(************** Content-type: application/mathematica ************** 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[ 243862, 5853]*) (*NotebookOutlinePosition[ 244505, 5875]*) (* CellTagsIndexPosition[ 244461, 5871]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(x[s_] := s; y[s_] := \(-Sin[s]\)\)], "Input"], Cell[BoxData[ \(\(track[s_] := {x[s], y[s]};\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(ParametricPlot[track[s], {s, 0, \[Pi]}, AspectRatio \[Rule] Automatic, Compiled \[Rule] False]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .31831 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 0.0238095 0.303152 0.310731 0.303152 [ [.17539 .29823 -9 -9 ] [.17539 .29823 9 0 ] [.32696 .29823 -3 -9 ] [.32696 .29823 3 0 ] [.47854 .29823 -9 -9 ] [.47854 .29823 9 0 ] [.63011 .29823 -3 -9 ] [.63011 .29823 3 0 ] [.78169 .29823 -9 -9 ] [.78169 .29823 9 0 ] [.93327 .29823 -3 -9 ] [.93327 .29823 3 0 ] [.01131 .00758 -12 -4.5 ] [.01131 .00758 0 4.5 ] [.01131 .06821 -24 -4.5 ] [.01131 .06821 0 4.5 ] [.01131 .12884 -24 -4.5 ] [.01131 .12884 0 4.5 ] [.01131 .18947 -24 -4.5 ] [.01131 .18947 0 4.5 ] [.01131 .2501 -24 -4.5 ] [.01131 .2501 0 4.5 ] [ 0 0 0 0 ] [ 1 .31831 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .31073 m .17539 .31698 L s [(0.5)] .17539 .29823 0 1 Mshowa .32696 .31073 m .32696 .31698 L s [(1)] .32696 .29823 0 1 Mshowa .47854 .31073 m .47854 .31698 L s [(1.5)] .47854 .29823 0 1 Mshowa .63011 .31073 m .63011 .31698 L s [(2)] .63011 .29823 0 1 Mshowa .78169 .31073 m .78169 .31698 L s [(2.5)] .78169 .29823 0 1 Mshowa .93327 .31073 m .93327 .31698 L s [(3)] .93327 .29823 0 1 Mshowa .125 Mabswid .05412 .31073 m .05412 .31448 L s .08444 .31073 m .08444 .31448 L s .11476 .31073 m .11476 .31448 L s .14507 .31073 m .14507 .31448 L s .2057 .31073 m .2057 .31448 L s .23602 .31073 m .23602 .31448 L s .26633 .31073 m .26633 .31448 L s .29665 .31073 m .29665 .31448 L s .35728 .31073 m .35728 .31448 L s .38759 .31073 m .38759 .31448 L s .41791 .31073 m .41791 .31448 L s .44822 .31073 m .44822 .31448 L s .50885 .31073 m .50885 .31448 L s .53917 .31073 m .53917 .31448 L s .56948 .31073 m .56948 .31448 L s .5998 .31073 m .5998 .31448 L s .66043 .31073 m .66043 .31448 L s .69074 .31073 m .69074 .31448 L s .72106 .31073 m .72106 .31448 L s .75138 .31073 m .75138 .31448 L s .81201 .31073 m .81201 .31448 L s .84232 .31073 m .84232 .31448 L s .87264 .31073 m .87264 .31448 L s .90295 .31073 m .90295 .31448 L s .96358 .31073 m .96358 .31448 L s .9939 .31073 m .9939 .31448 L s .25 Mabswid 0 .31073 m 1 .31073 L s .02381 .00758 m .03006 .00758 L s [(-1)] .01131 .00758 1 0 Mshowa .02381 .06821 m .03006 .06821 L s [(-0.8)] .01131 .06821 1 0 Mshowa .02381 .12884 m .03006 .12884 L s [(-0.6)] .01131 .12884 1 0 Mshowa .02381 .18947 m .03006 .18947 L s [(-0.4)] .01131 .18947 1 0 Mshowa .02381 .2501 m .03006 .2501 L s [(-0.2)] .01131 .2501 1 0 Mshowa .125 Mabswid .02381 .02274 m .02756 .02274 L s .02381 .03789 m .02756 .03789 L s .02381 .05305 m .02756 .05305 L s .02381 .08337 m .02756 .08337 L s .02381 .09852 m .02756 .09852 L s .02381 .11368 m .02756 .11368 L s .02381 .144 m .02756 .144 L s .02381 .15915 m .02756 .15915 L s .02381 .17431 m .02756 .17431 L s .02381 .20463 m .02756 .20463 L s .02381 .21979 m .02756 .21979 L s .02381 .23494 m .02756 .23494 L s .02381 .26526 m .02756 .26526 L s .02381 .28042 m .02756 .28042 L s .02381 .29557 m .02756 .29557 L s .25 Mabswid .02381 0 m .02381 .31831 L s 0 0 m 1 0 L 1 .31831 L 0 .31831 L closepath clip newpath .5 Mabswid .02381 .31073 m .06244 .2722 L .10458 .23091 L .14415 .19352 L .18221 .15944 L .22272 .12579 L .26171 .09651 L .30316 .06927 L .34309 .04729 L .3815 .03045 L .40095 .02362 L .42237 .01746 L .44268 .01298 L .45178 .0114 L .46172 .00999 L .4671 .00936 L .4721 .00886 L .47727 .00843 L .48196 .00811 L .48658 .00788 L .4887 .00779 L .49093 .00771 L .49332 .00765 L .49438 .00763 L .49552 .00761 L .49675 .0076 L .49789 .00759 L .49859 .00758 L .49925 .00758 L .50049 .00758 L .50163 .00758 L .50286 .00759 L .50401 .0076 L .50508 .00762 L .50754 .00767 L .51014 .00775 L .51268 .00784 L .51504 .00795 L .5204 .00826 L .5293 .00899 L .53882 .01006 L .54906 .01154 L .56016 .01353 L .58032 .01816 L .62123 .0315 L .66064 .04915 L .69852 .07029 L .73886 .09691 L .77769 .12611 L .81897 .16046 L Mistroke .85873 .19618 L .89697 .23241 L .93767 .27231 L .97619 .31073 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 91.625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`800000F@3oool2000005L0oooo00080?ooo`800000103oool2 000000@0oooo0P0000050?ooo`030000003oool0oooo04`0oooo0P00001M0?ooo`030000003oool0 oooo05@0oooo00070?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3oool00000103o ool00`000000oooo0?ooo`1:0?ooo`800000H03oool2000005@0oooo00070?ooo`040000003oool0 oooo000000P0oooo00@000000?ooo`3oool00000103oool2000004T0oooo0P00001T0?ooo`800000 DP3oool000030?ooo`0000000000008000000P3oool010000000oooo0?ooo`0000090?ooo`800000 1@3oool00`000000oooo0?ooo`170?ooo`030000003oool0oooo06H0oooo00<000000?ooo`3oool0 C`3oool000L0oooo00@000000?ooo`3oool00000203oool010000000oooo0?ooo`0000040?ooo`03 0000003oool0oooo04D0oooo0P00001Z0?ooo`800000C`3oool000P0oooo0P00000:0?ooo`800000 1@3oool00`000000oooo0?ooo`140?ooo`030000003oool0oooo06`0oooo00<000000?ooo`3oool0 C03oool001/0oooo0P0000130?ooo`800000L03oool2000004`0oooo000K0?ooo`030000003oool0 oooo0400oooo0P00001d0?ooo`800000BP3oool001/0oooo00<000000?ooo`3oool0?`3oool00`00 0000oooo0?ooo`1f0?ooo`030000003oool0oooo04L0oooo000K0?ooo`030000003oool0oooo03d0 oooo0P00001j0?ooo`800000A`3oool001/0oooo0P00000m0?ooo`030000003oool0oooo07`0oooo 00<000000?ooo`3oool0A03oool001/0oooo00<000000?ooo`3oool0>`3oool00`000000oooo0?oo o`1n0?ooo`030000003oool0oooo04<0oooo000K0?ooo`030000003oool0oooo03T0oooo0P000022 0?ooo`800000@`3oool001/0oooo00<000000?ooo`3oool0>03oool00`000000oooo0?ooo`240?oo o`030000003oool0oooo0400oooo000K0?ooo`800000>03oool00`000000oooo0?ooo`260?ooo`03 0000003oool0oooo03l0oooo000K0?ooo`030000003oool0oooo03H0oooo00<000000?ooo`3oool0 R03oool00`000000oooo0?ooo`0n0?ooo`00203oool2000000@0oooo0P0000030?ooo`<000001@3o ool00`000000oooo0?ooo`0d0?ooo`800000S03oool2000003h0oooo00070?ooo`040000003oool0 oooo000000P0oooo00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`0c0?ooo`030000 003oool0oooo08h0oooo00<000000?ooo`3oool0>`3oool000L0oooo00@000000?ooo`3oool00000 203oool010000000oooo0?ooo`0000040?ooo`800000<`3oool00`000000oooo0?ooo`2@0?ooo`03 0000003oool0oooo03X0oooo00000`3oool000000000000200000080oooo00@000000?ooo`3oool0 0000203oool3000000D0oooo00<000000?ooo`3oool0<@3oool00`000000oooo0?ooo`2B0?ooo`03 0000003oool0oooo03T0oooo00070?ooo`040000003oool0oooo000000T0oooo00<000000?ooo`3o ool0103oool00`000000oooo0?ooo`0_0?ooo`800000UP3oool2000003T0oooo00080?ooo`800000 2P3oool3000000@0oooo00<000000?ooo`3oool0;P3oool00`000000oooo0?ooo`2H0?ooo`030000 003oool0oooo03H0oooo000K0?ooo`800000;P3oool00`000000oooo0?ooo`2J0?ooo`030000003o ool0oooo03D0oooo000K0?ooo`030000003oool0oooo02`0oooo00<000000?ooo`3oool0W03oool0 0`000000oooo0?ooo`0d0?ooo`006`3oool00`000000oooo0?ooo`0[0?ooo`030000003oool0oooo 09h0oooo00<000000?ooo`3oool0<`3oool001/0oooo00<000000?ooo`3oool0:@3oool200000:80 oooo0P00000c0?ooo`006`3oool2000002T0oooo00<000000?ooo`3oool0Y03oool00`000000oooo 0?ooo`0`0?ooo`006`3oool00`000000oooo0?ooo`0W0?ooo`030000003oool0oooo0:H0oooo00<0 00000?ooo`3oool0;`3oool001/0oooo00<000000?ooo`3oool09P3oool00`000000oooo0?ooo`2X 0?ooo`030000003oool0oooo02h0oooo000K0?ooo`030000003oool0oooo02D0oooo00<000000?oo o`3oool0ZP3oool2000002h0oooo000K0?ooo`8000009@3oool00`000000oooo0?ooo`2]0?ooo`03 0000003oool0oooo02/0oooo000K0?ooo`030000003oool0oooo02<0oooo00<000000?ooo`3oool0 [`3oool00`000000oooo0?ooo`0Z0?ooo`00203oool2000000@0oooo0P0000050?ooo`<000000`3o ool00`000000oooo0?ooo`0Q0?ooo`800000/`3oool00`000000oooo0?ooo`0Y0?ooo`001`3oool0 10000000oooo0?ooo`00000;0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0803o ool00`000000oooo0?ooo`2d0?ooo`030000003oool0oooo02P0oooo00070?ooo`040000003oool0 oooo000000P0oooo1@0000030?ooo`800000803oool00`000000oooo0?ooo`2f0?ooo`800000:03o ool000030?ooo`0000000000008000000P3oool010000000oooo0?ooo`0000080?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool07P3oool00`000000oooo0?ooo`2i0?ooo`030000 003oool0oooo02D0oooo00070?ooo`040000003oool0oooo000000T0oooo00<000000?ooo`000000 103oool00`000000oooo0?ooo`0M0?ooo`030000003oool0oooo0;/0oooo00<000000?ooo`3oool0 903oool000P0oooo0P00000;0?ooo`800000103oool00`000000oooo0?ooo`0L0?ooo`030000003o ool0oooo0;d0oooo00<000000?ooo`3oool08`3oool001/0oooo00<000000?ooo`3oool06`3oool0 0`000000oooo0?ooo`2o0?ooo`030000003oool0oooo0280oooo000K0?ooo`8000006`3oool00`00 0000oooo0?ooo`310?ooo`030000003oool0oooo0240oooo000K0?ooo`030000003oool0oooo01T0 oooo00<000000?ooo`3oool0``3oool00`000000oooo0?ooo`0P0?ooo`006`3oool00`000000oooo 0?ooo`0G0?ooo`800000a`3oool00`000000oooo0?ooo`0O0?ooo`006`3oool00`000000oooo0?oo o`0F0?ooo`030000003oool0oooo0"], ImageRangeCache->{{{0, 287}, {90.625, 0}} -> {-0.338866, -1.07731, \ 0.0124008, 0.0124008}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(v\_0 = 0; g = 9.8;\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[\@Abs[\(\(x'\)[s]\^2 + \(y'\)[s]\^2\)\/\(v\_0\^2 - 2 g*y[s]\)], \ {s, 0, 2 \[Pi]}]\)], "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 0.0238095 0.151576 0.0147151 0.176765 [ [.17539 .00222 -3 -9 ] [.17539 .00222 3 0 ] [.32696 .00222 -3 -9 ] [.32696 .00222 3 0 ] [.47854 .00222 -3 -9 ] [.47854 .00222 3 0 ] [.63011 .00222 -3 -9 ] [.63011 .00222 3 0 ] [.78169 .00222 -3 -9 ] [.78169 .00222 3 0 ] [.93327 .00222 -3 -9 ] [.93327 .00222 3 0 ] [.01131 .1031 -18 -4.5 ] [.01131 .1031 0 4.5 ] [.01131 .19148 -6 -4.5 ] [.01131 .19148 0 4.5 ] [.01131 .27986 -18 -4.5 ] [.01131 .27986 0 4.5 ] [.01131 .36824 -6 -4.5 ] [.01131 .36824 0 4.5 ] [.01131 .45663 -18 -4.5 ] [.01131 .45663 0 4.5 ] [.01131 .54501 -6 -4.5 ] [.01131 .54501 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 .17539 .01472 m .17539 .02097 L s [(1)] .17539 .00222 0 1 Mshowa .32696 .01472 m .32696 .02097 L s [(2)] .32696 .00222 0 1 Mshowa .47854 .01472 m .47854 .02097 L s [(3)] .47854 .00222 0 1 Mshowa .63011 .01472 m .63011 .02097 L s [(4)] .63011 .00222 0 1 Mshowa .78169 .01472 m .78169 .02097 L s [(5)] .78169 .00222 0 1 Mshowa .93327 .01472 m .93327 .02097 L s [(6)] .93327 .00222 0 1 Mshowa .125 Mabswid .05412 .01472 m .05412 .01847 L s .08444 .01472 m .08444 .01847 L s .11476 .01472 m .11476 .01847 L s .14507 .01472 m .14507 .01847 L s .2057 .01472 m .2057 .01847 L s .23602 .01472 m .23602 .01847 L s .26633 .01472 m .26633 .01847 L s .29665 .01472 m .29665 .01847 L s .35728 .01472 m .35728 .01847 L s .38759 .01472 m .38759 .01847 L s .41791 .01472 m .41791 .01847 L s .44822 .01472 m .44822 .01847 L s .50885 .01472 m .50885 .01847 L s .53917 .01472 m .53917 .01847 L s .56948 .01472 m .56948 .01847 L s .5998 .01472 m .5998 .01847 L s .66043 .01472 m .66043 .01847 L s .69074 .01472 m .69074 .01847 L s .72106 .01472 m .72106 .01847 L s .75138 .01472 m .75138 .01847 L s .81201 .01472 m .81201 .01847 L s .84232 .01472 m .84232 .01847 L s .87264 .01472 m .87264 .01847 L s .90295 .01472 m .90295 .01847 L s .96358 .01472 m .96358 .01847 L s .9939 .01472 m .9939 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .1031 m .03006 .1031 L s [(0.5)] .01131 .1031 1 0 Mshowa .02381 .19148 m .03006 .19148 L s [(1)] .01131 .19148 1 0 Mshowa .02381 .27986 m .03006 .27986 L s [(1.5)] .01131 .27986 1 0 Mshowa .02381 .36824 m .03006 .36824 L s [(2)] .01131 .36824 1 0 Mshowa .02381 .45663 m .03006 .45663 L s [(2.5)] .01131 .45663 1 0 Mshowa .02381 .54501 m .03006 .54501 L s [(3)] .01131 .54501 1 0 Mshowa .125 Mabswid .02381 .03239 m .02756 .03239 L s .02381 .05007 m .02756 .05007 L s .02381 .06774 m .02756 .06774 L s .02381 .08542 m .02756 .08542 L s .02381 .12077 m .02756 .12077 L s .02381 .13845 m .02756 .13845 L s .02381 .15613 m .02756 .15613 L s .02381 .1738 m .02756 .1738 L s .02381 .20916 m .02756 .20916 L s .02381 .22683 m .02756 .22683 L s .02381 .24451 m .02756 .24451 L s .02381 .26219 m .02756 .26219 L s .02381 .29754 m .02756 .29754 L s .02381 .31521 m .02756 .31521 L s .02381 .33289 m .02756 .33289 L s .02381 .35057 m .02756 .35057 L s .02381 .38592 m .02756 .38592 L s .02381 .4036 m .02756 .4036 L s .02381 .42127 m .02756 .42127 L s .02381 .43895 m .02756 .43895 L s .02381 .4743 m .02756 .4743 L s .02381 .49198 m .02756 .49198 L s .02381 .50966 m .02756 .50966 L s .02381 .52733 m .02756 .52733 L s .02381 .56269 m .02756 .56269 L s .02381 .58036 m .02756 .58036 L s .02381 .59804 m .02756 .59804 L s .02381 .61571 m .02756 .61571 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02521 .61803 m .02605 .47864 L .02729 .38734 L .02846 .33715 L .02954 .30515 L .03053 .28274 L .03279 .24661 L .03396 .23277 L .03506 .22181 L .03756 .20194 L .04 .18718 L .04262 .1746 L .04793 .15568 L .05297 .14266 L .06244 .12536 L .0675 .11846 L .07289 .11225 L .08259 .10319 L .09315 .09543 L .10458 .08865 L .12599 .07884 L .14616 .07183 L .16571 .06644 L .18717 .06178 L .19702 .06004 L .20759 .05844 L .21749 .05719 L .22665 .05625 L .23683 .05546 L .24219 .05515 L .24494 .05502 L .24789 .0549 L .25047 .05481 L .25283 .05475 L .25508 .0547 L .25633 .05468 L .25746 .05467 L .25872 .05466 L .25941 .05465 L .26007 .05465 L .26123 .05464 L .2625 .05464 L .26316 .05464 L .26389 .05465 L .26465 .05465 L .26537 .05466 L .26664 .05467 L .26801 .05469 L .27056 .05474 L .27327 .05481 L Mistroke .27814 .05499 L .28394 .05527 L .28919 .05561 L .29955 .05648 L .30929 .05754 L .32941 .06048 L .34789 .06407 L .36676 .06868 L .38743 .07502 L .40698 .08267 L .42791 .09367 L .43811 .10072 L .44919 .11046 L .45427 .11599 L .45965 .12289 L .4647 .13068 L .46932 .13938 L .4739 .15013 L .47872 .16492 L .48355 .18579 L .48629 .20221 L .48883 .22256 L .48998 .23417 L .49122 .24921 L .49232 .26539 L .49347 .28674 L .49452 .31155 L .49566 .34856 L .49671 .39785 L .49768 .47143 L Mfstroke .49768 .47143 m .49855 .61803 L s .50144 .61803 m .50224 .47935 L .50347 .38797 L .50478 .33277 L .50589 .30103 L .50713 .27505 L .50834 .25534 L .50947 .2405 L .51203 .21492 L .51453 .19681 L .5172 .18197 L .52205 .16226 L .52645 .14921 L .53159 .13751 L .53717 .12762 L .5473 .1142 L .55675 .10491 L .56715 .0969 L .58818 .0849 L .60761 .07679 L .62849 .07001 L .64964 .06462 L .66973 .06063 L .67933 .05908 L .68956 .05768 L .69914 .05661 L .70795 .05582 L .71286 .05547 L .71824 .05515 L .72366 .05491 L .72661 .05481 L .72937 .05474 L .73063 .05471 L .73199 .05469 L .73319 .05467 L .73447 .05466 L .73562 .05465 L .73688 .05464 L .73803 .05464 L .73911 .05464 L .74039 .05465 L .74103 .05465 L .74174 .05466 L .74298 .05467 L .74414 .05469 L .74675 .05474 L .74955 .05481 L .75489 .05501 L .7598 .05525 L .77091 .05604 L Mistroke .7807 .05699 L .79107 .05825 L .81066 .06138 L .82897 .06517 L .84756 .06997 L .86782 .07651 L .88901 .08538 L .89956 .09095 L .90912 .09695 L .9186 .10419 L .92884 .11414 L .93448 .12102 L .93966 .12864 L .94457 .13746 L .94983 .14945 L .95324 .15928 L .95634 .17031 L .95946 .18434 L .96241 .20173 L .96408 .21424 L .96584 .23068 L .96735 .24844 L .96902 .27417 L .96995 .29288 L .9708 .31409 L .97178 .34586 L .97272 .38785 L .97358 .44498 L .97438 .53122 L Mfstroke .97438 .53122 m .97475 .61803 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{537.438, 332.188}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`<00000B`3oool20000 04`0oooo0`00000T0?ooo`00J03oool00`000000oooo0?ooo`1:0?ooo`030000003oool0oooo04d0 oooo00@000000?ooo`3oool00000CP3oool00`000000oooo0?ooo`190?ooo`040000003oool0oooo 000004/0oooo00@000000?ooo`3oool000008`3oool006P0oooo00<000000?ooo`3oool0B`3oool0 0`000000oooo0?ooo`1>0?ooo`030000003oool0oooo04X0oooo1@00001=0?ooo`030000003oool0 oooo04T0oooo00@000000?ooo`3oool000008`3oool006P0oooo00<000000?ooo`3oool0C03oool0 0`000000oooo0?ooo`1>0?ooo`030000003oool0oooo04T0oooo00@000000?ooo`3oool00000C03o ool2000004`0oooo0`00000T0?ooo`00J03oool00`000000oooo0?ooo`1:0?ooo`040000003oool0 oooo000004`0oooo00@000000?ooo`3oool00000C03oool00`000000oooo0000001<0?ooo`030000 003oool0oooo04`0oooo00<000000?ooo`3oool08`3oool006L0oooo0P00001=0?ooo`800000CP3o ool2000004h0oooo0P00001<0?ooo`<00000C03oool3000002<0oooo003o0?ooool0oooo6`3oool0 01T0oooo00<000000?ooo`3oool0o`3oooon0?ooo`006@3oool00`000000oooo0?ooo`3o0?ooooh0 oooo000I0?ooo`030000003oool0oooo0?l0oooooP3oool001T0oooo00<000000?ooo`3oool0o`3o ooon0?ooo`006@3oool00`000000oooo0?ooo`3o0?ooooh0oooo000I0?ooo`030000003oool0oooo 0?l0oooooP3oool001T0oooo00<000000?ooo`3oool0o`3oooon0?ooo`006@3oool00`000000oooo 0?ooo`3o0?ooooh0oooo000<0?ooool00000o`00000>00000040oooo000I0?ooo`030000003oool0 oooo00`0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00`0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0 oooo00d0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`020?ooo`006@3oool00`00 0000oooo0?ooo`0<0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0303oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0<0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool03@3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0303oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool00P3oool001T0 oooo00<000000?ooo`3oool0C03oool00`000000oooo0?ooo`1<0?ooo`030000003oool0oooo04d0 oooo00<000000?ooo`3oool0C03oool00`000000oooo0?ooo`1<0?ooo`030000003oool0oooo04`0 oooo00<000000?ooo`3oool08P3oool001T0oooo00<000000?ooo`3oool0o`3oooon0?ooo`006@3o ool00`000000oooo0?ooo`3o0?ooooh0oooo000I0?ooo`030000003oool0oooo0?l0oooooP3oool0 01T0oooo00<000000?ooo`3oool0o`3oooon0?ooo`006@3oool00`000000oooo0?ooo`3o0?ooooh0 oooo000I0?ooo`<00000o`3oooon0?ooo`006@3oool00`000000oooo0?ooo`3o0?ooooh0oooo000I 0?ooo`030000003oool0oooo0?l0oooooP3oool001T0oooo00<000000?ooo`3oool0o`3oooon0?oo o`006@3oool00`000000oooo0?ooo`3o0?ooooh0oooo000I0?ooo`030000003oool0oooo0?l0oooo oP3oool001T0oooo00<000000?ooo`3oool0o`3oooon0?ooo`006@3oool00`000000oooo0?ooo`3o 0?ooooh0oooo000I0?ooo`030000003oool0oooo0?l0oooooP3oool001T0oooo0`00003o0?ooooh0 oooo000I0?ooo`030000003oool0oooo0?l0oooooP3oool001T0oooo00<000000?ooo`3oool0o`3o ooon0?ooo`006@3oool00`000000oooo0?ooo`1Z0?ooob000000e`3ooolU000007L0oooo000I0?oo o`030000003oool0oooo0600oooo2P00000P0?ooo`/00000`P3oool:000002D0oooo1P00001a0?oo o`006@3oool00`000000oooo0?ooo`1K0?ooo`D00000=@3oool600000;L0oooo1@00000e0?ooo`L0 0000JP3oool001T0oooo00<000000?ooo`3oool0D@3oool:00000400oooo1@00002]0?ooo`D00000 @@3oool800000680oooo000I0?ooo`030000003oool0oooo04d0oooo1000001?0?ooo`@00000X`3o ool6000004h0oooo1@00001M0?ooo`006@3oool00`000000oooo0?ooo`190?ooo`@00000E`3oool5 000009X0oooo1000001I0?ooo`@00000F@3oool001T0oooo00<000000?ooo`3oool0AP3oool30000 0600oooo1@00002A0?ooo`@00000H@3oool3000005H0oooo000I0?ooo`<00000@`3oool3000006P0 oooo100000290?ooo`@00000J03oool400000580oooo000I0?ooo`030000003oool0oooo03l0oooo 1000001_0?ooo`@00000PP3oool300000700oooo0`00001?0?ooo`006@3oool00`000000oooo0?oo o`0l0?ooo`<00000M`3oool4000007X0oooo1000001f0?ooo`<00000C03oool001T0oooo00<00000 0?ooo`3oool0>03oool4000007h0oooo0`00001c0?ooo`@00000O@3oool4000004P0oooo000I0?oo o`030000003oool0oooo03@0oooo100000250?ooo`800000K`3oool2000008D0oooo0`0000150?oo o`006@3oool00`000000oooo0?ooo`0b0?ooo`800000R`3oool3000006X0oooo0P00002:0?ooo`80 0000@`3oool001T0oooo00<000000?ooo`3oool0<03oool200000900oooo0P00001V0?ooo`800000 SP3oool200000440oooo000I0?ooo`030000003oool0oooo02h0oooo0P00002D0?ooo`800000HP3o ool200000980oooo0P00000o0?ooo`006@3oool00`000000oooo0?ooo`0/0?ooo`800000V03oool2 000005h0oooo0P00002F0?ooo`800000?