(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing 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[ 68640, 1883]*) (*NotebookOutlinePosition[ 69284, 1905]*) (* CellTagsIndexPosition[ 69240, 1901]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(\(<< Graphics`Graphics`;\)\)], "Input"], Cell[BoxData[{ \(\(p[0, 0] = 1;\)\), "\[IndentingNewLine]", \(\(p[x_, 0]\ = \ 0;\)\), "\[IndentingNewLine]", \(\(p[x_, t_]\ := \ \(p[x, t] = \((1/2)\)\ \((p[x - 1, t - 1] + p[x + 1, t - 1])\)\);\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(time = 40;\)\), "\[IndentingNewLine]", \(\(exact = ListPlot[Table[{i, p[i, time]}, {i, \(-time\), time}], PlotRange \[Rule] All, PlotStyle -> PointSize[0.02]];\)\)}], "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 %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0119048 0.0147151 4.69491 [ [.02381 .00222 -9 -9 ] [.02381 .00222 9 0 ] [.2619 .00222 -9 -9 ] [.2619 .00222 9 0 ] [.7381 .00222 -6 -9 ] [.7381 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.4875 .10861 -24 -4.5 ] [.4875 .10861 0 4.5 ] [.4875 .20251 -24 -4.5 ] [.4875 .20251 0 4.5 ] [.4875 .29641 -24 -4.5 ] [.4875 .29641 0 4.5 ] [.4875 .39031 -24 -4.5 ] [.4875 .39031 0 4.5 ] [.4875 .48421 -18 -4.5 ] [.4875 .48421 0 4.5 ] [.4875 .5781 -24 -4.5 ] [.4875 .5781 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 .02381 .01472 m .02381 .02097 L s [(-40)] .02381 .00222 0 1 Mshowa .2619 .01472 m .2619 .02097 L s [(-20)] .2619 .00222 0 1 Mshowa .7381 .01472 m .7381 .02097 L s [(20)] .7381 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(40)] .97619 .00222 0 1 Mshowa .125 Mabswid .08333 .01472 m .08333 .01847 L s .14286 .01472 m .14286 .01847 L s .20238 .01472 m .20238 .01847 L s .32143 .01472 m .32143 .01847 L s .38095 .01472 m .38095 .01847 L s .44048 .01472 m .44048 .01847 L s .55952 .01472 m .55952 .01847 L s .61905 .01472 m .61905 .01847 L s .67857 .01472 m .67857 .01847 L s .79762 .01472 m .79762 .01847 L s .85714 .01472 m .85714 .01847 L s .91667 .01472 m .91667 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .5 .10861 m .50625 .10861 L s [(0.02)] .4875 .10861 1 0 Mshowa .5 .20251 m .50625 .20251 L s [(0.04)] .4875 .20251 1 0 Mshowa .5 .29641 m .50625 .29641 L s [(0.06)] .4875 .29641 1 0 Mshowa .5 .39031 m .50625 .39031 L s [(0.08)] .4875 .39031 1 0 Mshowa .5 .48421 m .50625 .48421 L s [(0.1)] .4875 .48421 1 0 Mshowa .5 .5781 m .50625 .5781 L s [(0.12)] .4875 .5781 1 0 Mshowa .125 Mabswid .5 .03819 m .50375 .03819 L s .5 .06166 m .50375 .06166 L s .5 .08514 m .50375 .08514 L s .5 .13209 m .50375 .13209 L s .5 .15556 m .50375 .15556 L s .5 .17904 m .50375 .17904 L s .5 .22599 m .50375 .22599 L s .5 .24946 m .50375 .24946 L s .5 .27294 m .50375 .27294 L s .5 .31988 m .50375 .31988 L s .5 .34336 m .50375 .34336 L s .5 .36683 m .50375 .36683 L s .5 .41378 m .50375 .41378 L s .5 .43726 m .50375 .43726 L s .5 .46073 m .50375 .46073 L s .5 .50768 m .50375 .50768 L s .5 .53115 m .50375 .53115 L s .5 .55463 m .50375 .55463 L s .5 .60158 m .50375 .60158 L s .25 Mabswid .5 0 m .5 .61803 L s .02 w .02381 .01472 Mdot .03571 .01472 Mdot .04762 .01472 Mdot .05952 .01472 Mdot .07143 .01472 Mdot .08333 .01472 Mdot .09524 .01472 Mdot .10714 .01472 Mdot .11905 .01472 Mdot .13095 .01472 Mdot .14286 .01472 Mdot .15476 .01472 Mdot .16667 .01473 Mdot .17857 .01472 Mdot .19048 .01479 Mdot .20238 .01472 Mdot .21429 .01504 Mdot .22619 .01472 Mdot .2381 .01588 Mdot .25 .01472 Mdot .2619 .01833 Mdot .27381 .01472 Mdot .28571 .02459 Mdot .29762 .01472 Mdot .30952 .03857 Mdot .32143 .01472 Mdot .33333 .0661 Mdot .34524 .01472 Mdot .35714 .11381 Mdot .36905 .01472 Mdot .38095 .18648 Mdot .39286 .01472 Mdot .40476 .28309 Mdot .41667 .01472 Mdot .42857 .3936 Mdot .44048 .01472 Mdot .45238 .49885 Mdot .46429 .01472 Mdot .47619 .57529 Mdot .4881 .01472 Mdot .5 .60332 Mdot .5119 .01472 Mdot .52381 .57529 Mdot .53571 .01472 Mdot .54762 .49885 Mdot .55952 .01472 Mdot .57143 .3936 Mdot .58333 .01472 Mdot .59524 .28309 Mdot .60714 .01472 Mdot .61905 .18648 Mdot .63095 .01472 Mdot .64286 .11381 Mdot .65476 .01472 Mdot .66667 .0661 Mdot .67857 .01472 Mdot .69048 .03857 Mdot .70238 .01472 Mdot .71429 .02459 Mdot .72619 .01472 Mdot .7381 .01833 Mdot .75 .01472 Mdot .7619 .01588 Mdot .77381 .01472 Mdot .78571 .01504 Mdot .79762 .01472 Mdot .80952 .01479 Mdot .82143 .01472 Mdot .83333 .01473 Mdot .84524 .01472 Mdot .85714 .01472 Mdot .86905 .01472 Mdot .88095 .01472 Mdot .89286 .01472 Mdot .90476 .01472 Mdot .91667 .01472 Mdot .92857 .01472 Mdot .94048 .01472 Mdot .95238 .01472 Mdot .96429 .01472 Mdot .97619 .01472 Mdot 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgP3oool300000080oooo0P00000:0?ooo`003`3oool010000000oooo0?ooo`0000020?oo o`030000003oool0oooo03D0oooo00<000000?ooo`3oool00`3oool010000000oooo0?ooo`00001e 0?ooo`030000003oool0oooo00<0oooo00@000000?ooo`3oool00000>P3oool010000000oooo0?oo o`0000020?ooo`030000003oool0oooo00L0oooo000<0?ooo`D0000000D0oooo0000003oool0oooo 0000000h0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000MP3oool00`000000 oooo0?ooo`020?ooo`040000003oool0oooo000003L0oooo1@0000001@3oool000000?ooo`3oool0 000000T0oooo00060?ooo`@000000P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0 oooo00000340oooo100000040?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo 0?ooo`1e0?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo0?ooo`0e0?ooo`04 0000003oool0oooo00000080oooo00@000000?ooo`3oool000002@3oool000d0oooo00<000000?oo o`0000000P3oool010000000oooo0?ooo`00000g0?ooo`040000003oool0oooo00000080oooo00@0 00000?ooo`3oool00000M@3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo0000 03P0oooo00<000000?ooo`0000000P3oool010000000oooo0?ooo`0000090?ooo`003P3oool20000 00<0oooo0P00000i0?ooo`800000103oool2000007L0oooo0P0000040?ooo`800000>P3oool20000 00<0oooo0P00000:0?ooo`00o`3ooolQ0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03o ool00`000000oooo0?ooo`2=0?ooo`003@3oool6000000030?ooo`000000000000X0000000<0oooo 0000000000002P0000000`3oool000000000000:000000030?ooo`000000000000X0000000<0oooo 000000000000100000030?ooo`<00000103oool3000000<0oooo0`0000040?ooo`<000000`3oool3 000000@0oooo0`0000030?ooo`<00000103oool3000000<0oooo0`0000040?ooo`<0000000<0oooo 0000003oool00`0000040?ooo`<000000`3oool3000000@0oooo0`0000030?ooo`<00000103oool3 000000<0oooo0`0000040?ooo`<000000`3oool3000000@0oooo0`0000030?ooo`H0000000<0oooo 0000000000002P0000000`3oool000000000000:000000030?ooo`000000000000X0000000<0oooo 0000000000002P0000000`3oool0000000000004000000`0oooo000<0?ooodT000000P3oool50000 00030?ooo`000000000000<000000P3oool5000000030?ooo`000000000000<000000P3oool50000 00030?ooo`000000000000<000000P3oool5000000030?ooo`000000000000<000000P3oool;0000 0080oooo1@0000000`3oool000000000000300000080oooo1@0000000`3oool00000000000030000 0080oooo1@0000000`3oool000000000000300000080oooo1@0000000`3oool00000000000030000 0080ooooB@00000;0?ooo`00203ooooo000001<000001P3oool000`0ooooD00000000`3oool00000 0000000300000080oooo1@0000000`3oool0000000000003000000030?ooo`000000000000@00000 00<0oooo0000000000000`0000020?ooo`D0000000<0oooo0000000000000`0000020?ooo`/00000 0P3oool5000000030?ooo`000000000000<000000P3oool5000000030?ooo`000000000000<00000 00<0oooo000000000000100000000`3oool000000000000300000080oooo1@0000000`3oool00000 0000001>000000/0oooo000=0?ooo`H0000000<0oooo0000000000002P0000000`3oool000000000 000:000000030?ooo`000000000000X0000000<0oooo0000000000002P0000000`3oool000000000 000A000000<0oooo0`0000040?ooo`<000000`3oool3000000@0oooo0`0000030?ooo`<00000103o ool3000000<0oooo0`0000040?ooo`<0000000<0oooo0000003oool00`0000040?ooo`<000000`3o ool3000000@0oooo0`0000030?ooo`<00000103oool3000000<0oooo0`0000040?ooo`<000000`3o oolC000000030?ooo`000000000000X0000000<0oooo0000000000002P0000000`3oool000000000 000:000000030?ooo`000000000000X0000000<0oooo0000000000001000000<0?ooo`00CP3oool3 000000<0oooo1@00000g0?ooo`030000003oool0oooo03H0oooo1@0000020?ooo`<00000C@3oool0 05@0oooo1@00000g0?ooo`030000003oool0oooo03H0oooo1@00001B0?ooo`00E@3oool3000000<0 oooo0`00000b0?ooo`030000003oool0oooo0300oooo0`0000040?ooo`<00000D`3oool005X0oooo 1@00000a0?ooo`800000<03oool5000005T0oooo001J0?ooo`D00000<@3oool00`000000oooo0?oo o`0_0?ooo`D00000F@3oool005X0oooo1@00000a0?ooo`030000003oool0oooo02l0oooo1@00001I 0?ooo`00F`3oool300000380oooo00<000000?ooo`3oool0<03oool3000005X0oooo002@0?ooo`03 0000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo001R0?ooo`<00000:`3o ool00`000000oooo0?ooo`0Z0?ooo`<00000H03oool00640oooo1@00000Z0?ooo`800000:P3oool5 000005l0oooo001Q0?ooo`D00000:P3oool00`000000oooo0?ooo`0Y0?ooo`D00000G`3oool00640 oooo1@00000Z0?ooo`030000003oool0oooo02T0oooo1@00001O0?ooo`00HP3oool3000002/0oooo 00<000000?ooo`3oool0:P3oool300000600oooo002@0?ooo`030000003oool0oooo08d0oooo002@ 0?ooo`030000003oool0oooo08d0oooo002@0?ooo`800000SP3oool00900oooo00<000000?ooo`3o ool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3o ool00900oooo00<000000?ooo`3oool0S@3oool007L0oooo0P0000040?ooo`800000103oool20000 00<0oooo100000040?ooo`030000003oool0oooo08d0oooo001X0?ooo`<000002`3oool010000000 oooo0?ooo`0000080?ooo`040000003oool0oooo00000080oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`0S0?ooo`<00000I`3oool006L0oooo1@00000:0?ooo`040000003oool0oooo 000000P0oooo00@000000?ooo`3oool000000`3oool00`000000oooo0?ooo`040?ooo`<000008P3o ool5000006H0oooo001W0?ooo`D000002P3oool010000000oooo0?ooo`0000080?