 L .06577 .16576 L .06693 .16589 L .06801 .16598 L .06903 .16605 L .06996 .16609 L .07047 .1661 L .07103 .16611 L .07205 .16612 L .07303 .1661 L Mistroke .07393 .16607 L .07496 .16602 L .07594 .16595 L .07768 .16578 L .07955 .16553 L .08159 .16519 L .08373 .16475 L .08748 .16375 L .09154 .16234 L .09515 .16077 L .10119 .15732 L .10611 .15349 L .10834 .15127 L .11012 .14915 L .11256 .14539 L .11347 .14342 L .11417 .14136 L .11442 .14032 L .11453 .13976 L .11461 .13924 L .11466 .13881 L .1147 .13834 L .11472 .13809 L .11473 .13783 L .11474 .13737 L .11474 .13711 L .11473 .13688 L .11472 .13661 L .1147 .13636 L .11466 .13592 L .1146 .13545 L .11451 .13494 L .1144 .13441 L .11414 .13349 L .11386 .13273 L .1135 .13195 L .11272 .13063 L .11158 .12922 L .11036 .12809 L .10907 .12716 L .10757 .12633 L .10605 .12569 L .10461 .12524 L .10371 .12503 L .10286 .12487 L .10191 .12473 L .10144 .12468 L .10091 .12464 L .10045 .12461 L .10002 .12459 L Mistroke .09979 .12459 L .09953 .12458 L .09907 .12458 L .09863 .12459 L .09818 .12461 L .09778 .12464 L .09735 .12467 L .09648 .12476 L .09554 .1249 L .09385 .12524 L .09227 .12568 L .09085 .12617 L .08789 .12753 L .08642 .12843 L .08521 .1293 L .08322 .13112 L .08185 .13286 L .08131 .13378 L .08086 .13478 L .08069 .13527 L .08055 .13579 L .08049 .13604 L .08045 .13627 L .08042 .13648 L .08039 .1367 L .08037 .13692 L .08036 .13711 L .08036 .13729 L .08036 .13748 L .08037 .13769 L .08038 .13787 L .0804 .13808 L .08044 .13829 L .08053 .13872 L .08064 .1391 L .08077 .13943 L .08092 .13978 L .08128 .14036 L .08173 .14093 L .08218 .14136 L .08272 .14177 L .08339 .14217 L .08408 .14247 L .08472 .14268 L .0851 .14278 L .08546 .14285 L .08588 .14292 L .08627 .14297 L .08649 .14298 L .08669 .143 L Mistroke .0868 .143 L .08691 .143 L .08703 .14301 L .08715 .14301 L .08735 .14301 L .08755 .143 L .08772 .14299 L .08791 .14298 L .08812 .14296 L .08833 .14294 L .08872 .14289 L .08947 .14275 L .09013 .14257 L .09083 .14234 L .09153 .14206 L .09261 .14149 L .09362 .14077 L .09448 .13993 L .09505 .13914 L .09528 .1387 L .09537 .13848 L .09545 .13824 L .09551 .13803 L .09553 .13793 L .09555 .13781 L .09557 .13771 L .09558 .13762 L .09559 .13753 L .09559 .13744 L .09559 .13735 L .09559 .13726 L .09559 .13718 L .09558 .1371 L .09557 .13702 L .09556 .13693 L .09553 .13675 L .09548 .13658 L .09541 .13641 L .09526 .13612 L .09508 .13585 L .09487 .13563 L .09466 .13545 L .09441 .13529 L .09412 .13514 L .09383 .13502 L .0935 .13493 L .09331 .13489 L .09313 .13486 L .09305 .13485 L .09295 .13484 L Mistroke .09286 .13483 L .09278 .13483 L .09273 .13483 L .09268 .13482 L .09263 .13482 L .09257 .13482 L .09248 .13482 L .09243 .13483 L .09238 .13483 L .09229 .13483 L .0922 .13484 L .09204 .13485 L .09186 .13488 L .09168 .13491 L .09135 .13499 L .09106 .13508 L .09073 .1352 L .09044 .13534 L .08992 .13565 L .08947 .13603 L .08931 .13621 L .08916 .1364 L .08906 .13656 L .08897 .13674 L .08892 .13685 L .08889 .13695 L .08886 .13704 L .08885 .13708 L .08884 .13713 L .08884 .13718 L .08883 .13722 L .08883 .13726 L .08883 .13729 L .08883 .13734 L .08883 .13738 L .08883 .13742 L .08883 .13744 L .08883 .13746 L .08884 .1375 L .08884 .13753 L .08886 .13761 L .08888 .13768 L .08891 .13776 L .08897 .13789 L .08905 .13799 L .08915 .1381 L .08927 .1382 L .08941 .13828 L .08954 .13834 L .08967 .13839 L Mistroke .08975 .13841 L .08982 .13843 L .08989 .13844 L .08992 .13844 L .08996 .13845 L .09 .13845 L .09003 .13845 L .09007 .13846 L .0901 .13846 L .09014 .13846 L .09018 .13846 L .0902 .13846 L .09022 .13846 L .09026 .13846 L .0903 .13846 L .09034 .13845 L .09041 .13845 L .09049 .13843 L .09056 .13842 L .09073 .13838 L .09073 .13838 L Mfstroke .09091 .30902 m .13155 .29077 L .17035 .26742 L .22855 .21905 L .24907 .19617 L .25762 .18478 L .26408 .1748 L .26877 .16614 L .27252 .15739 L .27376 .15373 L .2748 .14996 L .27548 .14684 L .27577 .14521 L .27601 .1435 L .2762 .14177 L .27632 .14018 L .27637 .13922 L .2764 .13833 L .27641 .13667 L .27636 .1351 L .27626 .13367 L .27611 .13212 L .27589 .1305 L .27536 .12775 L .27472 .12523 L .27271 .11966 L .27126 .11664 L .26969 .11384 L .2662 .10871 L .25594 .09773 L .24406 .08854 L .22884 .07952 L .21391 .07266 L .19565 .06633 L .18576 .06376 L .17501 .06161 L .17049 .0609 L .16562 .06027 L .1628 .05997 L .16023 .05973 L .15784 .05955 L .15519 .05938 L .15237 .05925 L .15083 .0592 L .14938 .05917 L .14679 .05913 L .14401 .05914 L .14245 .05917 L .14076 .05921 L .13916 .05927 L Mistroke .13768 .05934 L .13488 .05951 L .13191 .05973 L .12603 .06035 L .12054 .06113 L .11047 .06308 L .10098 .06557 L .091 .06894 L .07253 .07744 L .05782 .08687 L .04649 .09649 L .04118 .10209 L .03629 .10821 L .03276 .11358 L .02979 .11919 L .02779 .12413 L .02693 .12688 L .0263 .12941 L .02608 .13053 L .02588 .13169 L .02574 .13268 L .02561 .13373 L .02552 .13486 L .02546 .13589 L .02543 .1371 L .02544 .13819 L .02549 .13931 L .02556 .14035 L .02569 .14147 L .02586 .14265 L .02635 .145 L .02694 .14708 L .02847 .15087 L .03037 .15421 L .03305 .15772 L .03596 .16064 L .03958 .16346 L .04384 .166 L .04786 .16783 L .05174 .16919 L .05617 .17031 L .05845 .17074 L .05975 .17094 L .06098 .1711 L .06206 .17122 L .06323 .17132 L .06431 .1714 L .0653 .17145 L .06637 .17149 L .06755 .17151 L Mistroke .06878 .17151 L .06994 .17149 L .07102 .17144 L .07204 .17139 L .07396 .17124 L .07601 .17101 L .07823 .17069 L .08309 .16972 L .08752 .16849 L .09525 .16549 L .09921 .16346 L .10258 .16142 L .10913 .15636 L .11146 .15404 L .11363 .15151 L .11521 .1493 L .11663 .14691 L .11733 .14546 L .11789 .14414 L .11832 .14291 L .11869 .14158 L .11894 .14041 L .11903 .13988 L .11911 .13934 L .11917 .13875 L .1192 .13822 L .11923 .13766 L .11923 .13734 L .11923 .13705 L .11921 .13649 L .11919 .13621 L .11916 .13591 L .1191 .13538 L .11903 .13489 L .11881 .13382 L .11849 .13271 L .11811 .13172 L .11768 .13081 L .11672 .12922 L .11558 .12783 L .11438 .12666 L .11291 .12554 L .1112 .12453 L .10921 .12364 L .10729 .12302 L .10625 .12276 L .10509 .12254 L .1045 .12245 L .10386 .12237 L .10326 .12231 L Mistroke .10271 .12226 L .10218 .12223 L .10191 .12222 L .10161 .12221 L .10132 .12221 L .101 .1222 L .1007 .1222 L .10042 .12221 L .09989 .12222 L .09959 .12224 L .09932 .12225 L .09881 .12229 L .09827 .12234 L .09719 .12246 L .09618 .12262 L .09433 .123 L .09251 .1235 L .09059 .12418 L .08705 .12586 L .08425 .12773 L .0821 .12964 L .0811 .13075 L .0802 .13198 L .07955 .13306 L .07903 .1342 L .07869 .1352 L .07856 .13575 L .07851 .13601 L .07847 .13627 L .07844 .13649 L .07841 .13673 L .0784 .13695 L .07839 .13714 L .07839 .13738 L .07839 .13759 L .0784 .13782 L .07842 .13805 L .07845 .13826 L .07849 .13849 L .07857 .1389 L .0787 .13937 L .07885 .13978 L .07927 .14061 L .07978 .14132 L .08032 .1419 L .08089 .14238 L .08157 .14284 L .08236 .14324 L .0828 .14342 L .08327 .14359 L Mistroke .08414 .14382 L .08464 .14392 L .08511 .14398 L .08539 .14401 L .08563 .14403 L .08577 .14404 L .08592 .14405 L .08606 .14406 L .0862 .14406 L .08641 .14406 L .08664 .14406 L .08686 .14406 L .08707 .14405 L .08729 .14403 L .08753 .14402 L .08802 .14396 L .08849 .14389 L .089 .1438 L .08988 .14358 L .09079 .14329 L .09158 .14297 L .09319 .14209 L .09436 .1412 L .0949 .14068 L .09533 .14019 L .09566 .13973 L .09595 .13924 L .09619 .13872 L .09627 .13849 L .09635 .13824 L .0964 .13802 L .09643 .13781 L .09645 .1377 L .09646 .13759 L .09646 .13748 L .09647 .13736 L .09647 .13727 L .09646 .13717 L .09646 .13708 L .09645 .137 L .09644 .13691 L .09642 .13681 L .09638 .13662 L .09633 .13644 L .09626 .13625 L .0961 .13593 L .09586 .13558 L .0956 .1353 L .09529 .13505 L .09491 .13482 L Mistroke .09452 .13464 L .09414 .13452 L .09394 .13447 L .09374 .13443 L .09352 .13439 L .09341 .13438 L .09329 .13437 L .09318 .13436 L .09308 .13436 L .09303 .13436 L .09297 .13435 L .09286 .13435 L .09276 .13436 L .09266 .13436 L .09256 .13436 L .09246 .13437 L .09227 .13439 L .09209 .13441 L .09168 .13449 L .09134 .13458 L .09099 .13469 L .09033 .13498 L .08971 .13536 L .08923 .13576 L .08889 .13614 L .08875 .13636 L .08862 .13659 L .08854 .13678 L .08851 .13689 L .08848 .13699 L .08847 .13704 L .08846 .1371 L .08845 .13715 L .08845 .1372 L .08844 .13723 L .08844 .13726 L .08844 .13729 L .08844 .13732 L .08844 .13734 L .08844 .13737 L .08844 .13742 L .08845 .13747 L .08845 .13751 L .08846 .13756 L .08846 .1376 L .08849 .1377 L .08852 .13778 L .08858 .13793 L .08868 .13808 L .08879 .13822 L Mistroke .08892 .13833 L .08906 .13842 L .08919 .13849 L .08935 .13856 L .08951 .13861 L .08962 .13863 L Mfstroke .09091 .34335 m .13968 .32148 L .18628 .29382 L .25712 .23934 L .30216 .19722 L .32889 .16807 L .33661 .15792 L .34136 .15019 L .34278 .14726 L .3439 .14439 L .34434 .14297 L .34471 .14147 L .34484 .14083 L .34495 .14016 L .34503 .13954 L .34509 .13896 L .34512 .13864 L .34514 .13829 L .34516 .1377 L .34517 .13736 L .34516 .13701 L .34514 .13639 L .3451 .13582 L .34504 .13529 L .34496 .13472 L .34486 .13411 L .34453 .13277 L .34413 .13152 L .34311 .12922 L .34183 .12707 L .34038 .12509 L .33616 .12054 L .32522 .11178 L .30742 .1004 L .28195 .08655 L .25105 .07246 L .23249 .06548 L .21358 .05963 L .20266 .05688 L .19244 .05475 L .18079 .05287 L .17429 .05209 L .17132 .0518 L .16811 .05153 L .16512 .05132 L .16239 .05117 L .15964 .05106 L .15702 .05098 L .15399 .05094 L .15117 .05094 L Mistroke .14808 .05099 L .14636 .05104 L .1448 .0511 L .14162 .05126 L .1387 .05146 L .13214 .05206 L .12641 .0528 L .12043 .05376 L .10997 .05598 L .10052 .05859 L .08037 .0663 L .07079 .07114 L .06117 .0769 L .04607 .08834 L .03449 .1001 L .02662 .11102 L .02358 .11661 L .02111 .12249 L .02024 .12513 L .01951 .12787 L .01903 .13016 L .01883 .13135 L .01866 .13262 L .01857 .13341 L .0185 .13412 L .01841 .13551 L .01837 .13676 L .01838 .13806 L .01839 .13873 L .01843 .13945 L .01853 .14072 L .01861 .14149 L .0187 .14221 L .01891 .14355 L .01942 .14588 L .02003 .14798 L .02091 .15036 L .02188 .15247 L .02407 .15618 L .02694 .15984 L .02987 .16275 L .03333 .16551 L .03721 .16798 L .0417 .17021 L .04695 .17217 L .05208 .17352 L .0547 .17403 L .05751 .17444 L .05992 .1747 L .0613 .1748 L Mistroke .0626 .17487 L .06332 .1749 L .0641 .17493 L .06483 .17494 L .06552 .17495 L .06681 .17494 L .06819 .1749 L .06897 .17487 L .06981 .17482 L .07133 .17472 L .07281 .17458 L .07416 .17443 L .07893 .17369 L .08159 .17313 L .08403 .17252 L .0937 .16919 L .098 .16717 L .10234 .16473 L .10922 .15979 L .11454 .15459 L .11821 .14963 L .11963 .14707 L .12024 .14573 L .12079 .14434 L .12119 .14314 L .12154 .14183 L .12178 .14067 L .12195 .1396 L .12202 .13895 L .12204 .13859 L .12206 .13826 L .12209 .13765 L .12209 .13702 L .12207 .13646 L .12203 .13595 L .12198 .13539 L .1219 .1348 L .12179 .13418 L .12164 .13352 L .12131 .13236 L .12091 .13127 L .12046 .13031 L .11933 .12843 L .11782 .12662 L .11616 .12512 L .11446 .12394 L .11279 .12302 L .11085 .1222 L .10983 .12185 L .10872 .12153 L Mistroke .10775 .1213 L .10666 .12109 L .10549 .12091 L .10484 .12084 L .10424 .12078 L .10367 .12074 L .10315 .12072 L .10255 .1207 L .10197 .12069 L .10165 .1207 L .10136 .1207 L .10102 .12071 L .1007 .12072 L .10014 .12075 L .09952 .12079 L .09885 .12085 L .09814 .12094 L .09689 .12112 L .09468 .12157 L .09268 .12212 L .09058 .12286 L .08845 .12378 L .0849 .12582 L .08327 .12701 L .08174 .12835 L .08058 .12956 L .0795 .13091 L .07874 .13206 L .07809 .1333 L .07762 .1345 L .07743 .13513 L .0773 .13572 L .07725 .136 L .07721 .13626 L .07718 .13649 L .07716 .13674 L .07715 .137 L .07714 .13724 L .07714 .1375 L .07715 .13778 L .07716 .13792 L .07717 .13807 L .07721 .13835 L .07725 .13861 L .07729 .13885 L .07743 .13938 L .07761 .13992 L .07806 .14084 L .07858 .1416 L .0792 .1423 L Mistroke .07996 .14293 L .08068 .1434 L .08152 .14383 L .08249 .1442 L .08305 .14437 L .08357 .14449 L .08407 .14458 L .08433 .14462 L .08461 .14465 L .08486 .14468 L .08513 .1447 L .08538 .14472 L .08561 .14473 L .08586 .14473 L .08611 .14473 L .08636 .14473 L .08658 .14472 L .08684 .14471 L .08712 .14469 L .08763 .14463 L .08816 .14456 L .08871 .14446 L .08968 .14423 L .09054 .14396 L .0913 .14367 L .09291 .14288 L .09437 .14187 L .09547 .14082 L .09621 .13985 L .09652 .13929 L .09674 .13879 L .09683 .13855 L .0969 .1383 L .09693 .13817 L .09696 .13803 L .09698 .1379 L .09699 .13778 L .09701 .13767 L .09701 .13756 L .09702 .13744 L .09702 .13732 L .09702 .13721 L .09701 .1371 L .097 .13701 L .09699 .13691 L .09697 .13678 L .09695 .13667 L .0969 .13645 L .09683 .13623 L .09673 .136 L Mistroke .09651 .13562 L .09626 .1353 L .09595 .135 L .09557 .13472 L .09517 .1345 L .09478 .13434 L .09442 .13422 L .0942 .13417 L .094 .13413 L .09378 .1341 L .09358 .13408 L .09347 .13407 L .09342 .13407 L .09335 .13406 L .09324 .13406 L .09313 .13406 L .09303 .13406 L .09292 .13406 L .0928 .13406 L .09269 .13407 L .09259 .13408 L .09249 .13409 L .09228 .13411 L .09206 .13415 L .09182 .13419 L .0914 .1343 L .09102 .13442 L .09063 .13457 L .08999 .1349 L .08999 .1349 L Mfstroke .09091 .37769 m .28617 .26143 L .34356 .22231 L .35602 .21531 L .36829 .20935 L .379 .20506 L .38838 .2021 L .39742 .20001 L .40208 .19923 L .40444 .19892 L .40696 .19864 L .40916 .19844 L .41117 .1983 L .41318 .19819 L .41509 .19813 L .4173 .19809 L .41935 .19809 L .42053 .19811 L .4216 .19814 L .42284 .19818 L .424 .19823 L .42586 .19833 L .42789 .19847 L .43202 .19885 L .4395 .19982 L .4484 .20139 L .45694 .20323 L .49347 .21299 L .51494 .21882 L .53945 .22453 L .55234 .2269 L .55932 .22796 L .56692 .22892 L .57395 .22962 L .57703 .22986 L .58042 .23009 L .58364 .23026 L .58664 .23038 L .58981 .23047 L .5932 .23051 L .59491 .23051 L .59671 .2305 L .59994 .23044 L .60174 .23039 L .60342 .23032 L .60723 .23013 L .61056 .2299 L .61358 .22965 L .62036 .22891 L .62632 .22806 L Mistroke .63274 .22693 L .6442 .22433 L .65682 .22053 L .66813 .21623 L .68746 .20658 L .70521 .1945 L .72041 .1804 L .73016 .16789 L .73422 .16091 L .73708 .15457 L .73826 .15121 L .73915 .14808 L .73975 .14533 L .74001 .14382 L .74021 .14241 L .74037 .14092 L .74043 .14014 L .74048 .1393 L .74051 .13848 L .74053 .13762 L .74052 .13689 L .74051 .1361 L .74044 .13469 L .74037 .13391 L .7403 .13321 L .74013 .13185 L .73992 .1306 L .73939 .12819 L .73875 .12601 L .73782 .1235 L .73681 .1213 L .73429 .11706 L .73097 .11293 L .72769 .10976 L .72368 .10668 L .71986 .10432 L .71543 .10214 L .71056 .10027 L .70579 .09889 L .70295 .09826 L .69991 .09773 L .69729 .09738 L .6958 .09723 L .6944 .09712 L .69294 .09703 L .69211 .09699 L .69134 .09697 L .68993 .09694 L .68922 .09694 L .68844 .09694 L Mistroke .68709 .09697 L .68564 .09703 L .68427 .0971 L .68303 .0972 L .68007 .0975 L .67687 .09796 L .67116 .09912 L .66562 .10069 L .66064 .10249 L .65208 .10658 L .64418 .11181 L .63738 .11806 L .63303 .12372 L .63123 .12693 L .62997 .12987 L .62947 .13144 L .62909 .1329 L .62885 .13419 L .62875 .1349 L .62868 .13556 L .62862 .13625 L .6286 .13689 L .62859 .13726 L .62859 .13759 L .6286 .13795 L .62862 .13832 L .62864 .13867 L .62867 .13903 L .62874 .13967 L .62886 .14042 L .62899 .14109 L .62927 .14217 L .62965 .14331 L .63066 .14548 L .63186 .14731 L .63319 .14886 L .63499 .15048 L .63683 .15175 L .63914 .15297 L .64148 .15388 L .64269 .15424 L .64385 .15453 L .64492 .15475 L .64607 .15493 L .64667 .15501 L .64733 .15508 L .64794 .15513 L .64849 .15517 L .64883 .15518 L .64915 .1552 L Mistroke .64949 .15521 L .64986 .15521 L .65018 .15522 L .65052 .15522 L .65113 .1552 L .6517 .15518 L .65221 .15516 L .65281 .15511 L .65337 .15506 L .65436 .15495 L .65544 .1548 L .65784 .15433 L .66 .15375 L .66226 .15297 L .66457 .15198 L .66833 .14987 L .6714 .14751 L .67363 .14519 L .67458 .14394 L .67541 .1426 L .67602 .14135 L .67643 .14023 L .67662 .13955 L .67675 .13894 L .6768 .13863 L .67684 .13828 L .67686 .13811 L .67688 .13793 L .67689 .13776 L .67689 .1376 L .6769 .13732 L .67689 .13706 L .67688 .13677 L .67685 .13648 L .67683 .13633 L .67681 .13617 L .67676 .13588 L .67664 .13536 L .6765 .13488 L .67631 .13438 L .67588 .13353 L .67523 .13262 L .67453 .13188 L .67369 .13121 L .67268 .13061 L .67165 .13015 L .67064 .12982 L .67008 .12969 L .66956 .12959 L .66898 .1295 L Mistroke .66869 .12947 L .66836 .12944 L .66808 .12942 L .66782 .12941 L .66767 .12941 L .66751 .12941 L .66723 .12941 L .66696 .12941 L .66668 .12942 L .66644 .12944 L .66617 .12946 L .66564 .12951 L .66516 .12957 L .6641 .12978 L .66319 .13001 L .66227 .13032 L .6605 .1311 L .65887 .13211 L .65761 .13318 L .65672 .1342 L .65634 .13478 L .65601 .13538 L .65581 .13589 L .65572 .13618 L .65565 .13644 L .65562 .13659 L .65559 .13674 L .65557 .13688 L .65556 .13701 L .65555 .13715 L .65555 .13722 L .65555 .1373 L .65555 .13737 L .65555 .13744 L .65555 .13751 L .65555 .13759 L .65556 .13771 L .65558 .13784 L .6556 .13796 L .65562 .13806 L .65568 .13832 L .65576 .13854 L .65594 .13893 L .65619 .13933 L .65651 .13969 L .65686 .13999 L .65722 .14022 L .65757 .14041 L .658 .14058 L .65843 .14071 L Mistroke .65867 .14076 L .65891 .1408 L .65912 .14083 L .65924 .14084 L .65935 .14085 L .65947 .14086 L .65958 .14086 L .6597 .14087 L .65977 .14087 L .65983 .14087 L .65996 .14086 L .66003 .14086 L .6601 .14086 L .66022 .14085 L .66035 .14084 L .66056 .14082 L .66078 .14079 L .66118 .14071 L .66165 .14059 L .66206 .14045 L .66286 .1401 L .66351 .13969 L .66409 .1392 L .66436 .13891 L .66457 .13864 L .66472 .13839 L .66486 .13811 L .66491 .13797 L .66495 .13783 L .66497 .13776 L .66499 .13769 L .665 .13762 L .66501 .13755 L .66501 .13752 L .66502 .13749 L .66502 .13743 L .66502 .13737 L .66502 .13732 L .66502 .13729 L .66502 .13726 L .66502 .13722 L .66502 .13719 L .66501 .13714 L .665 .13708 L .66498 .13697 L .66495 .13686 L .66487 .13668 L .66478 .13653 L .66467 .13638 L .66452 .13623 L Mistroke .66437 .13612 L .66422 .13602 L .66406 .13595 L .66388 .13588 L .6637 .13583 L Mfstroke .09091 .41202 m .21822 .34725 L .31574 .2853 L .35282 .26513 L .37117 .25698 L .38754 .25103 L .39648 .24836 L .40596 .24598 L .41371 .24439 L .42213 .24302 L .42996 .24206 L .43423 .24166 L .43821 .24137 L .44192 .24116 L .4453 .24102 L .44717 .24097 L .4492 .24092 L .45291 .24088 L .45477 .24087 L .45674 .24089 L .46026 .24094 L .46405 .24104 L .46621 .24112 L .46822 .2412 L .47521 .24158 L .48273 .24211 L .5103 .24472 L .52619 .24632 L .54331 .24782 L .55041 .24831 L .55809 .24873 L .5625 .24891 L .56655 .24904 L .57042 .24912 L .57451 .24915 L .57829 .24914 L .58233 .24909 L .58614 .24898 L .5896 .24885 L .59366 .24864 L .59805 .24835 L .60599 .24763 L .61453 .24658 L .62347 .24516 L .63914 .24177 L .65324 .23769 L .66587 .2331 L .69213 .22033 L .71404 .20548 L .73069 .1904 L Mistroke .74209 .17675 L .74672 .16972 L .75072 .16231 L .75249 .1583 L .75385 .15468 L .7549 .15136 L .75579 .14779 L .75609 .14626 L .75637 .14465 L .75656 .14326 L .75673 .14178 L .75686 .14012 L .75692 .13857 L .75694 .13708 L .75691 .13572 L .75683 .13425 L .75669 .13269 L .75651 .13124 L .7563 .12993 L .75565 .12695 L .75475 .12392 L .75364 .12106 L .75243 .1185 L .74904 .11304 L .7453 .10857 L .74057 .10422 L .73554 .10058 L .73046 .09766 L .72514 .09521 L .71991 .0933 L .71423 .09171 L .71114 .09104 L .70779 .09045 L .70444 .09 L .70273 .08982 L .70085 .08966 L .69924 .08956 L .6975 .08949 L .69586 .08945 L .69435 .08944 L .6935 .08944 L .69258 .08946 L .69093 .08951 L .68992 .08955 L .68897 .08961 L .6872 .08973 L .68361 .09009 L .67975 .09064 L .67324 .09194 L .66659 .0938 L Mistroke .65546 .09818 L .64588 .10352 L .63727 .11007 L .63089 .11668 L .62661 .12283 L .62491 .12616 L .62416 .12796 L .62358 .12963 L .62313 .13117 L .62276 .13281 L .62263 .13353 L .62252 .13428 L .62244 .13496 L .62238 .1356 L .62234 .13641 L .62232 .13713 L .62232 .1379 L .62234 .13834 L .62236 .13873 L .62241 .13938 L .62249 .14009 L .6226 .14082 L .62273 .14149 L .6231 .143 L .62354 .14432 L .62418 .14582 L .62485 .14711 L .62629 .14925 L .62811 .1513 L .63005 .15298 L .63206 .15436 L .63461 .15572 L .63711 .15673 L .64 .15757 L .64149 .1579 L .64316 .15817 L .64461 .15834 L .64544 .1584 L .64621 .15845 L .64695 .15848 L .64762 .15849 L .64839 .1585 L .64912 .15848 L .64978 .15846 L .65048 .15842 L .65108 .15838 L .65173 .15832 L .65318 .15815 L .65452 .15795 L .65751 .15733 L Mistroke .66014 .15659 L .66303 .15554 L .6656 .15439 L .66987 .1519 L .67361 .14891 L .6761 .14619 L .67714 .14474 L .67807 .14315 L .67879 .14154 L .67905 .14081 L .67927 .14005 L .67943 .1393 L .67953 .13863 L .67957 .13832 L .67959 .13798 L .67961 .13766 L .67961 .13737 L .67961 .13704 L .67959 .13669 L .67956 .13636 L .67953 .13607 L .67948 .13573 L .67941 .13537 L .67924 .13473 L .67902 .13409 L .67874 .13344 L .6781 .13235 L .67736 .13143 L .67657 .13067 L .67561 .12995 L .6745 .12931 L .67346 .12885 L .67244 .12851 L .67129 .12823 L .67063 .12812 L .67032 .12808 L .67003 .12804 L .66972 .12801 L .66943 .12799 L .66911 .12797 L .66877 .12796 L .66844 .12795 L .66825 .12795 L .66808 .12795 L .66777 .12796 L .66743 .12798 L .66712 .12799 L .66678 .12802 L .66618 .12809 L .6656 .12817 L Mistroke .66507 .12827 L .66387 .12854 L .6626 .12892 L .66135 .12941 L .66024 .12993 L .6583 .13113 L .65685 .13235 L .65565 .13374 L .65515 .13453 L .65479 .13526 L .65457 .13589 L .65447 .13624 L .65444 .13641 L .65441 .13656 L .65439 .1367 L .65437 .13683 L .65436 .13697 L .65435 .13712 L .65434 .13726 L .65434 .13742 L .65435 .13756 L .65436 .13769 L .65437 .13783 L .65439 .13798 L .65444 .13824 L .65452 .13854 L .65461 .13881 L .65473 .13907 L .65488 .13934 L .6552 .1398 L .65555 .14018 L .65593 .1405 L .65639 .14079 L .65693 .14105 L .65749 .14126 L .65779 .14133 L .65812 .1414 L .6584 .14145 L .65856 .14147 L .65871 .14148 L .65885 .14149 L .659 .1415 L .65914 .14151 L .65927 .14151 L .65942 .14151 L .65955 .14151 L .65968 .1415 L .65981 .1415 L .65996 .14149 L .66011 .14147 L Mistroke .66039 .14144 L .66066 .1414 L .66092 .14135 L .6614 .14123 L .66194 .14106 L .66242 .14088 L .6634 .14037 L .66415 .13982 L .66471 .13928 L .66516 .13866 L .66534 .13831 L .6654 .13816 L .66545 .138 L .66549 .13786 L .66552 .13772 L .66553 .13764 L .66554 .13757 L .66555 .1375 L .66555 .13743 L .66556 .13737 L .66556 .1373 L .66555 .13724 L .66555 .13719 L .66554 .13713 L .66554 .13706 L .66551 .13694 L .66548 .13682 L .66544 .13669 L .66538 .13657 L .66532 .13645 L .66517 .13625 L .66502 .13608 L .66482 .13592 L .66462 .13579 L .66438 .13568 L .66425 .13563 L .66411 .13559 L .66397 .13555 L .66384 .13553 L .66371 .13551 L .66365 .1355 L .66358 .1355 L .66351 .13549 L .66346 .13549 L .66339 .13549 L .66332 .13549 L .66326 .13549 L .66321 .13549 L .66315 .13549 L .66309 .1355 L Mistroke .66297 .13551 L .66285 .13552 L .66264 .13556 L .66242 .13561 L .66219 .13568 L .66181 .13585 L .66149 .13603 L Mfstroke .09091 .44636 m .23423 .37431 L .34583 .31084 L .36934 .30048 L .39307 .29192 L .41445 .28601 L .43329 .28221 L .44459 .28052 L .45492 .27933 L .46617 .27837 L .47182 .27801 L .47803 .27768 L .48335 .27747 L .4884 .27731 L .49422 .27716 L .49953 .27707 L .50452 .277 L .50915 .27696 L .51422 .27692 L .51963 .27689 L .52973 .27682 L .53482 .27677 L .5404 .2767 L .54516 .27661 L .55027 .27649 L .55946 .27619 L .56499 .27595 L .57098 .27561 L .58183 .27481 L .59233 .27377 L .60196 .27254 L .61925 .2696 L .63782 .26525 L .65646 .25947 L .6731 .25296 L .70269 .23778 L .72901 .2195 L .74719 .20316 L .76249 .18548 L .76887 .17615 L .77366 .16763 L .77697 .16025 L .77954 .15258 L .78047 .14872 L .78089 .14655 L .78119 .14459 L .78143 .14256 L .78153 .14145 L .78161 .1404 L .78168 .13856 L Mistroke .7817 .13753 L .78169 .13659 L .78163 .13477 L .78151 .13309 L .78136 .1316 L .78114 .13001 L .78046 .12651 L .7796 .12338 L .7774 .1177 L .77584 .11466 L .77424 .11198 L .76661 .10267 L .76137 .09803 L .75497 .0935 L .74837 .08976 L .74173 .08672 L .73462 .08414 L .72783 .08222 L .72005 .08063 L .71589 .08001 L .71357 .07975 L .71147 .07954 L .70952 .07939 L .70741 .07927 L .70624 .07922 L .70517 .07918 L .70306 .07914 L .70125 .07914 L .69926 .07917 L .69718 .07923 L .69524 .07933 L .69295 .07949 L .69079 .07968 L .68675 .08015 L .68245 .08082 L .67784 .08172 L .67048 .08358 L .66381 .08573 L .64979 .09192 L .63805 .09928 L .62784 .10813 L .62115 .11622 L .61832 .1208 L .61629 .12501 L .61544 .12726 L .61479 .12936 L .61433 .13121 L .61397 .13318 L .61383 .13418 L .61377 .13476 L Mistroke .61373 .13528 L .61369 .13582 L .61367 .1364 L .61365 .13694 L .61365 .13744 L .61367 .13839 L .61372 .13925 L .61381 .14018 L .61387 .1407 L .61394 .14116 L .61424 .14274 L .61468 .14441 L .61527 .1461 L .61593 .14761 L .61736 .15015 L .61922 .15263 L .62181 .15523 L .6246 .15734 L .62736 .15896 L .63057 .1604 L .63376 .16147 L .63687 .1622 L .63868 .16251 L .64036 .16272 L .64125 .16281 L .64222 .16288 L .64271 .16291 L .64323 .16293 L .64373 .16295 L .64418 .16296 L .64512 .16297 L .64559 .16297 L .6461 .16296 L .64702 .16293 L .64787 .16288 L .64888 .16281 L .64979 .16273 L .65184 .16247 L .65358 .16219 L .65545 .16181 L .65877 .16095 L .66219 .15979 L .66524 .15851 L .6704 .15571 L .67507 .15223 L .67725 .15016 L .67898 .14817 L .68035 .14627 L .68137 .14454 L .68224 .14264 L Mistroke .68262 .1416 L .68289 .14066 L .68309 .13975 L .68317 .1393 L .68324 .13881 L .68326 .13857 L .68328 .13833 L .6833 .13806 L .68332 .13782 L .68332 .13738 L .68332 .13713 L .68332 .13691 L .68331 .13669 L .68329 .13647 L .68325 .13606 L .6832 .13567 L .68315 .13532 L .68297 .13454 L .68273 .13374 L .68245 .13303 L .68214 .13238 L .68145 .13124 L .68055 .13014 L .67941 .12908 L .67829 .12828 L .67701 .12756 L .67584 .12705 L .67448 .12661 L .67378 .12643 L .67299 .12627 L .67216 .12614 L .67176 .12609 L .67138 .12605 L .67103 .12602 L .67065 .126 L .6703 .12598 L .66997 .12598 L .66962 .12597 L .66924 .12598 L .66884 .12599 L .66846 .12601 L .66806 .12603 L .66762 .12607 L .66682 .12617 L .66605 .12629 L .66535 .12642 L .66378 .12681 L .66219 .12733 L .65949 .12856 L .65814 .12938 L Mistroke .65702 .13018 L .65528 .13177 L .65451 .13269 L .65393 .13352 L .6535 .13429 L .65313 .13512 L .65298 .13557 L .65287 .13597 L .65279 .13635 L .65276 .13654 L .65274 .13675 L .65272 .13693 L .65271 .13712 L .65271 .13727 L .65271 .13744 L .65271 .13762 L .65273 .13781 L .65275 .13799 L .65277 .13815 L .65283 .13845 L .65291 .13876 L .65312 .13931 L .65325 .13959 L .65342 .13988 L .65378 .14036 L .65427 .14087 L .65479 .14127 L .65538 .14163 L .65608 .14193 L .65641 .14205 L .65678 .14215 L .6571 .14222 L .65744 .14229 L .65777 .14233 L .65795 .14235 L .65812 .14237 L .65828 .14238 L .65842 .14238 L .65859 .14239 L .65875 .14239 L .65892 .14239 L .6591 .14238 L .65926 .14238 L .65943 .14237 L .65961 .14235 L .6598 .14233 L .66015 .14228 L .66082 .14216 L .66143 .142 L .66252 .14161 L Mistroke .66309 .14133 L .66358 .14106 L .66454 .14038 L .66525 .13969 L .66575 .13902 L .66595 .13867 L .66611 .13829 L .66617 .1381 L .66622 .1379 L .66624 .13781 L .66625 .13772 L .66626 .13764 L .66627 .13755 L .66628 .13748 L .66628 .1374 L .66628 .13733 L .66628 .13725 L .66628 .13718 L .66627 .1371 L .66626 .13704 L .66625 .13698 L .66622 .13683 L .66618 .13668 L .66613 .13654 L .66608 .13642 L .66594 .13617 L .66576 .13594 L .66557 .13576 L .66535 .13559 L .66509 .13543 L .66478 .1353 L .66462 .13525 L .66447 .1352 L .66434 .13517 L .66418 .13514 L .6641 .13513 L .66402 .13512 L .66395 .13511 L .66387 .13511 L .6638 .1351 L .66373 .1351 L .66366 .1351 L .66359 .1351 L .66351 .1351 L .66346 .1351 L .66342 .1351 L .66334 .13511 L .66325 .13511 L .66311 .13513 L .66295 .13515 L Mistroke .66268 .1352 L .66239 .13528 L .6619 .13546 L .66148 .13567 L .66109 .13594 L .66078 .13622 L .66056 .13649 L Mfstroke .09091 .48069 m .25027 .40163 L .31564 .36542 L .3764 .3378 L .40599 .32789 L .43178 .32136 L .45695 .31672 L .48024 .31368 L .53195 .3092 L .55972 .30677 L .58532 .30366 L .60627 .30014 L .62824 .29519 L .65172 .28821 L .67218 .28049 L .70758 .26299 L .73663 .24406 L .76228 .22304 L .78349 .2012 L .798 .18199 L .80689 .16603 L .81021 .15775 L .81146 .15374 L .81253 .14947 L .81319 .14591 L .81347 .14395 L .81365 .14219 L .81378 .14058 L .81386 .13884 L .81388 .13721 L .81385 .13573 L .81377 .13405 L .81362 .13226 L .81342 .1306 L .81319 .12909 L .81247 .12565 L .81146 .12213 L .81021 .11879 L .80883 .11575 L .80495 .10914 L .80059 .10351 L .795 .09775 L .78273 .08829 L .76846 .08045 L .75361 .07468 L .74531 .07229 L .74061 .07118 L .73608 .07027 L .73183 .06955 L .72715 .06891 L Mistroke .72286 .06847 L .72078 .0683 L .71886 .06817 L .71636 .06804 L .71504 .06799 L .71365 .06795 L .71131 .06791 L .70998 .06791 L .70874 .06792 L .70643 .06796 L .70432 .06803 L .70189 .06816 L .69959 .06832 L .69452 .0688 L .68987 .0694 L .68483 .07025 L .67955 .07134 L .6707 .07368 L .66291 .07629 L .64673 .08359 L .63434 .09131 L .62349 .10026 L .61489 .10981 L .6112 .11518 L .60853 .12 L .60662 .12442 L .60584 .1267 L .60517 .12908 L .60473 .13112 L .60454 .13219 L .60438 .13333 L .60427 .13436 L .6042 .13529 L .60415 .13622 L .60413 .13709 L .60414 .13806 L .60418 .1391 L .60425 .14006 L .60435 .14094 L .60448 .14189 L .60466 .14292 L .60514 .14494 L .60575 .14687 L .60655 .14885 L .60837 .1522 L .61063 .15526 L .61314 .15786 L .61866 .16194 L .62193 .16366 L .62576 .16521 L Mistroke .62777 .16585 L .62997 .16644 L .63191 .16686 L .63406 .16723 L .63509 .16737 L .63619 .1675 L .63715 .16759 L .63819 .16767 L .63927 .16773 L .64027 .16777 L .64126 .16779 L .64216 .16779 L .64306 .16778 L .64389 .16775 L .64481 .16771 L .64579 .16765 L .64777 .16747 L .64958 .16725 L .65353 .16656 L .65549 .16611 L .65761 .16554 L .66451 .16308 L .66808 .16139 L .67164 .15936 L .67724 .15527 L .68146 .15106 L .68334 .14861 L .68476 .14633 L .68592 .14394 L .68667 .14182 L .68696 .14067 L .68708 .14007 L .68718 .13944 L .68725 .1389 L .68728 .1386 L .6873 .13831 L .68732 .13782 L .68733 .1373 L .68733 .13703 L .68732 .13677 L .68729 .13631 L .68725 .13581 L .68721 .13553 L .68718 .13528 L .68701 .13442 L .68678 .13353 L .68645 .13261 L .68609 .13178 L .68505 .13004 L .68392 .12868 L Mistroke .68274 .12758 L .6812 .12649 L .67962 .12563 L .67808 .125 L .67629 .12446 L .67537 .12426 L .67436 .12408 L .67387 .12402 L .6734 .12396 L .67294 .12392 L .67252 .12389 L .67209 .12387 L .67169 .12385 L .67126 .12384 L .6708 .12384 L .6704 .12385 L .66997 .12387 L .66961 .12389 L .66921 .12391 L .66832 .124 L .66737 .12412 L .66568 .12444 L .66382 .12492 L .66217 .12547 L .66048 .12617 L .65875 .12706 L .65619 .12875 L .65505 .1297 L .654 .13074 L .65318 .1317 L .65243 .13276 L .65188 .13373 L .65149 .13461 L .65131 .1351 L .65116 .13562 L .6511 .13591 L .65105 .13616 L .65101 .13643 L .65098 .13667 L .65096 .13687 L .65095 .13709 L .65095 .13721 L .65094 .13733 L .65095 .13754 L .65096 .13776 L .65098 .13797 L .651 .13819 L .65104 .13842 L .65113 .13884 L .65126 .13926 L Mistroke .6514 .13961 L .65158 .13998 L .65206 .14074 L .65262 .14136 L .65322 .14187 L .65384 .14227 L .6546 .14265 L .65537 .14294 L .6561 .14313 L .65652 .14321 L .65692 .14326 L .65713 .14329 L .65735 .14331 L .65754 .14332 L .65774 .14333 L .65786 .14333 L .65797 .14333 L .65809 .14334 L .6582 .14334 L .65841 .14333 L .65852 .14333 L .65863 .14332 L .65881 .14331 L .659 .1433 L .65934 .14327 L .65974 .14322 L .6601 .14316 L .66088 .14299 L .66159 .14278 L .66298 .14223 L .66362 .1419 L .66427 .14149 L .66526 .14072 L .666 .13994 L .66634 .13948 L .66659 .13906 L .6668 .13862 L .66689 .13838 L .66695 .13815 L .667 .13796 L .66702 .13786 L .66703 .13776 L .66705 .13767 L .66705 .13758 L .66706 .13749 L .66706 .13742 L .66706 .13732 L .66706 .13723 L .66706 .13715 L .66705 .13706 L Mistroke .66704 .13697 L .66702 .13687 L .66699 .1367 L .66693 .13652 L .66686 .13633 L .6667 .13603 L .66649 .13573 L .6662 .13545 L .66592 .13524 L .66559 .13505 L .66526 .13491 L .66494 .13481 L .66478 .13477 L .66459 .13474 L .6645 .13472 L .6644 .13471 L .66432 .1347 L .66422 .13469 L .66413 .13468 L .66405 .13468 L .66396 .13468 L .66387 .13468 L .66378 .13468 L .6637 .13468 L .66362 .13468 L .66354 .13469 L .66345 .1347 L .66336 .1347 L .66316 .13473 L .66296 .13476 L .66276 .13481 L .6624 .1349 L .66208 .13501 L .66148 .13529 L .661 .1356 L .66056 .13598 L .66022 .1364 L .66014 .13653 L Mfstroke .09091 .51503 m .26634 .42921 L .33889 .39213 L .37504 .37688 L .4074 .36582 L .44132 .35695 L .47117 .35115 L .5277 .34324 L .55677 .33939 L .58695 .33452 L .61907 .32755 L .64756 .31925 L .69286 .30088 L .73558 .27683 L .79475 .23076 L .81767 .20757 L .83572 .18536 L .8418 .17629 L .84695 .16732 L .85038 .16001 L .85301 .15279 L .85398 .14925 L .85439 .14742 L .85476 .1455 L .85503 .14376 L .85522 .14219 L .85536 .14064 L .85544 .13919 L .85547 .1384 L .85548 .13753 L .85548 .13663 L .85545 .1358 L .85538 .13432 L .85531 .13349 L .85523 .13274 L .85503 .13116 L .85474 .12946 L .85395 .12609 L .85302 .12316 L .85198 .12054 L .84903 .11484 L .84554 .10971 L .84161 .105 L .83159 .09563 L .81829 .08619 L .80486 .07864 L .78806 .07112 L .77819 .06755 L .76838 .06455 L .75913 .06221 L Mistroke .74899 .06019 L .74311 .05928 L .73774 .05861 L .73513 .05834 L .7323 .0581 L .72964 .05791 L .72715 .05776 L .72423 .05764 L .72269 .0576 L .72103 .05757 L .71929 .05755 L .71764 .05755 L .71617 .05756 L .71456 .05759 L .71165 .05768 L .71018 .05775 L .70856 .05784 L .70569 .05803 L .70303 .05825 L .69787 .05881 L .69227 .05961 L .68121 .06179 L .67194 .06427 L .66243 .06747 L .64253 .0767 L .62715 .08677 L .61461 .09786 L .60584 .10838 L .60232 .11385 L .5993 .11976 L .59811 .12268 L .59706 .12577 L .5963 .12862 L .59602 .12995 L .59579 .13118 L .59561 .13239 L .59547 .13349 L .59537 .1347 L .59529 .13599 L .59527 .13715 L .59528 .1384 L .59531 .13902 L .59535 .13969 L .59545 .14087 L .59559 .14196 L .59577 .14312 L .59621 .14519 L .59677 .14714 L .59739 .14889 L .59919 .15268 L Mistroke .60172 .1565 L .60494 .16008 L .60842 .16303 L .61214 .16549 L .61656 .16775 L .62102 .16945 L .62323 .17012 L .62534 .17066 L .62745 .17112 L .62976 .17151 L .63188 .17179 L .63385 .17198 L .63495 .17206 L .63598 .17212 L .63712 .17216 L .63834 .17218 L .63962 .17218 L .64083 .17215 L .64191 .1721 L .64309 .17204 L .64426 .17195 L .64534 .17185 L .64774 .17156 L .64984 .17123 L .65203 .17082 L .65657 .16971 L .66134 .16818 L .66573 .1664 L .6701 .16423 L .67706 .15975 L .68273 .15471 L .68529 .15175 L .68722 .14901 L .68868 .14641 L .68971 .14401 L .69015 .14273 L .69046 .14157 L .69072 .14031 L .69083 .13962 L .69087 .13929 L .6909 .13898 L .69095 .1384 L .69097 .1381 L .69098 .13778 L .69098 .13725 L .69097 .13668 L .69094 .13618 L .69089 .13565 L .69083 .13515 L .69076 .13471 L Mistroke .69054 .13367 L .69022 .13258 L .68984 .1316 L .68943 .13072 L .68856 .12926 L .68741 .1278 L .68602 .12644 L .68456 .12532 L .68283 .12429 L .68079 .12338 L .67982 .12304 L .67876 .12273 L .67774 .12248 L .6768 .12229 L .67579 .12214 L .67526 .12207 L .67468 .12201 L .67418 .12197 L .67371 .12194 L .67321 .12192 L .67267 .12191 L .67218 .12191 L .67165 .12192 L .67115 .12194 L .67069 .12196 L .67028 .12199 L .66982 .12202 L .66891 .12212 L .66792 .12226 L .66685 .12245 L .66474 .12295 L .66286 .12353 L .66119 .12417 L .65773 .1259 L .65462 .1281 L .65231 .13038 L .6513 .1317 L .65056 .13293 L .65006 .13399 L .64966 .13513 L .64952 .13569 L .64946 .136 L .64942 .13629 L .64939 .13655 L .64937 .13669 L .64936 .13684 L .64935 .13709 L .64934 .13732 L .64935 .13757 L .64935 .13772 L Mistroke .64936 .13785 L .64937 .13798 L .64939 .1381 L .64942 .13838 L .64946 .13861 L .64951 .13885 L .64963 .13928 L .6498 .13977 L .65002 .14026 L .65051 .14108 L .65108 .14175 L .65168 .14231 L .65243 .14284 L .6533 .14331 L .65415 .14365 L .65498 .14389 L .65547 .144 L .65592 .14407 L .65617 .14411 L .65644 .14414 L .6567 .14416 L .65694 .14418 L .65717 .14419 L .65742 .14419 L .65765 .14419 L .65787 .14419 L .65812 .14418 L .65826 .14417 L .65839 .14417 L .65865 .14415 L .65889 .14412 L .65936 .14406 L .65987 .14398 L .66088 .14375 L .6617 .1435 L .66256 .14318 L .66412 .14238 L .66535 .14151 L .66628 .14064 L .6667 .14012 L .66708 .13957 L .66737 .13904 L .66756 .13856 L .66762 .13836 L .66768 .13814 L .66771 .13802 L .66773 .13791 L .66774 .1378 L .66775 .13769 L .66776 .13758 L Mistroke .66777 .13748 L .66777 .13741 L .66777 .13735 L .66777 .13725 L .66777 .13714 L .66776 .13705 L .66775 .13695 L .66773 .13684 L .66769 .13663 L .66764 .13644 L .6675 .1361 L .66741 .13592 L .66731 .13576 L .66705 .13543 L .66682 .1352 L .66652 .13497 L .66619 .13477 L .66585 .13461 L .66549 .13449 L .66527 .13443 L .66507 .13439 L .66485 .13435 L .66466 .13432 L .66454 .13431 L .66449 .13431 L .66442 .13431 L .66437 .1343 L .66431 .1343 L .6642 .1343 L .6641 .1343 L .664 .1343 L .66391 .1343 L .66381 .13431 L .66371 .13431 L .6636 .13432 L .6634 .13434 L .6632 .13437 L .66301 .13441 L .66267 .13449 L .66234 .13459 L .66199 .13471 L .66134 .13503 L .66082 .13536 L .66042 .13571 L Mfstroke .09091 .54936 m .28245 .45706 L .36229 .41951 L .40322 .40459 L .43877 .39446 L .47638 .38622 L .51094 .38014 L .57496 .36918 L .60979 .36149 L .64078 .35264 L .67321 .34083 L .7054 .32616 L .79298 .27049 L .84841 .22406 L .90624 .16609 L .91308 .15761 L .91812 .15024 L .91973 .14737 L .92101 .14459 L .92149 .14333 L .92186 .14219 L .92213 .14119 L .92235 .14016 L .92244 .13963 L .92251 .13915 L .92256 .13868 L .92259 .13823 L .92261 .13772 L .92262 .13726 L .92261 .13676 L .92259 .13651 L .92257 .13623 L .92252 .13572 L .92246 .13526 L .92237 .13476 L .92226 .13424 L .92203 .13338 L .92171 .13244 L .92097 .13081 L .91996 .1291 L .91753 .126 L .91378 .12233 L .9085 .11807 L .8953 .10916 L .87725 .09854 L .85003 .08438 L .81543 .06938 L .79764 .06314 L .77656 .05725 L .76485 .05473 L Mistroke .75903 .0537 L .7537 .05288 L .7485 .05221 L .74284 .05161 L .73971 .05135 L .73683 .05115 L .73406 .05099 L .73114 .05087 L .72801 .05078 L .72515 .05074 L .72357 .05074 L .72185 .05075 L .71873 .05082 L .71582 .05092 L .71273 .05108 L .7101 .05126 L .7072 .05149 L .70075 .05219 L .69386 .0532 L .68167 .05569 L .67058 .05878 L .66071 .06225 L .64018 .07197 L .62319 .08326 L .60877 .09638 L .59889 .10901 L .59489 .11601 L .59338 .11928 L .5922 .12229 L .59127 .12511 L .59059 .12763 L .59002 .13038 L .58979 .13187 L .58961 .13327 L .5895 .1346 L .58945 .13527 L .58942 .136 L .5894 .13729 L .58941 .13847 L .58944 .13915 L .58948 .13985 L .58959 .14109 L .58967 .14178 L .58976 .14241 L .58999 .14383 L .59055 .1463 L .59123 .14851 L .59214 .15084 L .59329 .15321 L .59562 .15695 L Mistroke .59874 .16069 L .60193 .16367 L .60577 .16651 L .60943 .16867 L .6136 .17063 L .61859 .17241 L .62343 .17365 L .62646 .17422 L .62796 .17444 L .62935 .17461 L .6306 .17474 L .63197 .17485 L .63336 .17494 L .63412 .17497 L .63482 .175 L .63613 .17502 L .63687 .17503 L .63755 .17502 L .63881 .175 L .64014 .17495 L .64132 .17488 L .64243 .1748 L .64495 .17455 L .64764 .17419 L .65008 .17377 L .65545 .17254 L .66 .17115 L .66464 .16937 L .6723 .16555 L .68002 .1602 L .68556 .15489 L .68775 .15219 L .68967 .14933 L .69099 .14687 L .69208 .14427 L .69255 .14283 L .69287 .14154 L .693 .14093 L .69312 .14027 L .69321 .13966 L .69327 .13909 L .6933 .13874 L .69333 .13837 L .69335 .13773 L .69335 .13737 L .69335 .13699 L .69334 .13667 L .69332 .13632 L .69328 .1357 L .69324 .13536 L Mistroke .6932 .13505 L .69311 .13446 L .693 .13391 L .69275 .1329 L .6924 .13184 L .69147 .12981 L .69044 .1282 L .68912 .12664 L .68734 .12504 L .68544 .12374 L .68358 .12278 L .68141 .12193 L .68031 .12159 L .67909 .12129 L .67792 .12106 L .67683 .12089 L .67583 .12078 L .67526 .12073 L .67473 .1207 L .67417 .12068 L .67366 .12066 L .67307 .12066 L .67251 .12067 L .67195 .12068 L .67163 .1207 L .67133 .12072 L .67074 .12076 L .6701 .12082 L .66894 .12096 L .6679 .12112 L .66553 .12163 L .66314 .12233 L .65936 .1239 L .65583 .12597 L .65308 .12818 L .65111 .13031 L .65025 .13152 L .64951 .13279 L .64902 .13387 L .64863 .13503 L .64848 .13566 L .64843 .13596 L .64838 .13623 L .64835 .13654 L .64833 .1367 L .64832 .13688 L .64831 .13704 L .64831 .13719 L .64831 .13747 L .64832 .13774 L Mistroke .64834 .13801 L .64836 .13824 L .6484 .13849 L .64844 .13875 L .6485 .13903 L .64864 .13952 L .64881 .14 L .64903 .14048 L .64952 .1413 L .65015 .14208 L .65098 .14283 L .65178 .14337 L .65272 .14386 L .65367 .14422 L .65458 .14447 L .65508 .14457 L .65553 .14464 L .65579 .14467 L .65606 .1447 L .65633 .14472 L .65657 .14473 L .65679 .14474 L .657 .14475 L .65723 .14475 L .65748 .14475 L .65774 .14474 L .65799 .14472 L .65821 .14471 L .65845 .14469 L .65895 .14463 L .6595 .14455 L .66059 .14432 L .66157 .14403 L .66245 .14371 L .66408 .14291 L .66554 .14191 L .66655 .14098 L .66701 .14043 L .66738 .13991 L .66764 .13948 L .66786 .13902 L .66802 .13861 L .66812 .13823 L .66817 .13802 L .6682 .13783 L .66821 .13773 L .66822 .13763 L .66823 .13752 L .66823 .13741 L .66823 .13731 L Mistroke .66823 .13721 L .66822 .13711 L .66822 .13702 L .66821 .13692 L .66819 .13681 L .66815 .13662 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{306, 189}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc00?o1@03ocl0000E00;o0P02o`030?l000P02?l?00?o2P000ol0001a00;o0P02o`D01Ol<00Ko 2`02o`H00_lm000050000ol00002o`<000Co00001_l800Oo2`02o`T00_m`0003o`0000;o1@02oaL0 0_l;00?o1@03ocX0000B00;o00<0ool01@04oaD00_l;00;o2@02ofd000Co0?oo1003o`X000?o0000 3P03o`/00_l600;o>00001000_l20003o`0000801?lJ00;o2`02o`T00omY0003o`3o00@00_l500So 00<0ool01ol:00;o2`000ol0000500?o=@0000l000Go0000o`0300;o0`000ol0000J00;o2`03o`T0 0_mU00;o00<0o`000P02o`<01?lB00;o2P02o`X000?o00001`02oc<0000>0003o`0000;o0P02o`D0 00Co00003Ol>00;o3002o`T00_mR0004o`3oo`800_l200?o6002o`X00_l900;o2@02oc40000>0003 o`3o00<000?o00001@04o`d00ol=00;o30000ol0000800;oG`000ol0o`030003o`0000;o1@0?o`T0 0_l:0003o`0000P000?o00002002obl0000=0003o`3o00<000?o00001003oa<00_l=0003o`0000X0 00?o00002@02oe`000?o0?l00`001?l00?l500;o3`03o`P00_l90003o`0000P000?o00002@02obd0 000<0003o`3o00<000?o00000P03o`8000?o00004`02o`/000?o00002`000ol0000:00;oF@000ol0 o`030004o`00o`<00ol200go1@02o`P000?o00001`000ol000080003o`0000X00_l[00002`000ol0 o`030003o`00008000?o00000`000ol0000E0003o`0000T000?o00002`000ol0o`03o`P00_lY00?o :P000ol0o`030004o`3oo`<000?o00000ol=00;o1@000ol000060003o`0000H000?o00000P02o`D0 00?o00002`02oa/00ol400;o1@0000X000?o0?l00`000ol000020003o`0000@03Ol<0003o`0000T0 00?o00002`000ol0o`0<00;o:0000ol0000X0003o`3o00<000So0?oo0?l0o`8000?o000040000ol0 000300;o1P000ol0000700;o00D0o`00o`050003o`0000`000?o00006@000ol000020004o`00o`@0 00090003o`3o00<000?o00000P000ol0000300?o3002o`/000?o00002@000ol0000;0003o`3o00d0 00?o00008`04obP000?o0?l00`001?l00?l200;o00<0ool05002o`D000?o000010000ol0000800;o 0P000ol000040003o`0000`00_lI0003o`00008000Co003o100000P000Co003o0P000ol000020003 o`0000<000Co003o3P000ol000080003o`0000X000?o00002P001?l00?l=0003o`00028000?o0?l0 :@000ol0o`020004o`0000Co00<0o`005`000ol000020003o`0000D000?o00001`001?l0ool80003 o`0000d000?o00005P000ol000020004o`00o`@000080003o`3o008000?o00000P000ol000030005 o`000?l03`000ol0000800;o2P000ol0000:00;o00<0o`003@000ol0000Q0003o`3o02P000?o0?l0 0P001?l00002o`040?l0oaX000?o00000P000ol000050003o`0000L000Co003o20000ol0000=0003 o`0001D000?o00000P001?l00?l400002002o`<000?o00000P001?l00002o`@000?o00003P000ol0 00080003o`0000T000?o00002P02oa0000?o00008@02obP000?o0?l00P001?l00?l200?o70000ol0 00020003o`0000@000?o00001`03o`T000?o00003P02oa@00_l500;o1@0000L000?o0?l00`001Ol0 003o00<000?o00000`08o`/000?o00001`000ol000090003o`0000/000?o00003`02odX000?o0?l0 0P001?l00?l20003o`3o00L02?l>0003o`00008000?o000010000ol000070003o`0000X000?o0000 3`000ol0000O00001`000ol0o`020005o`000?l010000ol0000200_o2@000ol000080003o`0000T0 00?o00002P000ol0000A0003o`0004L000?o0?l00P002?l00?l0o`3o1P0;o`h000?o00000P000ol0 00040003o`0000L000?o00002@000ol0000@0003o`0001h000060004o`3oo`8000Go0000o`030004 o`0000go2P000ol000070003o`0000T000?o00002P000ol0000A0003o`0004L000Go0?l0o`020006 o`00o`3o1@0=o`d000?o00000P000ol000040003o`0000L000?o00002@000ol0000A0003o`0001d0 00060003o`3o008000Go0000o`0300;o0`0>o`T000?o00001`000ol000090003o`0000X00_lC0003 o`0004H00ol01P3o003o00Co1006o`030?oo00Go3@000ol000020003o`0000@00_l80003o`0000T0 00?o00004@000ol0000M00001P000ol0o`020005o`000?l00`001?l0000?o`T000?o00001`02o`X0 00?o00002`000ol0000A0003o`0004H00_l20008o`00o`3o0?l500Oo00<0ool01?l=0003o`000080 00?o00001@000ol000060003o`0000T00_lB0003o`0001d000000`3oo`3oobSo200000H000?o0?l0 0P000ol00002o`<000Co00001ol00`3o0005o`<000?o00000`000ol000050003o`3o00X00_l<00;o 2`000ol000050003o`0000<000?o00002P000ol0000;0003o`0000X000?o00002P000ol0000;00;o 0P001Ol00?l000?o00<0o`000P07o`030?oo00Co2@001Ol0003o00@000?o00000P001?l00?l800;o 2P02o`030?l000/000Go0000o`090003o`0000X000?o00001P0000H000?o0?l00`000ol00002o`80 0_l300Go00<0ool01_l90003o`0000L000?o00002@000ol0000:0003o`00018000?o00007P000ol0 000U0005o`3o0?l00P000ol00004o`@01?l300Ko3@000ol000020003o`0000@000?o00001`02o`X0 00?o00004@000ol0000D0003o`0000H000060004o`00o`8000Go0000o`0300;o1P02o`050?ooo`00 0_l:0003o`0000L000?o00002@000ol0000:0003o`00014000?o0000A`001?l0o`02o`060?l00?l0 0_l900Go00<0ool03@000ol000020003o`0000@000?o00001`000ol000090003o`00014000?o0000 7@0000L000?o0?l00P02o`<000?o00000P07o`040?l000;o00<0o`0020000ol000080003o`0000T0 00?o00002P000ol0000A0003o`0004L00ol20004o`00o`801?l600?o00<0ool00ol>0003o`000080 00?o000010000ol000070003o`0000T000?o000040000ol0000N000020000ol0o`020003o`000080 00?o00001`02o`801?l:0003o`0000P000?o000020000ol0000;0003o`00010000?o0000B@000ol0 o`020004o`00o`800_l00`3oo`00003o`000280 000=00?o00<0ool02?l00`3oo`0=0003o`0000P000?o00002@000ol0000:0003o`00010000?o0000 DP0?oa<000?o00000P000ol000050003o`0000H000?o00002@000ol0000>0003o`0002<0000@00Wo 0`000ol0000;0003o`0000T000?o00002@000ol0000:0003o`0000l000?o0000EP09oaD000?o0000 0P000ol000050003o`0000H000?o00002@000ol0000>0003o`0002@0000L0003o`0000T00_l;0003 o`0000T000?o00002`000ol0000>0003o`0007@000?o00000`000ol000050003o`0000H000?o0000 2@000ol0000=0003o`0002D0000L0003o`0000P000?o00002P000ol0000:0003o`0000X000?o0000 3P000ol0001d0003o`0000<000?o00001@000ol000060003o`0000T000?o00003@000ol0000V0000 70000ol000070003o`0000/000?o00002@000ol0000:0003o`0000h000?o0000M0000ol000030003 o`0000D000?o00001`000ol000090003o`0000`000?o00009`0001`000?o00001@02o`d000?o0000 2@000ol0000:0003o`0000h000?o0000M0000ol000030003o`0000D000?o00001`000ol0000:0003 o`0000/000?o0000:00001`000?o00000`02o`h000?o00002P000ol000090003o`0000h000?o0000 M0000ol000030003o`0000D000?o00001`000ol0000:0003o`0000/000?o0000:@0001`000?o0000 0P000ol0000=0003o`0000X000?o00002@000ol0000>0003o`0007<00_l50003o`0000D000?o0000 20000ol000090003o`0000/000?o0000:P0001`000?o00000_l>00;o30000ol0000:0003o`0000`0 0_lK013oB@02o`H000?o00001@000ol000080003o`0000T000?o00002`000ol0000[00007003o`l0 00?o00002P02o``000?o000030000ol0000H00?o4005od<000?o00001@000ol000050003o`0000P0 00?o00002@000ol0000;0003o`0002`0000L00;o3`000ol0000:0003o`0000/000?o000030000ol0 000F00?o6004ocd00_l600;o1`000ol000080003o`0000T000?o00002`000ol0000]000070000ol0 000=0003o`0000X000?o00002`000ol0000<0003o`0001@00olO00?o>002o`H00_l80003o`0000P0 00?o00002@000ol0000;0003o`0002h0000L0003o`0000`000?o00002P000ol0000;0003o`0000`0 00?o00004`02obD01?lb00;o1`000ol000070003o`0000P000?o00002P000ol0000:0003o`0002l0 000L0003o`0000X00_l<0003o`0000/000?o000030000ol0000B00;o:`03obd00_l700;o2@000ol0 00080003o`0000X000?o00002P000ol0000`000070000ol0000800;o3002o``00_l>0003o`000180 00?o0000;P03obL00ol700;o2@02o`X000?o00002P000ol0000:0003o`000340000L0003o`0000L0 00?o00002`000ol0000;0003o`0000d000?o00004@02oc@01?lQ00;o2002o`X000?o00002002o``0 00?o00002P000ol0000b000070000ol0000500;o3@000ol0000;0003o`0000d000?o00004@000ol0 000h00Oo5@05o`P00_l;0003o`0000P000?o00002`000ol0000900;o=@0001`000?o00000`02o`h0 00?o00002`000ol0000=0003o`0001000_m201Go2`02o`/00_l:0003o`0000/000?o00002@000ol0 000e000070000ol00003o`l000?o00002`000ol0000=0003o`00010000?o0000H002o``000?o0000 2002o``00_l;0003o`0003H0000L00?o4@000ol0000:00;o3`000ol0000@0003o`00060000?o0000 2`000ol000080003o`0000/000?o00002P000ol0000g00007002oa4000?o00002P000ol0000=00;o 4@02of000ol<00;o2P000ol0000;0003o`0000T00_lj000070000ol0000>00;o30000ol0000=0003 o`00010000?o0000700HobL01Ol=00;o2P02o``00_l;0003o`0003X0000L0003o`0000`00_l=0003 o`0000d000?o00003`02oaX01OlH00co5@06o`l00ol;0003o`0000/000?o00002P000ol0000k0000 70000ol0000:00;o3@02o`h00_lA0003o`0001L00olY01Go4`02o`d000?o00002P02o``000?o0000 ?00001`000?o00002@000ol0000<0003o`0000d000?o000040000ol0000E00?oDP02o`d00_l<0003 o`0000/000?o0000?@0001`000?o00001`02o`h000?o00003@000ol0000?00;o5004oe800ol>0003 o`0000/000?o00002P02od00000L0003o`0000D00_l?0003o`0000`00_lA0003o`0001800_mD00;o 40000ol0000:00;o30000ol00010000070000ol0000300;o40000ol0000<0003o`0000l00_lC00;o D`03oa000_l<0003o`0000/000?o0000@@0001`000Co00000_l@00;o3P000ol0000>00;o4`02oe40 1?lA00;o3002o`d000?o0000@P0001<01?l50004o`00oa4000?o00003@000ol0000>0003o`000140 0_m>00Go4P03o`d000?o00002`02odD0000D0003o`0000D00ol@00;o3P02o`l00_lB00;oB@07oaD0 0_l?0003o`0000/000?o0000A@0001D000?o00001002o`l00_l?0003o`0000d00_lC0003o`0002P0 8OlJ00;o3`02o``00_m800005P000ol000030003o`0000d000?o00003P000ol0000=0003o`000140 0_lP00_o>@02o`l00_l=0003o`0004P0000C0004o`00o`D000?o00002`02o`l00_l>00;o4P02oah0 1?m200;o3`02o`d00_m;00005002o`H000?o00002P000ol0000>0003o`0000`00_lB00;o6`05od@0 0_l?00;o3P000ol0001;000070000ol0000800;o40000ol0000;00;o4`000ol0000H00?oAP03oa00 00?o00003002odh0000L0003o`0000H00_l@00;o3@000ol0000A00;o5`04odH00olA00;o3P000ol0 001>000070000ol0000400;o4002o`d00_lB00;o5P03odD01OlB00;o3P02oe40000L0003o`000080 0_lA0003o`0000/00_lC0003o`0001<00om200Ko5@02o`h00_mC000070000ol00002oa400_l=0003 o`0001400_lC00?o?P07oaT00_l?0003o`0005<0000L00?o4@02o`d00_lC0003o`0001400_li00So 7P02o`l00_mF00007002oa000_l=00;o4`02oa800_l_00co8`03oa0000?o0000EP0001`000?o0000 3P000ol0000<0003o`0001400_lB00;o9P0;obd00_lA00;oF@0001`000?o00003002o`d00_lC0003 o`00014000?o00007`07ocH00_lB0003o`0005T0000L0003o`0000X00_l=00;o4`02oa800_lL00Ko >P03oa800_mL000070000ol0000800;o3@02oa<00_lB00;o6P04oc/01OlD0003o`0005`0000L0003 o`0000H00_l>0003o`00018000?o00004002oaT00olk00Co5`02oel0000L0003o`0000@00_l>00;o 4`02oa8000?o00005P03ocT01OlH00?oH@0001`000?o00000P02o`h00_lD0003o`0001000_lF00?o >004oa/00_mT000070000ol00002o`l000?o00004P02oa400_lE00?o=P05oa`00omV00007003o`l0 0_lC00;o4@02oaD00_lc00Ko7`02ofT0000L00;o3P02oa@000?o000040000ol0000B00?o;009ob<0 0_m[000070000ol0000;00;o5002oa400_lC00;o9P09obT00om]000070000ol0000:0003o`000180 0_lA00;o4`02ob801_l`00;oL00001`000?o00002002oa<00_lB0003o`0001400_lP00Co<`03og80 000L0003o`0000H00_lC00;o4P02oa400olN00Co00;o4P02oa@00_oI000070000ol0000<00;o4P02oa@00_oK000070000ol0000:00;o 4P02oa@00_oM000070000ol0000800;o4P02oa@00_oO000070000ol0000600;o4P02oa@00_oQ0000 70000ol0000400;o4P02oa@00_oS000070000ol0000200;o4P02oa@00_oU000070000ol00002oa80 0_lD00;oi`0001`00olB00;o5002onT0000L00;o4@02oa<00oo[000070000ol0000>00;o4`02onh0 000L0003o`0000`00_lC00;ol00001`000?o00002P02oa<00_ob000070000ol0000800;o4`02oo@0 000L0003o`0000H00_lC00;omP0001`000?o00001002oa<00_oh000070000ol0000200;o4`02ooX0 000L0003o`0000;o4`02oo`0000L00?o4`02ooh0000L00;o4P02ool00@0001`000?o00003`02ool0 0`0001`000?o00003@02ool01@0001`000?o00002P03ool01`0001`000?o00002002ool02P0001`0 00?o00001P02ool0300001`000?o00001002ool03P0001`000?o00000P02ool0400001@00_l60003 o`0000;oo`0B00004`001?l00?l500?oo`0D00004`001?l00?l500;oo`0E00004`03o`H000?o0000 o`0D00004`000ol000060003o`000?l0500001@00ol50003o`000?l0500001`000?o0000o`0D0000 70000ol0003o01@0000L0003o`000?l0500001`000?o0000o`0D000070000ol0003o01@0000L0003 o`000?l0500001`00_oo01D0000L0003o`000?l0500001`000?o0000o`0D000070000ol0003o01@0 