@3oool001T0oooo0`00000Z0?ooo`800000W03oool20000 05X0oooo0P00002J0?ooo`800000>`3oool001T0oooo00<000000?ooo`3oool0:03oool200000:00 oooo0P00001F0?ooo`800000WP3oool2000003T0oooo000I0?ooo`030000003oool0oooo02L0oooo 00<000000?ooo`3oool0XP3oool200000580oooo0P00002R0?ooo`800000=`3oool001T0oooo00<0 00000?ooo`3oool09@3oool200000:L0oooo0P00001>0?ooo`800000YP3oool2000003D0oooo000I 0?ooo`030000003oool0oooo02<0oooo0P00002[0?ooo`030000003oool0oooo04T0oooo0P00002Z 0?ooo`800000<`3oool001T0oooo00<000000?ooo`3oool08@3oool200000:h0oooo00<000000?oo o`3oool0AP3oool200000:h0oooo0P00000a0?ooo`006@3oool00`000000oooo0?ooo`0O0?ooo`80 0000/@3oool2000004D0oooo00<000000?ooo`3oool0/03oool00`000000oooo0?ooo`0^0?ooo`00 0P3oool2000000@0oooo0P0000040?ooo`8000002@3oool00`000000oooo0?ooo`0N0?ooo`030000 003oool0oooo0;<0oooo00<000000?ooo`3oool0@03oool200000;@0oooo00<000000?ooo`3oool0 ;@3oool000050?ooo`000000oooo0?ooo`000000203oool010000000oooo0?ooo`0000080?ooo`03 0000003oool0oooo01`0oooo0P00002g0?ooo`030000003oool0oooo03h0oooo00<000000?ooo`3o ool0]@3oool2000002d0oooo00001@3oool000000?ooo`3oool0000000/0oooo00<000000?ooo`3o ool01P3oool4000001X0oooo00<000000?ooo`3oool0^03oool00`000000oooo0?ooo`0k0?ooo`80 0000^P3oool00`000000oooo0?ooo`0Z0?ooo`0000D0oooo0000003oool0oooo000000090?ooo`80 00002@3oool00`000000oooo0?ooo`0J0?ooo`030000003oool0oooo0;X0oooo00<000000?ooo`3o ool0>@3oool00`000000oooo0?ooo`2k0?ooo`030000003oool0oooo02T0oooo00001@3oool00000 0?ooo`3oool0000000T0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`0I0?ooo`03 0000003oool0oooo0;`0oooo0P00000h0?ooo`030000003oool0oooo0;d0oooo00<000000?ooo`3o ool0:03oool00080oooo0P00000:0?ooo`<00000203oool00`000000oooo0?ooo`0H0?ooo`030000 003oool0oooo0;l0oooo00<000000?ooo`3oool0=03oool00`000000oooo0?ooo`2o0?ooo`030000 003oool0oooo02L0oooo000I0?ooo`030000003oool0oooo01L0oooo00<000000?ooo`3oool0`@3o ool00`000000oooo0?ooo`0c0?ooo`030000003oool0oooo0<00oooo00<000000?ooo`3oool09P3o ool001T0oooo00<000000?ooo`3oool05P3oool00`000000oooo0?ooo`330?ooo`030000003oool0 oooo0340oooo00<000000?ooo`3oool0`P3oool00`000000oooo0?ooo`0U0?ooo`006@3oool00`00 0000oooo0?ooo`0E0?ooo`030000003oool0oooo00?ooo`030000003oool0oooo0=<0 oooo00<000000?ooo`3oool0803oool00`000000oooo0?ooo`3D0?ooo`030000003oool0oooo01`0 oooo000I0?ooo`030000003oool0oooo00h0oooo00<000000?ooo`3oool0e03oool00`000000oooo 0?ooo`0N0?ooo`030000003oool0oooo0=D0oooo00<000000?ooo`3oool0703oool001T0oooo0`00 000=0?ooo`030000003oool0oooo0=H0oooo00<000000?ooo`3oool07@3oool00`000000oooo0?oo o`3E0?ooo`030000003oool0oooo01`0oooo000I0?ooo`030000003oool0oooo00d0oooo00<00000 0?ooo`3oool0eP3oool00`000000oooo0?ooo`0L0?ooo`030000003oool0oooo0=L0oooo00<00000 0?ooo`3oool06`3oool001T0oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`3H0?oo o`030000003oool0oooo01/0oooo00<000000?ooo`3oool0e`3oool00`000000oooo0?ooo`0K0?oo o`006@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo0=P0oooo00<000000?ooo`3o ool06`3oool00`000000oooo0?ooo`3H0?ooo`030000003oool0oooo01X0oooo000I0?ooo`030000 003oool0oooo00/0oooo00<000000?ooo`3oool0f@3oool00`000000oooo0?ooo`0J0?ooo`030000 003oool0oooo0=T0oooo00<000000?ooo`3oool06P3oool001T0oooo00<000000?ooo`3oool02`3o ool00`000000oooo0?ooo`3J0?ooo`030000003oool0oooo01T0oooo00<000000?ooo`3oool0fP3o ool00`000000oooo0?ooo`0I0?ooo`006@3oool00`000000oooo0?ooo`0:0?ooo`030000003oool0 oooo0=/0oooo00<000000?ooo`3oool06@3oool00`000000oooo0?ooo`3J0?ooo`030000003oool0 oooo01T0oooo000I0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool0f`3oool00`00 0000oooo0?ooo`0H0?ooo`030000003oool0oooo0=`0oooo00<000000?ooo`3oool0603oool001T0 oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`3M0?ooo`030000003oool0oooo01L0 oooo00<000000?ooo`3oool0g03oool00`000000oooo0?ooo`0H0?ooo`006@3oool3000000T0oooo 00<000000?ooo`3oool0g@3oool00`000000oooo0?ooo`0F0?ooo`030000003oool0oooo0=h0oooo 00<000000?ooo`3oool05`3oool001T0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?oo o`3N0?ooo`030000003oool0oooo01D0oooo00<000000?ooo`3oool0gP3oool00`000000oooo0?oo o`0G0?ooo`006@3oool00`000000oooo0?ooo`080?ooo`030000003oool0oooo0=l0oooo00<00000 0?ooo`3oool0503oool00`000000oooo0?ooo`3O0?ooo`030000003oool0oooo01L0oooo000I0?oo o`030000003oool0oooo00P0oooo00<000000?ooo`3oool0h03oool00`000000oooo0?ooo`0C0?oo o`030000003oool0oooo0>00oooo00<000000?ooo`3oool05P3oool001T0oooo00<000000?ooo`3o ool0203oool00`000000oooo0?ooo`3P0?ooo`030000003oool0oooo01<0oooo00<000000?ooo`3o ool0h03oool00`000000oooo0?ooo`0F0?ooo`006@3oool00`000000oooo0?ooo`070?ooo`030000 003oool0oooo0>40oooo00<000000?ooo`3oool04`3oool00`000000oooo0?ooo`3P0?ooo`030000 003oool0oooo01H0oooo000I0?ooo`030000003oool0oooo00L0oooo00<000000?ooo`3oool0h@3o ool00`000000oooo0?ooo`0B0?ooo`030000003oool0oooo0>80oooo00<000000?ooo`3oool05@3o ool001T0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`3R0?ooo`030000003oool0 oooo0140oooo00<000000?ooo`3oool0hP3oool00`000000oooo0?ooo`0E0?ooo`006@3oool00`00 0000oooo0?ooo`060?ooo`030000003oool0oooo0><0oooo00<000000?ooo`3oool04@3oool00`00 0000oooo0?ooo`3R0?ooo`030000003oool0oooo01D0oooo000I0?ooo`<000001P3oool00`000000 oooo0?ooo`3S0?ooo`030000003oool0oooo0140oooo00<000000?ooo`3oool0hP3oool00`000000 oooo0?ooo`0E0?ooo`006@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo0><0oooo 00<000000?ooo`3oool04@3oool00`000000oooo0?ooo`3R0?ooo`030000003oool0oooo01D0oooo 000I0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool0h`3oool00`000000oooo0?oo o`0@0?ooo`030000003oool0oooo0><0oooo00<000000?ooo`3oool05@3oool001T0oooo00<00000 0?ooo`3oool01P3oool00`000000oooo0?ooo`3S0?ooo`030000003oool0oooo0100oooo00<00000 0?ooo`3oool0i03oool00`000000oooo0?ooo`0D0?ooo`006@3oool00`000000oooo0?ooo`050?oo o`030000003oool0oooo0>D0oooo00<000000?ooo`3oool03`3oool00`000000oooo0?ooo`3T0?oo o`030000003oool0oooo01@0oooo000I0?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3o ool0i@3oool00`000000oooo0?ooo`0?0?ooo`030000003oool0oooo0>@0oooo00<000000?ooo`3o ool0503oool001T0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`3U0?ooo`030000 003oool0oooo00h0oooo00<000000?ooo`3oool0i@3oool00`000000oooo0?ooo`0D0?ooo`003@3o ool5000000L0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`3U0?ooo`030000003o ool0oooo00h0oooo00<000000?ooo`3oool0i@3oool00`000000oooo0?ooo`0D0?ooo`003`3oool0 0`000000oooo0?ooo`070?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0i@3oool0 0`000000oooo0?ooo`0>0?ooo`030000003oool0oooo0>D0oooo00<000000?ooo`3oool0503oool0 00l0oooo00<000000?ooo`3oool01`3oool4000000@0oooo00<000000?ooo`3oool0iP3oool00`00 0000oooo0?ooo`0=0?ooo`030000003oool0oooo0>H0oooo00<000000?ooo`3oool04`3oool000l0 oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo0>H0 oooo00<000000?ooo`3oool0303oool00`000000oooo0?ooo`3W0?ooo`030000003oool0oooo01<0 oooo000?0?ooo`030000003oool0oooo00L0oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`3W0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool0i`3oool00`000000oooo 0?ooo`0C0?ooo`003P3oool2000000T0oooo00<000000?ooo`3oool0103oool00`000000oooo0?oo o`3W0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3oool0i`3oool00`000000oooo0?oo o`0C0?ooo`006@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo0>P0oooo00<00000 0?ooo`3oool02`3oool00`000000oooo0?ooo`3X0?ooo`030000003oool0oooo0180oooo000I0?oo o`030000003oool0oooo00@0oooo00<000000?ooo`3oool0j03oool00`000000oooo0?ooo`0;0?oo o`030000003oool0oooo0>P0oooo00<000000?ooo`3oool04P3oool001T0oooo00<000000?ooo`3o ool0103oool00`000000oooo0?ooo`3X0?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3o ool0j03oool00`000000oooo0?ooo`0B0?ooo`006@3oool00`000000oooo0?ooo`040?ooo`030000 003oool0oooo0>P0oooo00<000000?ooo`3oool02`3oool00`000000oooo0?ooo`3X0?ooo`030000 003oool0oooo0180oooo000I0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0j03o ool00`000000oooo0?ooo`0:0?ooo`030000003oool0oooo0>T0oooo00<000000?ooo`3oool04P3o ool001T0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`3X0?ooo`030000003oool0 oooo00X0oooo00<000000?ooo`3oool0j@3oool00`000000oooo0?ooo`0B0?ooo`006@3oool30000 00@0oooo00<000000?ooo`3oool0j03oool00`000000oooo0?ooo`0:0?ooo`030000003oool0oooo 0>X0oooo00<000000?ooo`3oool04@3oool001T0oooo00<000000?ooo`3oool00`3oool00`000000 oooo0?ooo`3Y0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool0jP3oool00`000000 oooo0?ooo`0A0?ooo`006@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0>X0oooo 00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`3Z0?ooo`030000003oool0oooo0140oooo 000I0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0jP3oool00`000000oooo0?oo o`090?ooo`030000003oool0oooo0>X0oooo00<000000?ooo`3oool04@3oool001T0oooo00<00000 0?ooo`3oool00`3oool00`000000oooo0?ooo`3Z0?ooo`030000003oool0oooo00T0oooo00<00000 0?ooo`3oool0jP3oool00`000000oooo0?ooo`0A0?ooo`006@3oool00`000000oooo0?ooo`030?oo o`030000003oool0oooo0>X0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`3Z0?oo o`030000003oool0oooo0140oooo000I0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3o ool0jP3oool00`000000oooo0?ooo`090?ooo`030000003oool0oooo0>X0oooo00<000000?ooo`3o ool04@3oool001T0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3Z0?ooo`030000 003oool0oooo00T0oooo00<000000?ooo`3oool0jP3oool00`000000oooo0?ooo`0A0?ooo`006@3o ool00`000000oooo0?ooo`030?ooo`030000003oool0oooo0>X0oooo00<000000?ooo`3oool02@3o ool00`000000oooo0?ooo`3Z0?ooo`030000003oool0oooo0140oooo000I0?ooo`<000000P3oool0 0`000000oooo0?ooo`3[0?ooo`030000003oool0oooo00T0oooo00<000000?ooo`3oool0jP3oool0 0`000000oooo0?ooo`0A0?ooo`006@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo 0>/0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`3[0?ooo`030000003oool0oooo 0140oooo000I0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0k03oool00`000000 oooo0?ooo`070?ooo`030000003oool0oooo0>/0oooo00<000000?ooo`3oool04@3oool001T0oooo 00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3/0?ooo`030000003oool0oooo00L0oooo 00<000000?ooo`3oool0j`3oool00`000000oooo0?ooo`0A0?ooo`006@3oool00`000000oooo0?oo o`020?ooo`030000003oool0oooo0>`0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?oo o`3[0?ooo`030000003oool0oooo0140oooo000I0?ooo`030000003oool0oooo0080oooo00<00000 0?ooo`3oool0k03oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo0>/0oooo00<00000 0?ooo`3oool04@3oool001T0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3/0?oo o`030000003oool0oooo00L0oooo00<000000?ooo`3oool0j`3oool00`000000oooo0?ooo`0A0?oo o`006@3oool01@000000oooo0?ooo`3oool000000>l0oooo00<000000?ooo`3oool01`3oool00`00 0000oooo0?ooo`3/0?ooo`030000003oool0oooo0100oooo000I0?ooo`050000003oool0oooo0?oo o`000000k`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo0>`0oooo00<000000?oo o`3oool0403oool001T0oooo0`0000000`3oool000000?ooo`3^0?ooo`030000003oool0oooo00L0 oooo00<000000?ooo`3oool0k03oool00`000000oooo0?ooo`0@0?ooo`006@3oool01@000000oooo 0?ooo`3oool000000>l0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`3/0?ooo`03 0000003oool0oooo0100oooo000I0?ooo`050000003oool0oooo0?ooo`000000k`3oool00`000000 oooo0?ooo`060?ooo`030000003oool0oooo0>d0oooo00<000000?ooo`3oool0403oool001T0oooo 00D000000?ooo`3oool0oooo0000003_0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3o ool0k@3oool00`000000oooo0?ooo`0@0?ooo`006@3oool01@000000oooo0?ooo`3oool000000>l0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`3]0?ooo`030000003oool0oooo0100 oooo000I0?ooo`050000003oool0oooo0?ooo`000000k`3oool00`000000oooo0?ooo`060?ooo`03 0000003oool0oooo0>d0oooo00<000000?ooo`3oool0403oool001T0oooo00D000000?ooo`3oool0 oooo0000003_0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool0k@3oool00`000000 oooo0?ooo`0@0?ooo`006@3oool01@000000oooo0?ooo`3oool000000>l0oooo00<000000?ooo`3o ool01P3oool00`000000oooo0?ooo`3]0?ooo`030000003oool0oooo0100oooo000I0?ooo`050000 003oool0oooo0?ooo`000000l03oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo0>d0 oooo00<000000?ooo`3oool0403oool001T0oooo0`0000000`3oool000000?ooo`3_0?ooo`030000 003oool0oooo00D0oooo00<000000?ooo`3oool0k@3oool00`000000oooo0?ooo`0@0?ooo`006@3o ool01@000000oooo0?ooo`3oool000000?00oooo00<000000?ooo`3oool01@3oool00`000000oooo 0?ooo`3^0?ooo`030000003oool0oooo00l0oooo000I0?ooo`040000003oool0oooo00000?40oooo 00<000000?ooo`3oool0103oool00`000000oooo0?ooo`3_0?ooo`030000003oool0oooo00l0oooo 000I0?ooo`040000003oool0oooo00000?40oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`3_0?ooo`030000003oool0oooo00l0oooo000I0?ooo`040000003oool0oooo00000?40oooo 00<000000?ooo`3oool0103oool00`000000oooo0?ooo`3_0?ooo`030000003oool0oooo00l0oooo 000I0?ooo`040000003oool0oooo00000?40oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`3_0?ooo`030000003oool0oooo00l0oooo000I0?ooo`040000003oool0oooo00000?40oooo 00<000000?ooo`3oool0103oool00`000000oooo0?ooo`3_0?ooo`030000003oool0oooo00l0oooo 000I0?ooo`040000003oool0oooo00000?40oooo00<000000?ooo`3oool0103oool00`000000oooo 0?ooo`3_0?ooo`030000003oool0oooo00l0oooo00000`3oool000000000000300000080oooo0P00 00040?ooo`8000002@3oool010000000oooo0?ooo`00003a0?ooo`030000003oool0oooo00@0oooo 00<000000?ooo`3oool0k`3oool00`000000oooo0?ooo`0?0?ooo`000`3oool00`000000oooo0?oo o`070?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3oool00000l@3oool00`000000 oooo0?ooo`040?ooo`030000003oool0oooo0>l0oooo00<000000?ooo`3oool03`3oool000<0oooo 00<000000?ooo`3oool02P3oool00`000000oooo0?ooo`060?ooo`@00000l@3oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo0>l0oooo00<000000?ooo`3oool03`3oool000<0oooo00<0 00000?ooo`3oool0203oool2000000T0oooo00@000000?ooo`3oool00000l@3oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo0>l0oooo00<000000?ooo`3oool03`3oool000<0oooo00<0 00000?ooo`3oool0203oool00`000000oooo0?ooo`080?ooo`040000003oool0oooo00000?40oooo 00<000000?ooo`3oool0103oool00`000000oooo0?ooo`3`0?ooo`030000003oool0oooo00h0oooo 00020?ooo`8000002P3oool3000000P0oooo00@000000?ooo`3oool00000l@3oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo0?00oooo00<000000?ooo`3oool03P3oool001T0oooo00@0 00000?ooo`3oool00000l@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo0?00oooo 00<000000?ooo`3oool03P3oool001T0oooo00@000000?ooo`3oool00000l@3oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo0?00oooo00<000000?ooo`3oool03P3oool001T0oooo00@0 00000?ooo`3oool00000l@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo0?00oooo 00<000000?ooo`3oool03P3oool001T0oooo00@000000?ooo`3oool00000l@3oool00`000000oooo 0?ooo`040?ooo`030000003oool0oooo0?00oooo00<000000?ooo`3oool03P3oool001T0oooo00@0 00000?ooo`3oool00000l@3oool00`000000oooo0?ooo`040?ooo`030000003oool0oooo0?00oooo 00<000000?ooo`3oool03P3oool001T0oooo1000003a0?ooo`030000003oool0oooo00@0oooo00<0 00000?ooo`3oool0l03oool00`000000oooo0?ooo`0>0?ooo`006@3oool010000000oooo0?ooo`00 003b0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0l03oool00`000000oooo0?oo o`0>0?ooo`006@3oool010000000oooo0?ooo`00003b0?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool0l03oool00`000000oooo0?ooo`0>0?ooo`006@3oool010000000oooo0?ooo`00 003b0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0l03oool00`000000oooo0?oo o`0>0?ooo`006@3oool010000000oooo0?ooo`00003b0?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool0l03oool00`000000oooo0?ooo`0>0?ooo`006@3oool010000000oooo0?ooo`00 003b0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0l03oool00`000000oooo0?oo o`0>0?ooo`006@3oool010000000oooo0?ooo`00003b0?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool0l03oool00`000000oooo0?ooo`0>0?ooo`006@3oool010000000oooo0?ooo`00 003b0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0l03oool00`000000oooo0?oo o`0>0?ooo`006@3oool010000000oooo0?ooo`00003b0?ooo`030000003oool0oooo00<0oooo00<0 00000?ooo`3oool0l03oool00`000000oooo0?ooo`0>0?ooo`006@3oool400000?80oooo00<00000 0?ooo`3oool00`3oool00`000000oooo0?ooo`3`0?ooo`030000003oool0oooo00h0oooo000I0?oo o`040000003oool0oooo00000?80oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3a 0?ooo`030000003oool0oooo00h0oooo000I0?ooo`040000003oool0oooo00000?80oooo00<00000 0?ooo`3oool00P3oool00`000000oooo0?ooo`3a0?ooo`030000003oool0oooo00h0oooo000I0?oo o`040000003oool0oooo00000?80oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3a 0?ooo`030000003oool0oooo00h0oooo000I0?ooo`030000003oool000000?<0oooo00<000000?oo o`3oool00P3oool00`000000oooo0?ooo`3a0?ooo`030000003oool0oooo00h0oooo000I0?ooo`03 0000003oool000000?<0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3a0?ooo`03 0000003oool0oooo00h0oooo000I0?ooo`030000003oool000000?<0oooo00<000000?ooo`3oool0 0P3oool00`000000oooo0?ooo`3a0?ooo`030000003oool0oooo00h0oooo000I0?ooo`030000003o ool000000?<0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3a0?ooo`030000003o ool0oooo00h0oooo000I0?ooo`030000003oool000000?