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`0R0?ooo`D00000 IP3oool006L0oooo1@00000:0?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3oool0 00000P3oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo0280oooo1@00001V0?oo o`00J03oool3000000`0oooo0P00000:0?ooo`800000103oool2000000D0oooo00<000000?ooo`3o ool08`3oool3000006L0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003o ool0oooo08d0oooo002@0?ooo`800000SP3oool00900oooo00<000000?ooo`3oool0S@3oool00900 oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<0 00000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo0P00002>0?oo o`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03o ool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`00 0000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00K`3oool3000001h0oooo 0P00000N0?ooo`<00000K@3oool006h0oooo1@00000M0?ooo`030000003oool0oooo01`0oooo1@00 001/0?ooo`00KP3oool5000001d0oooo00<000000?ooo`3oool0703oool5000006`0oooo001^0?oo o`D000007@3oool00`000000oooo0?ooo`0L0?ooo`D00000K03oool006l0oooo0`0000050?ooo`80 0000103oool2000000@0oooo0P0000050?ooo`<000000`3oool00`000000oooo0?ooo`0M0?ooo`<0 0000K@3oool007H0oooo00@000000?ooo`3oool00000203oool010000000oooo0?ooo`0000050?oo o`030000003oool0oooo0080oooo00<000000?ooo`3oool0S@3oool007H0oooo00@000000?ooo`3o ool00000203oool010000000oooo0?ooo`0000020?ooo`D000000`3oool3000008d0oooo001f0?oo o`040000003oool0oooo000000P0oooo00@000000?ooo`3oool000000P3oool010000000oooo0?oo o`0000040?ooo`030000003oool0oooo08d0oooo001f0?ooo`040000003oool0oooo000000P0oooo 00@000000?ooo`3oool000000`3oool00`000000oooo000000040?ooo`030000003oool0oooo08d0 oooo001g0?ooo`8000002P3oool2000000D0oooo0P0000040?ooo`030000003oool0oooo08d0oooo 002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?oo o`030000003oool0oooo08d0oooo002@0?ooo`800000SP3oool00900oooo00<000000?ooo`3oool0 S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool0 0900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo 0P00002>0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2= 0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00 T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool2000008h0oooo001e0?ooo`<00000603oool0 0`000000oooo0?ooo`0F0?ooo`<00000M03oool007@0oooo1@00000G0?ooo`030000003oool0oooo 01D0oooo1@00001c0?ooo`00M03oool5000001L0oooo00<000000?ooo`3oool05@3oool5000007<0 oooo001d0?ooo`D000005`3oool00`000000oooo0?ooo`0E0?ooo`D00000L`3oool007D0oooo1000 00040?ooo`800000103oool2000000<0oooo0`0000050?ooo`030000003oool0oooo01H0oooo0`00 001d0?ooo`00MP3oool010000000oooo0?ooo`0000080?ooo`040000003oool0oooo00000080oooo 00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`2=0?ooo`00MP3oool010000000oooo 0?ooo`0000080?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000103oool3 000008d0oooo001f0?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3oool000000P3o ool3000000D0oooo00<000000?ooo`3oool0S@3oool007H0oooo00@000000?ooo`3oool00000203o ool010000000oooo0?ooo`0000030?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0 S@3oool007L0oooo0P00000:0?ooo`800000103oool3000000@0oooo00<000000?ooo`3oool0S@3o ool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900 oooo0P00002>0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?oo o`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?oo o`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03o ool2000008h0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo 08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo 002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`800000SP3oool00900oooo00<000000?oo o`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0 S@3oool007L0oooo0P0000040?ooo`800000103oool2000000@0oooo0P0000050?ooo`030000003o ool0oooo08d0oooo001f0?ooo`040000003oool0oooo00000080oooo0`0000030?ooo`040000003o ool0oooo00000080oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`0@0?ooo`<0 0000NP3oool007H0oooo00D000000?ooo`3oool000000?ooo`0500000080oooo00@000000?ooo`3o ool000000P3oool010000000oooo0?ooo`0000040?ooo`<000003`3oool5000007T0oooo001f0?oo o`050000003oool0oooo0000003oool01@0000020?ooo`040000003oool0oooo000000<0oooo0P00 00050?ooo`030000003oool0oooo00l0oooo1@00001i0?ooo`00MP3oool01@000000oooo0?ooo`00 0000oooo00D000000P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo000000@0 oooo00<000000?ooo`3oool03`3oool5000007T0oooo001g0?ooo`8000000`3oool3000000@0oooo 0P0000040?ooo`8000001@3oool00`000000oooo0?ooo`0@0?ooo`<00000NP3oool00900oooo00<0 00000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?oo o`3oool0S@3oool00900oooo0P00002>0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03o ool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`00 0000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool2000008h0oooo 002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?oo o`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000 003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`800000SP3oool0 0900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo 00<000000?ooo`3oool0S@3oool007d0oooo0P0000040?ooo`8000000`3oool5000000<0oooo00<0 00000?ooo`3oool0S@3oool007`0oooo00@000000?ooo`3oool000002P3oool00`000000oooo0?oo o`030?ooo`030000003oool0oooo08d0oooo001l0?ooo`040000003oool0oooo000000X0oooo00<0 00000?ooo`3oool00`3oool3000008d0oooo001l0?ooo`040000003oool0oooo000000X0oooo00<0 00000?ooo`3oool00`3oool00`000000oooo0?ooo`2=0?ooo`00O03oool010000000oooo0?ooo`00 00020?ooo`<000001@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00T0oooo0`00 00210?ooo`00O@3oool200000080oooo1@0000030?ooo`8000001@3oool00`000000oooo0?ooo`08 0?ooo`D00000P03oool00840oooo1@00000:0?ooo`030000003oool0oooo00P0oooo1@0000200?oo o`00P@3oool5000000X0oooo00<000000?ooo`3oool0203oool500000800oooo00220?ooo`<00000 2`3oool2000000X0oooo0`0000210?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool0 0`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000 oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?oo o`2=0?ooo`00T03oool2000008h0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`03 0000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003o ool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`800000SP3oool00900 oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<0 00000?ooo`3oool0S@3oool008T0oooo0`0000040?ooo`030000003oool0oooo00<0oooo0`000027 0?ooo`00M`3oool2000000@0oooo0P0000030?ooo`D0000000<0oooo0000000000000`0000030?oo o`030000003oool0oooo0080oooo1@0000260?ooo`00MP3oool010000000oooo0?ooo`00000:0?oo o`040000003oool0oooo0?ooo`D000000`3oool00`000000oooo0?ooo`020?ooo`D00000QP3oool0 07H0oooo00@000000?ooo`3oool000002P3oool010000000oooo0?ooo`3oool5000000<0oooo0`00 00020?ooo`D00000QP3oool007H0oooo00@000000?ooo`3oool000002P3oool00`000000oooo0?oo o`020?ooo`<00000103oool00`000000oooo0?ooo`030?ooo`<00000Q`3oool007H0oooo00@00000 0?ooo`3oool000002P3oool01@000000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool0 0P3oool00`000000oooo0?ooo`2=0?ooo`00M`3oool2000000X0oooo0P0000040?ooo`8000001@3o ool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00S`3oool30000 08h0oooo002>0?ooo`D00000S@3oool008h0oooo1@00002=0?ooo`00SP3oool5000008d0oooo002? 