(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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[ 698394, 25495]*) (*NotebookOutlinePosition[ 699035, 25518]*) (* CellTagsIndexPosition[ 698991, 25514]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \(SetDirectory["\<~/Research/NLS/SplitStep\>"]\)], "Input"], Cell[BoxData[ \("/rknapp/rknapp/Research/NLS/SplitStep"\)], "Output"] }, Open ]], Cell[BoxData[ \(<< ../Soliton.m\)], "Input"], Cell[BoxData[ \(<< SplitStep.m\)], "Input"], Cell[CellGroupData[{ Cell["Basic Method", "Subsubsection"], Cell[CellGroupData[{ Cell[BoxData[ \(Developer`SetSystemOptions["\" \[Rule] False] \)], "Input"], Cell[BoxData[ \("CatchMachineUnderflow" \[Rule] False\)], "Output"] }, Open ]], Cell[BoxData[{ \(\(prec\ = \ Sequence[];\)\), "\[IndentingNewLine]", \(\($MinPrecision\ = \ \(-Infinity\);\)\), "\[IndentingNewLine]", \(\($MaxPrecision\ = \ Infinity;\)\)}], "Input"], Cell[BoxData[ \(\(prec\ = \ 100;\)\)], "Input"], Cell[BoxData[{ \(\(n\ \ = \ 2048;\)\), "\[IndentingNewLine]", \(\(L\ = \ 30\ \[Pi];\)\), "\[IndentingNewLine]", \(\(T\ = \ 1;\)\), "\[IndentingNewLine]", \(\(b\ = \ 1/2;\)\), "\[IndentingNewLine]", \(\(alp\ = \ 1;\)\), "\[IndentingNewLine]", \(xmin\ = \ L/2; xmax\ = \ \(-L\)/2;\), "\[IndentingNewLine]", \(\(grid\ = \ N[Discretize[x, {x, xmin, xmax}, n], prec];\)\), "\[IndentingNewLine]", \(\(u0\ = \ \(LinearPotentialSoliton[1, b, alp]\)[grid, 0];\)\), "\[IndentingNewLine]", \(\(exact\ = \ \(LinearPotentialSoliton[1, b, alp]\)[grid, T];\)\), "\[IndentingNewLine]", \(\(v\ = \ Function[2\ #\ Conjugate[#]\ - \ alp\ grid];\)\)}], "Input"], Cell[BoxData[ \(\(colors\ = \ {RGBColor[0, 0, 0], \ RGBColor[1, 0, 0], RGBColor[0, 1, 0], \ RGBColor[0, 0, 1], \ RGBColor[1, 0, 1]};\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Block[{$MaxPrecision\ = \ prec, \ $MinPrecision\ = \ prec}, Clear[errtab]; \[IndentingNewLine]Show[ Table[\[IndentingNewLine]splits\ = \ SplitStep`Private`SimplifySplitStep[ord, \ {hsym, vsym, Lsym}, prec]; \[IndentingNewLine]ListPlot[ \(Log[10, errtab[ord]\ = \ Table[nt\ = \ Ceiling[2^k]; \[IndentingNewLine]h\ = \ T/nt; \[IndentingNewLine]DownValues[ SplitStep`Private`CachedD2Vector]\ = \ Last[DownValues[ SplitStep`Private`CachedD2Vector]]; \ \[IndentingNewLine]time\ = \ First[Timing[ app\ = \ Nest[splits[h, v, \ L], u0, \ nt]]]/ Second; \[IndentingNewLine]err\ = \ Max[Abs[exact\ - \ app]]; \[IndentingNewLine]Print[ {ord, h, time, \ err}]; \[IndentingNewLine]{ord, \ h, \ time, \ err}, \[IndentingNewLine]{k, 0, 8}]]\)[ \([All, {2, 4}]\)], \ PlotStyle \[Rule] {PointSize[0.025], \ colors[\([ord/2]\)]}], \[IndentingNewLine]{ord, 6, 10, 2}], \ PlotRange \[Rule] All];]\)], "Input"], Cell[BoxData[ \({6, 1, 50.9`, 1.0941707064642257462119427984240010918016232247883837629604118450339974\ 80119413038756262075710472313`100}\)], "Print"], Cell[BoxData[ \({6, 1\/2, 96.53999999999999`, 0.6577983900725539928946500032985137629958809049088679580153982652718039\ 216445842608670059483977876676`100}\)], "Print"], Cell[BoxData[ \({6, 1\/4, 188.23`, 0.2269518862113686225528690780544799127341767575178770641773199700980765\ 994745906898255230753172065016`100}\)], "Print"], Cell[BoxData[ \({6, 1\/8, 370.57000000000005`, 0.0022909255631234031208203478964412281158716862137437287195633147651473\ 46485341440285992852197304467508`100}\)], "Print"], Cell[BoxData[ \({6, 1\/16, 732.8499999999999`, 0.0000104383706941304086891272435883299566322907938799128934015214960637\ 3474793977266436512799173371021673`100}\)], "Print"], Cell[BoxData[ \({6, 1\/32, 1444.3999999999999`, 1.6057182217201144452322230305183606223371727705930245218961321319013907\ 2731581136397043447237587254`100*^-7}\)], "Print"], Cell[BoxData[ \({6, 1\/64, 2857.29`, 3.2752600980707677177230478848242412106116715911261229727765030973078165\ 33481878399849967477732330912`100*^-9}\)], "Print"], Cell[BoxData[ \({6, 1\/128, 5604.669999999999`, 5.5080250899705381405642924290984680888671067664322833509355544592176430\ 17644068893495646062692150201`100*^-11}\)], "Print"], Cell[BoxData[ \({6, 1\/256, 11000.07`, 8.7748684251514359459184583334540856479983315982730948710635359514602869\ 98931186283463900036004304174`100*^-13}\)], "Print"], 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 0.97619 0.395468 0.601417 0.0486617 [ [.18526 .58892 -6 -9 ] [.18526 .58892 6 0 ] [.38299 .58892 -12 -9 ] [.38299 .58892 12 0 ] [.58072 .58892 -6 -9 ] [.58072 .58892 6 0 ] [.77846 .58892 -12 -9 ] [.77846 .58892 12 0 ] [.96369 .01748 -18 -4.5 ] [.96369 .01748 0 4.5 ] [.96369 .1148 -18 -4.5 ] [.96369 .1148 0 4.5 ] [.96369 .21212 -12 -4.5 ] [.96369 .21212 0 4.5 ] [.96369 .30945 -12 -4.5 ] [.96369 .30945 0 4.5 ] [.96369 .40677 -12 -4.5 ] [.96369 .40677 0 4.5 ] [.96369 .50409 -12 -4.5 ] [.96369 .50409 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 .18526 .60142 m .18526 .60767 L s [(-2)] .18526 .58892 0 1 Mshowa .38299 .60142 m .38299 .60767 L s [(-1.5)] .38299 .58892 0 1 Mshowa .58072 .60142 m .58072 .60767 L s [(-1)] .58072 .58892 0 1 Mshowa .77846 .60142 m .77846 .60767 L s [(-0.5)] .77846 .58892 0 1 Mshowa .125 Mabswid .2248 .60142 m .2248 .60517 L s .26435 .60142 m .26435 .60517 L s .3039 .60142 m .3039 .60517 L s .34344 .60142 m .34344 .60517 L s .42254 .60142 m .42254 .60517 L s .46208 .60142 m .46208 .60517 L s .50163 .60142 m .50163 .60517 L s .54118 .60142 m .54118 .60517 L s .62027 .60142 m .62027 .60517 L s .65982 .60142 m .65982 .60517 L s .69936 .60142 m .69936 .60517 L s .73891 .60142 m .73891 .60517 L s .818 .60142 m .818 .60517 L s .85755 .60142 m .85755 .60517 L s .8971 .60142 m .8971 .60517 L s .93664 .60142 m .93664 .60517 L s .14571 .60142 m .14571 .60517 L s .10616 .60142 m .10616 .60517 L s .06661 .60142 m .06661 .60517 L s .02707 .60142 m .02707 .60517 L s .25 Mabswid 0 .60142 m 1 .60142 L s .97619 .01748 m .98244 .01748 L s [(-12)] .96369 .01748 1 0 Mshowa .97619 .1148 m .98244 .1148 L s [(-10)] .96369 .1148 1 0 Mshowa .97619 .21212 m .98244 .21212 L s [(-8)] .96369 .21212 1 0 Mshowa .97619 .30945 m .98244 .30945 L s [(-6)] .96369 .30945 1 0 Mshowa .97619 .40677 m .98244 .40677 L s [(-4)] .96369 .40677 1 0 Mshowa .97619 .50409 m .98244 .50409 L s [(-2)] .96369 .50409 1 0 Mshowa .125 Mabswid .97619 .04181 m .97994 .04181 L s .97619 .06614 m .97994 .06614 L s .97619 .09047 m .97994 .09047 L s .97619 .13913 m .97994 .13913 L s .97619 .16346 m .97994 .16346 L s .97619 .18779 m .97994 .18779 L s .97619 .23645 m .97994 .23645 L s .97619 .26079 m .97994 .26079 L s .97619 .28512 m .97994 .28512 L s .97619 .33378 m .97994 .33378 L s .97619 .35811 m .97994 .35811 L s .97619 .38244 m .97994 .38244 L s .97619 .4311 m .97994 .4311 L s .97619 .45543 m .97994 .45543 L s .97619 .47976 m .97994 .47976 L s .97619 .52842 m .97994 .52842 L s .97619 .55276 m .97994 .55276 L s .97619 .57709 m .97994 .57709 L s .25 Mabswid .97619 0 m .97619 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 1 0 r .025 w .97619 .60332 Mdot .85714 .59257 Mdot .7381 .57008 Mdot .61905 .47295 Mdot .5 .35902 Mdot .38095 .27079 Mdot .2619 .18853 Mdot .14286 .1022 Mdot .02381 .01472 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@00<000I@00V@0`000`<00`I@0`V@0`cP0`o`1U001U<01UI@1UV@1UcP1Uo`2I002I<02I I@2IV@2IcP3><03>I@3>V@3>o`3o<03oI@3oV@3ocS000300<300IC00VC00cS00oc0`030`<30`VC0` cS0`oc1U031U<31UIC1UVC1UcS1Uoc2I032I<32IIC2IVC2IcS2Ioc3>033><33>IC3>VC3>cS3>oc3o 033o<33oIC3ocS3oofD006D0<6D0IFD0VFD0cVD0ofD`0?l160400`010@060@001P443Ol13P400`01 0@060@001@463Ol13@400`010@060@001@463Oh110020@@010400`010@060@001@463Ol10@401@01 0@4000L100<00@401P4000D11Pgo0@4100<00@400P400`010@040@<01P4000H110gi0@@010400`01 0@030@03004100<100<00@401P400?l130400`010@040@030041008100<00@401P400?l12P4300<1 00@00@4010400`010@060@00o`4<0@03004100810P050@03004100H1003o0AP100<00@401P400?l1 60400`010@060@00o`4H0@801`400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@40 1P400?l160400`010@060@00o`4H0@03004100H1003o0AP10P070@00o`4H0@03004100H1003o0AP1 00<00@401P400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`01 0@060@00o`4H0@801`4002P110g[0@03004100H1000W0@H=jP400`010@060@009`463NX100<00@40 1P4002L11PgZ0@03004100H1000W0@H=g04400<10P050@03004100H1000X0@@=g`401@010@400081 00<00@400P400`010@060@00o`4<0@0500410@000P400`010@020@<01P400?l1104400@100D00@41 00020@030041008100<00@401P400?l130401@010@40008100<00@400P400`010@060@00o`4:0@<0 0`4010010@040@03004100H1003o0@`100<00@400P4200D100<00@401P400?l160400`010@060@00 o`4H0@03004100H1003o0AP10P070@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`01 0@060@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@801`400?l1 60400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00BP443LT1 00<00@401P4004T11Pg80@03004100H100190@H=b04200L100190@H=b0400`010@060@00B@463LP1 00<00@401P4004X110g90@03004100H1003o0AP100<00@401P400?l14@4200D100<00@401P400?l1 404010010@040@03004100H1003o0A0100@00@40104300H1003o0@X110030@801@400`010@060@00 o`4@0@04004100@100<00@401P400?l1404010010@040@03004100H1003o0A410P050@03004100H1 003o0AP100<00@401P400?l160400`010@060@00o`4H0@801`400?l160400`010@060@00o`4H0@03 004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@40 1P4006`110fW0@801`4006/11PfV0@03004100H1001[0@H=YP400`010@060@00J`463JH100<00@40 1P4006/11PfV0@03004100H1001/0@@=Y`400`010@060@00o`4H0@03004100H1003o0AP10P070@00 o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@03004100H1003o0A41 0P050@03004100H1003o0A0100@00@4010400`010@060@00o`4@0@04004100@10`060@00o`4:0@@0 0P4300D100<00@401P400?l140400`010@050@03004100H1003o0A0100<00@401@400`010@060@00 o`4A0@<010400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l1604200L1003o0AP1 00<00@401P400?l160400`010@060@00o`4H0@03004100H1002>0@@=Q@400`010@060@00S@463H@1 00<00@401P4008d11Pf40@03004100H1002=0@H=Q04200L1002=0@H=Q0400`010@060@00SP443HD1 00<00@401P400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`01 0@060@00o`4H0@801`400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l1 60400`010@060@00o`4B0@03004100<100<00@401P400?l14P400`010@030@03004100H1003o0@l1 1@040@<01P400?l12P4400050@010@001@400`010@060@00o`4@0@03004000D100<00@401P400?l1 4@4200D100<00@401P400?l14P400`010@030@03004100H1003o0AP100<00@401P400?l160400`01 0@060@00o`4H0@801`400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l1 60400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l1604200L1003o0AP100<00@40 1P400;0110eS0@03004100H1002_0@H=HP400`010@060@00[`463F8100<00@401P400:l11PeR0@03 004100H1002_0@H=HP400`010@060@00/0443F<10P070@00o`4H0@03004100H1003o0AP100<00@40 1P400?l160400`010@060@00o`4H0@03004100H1003o0A0110040@03004100H1003o0A0100<00@40 1@400`010@060@00o`4A0@03004100@10`060@00o`4:0@@010400`010@030@03004100H1003o0A<1 00<00@400P400`010@060@00o`4@0@04004100@100<00@401P400?l14@4200D100<00@401P400?l1 60400`010@060@00o`4H0@03004100H1003o0AP10P070@00o`4H0@03004100H1003o0AP100<00@40 1P400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00 o`4H0@801`400?l160400`010@060@00dP443D4100<00@401P4003H1100_0@@00`400`010@020@<0 ;`4402H11Pd40@8010400`010@020@<0;P400`010@060@00=P400`010@0b0@03004100X100<00@40 ;P400`010@0U0@H=0`4010010@0;0@03004102/100<00@401P4003L100<00@40<@400`010@0:0@03 004102h100<00@409@463@<100@00@402`400`010@0[0@03004100H1000`0@@010400`010@0X0@@0 10400`010@070@<0:@4400@100<00@409@463@040041008100<00@401P4302h100<00@401P4003T1 00<00@40;`400`010@070@030041034100<00@409P443@@100@00@4020400`010@0^0@801`4003H1 00@00@40;`4300T100<00@40;`43030100@00@4020400`010@0;0@@=7`400`010@060@00=`420381 00<00@401`44030100<00@40;`4200T110090@H=7P400`010@060@00l`463Ah100<00@401P400?<1 1PdM0@@=1P400?<11PdL0@H=1@400?