<0oooo00<000000?ooo`3oool00P3oool0 0`000000oooo0?ooo`3b0?ooo`030000003oool0oooo00d0oooo000I0?ooo`<00000l`3oool00`00 0000oooo0?ooo`020?ooo`030000003oool0oooo0?80oooo00<000000?ooo`3oool03@3oool001T0 oooo00<000000?ooo`000000l`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?80 oooo00<000000?ooo`3oool03@3oool001T0oooo00<000000?ooo`000000l`3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo0?80oooo00<000000?ooo`3oool03@3oool001T0oooo00<0 00000?ooo`000000l`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?80oooo00<0 00000?ooo`3oool03@3oool001T0oooo00<000000?ooo`000000l`3oool00`000000oooo0?ooo`02 0?ooo`030000003oool0oooo0?80oooo00<000000?ooo`3oool03@3oool001T0oooo00<000000?oo o`000000l`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?80oooo00<000000?oo o`3oool03@3oool001T0oooo00<000000?ooo`000000l`3oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo0?80oooo00<000000?ooo`3oool03@3oool001T0oooo00<000000?ooo`000000 l`3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?80oooo00<000000?ooo`3oool0 3@3oool001T0oooo00<000000?ooo`000000l`3oool00`000000oooo0?ooo`020?ooo`030000003o ool0oooo0?80oooo00<000000?ooo`3oool03@3oool001T0oooo00<000000?ooo`000000l`3oool0 0`000000oooo0?ooo`020?ooo`030000003oool0oooo0?80oooo00<000000?ooo`3oool03@3oool0 01T0oooo0`00003c0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0lP3oool00`00 0000oooo0?ooo`0=0?ooo`006@3oool00`000000oooo0000003c0?ooo`030000003oool0oooo0080 oooo00<000000?ooo`3oool0lP3oool00`000000oooo0?ooo`0=0?ooo`006@3oool00`000000oooo 0000003c0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0lP3oool00`000000oooo 0?ooo`0=0?ooo`006@3oool00`000000oooo0000003c0?ooo`030000003oool0oooo0080oooo00<0 00000?ooo`3oool0lP3oool00`000000oooo0?ooo`0=0?ooo`006@3oool00`000000oooo0000003c 0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0lP3oool00`000000oooo0?ooo`0= 0?ooo`006@3oool00`000000oooo0000003c0?ooo`030000003oool0oooo0080oooo00<000000?oo o`3oool0lP3oool00`000000oooo0?ooo`0=0?ooo`006@3oool200000?@0oooo00<000000?ooo`3o ool00P3oool00`000000oooo0?ooo`3b0?ooo`030000003oool0oooo00d0oooo000=0?ooo`@00000 203oool200000?@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3b0?ooo`030000 003oool0oooo00d0oooo000=0?ooo`030000003oool0oooo00T0oooo0P00003d0?ooo`030000003o ool0oooo0080oooo00<000000?ooo`3oool0lP3oool00`000000oooo0?ooo`0=0?ooo`003P3oool0 0`000000oooo0?ooo`080?ooo`@00000lP3oool00`000000oooo0?ooo`020?ooo`030000003oool0 oooo0?80oooo00<000000?ooo`3oool03@3oool000l0oooo00<000000?ooo`3oool01`3oool20000 0?@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`3b0?ooo`030000003oool0oooo 00d0oooo000=0?ooo`040000003oool0oooo000000P0oooo0P00003d0?ooo`030000003oool0oooo 0080oooo00<000000?ooo`3oool0lP3oool00`000000oooo0?ooo`0=0?ooo`003P3oool2000000T0 oooo0P00003e0?ooo`050000003oool0oooo0?ooo`000000m03oool00`000000oooo0?ooo`0=0?oo o`006@3oool200000?D0oooo00D000000?ooo`3oool0oooo0000003d0?ooo`030000003oool0oooo 00d0oooo000I0?ooo`800000m@3oool01@000000oooo0?ooo`3oool000000?@0oooo00<000000?oo o`3oool03@3oool001T0oooo0P00003e0?ooo`050000003oool0oooo0?ooo`000000m03oool00`00 0000oooo0?ooo`0=0?ooo`006@3oool200000?D0oooo00D000000?ooo`3oool0oooo0000003d0?oo o`030000003oool0oooo00d0oooo000I0?ooo`800000m@3oool01@000000oooo0?ooo`3oool00000 0?@0oooo00<000000?ooo`3oool03@3oool001T0oooo0`00003d0?ooo`050000003oool0oooo0?oo o`000000m03oool00`000000oooo0?ooo`0=0?ooo`006@3oool200000?D0oooo00D000000?ooo`3o ool0oooo0000003d0?ooo`030000003oool0oooo00d0oooo000I0?ooo`800000m@3oool01@000000 oooo0?ooo`3oool000000?@0oooo00<000000?ooo`3oool03@3oool001T0oooo0P00003e0?ooo`05 0000003oool0oooo0?ooo`000000m03oool00`000000oooo0?ooo`0=0?ooo`006@3oool200000?D0 oooo00D000000?ooo`3oool0oooo0000003d0?ooo`030000003oool0oooo00d0oooo000I0?ooo`80 0000m@3oool01@000000oooo0?ooo`3oool000000?@0oooo00<000000?ooo`3oool03@3oool001T0 oooo0P00003e0?ooo`050000003oool0oooo0?ooo`000000m03oool00`000000oooo0?ooo`0=0?oo o`006@3oool200000?D0oooo00D000000?ooo`3oool0oooo0000003d0?ooo`030000003oool0oooo 00d0oooo000I0?ooo`800000m@3oool01@000000oooo0?ooo`3oool000000?@0oooo00<000000?oo o`3oool03@3oool001T0oooo0`00003d0?ooo`050000003oool0oooo0?ooo`000000m03oool00`00 0000oooo0?ooo`0=0?ooo`006@3oool200000?D0oooo00D000000?ooo`3oool0oooo0000003d0?oo o`030000003oool0oooo00d0oooo000I0?ooo`800000m@3oool01@000000oooo0?ooo`3oool00000 0?@0oooo00<000000?ooo`3oool03@3oool001T0oooo0P00003e0?ooo`050000003oool0oooo0?oo o`000000m03oool00`000000oooo0?ooo`0=0?ooo`006@3oool200000?D0oooo00D000000?ooo`3o ool0oooo0000003d0?ooo`030000003oool0oooo00d0oooo000I0?ooo`800000m@3oool01@000000 oooo0?ooo`3oool000000?@0oooo00<000000?ooo`3oool03@3oool001T0oooo0P00003e0?ooo`05 0000003oool0oooo0?ooo`000000m03oool00`000000oooo0?ooo`0=0?ooo`006@3oool200000?D0 oooo00D000000?ooo`3oool0oooo0000003d0?ooo`030000003oool0oooo00d0oooo000I0?ooo`80 0000m@3oool01@000000oooo0?ooo`3oool000000?D0oooo00<000000?ooo`3oool0303oool001T0 oooo0P00003e0?ooo`050000003oool0oooo0?ooo`000000m@3oool00`000000oooo0?ooo`0<0?oo o`006@3oool300000?@0oooo00D000000?ooo`3oool0oooo0000003e0?ooo`030000003oool0oooo 00`0oooo000I0?ooo`800000m@3oool01@000000oooo0?ooo`3oool000000?D0oooo00<000000?oo o`3oool0303oool001T0oooo0P00003e0?ooo`050000003oool0oooo0?ooo`000000m@3oool00`00 0000oooo0?ooo`0<0?ooo`006@3oool200000?D0oooo00D000000?ooo`3oool0oooo0000003e0?oo o`030000003oool0oooo00`0oooo000I0?ooo`800000m@3oool01@000000oooo0?ooo`3oool00000 0?D0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003e0?ooo`050000003oool0oooo0?oo o`000000m@3oool00`000000oooo0?ooo`0<0?ooo`006@3oool200000?D0oooo00@000000?ooo`3o ool00000mP3oool00`000000oooo0?ooo`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`00 0000mP3oool00`000000oooo0?ooo`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`000000 mP3oool00`000000oooo0?ooo`0<0?ooo`006@3oool300000?D0oooo00<000000?ooo`000000mP3o ool00`000000oooo0?ooo`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`000000mP3oool0 0`000000oooo0?ooo`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`000000mP3oool00`00 0000oooo0?ooo`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`000000mP3oool00`000000 oooo0?ooo`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`000000mP3oool00`000000oooo 0?ooo`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`000000mP3oool00`000000oooo0?oo o`0<0?ooo`006@3oool200000?H0oooo00<000000?ooo`000000mP3oool00`000000oooo0?ooo`0< 0?ooo`0000<0oooo0000000000000P0000030?ooo`800000103oool2000000T0oooo0P00003f0?oo o`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool000030?ooo`000000oooo00X0 oooo00@000000?ooo`3oool00000203oool200000?H0oooo00<000000?ooo`000000mP3oool00`00 0000oooo0?ooo`0<0?ooo`000P3oool00`000000oooo0?ooo`0;0?ooo`030000003oool0oooo00H0 oooo1000003d0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool000<0oooo 00<000000?ooo`3oool0203oool2000000T0oooo0P00003f0?ooo`030000003oool000000?H0oooo 00<000000?ooo`3oool0303oool000050?ooo`000000oooo0?ooo`0000002@3oool00`000000oooo 0?ooo`080?ooo`800000mP3oool00`000000oooo0000003f0?ooo`030000003oool0oooo00`0oooo 00020?ooo`8000002P3oool3000000P0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<0 00000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<00000 0?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?oo o`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3o ool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0 303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303o ool001T0oooo0`00003e0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool0 01T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0 oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo 0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00 003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f 0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?oo o`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`03 0000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000 003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003o ool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0`00003e0?ooo`030000003oool0 00000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool00000 0?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0 oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo 00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<0 00000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<00000 0?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?oo o`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3o ool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0 303oool001T0oooo0`00003e0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303o ool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool0 01T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0 oooo0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo 0P00003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00 003f0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f 0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?oo o`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`03 0000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0`00003e0?ooo`030000 003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003o ool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool0 00000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool00000 0?H0oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0 oooo00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo 00<000000?ooo`3oool0303oool001T0oooo0P00003f0?ooo`030000003oool000000?H0oooo00<0 00000?ooo`3oool0303oool000h0oooo0P0000090?ooo`800000mP3oool00`000000oooo0000003f 0?ooo`030000003oool0oooo00`0oooo000=0?ooo`040000003oool0oooo000000P0oooo0P00003f 0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool000l0oooo00<000000?oo o`3oool01`3oool400000?@0oooo00<000000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?oo o`00403oool00`000000oooo0?ooo`060?ooo`800000mP3oool00`000000oooo0000003f0?ooo`03 0000003oool0oooo00`0oooo000=0?ooo`040000003oool0oooo000000P0oooo00<000000?ooo`3o ool0m@3oool00`000000oooo0000003f0?ooo`030000003oool0oooo00`0oooo000>0?ooo`800000 2@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0 303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000oooo0000003f0?ooo`030000003o ool0oooo00`0oooo000I0?ooo`030000003oool0oooo0?D0oooo00<000000?ooo`000000mP3oool0 0`000000oooo0?ooo`0<0?ooo`006@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool00000 0?H0oooo00<000000?ooo`3oool0303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000 oooo0000003f0?ooo`030000003oool0oooo00`0oooo000I0?ooo`030000003oool0oooo0?D0oooo 00<000000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?ooo`006@3oool00`000000oooo0?oo o`3e0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo0`00003e 0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo00<000000?oo o`3oool0m@3oool00`000000oooo0000003f0?ooo`030000003oool0oooo00`0oooo000I0?ooo`03 0000003oool0oooo0?D0oooo00<000000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?ooo`00 6@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0 303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000oooo0000003f0?ooo`030000003o ool0oooo00`0oooo000I0?ooo`030000003oool0oooo0?D0oooo00<000000?ooo`000000mP3oool0 0`000000oooo0?ooo`0<0?ooo`006@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool00000 0?H0oooo00<000000?ooo`3oool0303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000 oooo0000003f0?ooo`030000003oool0oooo00`0oooo000I0?ooo`030000003oool0oooo0?D0oooo 00<000000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?ooo`006@3oool300000?D0oooo00<0 00000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?ooo`006@3oool00`000000oooo0?ooo`3e 0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo00<000000?oo o`3oool0m@3oool00`000000oooo0000003f0?ooo`030000003oool0oooo00`0oooo000I0?ooo`03 0000003oool0oooo0?D0oooo00<000000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?ooo`00 6@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0 303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000oooo0000003f0?ooo`030000003o ool0oooo00`0oooo000I0?ooo`030000003oool0oooo0?D0oooo00<000000?ooo`000000mP3oool0 0`000000oooo0?ooo`0<0?ooo`006@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool00000 0?H0oooo00<000000?ooo`3oool0303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000 oooo0000003f0?ooo`030000003oool0oooo00`0oooo000I0?ooo`<00000m@3oool00`000000oooo 0000003f0?ooo`030000003oool0oooo00`0oooo000I0?ooo`030000003oool0oooo0?D0oooo00<0 00000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?ooo`006@3oool00`000000oooo0?ooo`3e 0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0303oool001T0oooo00<000000?oo o`3oool0m@3oool00`000000oooo0000003f0?ooo`030000003oool0oooo00`0oooo000I0?ooo`03 0000003oool0oooo0?D0oooo00<000000?ooo`000000mP3oool00`000000oooo0?ooo`0<0?ooo`00 6@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool000000?H0oooo00<000000?ooo`3oool0 303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000oooo0000003f0?ooo`030000003o ool0oooo00`0oooo000I0?ooo`030000003oool0oooo0?D0oooo00<000000?ooo`000000mP3oool0 0`000000oooo0?ooo`0<0?ooo`006@3oool00`000000oooo0?ooo`3e0?ooo`030000003oool00000 0?H0oooo00<000000?ooo`3oool0303oool001T0oooo0`00003e0?ooo`030000003oool000000?H0 oooo00<000000?ooo`3oool0303oool001T0oooo00<000000?ooo`3oool0m@3oool00`000000oooo 0000003f0?ooo`030000003oool0oooo00`0oooo0000\ \>"], ImageRangeCache->{{{0, 536.438}, {331.188, 0}} -> {-0.3168, -0.168022, \ 0.0126099, 0.010813}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(t[\[Sigma]_] := NIntegrate[\@Abs[\(\(x'\)[s]\^2 + \(y'\)[s]\^2\)\/\(v\_0\^2 - 2 g*y[s]\ \)], {s, 0, \[Sigma]}]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(g0 = Plot[t[\[Sigma]], {\[Sigma], 0, 3.14158}]\)], "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 0.0238095 0.303154 0.0147151 0.387941 [ [.17539 .00222 -9 -9 ] [.17539 .00222 9 0 ] [.32696 .00222 -3 -9 ] [.32696 .00222 3 0 ] [.47854 .00222 -9 -9 ] [.47854 .00222 9 0 ] [.63012 .00222 -3 -9 ] [.63012 .00222 3 0 ] [.78169 .00222 -9 -9 ] [.78169 .00222 9 0 ] [.93327 .00222 -3 -9 ] [.93327 .00222 3 0 ] [.01131 .0923 -18 -4.5 ] [.01131 .0923 0 4.5 ] [.01131 .16989 -18 -4.5 ] [.01131 .16989 0 4.5 ] [.01131 .24748 -18 -4.5 ] [.01131 .24748 0 4.5 ] [.01131 .32507 -18 -4.5 ] [.01131 .32507 0 4.5 ] [.01131 .40266 -6 -4.5 ] [.01131 .40266 0 4.5 ] [.01131 .48024 -18 -4.5 ] [.01131 .48024 0 4.5 ] [.01131 .55783 -18 -4.5 ] [.01131 .55783 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 .17539 .01472 m .17539 .02097 L s [(0.5)] .17539 .00222 0 1 Mshowa .32696 .01472 m .32696 .02097 L s [(1)] .32696 .00222 0 1 Mshowa .47854 .01472 m .47854 .02097 L s [(1.5)] .47854 .00222 0 1 Mshowa .63012 .01472 m .63012 .02097 L s [(2)] .63012 .00222 0 1 Mshowa .78169 .01472 m .78169 .02097 L s [(2.5)] .78169 .00222 0 1 Mshowa .93327 .01472 m .93327 .02097 L s [(3)] .93327 .00222 0 1 Mshowa .125 Mabswid .05412 .01472 m .05412 .01847 L s .08444 .01472 m .08444 .01847 L s .11476 .01472 m .11476 .01847 L s .14507 .01472 m .14507 .01847 L s .2057 .01472 m .2057 .01847 L s .23602 .01472 m .23602 .01847 L s .26633 .01472 m .26633 .01847 L s .29665 .01472 m .29665 .01847 L s .35728 .01472 m .35728 .01847 L s .38759 .01472 m .38759 .01847 L s .41791 .01472 m .41791 .01847 L s .44822 .01472 m .44822 .01847 L s .50886 .01472 m .50886 .01847 L s .53917 .01472 m .53917 .01847 L s .56949 .01472 m .56949 .01847 L s .5998 .01472 m .5998 .01847 L s .66043 .01472 m .66043 .01847 L s .69075 .01472 m .69075 .01847 L s .72106 .01472 m .72106 .01847 L s .75138 .01472 m .75138 .01847 L s .81201 .01472 m .81201 .01847 L s .84232 .01472 m .84232 .01847 L s .87264 .01472 m .87264 .01847 L s .90295 .01472 m .90295 .01847 L s .96359 .01472 m .96359 .01847 L s .9939 .01472 m .9939 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .0923 m .03006 .0923 L s [(0.2)] .01131 .0923 1 0 Mshowa .02381 .16989 m .03006 .16989 L s [(0.4)] .01131 .16989 1 0 Mshowa .02381 .24748 m .03006 .24748 L s [(0.6)] .01131 .24748 1 0 Mshowa .02381 .32507 m .03006 .32507 L s [(0.8)] .01131 .32507 1 0 Mshowa .02381 .40266 m .03006 .40266 L s [(1)] .01131 .40266 1 0 Mshowa .02381 .48024 m .03006 .48024 L s [(1.2)] .01131 .48024 1 0 Mshowa .02381 .55783 m .03006 .55783 L s [(1.4)] .01131 .55783 1 0 Mshowa .125 Mabswid .02381 .03411 m .02756 .03411 L s .02381 .05351 m .02756 .05351 L s .02381 .07291 m .02756 .07291 L s .02381 .1117 m .02756 .1117 L s .02381 .1311 m .02756 .1311 L s .02381 .15049 m .02756 .15049 L s .02381 .18929 m .02756 .18929 L s .02381 .20869 m .02756 .20869 L s .02381 .22808 m .02756 .22808 L s .02381 .26688 m .02756 .26688 L s .02381 .28627 m .02756 .28627 L s .02381 .30567 m .02756 .30567 L s .02381 .34446 m .02756 .34446 L s .02381 .36386 m .02756 .36386 L s .02381 .38326 m .02756 .38326 L s .02381 .42205 m .02756 .42205 L s .02381 .44145 m .02756 .44145 L s .02381 .46085 m .02756 .46085 L s .02381 .49964 m .02756 .49964 L s .02381 .51904 m .02756 .51904 L s .02381 .53844 m .02756 .53844 L s .02381 .57723 m .02756 .57723 L s .02381 .59663 m .02756 .59663 L s .02381 .61602 m .02756 .61602 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .0148 m .02499 .03015 L .02605 .03604 L .02846 .0454 L .03279 .05736 L .03784 .06803 L .04262 .07644 L .06244 .10315 L .08265 .12377 L .10458 .14235 L .14545 .17088 L .1848 .19369 L .22263 .21272 L .26292 .23064 L .30169 .24612 L .34292 .26105 L .38262 .27427 L .42082 .28618 L .46146 .29828 L .50059 .30963 L .54217 .32171 L .58224 .33367 L .62079 .34575 L .6618 .35951 L .70128 .37394 L .73925 .38919 L .77968 .4073 L .81859 .42705 L .85995 .45147 L .89979 .48004 L .91838 .4961 L .93812 .51642 L .95622 .54059 L .96118 .54904 L .96652 .55993 L .96898 .56596 L .97156 .57358 L .97377 .58206 L .97503 .58882 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooool000004`00000001D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`4000000@3oool10?ooo`00 5@3oool00`000000oooo0?ooo`0V0?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool0 9`3oool00`000000oooo0?ooo`0V0?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool0 9P3oool00`000000oooo0?ooo`0A0?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E 0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0oooo0P00003o0?ooo`X0oooo000E0?ooo`80 0000o`3oool:0?ooo`005@3oool200000?l0oooo2P3oool001D0oooo0P00003o0?ooo`X0oooo000E 0?ooo`800000o`3oool:0?ooo`005@3oool200000?l0oooo2P3oool001D0oooo0`00003o0?ooo`T0 oooo000E0?ooo`030000003oool000000?l0oooo2@3oool001D0oooo00@000000?ooo`3oool00000 o`3oool80?ooo`005@3oool010000000oooo0?ooo`00003o0?ooo`P0oooo000E0?ooo`050000003o ool0oooo0?ooo`000000o`3oool70?ooo`005@3oool200000080oooo00<000000?ooo`3oool0o`3o ool50?ooo`005@3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?l0oooo103oool0 01D0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3o0?ooo`<0oooo00020?ooo`80 0000103oool2000000<0oooo100000040?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3o ool0o`3oool30?ooo`0000D0oooo0000003oool0oooo000000080?