000L0003o`000?l0500001`000?o0000o`0D000070000ol0003o01@0000L0003o`000?l0500001`0 00?o0000o`0D000070000ol0003o01@0000L0003o`000?l050000001\ \>"], ImageRangeCache->{{{0, 305}, {188, 0}} -> {-1.03875, -2.22076, 0.0370485, 0.0490465}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "Here the critical velocity appears to be around ", StyleBox["3.1", FontFamily->"Courier", FontWeight->"Bold"], ". For initial velocities below this, the pendulum swings back and forth \ with ever decreasing angles ", StyleBox["x", FontFamily->"Courier", FontWeight->"Bold"], " (", StyleBox["theta", FontFamily->"Courier", FontWeight->"Bold"], ") and velocity ", StyleBox["y", FontFamily->"Courier", FontWeight->"Bold"], " (", StyleBox["theta'", FontFamily->"Courier", FontWeight->"Bold"], ") coordinates. For initial velocities above ", StyleBox["3.1", FontFamily->"Courier", FontWeight->"Bold"], ", the pendulum swings around once, bringing all the angles to a range \ between ", StyleBox["Pi", FontFamily->"Courier", FontWeight->"Bold"], " and ", StyleBox["3Pi", FontFamily->"Courier", FontWeight->"Bold"], ". The damping causes the pendulum to slow down and again the velocity \ decreases to ", StyleBox["0", FontFamily->"Courier", FontWeight->"Bold"], " while the the angles approach ", StyleBox["2Pi", FontFamily->"Courier", FontWeight->"Bold"], ". Let's plot some solutions near the critical velocity." }], "Text"], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]]-0.5y[t], x[0] == 0, y[0] == 3.1}, {x[t],y[t]},{t,0,20}]]],{t,0,20},PlotRange->{{-1,8},{-2,4}}]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.111111 0.111111 0.206011 0.103006 [ [.33333 .19351 -3 -9 ] [.33333 .19351 3 0 ] [.55556 .19351 -3 -9 ] [.55556 .19351 3 0 ] [.77778 .19351 -3 -9 ] [.77778 .19351 3 0 ] [1 .19351 -3 -9 ] [1 .19351 3 0 ] [.09861 0 -12 -4.5 ] [.09861 0 0 4.5 ] [.09861 .10301 -12 -4.5 ] [.09861 .10301 0 4.5 ] [.09861 .30902 -6 -4.5 ] [.09861 .30902 0 4.5 ] [.09861 .41202 -6 -4.5 ] [.09861 .41202 0 4.5 ] [.09861 .51503 -6 -4.5 ] [.09861 .51503 0 4.5 ] [.09861 .61803 -6 -4.5 ] [.09861 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .33333 .20601 m .33333 .21226 L s [(2)] .33333 .19351 0 1 Mshowa .55556 .20601 m .55556 .21226 L s [(4)] .55556 .19351 0 1 Mshowa .77778 .20601 m .77778 .21226 L s [(6)] .77778 .19351 0 1 Mshowa 1 .20601 m 1 .21226 L s [(8)] 1 .19351 0 1 Mshowa .125 Mabswid .16667 .20601 m .16667 .20976 L s .22222 .20601 m .22222 .20976 L s .27778 .20601 m .27778 .20976 L s .38889 .20601 m .38889 .20976 L s .44444 .20601 m .44444 .20976 L s .5 .20601 m .5 .20976 L s .61111 .20601 m .61111 .20976 L s .66667 .20601 m .66667 .20976 L s .72222 .20601 m .72222 .20976 L s .83333 .20601 m .83333 .20976 L s .88889 .20601 m .88889 .20976 L s .94444 .20601 m .94444 .20976 L s .05556 .20601 m .05556 .20976 L s .25 Mabswid 0 .20601 m 1 .20601 L s .11111 0 m .11736 0 L s [(-2)] .09861 0 1 0 Mshowa .11111 .10301 m .11736 .10301 L s [(-1)] .09861 .10301 1 0 Mshowa .11111 .30902 m .11736 .30902 L s [(1)] .09861 .30902 1 0 Mshowa .11111 .41202 m .11736 .41202 L s [(2)] .09861 .41202 1 0 Mshowa .11111 .51503 m .11736 .51503 L s [(3)] .09861 .51503 1 0 Mshowa .11111 .61803 m .11736 .61803 L s [(4)] .09861 .61803 1 0 Mshowa .125 Mabswid .11111 .0206 m .11486 .0206 L s .11111 .0412 m .11486 .0412 L s .11111 .0618 m .11486 .0618 L s .11111 .0824 m .11486 .0824 L s .11111 .12361 m .11486 .12361 L s .11111 .14421 m .11486 .14421 L s .11111 .16481 m .11486 .16481 L s .11111 .18541 m .11486 .18541 L s .11111 .22661 m .11486 .22661 L s .11111 .24721 m .11486 .24721 L s .11111 .26781 m .11486 .26781 L s .11111 .28842 m .11486 .28842 L s .11111 .32962 m .11486 .32962 L s .11111 .35022 m .11486 .35022 L s .11111 .37082 m .11486 .37082 L s .11111 .39142 m .11486 .39142 L s .11111 .43262 m .11486 .43262 L s .11111 .45322 m .11486 .45322 L s .11111 .47383 m .11486 .47383 L s .11111 .49443 m .11486 .49443 L s .11111 .53563 m .11486 .53563 L s .11111 .55623 m .11486 .55623 L s .11111 .57683 m .11486 .57683 L s .11111 .59743 m .11486 .59743 L s .25 Mabswid .11111 0 m .11111 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .11111 .52533 m .17271 .49143 L .23158 .44869 L .32131 .36542 L .41591 .26132 L .44775 .22652 L .45494 .22006 L .45802 .21788 L .46048 .21657 L .46163 .21612 L .46285 .21577 L .46345 .21565 L .46377 .2156 L .46408 .21556 L .46437 .21553 L .46452 .21552 L .46468 .21551 L .46496 .2155 L .46523 .21549 L .46537 .21549 L .46552 .21549 L .46579 .2155 L .46594 .21551 L .46608 .21552 L .4664 .21555 L .46668 .21558 L .46693 .21561 L .46751 .21571 L .4686 .21595 L .46967 .21627 L .47201 .21718 L .47475 .21854 L .48065 .22201 L .49905 .23439 L .53497 .25886 L .59679 .29625 L .64268 .31759 L .66922 .32665 L .68509 .33074 L .69296 .33237 L .70029 .33365 L .70727 .33464 L .715 .33548 L .71904 .3358 L .72282 .33603 L .72491 .33613 L .72682 .3362 L .72902 .33626 L .73112 .33629 L .73465 .3363 L Mistroke .7384 .33623 L .74194 .3361 L .74514 .33593 L .74891 .33566 L .75298 .33527 L .7603 .33435 L .76682 .33328 L .77388 .33183 L .78786 .32807 L .80037 .32362 L .81157 .31869 L .83664 .30399 L .85683 .28749 L .87165 .27144 L .87853 .26222 L .88403 .25355 L .88882 .24452 L .89233 .23637 L .89527 .22754 L .89641 .22302 L .89733 .21835 L .89766 .2162 L .89792 .21419 L .89803 .21309 L .89814 .2119 L .89828 .20985 L .89836 .20791 L .89839 .20588 L .89836 .20418 L .89829 .20233 L .89822 .20122 L .89813 .20017 L .89793 .19824 L .89765 .1962 L .89727 .19401 L .89641 .19019 L .89539 .18678 L .89307 .18093 L .8899 .17512 L .88634 .17013 L .88262 .166 L .87765 .16161 L .87259 .15811 L .86693 .15507 L .86357 .15363 L .86039 .15248 L .85746 .1516 L .85418 .1508 L .85084 .15016 L .84898 .14989 L Mistroke .84727 .14969 L .84565 .14954 L .84411 .14943 L .84248 .14936 L .84155 .14933 L .8407 .14932 L .83913 .14933 L .83771 .14936 L .83608 .14944 L .83454 .14955 L .83316 .14968 L .83165 .14985 L .82863 .15028 L .82328 .15138 L .81719 .15313 L .81172 .1552 L .8061 .15784 L .80035 .16115 L .79104 .16809 L .78357 .17567 L .77819 .18306 L .77598 .18695 L .77406 .19112 L .77268 .195 L .77177 .19848 L .7714 .20044 L .77116 .20223 L .77106 .20324 L .77099 .20415 L .77097 .20465 L .77095 .20519 L .77094 .20616 L .77096 .20708 L .77098 .2076 L .77101 .20808 L .77109 .20904 L .7712 .21005 L .77134 .21097 L .7715 .21183 L .77186 .21339 L .77235 .21502 L .77289 .21648 L .7741 .21904 L .7757 .22155 L .77772 .22393 L .77971 .22575 L .78201 .22738 L .7841 .22853 L .7865 .22955 L .78786 .23 L Mistroke .78936 .23039 L .7908 .23069 L .79149 .2308 L .79214 .23089 L .79278 .23096 L .79336 .23101 L .79401 .23106 L .79471 .23109 L .79537 .23111 L .7961 .2311 L .79679 .23109 L .79743 .23105 L .79818 .231 L .79898 .23092 L .80043 .23073 L .80183 .23048 L .8031 .23019 L .80593 .22936 L .8088 .22824 L .81332 .2258 L .81751 .22262 L .82076 .21926 L .82307 .21603 L .82406 .21424 L .8249 .21233 L .82544 .21073 L .82567 .20989 L .82586 .20901 L .82594 .20855 L .82602 .20806 L .82607 .20762 L .82611 .20722 L .82613 .20698 L .82614 .20675 L .82615 .20651 L .82616 .20625 L .82616 .20603 L .82616 .2058 L .82614 .20538 L .82612 .205 L .82609 .2046 L .82604 .20423 L .82599 .20389 L .82584 .20309 L .82565 .20235 L .82515 .201 L .82458 .19989 L .82377 .19873 L .8229 .19778 L .822 .19701 L Mistroke .82111 .19641 L .82007 .19587 L .81891 .19542 L .8183 .19525 L .8177 .19511 L .81716 .19501 L .81657 .19494 L .81627 .19491 L .81609 .1949 L .81593 .19489 L .81576 .19488 L .81558 .19487 L .81524 .19487 L .81496 .19487 L .81464 .19488 L .81432 .1949 L .81401 .19493 L .81341 .195 L .81285 .19509 L .81182 .19531 L .81073 .19564 L .8096 .19607 L .80757 .19714 L .80564 .19857 L .8048 .19937 L .80401 .20027 L .80288 .20195 L .80243 .20286 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc002ocT00_li00?o7@000ol0000H00;o 2P0002<000?o0000[P000ol0000L00;o9@0002<000?o0000[@000ol000090003o`00018000?o0000 8`0002<000?o0000[@000ol0000600Go4`000ol0000S00008`000ol0002]0003o`0000D00_l300;o 4P000ol0000S00008`000ol0002/0003o`0000H000?o00000`000ol0000@0003o`0002<000060?oo 2ol:00005@000ol0000;0003o`0000`000?o000030000ol0000<0003o`0000/000?o000030000ol0 000<0003o`0000`000?o00002`000ol0000<0003o`0000`000?o00002`000ol0000:00?o30000ol0 o`0>0003o`3o00/000?o000030000ol0000800008`000ol0001J00?oD0000ol0000:0003o`000140 00?o00008`0002<000?o0000F@001?l00002odh000?o00002P000ol0000A0003o`0002<0000S0003 o`0005P000?o00001002odd000?o000020000ol0000B0003o`0002<0000S00;oF0000ol0000700;o C0000ol0000500;o50000ol0000T00008`000ol0001F0003o`0000X000?o0000BP07oaH000?o0000 900002<000?o0000E@000ol0000<00;oI`000ol0000T00008`000ol0001D0003o`0000l000?o0000 I0000ol0000T00008`000ol0001C0003o`0001400_mT0003o`0002@0000S0003o`00058000?o0000 50000ol0001P0003o`0002D0000S00;oDP000ol0000F0003o`0005h000?o00009P0002<000?o0000 D0000ol0000H00;oG@000ol0000W00008`000ol0001?0003o`0001/000?o0000FP000ol0000W0000 8`000ol0001>0003o`0001d00_mI0003o`0002P0000S0003o`0004h000?o00007`000ol0001F0003 o`0002P0000S00;oCP000ol0000Q00;oE@000ol0000Y00008`000ol0001<0003o`0002@00_mB0003 o`0002X0000S0003o`0004/000?o00009`000ol0001>0003o`0002/0000S0003o`0004X000?o0000 :@02odd000?o0000;00002<000?o0000B@000ol0000/0003o`0004T000?o0000;@0002<000?o0000 B0000ol0000^00;oB0000ol0000^00008`02odP000?o0000<@02odD000?o0000;`0002<000?o0000 AP000ol0000d0003o`00044000?o0000<00002<000?o0000AP000ol0000e00;o@0000ol0000a0000 6`03o`D000?o0000A@000ol0000h00?o?0000ol0000b000070000ol000040003o`0004@000?o0000 ?002ocP00_le000070000ol0000400?o@`000ol0000o00;o=002ocL0000L0003o`0000@000?o0000 @P000ol0001200?o<0000ol0000g000070000ol000040003o`00044000?o0000AP02ob`00_lj0000 6`02o`H000?o0000@0000ol0001900?o9`02oc`0000S0003o`0003l000?o0000C@02ob800oln0000 8`02ocl000?o0000D004oaX01?m100008`000ol0000m0003o`0005D01OlA00CoA@0002<000?o0000 ?@000ol0001J017oB@0002<000?o0000?0000ol0002e00008`000ol0000k0003o`000;H0000S0003 o`0003X000?o0000]`0002<00_lj0003o`000;P0000S0003o`0003P000?o0000^@0002<000?o0000 =`000ol0002j00008`000ol0000f0003o`000;/0000S0003o`0003@00_nn00008`02oc@000?o0000 _P0002<000?o0000"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-1.21441, -2.16465, 0.0339167, 0.0365854}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]]-0.5y[t], x[0] == 0, y[0] == 3.08}, {x[t],y[t]},{t,0,20}]]],{t,0,20},PlotRange->{{-1,8},{-2,4}}]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.111111 0.111111 0.206011 0.103006 [ [.33333 .19351 -3 -9 ] [.33333 .19351 3 0 ] [.55556 .19351 -3 -9 ] [.55556 .19351 3 0 ] [.77778 .19351 -3 -9 ] [.77778 .19351 3 0 ] [1 .19351 -3 -9 ] [1 .19351 3 0 ] [.09861 0 -12 -4.5 ] [.09861 0 0 4.5 ] [.09861 .10301 -12 -4.5 ] [.09861 .10301 0 4.5 ] [.09861 .30902 -6 -4.5 ] [.09861 .30902 0 4.5 ] [.09861 .41202 -6 -4.5 ] [.09861 .41202 0 4.5 ] [.09861 .51503 -6 -4.5 ] [.09861 .51503 0 4.5 ] [.09861 .61803 -6 -4.5 ] [.09861 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .33333 .20601 m .33333 .21226 L s [(2)] .33333 .19351 0 1 Mshowa .55556 .20601 m .55556 .21226 L s [(4)] .55556 .19351 0 1 Mshowa .77778 .20601 m .77778 .21226 L s [(6)] .77778 .19351 0 1 Mshowa 1 .20601 m 1 .21226 L s [(8)] 1 .19351 0 1 Mshowa .125 Mabswid .16667 .20601 m .16667 .20976 L s .22222 .20601 m .22222 .20976 L s .27778 .20601 m .27778 .20976 L s .38889 .20601 m .38889 .20976 L s .44444 .20601 m .44444 .20976 L s .5 .20601 m .5 .20976 L s .61111 .20601 m .61111 .20976 L s .66667 .20601 m .66667 .20976 L s .72222 .20601 m .72222 .20976 L s .83333 .20601 m .83333 .20976 L s .88889 .20601 m .88889 .20976 L s .94444 .20601 m .94444 .20976 L s .05556 .20601 m .05556 .20976 L s .25 Mabswid 0 .20601 m 1 .20601 L s .11111 0 m .11736 0 L s [(-2)] .09861 0 1 0 Mshowa .11111 .10301 m .11736 .10301 L s [(-1)] .09861 .10301 1 0 Mshowa .11111 .30902 m .11736 .30902 L s [(1)] .09861 .30902 1 0 Mshowa .11111 .41202 m .11736 .41202 L s [(2)] .09861 .41202 1 0 Mshowa .11111 .51503 m .11736 .51503 L s [(3)] .09861 .51503 1 0 Mshowa .11111 .61803 m .11736 .61803 L s [(4)] .09861 .61803 1 0 Mshowa .125 Mabswid .11111 .0206 m .11486 .0206 L s .11111 .0412 m .11486 .0412 L s .11111 .0618 m .11486 .0618 L s .11111 .0824 m .11486 .0824 L s .11111 .12361 m .11486 .12361 L s .11111 .14421 m .11486 .14421 L s .11111 .16481 m .11486 .16481 L s .11111 .18541 m .11486 .18541 L s .11111 .22661 m .11486 .22661 L s .11111 .24721 m .11486 .24721 L s .11111 .26781 m .11486 .26781 L s .11111 .28842 m .11486 .28842 L s .11111 .32962 m .11486 .32962 L s .11111 .35022 m .11486 .35022 L s .11111 .37082 m .11486 .37082 L s .11111 .39142 m .11486 .39142 L s .11111 .43262 m .11486 .43262 L s .11111 .45322 m .11486 .45322 L s .11111 .47383 m .11486 .47383 L s .11111 .49443 m .11486 .49443 L s .11111 .53563 m .11486 .53563 L s .11111 .55623 m .11486 .55623 L s .11111 .57683 m .11486 .57683 L s .11111 .59743 m .11486 .59743 L s .25 Mabswid .11111 0 m .11111 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .11111 .52327 m .17231 .48959 L .2308 .44709 L .31989 .36413 L .4131 .25943 L .44246 .22279 L .44779 .21496 L .44944 .21199 L .45009 .2106 L .45054 .20942 L .45088 .20829 L .45101 .20773 L .45106 .20745 L .45111 .20715 L .45114 .20689 L .45116 .20665 L .45118 .20642 L .45118 .20629 L .45118 .20618 L .45119 .20597 L .45118 .20574 L .45117 .20553 L .45116 .20534 L .45114 .20514 L .45111 .20494 L .45104 .20457 L .45094 .20413 L .45083 .20375 L .45051 .20291 L .45011 .20213 L .44909 .20062 L .44765 .19895 L .44401 .19554 L .43116 .18553 L .40475 .16663 L .35767 .13557 L .32181 .11493 L .29904 .10362 L .27184 .09227 L .25726 .08728 L .24297 .08319 L .22976 .08016 L .22282 .07887 L .21511 .07769 L .20784 .07682 L .20433 .0765 L .201 .07624 L .19721 .07601 L .19374 .07587 L .19001 .07578 L Mistroke .1879 .07576 L .18594 .07576 L .1824 .07582 L .17907 .07593 L .17608 .07608 L .17286 .07629 L .16935 .07659 L .16565 .07697 L .15906 .07785 L .15167 .07913 L .14476 .08062 L .13207 .08413 L .11886 .08889 L .10517 .09515 L .08265 .10881 L .06469 .12347 L .04852 .14085 L .03688 .15758 L .03175 .16711 L .02803 .17569 L .025 .18488 L .02388 .18938 L .02336 .19191 L .02296 .1942 L .02266 .19621 L .0224 .1984 L .0222 .20057 L .02212 .20174 L .02207 .20283 L .022 .20482 L .022 .20661 L .02201 .20759 L .02204 .20865 L .02215 .21056 L .02228 .21223 L .02248 .21406 L .02304 .21766 L .02374 .2209 L .02455 .22384 L .02708 .23058 L .03008 .23625 L .03405 .24189 L .03893 .24715 L .04381 .25123 L .04863 .25441 L .05456 .25745 L .06046 .25968 L .06318 .26048 L .06611 .2612 L .06867 .2617 L Mistroke .07144 .26212 L .073 .26231 L .07443 .26245 L .07588 .26255 L .07725 .26263 L .07884 .26268 L .08032 .26269 L .08195 .26266 L .08285 .26263 L .08367 .2626 L .08522 .2625 L .08665 .26238 L .0899 .262 L .09304 .26149 L .09637 .2608 L .10228 .25916 L .10749 .25728 L .11329 .25466 L .11923 .25135 L .12884 .24432 L .13624 .23697 L .14251 .22838 L .1449 .22401 L .14689 .21933 L .14761 .21721 L .14823 .21501 L .14866 .21314 L .14901 .21116 L .14915 .21012 L .14925 .20918 L .14932 .20828 L .14937 .20735 L .1494 .20652 L .1494 .20575 L .14938 .20492 L .14934 .20404 L .14927 .20312 L .14916 .20213 L .14903 .20122 L .14888 .20038 L .14854 .19885 L .14808 .19727 L .14693 .19434 L .14556 .19183 L .14412 .18979 L .14235 .18781 L .1402 .18594 L .13803 .18446 L .13549 .18314 L .13262 .18207 L Mistroke .13113 .18167 L .13034 .18149 L .12949 .18133 L .12875 .18121 L .12793 .18111 L .12718 .18103 L .12647 .18098 L .12573 .18094 L .12503 .18092 L .12441 .18092 L .12372 .18094 L .12298 .18097 L .12257 .181 L .12219 .18103 L .12077 .18118 L .11947 .18137 L .11806 .18165 L .11526 .18239 L .11276 .18328 L .11051 .18428 L .10587 .18701 L .10165 .19053 L .0985 .19418 L .0971 .19632 L .09605 .19831 L .09533 .20003 L .09475 .2019 L .09453 .20282 L .09444 .20329 L .09436 .20379 L .09431 .20422 L .09426 .20469 L .09423 .20511 L .09421 .2055 L .0942 .20592 L .0942 .20614 L .09421 .20637 L .09422 .20677 L .09425 .20714 L .09427 .20736 L .09429 .20757 L .09434 .20796 L .09449 .2088 L .09467 .20951 L .09486 .21015 L .09543 .21149 L .09608 .2126 L .09676 .2135 L .09765 .21442 L .09858 .21517 L Mistroke .09958 .2158 L .10075 .21634 L .10136 .21657 L .10202 .21676 L .10266 .21691 L .10325 .21702 L .10354 .21705 L .10384 .21709 L .1041 .21711 L .10439 .21713 L .1047 .21714 L .10488 .21715 L .10504 .21715 L .10533 .21715 L .10564 .21714 L .10591 .21713 L .1062 .21711 L .10672 .21705 L .10733 .21696 L .10788 .21686 L .10906 .21657 L .11025 .21615 L .11226 .21519 L .11417 .2139 L .11591 .21226 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLcom/0000S0003o`0000D01_l>00Oo e00002<00_l300?o6`03om40000S0003o`0000;o8@04old0000S00?o9`03olX0000K00?o0`03ob`0 0oo7000070001Ol0003o008000?o0000;@02olD0000E00Go0P001?l0ool300?o;`02ol<0000L00;o 1@000ol0000a00;o`@0001/00_l60003o`0003<00_no00006P03o`H000?o0000=@02okd0000I0003 o`0000L000?o0000=`02ok/0000H0003o`0000P000?o0000>@000ol0002h00005`000ol0000900;o >`02okP0000F0003o`0000X000?o0000?002okH0000E0003o`0000/000?o0000?P000ol0002c0000 50000ol0000<0003o`0003l00_nc00004`000ol0000=0003o`00044000?o0000/00001<000?o0000 3@02od<00_n`00004P000ol0000>0003o`0004@000?o0000[@00014000?o00003`000ol0001500;o [@00014000?o00003`000ol000170003o`000:X0000@0003o`00010000?o0000B002ojX0000?0003 o`00014000?o0000BP000ol0002W00003P000ol0000B00;o=`04oa400_lU00?o>002ocT00_l:0000 3P000ol0000B0003o`0003L000?o00004`000ol0000S0003o`0003H000Co003o=`001?l00?l90000 3@000ol0000C0003o`0003P000?o00004`02ob401?lg0004o`00ocL000Co003o2@0000d000?o0000 4`000ol0000i0003o`0001@000?o00007P000ol0o`0h00?o>@02o`X0000=0003o`0001<01olb0004 o`00oaL000?o00007@000ol0o`0h0003o`0003P000Co003o2@0000`000?o00005002o`D00_la00;o 6@02oah00_li00?o>002o`X0000<0003o`0001<00_l80003o`0004/000?o0000W@0000`000?o0000 4P000ol0o`080003o`0004`000?o0000W00000`000?o00004@001?l00?l90003o`0004`000?o0000 V`0000`000?o000040001Ol0003o00T000?o0000C@000ol0002J000030000ol0000@0005o`000?l0 2@000ol0001=00;oV`0000H0ool;o`X0000<0003o`0000H000?o00001`001ol0003o0?l01`000ol0 00020003o`0000`000?o000030000ol0000;0003o`0000`000?o00003002o`d000?o00002`000ol0 000<0003o`0000`000?o00002`000ol0000<0003o`0000`000?o000030000ol0000;0003o`0000`0 00?o0000200000`000?o00004003o`030?oo00P000?o0000C@000ol0002J000030000ol0000B00?o 2@000ol0001<0003o`0009/0000<0003o`0001@000?o00001P000ol0001<0003o`0009`0000<0003 o`0001@00_l70003o`0004`000?o0000W00000d000?o00004`000ol000060003o`0004/000?o0000 W@0000d000?o00004`000ol000050003o`0004/000?o0000WP0000h000?o00004P000ol000040003 o`0004/000?o0000W`0000l000?o00004@000ol000030003o`0004/000?o0000X00000l000?o0000 4@001?l00002odh000?o0000X000010000?o00004002o`030?l004h000?o0000X@0001400_l@0003 o`3o04l000?o0000XP0001<00ol<00?oC`000ol0002S00005P03o`H00ol00`3o001>0003o`000:@0 000I00Ko10000ol0001=0003o`000:@0000S00;oC@000ol0002U00008`000ol0001;0003o`000:H0 000S0003o`0004X000?o0000Y`0002<000?o0000B@000ol0002X00008`000ol000180003o`000:T0 000S0003o`0004L000?o0000ZP0002<00_m80003o`000:X0000S0003o`0004H000?o0000Z`0002<0 00?o0000A@000ol0002/00006`03o`D000?o0000A0000ol0002]000070000ol000040003o`0004<0 00?o0000[P0001`000?o00001003od8000?o0000[`0001`000?o000010000ol000110003o`000;00 000L0003o`0000@000?o0000@@000ol0002`00006`02o`H000?o0000@0000ol0002a00008`000ol0 000o0003o`000;80000S00;o?`000ol0002c00008`000ol0000m0003o`000;@0000S0003o`0003`0 00?o0000]@0002<000?o0000>`000ol0002f00008`000ol0000k0003o`000;H0000S0003o`0003X0 00?o0000]`0002<00_lj0003o`000;P0000S0003o`0003P000?o0000^@0002<000?o0000=`000ol0 002j00008`000ol0000f0003o`000;/0000S0003o`0003@00_nn00008`02oc@000?o0000_P0002<0 00?o0000"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-1.21441, -2.16465, 0.0339167, 0.0365854}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]]-0.5y[t], x[0] == 0, y[0] == 3.0885}, {x[t],y[t]},{t,0,20}]]],{t,0,20},PlotRange->{{-1,8},{-2,4}}]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.111111 0.111111 0.206011 0.103006 [ [.33333 .19351 -3 -9 ] [.33333 .19351 3 0 ] [.55556 .19351 -3 -9 ] [.55556 .19351 3 0 ] [.77778 .19351 -3 -9 ] [.77778 .19351 3 0 ] [1 .19351 -3 -9 ] [1 .19351 3 0 ] [.09861 0 -12 -4.5 ] [.09861 0 0 4.5 ] [.09861 .10301 -12 -4.5 ] [.09861 .10301 0 4.5 ] [.09861 .30902 -6 -4.5 ] [.09861 .30902 0 4.5 ] [.09861 .41202 -6 -4.5 ] [.09861 .41202 0 4.5 ] [.09861 .51503 -6 -4.5 ] [.09861 .51503 0 4.5 ] [.09861 .61803 -6 -4.5 ] [.09861 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .33333 .20601 m .33333 .21226 L s [(2)] .33333 .19351 0 1 Mshowa .55556 .20601 m .55556 .21226 L s [(4)] .55556 .19351 0 1 Mshowa .77778 .20601 m .77778 .21226 L s [(6)] .77778 .19351 0 1 Mshowa 1 .20601 m 1 .21226 L s [(8)] 1 .19351 0 1 Mshowa .125 Mabswid .16667 .20601 m .16667 .20976 L s .22222 .20601 m .22222 .20976 L s .27778 .20601 m .27778 .20976 L s .38889 .20601 m .38889 .20976 L s .44444 .20601 m .44444 .20976 L s .5 .20601 m .5 .20976 L s .61111 .20601 m .61111 .20976 L s .66667 .20601 m .66667 .20976 L s .72222 .20601 m .72222 .20976 L s .83333 .20601 m .83333 .20976 L s .88889 .20601 m .88889 .20976 L s .94444 .20601 m .94444 .20976 L s .05556 .20601 m .05556 .20976 L s .25 Mabswid 0 .20601 m 1 .20601 L s .11111 0 m .11736 0 L s [(-2)] .09861 0 1 0 Mshowa .11111 .10301 m .11736 .10301 L s [(-1)] .09861 .10301 1 0 Mshowa .11111 .30902 m .11736 .30902 L s [(1)] .09861 .30902 1 0 Mshowa .11111 .41202 m .11736 .41202 L s [(2)] .09861 .41202 1 0 Mshowa .11111 .51503 m .11736 .51503 L s [(3)] .09861 .51503 1 0 Mshowa .11111 .61803 m .11736 .61803 L s [(4)] .09861 .61803 1 0 Mshowa .125 Mabswid .11111 .0206 m .11486 .0206 L s .11111 .0412 m .11486 .0412 L s .11111 .0618 m .11486 .0618 L s .11111 .0824 m .11486 .0824 L s .11111 .12361 m .11486 .12361 L s .11111 .14421 m .11486 .14421 L s .11111 .16481 m .11486 .16481 L s .11111 .18541 m .11486 .18541 L s .11111 .22661 m .11486 .22661 L s .11111 .24721 m .11486 .24721 L s .11111 .26781 m .11486 .26781 L s .11111 .28842 m .11486 .28842 L s .11111 .32962 m .11486 .32962 L s .11111 .35022 m .11486 .35022 L s .11111 .37082 m .11486 .37082 L s .11111 .39142 m .11486 .39142 L s .11111 .43262 m .11486 .43262 L s .11111 .45322 m .11486 .45322 L s .11111 .47383 m .11486 .47383 L s .11111 .49443 m .11486 .49443 L s .11111 .53563 m .11486 .53563 L s .11111 .55623 m .11486 .55623 L s .11111 .57683 m .11486 .57683 L s .11111 .59743 m .11486 .59743 L s .25 Mabswid .11111 0 m .11111 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .11111 .52414 m .17248 .49037 L .23113 .44777 L .32049 .36468 L .41429 .26023 L .44471 .22436 L .45475 .21244 L .45839 .20812 L .45955 .20672 L .45993 .20624 L .46 .20613 L .46001 .20611 L .46002 .20608 L .46003 .20606 L .46004 .20605 L .46004 .20604 L .46004 .20603 L .46004 .20603 L .46004 .20602 L .46004 .20602 L .46004 .20602 L .46004 .20602 L .46004 .20601 L .46004 .20601 L .46004 .20601 L .46004 .206 L .46004 .206 L .46004 .206 L .46004 .206 L .46004 .20599 L .46004 .20599 L .46004 .20598 L .46003 .20597 L .46003 .20596 L .46002 .20595 L .46001 .20592 L .45998 .2059 L .45992 .20585 L .45972 .20569 L .45929 .20537 L .4585 .2048 L .45686 .20361 L .45379 .20139 L .44819 .19734 L .43675 .1891 L .41563 .17407 L .37821 .14857 L .34616 .12856 L .30788 .10779 L .28557 .09766 L Mistroke .25888 .08778 L .24594 .08395 L .23175 .08055 L .22472 .07918 L .21804 .07809 L .21197 .07727 L .20544 .07658 L .20172 .07628 L .19834 .07606 L .19492 .0759 L .19169 .0758 L .18793 .07575 L .18445 .07576 L .18064 .07585 L .17872 .07593 L .1766 .07603 L .17266 .07629 L .16905 .0766 L .16098 .07756 L .15392 .0787 L .14658 .08019 L .13369 .08361 L .12208 .08761 L .09742 .09934 L .08559 .10675 L .0738 .11553 L .05534 .13289 L .04124 .15069 L .03173 .16713 L .02806 .17561 L .02641 .1802 L .0251 .18449 L .02409 .18841 L .02322 .19261 L .02292 .19443 L .02264 .19635 L .02243 .19801 L .02226 .19975 L .02211 .20179 L .02202 .20364 L .02198 .20561 L .02199 .20671 L .022 .20773 L .02208 .20957 L .02219 .21122 L .02236 .21309 L .02258 .21484 L .02324 .21871 L .02405 .22215 L .02517 .2258 L Mistroke .02659 .2295 L .02726 .23101 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc002okX0000G0003o`0000T00_lk00;o ^00001H000?o00002P000ol0000l00;o]P0001D000?o00002`000ol0000n0003o`000;<0000E0003 o`0000/000?o0000?`02ok<0000D0003o`0000`000?o0000@@02ok40000C0003o`0000d00_m40003 o`000:h0000B0003o`0000h000?o0000A002ojh0000A0003o`0000l000?o0000AP000ol0002[0000 4@000ol0000?0003o`0004L00_n[000040000ol0000@0003o`0004T000?o0000Z00000l000?o0000 4@000ol0001:0003o`000:L0000>0003o`0001800_lg00Co4@02obD00olh00;o>@02o`X0000>0003 o`00018000?o0000=`000ol0000C0003o`0002<000?o0000=P001?l00?lg0004o`00o`T0000=0003 o`0001<000?o0000>0000ol0000C00;o8@04ocL000Co003o=`001?l00?l900003@000ol0000C0003 o`0003T000?o000050000ol0000N0003o`3o03P00oli00;o2P0000d000?o00004`000ol0000f0004 o`00oaL00_lN0003o`3o03P000?o0000>0001?l00?l9000030000ol0000D00;o>002oaX000?o0000 7002ocT00olh00;o2P0000`000?o000050000ol0001D00;oWP0000`000?o000050000ol0001F0003 o`0009/0000<0003o`0001@000?o0000E`000ol0002J000030000ol0000D0003o`0005P000?o0000 V@0000`000?o000050000ol0001I00;oV@0000H0ool;o`X0000<0003o`0000H000?o00002`000ol0 000<0003o`0000`000?o000030000ol0000;0003o`0000`000?o000030000ol0o`0<0003o`0000/0 00?o000030000ol0000<0003o`0000/000?o000030000ol0000<0003o`0000`000?o00002`000ol0 000<0003o`0000P0000<0003o`0001@000?o0000F0000ol0002I000030000ol0000D0003o`0005L0 00?o0000VP0000`000?o000050000ol0001G0003o`0009X0000=0003o`0001<00_mG0003o`0009/0 000=0003o`0001<000?o0000EP000ol0002K00008`000ol0001E0003o`0009`0000S0003o`0005@0 00?o0000W@0002<000?o0000D`000ol0002N00008`000ol0001B0003o`0009l0000S00;oDP000ol0 002P00008`000ol0001@0003o`000:40000S0003o`0004l000?o0000XP0002<000?o0000CP000ol0 002S00008`000ol0001>0003o`000:<0000S00;oCP000ol0002T00008`000ol0001<0003o`000:D0 000S0003o`0004/000?o0000YP0002<000?o0000BP000ol0002W00008`000ol000190003o`000:P0 000S0003o`0004P000?o0000Z@0002<00_m80003o`000:X0000S0003o`0004H000?o0000Z`0002<0 00?o0000AP000ol0002[00006`03o`D000?o0000A@000ol0002/000070000ol000040003o`0004@0 00?o0000[@0001`000?o00001003od<000?o0000[P0001`000?o000010000ol000120003o`000:l0 000L0003o`0000@000?o0000@@000ol0002`00006`02o`H000?o0000@0000ol0002a00008`000ol0 000o0003o`000;80000S00;o?