@110dM0@H=1@400?l05P063@@00@4000P100<00@4020400`01 0@080@03004100T100<00@4020400`010@080@03004100T100<00@4020400`010@080@03004100T1 00<00@4020400`010@080@03004100P100<00@402@400`010@080@03004100P100<00@402@400`01 0@080@03004100P100<00@402@400`010@080@03004100P100<00@402@400`010@080@03004100H1 1Pd50@00=@400`010@0f0@03004103D100<00@40=P400`010@0d0@@=1P400?l160400`010@060@00 o`4H0@03004100H10000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.47158, -12.3592, 0.00883248, 0.0717805}}], Cell[BoxData[ \({8, 1, 143.15000000000146`, 1.2251909788419708018969323597255968405868885503562764991133753870173527\ 72264460412474490388219261765`100}\)], "Print"], Cell[BoxData[ \({8, 1\/2, 276.630000000001`, 0.9891444463547778382054771791204282329212715133842809221113366165231059\ 785665003312151009861829106615`100}\)], "Print"], Cell[BoxData[ \({8, 1\/4, 543.4499999999971`, 0.7916973482925052521856960597687454453799335908112967705651911773847838\ 406966339868665794599658373105`100}\)], "Print"], Cell[BoxData[ \({8, 1\/8, 1074.1900000000023`, 0.5986114227732225587189131526100358903317045113518127829010163400939564\ 626031358816438598719881739901`100}\)], "Print"], Cell[BoxData[ \({8, 1\/16, 2127.8799999999974`, 0.0007384606079967635372129279356668028062625992603094265203999879052346\ 810591899924603756881562938599949`100}\)], "Print"], Cell[BoxData[ \({8, 1\/32, 4209.23`, 7.9082991855627910488748189279880943137566738986224706511851772355003412\ 56101043936890019079909163392`100*^-8}\)], "Print"], Cell[BoxData[ \({8, 1\/64, 8332.219999999998`, 4.9529632113943733048288646709753997239160653707237312792661027481722255\ 34429853324625365573562944312`100*^-10}\)], "Print"], Cell[BoxData[ \($Aborted\)], "Output"] }, Open ]], Cell[BoxData[ \(app\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Show[ Block[{$DisplayFunction\ = \ Identity}, Table[ListPlot[Log[10, \(errtab[ord]\)[\([All, {3, 4}]\)]], \ PlotStyle \[Rule] {PointSize[0.025], \ colors[\([ord/2]\)]}], {ord, 2, 8, 2}]], \ PlotRange \[Rule] All]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.392893 0.264019 0.601433 0.0487454 [ [.12887 .58893 -6 -9 ] [.12887 .58893 6 0 ] [.26088 .58893 -12 -9 ] [.26088 .58893 12 0 ] [.5249 .58893 -9 -9 ] [.5249 .58893 9 0 ] [.65691 .58893 -3 -9 ] [.65691 .58893 3 0 ] [.78892 .58893 -9 -9 ] [.78892 .58893 9 0 ] [.92093 .58893 -3 -9 ] [.92093 .58893 3 0 ] [.38039 .01649 -18 -4.5 ] [.38039 .01649 0 4.5 ] [.38039 .11398 -18 -4.5 ] [.38039 .11398 0 4.5 ] [.38039 .21147 -12 -4.5 ] [.38039 .21147 0 4.5 ] [.38039 .30896 -12 -4.5 ] [.38039 .30896 0 4.5 ] [.38039 .40645 -12 -4.5 ] [.38039 .40645 0 4.5 ] [.38039 .50394 -12 -4.5 ] [.38039 .50394 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 .12887 .60143 m .12887 .60768 L s [(-1)] .12887 .58893 0 1 Mshowa .26088 .60143 m .26088 .60768 L s [(-0.5)] .26088 .58893 0 1 Mshowa .5249 .60143 m .5249 .60768 L s [(0.5)] .5249 .58893 0 1 Mshowa .65691 .60143 m .65691 .60768 L s [(1)] .65691 .58893 0 1 Mshowa .78892 .60143 m .78892 .60768 L s [(1.5)] .78892 .58893 0 1 Mshowa .92093 .60143 m .92093 .60768 L s [(2)] .92093 .58893 0 1 Mshowa .125 Mabswid .02327 .60143 m .02327 .60518 L s .04967 .60143 m .04967 .60518 L s .07607 .60143 m .07607 .60518 L s .10247 .60143 m .10247 .60518 L s .15528 .60143 m .15528 .60518 L s .18168 .60143 m .18168 .60518 L s .20808 .60143 m .20808 .60518 L s .23448 .60143 m .23448 .60518 L s .28728 .60143 m .28728 .60518 L s .31369 .60143 m .31369 .60518 L s .34009 .60143 m .34009 .60518 L s .36649 .60143 m .36649 .60518 L s .41929 .60143 m .41929 .60518 L s .4457 .60143 m .4457 .60518 L s .4721 .60143 m .4721 .60518 L s .4985 .60143 m .4985 .60518 L s .5513 .60143 m .5513 .60518 L s .57771 .60143 m .57771 .60518 L s .60411 .60143 m .60411 .60518 L s .63051 .60143 m .63051 .60518 L s .68331 .60143 m .68331 .60518 L s .70972 .60143 m .70972 .60518 L s .73612 .60143 m .73612 .60518 L s .76252 .60143 m .76252 .60518 L s .81532 .60143 m .81532 .60518 L s .84173 .60143 m .84173 .60518 L s .86813 .60143 m .86813 .60518 L s .89453 .60143 m .89453 .60518 L s .94733 .60143 m .94733 .60518 L s .97373 .60143 m .97373 .60518 L s .25 Mabswid 0 .60143 m 1 .60143 L s .39289 .01649 m .39914 .01649 L s [(-12)] .38039 .01649 1 0 Mshowa .39289 .11398 m .39914 .11398 L s [(-10)] .38039 .11398 1 0 Mshowa .39289 .21147 m .39914 .21147 L s [(-8)] .38039 .21147 1 0 Mshowa .39289 .30896 m .39914 .30896 L s [(-6)] .38039 .30896 1 0 Mshowa .39289 .40645 m .39914 .40645 L s [(-4)] .38039 .40645 1 0 Mshowa .39289 .50394 m .39914 .50394 L s [(-2)] .38039 .50394 1 0 Mshowa .125 Mabswid .39289 .04086 m .39664 .04086 L s .39289 .06523 m .39664 .06523 L s .39289 .08961 m .39664 .08961 L s .39289 .13835 m .39664 .13835 L s .39289 .16272 m .39664 .16272 L s .39289 .1871 m .39664 .1871 L s .39289 .23584 m .39664 .23584 L s .39289 .26022 m .39664 .26022 L s .39289 .28459 m .39664 .28459 L s .39289 .33333 m .39664 .33333 L s .39289 .35771 m .39664 .35771 L s .39289 .38208 m .39664 .38208 L s .39289 .43082 m .39664 .43082 L s .39289 .4552 m .39664 .4552 L s .39289 .47957 m .39664 .47957 L s .39289 .52831 m .39664 .52831 L s .39289 .55269 m .39664 .55269 L s .39289 .57706 m .39664 .57706 L s .25 Mabswid .39289 0 m .39289 .61803 L s 0 0 0 r .025 w .02381 .58288 Mdot .10329 .56158 Mdot .18276 .53628 Mdot .26577 .50798 Mdot .34172 .47896 Mdot .42209 .44973 Mdot .50201 .42042 Mdot .58015 .39108 Mdot .66052 .36173 Mdot 1 0 0 r .12887 .56942 Mdot .19627 .5486 Mdot .27252 .51294 Mdot .35035 .46179 Mdot .43229 .4028 Mdot .50972 .34397 Mdot .58899 .2854 Mdot .66846 .22673 Mdot .74784 .16804 Mdot 0 1 0 r .21928 .60332 Mdot .30873 .59257 Mdot .38457 .56996 Mdot .46218 .47272 Mdot .53816 .3587 Mdot .62067 .27024 Mdot .69832 .18784 Mdot .77672 .10137 Mdot .85616 .01705 Mdot 0 0 1 r .34525 .60308 Mdot .42209 .60296 Mdot .50023 .59597 Mdot .57858 .59078 Mdot .65828 .44876 Mdot .73832 .25525 Mdot .81934 .14786 Mdot .8985 .03732 Mdot .97619 .01472 Mdot 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@00<000I@00V@0`000`<00`I@0`V@0`cP0`o`1U001U<01UI@1UV@1UcP1Uo`2I002I<02I