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`3o0?ooo`80oooo00001@3oool00000 0?ooo`3oool0000000T0oooo00<000000?ooo`3oool0103oool3000000D0oooo00<000000?ooo`3o ool0o`3oool10?ooo`0000D0oooo0000003oool0oooo0000000:0?ooo`030000003oool0oooo00<0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`3o0?ooo`0000D0oooo0000003oool0 oooo000000080?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3oool01P3oool00`00 0000oooo0?ooo`3o0?ooo`000P3oool2000000X0oooo0P0000050?ooo`030000003oool0oooo00L0 oooo00<000000?ooo`3oool0oP3oool001D0oooo00<000000?ooo`3oool0203oool00`000000oooo 0?ooo`3m0?ooo`005@3oool00`000000oooo0?ooo`090?ooo`030000003oool0oooo0?`0oooo000E 0?ooo`8000002`3oool00`000000oooo0?ooo`3k0?ooo`005@3oool00`000000oooo0?ooo`0;0?oo o`030000003oool0oooo0?X0oooo000E0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3o ool0n@3oool001D0oooo00<000000?ooo`3oool03@3oool00`000000oooo0?ooo`3h0?ooo`005@3o ool00`000000oooo0?ooo`0>0?ooo`030000003oool0oooo0?L0oooo000E0?ooo`800000403oool0 0`000000oooo0?ooo`3f0?ooo`005@3oool00`000000oooo0?ooo`0@0?ooo`800000mP3oool001D0 oooo00<000000?ooo`3oool04P3oool00`000000oooo0?ooo`3c0?ooo`005@3oool00`000000oooo 0?ooo`0C0?ooo`030000003oool0oooo0?80oooo000E0?ooo`030000003oool0oooo01@0oooo0P00 003b0?ooo`005@3oool2000001L0oooo00<000000?ooo`3oool0k`3oool001D0oooo00<000000?oo o`3oool05`3oool00`000000oooo0?ooo`3^0?ooo`005@3oool00`000000oooo0?ooo`0H0?ooo`80 0000kP3oool00080oooo0P0000040?ooo`8000001@3oool3000000<0oooo00<000000?ooo`3oool0 6P3oool00`000000oooo0?ooo`3[0?ooo`0000D0oooo0000003oool0oooo0000000;0?ooo`030000 003oool0oooo0080oooo00<000000?ooo`3oool06`3oool00`000000oooo0?ooo`3Z0?ooo`0000D0 oooo0000003oool0oooo000000080?ooo`D000000`3oool3000001`0oooo0P00003Z0?ooo`0000D0 oooo0000003oool0oooo000000080?ooo`040000003oool0oooo000000@0oooo00<000000?ooo`3o ool07P3oool00`000000oooo0?ooo`3W0?ooo`0000D0oooo0000003oool0oooo000000090?ooo`03 0000003oool0000000@0oooo00<000000?ooo`3oool07`3oool200000>L0oooo00020?ooo`800000 2`3oool2000000@0oooo00<000000?ooo`3oool08@3oool200000>D0oooo000E0?ooo`030000003o ool0oooo02<0oooo0P00003S0?ooo`005@3oool00`000000oooo0?ooo`0U0?ooo`800000h@3oool0 01D0oooo0P00000X0?ooo`800000g`3oool001D0oooo00<000000?ooo`3oool0:@3oool00`000000 oooo0?ooo`3L0?ooo`005@3oool00`000000oooo0?ooo`0Z0?ooo`800000g03oool001D0oooo00<0 00000?ooo`3oool0;03oool200000=X0oooo000E0?ooo`030000003oool0oooo02h0oooo0P00003H 0?ooo`005@3oool200000340oooo0P00003F0?ooo`005@3oool00`000000oooo0?ooo`0b0?ooo`<0 0000d`3oool001D0oooo00<000000?ooo`3oool0=@3oool200000=40oooo000E0?ooo`030000003o ool0oooo03L0oooo0P00003?0?ooo`005@3oool00`000000oooo0?ooo`0i0?ooo`800000c@3oool0 01D0oooo0P00000l0?ooo`800000b`3oool001D0oooo00<000000?ooo`3oool0?@3oool3000000?ooo`800000^03oool00080oooo 0P00000:0?ooo`<00000103oool00`000000oooo0?ooo`1@0?ooo`<00000]@3oool001D0oooo00<0 00000?ooo`3oool0D`3oool300000;80oooo000E0?ooo`030000003oool0oooo05H0oooo0`00002_ 0?ooo`005@3oool2000005X0oooo0P00002]0?ooo`005@3oool00`000000oooo0?ooo`1K0?ooo`<0 0000ZP3oool001D0oooo00<000000?ooo`3oool0GP3oool300000:L0oooo000E0?ooo`030000003o ool0oooo0640oooo0`00002T0?ooo`005@3oool00`000000oooo0?ooo`1T0?ooo`@00000X03oool0 01D0oooo0P00001Y0?ooo`<00000W@3oool001D0oooo00<000000?ooo`3oool0J`3oool4000009T0 oooo000E0?ooo`030000003oool0oooo06l0oooo1000002E0?ooo`005@3oool00`000000oooo0?oo o`1c0?ooo`<00000TP3oool001D0oooo00<000000?ooo`3oool0MP3oool4000008h0oooo000E0?oo o`800000N`3oool4000008X0oooo000E0?ooo`030000003oool0oooo07h0oooo0`0000270?ooo`00 5@3oool00`000000oooo0?ooo`210?ooo`<00000Q03oool001D0oooo00<000000?ooo`3oool0Q03o ool200000880oooo00020?ooo`800000103oool2000000@0oooo0P0000050?ooo`030000003oool0 oooo08H0oooo0`00001o0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000003oool0 oooo000000@0oooo00<000000?ooo`3oool0R@3oool3000007`0oooo00001@3oool000000?ooo`3o ool0000000P0oooo00@000000?ooo`3oool00000103oool3000008`0oooo1000001h0?ooo`0000D0 oooo0000003oool0oooo000000090?ooo`8000001@3oool00`000000oooo0?ooo`2@0?ooo`@00000 M03oool000050?ooo`000000oooo0?ooo`000000203oool010000000oooo0?ooo`0000040?ooo`03 0000003oool0oooo09@0oooo0`00001a0?ooo`000P3oool2000000X0oooo0P0000050?ooo`030000 003oool0oooo09L0oooo0`00001^0?ooo`005@3oool00`000000oooo0?ooo`2J0?ooo`@00000JP3o ool001D0oooo0P00002O0?ooo`<00000I`3oool001D0oooo00<000000?ooo`3oool0X@3oool30000 06@0oooo000E0?ooo`030000003oool0oooo0:@0oooo0P00001R0?ooo`005@3oool00`000000oooo 0?ooo`2V0?ooo`<00000G`3oool001D0oooo00<000000?ooo`3oool0Z@3oool3000005`0oooo000E 0?ooo`800000[@3oool3000005T0oooo000E0?ooo`030000003oool0oooo0:l0oooo0P00001G0?oo o`005@3oool00`000000oooo0?ooo`2a0?ooo`<00000E03oool001D0oooo00<000000?ooo`3oool0 ]03oool300000540oooo000E0?ooo`030000003oool0oooo0;L0oooo0`00001>0?ooo`005@3oool2 00000;/0oooo0P00001<0?ooo`005@3oool00`000000oooo0?ooo`2l0?ooo`<00000B@3oool001D0 oooo00<000000?ooo`3oool0_`3oool3000004H0oooo000E0?ooo`030000003oool0oooo0<80oooo 0P0000140?ooo`003@3oool5000000<0oooo00<000000?ooo`3oool0a03oool200000480oooo000? 0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0aP3oool200000400oooo000?0?oo o`030000003oool0oooo00<0oooo0`0000380?ooo`800000?P3oool000l0oooo00<000000?ooo`3o ool00`3oool00`000000oooo0?ooo`3:0?ooo`800000?03oool000l0oooo00<000000?ooo`3oool0 0`3oool00`000000oooo0?ooo`3<0?ooo`800000>P3oool000h0oooo0P0000050?ooo`030000003o ool0oooo040oooo0P00000U0?ooo`005@3oool00`000000oooo0?ooo`3S0?ooo`030000003oool0oooo 0280oooo000E0?ooo`800000i@3oool00`000000oooo0?ooo`0Q0?ooo`005@3oool00`000000oooo 0?ooo`3U0?ooo`8000008@3oool001D0oooo00<000000?ooo`3oool0i`3oool00`000000oooo0?oo o`0N0?ooo`0000<0oooo0000000000000`0000020?ooo`8000000`3oool4000000@0oooo00<00000 0?ooo`3oool0j03oool00`000000oooo0?ooo`0M0?ooo`000`3oool00`000000oooo0?ooo`070?oo o`030000003oool0oooo00D0oooo00<000000?ooo`3oool0j@3oool2000001d0oooo00030?ooo`03 0000003oool0oooo00P0oooo00<000000?ooo`3oool0103oool300000>/0oooo00<000000?ooo`3o ool06P3oool000<0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`030?ooo`030000 003oool0oooo0>`0oooo00<000000?ooo`3oool06@3oool000<0oooo00<000000?ooo`3oool01`3o ool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo0>d0oooo0P00000I0?ooo`000P3o ool2000000X0oooo0P0000050?ooo`030000003oool0oooo0>l0oooo00<000000?ooo`3oool05P3o ool001D0oooo00<000000?ooo`3oool0l03oool00`000000oooo0?ooo`0E0?ooo`005@3oool20000 0?80oooo00<000000?ooo`3oool0503oool001D0oooo00<000000?ooo`3oool0lP3oool00`000000 oooo0?ooo`0C0?ooo`005@3oool00`000000oooo0?ooo`3c0?ooo`030000003oool0oooo0180oooo 000E0?ooo`030000003oool0oooo0?@0oooo00<000000?ooo`3oool04@3oool001D0oooo00<00000 0?ooo`3oool0m@3oool00`000000oooo0?ooo`0@0?ooo`005@3oool200000?L0oooo00<000000?oo o`3oool03`3oool001D0oooo00<000000?ooo`3oool0m`3oool00`000000oooo0?ooo`0>0?ooo`00 5@3oool00`000000oooo0?ooo`3h0?ooo`030000003oool0oooo00d0oooo000E0?ooo`030000003o ool0oooo0?P0oooo00<000000?ooo`3oool03@3oool001D0oooo00<000000?ooo`3oool0n@3oool0 0`000000oooo0?ooo`0<0?ooo`005@3oool00`000000oooo0?ooo`3j0?ooo`030000003oool0oooo 00/0oooo000E0?ooo`800000o03oool00`000000oooo0?ooo`0:0?ooo`005@3oool00`000000oooo 0?ooo`3k0?ooo`030000003oool0oooo00X0oooo000E0?ooo`030000003oool0oooo0?`0oooo00<0 00000?ooo`3oool02@3oool000030?ooo`000000000000<000000P3oool2000000D0oooo0`000003 0?ooo`030000003oool0oooo0?`0oooo00<000000?ooo`3oool02@3oool000<0oooo00<000000?oo o`3oool02P3oool00`000000oooo0?ooo`020?ooo`030000003oool0oooo0?`0oooo00<000000?oo o`3oool02@3oool000<0oooo00<000000?ooo`3oool01`3oool5000000<0oooo0`00003m0?ooo`03 0000003oool0oooo00P0oooo00030?ooo`030000003oool0oooo00L0oooo00@000000?ooo`3oool0 0000103oool00`000000oooo0?ooo`3m0?ooo`030000003oool0oooo00P0oooo00030?ooo`030000 003oool0oooo00P0oooo00<000000?ooo`000000103oool00`000000oooo0?ooo`3n0?ooo`030000 003oool0oooo00L0oooo00020?ooo`8000002`3oool2000000@0oooo00<000000?ooo`3oool0oP3o ool00`000000oooo0?ooo`070?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`030000003oool0 oooo00H0oooo000E0?ooo`800000o`3oool10?ooo`030000003oool0oooo00H0oooo000E0?ooo`03 0000003oool0oooo0?l0oooo00<000000?ooo`3oool01P3oool001D0oooo00<000000?ooo`3oool0 o`3oool00`000000oooo0?ooo`060?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`40oooo00<0 00000?ooo`3oool01@3oool001D0oooo00<000000?ooo`3oool0o`3oool10?ooo`030000003oool0 oooo00D0oooo000E0?ooo`800000o`3oool20?ooo`030000003oool0oooo00D0oooo000E0?ooo`03 0000003oool0oooo0?l0oooo0@3oool00`000000oooo0?ooo`050?ooo`005@3oool00`000000oooo 0?ooo`3o0?ooo`40oooo00<000000?ooo`3oool01@3oool001D0oooo00<000000?ooo`3oool0o`3o ool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo 0?l0oooo2@3oool001D0oooo0P00003o0?ooo`X0oooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.259481, -0.119331, \ 0.0121241, 0.00947429}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(g1 = Plot[\((ArcSin[\(2 \[Sigma]\)\/\[Pi] - 1]\/\[Pi] + .5)\)* t[\[Pi]], {\[Sigma], 0, \[Pi]}, PlotStyle \[Rule] Hue[ .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 %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.303152 0.0147151 0.387408 [ [.17539 .00222 -9 -9 ] [.17539 .00222 9 0 ] [.32696 .00222 -3 -9 ] [.32696 .00222 3 0 ] [.47854 .00222 -9 -9 ] [.47854 .00222 9 0 ] [.63011 .00222 -3 -9 ] [.63011 .00222 3 0 ] [.78169 .00222 -9 -9 ] [.78169 .00222 9 0 ] [.93327 .00222 -3 -9 ] [.93327 .00222 3 0 ] [.01131 .0922 -18 -4.5 ] [.01131 .0922 0 4.5 ] [.01131 .16968 -18 -4.5 ] [.01131 .16968 0 4.5 ] [.01131 .24716 -18 -4.5 ] [.01131 .24716 0 4.5 ] [.01131 .32464 -18 -4.5 ] [.01131 .32464 0 4.5 ] [.01131 .40212 -6 -4.5 ] [.01131 .40212 0 4.5 ] [.01131 .4796 -18 -4.5 ] [.01131 .4796 0 4.5 ] [.01131 .55709 -18 -4.5 ] [.01131 .55709 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 .17539 .01472 m .17539 .02097 L s [(0.5)] .17539 .00222 0 1 Mshowa .32696 .01472 m .32696 .02097 L s [(1)] .32696 .00222 0 1 Mshowa .47854 .01472 m .47854 .02097 L s [(1.5)] .47854 .00222 0 1 Mshowa .63011 .01472 m .63011 .02097 L s [(2)] .63011 .00222 0 1 Mshowa .78169 .01472 m .78169 .02097 L s [(2.5)] .78169 .00222 0 1 Mshowa .93327 .01472 m .93327 .02097 L s [(3)] .93327 .00222 0 1 Mshowa .125 Mabswid .05412 .01472 m .05412 .01847 L s .08444 .01472 m .08444 .01847 L s .11476 .01472 m .11476 .01847 L s .14507 .01472 m .14507 .01847 L s .2057 .01472 m .2057 .01847 L s .23602 .01472 m .23602 .01847 L s .26633 .01472 m .26633 .01847 L s .29665 .01472 m .29665 .01847 L s .35728 .01472 m .35728 .01847 L s .38759 .01472 m .38759 .01847 L s .41791 .01472 m .41791 .01847 L s .44822 .01472 m .44822 .01847 L s .50885 .01472 m .50885 .01847 L s .53917 .01472 m .53917 .01847 L s .56948 .01472 m .56948 .01847 L s .5998 .01472 m .5998 .01847 L s .66043 .01472 m .66043 .01847 L s .69074 .01472 m .69074 .01847 L s .72106 .01472 m .72106 .01847 L s .75138 .01472 m .75138 .01847 L s .81201 .01472 m .81201 .01847 L s .84232 .01472 m .84232 .01847 L s .87264 .01472 m .87264 .01847 L s .90295 .01472 m .90295 .01847 L s .96358 .01472 m .96358 .01847 L s .9939 .01472 m .9939 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .0922 m .03006 .0922 L s [(0.2)] .01131 .0922 1 0 Mshowa .02381 .16968 m .03006 .16968 L s [(0.4)] .01131 .16968 1 0 Mshowa .02381 .24716 m .03006 .24716 L s [(0.6)] .01131 .24716 1 0 Mshowa .02381 .32464 m .03006 .32464 L s [(0.8)] .01131 .32464 1 0 Mshowa .02381 .40212 m .03006 .40212 L s [(1)] .01131 .40212 1 0 Mshowa .02381 .4796 m .03006 .4796 L s [(1.2)] .01131 .4796 1 0 Mshowa .02381 .55709 m .03006 .55709 L s [(1.4)] .01131 .55709 1 0 Mshowa .125 Mabswid .02381 .03409 m .02756 .03409 L s .02381 .05346 m .02756 .05346 L s .02381 .07283 m .02756 .07283 L s .02381 .11157 m .02756 .11157 L s .02381 .13094 m .02756 .13094 L s .02381 .15031 m .02756 .15031 L s .02381 .18905 m .02756 .18905 L s .02381 .20842 m .02756 .20842 L s .02381 .22779 m .02756 .22779 L s .02381 .26653 m .02756 .26653 L s .02381 .2859 m .02756 .2859 L s .02381 .30527 m .02756 .30527 L s .02381 .34401 m .02756 .34401 L s .02381 .36338 m .02756 .36338 L s .02381 .38275 m .02756 .38275 L s .02381 .42149 m .02756 .42149 L s .02381 .44086 m .02756 .44086 L s .02381 .46023 m .02756 .46023 L s .02381 .49898 m .02756 .49898 L s .02381 .51835 m .02756 .51835 L s .02381 .53772 m .02756 .53772 L s .02381 .57646 m .02756 .57646 L s .02381 .59583 m .02756 .59583 L s .02381 .6152 m .02756 .6152 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 1 .4 r .5 Mabswid .02381 .01479 m .02499 .02788 L .02605 .03292 L .02846 .04091 L .03279 .05116 L .04262 .06756 L .05281 .08045 L .06244 .09072 L .10458 .12546 L .14299 .15022 L .18386 .17301 L .22321 .19283 L .26105 .21055 L .30133 .22841 L .34011 .24489 L .38133 .26186 L .42104 .27784 L .45923 .29299 L .49988 .30901 L .53901 .32442 L .58059 .34092 L .62066 .35706 L .65921 .37293 L .70021 .39037 L .7397 .4079 L .77767 .42571 L .81809 .44613 L .857 .46788 L .89836 .49475 L .91906 .51066 L .93821 .52805 L .95662 .54949 L .96592 .56442 L .96847 .56961 L .97122 .5763 L .97248 .58 L .97381 .58466 L .97495 .58986 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`L0000000<00?mV0000 00000000o`000009000000005@3oool00`00ofH0oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo0@0000010?ooo`40oooo000E0?ooo`03003oIP3oool0oooo02H0oooo00<000000?ooo`3oool0 9P3oool00`000000oooo0?ooo`0W0?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool0 9P3oool00`000000oooo0?ooo`0V0?ooo`030000003oool0oooo0140oooo000E0?ooo`03003oIP3o ool0oooo0?l0oooo2@3oool001D0oooo00<00?mV0?ooo`3oool0o`3oool90?ooo`005@3oool00`00 00000?mV0?ooo`3o0?ooo`T0oooo000E0?ooo`0300000000ofH0oooo0?l0oooo2@3oool001D0oooo 00<00000003oIP3oool0o`3oool90?ooo`005@3oool00`0000000?mV0?ooo`3o0?ooo`T0oooo000E 0?ooo`030000003oool00?mV0?l0oooo2@3oool001D0oooo00<000000?ooo`00ofH0o`3oool90?oo o`005@3oool2000000030?ooo`00ofH0oooo0?l0oooo1`3oool001D0oooo00@000000?ooo`3oool0 0?mVo`3oool80?ooo`005@3oool01@000000oooo0?ooo`3oool00?mV0?l0oooo1`3oool001D0oooo 00D000000?ooo`3oool0oooo003oIP3o0?ooo`L0oooo000E0?ooo`030000003oool0oooo0080oooo 00<00?mV0?ooo`3oool0o`3oool40?ooo`005@3oool2000000@0oooo00<00?mV0?ooo`3oool0o`3o ool30?ooo`005@3oool00`000000oooo0?ooo`040?ooo`03003oIP3oool0oooo0?l0oooo0P3oool0 01D0oooo00<000000?ooo`3oool01@3oool00`00ofH0oooo0?ooo`3o0?ooo`40oooo00020?ooo`80 0000103oool2000000<0oooo100000040?ooo`030000003oool0oooo00H0oooo00<00?mV0?ooo`3o ool0o`3oool000050?ooo`000000oooo0?ooo`000000203oool00`000000oooo0?ooo`050?ooo`03 0000003oool0oooo00H0oooo00<00?mV0?ooo`3oool0o`3oool000050?ooo`000000oooo0?ooo`00 00002@3oool00`000000oooo0?ooo`040?ooo`<000001`3oool00`00ofH0oooo0?ooo`3n0?ooo`00 00D0oooo0000003oool0oooo0000000:0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3o ool0203oool00`00ofH0oooo0?ooo`3m0?ooo`0000D0oooo0000003oool0oooo000000080?ooo`04 0000003oool0oooo000000@0oooo00<000000?ooo`3oool02@3oool2003oI_d0oooo00020?ooo`80 00002P3oool2000000D0oooo00<000000?ooo`3oool02`3oool00`00ofH0oooo0?ooo`3j0?ooo`00 5@3oool00`000000oooo0?ooo`0<0?ooo`03003oIP3oool0oooo0?T0oooo000E0?ooo`030000003o ool0oooo00d0oooo0P00ofKi0?ooo`005@3oool200000100oooo00<00?mV0?ooo`3oool0mP3oool0 01D0oooo00<000000?ooo`3oool0403oool00`00ofH0oooo0?ooo`3e0?ooo`005@3oool00`000000 oooo0?ooo`0A0?ooo`800?mVm@3oool001D0oooo00<000000?ooo`3oool04`3oool00`00ofH0oooo 0?ooo`3b0?ooo`005@3oool00`000000oooo0?ooo`0D0?ooo`800?mVlP3oool001D0oooo0P00000G 0?ooo`03003oIP3oool0oooo0>l0oooo000E0?ooo`030000003oool0oooo01L0oooo00<00?mV0?oo o`3oool0kP3oool001D0oooo00<000000?ooo`3oool0603oool2003oI^h0oooo000E0?ooo`030000 003oool0oooo01X0oooo00<00?mV0?ooo`3oool0j`3oool001D0oooo00<000000?ooo`3oool06`3o ool2003oI^/0oooo000E0?ooo`8000007P3oool00`00ofH0oooo0?ooo`3X0?ooo`005@3oool00`00 0000oooo0?ooo`0N0?ooo`800?mVj03oool001D0oooo00<000000?ooo`3oool0803oool2003oI^H0 oooo00020?ooo`800000103oool2000000D0oooo0`0000030?ooo`030000003oool0oooo0280oooo 0P00ofKT0?ooo`0000D0oooo0000003oool0oooo0000000;0?ooo`030000003oool0oooo0080oooo 00<000000?ooo`3oool0903oool2003oI^80oooo00001@3oool000000?ooo`3oool0000000P0oooo 1@0000030?ooo`<000009P3oool2003oI^00oooo00001@3oool000000?ooo`3oool0000000P0oooo 00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`0X0?ooo`03003oIP3oool0oooo0=d0 oooo00001@3oool000000?ooo`3oool0000000T0oooo00<000000?ooo`000000103oool00`000000 oooo0?ooo`0Y0?ooo`800?mVg@3oool00080oooo0P00000;0?ooo`800000103oool00`000000oooo 0?ooo`0[0?ooo`800?mVf`3oool001D0oooo00<000000?ooo`3oool0;@3oool2003oI]T0oooo000E 0?ooo`030000003oool0oooo02l0oooo0P00ofKG0?ooo`005@3oool200000380oooo0P00ofKE0?oo o`005@3oool00`000000oooo0?ooo`0c0?ooo`800?mVd`3oool001D0oooo00<000000?ooo`3oool0 =@3oool2003oI]40oooo000E0?ooo`030000003oool0oooo03L0oooo0`00ofK>0?ooo`005@3oool0 0`000000oooo0?ooo`0j0?ooo`800?mVc03oool001D0oooo0P00000m0?ooo`<00?mVb@3oool001D0 oooo00<000000?ooo`3oool0?`3oool2003oI/L0oooo000E0?ooo`030000003oool0oooo0440oooo 0P00ofK50?ooo`005@3oool00`000000oooo0?ooo`130?ooo`800?mV``3oool001D0oooo00<00000 0?ooo`3oool0A@3oool2003oI/40oooo000E0?ooo`800000B03oool3003oI[h0oooo000E0?ooo`03 0000003oool0oooo04X0oooo0P00ofJl0?ooo`005@3oool00`000000oooo0?ooo`1<0?ooo`800?mV ^P3oool00080oooo0P0000040?ooo`8000000`3oool3000000D0oooo00<000000?ooo`3oool0CP3o ool2003oI[P0oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000 103oool00`000000oooo0?ooo`1@0?ooo`800?mV]P3oool000050?ooo`000000oooo0?ooo`000000 203oool010000000oooo0?ooo`0000040?ooo`<00000DP3oool3003oI[<0oooo00001@3oool00000 0?ooo`3oool0000000P0oooo0`0000050?ooo`030000003oool0oooo05D0oooo0`00ofJ`0?ooo`00 00D0oooo0000003oool0oooo000000090?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3o ool0F03oool2003oIZh0oooo00020?ooo`8000002P3oool3000000@0oooo00<000000?ooo`3oool0 FP3oool3003oIZ/0oooo000E0?ooo`030000003oool0oooo05d0oooo0`00ofJX0?ooo`005@3oool0 0`000000oooo0?ooo`1P0?ooo`800?mVYP3oool001D0oooo0P00001S0?ooo`800?mVY03oool001D0 oooo00<000000?ooo`3oool0I03oool2003oIZ80oooo000E0?ooo`030000003oool0oooo06H0oooo 0P00ofJP0?ooo`005@3oool00`000000oooo0?ooo`1X0?ooo`<00?mVW@3oool001D0oooo00<00000 0?ooo`3oool0J`3oool2003oIY/0oooo000E0?ooo`800000KP3oool3003oIYP0oooo000E0?ooo`03 0000003oool0oooo0700oooo0P00ofJF0?ooo`005@3oool00`000000oooo0?ooo`1b0?ooo`<00?mV T`3oool001D0oooo00<000000?ooo`3oool0M@3oool3003oIY00oooo000E0?ooo`030000003oool0 oooo07P0oooo0P00ofJ>0?ooo`005@3oool2000007/0oooo0`00ofJ;0?ooo`005@3oool00`000000 oooo0?ooo`1m0?ooo`<00?mVR03oool001D0oooo00<000000?ooo`3oool0P03oool3003oIXD0oooo 00020?ooo`800000103oool2000000@0oooo0P0000050?ooo`030000003oool0oooo08<0oooo0P00 ofJ30?