0?ooo`<00000SP3oool00900oooo00<000000?ooo`3oool0S@3oool00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-44.5872, -0.00969148, \ 0.308022, 0.000781045}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p[0, time]\)], "Input"], Cell[BoxData[ \(34461632205\/274877906944\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \(0.12537068761957926`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(u[x_, t_]\ = \ \((1/\((2\ Sqrt[ Pi\ d\ t])\))\)\ Exp[\(-x^2\)/\((4\ d\ t)\)]\)], "Input"], Cell[BoxData[ \(\[ExponentialE]\^\(-\(x\^2\/\(4\ d\ t\)\)\)\/\(2\ \@\[Pi]\ \@\(d\ t\)\)\ \)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(D[u[x, t], t] - d\ D[u[x, t], {x, 2}]\)], "Input"], Cell[BoxData[ \(\(-\(\(d\ \[ExponentialE]\^\(-\(x\^2\/\(4\ d\ t\)\)\)\)\/\(4\ \@\[Pi]\ \ \((d\ t)\)\^\(3/2\)\)\)\) + \(\[ExponentialE]\^\(-\(x\^2\/\(4\ d\ t\)\)\)\ \ x\^2\)\/\(8\ d\ \@\[Pi]\ t\^2\ \@\(d\ t\)\) - \(d\ \ \((\(-\(\[ExponentialE]\^\(-\(x\^2\/\(4\ d\ t\)\)\)\/\(2\ d\ t\)\)\) + \(\ \[ExponentialE]\^\(-\(x\^2\/\(4\ d\ t\)\)\)\ x\^2\)\/\(4\ d\^2\ t\^2\))\)\)\/\ \(2\ \@\[Pi]\ \@\(d\ t\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[%]\)], "Input"], Cell[BoxData[ \(0\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(d = 1/2;\)\), "\[IndentingNewLine]", \(\(approximation = Plot[u[x, time], {x, \(-time\), time}, PlotRange \[Rule] All];\)\)}], "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 %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0119048 0.0147151 9.33154 [ [.02381 .00222 -9 -9 ] [.02381 .00222 9 0 ] [.2619 .00222 -9 -9 ] [.2619 .00222 9 0 ] [.7381 .00222 -6 -9 ] [.7381 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.4875 .10803 -24 -4.5 ] [.4875 .10803 0 4.5 ] [.4875 .20135 -24 -4.5 ] [.4875 .20135 0 4.5 ] [.4875 .29466 -24 -4.5 ] [.4875 .29466 0 4.5 ] [.4875 .38798 -24 -4.5 ] [.4875 .38798 0 4.5 ] [.4875 .48129 -24 -4.5 ] [.4875 .48129 0 4.5 ] [.4875 .57461 -24 -4.5 ] [.4875 .57461 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 .02381 .01472 m .02381 .02097 L s [(-40)] .02381 .00222 0 1 Mshowa .2619 .01472 m .2619 .02097 L s [(-20)] .2619 .00222 0 1 Mshowa .7381 .01472 m .7381 .02097 L s [(20)] .7381 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(40)] .97619 .00222 0 1 Mshowa .125 Mabswid .08333 .01472 m .08333 .01847 L s .14286 .01472 m .14286 .01847 L s .20238 .01472 m .20238 .01847 L s .32143 .01472 m .32143 .01847 L s .38095 .01472 m .38095 .01847 L s .44048 .01472 m .44048 .01847 L s .55952 .01472 m .55952 .01847 L s .61905 .01472 m .61905 .01847 L s .67857 .01472 m .67857 .01847 L s .79762 .01472 m .79762 .01847 L s .85714 .01472 m .85714 .01847 L s .91667 .01472 m .91667 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .5 .10803 m .50625 .10803 L s [(0.01)] .4875 .10803 1 0 Mshowa .5 .20135 m .50625 .20135 L s [(0.02)] .4875 .20135 1 0 Mshowa .5 .29466 m .50625 .29466 L s [(0.03)] .4875 .29466 1 0 Mshowa .5 .38798 m .50625 .38798 L s [(0.04)] .4875 .38798 1 0 Mshowa .5 .48129 m .50625 .48129 L s [(0.05)] .4875 .48129 1 0 Mshowa .5 .57461 m .50625 .57461 L s [(0.06)] .4875 .57461 1 0 Mshowa .125 Mabswid .5 .03338 m .50375 .03338 L s .5 .05204 m .50375 .05204 L s .5 .0707 m .50375 .0707 L s .5 .08937 m .50375 .08937 L s .5 .12669 m .50375 .12669 L s .5 .14536 m .50375 .14536 L s .5 .16402 m .50375 .16402 L s .5 .18268 m .50375 .18268 L s .5 .22001 m .50375 .22001 L s .5 .23867 m .50375 .23867 L s .5 .25734 m .50375 .25734 L s .5 .276 m .50375 .276 L s .5 .31332 m .50375 .31332 L s .5 .33199 m .50375 .33199 L s .5 .35065 m .50375 .35065 L s .5 .36931 m .50375 .36931 L s .5 .40664 m .50375 .40664 L s .5 .4253 m .50375 .4253 L s .5 .44397 m .50375 .44397 L s .5 .46263 m .50375 .46263 L s .5 .49996 m .50375 .49996 L s .5 .51862 m .50375 .51862 L s .5 .53728 m .50375 .53728 L s .5 .55594 m .50375 .55594 L s .5 .59327 m .50375 .59327 L s .5 .61193 m .50375 .61193 L s .25 Mabswid .5 0 m .5 .61803 L s .5 Mabswid .02381 .01472 m .02605 .01472 L .02846 .01472 L .03279 .01472 L .03543 .01472 L .03793 .01472 L .04262 .01472 L .04502 .01472 L .04756 .01472 L .05212 .01472 L .05466 .01472 L .05704 .01472 L .06244 .01472 L .06504 .01472 L .06788 .01472 L .07038 .01472 L .07305 .01472 L .07807 .01472 L .08274 .01472 L .08558 .01472 L .08864 .01472 L .09134 .01472 L .0942 .01472 L .09677 .01472 L .0996 .01472 L .10458 .01472 L .10982 .01472 L .11478 .01472 L .11924 .01472 L .12409 .01472 L .12936 .01472 L .13495 .01472 L .13973 .01472 L .145 .01472 L .14992 .01473 L .1551 .01473 L .15952 .01474 L .16435 .01474 L .16957 .01475 L .17516 .01477 L .18042 .01479 L .18521 .01481 L .19006 .01484 L .19519 .01488 L .19957 .01492 L .20439 .01498 L .20957 .01506 L .21514 .01517 L .22039 .01531 L .22519 .01547 L Mistroke .22997 .01566 L .23506 .01592 L .24421 .01655 L .24982 .01707 L .2551 .01768 L .2598 .01834 L .26495 .01922 L .27474 .02142 L .28008 .02298 L .28507 .02472 L .294 .02865 L .30355 .03429 L .31375 .04233 L .32483 .05403 L .3353 .06851 L .34497 .08537 L .36367 .12897 L .38428 .1954 L .42454 .37094 L .44305 .45691 L .45354 .50129 L .46328 .53733 L .47299 .56666 L .47797 .57867 L .48336 .58913 L .48633 .5937 L .48906 .59715 L .49167 .59974 L .493 .60079 L .49443 .60172 L .49572 .60238 L .4969 .60283 L .49809 .60314 L .49921 .6033 L .50052 .60332 L .50173 .60318 L .50236 .60304 L .50306 .60285 L .50447 .6023 L .50568 .60166 L .50681 .60093 L .50938 .59878 L .51188 .59605 L .51455 .59245 L .51939 .58413 L .5238 .57466 L .53451 .54463 L .54464 .50845 L .58308 .33495 L .60254 .24757 L Mistroke .62396 .16649 L .63376 .13619 L .6443 .10853 L .66333 .07068 L .67345 .05616 L .68448 .04397 L .69491 .03535 L .70458 .02939 L .71516 .02464 L .72512 .02146 L .73406 .01941 L .73906 .01852 L .74373 .01784 L .75324 .01677 L .75828 .01635 L .76368 .01599 L .76934 .01569 L .77471 .01547 L .77948 .01531 L .78475 .01518 L .7894 .01508 L .79441 .015 L .79971 .01493 L .80468 .01488 L .80936 .01484 L .81429 .01481 L .8185 .01479 L .8231 .01477 L .82839 .01476 L .83339 .01475 L .83787 .01474 L .84273 .01473 L .84802 .01473 L .85363 .01472 L .85842 .01472 L .86368 .01472 L .8689 .01472 L .87385 .01472 L .8783 .01472 L .88314 .01472 L .8884 .01472 L .89133 .01472 L .89399 .01472 L .89917 .01472 L .90404 .01472 L .90872 .01472 L .91384 .01472 L .91642 .01472 L .91919 .01472 L .92158 .01472 L Mistroke .92417 .01472 L .92676 .01472 L .92915 .01472 L .93385 .01472 L .93813 .01472 L .94266 .01472 L .94702 .01472 L .951 .01472 L .9532 .01472 L .9556 .01472 L .95997 .01472 L .96404 .01472 L .96838 .01472 L .97248 .01472 L .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgP3oool300000080oooo0P00000:0?ooo`003`3oool010000000oooo0?ooo`0000020?oo o`030000003oool0oooo03D0oooo00<000000?ooo`3oool00`3oool010000000oooo0?ooo`00001e 0?ooo`030000003oool0oooo00<0oooo00@000000?ooo`3oool00000>P3oool010000000oooo0?oo o`0000020?ooo`030000003oool0oooo00L0oooo000<0?ooo`D0000000D0oooo0000003oool0oooo 0000000h0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000MP3oool00`000000 oooo0?ooo`020?ooo`040000003oool0oooo000003L0oooo1@0000001@3oool000000?ooo`3oool0 000000T0oooo00060?ooo`@000000P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0 oooo00000340oooo100000040?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo 0?ooo`1e0?