`000ol0002c00008`000ol0000m0003o`000;@0000S0003o`0003d0 00?o0000]00002<000?o0000?0000ol0002e00008`000ol0000k0003o`000;H0000S0003o`0003X0 00?o0000]`0002<00_lj0003o`000;P0000S0003o`0003P000?o0000^@0002<000?o0000=`000ol0 002j00008`000ol0000f0003o`000;/0000S0003o`0003@00_nn00008`02oc@000?o0000_P0002<0 00?o0000"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-1.21441, -2.16465, 0.0339167, 0.0365854}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ ParametricPlot[Evaluate[{x[t],y[t]} /. First[NDSolve[ {x'[t] == y[t],y'[t] == -Sin[x[t]]-0.5y[t], x[0] == 0, y[0] == 3.0885098}, {x[t],y[t]},{t,0,20}]]],{t,0,20},PlotRange->{{-1,8},{-2,4}}]\ \>", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.111111 0.111111 0.206011 0.103006 [ [.33333 .19351 -3 -9 ] [.33333 .19351 3 0 ] [.55556 .19351 -3 -9 ] [.55556 .19351 3 0 ] [.77778 .19351 -3 -9 ] [.77778 .19351 3 0 ] [1 .19351 -3 -9 ] [1 .19351 3 0 ] [.09861 0 -12 -4.5 ] [.09861 0 0 4.5 ] [.09861 .10301 -12 -4.5 ] [.09861 .10301 0 4.5 ] [.09861 .30902 -6 -4.5 ] [.09861 .30902 0 4.5 ] [.09861 .41202 -6 -4.5 ] [.09861 .41202 0 4.5 ] [.09861 .51503 -6 -4.5 ] [.09861 .51503 0 4.5 ] [.09861 .61803 -6 -4.5 ] [.09861 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .33333 .20601 m .33333 .21226 L s [(2)] .33333 .19351 0 1 Mshowa .55556 .20601 m .55556 .21226 L s [(4)] .55556 .19351 0 1 Mshowa .77778 .20601 m .77778 .21226 L s [(6)] .77778 .19351 0 1 Mshowa 1 .20601 m 1 .21226 L s [(8)] 1 .19351 0 1 Mshowa .125 Mabswid .16667 .20601 m .16667 .20976 L s .22222 .20601 m .22222 .20976 L s .27778 .20601 m .27778 .20976 L s .38889 .20601 m .38889 .20976 L s .44444 .20601 m .44444 .20976 L s .5 .20601 m .5 .20976 L s .61111 .20601 m .61111 .20976 L s .66667 .20601 m .66667 .20976 L s .72222 .20601 m .72222 .20976 L s .83333 .20601 m .83333 .20976 L s .88889 .20601 m .88889 .20976 L s .94444 .20601 m .94444 .20976 L s .05556 .20601 m .05556 .20976 L s .25 Mabswid 0 .20601 m 1 .20601 L s .11111 0 m .11736 0 L s [(-2)] .09861 0 1 0 Mshowa .11111 .10301 m .11736 .10301 L s [(-1)] .09861 .10301 1 0 Mshowa .11111 .30902 m .11736 .30902 L s [(1)] .09861 .30902 1 0 Mshowa .11111 .41202 m .11736 .41202 L s [(2)] .09861 .41202 1 0 Mshowa .11111 .51503 m .11736 .51503 L s [(3)] .09861 .51503 1 0 Mshowa .11111 .61803 m .11736 .61803 L s [(4)] .09861 .61803 1 0 Mshowa .125 Mabswid .11111 .0206 m .11486 .0206 L s .11111 .0412 m .11486 .0412 L s .11111 .0618 m .11486 .0618 L s .11111 .0824 m .11486 .0824 L s .11111 .12361 m .11486 .12361 L s .11111 .14421 m .11486 .14421 L s .11111 .16481 m .11486 .16481 L s .11111 .18541 m .11486 .18541 L s .11111 .22661 m .11486 .22661 L s .11111 .24721 m .11486 .24721 L s .11111 .26781 m .11486 .26781 L s .11111 .28842 m .11486 .28842 L s .11111 .32962 m .11486 .32962 L s .11111 .35022 m .11486 .35022 L s .11111 .37082 m .11486 .37082 L s .11111 .39142 m .11486 .39142 L s .11111 .43262 m .11486 .43262 L s .11111 .45322 m .11486 .45322 L s .11111 .47383 m .11486 .47383 L s .11111 .49443 m .11486 .49443 L s .11111 .53563 m .11486 .53563 L s .11111 .55623 m .11486 .55623 L s .11111 .57683 m .11486 .57683 L s .11111 .59743 m .11486 .59743 L s .25 Mabswid .11111 0 m .11111 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .11111 .52415 m .17248 .49037 L .23113 .44777 L .3205 .36468 L .41429 .26023 L .44471 .22437 L .45476 .21245 L .4584 .20812 L .45957 .20673 L .45996 .20627 L .4601 .2061 L .46015 .20604 L .46017 .20602 L .46017 .20601 L .46017 .20601 L .46017 .20601 L .46017 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46018 .20601 L .46017 .20601 L .46017 .20601 L .46017 .20601 L .46017 .20601 L .46017 .20601 L .46017 .20601 L .46016 .206 L .46015 .20599 L .46013 .20598 L .46009 .20595 L .46002 .2059 L .45987 .20579 L Mistroke .45958 .20558 L .45906 .2052 L .45802 .20445 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{282, 174}, ImageMargins->{{34, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggYjN[Vi^OShn03ooeGooj[oooclo5H/1EGooj[ooc/k>gYjN[Vi^OShn03o oclo?ginO[fm_Oclo5D00:X00?l00000EED0EJX00=d81Slo?ginO[fm_Oclo0<30d92@X61PL30`000 EED0EJX0EOl0E@00ZUD0ZZX0E@<30d92@X61PL30`000E@L71dI6AXF5QLC4a000ZUD0ZZX0Z_l0ZP00 e5D0ojX0ZPL71dI6AXF5QLC4a000ZP/;2dY:BXV9RLS8b000oeD0ojX0ool0o`1E05EE0:X0o`/;2dY: BXV9RLS8b000o`l?3di>CXf=SLcCXf=SLc@02o`X0000S0003o`0003L000?o0000>@000ol0000f0004o`00ocL000Co003o2@0002<000?o0000 >0000ol0000f00Co=`001?l00?lg0004o`00o`T0000S0003o`0003T000?o0000=@000ol0o`0h00?o >@02o`X0000S0003o`0003H000Co003o=`000ol0o`0h0003o`0003P000Co003o2@0002<00_lh00;o >@02ocT00olh00;o2P0002<000?o0000m00002<000?o0000m00002<000?o0000m00002<000?o0000 m00002<000?o0000F@02oiT000060?oo2ol:00005@000ol0000;0003o`0000`000?o000030000ol0 000<0003o`0000/000?o000030000ol0000<0003o`3o00`000?o00002`000ol0000<0003o`0000`0 00?o00002`000ol0000<0003o`0000`000?o000030000ol0000;0003o`0000`000?o0000200002<0 00?o0000F0000ol0002I00008`000ol0001G0003o`0009X0000S0003o`0005L000?o0000VP0002<0 0_mG0003o`0009/0000S0003o`0005H000?o0000V`0002<000?o0000E@000ol0002L00008`000ol0 001D0003o`0009d0000S0003o`0005<000?o0000WP0002<000?o0000DP000ol0002O00008`02oe80 00?o0000X00002<000?o0000D0000ol0002Q00008`000ol0001?0003o`000:80000S0003o`0004h0 00?o0000X`0002<000?o0000CP000ol0002S00008`02odh000?o0000Y00002<000?o0000C0000ol0 002U00008`000ol0001;0003o`000:H0000S0003o`0004X000?o0000Y`0002<000?o0000B@000ol0 002X00008`000ol000180003o`000:T0000S00;oB0000ol0002Z00008`000ol000160003o`000:/0 000S0003o`0004H000?o0000Z`0001/00ol50003o`0004D000?o0000[00001`000?o000010000ol0 00140003o`000:d0000L0003o`0000@00om30003o`000:h0000L0003o`0000@000?o0000@P000ol0 002_000070000ol000040003o`00044000?o0000/00001/00_l60003o`00040000?o0000/@0002<0 00?o0000?`000ol0002b00008`02ocl000?o0000/`0002<000?o0000?@000ol0002d00008`000ol0 000m0003o`000;@0000S0003o`0003`000?o0000]@0002<000?o0000>`000ol0002f00008`000ol0 000j0003o`000;L0000S00;o>P000ol0002h00008`000ol0000h0003o`000;T0000S0003o`0003L0 00?o0000^P0002<000?o0000=P000ol0002k00008`000ol0000d00;o_P0002<00_ld0003o`000;h0 000S0003o`00038000?o0000_`0002<000?o0000<@000ol0003000008`000ol0000`0003o`000<40 000S0003o`0002l000?o0000`P0002<000?o0000;P000ol0003300008`02obh000?o0000a00002<0 00?o0000;0000ol0003500008`000ol0000[0003o`00000008`000ol0000R0003o`00040 000S0003o`0000l000?o0000hP0002<000?o00003@02onD0000S00;o3002onL0000S0003o`0000T0 0_oY00008`000ol0000700;oj`0002<000?o00001@02ond0000K00?o1@000ol000040003o`000>d0 000N0003o`00008000?o00000P02oo00000N0003o`0000801Oob00007002o`D00ood00007P000ol0 00020003o`000?@0000K00?o1@000ol0003d00008`000ol0003d00008`02ooD0000S0003o`000?@0 000S0003o`000?@0000S0003o`000?@0000S0003o`000?@0000S0003o`000?@0000S00;om@0002<0 00?o0000m00002<000?o0000m00002<000?o0000m00002<000?o0000m00002<00_oe00008`000ol0 003d00008`000ol0003d00008`000ol0003d00008`000ol0003d00008`000ol0003d00008`02ooD0 000S0003o`000?@0000S0003o`000?@0000L00?o10000ol0003d00007@000ol000030003o`000?@0 000K00Co1003oo@0000K0003o`3o0?`0000K0003o`3o0?`0000L00;oo0000?l06`000001\ \>"], ImageRangeCache->{{{0, 281}, {173, 0}} -> {-1.21441, -2.16465, 0.0339167, 0.0365854}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "It looks like an initial velocity of ", StyleBox["3.0885098", FontFamily->"Courier", FontWeight->"Bold"], " is close to the critical value." }], "Text"] }, Open ]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 1024}, {0, 748}}, AutoGeneratedPackage->None, CellGrouping->Manual, WindowSize->{659, 667}, WindowMargins->{{2, Automatic}, {Automatic, 2}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, MacintoshSystemPageSetup->"\<\ 00<0004/0B`000003]X;>omOoel?O0_B0fL5:0?l0080004/0B`000000]P2:001 0000D00000400`<300000BL?00400@6Cei000000000006P801T1T00000000000 00000000004000000000000000000000\>" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1709, 49, 104, 3, 44, "Subsection"], Cell[CellGroupData[{ Cell[1838, 56, 239, 5, 41, "Subsubsection", PageBreakWithin->Automatic], Cell[2080, 63, 237, 5, 27, "Input", PageBreakWithin->Automatic, InitializationCell->True] }, Open ]], Cell[CellGroupData[{ Cell[2354, 73, 34, 0, 41, "Subsubsection"], Cell[2391, 75, 945, 31, 249, "Text"], Cell[3339, 108, 33, 0, 41, "Subsubsection"], Cell[3375, 110, 75, 4, 31, "Text"], Cell[3453, 116, 77, 0, 42, "Input"], Cell[CellGroupData[{ Cell[3555, 120, 31, 0, 27, "Input"], Cell[3589, 122, 99, 2, 26, "Output"] }, Open ]], Cell[3703, 127, 45, 0, 30, "Text"], Cell[3751, 129, 45, 0, 27, "Input"], Cell[3799, 131, 144, 4, 31, "Text"], Cell[CellGroupData[{ Cell[3968, 139, 49, 0, 22, "Input"], Cell[4020, 141, 125, 2, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4182, 148, 49, 0, 22, "Input"], Cell[4234, 150, 120, 2, 22, "Output"] }, Open ]], Cell[4369, 155, 39, 0, 25, "Text"], Cell[CellGroupData[{ Cell[4433, 159, 44, 0, 22, "Input"], Cell[4480, 161, 246, 4, 22, "Output"] }, Open ]], Cell[4741, 168, 39, 0, 25, "Text"], Cell[CellGroupData[{ Cell[4805, 172, 32, 0, 22, "Input"], Cell[4840, 174, 221, 5, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5098, 184, 33, 0, 22, "Input"], Cell[5134, 186, 221, 5, 22, "Output"] }, Open ]], Cell[5370, 194, 94, 2, 25, "Text"], Cell[5467, 198, 94, 1, 22, "Input"], Cell[5564, 201, 355, 11, 38, "Text"], Cell[CellGroupData[{ Cell[5944, 216, 27, 0, 22, "Input"], Cell[5974, 218, 128, 2, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6139, 225, 58, 0, 22, "Input"], Cell[6200, 227, 17242, 751, 185, 9588, 652, "GraphicsData", "PostScript", "Graphics"], Cell[23445, 980, 130, 3, 22, "Output"] }, Open ]], Cell[23590, 986, 123, 2, 25, "Text"], Cell[23716, 990, 75, 4, 25, "Text"], Cell[23794, 996, 97, 1, 43, "Input"], Cell[CellGroupData[{ Cell[23916, 1001, 31, 0, 22, "Input"], Cell[23950, 1003, 98, 2, 22, "Output"] }, Open ]], Cell[24063, 1008, 42, 0, 25, "Text"], Cell[24108, 1010, 96, 4, 40, "Input"], Cell[24207, 1016, 39, 0, 25, "Text"], Cell[CellGroupData[{ Cell[24271, 1020, 55, 0, 22, "Input"], Cell[24329, 1022, 212, 3, 22, "Output"] }, Open ]], Cell[24556, 1028, 22, 0, 25, "Text"], Cell[CellGroupData[{ Cell[24603, 1032, 32, 0, 22, "Input"], Cell[24638, 1034, 235, 4, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24910, 1043, 33, 0, 22, "Input"], Cell[24946, 1045, 235, 4, 22, "Output"] }, Open ]], Cell[25196, 1052, 70, 2, 25, "Text"], Cell[25269, 1056, 115, 4, 22, "Input"], Cell[25387, 1062, 189, 6, 25, "Text"], Cell[CellGroupData[{ Cell[25601, 1072, 60, 0, 22, "Input"], Cell[25664, 1074, 91536, 6125, 299, 65866, 5804, "GraphicsData", "PostScript", "Graphics"], Cell[117203, 7201, 132, 3, 22, "Output"] }, Open ]], Cell[117350, 7207, 75, 4, 25, "Text"], Cell[117428, 7213, 103, 1, 43, "Input"], Cell[CellGroupData[{ Cell[117556, 7218, 31, 0, 22, "Input"], Cell[117590, 7220, 121, 2, 22, "Output"] }, Open ]], Cell[117726, 7225, 76, 0, 25, "Text"], Cell[117805, 7227, 78, 3, 30, "Input"], Cell[117886, 7232, 144, 4, 25, "Text"], Cell[CellGroupData[{ Cell[118055, 7240, 49, 0, 22, "Input"], Cell[118107, 7242, 97, 2, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[118241, 7249, 49, 0, 22, "Input"], Cell[118293, 7251, 97, 2, 22, "Output"] }, Open ]], Cell[118405, 7256, 39, 0, 25, "Text"], Cell[CellGroupData[{ Cell[118469, 7260, 55, 0, 22, "Input"], Cell[118527, 7262, 312, 5, 33, "Output"] }, Open ]], Cell[118854, 7270, 22, 0, 25, "Text"], Cell[CellGroupData[{ Cell[118901, 7274, 32, 0, 22, "Input"], Cell[118936, 7276, 324, 6, 33, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[119297, 7287, 33, 0, 22, "Input"], Cell[119333, 7289, 324, 6, 33, "Output"] }, Open ]], Cell[119672, 7298, 22, 0, 25, "Text"], Cell[119697, 7300, 115, 4, 22, "Input"], Cell[CellGroupData[{ Cell[119837, 7308, 145, 4, 40, "Input"], Cell[119985, 7314, 55040, 3657, 237, 39954, 3466, "GraphicsData", "PostScript", "Graphics"], Cell[175028, 10973, 132, 3, 22, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[175209, 10982, 34, 0, 33, "Subsubsection"], Cell[175246, 10984, 1576, 54, 259, "Text"], Cell[176825, 11040, 33, 0, 33, "Subsubsection"], Cell[176861, 11042, 75, 4, 25, "Text"], Cell[176939, 11048, 317, 11, 43, "Input"], Cell[CellGroupData[{ Cell[177281, 11063, 57, 1, 22, "Input"], Cell[177341, 11066, 103, 2, 22, "Output"] }, Open ]], Cell[177459, 11071, 38, 0, 25, "Text"], Cell[177500, 11073, 99, 4, 40, "Input"], Cell[177602, 11079, 289, 10, 25, "Text"], Cell[CellGroupData[{ Cell[177916, 11093, 87, 3, 30, "Input"], Cell[178006, 11098, 359, 9, 47, "Output"] }, Open ]], Cell[178380, 11110, 289, 10, 25, "Text"], Cell[CellGroupData[{ Cell[178694, 11124, 77, 3, 30, "Input"], Cell[178774, 11129, 630, 16, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[179441, 11150, 61, 1, 22, "Input"], Cell[179505, 11153, 200, 7, 44, "Output"] }, Open ]], Cell[179720, 