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000003oool0oooo000000@0oooo 00<000000?ooo`3oool0Q@3oool3003oIX00oooo00001@3oool000000?ooo`3oool0000000P0oooo 00@000000?ooo`3oool00000103oool3000008P0oooo0`00ofIm0?ooo`0000D0oooo0000003oool0 oooo000000090?ooo`8000001@3oool00`000000oooo0?ooo`2;0?ooo`800?mVN`3oool000050?oo o`000000oooo0?ooo`000000203oool010000000oooo0?ooo`0000040?ooo`030000003oool0oooo 08d0oooo0P00ofIi0?ooo`000P3oool2000000X0oooo0P0000050?ooo`030000003oool0oooo08l0 oooo0P00ofIg0?ooo`005@3oool00`000000oooo0?ooo`2A0?ooo`800?mVM@3oool001D0oooo00<0 00000?ooo`3oool0T`3oool3003oIW80oooo000E0?ooo`800000U`3oool3003oIVl0oooo000E0?oo o`030000003oool0oooo09T0oooo0P00ofI]0?ooo`005@3oool00`000000oooo0?ooo`2K0?ooo`<0 0?mVJP3oool001D0oooo00<000000?ooo`3oool0WP3oool3003oIVL0oooo000E0?ooo`030000003o ool0oooo0:40oooo0P00ofIU0?ooo`005@3oool200000:@0oooo0P00ofIS0?ooo`005@3oool00`00 0000oooo0?ooo`2U0?ooo`800?mVH@3oool001D0oooo00<000000?ooo`3oool0Y`3oool2003oIUl0 oooo000E0?ooo`030000003oool0oooo0:T0oooo0`00ofIL0?ooo`005@3oool00`000000oooo0?oo o`2/0?ooo`<00?mVF@3oool001D0oooo0P00002`0?ooo`800?mVE`3oool001D0oooo00<000000?oo o`3oool0/@3oool3003oIU@0oooo000E0?ooo`030000003oool0oooo0;@0oooo0`00ofIA0?ooo`00 5@3oool00`000000oooo0?ooo`2g0?ooo`800?mVC`3oool000d0oooo1@0000030?ooo`030000003o ool0oooo0;T0oooo0P00ofI=0?ooo`003`3oool00`000000oooo0?ooo`030?ooo`030000003oool0 oooo0;/0oooo0P00ofI;0?ooo`003`3oool00`000000oooo0?ooo`030?ooo`<00000_@3oool2003o ITT0oooo000?0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0_`3oool2003oITL0 oooo000?0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0`@3oool2003oITD0oooo 000>0?ooo`8000001@3oool00`000000oooo0?ooo`330?ooo`800?mV@`3oool001D0oooo00<00000 0?ooo`3oool0a@3oool2003oIT40oooo000E0?ooo`800000b03oool2003oISl0oooo000E0?ooo`03 0000003oool0oooo0`3oool001D0oooo00<000000?ooo`3oool0c@3oool2003oIST0oooo000E0?ooo`030000003oool0 oooo0<0oooo00<00?mV0?ooo`3oool08P3oool0 00<0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 0>@0oooo00<00?mV0?ooo`3oool08@3oool000<0oooo00<000000?ooo`3oool0203oool00`000000 oooo0?ooo`040?ooo`<00000i@3oool2003oIR40oooo00030?ooo`030000003oool0oooo00T0oooo 00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`3W0?ooo`03003oIP3oool0oooo01h0oooo 00030?ooo`030000003oool0oooo00L0oooo00@000000?ooo`3oool00000103oool00`000000oooo 0?ooo`3X0?ooo`03003oIP3oool0oooo01d0oooo00020?ooo`8000002P3oool2000000D0oooo00<0 00000?ooo`3oool0j@3oool2003oIQd0oooo000E0?ooo`030000003oool0oooo0>/0oooo00<00?mV 0?ooo`3oool06P3oool001D0oooo0P00003]0?ooo`03003oIP3oool0oooo01T0oooo000E0?ooo`03 0000003oool0oooo0>d0oooo0P00ofHI0?ooo`005@3oool00`000000oooo0?ooo`3_0?ooo`03003o IP3oool0oooo01H0oooo000E0?ooo`030000003oool0oooo0?00oooo00<00?mV0?ooo`3oool05@3o ool001D0oooo00<000000?ooo`3oool0l@3oool00`00ofH0oooo0?ooo`0D0?ooo`005@3oool20000 0?<0oooo00<00?mV0?ooo`3oool04`3oool001D0oooo00<000000?ooo`3oool0l`3oool2003oIQ<0 oooo000E0?ooo`030000003oool0oooo0?D0oooo00<00?mV0?ooo`3oool0403oool001D0oooo00<0 00000?ooo`3oool0mP3oool00`00ofH0oooo0?ooo`0?0?ooo`005@3oool00`000000oooo0?ooo`3g 0?ooo`03003oIP3oool0oooo00h0oooo000E0?ooo`800000n@3oool00`00ofH0oooo0?ooo`0=0?oo o`005@3oool00`000000oooo0?ooo`3h0?ooo`03003oIP3oool0oooo00d0oooo000E0?ooo`030000 003oool0oooo0?T0oooo00<00?mV0?ooo`3oool0303oool001D0oooo00<000000?ooo`3oool0nP3o ool00`00ofH0oooo0?ooo`0;0?ooo`0000<0oooo0000000000000`0000020?ooo`8000001@3oool3 000000<0oooo00<000000?ooo`3oool0n`3oool00`00ofH0oooo0?ooo`0:0?ooo`000`3oool00`00 0000oooo0?ooo`0:0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool0n`3oool00`00 ofH0oooo0?ooo`0:0?ooo`000`3oool00`000000oooo0?ooo`070?ooo`D000000`3oool300000?`0 oooo00<00?mV0?ooo`3oool02@3oool000<0oooo00<000000?ooo`3oool01`3oool010000000oooo 0?ooo`0000040?ooo`030000003oool0oooo0?`0oooo00<00?mV0?ooo`3oool02@3oool000<0oooo 00<000000?ooo`3oool0203oool00`000000oooo000000040?ooo`030000003oool0oooo0?d0oooo 00<00?mV0?ooo`3oool0203oool00080oooo0P00000;0?ooo`800000103oool00`000000oooo0?oo o`3n0?ooo`03003oIP3oool0oooo00L0oooo000E0?ooo`030000003oool0oooo0?h0oooo00<00?mV 0?ooo`3oool01`3oool001D0oooo0P00003o0?ooo`40oooo00<00?mV0?ooo`3oool01P3oool001D0 oooo00<000000?ooo`3oool0o`3oool00`00ofH0oooo0?ooo`060?ooo`005@3oool00`000000oooo 0?ooo`3o0?ooo`03003oIP3oool0oooo00H0oooo000E0?ooo`030000003oool0oooo0?l0oooo00<0 0?mV0?ooo`3oool01P3oool001D0oooo00<000000?ooo`3oool0o`3oool10?ooo`03003oIP3oool0 oooo00D0oooo000E0?ooo`800000o`3oool20?ooo`03003oIP3oool0oooo00D0oooo000E0?ooo`03 0000003oool0oooo0?l0oooo0@3oool00`00ofH0oooo0?ooo`050?ooo`005@3oool00`000000oooo 0?ooo`3o0?ooo`40oooo00<00?mV0?ooo`3oool01@3oool001D0oooo00<000000?ooo`3oool0o`3o ool90?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo 0?l0oooo2@3oool001D0oooo0P00003o0?ooo`X0oooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.259483, -0.119495, \ 0.0121242, 0.00948732}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(g2 = Plot[\((ArcSin[\(Sin[2 \[Sigma]]\/a + 2 \[Sigma]\)\/\[Pi] - 1]\/\[Pi] \ + .5)\)*t[\[Pi]], {\[Sigma], 0, \[Pi]}, PlotStyle \[Rule] Hue[ .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 %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.303152 0.0147151 0.387415 [ [.17539 .00222 -9 -9 ] [.17539 .00222 9 0 ] [.32696 .00222 -3 -9 ] [.32696 .00222 3 0 ] [.47854 .00222 -9 -9 ] [.47854 .00222 9 0 ] [.63011 .00222 -3 -9 ] [.63011 .00222 3 0 ] [.78169 .00222 -9 -9 ] [.78169 .00222 9 0 ] [.93327 .00222 -3 -9 ] [.93327 .00222 3 0 ] [.01131 .0922 -18 -4.5 ] [.01131 .0922 0 4.5 ] [.01131 .16968 -18 -4.5 ] [.01131 .16968 0 4.5 ] [.01131 .24716 -18 -4.5 ] [.01131 .24716 0 4.5 ] [.01131 .32465 -18 -4.5 ] [.01131 .32465 0 4.5 ] [.01131 .40213 -6 -4.5 ] [.01131 .40213 0 4.5 ] [.01131 .47961 -18 -4.5 ] [.01131 .47961 0 4.5 ] [.01131 .5571 -18 -4.5 ] [.01131 .5571 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 .17539 .01472 m .17539 .02097 L s [(0.5)] .17539 .00222 0 1 Mshowa .32696 .01472 m .32696 .02097 L s [(1)] .32696 .00222 0 1 Mshowa .47854 .01472 m .47854 .02097 L s [(1.5)] .47854 .00222 0 1 Mshowa .63011 .01472 m .63011 .02097 L s [(2)] .63011 .00222 0 1 Mshowa .78169 .01472 m .78169 .02097 L s [(2.5)] .78169 .00222 0 1 Mshowa .93327 .01472 m .93327 .02097 L s [(3)] .93327 .00222 0 1 Mshowa .125 Mabswid .05412 .01472 m .05412 .01847 L s .08444 .01472 m .08444 .01847 L s .11476 .01472 m .11476 .01847 L s .14507 .01472 m .14507 .01847 L s .2057 .01472 m .2057 .01847 L s .23602 .01472 m .23602 .01847 L s .26633 .01472 m .26633 .01847 L s .29665 .01472 m .29665 .01847 L s .35728 .01472 m .35728 .01847 L s .38759 .01472 m .38759 .01847 L s .41791 .01472 m .41791 .01847 L s .44822 .01472 m .44822 .01847 L s .50885 .01472 m .50885 .01847 L s .53917 .01472 m .53917 .01847 L s .56948 .01472 m .56948 .01847 L s .5998 .01472 m .5998 .01847 L s .66043 .01472 m .66043 .01847 L s .69074 .01472 m .69074 .01847 L s .72106 .01472 m .72106 .01847 L s .75138 .01472 m .75138 .01847 L s .81201 .01472 m .81201 .01847 L s .84232 .01472 m .84232 .01847 L s .87264 .01472 m .87264 .01847 L s .90295 .01472 m .90295 .01847 L s .96358 .01472 m .96358 .01847 L s .9939 .01472 m .9939 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .0922 m .03006 .0922 L s [(0.2)] .01131 .0922 1 0 Mshowa .02381 .16968 m .03006 .16968 L s [(0.4)] .01131 .16968 1 0 Mshowa .02381 .24716 m .03006 .24716 L s [(0.6)] .01131 .24716 1 0 Mshowa .02381 .32465 m .03006 .32465 L s [(0.8)] .01131 .32465 1 0 Mshowa .02381 .40213 m .03006 .40213 L s [(1)] .01131 .40213 1 0 Mshowa .02381 .47961 m .03006 .47961 L s [(1.2)] .01131 .47961 1 0 Mshowa .02381 .5571 m .03006 .5571 L s [(1.4)] .01131 .5571 1 0 Mshowa .125 Mabswid .02381 .03409 m .02756 .03409 L s .02381 .05346 m .02756 .05346 L s .02381 .07283 m .02756 .07283 L s .02381 .11157 m .02756 .11157 L s .02381 .13094 m .02756 .13094 L s .02381 .15031 m .02756 .15031 L s .02381 .18905 m .02756 .18905 L s .02381 .20842 m .02756 .20842 L s .02381 .22779 m .02756 .22779 L s .02381 .26653 m .02756 .26653 L s .02381 .28591 m .02756 .28591 L s .02381 .30528 m .02756 .30528 L s .02381 .34402 m .02756 .34402 L s .02381 .36339 m .02756 .36339 L s .02381 .38276 m .02756 .38276 L s .02381 .4215 m .02756 .4215 L s .02381 .44087 m .02756 .44087 L s .02381 .46024 m .02756 .46024 L s .02381 .49898 m .02756 .49898 L s .02381 .51835 m .02756 .51835 L s .02381 .53773 m .02756 .53773 L s .02381 .57647 m .02756 .57647 L s .02381 .59584 m .02756 .59584 L s .02381 .61521 m .02756 .61521 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .8 1 0 r .5 Mabswid .02381 .0148 m .02499 .02969 L .02605 .03542 L .02846 .04452 L .03279 .05617 L .04262 .07485 L .05281 .08953 L .06244 .10122 L .10458 .14052 L .14299 .16801 L .18386 .19251 L .22321 .2129 L .26105 .23022 L .30133 .24664 L .34011 .26082 L .38133 .2745 L .42104 .28664 L .45923 .29766 L .49988 .30903 L .53901 .31996 L .58059 .33196 L .62066 .34425 L .65921 .35706 L .70021 .37208 L .7397 .38823 L .77767 .40565 L .81809 .4267 L .857 .45011 L .89836 .47995 L .91906 .49791 L .93821 .51765 L .95662 .54206 L .96592 .55906 L .96847 .56497 L .97122 .57258 L .97248 .57679 L .97381 .5821 L .97495 .58801 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`L0000000<0c?l00000 00000000o`000009000000005@3oool00`3h0oooo000E0?ooo`030000003oool0oooo01P0oooo00<0c?l00?ooo`3oool0k@3oool001D0 oooo00<000000?ooo`3oool06@3oool00`3P0oooo00001@3oool000000?ooo`3oool0000000P0oooo 00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`0N0?ooo`80c?l0j03oool000050?oo o`000000oooo0?ooo`0000002@3oool00`000000oooo000000040?ooo`030000003oool0oooo0200 oooo00<0c?l00?ooo`3oool0i@3oool00080oooo0P00000;0?ooo`800000103oool00`000000oooo 0?ooo`0Q0?ooo`80c?l0i@3oool001D0oooo00<000000?ooo`3oool08`3oool20<0oooo000E 0?ooo`030000003oool0oooo02D0oooo00<0c?l00?ooo`3oool0h03oool001D0oooo0P00000W0?oo o`80c?l0h03oool001D0oooo00<000000?ooo`3oool0:03oool200?ooo`005@3oool2000003/0oooo0P300oooo00<0 c?l00?ooo`3oool09@3oool001D0oooo00<000000?ooo`3oool0h@3oool20D0oooo0P3h0oooo00<0c?l00?ooo`3oool05`3oool001D0oooo00<00000 0?ooo`3oool0k`3oool00`3"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.259483, -0.119493, \ 0.0121242, 0.00948715}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(g3 = Plot[\((ArcSin[\(Sin[4 \[Sigma]]\/a\^3 + Sin[2 \[Sigma]]\/a + 2 \ \[Sigma]\)\/\[Pi] - 1]\/\[Pi] + .5)\)*t[\[Pi]], {\[Sigma], 0, \[Pi]}, PlotStyle \[Rule] Hue[ .6]]\)], "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 0.0238095 0.303152 0.0147151 0.387416 [ [.17539 .00222 -9 -9 ] [.17539 .00222 9 0 ] [.32696 .00222 -3 -9 ] [.32696 .00222 3 0 ] [.47854 .00222 -9 -9 ] [.47854 .00222 9 0 ] [.63011 .00222 -3 -9 ] [.63011 .00222 3 0 ] [.78169 .00222 -9 -9 ] [.78169 .00222 9 0 ] [.93327 .00222 -3 -9 ] [.93327 .00222 3 0 ] [.01131 .0922 -18 -4.5 ] [.01131 .0922 0 4.5 ] [.01131 .16968 -18 -4.5 ] [.01131 .16968 0 4.5 ] [.01131 .24716 -18 -4.5 ] [.01131 .24716 0 4.5 ] [.01131 .32465 -18 -4.5 ] [.01131 .32465 0 4.5 ] [.01131 .40213 -6 -4.5 ] [.01131 .40213 0 4.5 ] [.01131 .47961 -18 -4.5 ] [.01131 .47961 0 4.5 ] [.01131 .5571 -18 -4.5 ] [.01131 .5571 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 .17539 .01472 m .17539 .02097 L s [(0.5)] .17539 .00222 0 1 Mshowa .32696 .01472 m .32696 .02097 L s [(1)] .32696 .00222 0 1 Mshowa .47854 .01472 m .47854 .02097 L s [(1.5)] .47854 .00222 0 1 Mshowa .63011 .01472 m .63011 .02097 L s [(2)] .63011 .00222 0 1 Mshowa .78169 .01472 m .78169 .02097 L s [(2.5)] .78169 .00222 0 1 Mshowa .93327 .01472 m .93327 .02097 L s [(3)] .93327 .00222 0 1 Mshowa .125 Mabswid .05412 .01472 m .05412 .01847 L s .08444 .01472 m .08444 .01847 L s .11476 .01472 m .11476 .01847 L s .14507 .01472 m .14507 .01847 L s .2057 .01472 m .2057 .01847 L s .23602 .01472 m .23602 .01847 L s .26633 .01472 m .26633 .01847 L s .29665 .01472 m .29665 .01847 L s .35728 .01472 m .35728 .01847 L s .38759 .01472 m .38759 .01847 L s .41791 .01472 m .41791 .01847 L s .44822 .01472 m .44822 .01847 L s .50885 .01472 m .50885 .01847 L s .53917 .01472 m .53917 .01847 L s .56948 .01472 m .56948 .01847 L s .5998 .01472 m .5998 .01847 L s .66043 .01472 m .66043 .01847 L s .69074 .01472 m .69074 .01847 L s .72106 .01472 m .72106 .01847 L s .75138 .01472 m .75138 .01847 L s .81201 .01472 m .81201 .01847 L s .84232 .01472 m .84232 .01847 L s .87264 .01472 m .87264 .01847 L s .90295 .01472 m .90295 .01847 L s .96358 .01472 m .96358 .01847 L s .9939 .01472 m .9939 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .0922 m .03006 .0922 L s [(0.2)] .01131 .0922 1 0 Mshowa .02381 .16968 m .03006 .16968 L s [(0.4)] .01131 .16968 1 0 Mshowa .02381 .24716 m .03006 .24716 L s [(0.6)] .01131 .24716 1 0 Mshowa .02381 .32465 m .03006 .32465 L s [(0.8)] .01131 .32465 1 0 Mshowa .02381 .40213 m .03006 .40213 L s [(1)] .01131 .40213 1 0 Mshowa .02381 .47961 m .03006 .47961 L s [(1.2)] .01131 .47961 1 0 Mshowa .02381 .5571 m .03006 .5571 L s [(1.4)] .01131 .5571 1 0 Mshowa .125 Mabswid .02381 .03409 m .02756 .03409 L s .02381 .05346 m .02756 .05346 L s .02381 .07283 m .02756 .07283 L s .02381 .11157 m .02756 .11157 L s .02381 .13094 m .02756 .13094 L s .02381 .15031 m .02756 .15031 L s .02381 .18905 m .02756 .18905 L s .02381 .20842 m .02756 .20842 L s .02381 .22779 m .02756 .22779 L s .02381 .26654 m .02756 .26654 L s .02381 .28591 m .02756 .28591 L s .02381 .30528 m .02756 .30528 L s .02381 .34402 m .02756 .34402 L s .02381 .36339 m .02756 .36339 L s .02381 .38276 m .02756 .38276 L s .02381 .4215 m .02756 .4215 L s .02381 .44087 m .02756 .44087 L s .02381 .46024 m .02756 .46024 L s .02381 .49899 m .02756 .49899 L s .02381 .51836 m .02756 .51836 L s .02381 .53773 m .02756 .53773 L s .02381 .57647 m .02756 .57647 L s .02381 .59584 m .02756 .59584 L s .02381 .61521 m .02756 .61521 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 .4 1 r .5 Mabswid .02381 .0148 m .02499 .02998 L .02605 .03582 L .02846 .04509 L .03279 .05698 L .04262 .07601 L .05281 .09096 L .06244 .10285 L .10458 .14262 L .14299 .17006 L .18386 .19409 L .22321 .21374 L .26105 .23023 L .30133 .24585 L .34011 .25949 L .38133 .27297 L .42104 .28533 L .45923 .29689 L .49988 .30902 L .53901 .32071 L .58059 .33329 L .62066 .34578 L .65921 .3584 L .70021 .37284 L .7397 .38819 L .77767 .40479 L .81809 .42509 L .857 .44806 L .89836 .47786 L .91906 .496 L .93821 .51603 L .95662 .54088 L .96592 .5582 L .96847 .56423 L .97122 .57199 L .97248 .57628 L .97381 .58169 L .97495 .58771 L .97619 .60332 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`L0000000<006Ko0000 00000000o`000009000000005@3oool00`00I_l0oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00D0 oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00D0 oooo0@0000010?ooo`40oooo000E0?ooo`03001Vo`3oool0oooo02H0oooo00<000000?ooo`3oool0 9P3oool00`000000oooo0?ooo`0W0?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool0 9P3oool00`000000oooo0?ooo`0V0?ooo`030000003oool0oooo0140oooo000E0?ooo`03001Vo`3o ool0oooo0?l0oooo2@3oool001D0oooo00<006Ko0?ooo`3oool0o`3oool90?ooo`005@3oool00`00 I_l000000?ooo`3o0?ooo`T0oooo000E0?ooo`0300000000I_l0oooo0?l0oooo2@3oool001D0oooo 00<00000001Vo`3oool0o`3oool90?ooo`005@3oool00`00000006Ko0?ooo`3o0?ooo`T0oooo000E 0?ooo`0300000000I_l0oooo0?l0oooo2@3oool001D0oooo00<00000001Vo`3oool0o`3oool90?oo o`005@3oool200000003001Vo`3oool0oooo0?l0oooo1`3oool001D0oooo00<000000?ooo`00I_l0 o`3oool90?ooo`005@3oool010000000oooo0?ooo`00I_oo0?ooo`P0oooo000E0?ooo`040000003o ool0oooo001Vool0oooo203oool001D0oooo00D000000?ooo`3oool0oooo001Vo`3o0?ooo`L0oooo 000E0?ooo`8000000P3oool00`00I_l0oooo0?ooo`3o0?ooo`D0oooo000E0?ooo`030000003oool0 oooo0080oooo00<006Ko0?ooo`3oool0o`3oool40?ooo`005@3oool00`000000oooo0?ooo`030?oo o`03001Vo`3oool0oooo0?l0oooo0`3oool00080oooo0P0000040?ooo`8000000`3oool4000000@0 oooo00<000000?ooo`3oool00`3oool00`00I_l0oooo0?ooo`3o0?ooo`<0oooo00001@3oool00000 0?ooo`3oool0000000P0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`040?ooo`03 001Vo`3oool0oooo0?l0oooo0P3oool000050?ooo`000000oooo0?ooo`0000002@3oool00`000000 oooo0?ooo`040?ooo`<000001@3oool00`00I_l0oooo0?ooo`3o0?ooo`40oooo00001@3oool00000 0?ooo`3oool0000000X0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`060?ooo`03 001Vo`3oool0oooo0?l0oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3o ool00000103oool00`000000oooo0?ooo`060?ooo`03001Vo`3oool0oooo0?l0oooo00020?ooo`80 00002P3oool2000000D0oooo00<000000?ooo`3oool01`3oool00`00I_l0oooo0?ooo`3n0?ooo`00 5@3oool00`000000oooo0?ooo`080?ooo`03001Vo`3oool0oooo0?d0oooo000E0?ooo`030000003o ool0oooo00T0oooo00<006Ko0?ooo`3oool0o03oool001D0oooo0P00000;0?ooo`03001Vo`3oool0 oooo0?/0oooo000E0?ooo`030000003oool0oooo00/0oooo00<006Ko0?ooo`3oool0nP3oool001D0 oooo00<000000?ooo`3oool0303oool00`00I_l0oooo0?ooo`3i0?ooo`005@3oool00`000000oooo 0?ooo`0=0?ooo`8006Kon@3oool001D0oooo00<000000?ooo`3oool03`3oool00`00I_l0oooo0?oo o`3f0?ooo`005@3oool200000140oooo00<006Ko0?ooo`3oool0m@3oool001D0oooo00<000000?oo o`3oool04@3oool00`00I_l0oooo0?ooo`3d0?ooo`005@3oool00`000000oooo0?ooo`0B0?ooo`03 001Vo`3oool0oooo0?<0oooo000E0?ooo`030000003oool0oooo01<0oooo00<006Ko0?ooo`3oool0 lP3oool001D0oooo00<000000?ooo`3oool0503oool2001Voo80oooo000E0?ooo`8000005`3oool0 0`00I_l0oooo0?ooo`3_0?ooo`005@3oool00`000000oooo0?ooo`0G0?ooo`03001Vo`3oool0oooo 0>h0oooo000E0?ooo`030000003oool0oooo01P0oooo0P00I_o^0?ooo`000P3oool2000000@0oooo 0P0000050?ooo`<000000`3oool00`000000oooo0?ooo`0J0?ooo`03001Vo`3oool0oooo0>/0oooo 00001@3oool000000?ooo`3oool0000000/0oooo00<000000?ooo`3oool00P3oool00`000000oooo 0?ooo`0K0?ooo`8006Koj`3oool000050?ooo`000000oooo0?ooo`000000203oool5000000<0oooo 0`00000M0?ooo`03001Vo`3oool0oooo0>P0oooo00001@3oool000000?ooo`3oool0000000P0oooo 00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`0N0?ooo`8006Koj03oool000050?oo o`000000oooo0?ooo`0000002@3oool00`000000oooo000000040?ooo`030000003oool0oooo0200 oooo00<006Ko0?ooo`3oool0i@3oool00080oooo0P00000;0?ooo`800000103oool00`000000oooo 0?ooo`0Q0?ooo`8006Koi@3oool001D0oooo00<000000?ooo`3oool08`3oool2001Von<0oooo000E 0?ooo`030000003oool0oooo02D0oooo00<006Ko0?ooo`3oool0h03oool001D0oooo0P00000W0?oo o`8006Koh03oool001D0oooo00<000000?ooo`3oool0:03oool2001Vomh0oooo000E0?ooo`030000 003oool0oooo02X0oooo0P00I_oL0?ooo`005@3oool00`000000oooo0?ooo`0/0?ooo`8006KofP3o ool001D0oooo00<000000?ooo`3oool0;P3oool2001VomP0oooo000E0?ooo`800000<@3oool2001V omH0oooo000E0?ooo`030000003oool0oooo0380oooo0P00I_oD0?ooo`005@3oool00`000000oooo 0?ooo`0d0?ooo`8006KodP3oool001D0oooo00<000000?ooo`3oool0=P3oool2001Vom00oooo000E 0?ooo`030000003oool0oooo03P0oooo0P00I_o>0?ooo`005@3oool2000003/0oooo0P00I_o<0?oo o`005@3oool00`000000oooo0?ooo`0l0?ooo`<006Kob@3oool001D0oooo00<000000?ooo`3oool0 ?