I@2IV@2IcP3><03>I@3>V@3>o`3o<03oI@3oV@3ocS000300<300IC00VC00cS00oc0`030`<30`VC0` cS0`oc1U031U<31UIC1UVC1UcS1Uoc2I032I<32IIC2IVC2IcS2Ioc3>033><33>IC3>VC3>cS3>oc3o 033o<33oIC3ocS3oofD006D0<6D0IFD0VFD0cVD0ofD`070100<00@40[@40070100<00@40X`443`H1 001R0@@00P4400@100<00@40P@443Ad11Pl50@00I0401@010@4000L100<00@40P0463A`11Pl50@00 I0400`010@020@03004100@10`200@H=70463`D1001L0@@010400`010@030@03004100<100<00@40 P0463A`11Pl50@00I0400`010@040@030041008100<00@40P0463Ad110l60@00HP4300<100@00@40 10400`010@210@@=20443a`1001T0@03004100810P050@03004108`11PlK0@00L0400`010@2<0@H? 6`40070100<00@40S0463a/1001`0@80S@463a/1001`0@03004108d110lL0@00L0400`010@2]0@00 L0400`010@2]0@00L0400`010@2]0@00L0400`010@2]0@00L0400`010@2]0@00L0420:h1001`0@03 00410:d1001`0@0300410:d1001`0@0300410:d1001`0@0300410:d1001`0@0300410:d1001`0@03 00410:d1001`0@80[P40070100<00@40JP443Cl1001`0@03004106T11Pdn0@00L0400`010@1Y0@H= ?P40070100<00@40J@463Ch1001R0@@00`4200D100<00@40J@463Ch1001T0@0500410@000P400`01 0@020@03004106X110do0@00I0401@010@40008100<00@400P430:d1001L0@@010401@010@400081 00<00@400P400`010@2]0@00I0401@010@40008100<00@400P400`010@2]0@00HP4300<100@00@40 10400`010@2]0@00I0400`010@020@801@400`010@2]0@00L0400`010@2]0@00L0400`010@2]0@00 L04207L110lc0@00L0400`010@1e0@H?@400`010@2]0@00"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-1.49282, -12.3383, 0.01323, 0.0716573}}], Cell[BoxData[ TagBox[\(\[SkeletonIndicator] Graphics \[SkeletonIndicator]\), False, Editable->False]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Length[exact]\)], "Input"], Cell[BoxData[ \(720\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(exact[\([1]\)]\)], "Input"], Cell[BoxData[ \(\(\(0.0000515363365781905`\)\(\[InvisibleSpace]\)\) - 2.524469009055227`*^-20\ \[ImaginaryI]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Max[ Abs[exact\ - \ N[\(Soliton[1, 1]\)[Discretize[x, {x, xmin, xmax}, n], 1], 100]]] \)], "Input"], Cell[BoxData[ \(4.002966042486721`*^-16\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(u0[\([1]\)]\)], "Input"], Cell[BoxData[ \(6.974684712333172`*^-6 - 3.4164972858524004`*^-21\ \[ImaginaryI]\)], "Output"] }, Open ]], Cell[BoxData[ \(exact\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(h\)], "Input"], Cell[BoxData[ \(1\/256\)], "Output"], 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 0.97619 0.395468 0.583719 0.11049 [ [.18526 .57122 -6 -9 ] [.18526 .57122 6 0 ] [.38299 .57122 -12 -9 ] [.38299 .57122 12 0 ] [.58072 .57122 -6 -9 ] [.58072 .57122 6 0 ] [.77846 .57122 -12 -9 ] [.77846 .57122 12 0 ] [.96369 .03127 -12 -4.5 ] [.96369 .03127 0 4.5 ] [.96369 .14176 -12 -4.5 ] [.96369 .14176 0 4.5 ] [.96369 .25225 -12 -4.5 ] [.96369 .25225 0 4.5 ] [.96369 .36274 -12 -4.5 ] [.96369 .36274 0 4.5 ] [.96369 .47323 -12 -4.5 ] [.96369 .47323 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 .18526 .58372 m .18526 .58997 L s [(-2)] .18526 .57122 0 1 Mshowa .38299 .58372 m .38299 .58997 L s [(-1.5)] .38299 .57122 0 1 Mshowa .58072 .58372 m .58072 .58997 L s [(-1)] .58072 .57122 0 1 Mshowa .77846 .58372 m .77846 .58997 L s [(-0.5)] .77846 .57122 0 1 Mshowa .125 Mabswid .2248 .58372 m .2248 .58747 L s .26435 .58372 m .26435 .58747 L s .3039 .58372 m .3039 .58747 L s .34344 .58372 m .34344 .58747 L s .42254 .58372 m .42254 .58747 L s .46208 .58372 m .46208 .58747 L s .50163 .58372 m .50163 .58747 L s .54118 .58372 m .54118 .58747 L s .62027 .58372 m .62027 .58747 L s .65982 .58372 m .65982 .58747 L s .69936 .58372 m .69936 .58747 L s .73891 .58372 m .73891 .58747 L s .818 .58372 m .818 .58747 L s .85755 .58372 m .85755 .58747 L s .8971 .58372 m .8971 .58747 L s .93664 .58372 m .93664 .58747 L s .14571 .58372 m .14571 .58747 L s .10616 .58372 m .10616 .58747 L s .06661 .58372 m .06661 .58747 L s .02707 .58372 m .02707 .58747 L s .25 Mabswid 0 .58372 m 1 .58372 L s .97619 .03127 m .98244 .03127 L s [(-5)] .96369 .03127 1 0 Mshowa .97619 .14176 m .98244 .14176 L s [(-4)] .96369 .14176 1 0 Mshowa .97619 .25225 m .98244 .25225 L s [(-3)] .96369 .25225 1 0 Mshowa .97619 .36274 m .98244 .36274 L s [(-2)] .96369 .36274 1 0 Mshowa .97619 .47323 m .98244 .47323 L s [(-1)] .96369 .47323 1 0 Mshowa .125 Mabswid .97619 .05336 m .97994 .05336 L s .97619 .07546 m .97994 .07546 L s .97619 .09756 m .97994 .09756 L s .97619 .11966 m .97994 .11966 L s .97619 .16385 m .97994 .16385 L s .97619 .18595 m .97994 .18595 L s .97619 .20805 m .97994 .20805 L s .97619 .23015 m .97994 .23015 L s .97619 .27435 m .97994 .27435 L s .97619 .29644 m .97994 .29644 L s .97619 .31854 m .97994 .31854 L s .97619 .34064 m .97994 .34064 L s .97619 .38484 m .97994 .38484 L s .97619 .40693 m .97994 .40693 L s .97619 .42903 m .97994 .42903 L s .97619 .45113 m .97994 .45113 L s .97619 .49533 m .97994 .49533 L s .97619 .51742 m .97994 .51742 L s .97619 .53952 m .97994 .53952 L s .97619 .56162 m .97994 .56162 L s .97619 .00917 m .97994 .00917 L s .97619 .60582 m .97994 .60582 L s .25 Mabswid .97619 0 m .97619 .61803 L s 0 0 0 r .025 w .97619 .51929 Mdot .85714 .4789 Mdot .7381 .42418 Mdot .61905 .36063 Mdot .5 .29506 Mdot .38095 .22889 Mdot .2619 .16249 Mdot .14286 .09611 Mdot .02381 .03007 Mdot 1 0 0 r .97619 .51115 Mdot .85714 .46395 Mdot .7381 .38313 Mdot .61905 .2672 Mdot .5 .13354 Mdot .38095 .01472 Mdot .2619 .01725 Mdot .14286 .01744 Mdot .02381 .01745 Mdot 0 1 0 r .97619 .5889 Mdot .85714 .57467 Mdot .7381 .51245 Mdot .61905 .29196 Mdot .5 .04458 Mdot .38095 .01686 Mdot .2619 .01746 Mdot .14286 .01746 Mdot .02381 .01745 Mdot 0 0 1 r .97619 .59337 Mdot .85714 .60332 Mdot .7381 .59012 Mdot .61905 .57018 Mdot .5 .25146 Mdot .38095 .01843 Mdot .2619 .01746 Mdot .14286 .01745 Mdot .02381 .01745 Mdot 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@1E001EE@1EZP1Eo`2Z002ZE@2ZZP2ZoeEE05EEEEEEZUEEoeFZ05FZEEFZZUFZo`2I<:YE 