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo0?ooo`0e0?ooo`04 0000003oool0oooo00000080oooo00@000000?ooo`3oool000002@3oool000d0oooo00<000000?oo o`0000000P3oool010000000oooo0?ooo`00000g0?ooo`040000003oool0oooo00000080oooo00@0 00000?ooo`3oool00000M@3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo0000 03P0oooo00<000000?ooo`0000000P3oool010000000oooo0?ooo`0000090?ooo`003P3oool20000 00<0oooo0P00000i0?ooo`800000103oool2000007L0oooo0P0000040?ooo`800000>P3oool20000 00<0oooo0P00000:0?ooo`00o`3ooolQ0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03o ool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`00 0000oooo0?ooo`2=0?ooo`00203ooooo000001<000001P3oool000h0oooo00<000000?ooo`3oool0 3P3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0 2@3oool7000000h0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000 003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0>0?ooo`030000 003oool0oooo00d0oooo00<000000?ooo`3oool0303oool7000000X0oooo00<000000?ooo`3oool0 3P3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0 2`3oool000h0oooo00<000000?ooo`3oool0?P3oool00`000000oooo0?ooo`03000003/0oooo00<0 00000?ooo`3oool0>P3oool3000000030?ooo`000000oooo03l0oooo00<000000?ooo`3oool02`3o ool005D0oooo0P00000i0?ooo`030000003oool0oooo03L0oooo0`00001C0?ooo`00E`3oool30000 03H0oooo00<000000?ooo`3oool0=@3oool2000005H0oooo001J0?ooo`800000=03oool2000003@0 oooo0P00001H0?ooo`00G03oool00`000000oooo0?ooo`0a0?ooo`030000003oool0oooo0380oooo 00<000000?ooo`3oool0F03oool005d0oooo00<000000?ooo`3oool0<03oool00`000000oooo0?oo o`0a0?ooo`030000003oool0oooo05T0oooo001N0?ooo`030000003oool0oooo02l0oooo00<00000 0?ooo`3oool0<03oool00`000000oooo0?ooo`1J0?ooo`00GP3oool00`000000oooo0?ooo`0_0?oo o`030000003oool0oooo02l0oooo00<000000?ooo`3oool0F`3oool005l0oooo00<000000?ooo`3o ool0;P3oool2000002l0oooo00<000000?ooo`3oool0G03oool00600oooo00<000000?ooo`3oool0 ;@3oool00`000000oooo0?ooo`0]0?ooo`030000003oool0oooo05d0oooo001Q0?ooo`030000003o ool0oooo02`0oooo00<000000?ooo`3oool0;03oool00`000000oooo0?ooo`1N0?ooo`00H@3oool0 0`000000oooo0?ooo`0/0?ooo`030000003oool0oooo02/0oooo00<000000?ooo`3oool0G`3oool0 0680oooo00<000000?ooo`3oool0:`3oool00`000000oooo0?ooo`0[0?ooo`030000003oool0oooo 05l0oooo001S0?ooo`030000003oool0oooo02X0oooo0P00000[0?ooo`030000003oool0oooo0600 oooo001T0?ooo`030000003oool0oooo02T0oooo00<000000?ooo`3oool0:P3oool00`000000oooo 0?ooo`1P0?ooo`00I03oool00`000000oooo0?ooo`0Y0?ooo`030000003oool0oooo02T0oooo00<0 00000?ooo`3oool0H@3oool006D0oooo00<000000?ooo`3oool0:03oool00`000000oooo0?ooo`0Y 0?ooo`030000003oool0oooo0640oooo001V0?ooo`030000003oool0oooo02L0oooo00<000000?oo o`3oool0:03oool00`000000oooo0?ooo`1R0?ooo`00IP3oool00`000000oooo0?ooo`0W0?ooo`80 0000:@3oool00`000000oooo0?ooo`1R0?ooo`00I`3oool00`000000oooo0?ooo`0V0?ooo`030000 003oool0oooo02L0oooo00<000000?ooo`3oool0H`3oool006L0oooo00<000000?ooo`3oool09P3o ool00`000000oooo0?ooo`0W0?ooo`030000003oool0oooo06<0oooo001X0?ooo`030000003oool0 oooo00`0oooo0P0000040?ooo`800000103oool2000000<0oooo1@0000030?ooo`030000003oool0 oooo02H0oooo00<000000?ooo`3oool0I03oool006P0oooo00<000000?ooo`3oool02`3oool01000 0000oooo0?ooo`0000080?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool00`3o ool00`000000oooo0?ooo`0V0?ooo`030000003oool0oooo06@0oooo001X0?ooo`030000003oool0 oooo00/0oooo00@000000?ooo`3oool00000203oool010000000oooo0?ooo`0000040?ooo`030000 003oool0oooo00<0oooo0`00000U0?ooo`030000003oool0oooo06D0oooo001Y0?ooo`030000003o ool0oooo00X0oooo00@000000?ooo`3oool00000203oool010000000oooo0?ooo`0000040?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool09@3oool00`000000oooo0?ooo`1U0?ooo`00 J@3oool00`000000oooo0?ooo`0:0?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3o ool00000103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo02D0oooo00<000000?oo o`3oool0I@3oool006X0oooo00<000000?ooo`3oool02P3oool2000000X0oooo0P0000040?ooo`80 00001@3oool00`000000oooo0?ooo`0T0?ooo`030000003oool0oooo06H0oooo001Z0?ooo`030000 003oool0oooo02<0oooo00<000000?ooo`3oool0903oool00`000000oooo0?ooo`1V0?ooo`00J`3o ool00`000000oooo0?ooo`0R0?ooo`030000003oool0oooo02<0oooo00<000000?ooo`3oool0I`3o ool006/0oooo00<000000?ooo`3oool08P3oool2000002@0oooo00<000000?ooo`3oool0I`3oool0 06/0oooo00<000000?ooo`3oool08P3oool00`000000oooo0?ooo`0R0?ooo`030000003oool0oooo 06P0oooo001/0?ooo`030000003oool0oooo0240oooo00<000000?ooo`3oool08P3oool00`000000 oooo0?ooo`1X0?ooo`00K03oool00`000000oooo0?ooo`0Q0?ooo`030000003oool0oooo0280oooo 00<000000?ooo`3oool0J03oool006`0oooo00<000000?ooo`3oool08@3oool00`000000oooo0?oo o`0Q0?ooo`030000003oool0oooo06T0oooo001]0?ooo`030000003oool0oooo0200oooo0P00000R 0?ooo`030000003oool0oooo06T0oooo001]0?ooo`030000003oool0oooo0200oooo00<000000?oo o`3oool0803oool00`000000oooo0?ooo`1Z0?ooo`00K@3oool00`000000oooo0?ooo`0P0?ooo`03 0000003oool0oooo0200oooo00<000000?ooo`3oool0JP3oool006h0oooo00<000000?ooo`3oool0 7`3oool00`000000oooo0?ooo`0P0?ooo`030000003oool0oooo06X0oooo001^0?ooo`030000003o ool0oooo01l0oooo00<000000?ooo`3oool07`3oool00`000000oooo0?ooo`1[0?ooo`00KP3oool0 0`000000oooo0?ooo`0O0?ooo`800000803oool00`000000oooo0?ooo`1[0?ooo`00K`3oool00`00 0000oooo0?ooo`0N0?ooo`030000003oool0oooo01l0oooo00<000000?ooo`3oool0J`3oool006l0 oooo00<000000?ooo`3oool07P3oool00`000000oooo0?ooo`0N0?ooo`030000003oool0oooo06`0 oooo001_0?ooo`030000003oool0oooo01h0oooo00<000000?ooo`3oool07P3oool00`000000oooo 0?ooo`1/0?ooo`00L03oool00`000000oooo0?ooo`0M0?ooo`030000003oool0oooo01h0oooo00<0 00000?ooo`3oool0K03oool00700oooo00<000000?ooo`3oool07@3oool2000001l0oooo00<00000 0?ooo`3oool0K03oool00700oooo00<000000?ooo`3oool07@3oool00`000000oooo0?ooo`0M0?oo o`030000003oool0oooo06d0oooo001a0?ooo`030000003oool0oooo01`0oooo00<000000?ooo`3o ool07@3oool00`000000oooo0?ooo`1]0?ooo`00L@3oool00`000000oooo0?ooo`030?ooo`800000 103oool2000000@0oooo0P0000030?ooo`@00000103oool00`000000oooo0?ooo`0M0?ooo`030000 003oool0oooo06d0oooo001a0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000 203oool010000000oooo0?ooo`0000020?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3o ool07@3oool00`000000oooo0?ooo`1]0?ooo`00L@3oool00`000000oooo0?ooo`020?ooo`040000 003oool0oooo000000P0oooo00@000000?ooo`3oool000000`3oool00`000000oooo0?ooo`040?oo o`<00000703oool00`000000oooo0?ooo`1^0?ooo`00LP3oool01@000000oooo0?ooo`3oool00000 0080oooo00<000000?ooo`3oool01P3oool010000000oooo0?ooo`0000040?ooo`030000003oool0 oooo00<0oooo00<000000?ooo`3oool0703oool00`000000oooo0?ooo`1^0?ooo`00LP3oool01@00 0000oooo0?ooo`3oool000000080oooo00<000000?ooo`3oool01P3oool010000000oooo0?ooo`00 00020?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0703oool00`000000oooo 0?ooo`1^0?ooo`00LP3oool00`000000oooo0?ooo`020?ooo`8000002P3oool2000000@0oooo0P00 00050?ooo`030000003oool0oooo01/0oooo00<000000?ooo`3oool0K`3oool00780oooo00<00000 0?ooo`3oool06`3oool00`000000oooo0?ooo`0K0?ooo`030000003oool0oooo06l0oooo001c0?oo o`030000003oool0oooo01X0oooo0P00000L0?ooo`030000003oool0oooo06l0oooo001c0?ooo`03 0000003oool0oooo01X0oooo00<000000?ooo`3oool06`3oool00`000000oooo0?ooo`1_0?ooo`00 L`3oool00`000000oooo0?ooo`0J0?ooo`030000003oool0oooo01X0oooo00<000000?ooo`3oool0 L03oool007<0oooo00<000000?ooo`3oool06P3oool00`000000oooo0?ooo`0J0?ooo`030000003o ool0oooo0700oooo001d0?ooo`030000003oool0oooo01T0oooo00<000000?ooo`3oool06P3oool0 0`000000oooo0?ooo`1`0?ooo`00M03oool00`000000oooo0?ooo`0I0?ooo`8000006`3oool00`00 0000oooo0?ooo`1`0?ooo`00M03oool00`000000oooo0?ooo`0I0?ooo`030000003oool0oooo01T0 oooo00<000000?ooo`3oool0L@3oool007@0oooo00<000000?ooo`3oool06@3oool00`000000oooo 0?ooo`0I0?ooo`030000003oool0oooo0740oooo001d0?ooo`030000003oool0oooo01T0oooo00<0 00000?ooo`3oool06@3oool00`000000oooo0?ooo`1a0?ooo`00M@3oool00`000000oooo0?ooo`0H 0?ooo`030000003oool0oooo01T0oooo00<000000?ooo`3oool0L@3oool007D0oooo00<000000?oo o`3oool0603oool2000001T0oooo00<000000?ooo`3oool0LP3oool007D0oooo00<000000?ooo`3o ool0603oool00`000000oooo0?ooo`0H0?ooo`030000003oool0oooo0780oooo001e0?ooo`030000 003oool0oooo01P0oooo00<000000?ooo`3oool0603oool00`000000oooo0?ooo`1b0?ooo`00MP3o ool00`000000oooo0?ooo`0G0?ooo`030000003oool0oooo01P0oooo00<000000?ooo`3oool0LP3o ool007H0oooo00<000000?ooo`3oool05`3oool00`000000oooo0?ooo`0H0?ooo`030000003oool0 oooo0780oooo001f0?ooo`030000003oool0oooo01L0oooo0P00000H0?ooo`030000003oool0oooo 07<0oooo001f0?ooo`030000003oool0oooo01L0oooo00<000000?ooo`3oool05`3oool00`000000 oooo0?ooo`1c0?ooo`00MP3oool00`000000oooo0?ooo`0G0?ooo`030000003oool0oooo01L0oooo 00<000000?ooo`3oool0L`3oool007L0oooo0P0000040?ooo`800000103oool2000000@0oooo0P00 00050?ooo`030000003oool0oooo01L0oooo00<000000?ooo`3oool0L`3oool007H0oooo0P000000 0`3oool000000?ooo`070?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000 103oool00`000000oooo0?ooo`0F0?ooo`030000003oool0oooo07@0oooo001f0?ooo`80000000<0 oooo0000003oool01`3oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo00<0oooo 0`00000F0?ooo`030000003oool0oooo07@0oooo001f0?ooo`80000000<0oooo0000003oool01`3o ool010000000oooo0?ooo`0000050?