`3oool3001VolH0oooo00020?ooo`800000103oool2000000<0oooo0`0000050?ooo`030000003o ool0oooo0480oooo0P00I_o40?ooo`0000D0oooo0000003oool0oooo000000080?ooo`040000003o ool0oooo000000@0oooo00<000000?ooo`3oool0A03oool3001Vol40oooo00001@3oool000000?oo o`3oool0000000P0oooo00@000000?ooo`3oool00000103oool3000004L0oooo0`00I_nn0?ooo`00 00D0oooo0000003oool0oooo000000080?ooo`<000001@3oool00`000000oooo0?ooo`1:0?ooo`<0 06Ko^`3oool000050?ooo`000000oooo0?ooo`0000002@3oool00`000000oooo0?ooo`040?ooo`03 0000003oool0oooo04d0oooo0P00I_ni0?ooo`000P3oool2000000X0oooo0`0000040?ooo`030000 003oool0oooo04l0oooo0`00I_nf0?ooo`005@3oool00`000000oooo0?ooo`1B0?ooo`<006Ko/`3o ool001D0oooo00<000000?ooo`3oool0E@3oool4001Vojl0oooo000E0?ooo`800000FP3oool4001V oj/0oooo000E0?ooo`030000003oool0oooo05d0oooo0`00I_nX0?ooo`005@3oool00`000000oooo 0?ooo`1P0?ooo`<006KoY@3oool001D0oooo00<000000?ooo`3oool0H`3oool2001Voj<0oooo000E 0?ooo`030000003oool0oooo06D0oooo0`00I_nP0?ooo`005@3oool2000006T0oooo0`00I_nM0?oo o`005@3oool00`000000oooo0?ooo`1[0?ooo`<006KoVP3oool001D0oooo00<000000?ooo`3oool0 KP3oool4001VoiH0oooo000E0?ooo`030000003oool0oooo0780oooo0`00I_nC0?ooo`005@3oool0 0`000000oooo0?ooo`1e0?ooo`@006KoS`3oool001D0oooo0P00001j0?ooo`@006KoR`3oool001D0 oooo00<000000?ooo`3oool0O@3oool3001VohP0oooo000E0?ooo`030000003oool0oooo0800oooo 1000I_n40?ooo`000P3oool2000000@0oooo0P0000040?ooo`8000001@3oool00`000000oooo0?oo o`240?ooo`@006KoP03oool000050?ooo`000000oooo0?ooo`000000203oool010000000oooo0?oo o`0000040?ooo`030000003oool0oooo08P0oooo0`00I_mm0?ooo`0000D0oooo0000003oool0oooo 000000080?ooo`040000003oool0oooo000000@0oooo0`00002;0?ooo`<006KoNP3oool000050?oo o`000000oooo0?ooo`0000002@3oool2000000D0oooo00<000000?ooo`3oool0SP3oool2001VogP0 oooo00001@3oool000000?ooo`3oool0000000P0oooo00@000000?ooo`3oool00000103oool00`00 0000oooo0?ooo`2@0?ooo`<006KoM@3oool00080oooo0P00000:0?ooo`8000001@3oool00`000000 oooo0?ooo`2C0?ooo`<006KoLP3oool001D0oooo00<000000?ooo`3oool0UP3oool4001Vofh0oooo 000E0?ooo`030000003oool0oooo09X0oooo1000I_mZ0?ooo`005@3oool2000009l0oooo0`00I_mW 0?ooo`005@3oool00`000000oooo0?ooo`2Q0?ooo`<006KoI03oool001D0oooo00<000000?ooo`3o ool0Y03oool2001Vof80oooo000E0?ooo`030000003oool0oooo0:H0oooo0`00I_mO0?ooo`005@3o ool00`000000oooo0?ooo`2Y0?ooo`<006KoG03oool001D0oooo0P00002]0?ooo`<006KoF@3oool0 01D0oooo00<000000?ooo`3oool0[`3oool2001VoeL0oooo000E0?ooo`030000003oool0oooo0;40 oooo0`00I_mD0?ooo`005@3oool00`000000oooo0?ooo`2d0?ooo`<006KoD@3oool001D0oooo00<0 00000?ooo`3oool0]`3oool3001Vodh0oooo000E0?ooo`800000^`3oool2001Vod`0oooo000E0?oo o`030000003oool0oooo0;`0oooo0`00I_m90?ooo`005@3oool00`000000oooo0?ooo`2o0?ooo`<0 06KoAP3oool001D0oooo00<000000?ooo`3oool0`P3oool2001Vod@0oooo000=0?ooo`D000000`3o ool00`000000oooo0?ooo`340?ooo`<006Ko@@3oool000l0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`370?ooo`8006Ko?`3oool000l0oooo00<000000?ooo`3oool00`3oool30000 040oooo0P00 I_lU0?ooo`005@3oool00`000000oooo0?ooo`3S0?ooo`03001Vo`3oool0oooo0280oooo000E0?oo o`800000i@3oool00`00I_l0oooo0?ooo`0Q0?ooo`005@3oool00`000000oooo0?ooo`3U0?ooo`80 06Ko8@3oool001D0oooo00<000000?ooo`3oool0i`3oool00`00I_l0oooo0?ooo`0N0?ooo`005@3o ool00`000000oooo0?ooo`3X0?ooo`03001Vo`3oool0oooo01d0oooo00000`3oool0000000000003 00000080oooo0P0000030?ooo`@00000103oool00`000000oooo0?ooo`3Y0?ooo`8006Ko7@3oool0 00<0oooo00<000000?ooo`3oool01`3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 0>/0oooo00<006Ko0?ooo`3oool06P3oool000<0oooo00<000000?ooo`3oool0203oool00`000000 oooo0?ooo`040?ooo`<00000k03oool00`00I_l0oooo0?ooo`0I0?ooo`000`3oool00`000000oooo 0?ooo`090?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0k@3oool00`00I_l0oooo 0?ooo`0H0?ooo`000`3oool00`000000oooo0?ooo`070?ooo`040000003oool0oooo000000@0oooo 00<000000?ooo`3oool0kP3oool00`00I_l0oooo0?ooo`0G0?ooo`000P3oool2000000X0oooo0P00 00050?ooo`030000003oool0oooo0>l0oooo00<006Ko0?ooo`3oool05P3oool001D0oooo00<00000 0?ooo`3oool0l03oool00`00I_l0oooo0?ooo`0E0?ooo`005@3oool200000?80oooo00<006Ko0?oo o`3oool0503oool001D0oooo00<000000?ooo`3oool0lP3oool00`00I_l0oooo0?ooo`0C0?ooo`00 5@3oool00`000000oooo0?ooo`3c0?ooo`03001Vo`3oool0oooo0180oooo000E0?ooo`030000003o ool0oooo0?@0oooo00<006Ko0?ooo`3oool04@3oool001D0oooo00<000000?ooo`3oool0m@3oool0 0`00I_l0oooo0?ooo`0@0?ooo`005@3oool200000?L0oooo00<006Ko0?ooo`3oool03`3oool001D0 oooo00<000000?ooo`3oool0m`3oool00`00I_l0oooo0?ooo`0>0?ooo`005@3oool00`000000oooo 0?ooo`3h0?ooo`03001Vo`3oool0oooo00d0oooo000E0?ooo`030000003oool0oooo0?P0oooo00<0 06Ko0?ooo`3oool03@3oool001D0oooo00<000000?ooo`3oool0n@3oool00`00I_l0oooo0?ooo`0< 0?ooo`005@3oool200000?/0oooo00<006Ko0?ooo`3oool02`3oool001D0oooo00<000000?ooo`3o ool0n`3oool00`00I_l0oooo0?ooo`0:0?ooo`005@3oool00`000000oooo0?ooo`3k0?ooo`03001V o`3oool0oooo00X0oooo000E0?ooo`030000003oool0oooo0?`0oooo00<006Ko0?ooo`3oool02@3o ool000030?ooo`000000000000<000000P3oool2000000D0oooo0`0000030?ooo`030000003oool0 oooo0?`0oooo00<006Ko0?ooo`3oool02@3oool000<0oooo00<000000?ooo`3oool02P3oool00`00 0000oooo0?ooo`020?ooo`030000003oool0oooo0?d0oooo00<006Ko0?ooo`3oool0203oool000<0 oooo00<000000?ooo`3oool01`3oool5000000<0oooo0`00003m0?ooo`03001Vo`3oool0oooo00P0 oooo00030?ooo`030000003oool0oooo00L0oooo00@000000?ooo`3oool00000103oool00`000000 oooo0?ooo`3m0?ooo`03001Vo`3oool0oooo00P0oooo00030?ooo`030000003oool0oooo00P0oooo 00<000000?ooo`000000103oool00`000000oooo0?ooo`3n0?ooo`03001Vo`3oool0oooo00L0oooo 00020?ooo`8000002`3oool2000000@0oooo00<000000?ooo`3oool0oP3oool00`00I_l0oooo0?oo o`070?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`03001Vo`3oool0oooo00H0oooo000E0?oo o`800000o`3oool10?ooo`03001Vo`3oool0oooo00H0oooo000E0?ooo`030000003oool0oooo0?l0 oooo00<006Ko0?ooo`3oool01P3oool001D0oooo00<000000?ooo`3oool0o`3oool00`00I_l0oooo 0?ooo`060?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`40oooo00<006Ko0?ooo`3oool01@3o ool001D0oooo00<000000?ooo`3oool0o`3oool10?ooo`03001Vo`3oool0oooo00D0oooo000E0?oo o`800000o`3oool20?ooo`03001Vo`3oool0oooo00D0oooo000E0?ooo`030000003oool0oooo0?l0 oooo0@3oool00`00I_l0oooo0?ooo`050?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`40oooo 00<006Ko0?ooo`3oool01@3oool001D0oooo00<000000?ooo`3oool0o`3oool90?ooo`005@3oool0 0`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003oool0oooo0?l0oooo2@3oool001D0 oooo0P00003o0?ooo`X0oooo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.259483, -0.119493, \ 0.0121242, 0.00948713}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Show[g0, g1, g2, g3]\)], "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 0.0238095 0.303152 0.0147151 0.387408 [ [.17539 .00222 -9 -9 ] [.17539 .00222 9 0 ] [.32696 .00222 -3 -9 ] [.32696 .00222 3 0 ] [.47854 .00222 -9 -9 ] [.47854 .00222 9 0 ] [.63011 .00222 -3 -9 ] [.63011 .00222 3 0 ] [.78169 .00222 -9 -9 ] [.78169 .00222 9 0 ] [.93327 .00222 -3 -9 ] [.93327 .00222 3 0 ] [.01131 .0922 -18 -4.5 ] [.01131 .0922 0 4.5 ] [.01131 .16968 -18 -4.5 ] [.01131 .16968 0 4.5 ] [.01131 .24716 -18 -4.5 ] [.01131 .24716 0 4.5 ] [.01131 .32464 -18 -4.5 ] [.01131 .32464 0 4.5 ] [.01131 .40212 -6 -4.5 ] [.01131 .40212 0 4.5 ] [.01131 .4796 -18 -4.5 ] [.01131 .4796 0 4.5 ] [.01131 .55709 -18 -4.5 ] [.01131 .55709 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 .17539 .01472 m .17539 .02097 L s [(0.5)] .17539 .00222 0 1 Mshowa .32696 .01472 m .32696 .02097 L s [(1)] .32696 .00222 0 1 Mshowa .47854 .01472 m .47854 .02097 L s [(1.5)] .47854 .00222 0 1 Mshowa .63011 .01472 m .63011 .02097 L s [(2)] .63011 .00222 0 1 Mshowa .78169 .01472 m .78169 .02097 L s [(2.5)] .78169 .00222 0 1 Mshowa .93327 .01472 m .93327 .02097 L s [(3)] .93327 .00222 0 1 Mshowa .125 Mabswid .05412 .01472 m .05412 .01847 L s .08444 .01472 m .08444 .01847 L s .11476 .01472 m .11476 .01847 L s .14507 .01472 m .14507 .01847 L s .2057 .01472 m .2057 .01847 L s .23602 .01472 m .23602 .01847 L s .26633 .01472 m .26633 .01847 L s .29665 .01472 m .29665 .01847 L s .35728 .01472 m .35728 .01847 L s .38759 .01472 m .38759 .01847 L s .41791 .01472 m .41791 .01847 L s .44822 .01472 m .44822 .01847 L s .50885 .01472 m .50885 .01847 L s .53917 .01472 m .53917 .01847 L s .56948 .01472 m .56948 .01847 L s .5998 .01472 m .5998 .01847 L s .66043 .01472 m .66043 .01847 L s .69074 .01472 m .69074 .01847 L s .72106 .01472 m .72106 .01847 L s .75138 .01472 m .75138 .01847 L s .81201 .01472 m .81201 .01847 L s .84232 .01472 m .84232 .01847 L s .87264 .01472 m .87264 .01847 L s .90295 .01472 m .90295 .01847 L s .96358 .01472 m .96358 .01847 L s .9939 .01472 m .9939 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .0922 m .03006 .0922 L s [(0.2)] .01131 .0922 1 0 Mshowa .02381 .16968 m .03006 .16968 L s [(0.4)] .01131 .16968 1 0 Mshowa .02381 .24716 m .03006 .24716 L s [(0.6)] .01131 .24716 1 0 Mshowa .02381 .32464 m .03006 .32464 L s [(0.8)] .01131 .32464 1 0 Mshowa .02381 .40212 m .03006 .40212 L s [(1)] .01131 .40212 1 0 Mshowa .02381 .4796 m .03006 .4796 L s [(1.2)] .01131 .4796 1 0 Mshowa .02381 .55709 m .03006 .55709 L s [(1.4)] .01131 .55709 1 0 Mshowa .125 Mabswid .02381 .03409 m .02756 .03409 L s .02381 .05346 m .02756 .05346 L s .02381 .07283 m .02756 .07283 L s .02381 .11157 m .02756 .11157 L s .02381 .13094 m .02756 .13094 L s .02381 .15031 m .02756 .15031 L s .02381 .18905 m .02756 .18905 L s .02381 .20842 m .02756 .20842 L s .02381 .22779 m .02756 .22779 L s .02381 .26653 m .02756 .26653 L s .02381 .2859 m .02756 .2859 L s .02381 .30527 m .02756 .30527 L s .02381 .34401 m .02756 .34401 L s .02381 .36338 m .02756 .36338 L s .02381 .38275 m .02756 .38275 L s .02381 .42149 m .02756 .42149 L s .02381 .44086 m .02756 .44086 L s .02381 .46023 m .02756 .46023 L s .02381 .49898 m .02756 .49898 L s .02381 .51835 m .02756 .51835 L s .02381 .53772 m .02756 .53772 L s .02381 .57646 m .02756 .57646 L s .02381 .59583 m .02756 .59583 L s .02381 .6152 m .02756 .6152 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .0148 m .02499 .03013 L .02605 .03602 L .02846 .04536 L .03279 .0573 L .03784 .06796 L .04262 .07636 L .06244 .10303 L .08265 .12362 L .10458 .14217 L .14545 .17067 L .1848 .19345 L .22263 .21244 L .26292 .23035 L .30169 .2458 L .34291 .26071 L .38262 .27392 L .42082 .28581 L .46146 .29789 L .50059 .30923 L .54217 .32129 L .58224 .33323 L .62079 .34529 L .66179 .35903 L .70128 .37344 L .73925 .38868 L .77968 .40676 L .81858 .42649 L .85995 .45087 L .89979 .4794 L .91838 .49544 L .93812 .51573 L .95621 .53987 L .96117 .54831 L .96652 .55918 L .96897 .56521 L .97156 .57281 L .97377 .58128 L .97502 .58803 L .97619 .60251 L s 0 1 .4 r .02381 .01479 m .02499 .02788 L .02605 .03292 L .02846 .04091 L .03279 .05116 L .04262 .06756 L .05281 .08045 L .06244 .09072 L .10458 .12546 L .14299 .15022 L .18386 .17301 L .22321 .19283 L .26105 .21055 L .30133 .22841 L .34011 .24489 L .38133 .26186 L .42104 .27784 L .45923 .29299 L .49988 .30901 L .53901 .32442 L .58059 .34092 L .62066 .35706 L .65921 .37293 L .70021 .39037 L .7397 .4079 L .77767 .42571 L .81809 .44613 L .857 .46788 L .89836 .49475 L .91906 .51066 L .93821 .52805 L .95662 .54949 L .96592 .56442 L .96847 .56961 L .97122 .5763 L .97248 .58 L .97381 .58466 L .97495 .58986 L .97619 .60332 L s .8 1 0 r .02381 .0148 m .02499 .02969 L .02605 .03542 L .02846 .04452 L .03279 .05617 L .04262 .07485 L .05281 .08953 L .06244 .10122 L .10458 .14052 L .14299 .168 L .18386 .19251 L .22321 .2129 L .26105 .23021 L .30133 .24663 L .34011 .26082 L .38133 .2745 L .42104 .28664 L .45923 .29765 L .49988 .30902 L .53901 .31996 L .58059 .33196 L .62066 .34424 L .65921 .35705 L .70021 .37207 L .7397 .38822 L .77767 .40564 L .81809 .42669 L .857 .4501 L .89836 .47994 L .91906 .4979 L .93821 .51764 L .95662 .54205 L .96592 .55905 L .96847 .56496 L .97122 .57257 L .97248 .57678 L .97381 .58209 L .97495 .588 L .97619 .60331 L s 0 .4 1 r .02381 .0148 m .02499 .02998 L .02605 .03582 L .02846 .04509 L .03279 .05697 L .04262 .07601 L .05281 .09096 L .06244 .10285 L .10458 .14262 L .14299 .17005 L .18386 .19409 L .22321 .21374 L .26105 .23023 L .30133 .24584 L .34011 .25948 L .38133 .27297 L .42104 .28533 L .45923 .29688 L .49988 .30902 L .53901 .3207 L .58059 .33328 L .62066 .34577 L .65921 .35839 L .70021 .37284 L .7397 .38819 L .77767 .40478 L .81809 .42508 L .857 .44805 L .89836 .47785 L .91906 .49599 L .93821 .51602 L .95662 .54087 L .96592 .55819 L .96847 .56422 L .97122 .57197 L .97248 .57627 L .97381 .58168 L .97495 .5877 L .97619 .60331 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{794.063, 490.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`007@3oool00`000000 oooo0?ooo`0P0?ooo`03001Vo`3@3o ool00`00000006Ko00?ooo`03001Vo`000000c?l001D0oooo0P00ofKo0?ooool0ooooU03o ool001d0oooo00<000000?ooo`3oool0C`3oool01000I_l000000@3o ool001d0oooo00<000000?ooo`3oool0W`3oool2001Vo`80c?l0803oool2003oI_l0ooooo`3ooolg 0?ooo`007@3oool00`000000oooo0?ooo`2Q0?ooo`<006Ko00<0c?l00?ooo`3oool07P3oool3003o I_l0ooooo`3ooold0?ooo`007@3oool00`000000oooo0?ooo`2T0?ooo`8006Ko00<0c?l00?ooo`3o ool07`3oool2003oI_l0ooooo`3ooolb0?ooo`007@3oool00`000000oooo0?ooo`2V0?ooo`8006Ko 00<0c?l00000003oool07`3oool2003oI_l0ooooo`3oool`0?ooo`007@3oool00`000000oooo0?oo o`2X0?ooo`8006Ko00<0c?l00000003oool07`3oool2003oI_l0ooooo`3oool^0?ooo`007@3oool0 0`000000oooo0?ooo`2Z0?ooo`8006Ko00<0c?l00000003oool07`3oool3003oI_l0ooooo`3oool[ 0?ooo`007@3oool00`000000oooo0?ooo`2/0?ooo`<006Ko00<000000?ooo`3oool07`3oool2003o I_l0ooooo`3ooolY0?ooo`007@3oool00`000000oooo0?ooo`2_0?ooo`8006Ko0P00000P0?ooo`80 0?mVo`3ooooo0?ooobL0oooo000M0?ooo`@00000/03oool2001Vo`800000803oool3003oI_l0oooo o`3ooolT0?ooo`007@3oool00`000000oooo0?ooo`2c0?ooo`8006Ko0P00000Q0?ooo`800?mVo`3o oooo0?ooob80oooo000M0?ooo`030000003oool0oooo0;D0oooo0`00I_l200000200oooo0P00ofKo 0?ooool0oooo803oool001d0oooo00<000000?ooo`3oool0^03oool2001Vo`800000803oool3003o I_l0ooooo`3ooolM0?ooo`007@3oool00`000000oooo0?ooo`2j0?ooo`<006Ko0P00000P0?ooo`80 0?mVo`3ooooo0?oooa/0oooo000M0?ooo`030000003oool0oooo0;d0oooo0`00I_l00`000000oooo 0?ooo`0N0?ooo`800?mVo`3ooooo0?oooaT0oooo000M0?ooo`030000003oool0oooo0;l0oooo00<0 c?l0001Vo`00I_l00P00000O0?ooo`800?mVo`3ooooo0?oooaL0oooo000M0?ooo`030000003oool0 oooo0<80oooo0`00I_l00`000000oooo0?ooo`0M0?ooo`<00?mVo`3ooooo0?oooa@0oooo000M0?oo o`030000003oool0oooo0<@0oooo00D0c?l0001Vo`00I_l006Ko0000000O0?ooo`800?mVo`3ooooo 0?oooa80oooo000M0?ooo`030000003oool0oooo00?ooo`80c?l00P00I_l00`000000oooo0?ooo`0L0?ooo`800?mVo`3ooooo0?ooo`T0oooo 00030?ooo`800000103oool2000000<0oooo0`00000<0?ooo`030000003oool0oooo0=00oooo0P3< o`03001Voah0oooo0`00ofKo0?ooool0oooo1P3oool00080oooo00@000000?ooo`3oool00000203o ool010000000oooo0?ooo`00000;0?ooo`030000003oool0oooo0=<0oooo0P30?ooo`<00?mVo`3oooo10?oo o`007@3oool00`000000oooo0?ooo`3o0?ooobL0oooo0`3P3oool300?ooo`<006Ko103/0oooo000M0?ooo`030000003oool0oooo0?l0ooook@3oool3003oIQ`0oooo00@00000 001Vo`00I_l006Ko0P3L0oooo000M0?ooo`030000003oool0oooo0?l0oooolP3oool2003o IQd0oooo00@00000001Vo`00I_l006Ko0P3P3oool2003oIQ`0oooo0P3< o`02001Voj00oooo000M0?ooo`030000003oool0oooo0?l0ooooo`3oooll0?ooo`800?mV703oool2 00?ooo`80c?l000<0 oooo001Vo`3oool0C`3oool000@0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`0: 0?ooo`030000003oool0oooo0?l0ooooo`3ooonH0?ooo`800?mV403oool00`3`3oool001d0oooo00<000000?ooo`3oool0o`3ooooo0?oook@0oooo00<00?mV0?ooo`3oool0203o ool00`303oool001d0 oooo00<000000?ooo`3oool0o`3ooooo0?oookL0oooo0P00ofH90?ooo`030"], ImageRangeCache->{{{0, 793.063}, {489.75, 0}} -> {-0.124094, -0.0620192, \ 0.00422543, 0.00330646}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\@NIntegrate[\((t[\[Sigma]] - \((ArcSin[\(Sin[2 \[Sigma]]\/a + 2 \ \[Sigma]\)\/\[Pi] - 1]\/\[Pi] + .5)\)*t[\[Pi]])\)\^2, {\[Sigma], 0, \ 3.14158}]\)], "Input"], Cell[BoxData[ \(0.004651934591010413`\)], "Output"] }, Open ]], Cell[BoxData[ \(\(\(This\ is\ the\ R\^2\ for\ g2\)\(\[IndentingNewLine]\) \)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\@NIntegrate[\((t[\[Sigma]] - \((ArcSin[\(Sin[4 \[Sigma]]\/a\^3 + \ Sin[2 \[Sigma]]\/a + 2 \[Sigma]\)\/\[Pi] - 1]\/\[Pi] + \ .5)\)*t[\[Pi]])\)\^2, {\[Sigma], 0, 3.14158}]\)], "Input"], Cell[BoxData[ \(0.002876877321934732`\)], "Output"] }, Open ]], Cell[BoxData[ \(Solve[\((ArcSin[\(2 \[Sigma]\)\/\[Pi] - 1]\/\[Pi] + .5)\)* t[\[Pi]] \[Equal] \[Tau], \[Sigma]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[\((ArcSin[\(2 \[Sigma]\)\/k2 - 1]\/k2 + 1\/2)\)* k1 \[Equal] \[Tau], \[Sigma]]\)], "Input"], Cell[BoxData[ \({{\[Sigma] \[Rule] \(-\(1\/2\)\)\ k2\ \((\(-1\) + Sin[\(k2\ \((k1 - 2\ \[Tau])\)\)\/\(2\ k1\)])\)}}\)], "Output"] }, Open ]], Cell[BoxData[ \(pos[\[Tau]_] := \(-\(\[Pi]\/2\)\) \((\(-1\) + Sin[\(\[Pi]\ \((t[\[Pi]] - 2\ \[Tau])\)\)\/\(2 \ t[\[Pi]]\)])\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Plot[pos[\[Tau]], {\[Tau], 0, 6}]\)], "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 0.0238095 0.15873 0.0147151 0.187359 [ [.18254 .00222 -3 -9 ] [.18254 .00222 3 0 ] [.34127 .00222 -3 -9 ] [.34127 .00222 3 0 ] [.5 .00222 -3 -9 ] [.5 .00222 3 0 ] [.65873 .00222 -3 -9 ] [.65873 .00222 3 0 ] [.81746 .00222 -3 -9 ] [.81746 .00222 3 0 ] [.97619 .00222 -3 -9 ] [.97619 .00222 3 0 ] [.01131 .10839 -18 -4.5 ] [.01131 .10839 0 4.5 ] [.01131 .20207 -6 -4.5 ] [.01131 .20207 0 4.5 ] [.01131 .29575 -18 -4.5 ] [.01131 .29575 0 4.5 ] [.01131 .38943 -6 -4.5 ] [.01131 .38943 0 4.5 ] [.01131 .48311 -18 -4.5 ] [.01131 .48311 0 4.5 ] [.01131 .57679 -6 -4.5 ] [.01131 .57679 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 .18254 .01472 m .18254 .02097 L s [(1)] .18254 .00222 0 1 Mshowa .34127 .01472 m .34127 .02097 L s [(2)] .34127 .00222 0 1 Mshowa .5 .01472 m .5 .02097 L s [(3)] .5 .00222 0 1 Mshowa .65873 .01472 m .65873 .02097 L s [(4)] .65873 .00222 0 1 Mshowa .81746 .01472 m .81746 .02097 L s [(5)] .81746 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(6)] .97619 .00222 0 1 Mshowa .125 Mabswid .05556 .01472 m .05556 .01847 L s .0873 .01472 m .0873 .01847 L s .11905 .01472 m .11905 .01847 L s .15079 .01472 m .15079 .01847 L s .21429 .01472 m .21429 .01847 L s .24603 .01472 m .24603 .01847 L s .27778 .01472 m .27778 .01847 L s .30952 .01472 m .30952 .01847 L s .37302 .01472 m .37302 .01847 L s .40476 .01472 m .40476 .01847 L s .43651 .01472 m .43651 .01847 L s .46825 .01472 m .46825 .01847 L s .53175 .01472 m .53175 .01847 L s .56349 .01472 m .56349 .01847 L s .59524 .01472 m .59524 .01847 L s .62698 .01472 m .62698 .01847 L s .69048 .01472 m .69048 .01847 L s .72222 .01472 m .72222 .01847 L s .75397 .01472 m .75397 .01847 L s .78571 .01472 m .78571 .01847 L s .84921 .01472 m .84921 .01847 L s .88095 .01472 m .88095 .01847 L s .9127 .01472 m .9127 .01847 L s .94444 .01472 m .94444 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s .02381 .10839 m .03006 .10839 L s [(0.5)] .01131 .10839 1 0 Mshowa .02381 .20207 m .03006 .20207 L s [(1)] .01131 .20207 1 0 Mshowa .02381 .29575 m .03006 .29575 L s [(1.5)] .01131 .29575 1 0 Mshowa .02381 .38943 m .03006 .38943 L s [(2)] .01131 .38943 1 0 Mshowa .02381 .48311 m .03006 .48311 L s [(2.5)] .01131 .48311 1 0 Mshowa .02381 .57679 m .03006 .57679 L s [(3)] .01131 .57679 1 0 Mshowa .125 Mabswid .02381 .03345 m .02756 .03345 L s .02381 .05219 m .02756 .05219 L s .02381 .07092 m .02756 .07092 L s .02381 .08966 m .02756 .08966 L s .02381 .12713 m .02756 .12713 L s .02381 .14587 m .02756 .14587 L s .02381 .1646 m .02756 .1646 L s .02381 .18334 m .02756 .18334 L s .02381 .22081 m .02756 .22081 L s .02381 .23955 m .02756 .23955 L s .02381 .25828 m .02756 .25828 L s .02381 .27702 m .02756 .27702 L s .02381 .31449 m .02756 .31449 L s .02381 .33322 m .02756 .33322 L s .02381 .35196 m .02756 .35196 L s .02381 .3707 m .02756 .3707 L s .02381 .40817 m .02756 .40817 L s .02381 .4269 m .02756 .4269 L s .02381 .44564 m .02756 .44564 L s .02381 .46438 m .02756 .46438 L s .02381 .50185 m .02756 .50185 L s .02381 .52058 m .02756 .52058 L s .02381 .53932 m .02756 .53932 L s .02381 .55806 m .02756 .55806 L s .02381 .59553 m .02756 .59553 L s .02381 .61426 m .02756 .61426 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .02499 .01475 L .02605 .01484 L .02729 .01502 L .02846 .01525 L .03053 .01584 L .03279 .01672 L .03527 .01799 L .0379 .01966 L .04262 .0235 L .05205 .0344 L .06244 .0512 L .0842 .10116 L .10458 .1631 L .14335 .30497 L .18458 .45607 L .20517 .51837 L .21519 .54352 L .22428 .56289 L .23316 .57837 L .24277 .59106 L .24806 .59618 L .25037 .59799 L .25292 .59968 L .25516 .6009 L .25757 .60194 L .2589 .60239 L .26011 .60272 L .26132 .60298 L .26248 .60316 L .26362 .60327 L .26484 .60332 L .266 .60329 L .26707 .60321 L .26824 .60306 L .26953 .60281 L .27088 .60246 L .27213 .60205 L .27473 .60096 L .27709 .59968 L .28239 .59581 L .28693 .5914 L .29186 .5855 L .30081 .5719 L .32068 .52926 L .34173 .46821 L .37961 .33196 L .41995 .18169 L .43853 .12183 L .45878 .0691 L Mistroke .46976 .04724 L .47511 .03852 L .47995 .03175 L .48463 .02625 L .48969 .0215 L .49247 .01941 L .49503 .01783 L .49747 .01661 L .49871 .01611 L .50005 .01566 L .50138 .01529 L .50261 .01504 L .50378 .01486 L .50503 .01475 L .50614 .01472 L .50718 .01474 L .50833 .01483 L .50956 .015 L .51079 .01524 L .51215 .0156 L .51487 .01659 L .51739 .01783 L .51973 .01927 L .52438 .02293 L .52861 .02716 L .53808 .03972 L .54809 .05743 L .5573 .07753 L .57811 .13464 L .61757 .27371 L .65551 .41651 L .67663 .48689 L .6959 .53956 L .70545 .56048 L .71585 .57883 L .72062 .58559 L .72568 .59162 L .73011 .59589 L .73477 .59935 L .7371 .60068 L .73965 .60182 L .74077 .60222 L .74197 .60258 L .74309 .60286 L .74413 .60305 L .74543 .60322 L .74612 .60328 L .74685 .60331 L .74807 .60331 L .74876 .60327 L Mistroke .74941 .60322 L .75062 .60306 L .75173 .60285 L .75301 .60253 L .75422 .60216 L .75642 .60129 L .75875 .60011 L .76296 .59729 L .76796 .59283 L .77249 .58774 L .78253 .57304 L .79175 .55555 L .81258 .50347 L .85209 .36956 L .89008 .22553 L .91124 .15188 L .93052 .09496 L .9401 .07149 L .95052 .05017 L .96036 .0344 L .96468 .02888 L .96945 .02382 L .97619 .01855 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]HGAYHf4PAg9QL6QYHg 0?ooool000004`00000001D0oooo00@000000?ooo`00000000001@3oool00`000000oooo0?ooo`05 0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`06 0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`06 0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`06 0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`06 0?ooo`030000003oool0oooo00<0oooo0`0000040?ooo`8000000P3oool00`000000oooo0?ooo`06 0?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`06 0?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`06 0?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`05 0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`05 0?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool001D0oooo00D000000?oo o`3oool0oooo0000000V0?ooo`030000003oool0oooo02P0oooo00<000000?ooo`3oool09P3oool0 0`000000oooo000000060?ooo`030000003oool0oooo0280oooo00<000000?ooo`3oool0:03oool0 0`000000oooo0?ooo`0W0?ooo`8000001`3oool001D0oooo00<000000?ooo`3oool00P3oool00`00 0000oooo0?ooo`1e0?ooo`8000002@3oool00`000000oooo0?ooo`1f0?ooo`030000003oool0oooo 00L0oooo000E0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0L`3oool00`000000 oooo0?ooo`0:0?ooo`030000003oool0oooo07@0oooo00<000000?ooo`3oool0203oool001D0oooo 0P0000050?ooo`030000003oool0oooo0780oooo00<000000?ooo`3oool02`3oool00`000000oooo 0?ooo`1b0?ooo`030000003oool0oooo00T0oooo000E0?ooo`030000003oool0oooo00D0oooo00<0 00000?ooo`3oool0L03oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo0740oooo00<0 00000?ooo`3oool02@3oool001D0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`1` 0?ooo`030000003oool0oooo00h0oooo00<000000?ooo`3oool0K`3oool00`000000oooo0?ooo`0: 0?ooo`005@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo06h0oooo00<000000?oo o`3oool0403oool00`000000oooo0?ooo`1]0?ooo`030000003oool0oooo00/0oooo000E0?ooo`03 0000003oool0oooo00H0oooo00<000000?ooo`3oool0K@3oool00`000000oooo0?ooo`0A0?ooo`03 0000003oool0oooo06d0oooo00<000000?ooo`3oool02`3oool001D0oooo0P0000080?ooo`030000 003oool0oooo06/0oooo00<000000?ooo`3oool04`3oool00`000000oooo0?ooo`1[0?ooo`030000 003oool0oooo00`0oooo000E0?ooo`030000003oool0oooo00L0oooo00<000000?ooo`3oool0J`3o ool00`000000oooo0?ooo`0C0?ooo`030000003oool0oooo06X0oooo00<000000?ooo`3oool03@3o ool001D0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`1Y0?ooo`030000003oool0 oooo01D0oooo00<000000?ooo`3oool0J@3oool00`000000oooo0?ooo`0=0?ooo`005@3oool00`00 0000oooo0?ooo`080?ooo`030000003oool0oooo06T0oooo00<000000?ooo`3oool05@3oool00`00 0000oooo0?ooo`1X0?ooo`030000003oool0oooo00h0oooo000E0?ooo`030000003oool0oooo00T0 oooo00<000000?ooo`3oool0I`3oool00`000000oooo0?ooo`0G0?ooo`030000003oool0oooo06L0 oooo00<000000?ooo`3oool03P3oool001D0oooo0P00000:0?ooo`030000003oool0oooo06L0oooo 00<000000?ooo`3oool05`3oool00`000000oooo0?ooo`1V0?ooo`030000003oool0oooo00l0oooo 000E0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool0IP3oool00`000000oooo0?oo o`0H0?ooo`030000003oool0oooo06D0oooo00<000000?ooo`3oool03`3oool001D0oooo00<00000 0?ooo`3oool02P3oool00`000000oooo0?ooo`1U0?ooo`030000003oool0oooo01T0oooo00<00000 0?ooo`3oool0I@3oool00`000000oooo0?ooo`0?0?ooo`005@3oool00`000000oooo0?ooo`0:0?oo o`030000003oool0oooo06D0oooo00<000000?ooo`3oool06@3oool00`000000oooo0?ooo`1T0?oo o`030000003oool0oooo0100oooo000E0?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3o ool0I03oool00`000000oooo0?ooo`0J0?ooo`030000003oool0oooo06<0oooo00<000000?ooo`3o ool0403oool001D0oooo00<000000?ooo`3oool02`3oool00`000000oooo0?ooo`1S0?ooo`030000 003oool0oooo01/0oooo00<000000?ooo`3oool0H`3oool00`000000oooo0?ooo`0@0?ooo`005@3o ool2000000d0oooo00<000000?ooo`3oool0HP3oool00`000000oooo0?ooo`0K0?ooo`030000003o ool0oooo0680oooo00<000000?ooo`3oool04@3oool001D0oooo00<000000?ooo`3oool0303oool0 0`000000oooo0?ooo`1Q0?ooo`030000003oool0oooo01d0oooo00<000000?ooo`3oool0H@3oool0 0`000000oooo0?ooo`0A0?ooo`005@3oool00`000000oooo0?ooo`0=0?ooo`030000003oool0oooo 0600oooo00<000000?ooo`3oool07@3oool00`000000oooo0?ooo`1Q0?ooo`030000003oool0oooo 0140oooo00020?ooo`800000103oool2000000@0oooo0P0000050?ooo`030000003oool0oooo00d0 oooo00<000000?ooo`3oool0H03oool00`000000oooo0?ooo`0N0?ooo`030000003oool0oooo05l0 oooo00<000000?ooo`3oool04P3oool000050?ooo`000000oooo0?ooo`000000203oool010000000 oooo0?ooo`0000040?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0G`3oool00`00 0000oooo0?ooo`0O0?ooo`030000003oool0oooo05l0oooo00<000000?ooo`3oool04P3oool00005 0?ooo`000000oooo0?ooo`0000002`3oool00`000000oooo0?ooo`020?ooo`<000003P3oool00`00 0000oooo0?ooo`1N0?ooo`030000003oool0oooo01l0oooo00<000000?ooo`3oool0GP3oool00`00 0000oooo0?ooo`0C0?ooo`0000D0oooo0000003oool0oooo000000090?ooo`8000001@3oool00`00 0000oooo0?ooo`0>0?ooo`030000003oool0oooo05h0oooo00<000000?ooo`3oool0803oool00`00 0000oooo0?ooo`1M0?ooo`030000003oool0oooo01<0oooo00001@3oool000000?ooo`3oool00000 00T0oooo00<000000?ooo`3oool0103oool00`000000oooo0?ooo`0>0?ooo`030000003oool0oooo 05d0oooo00<000000?ooo`3oool08@3oool00`000000oooo0?ooo`1M0?ooo`030000003oool0oooo 01<0oooo00020?ooo`8000002P3oool3000000@0oooo00<000000?ooo`3oool03`3oool00`000000 oooo0?ooo`1L0?ooo`030000003oool0oooo0240oooo00<000000?ooo`3oool0G03oool00`000000 oooo0?ooo`0D0?ooo`005@3oool00`000000oooo0?ooo`0?0?ooo`030000003oool0oooo05`0oooo 00<000000?ooo`3oool08P3oool00`000000oooo0?ooo`1K0?ooo`030000003oool0oooo01@0oooo 000E0?ooo`800000403oool00`000000oooo0?ooo`1K0?ooo`030000003oool0oooo02<0oooo00<0 00000?ooo`3oool0FP3oool00`000000oooo0?ooo`0E0?ooo`005@3oool00`000000oooo0?ooo`0@ 0?ooo`030000003oool0oooo05X0oooo00<000000?ooo`3oool0903oool00`000000oooo0?ooo`1I 0?ooo`030000003oool0oooo01D0oooo000E0?ooo`030000003oool0oooo0100oooo00<000000?oo o`3oool0FP3oool00`000000oooo0?ooo`0T0?ooo`030000003oool0oooo05T0oooo00<000000?oo o`3oool05@3oool001D0oooo00<000000?ooo`3oool04@3oool00`000000oooo0?ooo`1I0?ooo`03 0000003oool0oooo02@0oooo00<000000?ooo`3oool0F03oool00`000000oooo0?ooo`0F0?ooo`00 5@3oool00`000000oooo0?ooo`0A0?ooo`030000003oool0oooo05P0oooo00<000000?ooo`3oool0 9P3oool00`000000oooo0?ooo`1G0?ooo`030000003oool0oooo01H0oooo000E0?ooo`8000004P3o ool00`000000oooo0?ooo`1H0?ooo`030000003oool0oooo02H0oooo00<000000?ooo`3oool0EP3o ool00`000000oooo0?ooo`0G0?ooo`005@3oool00`000000oooo0?ooo`0B0?ooo`030000003oool0 oooo05L0oooo00<000000?ooo`3oool09P3oool00`000000oooo0?ooo`1F0?ooo`030000003oool0 oooo01L0oooo000E0?ooo`030000003oool0oooo0180oooo00<000000?ooo`3oool0EP3oool00`00 0000oooo0?ooo`0W0?ooo`030000003oool0oooo05H0oooo00<000000?ooo`3oool05`3oool001D0 oooo00<000000?ooo`3oool04P3oool00`000000oooo0?ooo`1F0?ooo`030000003oool0oooo02P0 oooo00<000000?ooo`3oool0E@3oool00`000000oooo0?ooo`0G0?ooo`005@3oool00`000000oooo 0?ooo`0C0?ooo`030000003oool0oooo05D0oooo00<000000?ooo`3oool0:03oool00`000000oooo 0?ooo`1D0?ooo`030000003oool0oooo01P0oooo000E0?ooo`800000503oool00`000000oooo0?oo o`1D0?ooo`030000003oool0oooo02T0oooo00<000000?ooo`3oool0E03oool00`000000oooo0?oo o`0H0?ooo`005@3oool00`000000oooo0?ooo`0C0?ooo`030000003oool0oooo05@0oooo00<00000 0?ooo`3oool0:@3oool00`000000oooo0?ooo`1D0?ooo`030000003oool0oooo01P0oooo000E0?oo o`030000003oool0oooo01@0oooo00<000000?ooo`3oool0D`3oool00`000000oooo0?ooo`0Z0?oo o`030000003oool0oooo05<0oooo00<000000?ooo`3oool0603oool001D0oooo00<000000?ooo`3o ool0503oool00`000000oooo0?ooo`1C0?ooo`030000003oool0oooo02X0oooo00<000000?ooo`3o ool0DP3oool00`000000oooo0?ooo`0I0?ooo`005@3oool00`000000oooo0?ooo`0D0?ooo`030000 003oool0oooo0580oooo00<000000?ooo`3oool0:`3oool00`000000oooo0?ooo`1B0?ooo`030000 003oool0oooo01T0oooo000E0?ooo`8000005@3oool00`000000oooo0?ooo`1B0?ooo`030000003o ool0oooo02/0oooo00<000000?ooo`3oool0DP3oool00`000000oooo0?ooo`0I0?ooo`005@3oool0 0`000000oooo0?ooo`0E0?ooo`030000003oool0oooo0540oooo00<000000?ooo`3oool0;03oool0 0`000000oooo0?ooo`1A0?ooo`030000003oool0oooo01T0oooo000E0?ooo`030000003oool0oooo 01D0oooo00<000000?ooo`3oool0D03oool00`000000oooo0?ooo`0]0?ooo`030000003oool0oooo 0500oooo00<000000?ooo`3oool06P3oool000d0oooo1@0000030?ooo`030000003oool0oooo01D0 oooo00<000000?ooo`3oool0D03oool00`000000oooo0?ooo`0]0?ooo`030000003oool0oooo0500 oooo00<000000?ooo`3oool06P3oool000l0oooo00<000000?ooo`3oool00`3oool00`000000oooo 0?ooo`0E0?ooo`030000003oool0oooo0500oooo00<000000?ooo`3oool0;@3oool00`000000oooo 0?ooo`1@0?ooo`030000003oool0oooo01X0oooo000?0?ooo`030000003oool0oooo00<0oooo0`00 000F0?ooo`030000003oool0oooo04l0oooo00<000000?ooo`3oool0;P3oool00`000000oooo0?oo o`1?0?ooo`030000003oool0oooo01X0oooo000?0?ooo`030000003oool0oooo00<0oooo00<00000 0?ooo`3oool05P3oool00`000000oooo0?ooo`1>0?ooo`030000003oool0oooo02l0oooo00<00000 0?ooo`3oool0CP3oool00`000000oooo0?ooo`0K0?ooo`003`3oool00`000000oooo0?ooo`030?oo o`030000003oool0oooo01H0oooo00<000000?ooo`3oool0CP3oool00`000000oooo0?ooo`0_0?oo o`030000003oool0oooo04h0oooo00<000000?ooo`3oool06`3oool000h0oooo0P0000050?ooo`03 0000003oool0oooo01H0oooo00<000000?ooo`3oool0CP3oool00`000000oooo0?ooo`0`0?ooo`03 0000003oool0oooo04d0oooo00<000000?ooo`3oool06`3oool001D0oooo00<000000?ooo`3oool0 5`3oool00`000000oooo0?ooo`1=0?ooo`030000003oool0oooo0300oooo00<000000?ooo`3oool0 C@3oool00`000000oooo0?ooo`0K0?ooo`005@3oool2000001P0oooo00<000000?ooo`3oool0C03o ool00`000000oooo0?ooo`0a0?ooo`030000003oool0oooo04`0oooo00<000000?ooo`3oool0703o ool001D0oooo00<000000?ooo`3oool05`3oool00`000000oooo0?ooo`1<0?ooo`030000003oool0 oooo0340oooo00<000000?ooo`3oool0C03oool00`000000oooo0?ooo`0L0?ooo`005@3oool00`00 0000oooo0?ooo`0G0?ooo`030000003oool0oooo04`0oooo00<000000?ooo`3oool0@3oool00`000000oooo0?oo o`140?ooo`030000003oool0oooo0200oooo000E0?ooo`800000703oool00`000000oooo0?ooo`14 0?ooo`030000003oool0oooo03T0oooo00<000000?ooo`3oool0A03oool00`000000oooo0?ooo`0P 0?ooo`005@3oool00`000000oooo0?ooo`0K0?ooo`030000003oool0oooo04@0oooo00<000000?oo o`3oool0>P3oool00`000000oooo0?ooo`130?ooo`030000003oool0oooo0200oooo000E0?ooo`03 0000003oool0oooo01`0oooo00<000000?ooo`3oool0@P3oool00`000000oooo0?ooo`0k0?ooo`03 0000003oool0oooo0480oooo00<000000?ooo`3oool08@3oool000030?ooo`000000000000<00000 0P3oool2000000@0oooo0P0000050?ooo`030000003oool0oooo01`0oooo00<000000?ooo`3oool0 @P3oool00`000000oooo0?ooo`0k0?ooo`030000003oool0oooo0480oooo00<000000?ooo`3oool0 8@3oool000<0oooo00<000000?ooo`3oool01`3oool010000000oooo0?ooo`0000040?ooo`030000 003oool0oooo01`0oooo00<000000?ooo`3oool0@P3oool00`000000oooo0?ooo`0k0?ooo`030000 003oool0oooo0480oooo00<000000?ooo`3oool08@3oool000<0oooo00<000000?ooo`3oool02P3o ool00`000000oooo0?ooo`020?ooo`<00000703oool00`000000oooo0?ooo`110?ooo`030000003o ool0oooo03d0oooo00<000000?ooo`3oool0@@3oool00`000000oooo0?ooo`0Q0?ooo`000`3oool0 0`000000oooo0?ooo`080?ooo`8000001@3oool00`000000oooo0?ooo`0M0?ooo`030000003oool0 oooo0400oooo00<000000?ooo`3oool0?@3oool00`000000oooo0?ooo`100?ooo`030000003oool0 oooo0280oooo00030?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool0103oool00`00 0000oooo0?ooo`0M0?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0?@3oool00`00 0000oooo0?ooo`100?ooo`030000003oool0oooo0280oooo00020?ooo`8000002P3oool3000000@0 oooo00<000000?ooo`3oool07@3oool00`000000oooo0?ooo`100?ooo`030000003oool0oooo03h0 oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`0R0?ooo`005@3oool00`000000oooo 0?ooo`0N0?ooo`030000003oool0oooo03h0oooo00<000000?ooo`3oool0?`3oool00`000000oooo 0?ooo`0o0?ooo`030000003oool0oooo0280oooo000E0?ooo`8000007`3oool00`000000oooo0?oo o`0n0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0?P3oool00`000000oooo0?oo o`0S0?ooo`005@3oool00`000000oooo0?ooo`0N0?ooo`030000003oool0oooo03h0oooo00<00000 0?ooo`3oool0?`3oool00`000000oooo0?ooo`0n0?ooo`030000003oool0oooo02<0oooo000E0?oo o`030000003oool0oooo01h0oooo00<000000?ooo`3oool0?P3oool00`000000oooo0?ooo`100?oo o`030000003oool0oooo03d0oooo00<000000?ooo`3oool08`3oool001D0oooo00<000000?ooo`3o ool07`3oool00`000000oooo0?ooo`0l0?ooo`030000003oool0oooo0440oooo00<000000?ooo`3o ool0?03oool00`000000oooo0?ooo`0T0?ooo`005@3oool00`000000oooo0?ooo`0O0?ooo`030000 003oool0oooo03`0oooo00<000000?ooo`3oool0@@3oool00`000000oooo0?ooo`0l0?ooo`030000 003oool0oooo02@0oooo000E0?ooo`800000803oool00`000000oooo0?ooo`0l0?ooo`030000003o ool0oooo0480oooo00<000000?ooo`3oool0>`3oool00`000000oooo0?ooo`0T0?ooo`005@3oool0 0`000000oooo0?ooo`0P0?ooo`030000003oool0oooo03X0oooo00<000000?ooo`3oool0@`3oool0 0`000000oooo0?ooo`0k0?ooo`030000003oool0oooo02@0oooo000E0?ooo`030000003oool0oooo 0200oooo00<000000?ooo`3oool0>P3oool00`000000oooo0?ooo`130?ooo`030000003oool0oooo 03X0oooo00<000000?ooo`3oool09@3oool001D0oooo00<000000?ooo`3oool0803oool00`000000 oooo0?ooo`0j0?ooo`030000003oool0oooo04<0oooo00<000000?ooo`3oool0>P3oool00`000000 oooo0?ooo`0U0?ooo`005@3oool00`000000oooo0?ooo`0Q0?ooo`030000003oool0oooo03T0oooo 00<000000?ooo`3oool0A03oool00`000000oooo0?ooo`0i0?ooo`030000003oool0oooo02D0oooo 000E0?ooo`8000008P3oool00`000000oooo0?ooo`0h0?ooo`030000003oool0oooo04D0oooo00<0 00000?ooo`3oool0>03oool00`000000oooo0?ooo`0V0?ooo`005@3oool00`000000oooo0?ooo`0Q 0?ooo`030000003oool0oooo03P0oooo00<000000?ooo`3oool0A@3oool00`000000oooo0?ooo`0h 0?ooo`030000003oool0oooo02H0oooo000E0?ooo`030000003oool0oooo0240oooo00<000000?oo o`3oool0>03oool00`000000oooo0?ooo`160?ooo`030000003oool0oooo03L0oooo00<000000?oo o`3oool09P3oool001D0oooo00<000000?ooo`3oool08P3oool00`000000oooo0?ooo`0f0?ooo`03 0000003oool0oooo04L0oooo00<000000?ooo`3oool0=`3oool00`000000oooo0?ooo`0V0?ooo`00 5@3oool00`000000oooo0?ooo`0R0?ooo`030000003oool0oooo03H0oooo00<000000?ooo`3oool0 A`3oool00`000000oooo0?ooo`0f0?ooo`030000003oool0oooo02L0oooo000E0?ooo`8000008`3o ool00`000000oooo0?ooo`0f0?ooo`030000003oool0oooo04P0oooo00<000000?ooo`3oool0=@3o ool00`000000oooo0?ooo`0W0?ooo`005@3oool00`000000oooo0?ooo`0S0?ooo`030000003oool0 oooo03D0oooo00<000000?ooo`3oool0B03oool00`000000oooo0?ooo`0e0?ooo`030000003oool0 oooo02L0oooo000E0?ooo`030000003oool0oooo02<0oooo00<000000?ooo`3oool0=03oool00`00 0000oooo0?ooo`190?ooo`030000003oool0oooo03@0oooo00<000000?ooo`3oool0:03oool000d0 oooo100000040?ooo`030000003oool0oooo02<0oooo00<000000?ooo`3oool0=03oool00`000000 oooo0?ooo`190?ooo`030000003oool0oooo03@0oooo00<000000?ooo`3oool0:03oool000d0oooo 00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`0S0?ooo`030000003oool0oooo03@0oooo 00<000000?ooo`3oool0BP3oool00`000000oooo0?ooo`0c0?ooo`030000003oool0oooo02P0oooo 000>0?ooo`030000003oool0oooo00@0oooo0`00000T0?ooo`030000003oool0oooo0380oooo00<0 00000?ooo`3oool0B`3oool00`000000oooo0?ooo`0c0?ooo`030000003oool0oooo02P0oooo000? 