0:YEEJYEZZYEojZZ0:ZZEJZZZZZZoomE0?mEEOmEZ_mEoonZ0?nZEOnZZ_nZohf=SIVIVLk>c][Jf/k> YHf=LOKN//JbSHUiHO;VeS1UcX5]EJj^[S2I<7UiNKjQOJ4Pl];BdT3RdXG>j_o2bYT`cS3>c[8P89Wj VD1YhR2986EUIJk^k[K^]S`003`0?3`0OC`0_S`0oc`l0?l160400`010@060@00K0443JL100<00@40 1P4000H110lN0@@?7P443ad100<=3`l00Pl00`d10@2T0@801`4000D11PlL0@H?70463a`11PnV0@03 004100H100050@H?70463a`11PlL0@H?YP400`010@060@001@463a`11PlL0@H?70463jH100<00@40 1P4000D11PlL0@H?70463a`11PnV0@03004100H100050@0300l?008?00<00@406`443ah110lN0@@? W`4300D100<00@401P4000D11P3o0@P100<00@400P400`010@060@001@4608<110f00@0300410081 0`060@001P4408<11Pef0@@00P4300D100<00@401P4008d11Pel0@03004100D100<00@401P4008d1 1Pel0@03004100D100<00@401P4008d11Pel0@@010400`010@060@00SP443HD100<00@401P400?l1 604200L1003o0AP100<00@401P400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@40 1P400?l160400`010@060@00o`4H0@801`400?l160400`010@060@00o`4H0@03004100H1000X0@@0 j`400`010@060@009`460>X100<00@401P4002L11P3Z0@03004100H1000W0@H0jP4200L1000W0@H0 jP400`010@060@00:0440>/100<00@401P400?l160400`010@060@00o`4H0@03004100H1003o0AP1 00<00@401P400?l160400`010@060@00o`4H0@801`4008h110b50@03004100H1002=0@H0@@?Q@400`010@060@00S@463gd1 0P050@03004100H1002=0@H?O04010010@040@03004100H1002=0@H?O`400`010@020@<01P4008d1 1PlM0@@0@@?7@4635d100<00@400P400`010@060@00[`4635X1 00@00@4010400`010@060@00[`4635/10P050@03004100H1002_0@H"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.47158, -5.28303, 0.00883248, 0.0316134}}] }, Open ]], Cell["With 512 modes", "Text"], 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 0.97619 0.395468 0.585028 0.119744 [ [.18526 .57253 -6 -9 ] [.18526 .57253 6 0 ] [.38299 .57253 -12 -9 ] [.38299 .57253 12 0 ] [.58072 .57253 -6 -9 ] [.58072 .57253 6 0 ] [.77846 .57253 -12 -9 ] [.77846 .57253 12 0 ] [.96369 .10605 -12 -4.5 ] [.96369 .10605 0 4.5 ] [.96369 .22579 -12 -4.5 ] [.96369 .22579 0 4.5 ] [.96369 .34554 -12 -4.5 ] [.96369 .34554 0 4.5 ] [.96369 .46528 -12 -4.5 ] [.96369 .46528 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 .18526 .58503 m .18526 .59128 L s [(-2)] .18526 .57253 0 1 Mshowa .38299 .58503 m .38299 .59128 L s [(-1.5)] .38299 .57253 0 1 Mshowa .58072 .58503 m .58072 .59128 L s [(-1)] .58072 .57253 0 1 Mshowa .77846 .58503 m .77846 .59128 L s [(-0.5)] .77846 .57253 0 1 Mshowa .125 Mabswid .2248 .58503 m .2248 .58878 L s .26435 .58503 m .26435 .58878 L s .3039 .58503 m .3039 .58878 L s .34344 .58503 m .34344 .58878 L s .42254 .58503 m .42254 .58878 L s .46208 .58503 m .46208 .58878 L s .50163 .58503 m .50163 .58878 L s .54118 .58503 m .54118 .58878 L s .62027 .58503 m .62027 .58878 L s .65982 .58503 m .65982 .58878 L s .69936 .58503 m .69936 .58878 L s .73891 .58503 m .73891 .58878 L s .818 .58503 m .818 .58878 L s .85755 .58503 m .85755 .58878 L s .8971 .58503 m .8971 .58878 L s .93664 .58503 m .93664 .58878 L s .14571 .58503 m .14571 .58878 L s .10616 .58503 m .10616 .58878 L s .06661 .58503 m .06661 .58878 L s .02707 .58503 m .02707 .58878 L s .25 Mabswid 0 .58503 m 1 .58503 L s .97619 .10605 m .98244 .10605 L s [(-4)] .96369 .10605 1 0 Mshowa .97619 .22579 m .98244 .22579 L s [(-3)] .96369 .22579 1 0 Mshowa .97619 .34554 m .98244 .34554 L s [(-2)] .96369 .34554 1 0 Mshowa .97619 .46528 m .98244 .46528 L s [(-1)] .96369 .46528 1 0 Mshowa .125 Mabswid .97619 .13 m .97994 .13 L s .97619 .15395 m .97994 .15395 L s .97619 .1779 m .97994 .1779 L s .97619 .20185 m .97994 .20185 L s .97619 .24974 m .97994 .24974 L s .97619 .27369 m .97994 .27369 L s .97619 .29764 m .97994 .29764 L s .97619 .32159 m .97994 .32159 L s .97619 .36949 m .97994 .36949 L s .97619 .39344 m .97994 .39344 L s .97619 .41739 m .97994 .41739 L s .97619 .44133 m .97994 .44133 L s .97619 .48923 m .97994 .48923 L s .97619 .51318 m .97994 .51318 L s .97619 .53713 m .97994 .53713 L s .97619 .56108 m .97994 .56108 L s .97619 .0821 m .97994 .0821 L s .97619 .05815 m .97994 .05815 L s .97619 .0342 m .97994 .0342 L s .97619 .01025 m .97994 .01025 L s .97619 .60898 m .97994 .60898 L s .25 Mabswid .97619 0 m .97619 .61803 L s 0 0 0 r .025 w .97619 .51518 Mdot .85714 .47141 Mdot .7381 .4121 Mdot .61905 .34324 Mdot .5 .27218 Mdot .38095 .20047 Mdot .2619 .1285 Mdot .14286 .05654 Mdot .02381 .01561 Mdot 1 0 0 r .97619 .50635 Mdot .85714 .4552 Mdot .7381 .36757 Mdot .61905 .24191 Mdot .5 .09709 Mdot .38095 .01472 Mdot .2619 .01573 Mdot .14286 .01579 Mdot .02381 .01579 Mdot 0 1 0 r .97619 .59379 Mdot .85714 .57268 Mdot .7381 .50789 Mdot .61905 .26894 Mdot .5 .01805 Mdot .38095 .01562 Mdot .2619 .01579 Mdot .14286 .0158 Mdot .02381 .01579 Mdot 0 0 1 r .97619 .60332 Mdot .85714 .59962 Mdot .7381 .59188 Mdot .61905 .56782 Mdot .5 .22227 Mdot .38095 .01576 Mdot .2619 .01581 Mdot .14286 .0159 Mdot .02381 .0158 Mdot 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@1E001EE@1EZP1Eo`2Z002ZE@2ZZP2ZoeEE05EEEEEEZUEEoeFZ05FZEEFZZUFZo`2I<:YE 0:YEEJYEZZYEojZZ0:ZZEJZZZZZZoomE0?mEEOmEZ_mEoonZ0?nZEOnZZ_nZohf=SIVIVLk>c][Jf/k> YHf=LOKN//JbSHUiHO;VeS1UcX5]EJj^[S2I<7UiNKjQOJ4Pl];BdT3RdXG>j_o2bYT`cS3>c[8P89Wj VD1YhR2986EUIJk^k[K^]S`003`0?3`0OC`0_S`0oc`l0?l160400`010@060@001P443ah110lN0@@? 