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0 5P3oool00`000000oooo0?ooo`1d0?ooo`00MP3oool010000000oooo0000000000080?ooo`040000 003oool0oooo00000080oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`0F0?oo o`030000003oool0oooo07@0oooo001g0?ooo`8000002P3oool2000000@0oooo0P0000050?ooo`03 0000003oool0oooo01H0oooo00<000000?ooo`3oool0M03oool007P0oooo00<000000?ooo`3oool0 5@3oool00`000000oooo0?ooo`0E0?ooo`030000003oool0oooo07D0oooo001h0?ooo`030000003o ool0oooo01D0oooo0P00000F0?ooo`030000003oool0oooo07D0oooo001i0?ooo`030000003oool0 oooo01@0oooo00<000000?ooo`3oool05@3oool00`000000oooo0?ooo`1e0?ooo`00N@3oool00`00 0000oooo0?ooo`0D0?ooo`030000003oool0oooo01D0oooo00<000000?ooo`3oool0M@3oool007T0 oooo00<000000?ooo`3oool0503oool00`000000oooo0?ooo`0E0?ooo`030000003oool0oooo07D0 oooo001i0?ooo`030000003oool0oooo01@0oooo00<000000?ooo`3oool0503oool00`000000oooo 0?ooo`1f0?ooo`00N@3oool00`000000oooo0?ooo`0D0?ooo`8000005@3oool00`000000oooo0?oo o`1f0?ooo`00NP3oool00`000000oooo0?ooo`0C0?ooo`030000003oool0oooo01@0oooo00<00000 0?ooo`3oool0MP3oool007X0oooo00<000000?ooo`3oool04`3oool00`000000oooo0?ooo`0D0?oo o`030000003oool0oooo07H0oooo001j0?ooo`030000003oool0oooo01<0oooo00<000000?ooo`3o ool0503oool00`000000oooo0?ooo`1f0?ooo`00NP3oool00`000000oooo0?ooo`0C0?ooo`030000 003oool0oooo01<0oooo00<000000?ooo`3oool0M`3oool007/0oooo00<000000?ooo`3oool04P3o ool00`000000oooo0?ooo`0C0?ooo`030000003oool0oooo07L0oooo001k0?ooo`030000003oool0 oooo0180oooo0P00000D0?ooo`030000003oool0oooo07L0oooo001k0?ooo`030000003oool0oooo 0180oooo00<000000?ooo`3oool04`3oool00`000000oooo0?ooo`1g0?ooo`00N`3oool00`000000 oooo0?ooo`0B0?ooo`030000003oool0oooo0180oooo00<000000?ooo`3oool0N03oool007`0oooo 00<000000?ooo`3oool04@3oool00`000000oooo0?ooo`0B0?ooo`030000003oool0oooo07P0oooo 001l0?ooo`030000003oool0oooo0140oooo00<000000?ooo`3oool04P3oool00`000000oooo0?oo o`1h0?ooo`00O03oool00`000000oooo0?ooo`0A0?ooo`8000004`3oool00`000000oooo0?ooo`1h 0?ooo`00O03oool00`000000oooo0?ooo`0A0?ooo`030000003oool0oooo0140oooo00<000000?oo o`3oool0N@3oool007`0oooo00<000000?ooo`3oool04@3oool00`000000oooo0?ooo`0A0?ooo`03 0000003oool0oooo07T0oooo001g0?ooo`800000103oool2000000@0oooo0P0000050?ooo`<00000 0`3oool00`000000oooo0?ooo`0A0?ooo`030000003oool0oooo07T0oooo001f0?ooo`040000003o ool0oooo000000<0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`0000050?ooo`03 0000003oool0oooo0080oooo00<000000?ooo`3oool04@3oool00`000000oooo0?ooo`1i0?ooo`00 MP3oool010000000oooo0?ooo`0000030?ooo`030000003oool0oooo0080oooo00@000000?ooo`3o ool000000P3oool5000000<0oooo0`00000A0?ooo`030000003oool0oooo07T0oooo001f0?ooo`04 0000003oool0oooo000000<0oooo00<000000?ooo`3oool00P3oool010000000oooo0?ooo`000002 0?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool0403oool00`000000oooo0?oo o`1j0?ooo`00MP3oool010000000oooo0?ooo`0000030?ooo`030000003oool0oooo0080oooo00@0 00000?ooo`3oool000000`3oool00`000000oooo000000040?ooo`030000003oool0oooo0100oooo 00<000000?ooo`3oool0NP3oool007L0oooo0P0000050?ooo`030000003oool0oooo0080oooo0P00 00050?ooo`800000103oool00`000000oooo0?ooo`0@0?ooo`030000003oool0oooo07X0oooo001n 0?ooo`030000003oool0oooo00l0oooo00<000000?ooo`3oool0403oool00`000000oooo0?ooo`1j 0?ooo`00OP3oool00`000000oooo0?ooo`0?0?ooo`800000403oool00`000000oooo0?ooo`1k0?oo o`00OP3oool00`000000oooo0?ooo`0?0?ooo`030000003oool0oooo00l0oooo00<000000?ooo`3o ool0N`3oool007h0oooo00<000000?ooo`3oool03`3oool00`000000oooo0?ooo`0?0?ooo`030000 003oool0oooo07/0oooo001o0?ooo`030000003oool0oooo00h0oooo00<000000?ooo`3oool03`3o ool00`000000oooo0?ooo`1k0?ooo`00O`3oool00`000000oooo0?ooo`0>0?ooo`030000003oool0 oooo00h0oooo00<000000?ooo`3oool0O03oool007l0oooo00<000000?ooo`3oool03P3oool20000 00l0oooo00<000000?ooo`3oool0O03oool007l0oooo00<000000?ooo`3oool03P3oool00`000000 oooo0?ooo`0>0?ooo`030000003oool0oooo07`0oooo00200?ooo`030000003oool0oooo00d0oooo 00<000000?ooo`3oool03P3oool00`000000oooo0?ooo`1l0?ooo`00P03oool00`000000oooo0?oo o`0=0?ooo`030000003oool0oooo00h0oooo00<000000?ooo`3oool0O03oool00800oooo00<00000 0?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo07d0oooo00200?oo o`030000003oool0oooo00d0oooo0P00000>0?ooo`030000003oool0oooo07d0oooo00200?ooo`03 0000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`1m0?ooo`00 P@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0 O@3oool00840oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0<0?ooo`030000003o ool0oooo07h0oooo00210?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool0303oool0 0`000000oooo0?ooo`1n0?ooo`00P@3oool00`000000oooo0?ooo`0<0?ooo`8000003@3oool00`00 0000oooo0?ooo`1n0?ooo`00P@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo00`0 oooo00<000000?ooo`3oool0OP3oool00880oooo00<000000?ooo`3oool02`3oool00`000000oooo 0?ooo`0<0?ooo`030000003oool0oooo07h0oooo001g0?ooo`800000103oool2000000<0oooo0`00 00040?ooo`8000001@3oool00`000000oooo0?ooo`0;0?ooo`030000003oool0oooo07l0oooo001f 0?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3oool000000P3oool010000000oooo 0?ooo`0000040?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3oool0O`3oool007H0oooo 00@000000?ooo`3oool00000203oool010000000oooo0?ooo`0000050?ooo`030000003oool0oooo 0080oooo0`00000;0?ooo`030000003oool0oooo07l0oooo001f0?ooo`040000003oool0oooo0000 00P0oooo0P0000000`3oool000000?ooo`020?ooo`8000001@3oool00`000000oooo0?ooo`0;0?oo o`030000003oool0oooo07l0oooo001f0?ooo`040000003oool0oooo000000P0oooo0P0000000`3o ool000000?ooo`020?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool02P3oool00`00 0000oooo0?ooo`200?ooo`00M`3oool2000000X0oooo0P0000040?ooo`<00000103oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo0800oooo00230?ooo`030000003oool0oooo00X0oooo 00<000000?ooo`3oool02P3oool00`000000oooo0?ooo`200?ooo`00Q03oool00`000000oooo0?oo o`090?ooo`8000002`3oool00`000000oooo0?ooo`200?ooo`00Q03oool00`000000oooo0?ooo`09 0?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool0P@3oool008@0oooo00<000000?oo o`3oool02@3oool00`000000oooo0?ooo`090?ooo`030000003oool0oooo0840oooo00240?ooo`03 0000003oool0oooo00T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`210?ooo`00 Q@3oool00`000000oooo0?ooo`080?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool0 P@3oool008D0oooo00<000000?ooo`3oool0203oool2000000X0oooo00<000000?ooo`3oool0P@3o ool008D0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`030000003oool0 oooo0880oooo00250?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool0203oool00`00 0000oooo0?ooo`220?ooo`00QP3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00P0 oooo00<000000?ooo`3oool0PP3oool008H0oooo00<000000?ooo`3oool01`3oool00`000000oooo 0?ooo`080?ooo`030000003oool0oooo0880oooo00260?ooo`030000003oool0oooo00L0oooo0P00 00080?ooo`030000003oool0oooo08<0oooo00260?ooo`030000003oool0oooo00L0oooo00<00000 0?ooo`3oool01`3oool00`000000oooo0?ooo`230?ooo`00Q`3oool00`000000oooo0?ooo`060?oo o`030000003oool0oooo00L0oooo00<000000?ooo`3oool0P`3oool008L0oooo00<000000?ooo`3o ool01P3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo08<0oooo00270?ooo`030000 003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`240?ooo`00R03o ool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool0Q03o ool008P0oooo00<000000?ooo`3oool01@3oool2000000L0oooo00<000000?ooo`3oool0Q03oool0 08T0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 08D0oooo00290?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool01@3oool00`000000 oooo0?ooo`250?ooo`00M`3oool2000000@0oooo0P0000040?ooo`8000000`3oool3000000D0oooo 00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`250?ooo`00MP3oool010000000oooo0?oo o`0000080?ooo`040000003oool0oooo00000080oooo0P0000000`3oool000000?ooo`030?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool0QP3oool007H0oooo00@000000?ooo`3oool0 0000203oool010000000oooo0?ooo`0000020?ooo`040000003oool00000000000@0oooo0`000004 0?ooo`030000003oool0oooo08H0oooo001f0?ooo`040000003oool0oooo000000P0oooo00@00000 0?ooo`3oool000000P3oool3000000D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?oo o`270?ooo`00MP3oool010000000oooo0?ooo`0000080?ooo`040000003oool0oooo000000<0oooo 00<000000?ooo`000000103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo08L0oooo 001g0?ooo`8000002P3oool2000000@0oooo0`0000040?