0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool0903oool00`000000oooo0?ooo`0b 0?ooo`030000003oool0oooo04/0oooo00<000000?ooo`3oool003oool001D0oooo 00<000000?ooo`3oool0<`3oool00`000000oooo0?ooo`0C0?ooo`030000003oool0oooo06X0oooo 00<000000?ooo`3oool0503oool00`000000oooo0?ooo`0h0?ooo`005@3oool00`000000oooo0?oo o`0d0?ooo`030000003oool0oooo0180oooo00<000000?ooo`3oool0J`3oool00`000000oooo0?oo o`0B0?ooo`030000003oool0oooo03T0oooo000>0?ooo`8000001@3oool00`000000oooo0?ooo`0d 0?ooo`030000003oool0oooo0140oooo00<000000?ooo`3oool0K03oool00`000000oooo0?ooo`0B 0?ooo`030000003oool0oooo03T0oooo000=0?ooo`040000003oool0oooo000000@0oooo00<00000 0?ooo`3oool0=@3oool00`000000oooo0?ooo`0@0?ooo`030000003oool0oooo06d0oooo00<00000 0?ooo`3oool0403oool00`000000oooo0?ooo`0j0?ooo`003`3oool00`000000oooo0?ooo`030?oo o`<00000=@3oool00`000000oooo0?ooo`0?0?ooo`030000003oool0oooo06h0oooo00<000000?oo o`3oool03`3oool00`000000oooo0?ooo`0k0?ooo`00403oool00`000000oooo0?ooo`020?ooo`03 0000003oool0oooo03H0oooo00<000000?ooo`3oool03P3oool00`000000oooo0?ooo`1_0?ooo`03 0000003oool0oooo00h0oooo00<000000?ooo`3oool0>`3oool000d0oooo00@000000?ooo`3oool0 0000103oool00`000000oooo0?ooo`0g0?ooo`030000003oool0oooo00`0oooo00<000000?ooo`3o ool0L@3oool00`000000oooo0?ooo`0<0?ooo`030000003oool0oooo03`0oooo000>0?ooo`800000 1@3oool00`000000oooo0?ooo`0g0?ooo`030000003oool0oooo00/0oooo00<000000?ooo`3oool0 L`3oool00`000000oooo0?ooo`0;0?ooo`030000003oool0oooo03`0oooo000E0?ooo`030000003o ool0oooo03P0oooo00<000000?ooo`3oool02@3oool00`000000oooo0?ooo`1e0?ooo`030000003o ool0oooo00P0oooo0P00000o0?ooo`005@3oool2000003X0oooo0P0000080?ooo`030000003oool0 oooo07L0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`0o0?ooo`005@3oool00`00 0000oooo0?ooo`0k0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool0N@3oool00`00 0000oooo0?ooo`040?ooo`800000@@3oool001D0oooo00<000000?ooo`3oool0?03oool6000007d0 oooo1P0000130?ooo`005@3oool00`000000oooo0?ooo`3o0?ooo`T0oooo000E0?ooo`030000003o ool0oooo0?l0oooo2@3oool001D0oooo0P00003o0?ooo`X0oooo000E0?ooo`030000003oool0oooo 0?l0oooo2@3oool00001\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.495576, -0.247084, \ 0.0231554, 0.0196172}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(pos[k_] := If[EvenQ[IntegerPart[k\/t[\[Pi]]]], FindRoot[ t[\[Sigma]] \[Equal] k, {\[Sigma], Round[k\/t[\[Pi]]] 3.1415 + .00008, 0, \[Pi]}, Compiled \[Rule] False, MaxIterations \[Rule] 100], FindRoot[ t[\[Sigma]] \[Equal] 2 t[\[Pi]] - k, {\[Sigma], \((2 - Round[k\/t[\[Pi]]])\) 3.1415 + .00008, 0, \[Pi]}, Compiled \[Rule] False, MaxIterations \[Rule] 100]]\)], "Text"], Cell[BoxData[ \(test[k_] := If[EvenQ[IntegerPart[k\/t[\[Pi]]]], even, odd]\)], "Text"], Cell[BoxData[ \(k = 6; dk = .1;\)], "Input"], Cell[BoxData[ \(Off[Solve::"\"]; Off[NIntegrate::"\"]; << Graphics`Animation`\)], "Input"], Cell[BoxData[ \(MatrixForm[Table[pos[a], {a, dk, k, dk}]]\)], "Input"], Cell[BoxData[ \(\(A = Join[{0}, %];\)\)], "Input"], Cell[BoxData[ \(\(B = MatrixForm[ Table[{n, A[\([IntegerPart[\(n + dk\)\/dk]]\)]}, {n, 0, k, dk}]];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(g1 = ParametricPlot[{x[s], y[s]}, {s, 0, \[Pi]}, AspectRatio -> Automatic]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .31831 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 0.0238095 0.303152 0.310731 0.303152 [ [.17539 .29823 -9 -9 ] [.17539 .29823 9 0 ] [.32696 .29823 -3 -9 ] [.32696 .29823 3 0 ] [.47854 .29823 -9 -9 ] [.47854 .29823 9 0 ] [.63011 .29823 -3 -9 ] [.63011 .29823 3 0 ] [.78169 .29823 -9 -9 ] [.78169 .29823 9 0 ] [.93327 .29823 -3 -9 ] [.93327 .29823 3 0 ] [.01131 .00758 -12 -4.5 ] [.01131 .00758 0 4.5 ] [.01131 .06821 -24 -4.5 ] [.01131 .06821 0 4.5 ] [.01131 .12884 -24 -4.5 ] [.01131 .12884 0 4.5 ] [.01131 .18947 -24 -4.5 ] [.01131 .18947 0 4.5 ] [.01131 .2501 -24 -4.5 ] [.01131 .2501 0 4.5 ] [ 0 0 0 0 ] [ 1 .31831 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .31073 m .17539 .31698 L s [(0.5)] .17539 .29823 0 1 Mshowa .32696 .31073 m .32696 .31698 L s [(1)] .32696 .29823 0 1 Mshowa .47854 .31073 m .47854 .31698 L s [(1.5)] .47854 .29823 0 1 Mshowa .63011 .31073 m .63011 .31698 L s [(2)] .63011 .29823 0 1 Mshowa .78169 .31073 m .78169 .31698 L s [(2.5)] .78169 .29823 0 1 Mshowa .93327 .31073 m .93327 .31698 L s [(3)] .93327 .29823 0 1 Mshowa .125 Mabswid .05412 .31073 m .05412 .31448 L s .08444 .31073 m .08444 .31448 L s .11476 .31073 m .11476 .31448 L s .14507 .31073 m .14507 .31448 L s .2057 .31073 m .2057 .31448 L s .23602 .31073 m .23602 .31448 L s .26633 .31073 m .26633 .31448 L s .29665 .31073 m .29665 .31448 L s .35728 .31073 m .35728 .31448 L s .38759 .31073 m .38759 .31448 L s .41791 .31073 m .41791 .31448 L s .44822 .31073 m .44822 .31448 L s .50885 .31073 m .50885 .31448 L s .53917 .31073 m .53917 .31448 L s .56948 .31073 m .56948 .31448 L s .5998 .31073 m .5998 .31448 L s .66043 .31073 m .66043 .31448 L s .69074 .31073 m .69074 .31448 L s .72106 .31073 m .72106 .31448 L s .75138 .31073 m .75138 .31448 L s .81201 .31073 m .81201 .31448 L s .84232 .31073 m .84232 .31448 L s .87264 .31073 m .87264 .31448 L s .90295 .31073 m .90295 .31448 L s .96358 .31073 m .96358 .31448 L s .9939 .31073 m .9939 .31448 L s .25 Mabswid 0 .31073 m 1 .31073 L s .02381 .00758 m .03006 .00758 L s [(-1)] .01131 .00758 1 0 Mshowa .02381 .06821 m .03006 .06821 L s [(-0.8)] .01131 .06821 1 0 Mshowa .02381 .12884 m .03006 .12884 L s [(-0.6)] .01131 .12884 1 0 Mshowa .02381 .18947 m .03006 .18947 L s [(-0.4)] .01131 .18947 1 0 Mshowa .02381 .2501 m .03006 .2501 L s [(-0.2)] .01131 .2501 1 0 Mshowa .125 Mabswid .02381 .02274 m .02756 .02274 L s .02381 .03789 m .02756 .03789 L s .02381 .05305 m .02756 .05305 L s .02381 .08337 m .02756 .08337 L s .02381 .09852 m .02756 .09852 L s .02381 .11368 m .02756 .11368 L s .02381 .144 m .02756 .144 L s .02381 .15915 m .02756 .15915 L s .02381 .17431 m .02756 .17431 L s .02381 .20463 m .02756 .20463 L s .02381 .21979 m .02756 .21979 L s .02381 .23494 m .02756 .23494 L s .02381 .26526 m .02756 .26526 L s .02381 .28042 m .02756 .28042 L s .02381 .29557 m .02756 .29557 L s .25 Mabswid .02381 0 m .02381 .31831 L s 0 0 m 1 0 L 1 .31831 L 0 .31831 L closepath clip newpath .5 Mabswid .02381 .31073 m .06244 .2722 L .10458 .23091 L .14415 .19352 L .18221 .15944 L .22272 .12579 L .26171 .09651 L .30316 .06927 L .34309 .04729 L .3815 .03045 L .40095 .02362 L .42237 .01746 L .44268 .01298 L .45178 .0114 L .46172 .00999 L .4671 .00936 L .4721 .00886 L .47727 .00843 L .48196 .00811 L .48658 .00788 L .4887 .00779 L .49093 .00771 L .49332 .00765 L .49438 .00763 L .49552 .00761 L .49675 .0076 L .49789 .00759 L .49859 .00758 L .49925 .00758 L .50049 .00758 L .50163 .00758 L .50286 .00759 L .50401 .0076 L .50508 .00762 L .50754 .00767 L .51014 .00775 L .51268 .00784 L .51504 .00795 L .5204 .00826 L .5293 .00899 L .53882 .01006 L .54906 .01154 L .56016 .01353 L .58032 .01816 L .62123 .0315 L .66064 .04915 L .69852 .07029 L .73886 .09691 L .77769 .12611 L .81897 .16046 L Mistroke .85873 .19618 L .89697 .23241 L .93767 .27231 L .97619 .31073 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{496.75, 158.125}, ImageMargins->{{41, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`<00000a03oool001d0oooo0`00002c0?ooo`@00000E@3o ool400000<00oooo000M0?ooo`030000003oool0oooo0;00oooo0`00001M0?ooo`<00000_@3oool0 01d0oooo00<000000?ooo`3oool0[@3oool3000006<0oooo0`00002j0?ooo`007@3oool00`000000 oooo0?ooo`2Z0?ooo`<00000J@3oool400000;H0oooo000M0?ooo`030000003oool0oooo0:L0oooo 0`00001`0?ooo`800000]03oool001d0oooo00<000000?ooo`3oool0Y@3oool2000007D0oooo0P00 002b0?ooo`007@3oool00`000000oooo0?ooo`2S0?ooo`800000N@3oool200000;00oooo000M0?oo o`030000003oool0oooo0:40oooo0P00001m0?ooo`800000[P3oool001d0oooo0`00002N0?ooo`<0 0000P@3oool200000:`0oooo000M0?ooo`030000003oool0oooo09`0oooo0P0000260?ooo`800000 ZP3oool001d0oooo00<000000?ooo`3oool0VP3oool2000008X0oooo0P00002X0?ooo`007@3oool0 0`000000oooo0?ooo`2H0?ooo`800000SP3oool200000:H0oooo000M0?ooo`030000003oool0oooo 09H0oooo0P00002B0?ooo`800000Y03oool001d0oooo00<000000?ooo`3oool0U03oool2000009H0 oooo0P00002R0?ooo`007@3oool00`000000oooo0?ooo`2B0?ooo`800000VP3oool200000:00oooo 000M0?ooo`<00000T03oool2000009h0oooo0P00002N0?ooo`007@3oool00`000000oooo0?ooo`2> 0?ooo`800000XP3oool2000009`0oooo000M0?ooo`030000003oool0oooo08`0oooo0P00002V0?oo o`800000VP3oool001d0oooo00<000000?ooo`3oool0RP3oool200000:X0oooo00<000000?ooo`3o ool0U`3oool001d0oooo00<000000?ooo`3oool0R03oool200000:d0oooo0P00002G0?ooo`00203o ool2000000@0oooo0P0000040?ooo`8000001`3oool00`000000oooo0?ooo`260?ooo`800000/@3o ool2000009D0oooo00070?ooo`040000003oool0oooo000000P0oooo00@000000?ooo`3oool00000 1P3oool00`000000oooo0?ooo`240?ooo`800000]@3oool2000009<0oooo00070?ooo`040000003o ool0oooo000000P0oooo00@000000?ooo`3oool000001P3oool400000880oooo00<000000?ooo`3o ool0]`3oool200000940oooo00000`3oool000000000000200000080oooo00@000000?ooo`3oool0 00002@3oool2000000L0oooo00<000000?ooo`3oool0P@3oool200000;`0oooo00<000000?ooo`3o ool0SP3oool000L0oooo00@000000?ooo`3oool00000203oool010000000oooo0?ooo`0000060?oo o`030000003oool0oooo0800oooo00<000000?ooo`3oool0_@3oool2000008h0oooo00080?ooo`80 00002P3oool2000000L0oooo00<000000?ooo`3oool0OP3oool200000<80oooo00<000000?ooo`3o ool0R`3oool001d0oooo00<000000?ooo`3oool0O@3oool00`000000oooo0?ooo`330?ooo`800000 R`3oool001d0oooo00<000000?ooo`3oool0N`3oool200000@0oooo00<000000?ooo`3oool0 NP3oool001d0oooo00<000000?ooo`3oool0K03oool00`000000oooo0?ooo`3U0?ooo`030000003o ool0oooo07T0oooo000M0?ooo`030000003oool0oooo06/0oooo00<000000?ooo`3oool0i`3oool2 000007T0oooo000M0?ooo`030000003oool0oooo06T0oooo0P00003/0?ooo`030000003oool0oooo 07H0oooo000M0?ooo`030000003oool0oooo06P0oooo00<000000?ooo`3oool0k@3oool00`000000 oooo0?ooo`1e0?ooo`007@3oool00`000000oooo0?ooo`1W0?ooo`030000003oool0oooo0>l0oooo 0P00001e0?ooo`007@3oool00`000000oooo0?ooo`1U0?ooo`800000m03oool00`000000oooo0?oo o`1b0?ooo`007@3oool00`000000oooo0?ooo`1T0?ooo`030000003oool0oooo0?D0oooo00<00000 0?ooo`3oool0L@3oool001d0oooo0`00001S0?ooo`030000003oool0oooo0?L0oooo00<000000?oo o`3oool0L03oool001d0oooo00<000000?ooo`3oool0H@3oool200000?/0oooo0P00001`0?ooo`00 7@3oool00`000000oooo0?ooo`1P0?ooo`030000003oool0oooo0?d0oooo00<000000?ooo`3oool0 K@3oool001d0oooo00<000000?ooo`3oool0G`3oool00`000000oooo0?ooo`3o0?ooo`030000003o ool0oooo06`0oooo000M0?ooo`030000003oool0oooo05d0oooo0P00003o0?ooo`@0oooo0P00001/ 0?ooo`00203oool2000000@0oooo0P0000030?ooo`<000001`3oool00`000000oooo0?ooo`1L0?oo o`030000003oool0oooo0?l0oooo1P3oool00`000000oooo0?ooo`1Y0?ooo`001`3oool010000000 oooo0?ooo`0000080?ooo`040000003oool0oooo000000H0oooo00<000000?ooo`3oool0F`3oool0 0`000000oooo0?ooo`3o0?ooo`P0oooo00<000000?ooo`3oool0J03oool000L0oooo00@000000?oo o`3oool00000203oool010000000oooo0?ooo`0000060?ooo`@00000F@3oool00`000000oooo0?oo o`3o0?ooo`X0oooo00<000000?ooo`3oool0I`3oool000030?ooo`0000000000008000000P3oool0 10000000oooo0?ooo`0000080?ooo`<000001`3oool00`000000oooo0?ooo`1I0?ooo`030000003o ool0oooo0?l0oooo303oool2000006L0oooo00070?ooo`040000003oool0oooo000000T0oooo00<0 00000?ooo`3oool01P3oool00`000000oooo0?ooo`1G0?ooo`800000o`3ooolA0?ooo`030000003o ool0oooo06@0oooo00080?ooo`8000002P3oool3000000H0oooo00<000000?ooo`3oool0EP3oool0 0`000000oooo0?ooo`3o0?oooa80oooo00<000000?ooo`3oool0H`3oool001d0oooo00<000000?oo o`3oool0E@3oool00`000000oooo0?ooo`3o0?oooa@0oooo00<000000?ooo`3oool0HP3oool001d0 oooo00<000000?ooo`3oool0E03oool00`000000oooo0?ooo`3o0?oooaH0oooo0P00001R0?ooo`00 7@3oool00`000000oooo0?ooo`1C0?ooo`030000003oool0oooo0?l0oooo6@3oool00`000000oooo 0?ooo`1O0?ooo`007@3oool300000580oooo00<000000?ooo`3oool0o`3ooolK0?ooo`030000003o ool0oooo05h0oooo000M0?ooo`030000003oool0oooo0540oooo00<000000?ooo`3oool0o`3ooolM 0?ooo`030000003oool0oooo05d0oooo000M0?ooo`030000003oool0oooo0500oooo00<000000?oo o`3oool0o`3ooolO0?ooo`800000G@3oool001d0oooo00<000000?ooo`3oool0C`3oool00`000000 oooo0?ooo`3o0?ooob80oooo00<000000?ooo`3oool0FP3oool001d0oooo00<000000?ooo`3oool0 C@3oool200000?l0oooo9P3oool00`000000oooo0?ooo`1I0?ooo`007@3oool00`000000oooo0?oo o`1<0?ooo`030000003oool0oooo0?l0oooo9`3oool00`000000oooo0?ooo`1H0?ooo`007@3oool0 0`000000oooo0?ooo`1;0?ooo`030000003oool0oooo0?l0oooo:@3oool2000005P0oooo000M0?oo o`<00000BP3oool00`000000oooo0?ooo`3o0?ooob`0oooo00<000000?ooo`3oool0E@3oool001d0 oooo00<000000?ooo`3oool0B@3oool00`000000oooo0?ooo`3o0?ooobh0oooo00<000000?ooo`3o ool0E03oool001d0oooo00<000000?ooo`3oool0B03oool00`000000oooo0?ooo`3o0?oooc00oooo 00<000000?ooo`3oool0D`3oool001d0oooo00<000000?ooo`3oool0A`3oool00`000000oooo0?oo o`3o0?oooc80oooo00<000000?ooo`3oool0DP3oool001d0oooo00<000000?ooo`3oool0AP3oool0 0`000000oooo0?ooo`3o0?oooc@0oooo00<000000?ooo`3oool0D@3oool001d0oooo00<000000?oo o`3oool0A03oool200000?l0oooo>03oool200000540oooo000M0?ooo`030000003oool0oooo04<0 oooo00<000000?ooo`3oool0o`3ooolj0?ooo`030000003oool0oooo04h0oooo000M0?ooo`030000 003oool0oooo0480oooo00<000000?ooo`3oool0o`3oooll0?ooo`030000003oool0oooo04d0oooo 000M0?ooo`<00000@@3oool00`000000oooo0?ooo`3o0?oooch0oooo00<000000?ooo`3oool0C03o ool001d0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`3o0?oood00oooo00<00000 0?ooo`3oool0B`3oool001d0oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`3o0?oo od80oooo00<000000?ooo`3oool0BP3oool001d0oooo00<000000?ooo`3oool0?P3oool00`000000 oooo0?ooo`3o0?oood@0oooo00<000000?ooo`3oool0B@3oool001d0oooo00<000000?ooo`3oool0 ?@3oool00`000000oooo0?ooo`3o0?ooodH0oooo00<000000?ooo`3oool0B03oool000P0oooo0P00 00040?ooo`8000001@3oool3000000D0oooo00<000000?ooo`3oool0>`3oool200000?l0ooooBP3o ool00`000000oooo0?ooo`170?ooo`001`3oool010000000oooo0?ooo`00000;0?ooo`030000003o ool0oooo00@0oooo00<000000?ooo`3oool0>P3oool00`000000oooo0?ooo`3o0?oood/0oooo0P00 00170?ooo`001`3oool010000000oooo0?ooo`0000080?ooo`D000001@3oool4000003P0oooo00<0 00000?ooo`3oool0o`3ooom>0?ooo`030000003oool0oooo04@0oooo00000`3oool0000000000002 00000080oooo00@000000?ooo`3oool00000203oool010000000oooo0?ooo`0000060?ooo`030000 003oool0oooo03P0oooo00<000000?ooo`3oool0o`3ooom@0?ooo`030000003oool0oooo04<0oooo 00070?ooo`040000003oool0oooo000000T0oooo00<000000?ooo`0000001P3oool00`000000oooo 0?ooo`0g0?ooo`030000003oool0oooo0?l0ooooDP3oool00`000000oooo0?ooo`120?ooo`00203o ool2000000/0oooo0P0000060?ooo`030000003oool0oooo03H0oooo00<000000?ooo`3oool0o`3o oomD0?ooo`030000003oool0oooo0440oooo000M0?ooo`030000003oool0oooo03D0oooo00<00000 0?ooo`3oool0o`3ooomF0?ooo`030000003oool0oooo0400oooo000M0?ooo`030000003oool0oooo 03@0oooo00<000000?ooo`3oool0o`3ooomH0?ooo`030000003oool0oooo03l0oooo000M0?ooo`03 0000003oool0oooo03<0oooo00<000000?ooo`3oool0o`3ooomJ0?ooo`030000003oool0oooo03h0 oooo000M0?ooo`<00000`3oool001d0oooo00<000000?ooo`3oool0;`3oool00`00 0000oooo0?ooo`3o0?ooof80oooo00<000000?ooo`3oool0>P3oool001d0oooo00<000000?ooo`3o ool0;@3oool200000?l0ooooIP3oool00`000000oooo0?ooo`0i0?ooo`007@3oool00`000000oooo 0?ooo`0/0?ooo`030000003oool0oooo0?l0ooooI`3oool2000003T0oooo000M0?ooo`030000003o ool0oooo02/0oooo00<000000?ooo`3oool0o`3ooomZ0?ooo`030000003oool0oooo03H0oooo000M 0?ooo`<00000:P3oool00`000000oooo0?ooo`3o0?ooof`0oooo00<000000?ooo`3oool0=@3oool0 01d0oooo00<000000?ooo`3oool0:@3oool00`000000oooo0?ooo`3o0?ooofh0oooo00<000000?oo o`3oool0=03oool001d0oooo00<000000?ooo`3oool0:03oool00`000000oooo0?ooo`3o0?ooog00 oooo00<000000?ooo`3oool0<`3oool001d0oooo00<000000?ooo`3oool09`3oool00`000000oooo 0?ooo`3o0?ooog80oooo00<000000?ooo`3oool0"], ImageRangeCache->{{{0, 495.75}, {157.125, 0}} -> {-0.20717, -1.04619, \ 0.00691341, 0.00691341}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[BoxData[ \(Table[ Show[{g1, Graphics[{PointSize[ .05], Point[{x[B[\([1, IntegerPart[\(t + dk\)\/dk], 2]\)]], y[B[\([1, IntegerPart[\(t + dk\)\/dk], 2]\)]]}]}]}, AspectRatio \[Rule] 1, PlotRange \[Rule] {{\(-0.1\), \[Pi] + .1}, {\(-1.1\), 1}}], {t, 0, k, dk}]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Export["\", %, AnimationDisplayTime \[Rule] dk]\)], "Input"], Cell[BoxData[ \("Sine.GIF"\)], "Output"] }, Open ]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowSize->{928, 625}, 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[1705, 50, 65, 1, 30, "Input"], Cell[1773, 53, 63, 1, 30, "Input"], Cell[CellGroupData[{ Cell[1861, 58, 134, 2, 30, "Input"], Cell[1998, 62, 14450, 426, 100, 4234, 295, "GraphicsData", "PostScript", \ "Graphics"], Cell[16451, 490, 130, 3, 29, "Output"] }, Open ]], Cell[16596, 496, 51, 1, 30, "Input"], Cell[CellGroupData[{ Cell[16672, 501, 122, 2, 50, "Input"], Cell[16797, 505, 43678, 916, 341, 6530, 453, "GraphicsData", "PostScript", \ "Graphics"], Cell[60478, 1423, 130, 3, 29, "Output"] }, Open ]], Cell[60623, 1429, 151, 3, 50, "Input"], Cell[CellGroupData[{ Cell[60799, 1436, 79, 1, 30, "Input"], Cell[60881, 1439, 17866, 488, 186, 4532, 319, "GraphicsData", "PostScript", \ "Graphics"], Cell[78750, 1929, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[78917, 1937, 183, 4, 56, "Input"], Cell[79103, 1943, 17771, 487, 186, 4518, 319, "GraphicsData", "PostScript", \ "Graphics"], Cell[96877, 2432, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[97044, 2440, 196, 4, 76, "Input"], Cell[97243, 2446, 17984, 490, 186, 4520, 319, "GraphicsData", "PostScript", \ "Graphics"], Cell[115230, 2938, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[115397, 2946, 221, 4, 81, "Input"], Cell[115621, 2952, 17996, 490, 186, 4520, 319, "GraphicsData", "PostScript", \ "Graphics"], Cell[133620, 3444, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[133787, 3452, 53, 1, 30, "Input"], Cell[133843, 3455, 53680, 1030, 499, 6407, 442, "GraphicsData", "PostScript", \ "Graphics"], Cell[187526, 4487, 130, 3, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[187693, 4495, 182, 3, 81, "Input"], Cell[187878, 4500, 55, 1, 29, "Output"] }, Open ]], Cell[187948, 4504, 97, 2, 50, "Input"], Cell[CellGroupData[{ Cell[188070, 4510, 207, 3, 87, "Input"], Cell[188280, 4515, 55, 1, 29, "Output"] }, Open ]], Cell[188350, 4519, 139, 2, 56, "Input"], Cell[CellGroupData[{ Cell[188514, 4525, 128, 2, 56, "Input"], Cell[188645, 4529, 150, 2, 42, "Output"] }, Open ]], Cell[188810, 4534, 156, 3, 44, "Input"], Cell[CellGroupData[{ Cell[188991, 4541, 66, 1, 30, "Input"], Cell[189060, 4544, 31908, 726, 186, 5724, 398, "GraphicsData", "PostScript", \ "Graphics"], Cell[220971, 5272, 130, 3, 29, "Output"] }, Open ]], Cell[221116, 5278, 513, 12, 102, "Text"], Cell[221632, 5292, 90, 1, 46, "Text"], Cell[221725, 5295, 49, 1, 30, "Input"], Cell[221777, 5298, 113, 2, 30, "Input"], Cell[221893, 5302, 74, 1, 30, "Input"], Cell[221970, 5305, 54, 1, 30, "Input"], Cell[222027, 5308, 152, 4, 42, "Input"], Cell[CellGroupData[{ Cell[222204, 5316, 123, 3, 30, "Input"], Cell[222330, 5321, 20846, 505, 167, 4234, 295, "GraphicsData", "PostScript", \ "Graphics"], Cell[243179, 5828, 130, 3, 29, "Output"] }, Open ]], Cell[243324, 5834, 359, 8, 64, "Input"], Cell[CellGroupData[{ Cell[243708, 5846, 91, 1, 30, "Input"], Cell[243802, 5849, 44, 1, 29, "Output"] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)