7P443jL100<00@401P4000D11PlL0@H?70463a`11PlM0@@=Q@4200L100050@H?70463a`11PlL0@H? 70463H@100<00@401P4000D11PlL0@H?70463a`11PlL0@H=Q0400`010@060@001@463a`11PlL0@H? 70463a`11Pf40@03004100H100060@@?7P443ah110lN0@@?7@463H@100<00@401P4008h110f50@03 004100H1003o0AP100<00@401P400?l1604200L1003o0AP100<00@401P400?l160400`010@060@00 o`4H0@03004100H1000X0@@0j`400`010@060@009`460>X100<00@401P4002L11P3Z0@03004100H1 000W0@H0jP4200L1000W0@H0jP400`010@060@00:0440>/100<00@401P400?l160400`010@060@00 o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@801`4008h110b50@03 004100H1002=0@H0@@"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.47158, -4.88568, 0.00883248, 0.0291703}}], Cell["with 1024 modes", "Text"], 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 0.97619 0.395468 0.58284 0.119521 [ [.18526 .57034 -6 -9 ] [.18526 .57034 6 0 ] [.38299 .57034 -12 -9 ] [.38299 .57034 12 0 ] [.58072 .57034 -6 -9 ] [.58072 .57034 6 0 ] [.77846 .57034 -12 -9 ] [.77846 .57034 12 0 ] [.96369 .10475 -12 -4.5 ] [.96369 .10475 0 4.5 ] [.96369 .22428 -12 -4.5 ] [.96369 .22428 0 4.5 ] [.96369 .3438 -12 -4.5 ] [.96369 .3438 0 4.5 ] [.96369 .46332 -12 -4.5 ] [.96369 .46332 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 .18526 .58284 m .18526 .58909 L s [(-2)] .18526 .57034 0 1 Mshowa .38299 .58284 m .38299 .58909 L s [(-1.5)] .38299 .57034 0 1 Mshowa .58072 .58284 m .58072 .58909 L s [(-1)] .58072 .57034 0 1 Mshowa .77846 .58284 m .77846 .58909 L s [(-0.5)] .77846 .57034 0 1 Mshowa .125 Mabswid .2248 .58284 m .2248 .58659 L s .26435 .58284 m .26435 .58659 L s .3039 .58284 m .3039 .58659 L s .34344 .58284 m .34344 .58659 L s .42254 .58284 m .42254 .58659 L s .46208 .58284 m .46208 .58659 L s .50163 .58284 m .50163 .58659 L s .54118 .58284 m .54118 .58659 L s .62027 .58284 m .62027 .58659 L s .65982 .58284 m .65982 .58659 L s .69936 .58284 m .69936 .58659 L s .73891 .58284 m .73891 .58659 L s .818 .58284 m .818 .58659 L s .85755 .58284 m .85755 .58659 L s .8971 .58284 m .8971 .58659 L s .93664 .58284 m .93664 .58659 L s .14571 .58284 m .14571 .58659 L s .10616 .58284 m .10616 .58659 L s .06661 .58284 m .06661 .58659 L s .02707 .58284 m .02707 .58659 L s .25 Mabswid 0 .58284 m 1 .58284 L s .97619 .10475 m .98244 .10475 L s [(-4)] .96369 .10475 1 0 Mshowa .97619 .22428 m .98244 .22428 L s [(-3)] .96369 .22428 1 0 Mshowa .97619 .3438 m .98244 .3438 L s [(-2)] .96369 .3438 1 0 Mshowa .97619 .46332 m .98244 .46332 L s [(-1)] .96369 .46332 1 0 Mshowa .125 Mabswid .97619 .12866 m .97994 .12866 L s .97619 .15256 m .97994 .15256 L s .97619 .17647 m .97994 .17647 L s .97619 .20037 m .97994 .20037 L s .97619 .24818 m .97994 .24818 L s .97619 .27208 m .97994 .27208 L s .97619 .29599 m .97994 .29599 L s .97619 .31989 m .97994 .31989 L s .97619 .3677 m .97994 .3677 L s .97619 .39161 m .97994 .39161 L s .97619 .41551 m .97994 .41551 L s .97619 .43941 m .97994 .43941 L s .97619 .48722 m .97994 .48722 L s .97619 .51113 m .97994 .51113 L s .97619 .53503 m .97994 .53503 L s .97619 .55894 m .97994 .55894 L s .97619 .08085 m .97994 .08085 L s .97619 .05695 m .97994 .05695 L s .97619 .03304 m .97994 .03304 L s .97619 .00914 m .97994 .00914 L s .97619 .60674 m .97994 .60674 L s .25 Mabswid .97619 0 m .97619 .61803 L s 0 0 0 r .025 w .97619 .51314 Mdot .85714 .46946 Mdot .7381 .41026 Mdot .61905 .34152 Mdot .5 .27059 Mdot .38095 .199 Mdot .2619 .12717 Mdot .14286 .05534 Mdot .02381 .01564 Mdot 1 0 0 r .97619 .50433 Mdot .85714 .45328 Mdot .7381 .36585 Mdot .61905 .24044 Mdot .5 .09584 Mdot .38095 .01472 Mdot .2619 .01577 Mdot .14286 .01583 Mdot .02381 .01583 Mdot 0 1 0 r .97619 .59199 Mdot .85714 .5717 Mdot .7381 .50588 Mdot .61905 .26739 Mdot .5 .01714 Mdot .38095 .01567 Mdot .2619 .01582 Mdot .14286 .01583 Mdot .02381 .01583 Mdot 0 0 1 r .97619 .60332 Mdot .85714 .59871 Mdot .7381 .59039 Mdot .61905 .56827 Mdot .5 .22024 Mdot .38095 .01578 Mdot .2619 .01595 Mdot .14286 .01594 Mdot .02381 .01583 Mdot 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@1E001EE@1EZP1Eo`2Z002ZE@2ZZP2ZoeEE05EEEEEEZUEEoeFZ05FZEEFZZUFZo`2I<:YE 0:YEEJYEZZYEojZZ0:ZZEJZZZZZZoomE0?mEEOmEZ_mEoonZ0?nZEOnZZ_nZohf=SIVIVLk>c][Jf/k> YHf=LOKN//JbSHUiHO;VeS1UcX5]EJj^[S2I<7UiNKjQOJ4Pl];BdT3RdXG>j_o2bYT`cS3>c[8P89Wj VD1YhR2986EUIJk^k[K^]S`003`0?3`0OC`0_S`0oc`l0?l160400`010@060@001P443ah110lN0@@? 7P443jL100<00@401P4000D11PlL0@H?70463a`11PlM0@@=Q@4200L100050@H?70463a`11PlL0@H? 70463H@100<00@401P4000D11PlL0@H?70463a`11PlL0@H=Q0400`010@060@001@463a`11PlL0@H? 70463a`11Pf40@03004100H100060@@?7P443ah110lN0@@?7@463H@100<00@401P4008h110f50@03 004100H1003o0AP100<00@401P400?l1604200L1003o0AP100<00@401P400?l160400`010@060@00 :0440>/100<00@401P4002L11P3Z0@03004100H1000W0@H0jP400`010@060@009`460>X100<00@40 1P4002L11P3Z0@801`4002P1103[0@03004100H1003o0AP100<00@401P400?l160400`010@060@00 o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@801`4008h110b50@03 004100H1002=0@H0@@@4010010@040@03004100H1003A0@H<>@4200D100<00@401P400=41 1Pa00@03004100H1003A0@H<@0400`010@060@00d@4634010P070@00dP44344100<00@401P400?l1 60400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@03 004100H1003o0AP10P070@00o`4H0@03004100H1003B0@@0@@400`010@060@00d@46040100<00@40 1P400=411P100@03004100H1003A0@H0@0400`010@060@00d@46040100<00@401P400=8110110@80 1`400?l160400`010@060@00o`4H0@03004100H1003o0AP100<00@401P400?l160400`010@060@00 o`4H0@03004100H1003o0AP10P070@00m04431l100<00@401P400?<11P`N0@03004100H1003c0@H< 7P400`010@060@00l`4631h100<00@401P400?<11P`F0@@010400`010@060@00m04431T100<00@40 0`400`010@060@00l`4601P100<00@400`4300H1003c0@H0404400@100<00@400`400`010@060@00 l`4601P100<00@400`400`010@060@00l`4601H10`050@03004100H1003d0@@06@400`010@030@03 004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@801`400?l160400`010@060@00 dP443D0110`60@00d@463Ch11P`50@00d@463Ch11P`50@00d@463Ch11P`50@00d@463Ch11P`50@00 dP443Cl100<030`00P`00`010@030@00o`4F0@H01@400?l15P4600D1003o0AL110060@00o`4H0@03 004100H1003o0AP100<00@401P400?l160400`010@060@00o`4H0@801`400?l160400`010@060@00 o`4H0@03004100H1000f0@@0;`4400<100<00@400P4302l1100`0@8010400`010@020@<0;P400`01 0@060@00=P400`010@0b0@03004100X100<00@40;P400`010@0^0@04004100/100<00@40:`400`01 0@060@00=`400`010@0a0@03004100X100<00@40;P400`010@0^0@04004100/100<00@40:`400`01 0@060@00<04400@100<00@40:04400@100<00@401`4302T110040@03004100@110lP0@@00P401001 0@080@<0;P400`010@060@00>@400`010@0_0@03004100L100<00@40<@400`010@030@H?9@401001 0@080@03004100/110dO0@801`4003H100@00@40;`4300T100<00@40;`4300D11PlU0@04004100P1 00<00@402P463Ah100<00@401P4003L10P0b0@03004100L1100`0@03004100<11PlV0@802@4400T1 1PdN0@03004100H1002_0@H??P463Ah100<00@401P400;0110lo0@H=7P400`010@060@00m0443Al1 00<00@401P400=8010m000@=1@010@0020400`010@080@03004100P100<00@402@400`010@080@03 004100P100<00@402@400`010@080@03004100P100<00@402@400`010@080@03004100P100<00@40 20400`010@090@03004100P100<00@4020400`010@090@03004100P100<00@401P463`P100<00@40 20400`010@080@03004100T100<00@4020400`010@060@H=1@4003D100<00@40=P400`010@0e0@03 004102P11Pl80@030041018110lM0@H=1@400=411PlL0@H?70400`d?3`023`033@4100<1003A0@H? 70463a`11Pl50@00dP443ad11PlL0@H?1@400?