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool0R03oool008`0oooo00D000000?ooo`3oool0oooo000000040?ooo`030000003o ool0oooo08P0oooo002=0?ooo`030000003oool0oooo008000000P3oool00`000000oooo0?ooo`29 0?ooo`00S@3oool010000000oooo0?ooo`0000020?ooo`030000003oool0oooo08X0oooo002>0?oo o`D00000S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0 S@3oool00900oooo0P00002>0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-44.5872, -0.004876, \ 0.308022, 0.000392962}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[exact, approximation];\)\)], "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 %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0119048 0.0147151 4.69491 [ [.02381 .00222 -9 -9 ] [.02381 .00222 9 0 ] [.2619 .00222 -9 -9 ] [.2619 .00222 9 0 ] [.7381 .00222 -6 -9 ] [.7381 .00222 6 0 ] [.97619 .00222 -6 -9 ] [.97619 .00222 6 0 ] [.4875 .10861 -24 -4.5 ] [.4875 .10861 0 4.5 ] [.4875 .20251 -24 -4.5 ] [.4875 .20251 0 4.5 ] [.4875 .29641 -24 -4.5 ] [.4875 .29641 0 4.5 ] [.4875 .39031 -24 -4.5 ] [.4875 .39031 0 4.5 ] [.4875 .48421 -18 -4.5 ] [.4875 .48421 0 4.5 ] [.4875 .5781 -24 -4.5 ] [.4875 .5781 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 .02381 .01472 m .02381 .02097 L s [(-40)] .02381 .00222 0 1 Mshowa .2619 .01472 m .2619 .02097 L s [(-20)] .2619 .00222 0 1 Mshowa .7381 .01472 m .7381 .02097 L s [(20)] .7381 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(40)] .97619 .00222 0 1 Mshowa .125 Mabswid .08333 .01472 m .08333 .01847 L s .14286 .01472 m .14286 .01847 L s .20238 .01472 m .20238 .01847 L s .32143 .01472 m .32143 .01847 L s .38095 .01472 m .38095 .01847 L s .44048 .01472 m .44048 .01847 L s .55952 .01472 m .55952 .01847 L s .61905 .01472 m .61905 .01847 L s .67857 .01472 m .67857 .01847 L s .79762 .01472 m .79762 .01847 L s .85714 .01472 m .85714 .01847 L s .91667 .01472 m .91667 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .5 .10861 m .50625 .10861 L s [(0.02)] .4875 .10861 1 0 Mshowa .5 .20251 m .50625 .20251 L s [(0.04)] .4875 .20251 1 0 Mshowa .5 .29641 m .50625 .29641 L s [(0.06)] .4875 .29641 1 0 Mshowa .5 .39031 m .50625 .39031 L s [(0.08)] .4875 .39031 1 0 Mshowa .5 .48421 m .50625 .48421 L s [(0.1)] .4875 .48421 1 0 Mshowa .5 .5781 m .50625 .5781 L s [(0.12)] .4875 .5781 1 0 Mshowa .125 Mabswid .5 .03819 m .50375 .03819 L s .5 .06166 m .50375 .06166 L s .5 .08514 m .50375 .08514 L s .5 .13209 m .50375 .13209 L s .5 .15556 m .50375 .15556 L s .5 .17904 m .50375 .17904 L s .5 .22599 m .50375 .22599 L s .5 .24946 m .50375 .24946 L s .5 .27294 m .50375 .27294 L s .5 .31988 m .50375 .31988 L s .5 .34336 m .50375 .34336 L s .5 .36683 m .50375 .36683 L s .5 .41378 m .50375 .41378 L s .5 .43726 m .50375 .43726 L s .5 .46073 m .50375 .46073 L s .5 .50768 m .50375 .50768 L s .5 .53115 m .50375 .53115 L s .5 .55463 m .50375 .55463 L s .5 .60158 m .50375 .60158 L s .25 Mabswid .5 0 m .5 .61803 L s .02 w .02381 .01472 Mdot .03571 .01472 Mdot .04762 .01472 Mdot .05952 .01472 Mdot .07143 .01472 Mdot .08333 .01472 Mdot .09524 .01472 Mdot .10714 .01472 Mdot .11905 .01472 Mdot .13095 .01472 Mdot .14286 .01472 Mdot .15476 .01472 Mdot .16667 .01473 Mdot .17857 .01472 Mdot .19048 .01479 Mdot .20238 .01472 Mdot .21429 .01504 Mdot .22619 .01472 Mdot .2381 .01588 Mdot .25 .01472 Mdot .2619 .01833 Mdot .27381 .01472 Mdot .28571 .02459 Mdot .29762 .01472 Mdot .30952 .03857 Mdot .32143 .01472 Mdot .33333 .0661 Mdot .34524 .01472 Mdot .35714 .11381 Mdot .36905 .01472 Mdot .38095 .18648 Mdot .39286 .01472 Mdot .40476 .28309 Mdot .41667 .01472 Mdot .42857 .3936 Mdot .44048 .01472 Mdot .45238 .49885 Mdot .46429 .01472 Mdot .47619 .57529 Mdot .4881 .01472 Mdot .5 .60332 Mdot .5119 .01472 Mdot .52381 .57529 Mdot .53571 .01472 Mdot .54762 .49885 Mdot .55952 .01472 Mdot .57143 .3936 Mdot .58333 .01472 Mdot .59524 .28309 Mdot .60714 .01472 Mdot .61905 .18648 Mdot .63095 .01472 Mdot .64286 .11381 Mdot .65476 .01472 Mdot .66667 .0661 Mdot .67857 .01472 Mdot .69048 .03857 Mdot .70238 .01472 Mdot .71429 .02459 Mdot .72619 .01472 Mdot .7381 .01833 Mdot .75 .01472 Mdot .7619 .01588 Mdot .77381 .01472 Mdot .78571 .01504 Mdot .79762 .01472 Mdot .80952 .01479 Mdot .82143 .01472 Mdot .83333 .01473 Mdot .84524 .01472 Mdot .85714 .01472 Mdot .86905 .01472 Mdot .88095 .01472 Mdot .89286 .01472 Mdot .90476 .01472 Mdot .91667 .01472 Mdot .92857 .01472 Mdot .94048 .01472 Mdot .95238 .01472 Mdot .96429 .01472 Mdot .97619 .01472 Mdot .5 Mabswid .02381 .01472 m .02605 .01472 L .02846 .01472 L .03279 .01472 L .03543 .01472 L .03793 .01472 L .04262 .01472 L .04502 .01472 L .04756 .01472 L .05212 .01472 L .05466 .01472 L .05704 .01472 L .06244 .01472 L .06504 .01472 L .06788 .01472 L .07038 .01472 L .07305 .01472 L .07807 .01472 L .08274 .01472 L .08558 .01472 L .08864 .01472 L .09134 .01472 L .0942 .01472 L .09677 .01472 L .0996 .01472 L .10458 .01472 L .10982 .01472 L .11478 .01472 L .11924 .01472 L .12409 .01472 L .12936 .01472 L .13495 .01472 L .13973 .01472 L .145 .01472 L .14992 .01472 L .1551 .01472 L .15952 .01473 L .16435 .01473 L .16957 .01473 L .17516 .01474 L .18042 .01475 L .18521 .01476 L .19006 .01478 L .19519 .0148 L .19957 .01482 L .20439 .01485 L .20957 .01489 L .21514 .01495 L .22039 .01501 L .22519 .01509 L Mistroke .22997 .01519 L .23506 .01532 L .24421 .01564 L .24982 .0159 L .2551 .01621 L .2598 .01654 L .26495 .01698 L .27474 .01809 L .28008 .01887 L .28507 .01975 L .294 .02173 L .30355 .02456 L .31375 .02861 L .32483 .03449 L .3353 .04178 L .34497 .05026 L .36367 .0722 L .38428 .10562 L .42454 .19394 L .44305 .2372 L .45354 .25952 L .46328 .27766 L .47299 .29241 L .47797 .29845 L .48336 .30372 L .48633 .30602 L .48906 .30775 L .49167 .30905 L .493 .30958 L .49443 .31005 L .49572 .31038 L .4969 .31061 L .49809 .31077 L .49921 .31085 L .50052 .31085 L .50173 .31078 L .50236 .31072 L .50306 .31062 L .50447 .31034 L .50568 .31002 L .50681 .30965 L .50938 .30857 L .51188 .3072 L .51455 .30538 L .51939 .3012 L .5238 .29644 L .53451 .28132 L .54464 .26312 L .58308 .17583 L .60254 .13187 L Mistroke .62396 .09108 L .63376 .07583 L .6443 .06192 L .66333 .04287 L .67345 .03557 L .68448 .02943 L .69491 .0251 L .70458 .0221 L .71516 .01971 L .72512 .01811 L .73406 .01708 L .73906 .01663 L .74373 .01629 L .75324 .01575 L .75828 .01554 L .76368 .01536 L .76934 .01521 L .77471 .0151 L .77948 .01502 L .78475 .01495 L .7894 .0149 L .79441 .01486 L .79971 .01482 L .80468 .0148 L .80936 .01478 L .81429 .01476 L .8185 .01475 L .8231 .01474 L .82839 .01474 L .83339 .01473 L .83787 .01473 L .84273 .01472 L .84802 .01472 L .85363 .01472 L .85842 .01472 L .86368 .01472 L .8689 .01472 L .87385 .01472 L .8783 .01472 L .88314 .01472 L .8884 .01472 L .89133 .01472 L .89399 .01472 L .89917 .01472 L .90404 .01472 L .90872 .01472 L .91384 .01472 L .91642 .01472 L .91919 .01472 L .92158 .01472 L Mistroke .92417 .01472 L .92676 .01472 L .92915 .01472 L .93385 .01472 L .93813 .01472 L .94266 .01472 L .94702 .01472 L .951 .01472 L .9532 .01472 L .9556 .01472 L .95997 .01472 L .96404 .01472 L .96838 .01472 L .97248 .01472 L .97619 .01472 L Mfstroke 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgP3oool300000080oooo0P00000:0?ooo`003`3oool010000000oooo0?ooo`0000020?oo o`030000003oool0oooo03D0oooo00<000000?ooo`3oool00`3oool010000000oooo0?ooo`00001e 0?ooo`030000003oool0oooo00<0oooo00@000000?ooo`3oool00000>P3oool010000000oooo0?oo o`0000020?ooo`030000003oool0oooo00L0oooo000<0?ooo`D0000000D0oooo0000003oool0oooo 0000000h0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000MP3oool00`000000 oooo0?ooo`020?ooo`040000003oool0oooo000003L0oooo1@0000001@3oool000000?ooo`3oool0 000000T0oooo00060?ooo`@000000P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0 oooo00000340oooo100000040?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo 0?ooo`1e0?