11163, 152, 6, 25, "Text"], Cell[CellGroupData[{ Cell[179897, 11173, 46, 0, 22, "Input"], Cell[179946, 11175, 664, 16, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[180647, 11196, 47, 0, 22, "Input"], Cell[180697, 11198, 664, 16, 47, "Output"] }, Open ]], Cell[181376, 11217, 89, 3, 25, "Text"], Cell[CellGroupData[{ Cell[181490, 11224, 123, 5, 22, "Input"], Cell[181616, 11231, 357, 6, 22, "Output"] }, Open ]], Cell[181988, 11240, 75, 4, 25, "Text"], Cell[182066, 11246, 319, 11, 53, "Input"], Cell[CellGroupData[{ Cell[182410, 11261, 57, 1, 22, "Input"], Cell[182470, 11264, 98, 2, 22, "Output"] }, Open ]], Cell[182583, 11269, 59, 0, 25, "Text"], Cell[182645, 11271, 157, 6, 30, "Input"], Cell[182805, 11279, 351, 12, 25, "Text"], Cell[CellGroupData[{ Cell[183181, 11295, 187, 7, 22, "Input"], Cell[183371, 11304, 133, 3, 20, "Message"], Cell[183507, 11309, 85, 1, 28, "Output"] }, Open ]], Cell[183607, 11313, 155, 4, 25, "Text"], Cell[183765, 11319, 184, 8, 22, "Input"], Cell[183952, 11329, 40, 0, 25, "Text"], Cell[CellGroupData[{ Cell[184017, 11333, 55, 0, 22, "Input"], Cell[184075, 11335, 356, 6, 29, "Output"] }, Open ]], Cell[184446, 11344, 22, 0, 25, "Text"], Cell[CellGroupData[{ Cell[184493, 11348, 30, 0, 22, "Input"], Cell[184526, 11350, 358, 6, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[184921, 11361, 31, 0, 22, "Input"], Cell[184955, 11363, 358, 6, 22, "Output"] }, Open ]], Cell[185328, 11372, 35, 0, 25, "Text"], Cell[CellGroupData[{ Cell[185388, 11376, 87, 3, 30, "Input"], Cell[185478, 11381, 497, 13, 50, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[186012, 11399, 77, 3, 30, "Input"], Cell[186092, 11404, 1079, 21, 57, "Output"] }, Open ]], Cell[187186, 11428, 71, 0, 25, "Text"], Cell[CellGroupData[{ Cell[187282, 11432, 133, 5, 22, "Input"], Cell[187418, 11439, 147, 2, 22, "Output"] }, Open ]], Cell[187580, 11444, 75, 4, 25, "Text"], Cell[187658, 11450, 322, 11, 43, "Input"], Cell[CellGroupData[{ Cell[188005, 11465, 57, 1, 22, "Input"], Cell[188065, 11468, 126, 3, 22, "Output"] }, Open ]], Cell[188206, 11474, 74, 3, 30, "Input"], Cell[CellGroupData[{ Cell[188305, 11481, 49, 0, 22, "Input"], Cell[188357, 11483, 87, 1, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[188481, 11489, 49, 0, 22, "Input"], Cell[188533, 11491, 92, 1, 22, "Output"] }, Open ]], Cell[188640, 11495, 33, 0, 25, "Text"], Cell[CellGroupData[{ Cell[188698, 11499, 55, 0, 22, "Input"], Cell[188756, 11501, 241, 4, 32, "Output"] }, Open ]], Cell[189012, 11508, 22, 0, 25, "Text"], Cell[CellGroupData[{ Cell[189059, 11512, 32, 0, 22, "Input"], Cell[189094, 11514, 245, 4, 32, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[189376, 11523, 33, 0, 22, "Input"], Cell[189412, 11525, 245, 4, 32, "Output"] }, Open ]], Cell[189672, 11532, 35, 0, 25, "Text"], Cell[CellGroupData[{ Cell[189732, 11536, 87, 3, 30, "Input"], Cell[189822, 11541, 347, 9, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[190206, 11555, 87, 3, 30, "Input"], Cell[190296, 11560, 561, 14, 47, "Output"] }, Open ]], Cell[190872, 11577, 71, 0, 25, "Text"], Cell[CellGroupData[{ Cell[190968, 11581, 132, 5, 22, "Input"], Cell[191103, 11588, 170, 3, 22, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[191322, 11597, 34, 0, 33, "Subsubsection"], Cell[191359, 11599, 2217, 80, 324, "Text"], Cell[193579, 11681, 33, 0, 33, "Subsubsection"], Cell[193615, 11683, 75, 4, 25, "Text"], Cell[193693, 11689, 337, 11, 63, "Input"], Cell[194033, 11702, 333, 13, 25, "Text"], Cell[CellGroupData[{ Cell[194391, 11719, 191, 7, 70, "Input"], Cell[194585, 11728, 295, 7, 47, "Output"] }, Open ]], Cell[194895, 11738, 696, 28, 38, "Text"], Cell[CellGroupData[{ Cell[195616, 11770, 29, 0, 22, "Input"], Cell[195648, 11772, 169, 3, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[195854, 11780, 61, 0, 22, "Input"], Cell[195918, 11782, 198, 3, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[196153, 11790, 46, 0, 22, "Input"], Cell[196202, 11792, 164, 3, 28, "Output"] }, Open ]], Cell[196381, 11798, 112, 2, 25, "Text"], Cell[CellGroupData[{ Cell[196518, 11804, 88, 1, 22, "Input"], Cell[196609, 11807, 365, 6, 48, "Output"] }, Open ]], Cell[196989, 11816, 22, 0, 25, "Text"], Cell[CellGroupData[{ Cell[197036, 11820, 32, 0, 22, "Input"], Cell[197071, 11822, 287, 5, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[197395, 11832, 40, 0, 22, "Input"], Cell[197438, 11834, 287, 5, 28, "Output"] }, Open ]], Cell[197740, 11842, 308, 12, 25, "Text"], Cell[CellGroupData[{ Cell[198073, 11858, 158, 7, 22, "Input"], Cell[198234, 11867, 103, 2, 28, "Output"] }, Open ]], Cell[198352, 11872, 113, 2, 25, "Text"], Cell[CellGroupData[{ Cell[198490, 11878, 79, 1, 22, "Input"], Cell[198572, 11881, 396, 7, 51, "Output"] }, Open ]], Cell[198983, 11891, 75, 4, 25, "Text"], Cell[199061, 11897, 345, 11, 53, "Input"], Cell[199409, 11910, 333, 13, 25, "Text"], Cell[CellGroupData[{ Cell[199767, 11927, 417, 13, 71, "Input"], Cell[200187, 11942, 434, 10, 53, "Output"] }, Open ]], Cell[200636, 11955, 251, 10, 25, "Text"], Cell[CellGroupData[{ Cell[200912, 11969, 106, 2, 22, "Input"], Cell[201021, 11973, 247, 4, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[201305, 11982, 71, 0, 22, "Input"], Cell[201379, 11984, 268, 4, 28, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[201684, 11993, 46, 0, 22, "Input"], Cell[201733, 11995, 197, 3, 28, "Output"] }, Open ]], Cell[201945, 12001, 112, 2, 25, "Text"], Cell[CellGroupData[{ Cell[202082, 12007, 88, 1, 22, "Input"], Cell[202173, 12010, 535, 9, 71, "Output"] }, Open ]], Cell[202723, 12022, 22, 0, 25, "Text"], Cell[CellGroupData[{ Cell[202770, 12026, 32, 0, 22, "Input"], Cell[202805, 12028, 501, 8, 69, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[203343, 12041, 40, 0, 22, "Input"], Cell[203386, 12043, 501, 8, 69, "Output"] }, Open ]], Cell[203902, 12054, 308, 12, 25, "Text"], Cell[CellGroupData[{ Cell[204235, 12070, 158, 7, 22, "Input"], Cell[204396, 12079, 105, 2, 28, "Output"] }, Open ]], Cell[204516, 12084, 113, 2, 25, "Text"], Cell[CellGroupData[{ Cell[204654, 12090, 79, 1, 22, "Input"], Cell[204736, 12093, 453, 9, 48, "Output"] }, Open ]], Cell[205204, 12105, 75, 4, 25, "Text"], Cell[205282, 12111, 347, 11, 63, "Input"], Cell[205632, 12124, 333, 13, 25, "Text"], Cell[CellGroupData[{ Cell[205990, 12141, 251, 7, 70, "Input"], Cell[206244, 12150, 388, 11, 45, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[206669, 12166, 39, 0, 22, "Input"], Cell[206711, 12168, 240, 5, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[206988, 12178, 71, 0, 22, "Input"], Cell[207062, 12180, 375, 8, 48, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[207474, 12193, 46, 0, 22, "Input"], Cell[207523, 12195, 236, 4, 29, "Output"] }, Open ]], Cell[207774, 12202, 112, 2, 25, "Text"], Cell[CellGroupData[{ Cell[207911, 12208, 88, 1, 22, "Input"], Cell[208002, 12211, 451, 7, 72, "Output"] }, Open ]], Cell[208468, 12221, 22, 0, 25, "Text"], Cell[CellGroupData[{ Cell[208515, 12225, 32, 0, 22, "Input"], Cell[208550, 12227, 399, 6, 50, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[208986, 12238, 40, 0, 22, "Input"], Cell[209029, 12240, 399, 6, 50, "Output"] }, Open ]], Cell[209443, 12249, 308, 12, 25, "Text"], Cell[CellGroupData[{ Cell[209776, 12265, 157, 7, 22, "Input"], Cell[209936, 12274, 118, 2, 28, "Output"] }, Open ]], Cell[210069, 12279, 113, 2, 25, "Text"], Cell[CellGroupData[{ Cell[210207, 12285, 79, 1, 22, "Input"], Cell[210289, 12288, 401, 9, 48, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[210739, 12303, 34, 0, 33, "Subsubsection"], Cell[210776, 12305, 1402, 41, 116, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[212215, 12351, 233, 5, 33, "Subsubsection", PageBreakWithin->Automatic], Cell[212451, 12358, 92, 4, 30, "Input"], Cell[212546, 12364, 150, 6, 25, "Text"], Cell[CellGroupData[{ Cell[212721, 12374, 81, 1, 22, "Input"], Cell[212805, 12377, 184, 3, 22, "Output"] }, Open ]], Cell[213004, 12383, 363, 13, 25, "Text"], Cell[CellGroupData[{ Cell[213392, 12400, 131, 5, 40, "Input"], Cell[213526, 12407, 180, 6, 33, "Output"] }, Open ]], Cell[213721, 12416, 183, 8, 25, "Text"], Cell[CellGroupData[{ Cell[213929, 12428, 84, 4, 30, "Input"], Cell[214016, 12434, 164, 6, 32, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[214217, 12445, 58, 1, 22, "Input"], Cell[214278, 12448, 97, 2, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[214412, 12455, 47, 1, 22, "Input"], Cell[214462, 12458, 168, 3, 22, "Output"] }, Open ]], Cell[214645, 12464, 333, 12, 38, "Text"], Cell[CellGroupData[{ Cell[215003, 12480, 84, 4, 30, "Input"], Cell[215090, 12486, 170, 6, 32, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[215297, 12497, 58, 1, 22, "Input"], Cell[215358, 12500, 70, 1, 22, "Output"] }, Open ]], Cell[215443, 12504, 333, 9, 38, "Text"], Cell[215779, 12515, 109, 3, 25, "Text"], Cell[CellGroupData[{ Cell[215913, 12522, 59, 1, 22, "Input"], Cell[215975, 12525, 178, 3, 28, "Print"] }, Open ]], Cell[CellGroupData[{ Cell[216190, 12533, 148, 4, 30, "Input"], Cell[216341, 12539, 63715, 2115, 266, 34596, 1749, "GraphicsData", "PostScript", "Graphics"], Cell[280059, 14656, 130, 3, 22, "Output"] }, Open ]], Cell[280204, 14662, 628, 19, 51, "Text"], Cell[280835, 14683, 235, 6, 60, "Input"], Cell[281073, 14691, 235, 6, 60, "Input"], Cell[CellGroupData[{ Cell[281333, 14701, 112, 3, 30, "Input"], Cell[281448, 14706, 50820, 2698, 182, 37221, 2524, "GraphicsData", "PostScript", "Graphics"], Cell[332271, 17406, 130, 3, 26, "Output"] }, Closed]], Cell[332416, 17412, 437, 13, 36, "Text"], Cell[332856, 17427, 83, 5, 22, "Output"], Cell[CellGroupData[{ Cell[332964, 17436, 53, 0, 22, "Input"], Cell[333020, 17438, 87379, 3865, 182, 60852, 3531, "GraphicsData", "PostScript", "Graphics"], Cell[420402, 21305, 130, 3, 22, "Output"] }, Open ]] }, Open ]], Cell[420559, 21312, 34, 0, 33, "Subsubsection"], Cell[420596, 21314, 2226, 75, 259, "Text"], Cell[CellGroupData[{ Cell[422847, 21393, 233, 5, 33, "Subsubsection", PageBreakWithin->Automatic], Cell[423083, 21400, 498, 18, 64, "Text"], Cell[CellGroupData[{ Cell[423606, 21422, 144, 4, 30, "Input"], Cell[423753, 21428, 44801, 1853, 130, 33689, 1710, "GraphicsData", "PostScript", "Graphics"], Cell[468557, 23283, 130, 3, 22, "Output"] }, Open ]], Cell[468702, 23289, 232, 7, 60, "Input"], Cell[CellGroupData[{ Cell[468959, 23300, 139, 5, 30, "Input"], Cell[469101, 23307, 34280, 1706, 169, 23949, 1572, "GraphicsData", "PostScript", "Graphics"], Cell[503384, 25015, 130, 3, 22, "Output"] }, Open ]], Cell[503529, 25021, 1874, 64, 77, "Text"], Cell[CellGroupData[{ Cell[505428, 25089, 204, 4, 40, "Input"], Cell[505635, 25095, 13885, 500, 198, 5612, 392, "GraphicsData", "PostScript", "Graphics"], Cell[519523, 25597, 130, 3, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[519690, 25605, 206, 4, 40, "Input"], Cell[519899, 25611, 12266, 442, 188, 4965, 346, "GraphicsData", "PostScript", "Graphics"], Cell[532168, 26055, 130, 3, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[532335, 26063, 207, 4, 40, "Input"], Cell[532545, 26069, 12881, 460, 254, 4947, 356, "GraphicsData", "PostScript", "Graphics"], Cell[545429, 26531, 130, 3, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[545596, 26539, 205, 4, 40, "Input"], Cell[545804, 26545, 9167, 363, 132, 4145, 295, "GraphicsData", "PostScript", "Graphics"], Cell[554974, 26910, 130, 3, 22, "Output"] }, Open ]], Cell[555119, 26916, 326, 8, 38, "Text"], Cell[555448, 26926, 348, 12, 64, "Text"], Cell[CellGroupData[{ Cell[555821, 26942, 124, 3, 30, "Input"], Cell[555948, 26947, 47828, 1932, 151, 33974, 1755, "GraphicsData", "PostScript", "Graphics"], Cell[603779, 28881, 130, 3, 22, "Output"] }, Open ]], Cell[603924, 28887, 219, 6, 60, "Input"], Cell[CellGroupData[{ Cell[604168, 28897, 95, 3, 22, "Input"], Cell[604266, 28902, 75795, 4128, 197, 61362, 3944, "GraphicsData", "PostScript", "Graphics"], Cell[680064, 33032, 130, 3, 22, "Output"] }, Open ]], Cell[680209, 33038, 1259, 45, 64, "Text"], Cell[CellGroupData[{ Cell[681493, 33087, 236, 6, 50, "Input"], Cell[681732, 33095, 12973, 536, 182, 6624, 452, "GraphicsData", "PostScript", "Graphics"], Cell[694708, 33633, 130, 3, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[694875, 33641, 237, 6, 50, "Input"], Cell[695115, 33649, 12851, 532, 182, 6591, 449, "GraphicsData", "PostScript", "Graphics"], Cell[707969, 34183, 130, 3, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[708136, 34191, 239, 6, 50, "Input"], Cell[708378, 34199, 10644, 404, 182, 4627, 324, "GraphicsData", "PostScript", "Graphics"], Cell[719025, 34605, 130, 3, 22, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[719192, 34613, 242, 6, 50, "Input"], Cell[719437, 34621, 9311, 347, 182, 3853, 274, "GraphicsData", "PostScript", "Graphics"], Cell[728751, 34970, 130, 3, 22, "Output"] }, Open ]], Cell[728896, 34976, 183, 6, 25, "Text"] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)