<11PlL0@H?1@400?@110lM0@H?1@400?l15`443`H1 003o0AP100<00@401P400?l160400`010@060@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-2.47158, -4.87649, 0.00883248, 0.0292247}}], Cell[CellGroupData[{ Cell[BoxData[ \(splits[N[h], v, L]\)], "Input"], Cell[BoxData[ \(\(SplitStep`Private`Linear[0.5`\ 0.00390625`, 8\ \[Pi]]\)[ \(SplitStep`Private`Nonlinear[0.00390625`, {0, 0, 0, 0, 0, 0, 0, 0}]\)[ \(SplitStep`Private`Linear[0.5`\ 0.00390625`, 8\ \[Pi]]\)[#1]]] & \)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Split StepSolve", "Subsubsection"], Cell[BoxData[ \(\(prec\ = \ Sequence[];\)\)], "Input"], Cell[BoxData[{ \(\(n\ \ = \ 720;\)\), "\[IndentingNewLine]", \(\(L\ = \ 30\ \[Pi];\)\), "\[IndentingNewLine]", \(\(Tend\ = \ 4;\)\), "\[IndentingNewLine]", \(\(b\ = \ 1;\)\), "\[IndentingNewLine]", \(\(alp\ = \ 1/2;\)\), "\[IndentingNewLine]", \(xmin\ = \ \(-L\)/2; xmax\ = \ L/2;\), "\[IndentingNewLine]", \(\(grid\ = \ N[Discretize[x, {x, xmin, xmax}, n], prec];\)\), "\[IndentingNewLine]", \(\(u0\ = \ \(LinearPotentialSoliton[1, b, \ alp]\)[grid, 0];\)\), "\[IndentingNewLine]", \(\(uend\ = \ \(LinearPotentialSoliton[1, b, alp]\)[grid, Tend];\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Timing[ \(sol\ = \ SplitStepSolve[u0, {x, xmin, xmax}, \ {{0, Tend, Tend}, Automatic}, \ Order \[Rule] 4, \ Potential \[Rule] alp\ grid];\)]\)], "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 0.500662 0.0101191 0 0.618034 [ [.0959 -0.0125 -9 -9 ] [.0959 -0.0125 9 0 ] [.29828 -0.0125 -9 -9 ] [.29828 -0.0125 9 0 ] [.70304 -0.0125 -6 -9 ] [.70304 -0.0125 6 0 ] [.90543 -0.0125 -6 -9 ] [.90543 -0.0125 6 0 ] [.48816 .12361 -18 -4.5 ] [.48816 .12361 0 4.5 ] [.48816 .24721 -18 -4.5 ] [.48816 .24721 0 4.5 ] [.48816 .37082 -18 -4.5 ] [.48816 .37082 0 4.5 ] [.48816 .49443 -18 -4.5 ] [.48816 .49443 0 4.5 ] [.48816 .61803 -6 -4.5 ] [.48816 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .0959 0 m .0959 .00625 L s [(-40)] .0959 -0.0125 0 1 Mshowa .29828 0 m .29828 .00625 L s [(-20)] .29828 -0.0125 0 1 Mshowa .70304 0 m .70304 .00625 L s [(20)] .70304 -0.0125 0 1 Mshowa .90543 0 m .90543 .00625 L s [(40)] .90543 -0.0125 0 1 Mshowa .125 Mabswid .14649 0 m .14649 .00375 L s .19709 0 m .19709 .00375 L s .24768 0 m .24768 .00375 L s .34888 0 m .34888 .00375 L s .39947 0 m .39947 .00375 L s .45007 0 m .45007 .00375 L s .55126 0 m .55126 .00375 L s .60185 0 m .60185 .00375 L s .65245 0 m .65245 .00375 L s .75364 0 m .75364 .00375 L s .80424 0 m .80424 .00375 L s .85483 0 m .85483 .00375 L s .0453 0 m .0453 .00375 L s .95602 0 m .95602 .00375 L s .25 Mabswid 0 0 m 1 0 L s .50066 .12361 m .50691 .12361 L s [(0.2)] .48816 .12361 1 0 Mshowa .50066 .24721 m .50691 .24721 L s [(0.4)] .48816 .24721 1 0 Mshowa .50066 .37082 m .50691 .37082 L s [(0.6)] .48816 .37082 1 0 Mshowa .50066 .49443 m .50691 .49443 L s [(0.8)] .48816 .49443 1 0 Mshowa .50066 .61803 m .50691 .61803 L s [(1)] .48816 .61803 1 0 Mshowa .125 Mabswid .50066 .0309 m .50441 .0309 L s .50066 .0618 m .50441 .0618 L s .50066 .09271 m .50441 .09271 L s .50066 .15451 m .50441 .15451 L s .50066 .18541 m .50441 .18541 L s .50066 .21631 m .50441 .21631 L s .50066 .27812 m .50441 .27812 L s .50066 .30902 m .50441 .30902 L s .50066 .33992 m .50441 .33992 L s .50066 .40172 m .50441 .40172 L s .50066 .43262 m .50441 .43262 L s .50066 .46353 m .50441 .46353 L s .50066 .52533 m .50441 .52533 L s .50066 .55623 m .50441 .55623 L s .50066 .58713 m .50441 .58713 L s .25 Mabswid .50066 0 m .50066 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .008 w .02381 0 Mdot .02513 0 Mdot .02646 0 Mdot .02778 0 Mdot .02911 0 Mdot .03043 0 Mdot .03176 0 Mdot .03308 0 Mdot .03441 0 Mdot .03573 0 Mdot .03706 0 Mdot .03838 0 Mdot .0397 0 Mdot .04103 0 Mdot .04235 0 Mdot .04368 0 Mdot .045 0 Mdot .04633 0 Mdot .04765 0 Mdot .04898 0 Mdot .0503 0 Mdot .05163 0 Mdot .05295 0 Mdot .05428 0 Mdot .0556 0 Mdot .05692 0 Mdot .05825 0 Mdot .05957 0 Mdot .0609 0 Mdot .06222 0 Mdot .06355 0 Mdot .06487 0 Mdot .0662 0 Mdot .06752 0 Mdot .06885 0 Mdot .07017 0 Mdot .07149 0 Mdot .07282 0 Mdot .07414 0 Mdot .07547 0 Mdot .07679 0 Mdot .07812 0 Mdot .07944 0 Mdot .08077 0 Mdot .08209 0 Mdot .08342 0 Mdot .08474 0 Mdot .08607 0 Mdot .08739 0 Mdot .08871 0 Mdot .09004 0 Mdot .09136 0 Mdot .09269 0 Mdot .09401 0 Mdot .09534 0 Mdot .09666 0 Mdot .09799 0 Mdot .09931 0 Mdot .10064 0 Mdot .10196 0 Mdot .10328 0 Mdot .10461 0 Mdot .10593 0 Mdot .10726 0 Mdot .10858 0 Mdot .10991 0 Mdot .11123 0 Mdot .11256 0 Mdot .11388 0 Mdot .11521 0 Mdot .11653 0 Mdot .11786 0 Mdot .11918 0 Mdot .1205 0 Mdot .12183 0 Mdot .12315 0 Mdot .12448 0 Mdot .1258 0 Mdot .12713 0 Mdot .12845 0 Mdot .12978 0 Mdot .1311 0 Mdot .13243 0 Mdot .13375 0 Mdot .13508 0 Mdot .1364 0 Mdot .13772 0 Mdot .13905 0 Mdot .14037 0 Mdot .1417 0 Mdot .14302 0 Mdot .14435 0 Mdot .14567 0 Mdot .147 0 Mdot .14832 0 Mdot .14965 0 Mdot .15097 0 Mdot .15229 0 Mdot .15362 0 Mdot .15494 0 Mdot .15627 0 Mdot .15759 0 Mdot .15892 0 Mdot .16024 0 Mdot .16157 0 Mdot .16289 0 Mdot .16422 0 Mdot .16554 0 Mdot .16687 0 Mdot .16819 0 Mdot .16951 0 Mdot .17084 0 Mdot .17216 0 Mdot .17349 0 Mdot .17481 0 Mdot .17614 0 Mdot .17746 0 Mdot .17879 0 Mdot .18011 0 Mdot .18144 0 Mdot .18276 0 Mdot .18409 0 Mdot .18541 0 Mdot .18673 0 Mdot .18806 0 Mdot .18938 0 Mdot .19071 0 Mdot .19203 0 Mdot .19336 0 Mdot .19468 0 Mdot .19601 0 Mdot .19733 0 Mdot .19866 0 Mdot .19998 0 Mdot .2013 0 Mdot .20263 0 Mdot .20395 0 Mdot .20528 0 