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo0?ooo`0e0?ooo`04 0000003oool0oooo00000080oooo00@000000?ooo`3oool000002@3oool000d0oooo00<000000?oo o`0000000P3oool010000000oooo0?ooo`00000g0?ooo`040000003oool0oooo00000080oooo00@0 00000?ooo`3oool00000M@3oool010000000oooo0?ooo`0000020?ooo`040000003oool0oooo0000 03P0oooo00<000000?ooo`0000000P3oool010000000oooo0?ooo`0000090?ooo`003P3oool20000 00<0oooo0P00000i0?ooo`800000103oool2000007L0oooo0P0000040?ooo`800000>P3oool20000 00<0oooo0P00000:0?ooo`00o`3ooolQ0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03o ool00`000000oooo0?ooo`2=0?ooo`003@3oool6000000030?ooo`000000000000X0000000<0oooo 0000000000002P0000000`3oool000000000000:000000030?ooo`000000000000X0000000<0oooo 000000000000100000030?ooo`<00000103oool3000000<0oooo0`0000040?ooo`<000000`3oool3 000000@0oooo0`0000030?ooo`<00000103oool3000000<0oooo0`0000040?ooo`<0000000<0oooo 0000003oool00`0000040?ooo`<000000`3oool3000000@0oooo0`0000030?ooo`<00000103oool3 000000<0oooo0`0000040?ooo`<000000`3oool3000000@0oooo0`0000030?ooo`H0000000<0oooo 0000000000002P0000000`3oool000000000000:000000030?ooo`000000000000X0000000<0oooo 0000000000002P0000000`3oool0000000000004000000`0oooo000<0?ooodT000000P3oool50000 00030?ooo`000000000000<000000P3oool5000000030?ooo`000000000000<000000P3oool50000 00030?ooo`000000000000<000000P3oool5000000030?ooo`000000000000<000000P3oool;0000 0080oooo1@0000000`3oool000000000000300000080oooo1@0000000`3oool00000000000030000 0080oooo1@0000000`3oool000000000000300000080oooo1@0000000`3oool00000000000030000 0080ooooB@00000;0?ooo`00203ooooo000001<000001P3oool000`0ooooD00000000`3oool00000 0000000300000080oooo1@0000000`3oool0000000000003000000030?ooo`000000000000@00000 00<0oooo0000000000000`0000020?ooo`D0000000<0oooo0000000000000`0000020?ooo`/00000 0P3oool5000000030?ooo`000000000000<000000P3oool5000000030?ooo`000000000000<00000 00<0oooo000000000000100000000`3oool000000000000300000080oooo1@0000000`3oool00000 0000001>000000/0oooo000=0?ooo`H0000000<0oooo0000000000002P0000000`3oool000000000 000:000000030?ooo`000000000000X0000000<0oooo0000000000002P0000000`3oool000000000 000A000000<0oooo0`0000040?ooo`<000000`3oool3000000@0oooo0`0000030?ooo`<00000103o ool3000000<0oooo0`0000040?ooo`<0000000<0oooo0000003oool00`0000040?ooo`<000000`3o ool3000000@0oooo0`0000030?ooo`<00000103oool3000000<0oooo0`0000040?ooo`<000000`3o oolC000000030?ooo`000000000000X0000000<0oooo0000000000002P0000000`3oool000000000 000:000000030?ooo`000000000000X0000000<0oooo0000000000001000000<0?ooo`00CP3oool3 000000<0oooo1@0000000`3oool000000000000d0?ooo`030000003oool0oooo0380oooo0P000002 0?ooo`D000000P3oool3000004d0oooo001D0?ooo`D000000`3oool300000340oooo00<000000?oo o`3oool0<03oool2000000@0oooo1@00001B0?ooo`00E@3oool3000000<0oooo0`0000000`3oool0 00000000000_0?ooo`030000003oool0oooo02h0oooo1@0000040?ooo`<00000D`3oool005X0oooo 1@0000020?ooo`800000;@3oool2000002h0oooo00<000000?ooo`0000001000001I0?ooo`00FP3o ool5000000@0oooo00<000000?ooo`3oool0:P3oool00`000000oooo0?ooo`0[0?ooo`8000000P3o ool5000005T0oooo001J0?ooo`D000001@3oool00`000000oooo0?ooo`0Y0?ooo`030000003oool0 oooo02X0oooo00<000000?ooo`3oool00P3oool5000005T0oooo001K0?ooo`<000001`3oool00`00 0000oooo0?ooo`0X0?ooo`030000003oool0oooo02T0oooo00<000000?ooo`3oool0103oool30000 05X0oooo001V0?ooo`030000003oool0oooo02L0oooo00<000000?ooo`3oool0:03oool00`000000 oooo0?ooo`1R0?ooo`00I`3oool00`000000oooo0?ooo`0V0?ooo`030000003oool0oooo02L0oooo 00<000000?ooo`3oool0H`3oool00680oooo0`0000030?ooo`030000003oool0oooo02D0oooo00<0 00000?ooo`3oool09P3oool010000000oooo0?ooo`3oool300000600oooo001Q0?ooo`D000000P3o ool00`000000oooo0?ooo`0U0?ooo`8000009P3oool010000000oooo0?ooo`3oool5000005l0oooo 001Q0?ooo`D000000`3oool00`000000oooo0?ooo`0T0?ooo`030000003oool0oooo02@0oooo00<0 00000?ooo`3oool00P3oool5000005l0oooo001Q0?ooo`D00000103oool00`000000oooo0?ooo`0S 0?ooo`030000003oool0oooo02<0oooo00<000000?ooo`3oool00`3oool5000005l0oooo001R0?oo o`<000001P3oool00`000000oooo0?ooo`0R0?ooo`030000003oool0oooo02<0oooo00<000000?oo o`3oool0103oool300000600oooo001/0?ooo`030000003oool0oooo0240oooo00<000000?ooo`3o ool08P3oool00`000000oooo0?ooo`1X0?ooo`00K03oool00`000000oooo0?ooo`0Q0?ooo`030000 003oool0oooo0240oooo00<000000?ooo`3oool0J@3oool006d0oooo00<000000?ooo`3oool0803o ool200000240oooo00<000000?ooo`3oool0JP3oool006h0oooo00<000000?ooo`3oool07`3oool0 0`000000oooo0?ooo`0P0?ooo`030000003oool0oooo06X0oooo001^0?ooo`030000003oool0oooo 01l0oooo00<000000?ooo`3oool07`3oool00`000000oooo0?ooo`1[0?ooo`00K`3oool00`000000 oooo0?ooo`0N0?ooo`030000003oool0oooo01h0oooo00<000000?ooo`3oool0K03oool00700oooo 00<000000?ooo`3oool07@3oool00`000000oooo0?ooo`0N0?ooo`030000003oool0oooo06`0oooo 001`0?ooo`030000003oool0oooo00@0oooo0P0000040?ooo`800000103oool2000000<0oooo1000 00040?ooo`030000003oool0oooo01d0oooo00<000000?ooo`3oool0K@3oool006P0oooo0`000006 0?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000203oool010000000oooo0?oo o`0000020?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool07@3oool00`000000oooo 0?ooo`030?ooo`<00000I`3oool006L0oooo1@0000050?ooo`030000003oool0oooo0080oooo00@0 00000?ooo`3oool00000203oool010000000oooo0?ooo`0000030?ooo`030000003oool0oooo00@0 oooo0`00000L0?ooo`030000003oool0oooo00<0oooo1@00001V0?ooo`00I`3oool5000000H0oooo 00D000000?ooo`3oool0oooo000000020?ooo`030000003oool0oooo00H0oooo00@000000?ooo`3o ool00000103oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo01`0oooo00<000000?oo o`3oool00`3oool5000006H0oooo001W0?ooo`D000001P3oool01@000000oooo0?ooo`3oool00000 0080oooo00<000000?ooo`3oool01P3oool010000000oooo0?ooo`0000020?ooo`040000003oool0 oooo000000@0oooo00<000000?ooo`3oool06`3oool00`000000oooo0?ooo`040?ooo`D00000IP3o ool006P0oooo0`0000080?ooo`040000003oool0oooo0?ooo`8000002P3oool2000000@0oooo0P00 00050?ooo`030000003oool0oooo01/0oooo00<000000?ooo`3oool01@3oool3000006L0oooo001c 0?ooo`030000003oool0oooo01X0oooo00<000000?ooo`3oool06P3oool00`000000oooo0?ooo`1` 0?ooo`00M03oool00`000000oooo0?ooo`0I0?ooo`030000003oool0oooo01X0oooo00<000000?oo o`3oool0L03oool007@0oooo00<000000?ooo`3oool06@3oool2000001X0oooo00<000000?ooo`3o ool0L@3oool007D0oooo00<000000?ooo`3oool0603oool00`000000oooo0?ooo`0I0?ooo`030000 003oool0oooo0740oooo001e0?ooo`030000003oool0oooo01P0oooo00<000000?ooo`3oool0603o ool00`000000oooo0?ooo`1b0?ooo`00MP3oool00`000000oooo0?ooo`0G0?ooo`030000003oool0 oooo01P0oooo00<000000?ooo`3oool0LP3oool007H0oooo00<000000?ooo`3oool05`3oool00`00 0000oooo0?ooo`0G0?ooo`030000003oool0oooo07<0oooo001f0?ooo`030000003oool0oooo01L0 oooo00<000000?ooo`3oool05`3oool00`000000oooo0?ooo`1c0?ooo`00M`3oool00`000000oooo 0?ooo`0F0?ooo`8000005`3oool00`000000oooo0?ooo`1d0?ooo`00M`3oool00`000000oooo0?oo o`0F0?ooo`030000003oool0oooo01H0oooo00<000000?ooo`3oool0M03oool007P0oooo00<00000 0?ooo`3oool05@3oool00`000000oooo0?ooo`0F0?ooo`030000003oool0oooo07@0oooo001h0?oo o`030000003oool0oooo01D0oooo00<000000?ooo`3oool05@3oool00`000000oooo0?ooo`1e0?oo o`00N@3oool00`000000oooo0?ooo`0D0?ooo`030000003oool0oooo01D0oooo00<000000?ooo`3o ool0M@3oool007T0oooo00<000000?ooo`3oool0503oool00`000000oooo0?ooo`0D0?ooo`030000 003oool0oooo07H0oooo001j0?ooo`030000003oool0oooo01<0oooo00<000000?ooo`3oool0503o ool00`000000oooo0?ooo`1f0?ooo`00K`3oool3000000P0oooo00<000000?ooo`3oool04`3oool2 000001D0oooo00<000000?ooo`3oool01P3oool3000006d0oooo001^0?ooo`D00000203oool00`00 0000oooo0?ooo`0B0?ooo`030000003oool0oooo01<0oooo00<000000?ooo`3oool01P3oool50000 06`0oooo001^0?ooo`D00000203oool00`000000oooo0?ooo`0B0?ooo`030000003oool0oooo01<0 oooo00<000000?ooo`3oool01P3oool5000006`0oooo001^0?ooo`D000002@3oool00`000000oooo 0?ooo`0A0?ooo`030000003oool0oooo0180oooo00<000000?ooo`3oool01`3oool5000006`0oooo 001_0?ooo`<000001@3oool2000000<0oooo0`0000040?ooo`8000001@3oool3000000<0oooo00<0 00000?ooo`3oool04P3oool00`000000oooo0?ooo`080?ooo`<00000K@3oool007H0oooo00@00000 0?ooo`3oool000000P3oool00`000000oooo0?ooo`030?ooo`040000003oool0oooo000000D0oooo 00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0A0?ooo`030000003oool0oooo07T0oooo 001f0?ooo`040000003oool0oooo000000<0oooo00<000000?ooo`3oool00P3oool010000000oooo 0?ooo`0000020?ooo`D000000`3oool300000140oooo00<000000?ooo`3oool0N@3oool007H0oooo 00@000000?ooo`3oool000000`3oool00`000000oooo0?ooo`020?ooo`040000003oool0oooo0000 0080oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`0@0?ooo`030000003oool0 oooo07X0oooo001f0?ooo`040000003oool0oooo000000@0oooo00D000000?ooo`3oool0oooo0000 00020?ooo`070000003oool0oooo0?ooo`000000oooo000000040?ooo`030000003oool0oooo0100 oooo00<000000?ooo`3oool0NP3oool007L0oooo0P0000050?ooo`030000003oool0oooo0080oooo 0P0000050?ooo`800000103oool00`000000oooo0?ooo`0?0?ooo`030000003oool0oooo07/0oooo 001n0?ooo`030000003oool0oooo00l0oooo00<000000?ooo`3oool03`3oool00`000000oooo0?oo o`1k0?ooo`00O`3oool00`000000oooo0?ooo`0>0?ooo`030000003oool0oooo00h0oooo00<00000 0?ooo`3oool0O03oool007l0oooo00<000000?ooo`3oool03P3oool00`000000oooo0?ooo`0>0?oo o`030000003oool0oooo07`0oooo00200?ooo`030000003oool0oooo00d0oooo0P00000?0?ooo`03 0000003oool0oooo07`0oooo00200?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0 3@3oool00`000000oooo0?ooo`1m0?ooo`00P@3oool00`000000oooo0?ooo`0<0?ooo`030000003o ool0oooo00d0oooo00<000000?ooo`3oool0O@3oool00840oooo00<000000?ooo`3oool0303oool0 0`000000oooo0?ooo`0<0?ooo`030000003oool0oooo07h0oooo00210?ooo`030000003oool0oooo 00`0oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`1n0?ooo`00PP3oool00`000000 oooo0?ooo`0;0?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3oool0O`3oool00880oooo 00<000000?ooo`3oool02`3oool2000000`0oooo00<000000?ooo`3oool0O`3oool008<0oooo00<0 00000?ooo`3oool02P3oool00`000000oooo0?ooo`0:0?ooo`030000003oool0oooo0800oooo0023 0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool02P3oool00`000000oooo0?ooo`20 0?ooo`00Q03oool00`000000oooo0?ooo`090?ooo`030000003oool0oooo00T0oooo00<000000?oo o`3oool0P@3oool008@0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`090?ooo`03 0000003oool0oooo0840oooo00250?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool0 2@3oool00`000000oooo0?ooo`210?ooo`00Q@3oool00`000000oooo0?ooo`080?ooo`8000002@3o ool00`000000oooo0?ooo`220?ooo`00M@3oool3000000h0oooo00<000000?ooo`3oool01`3oool0 0`000000oooo0?ooo`080?ooo`030000003oool0oooo00/0oooo0`00001d0?ooo`00M03oool50000 00d0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo 00/0oooo1@00001c0?ooo`00M03oool5000000h0oooo00<000000?ooo`3oool01P3oool00`000000 oooo0?ooo`070?ooo`030000003oool0oooo00/0oooo1@00001c0?ooo`00M03oool5000000h0oooo 00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00`0oooo 1@00001c0?ooo`00M@3oool4000000@0oooo0P0000040?ooo`8000000`3oool3000000D0oooo00<0 00000?ooo`3oool01@3oool00`000000oooo0?ooo`0>0?ooo`<00000M03oool007H0oooo00@00000 0?ooo`3oool00000203oool010000000oooo0?ooo`0000020?ooo`80000000<0oooo0000003oool0 0`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo08D0oooo001f0?ooo`040000003o ool0oooo000000P0oooo00@000000?ooo`3oool000000P3oool010000000oooo0000000000040?oo o`<00000103oool00`000000oooo0?ooo`260?ooo`00MP3oool010000000oooo0?ooo`0000080?oo o`040000003oool0oooo00000080oooo100000040?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool0Q`3oool007H0oooo00@000000?ooo`3oool00000203oool010000000oooo0?ooo`00 00030?ooo`030000003oool0oooo008000000P3oool010000000oooo0?ooo`3oool2000008X0oooo 001g0?ooo`8000002P3oool2000000@0oooo0`0000001P3oool000000000003oool000000?ooo`80 0000S03oool008l0oooo1000002=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool2 000008h0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0 oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@ 0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`80 0000SP3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3o ool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900 oooo00<000000?ooo`3oool0S@3oool00900oooo0P00002>0?ooo`00T03oool00`000000oooo0?oo o`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?oo o`00M`3oool2000000@0oooo0P0000040?ooo`800000103oool2000000D0oooo00<000000?ooo`3o ool0S@3oool007H0oooo00@000000?ooo`3oool000000P3oool3000000<0oooo00@000000?ooo`3o ool000000P3oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo0100oooo0`00001j 0?ooo`00MP3oool01@000000oooo0?ooo`000000oooo00D000000P3oool010000000oooo0?ooo`00 00020?ooo`040000003oool0oooo000000@0oooo0`00000?0?ooo`D00000N@3oool007H0oooo00D0 00000?ooo`3oool000000?ooo`0500000080oooo00@000000?ooo`3oool000000`3oool2000000D0 oooo00<000000?ooo`3oool03`3oool5000007T0oooo001f0?ooo`050000003oool0oooo0000003o ool01@0000020?ooo`040000003oool0oooo00000080oooo00@000000?ooo`3oool00000103oool0 0`000000oooo0?ooo`0?0?ooo`D00000N@3oool007L0oooo0P0000030?ooo`<00000103oool20000 00@0oooo0P0000050?ooo`030000003oool0oooo0100oooo0`00001j0?ooo`00T03oool00`000000 oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?oo o`2=0?ooo`00T03oool2000008h0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`03 0000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003o ool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`800000SP3oool00900 oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<0 00000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?oo o`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo0P00002>0?ooo`00T03o ool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`00 0000oooo0?ooo`2=0?ooo`00O@3oool2000000@0oooo0P0000030?ooo`D000000`3oool00`000000 oooo0?ooo`2=0?ooo`00O03oool010000000oooo0?ooo`00000:0?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool0S@3oool007`0oooo00@000000?ooo`3oool000002P3oool00`000000 oooo0?ooo`030?ooo`<00000S@3oool007`0oooo00@000000?ooo`3oool000002P3oool00`000000 oooo0?ooo`030?ooo`030000003oool0oooo08d0oooo001l0?ooo`040000003oool0oooo00000080 oooo0`0000050?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool02@3oool300000840 oooo001m0?ooo`8000000P3oool5000000<0oooo0P0000050?ooo`030000003oool0oooo00P0oooo 1@0000200?ooo`00P@3oool5000000X0oooo00<000000?ooo`3oool0203oool500000800oooo0021 0?ooo`D000002P3oool00`000000oooo0?ooo`080?ooo`D00000P03oool00880oooo0`00000;0?oo o`8000002P3oool300000840oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000 003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0 oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0 oooo002@0?ooo`800000SP3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<00000 0?ooo`3oool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo00<000000?ooo`3o ool0S@3oool00900oooo00<000000?ooo`3oool0S@3oool00900oooo0P00002>0?ooo`00T03oool0 0`000000oooo0?ooo`2=0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00T03oool00`000000 oooo0?ooo`2=0?ooo`00R@3oool3000000@0oooo00<000000?ooo`3oool00`3oool3000008L0oooo 001g0?ooo`800000103oool2000000<0oooo1@0000000`3oool0000000000003000000<0oooo00<0 00000?ooo`3oool00P3oool5000008H0oooo001f0?ooo`040000003oool0oooo000000X0oooo00@0 00000?ooo`3oool0oooo1@0000030?ooo`030000003oool0oooo0080oooo1@0000260?ooo`00MP3o ool010000000oooo0?ooo`00000:0?ooo`040000003oool0oooo0?ooo`D000000`3oool300000080 oooo1@0000260?ooo`00MP3oool010000000oooo0?ooo`00000:0?ooo`030000003oool0oooo0080 oooo0`0000040?ooo`030000003oool0oooo00<0oooo0`0000270?ooo`00MP3oool010000000oooo 0?ooo`00000:0?ooo`050000003oool0oooo0?ooo`0000000P3oool00`000000oooo0?ooo`020?oo o`030000003oool0oooo08d0oooo001g0?ooo`8000002P3oool2000000@0oooo0P0000050?ooo`03 0000003oool0oooo08d0oooo002@0?ooo`030000003oool0oooo08d0oooo002?0?ooo`<00000SP3o ool008h0oooo1@00002=0?ooo`00SP3oool5000008d0oooo002>0?ooo`D00000S@3oool008l0oooo 0`00002>0?ooo`00T03oool00`000000oooo0?ooo`2=0?ooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-44.5872, -0.00969148, \ 0.308022, 0.000781045}}] }, Open ]], Cell[BoxData[{ \(\(p[0, 0] = 1/2;\)\), "\[IndentingNewLine]", \(\(p[1, 0] = 1/4;\)\), "\[IndentingNewLine]", \(\(p[\(-1\), 0] = 1/4;\)\), "\[IndentingNewLine]", \(\)}], "Input"] }, FrontEndVersion->"5.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 685}}, WindowSize->{1016, 651}, WindowMargins->{{0, Automatic}, {Automatic, 0}} ] (******************************************************************* 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[1754, 51, 59, 1, 30, "Input"], Cell[1816, 54, 267, 6, 70, "Input"], Cell[CellGroupData[{ Cell[2108, 64, 223, 4, 50, "Input"], Cell[2334, 70, 17005, 445, 186, 4306, 284, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[19376, 520, 43, 1, 30, "Input"], Cell[19422, 523, 59, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19518, 529, 37, 1, 30, "Input"], Cell[19558, 532, 54, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19649, 538, 137, 3, 30, "Input"], Cell[19789, 543, 107, 2, 60, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19933, 550, 70, 1, 30, "Input"], Cell[20006, 553, 417, 6, 82, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20460, 564, 44, 1, 30, "Input"], Cell[20507, 567, 35, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20579, 573, 183, 4, 50, "Input"], Cell[20765, 579, 24020, 624, 186, 5645, 393, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[44822, 1208, 64, 1, 30, "Input"], Cell[44889, 1211, 23536, 663, 186, 6957, 454, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[68440, 1877, 196, 4, 90, "Input"] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)