Mdot .2066 0 Mdot .20793 0 Mdot .20925 0 Mdot .21058 0 Mdot .2119 0 Mdot .21323 0 Mdot .21455 0 Mdot .21588 0 Mdot .2172 0 Mdot .21852 0 Mdot .21985 0 Mdot .22117 0 Mdot .2225 0 Mdot .22382 0 Mdot .22515 0 Mdot .22647 0 Mdot .2278 0 Mdot .22912 0 Mdot .23045 0 Mdot .23177 0 Mdot .23309 0 Mdot .23442 0 Mdot .23574 0 Mdot .23707 0 Mdot .23839 0 Mdot .23972 0 Mdot .24104 0 Mdot .24237 0 Mdot .24369 0 Mdot .24502 0 Mdot .24634 0 Mdot .24767 0 Mdot .24899 0 Mdot .25031 0 Mdot .25164 0 Mdot .25296 0 Mdot .25429 0 Mdot .25561 0 Mdot .25694 0 Mdot .25826 0 Mdot .25959 0 Mdot .26091 0 Mdot .26224 0 Mdot .26356 0 Mdot .26489 0 Mdot .26621 0 Mdot .26753 0 Mdot .26886 0 Mdot .27018 0 Mdot .27151 0 Mdot .27283 0 Mdot .27416 0 Mdot .27548 0 Mdot .27681 0 Mdot .27813 0 Mdot .27946 0 Mdot .28078 0 Mdot .2821 0 Mdot .28343 0 Mdot .28475 0 Mdot .28608 0 Mdot .2874 0 Mdot .28873 0 Mdot .29005 0 Mdot .29138 0 Mdot .2927 0 Mdot .29403 0 Mdot .29535 0 Mdot .29668 0 Mdot .298 0 Mdot .29932 0 Mdot .30065 0 Mdot .30197 0 Mdot .3033 0 Mdot .30462 0 Mdot .30595 0 Mdot .30727 0 Mdot .3086 0 Mdot .30992 0 Mdot .31125 0 Mdot .31257 0 Mdot .31389 0 Mdot .31522 0 Mdot .31654 0 Mdot .31787 0 Mdot .31919 0 Mdot .32052 0 Mdot .32184 0 Mdot .32317 0 Mdot .32449 0 Mdot .32582 0 Mdot .32714 0 Mdot .32847 0 Mdot .32979 0 Mdot .33111 0 Mdot .33244 0 Mdot .33376 0 Mdot .33509 0 Mdot .33641 0 Mdot .33774 0 Mdot .33906 0 Mdot .34039 0 Mdot .34171 0 Mdot .34304 0 Mdot .34436 0 Mdot .34569 0 Mdot .34701 0 Mdot .34833 0 Mdot .34966 0 Mdot .35098 0 Mdot .35231 0 Mdot .35363 0 Mdot .35496 0 Mdot .35628 0 Mdot .35761 0 Mdot .35893 0 Mdot .36026 0 Mdot .36158 0 Mdot .3629 0 Mdot .36423 0 Mdot .36555 0 Mdot .36688 0 Mdot .3682 0 Mdot .36953 0 Mdot .37085 0 Mdot .37218 0 Mdot .3735 0 Mdot .37483 0 Mdot .37615 1e-05 Mdot .37748 1e-05 Mdot .3788 1e-05 Mdot .38012 1e-05 Mdot .38145 1e-05 Mdot .38277 1e-05 Mdot .3841 1e-05 Mdot .38542 1e-05 Mdot .38675 2e-05 Mdot .38807 2e-05 Mdot .3894 2e-05 Mdot .39072 2e-05 Mdot .39205 3e-05 Mdot .39337 3e-05 Mdot .3947 4e-05 Mdot .39602 4e-05 Mdot .39734 5e-05 Mdot .39867 5e-05 Mdot .39999 6e-05 Mdot .40132 7e-05 Mdot .40264 8e-05 Mdot .40397 9e-05 Mdot .40529 .0001 Mdot .40662 .00011 Mdot .40794 .00013 Mdot .40927 .00015 Mdot .41059 .00017 Mdot .41191 .00019 Mdot .41324 .00022 Mdot .41456 .00025 Mdot .41589 .00028 Mdot .41721 .00032 Mdot .41854 .00037 Mdot .41986 .00042 Mdot .42119 .00048 Mdot .42251 .00055 Mdot .42384 .00062 Mdot .42516 .00071 Mdot .42649 .00081 Mdot .42781 .00092 Mdot .42913 .00105 Mdot .43046 .0012 Mdot .43178 .00137 Mdot .43311 .00156 Mdot .43443 .00178 Mdot .43576 .00203 Mdot .43708 .00231 Mdot .43841 .00263 Mdot .43973 .003 Mdot .44106 .00342 Mdot .44238 .0039 Mdot .4437 .00444 Mdot .44503 .00506 Mdot .44635 .00577 Mdot .44768 .00658 Mdot .449 .0075 Mdot .45033 .00855 Mdot .45165 .00974 Mdot .45298 .0111 Mdot .4543 .01266 Mdot .45563 .01443 Mdot .45695 .01644 Mdot .45828 .01874 Mdot .4596 .02136 Mdot .46092 .02434 Mdot .46225 .02775 Mdot .46357 .03162 Mdot .4649 .03604 Mdot .46622 .04107 Mdot .46755 .04679 Mdot .46887 .05332 Mdot .4702 .06074 Mdot .47152 .06918 Mdot .47285 .07878 Mdot .47417 .08969 Mdot .4755 .10207 Mdot .47682 .11611 Mdot .47814 .132 Mdot .47947 .14994 Mdot .48079 .17015 Mdot .48212 .19283 Mdot .48344 .21817 Mdot .48477 .24631 Mdot .48609 .27732 Mdot .48742 .31115 Mdot .48874 .3476 Mdot .49007 .3862 Mdot .49139 .42623 Mdot .49271 .46658 Mdot .49404 .50578 Mdot .49536 .54202 Mdot .49669 .57326 Mdot .49801 .59744 Mdot .49934 .61278 Mdot .50066 .61803 Mdot .50199 .61278 Mdot .50331 .59744 Mdot .50464 .57326 Mdot .50596 .54202 Mdot .50729 .50578 Mdot .50861 .46658 Mdot .50993 .42623 Mdot .51126 .3862 Mdot .51258 .3476 Mdot .51391 .31115 Mdot .51523 .27732 Mdot .51656 .24631 Mdot .51788 .21817 Mdot .51921 .19283 Mdot .52053 .17015 Mdot .52186 .14994 Mdot .52318 .132 Mdot .5245 .11611 Mdot .52583 .10207 Mdot .52715 .08969 Mdot .52848 .07878 Mdot .5298 .06918 Mdot .53113 .06074 Mdot .53245 .05332 Mdot .53378 .04679 Mdot .5351 .04107 Mdot .53643 .03604 Mdot .53775 .03162 Mdot .53908 .02775 Mdot .5404 .02434 Mdot .54172 .02136 Mdot .54305 .01874 Mdot .54437 .01644 Mdot .5457 .01443 Mdot .54702 .01266 Mdot .54835 .0111 Mdot .54967 .00974 Mdot .551 .00855 Mdot .55232 .0075 Mdot .55365 .00658 Mdot .55497 .00577 Mdot .5563 .00506 Mdot .55762 .00444 Mdot .55894 .0039 Mdot .56027 .00342 Mdot .56159 .003 Mdot .56292 .00263 Mdot .56424 .00231 Mdot .56557 .00203 Mdot .56689 .00178 Mdot .56822 .00156 Mdot .56954 .00137 Mdot .57087 .0012 Mdot .57219 .00105 Mdot .57351 .00092 Mdot .57484 .00081 Mdot .57616 .00071 Mdot .57749 .00062 Mdot .57881 .00055 Mdot .58014 .00048 Mdot .58146 .00042 Mdot .58279 .00037 Mdot .58411 .00032 Mdot .58544 .00028 Mdot .58676 .00025 Mdot .58809 .00022 Mdot .58941 .00019 Mdot .59073 .00017 Mdot .59206 .00015 Mdot .59338 .00013 Mdot .59471 .00011 Mdot .59603 .0001 Mdot .59736 9e-05 Mdot .59868 8e-05 Mdot .60001 7e-05 Mdot .60133 6e-05 Mdot .60266 5e-05 Mdot .60398 5e-05 Mdot .6053 4e-05 Mdot .60663 4e-05 Mdot .60795 3e-05 Mdot .60928 3e-05 Mdot .6106 2e-05 Mdot .61193 2e-05 Mdot .61325 2e-05 Mdot .61458 2e-05 Mdot .6159 1e-05 Mdot .61723 1e-05 Mdot .61855 1e-05 Mdot .61988 1e-05 Mdot .6212 1e-05 Mdot .62252 1e-05 Mdot .62385 1e-05 Mdot .62517 1e-05 Mdot .6265 0 Mdot .62782 0 Mdot .62915 0 Mdot .63047 0 Mdot .6318 0 Mdot .63312 0 Mdot .63445 0 Mdot .63577 0 Mdot .6371 0 Mdot .63842 0 Mdot .63974 0 Mdot .64107 0 Mdot .64239 0 Mdot .64372 0 Mdot .64504 0 Mdot .64637 0 Mdot .64769 0 Mdot .64902 0 Mdot .65034 0 Mdot .65167 0 Mdot .65299 0 Mdot .65431 0 Mdot .65564 0 Mdot .65696 0 Mdot .65829 0 Mdot .65961 0 Mdot .66094 0 Mdot .66226 0 Mdot .66359 0 Mdot .66491 0 Mdot .66624 0 Mdot .66756 0 Mdot .66889 0 Mdot .67021 0 Mdot .67153 0 Mdot .67286 0 Mdot .67418 0 Mdot .67551 0 Mdot .67683 0 Mdot .67816 0 Mdot .67948 0 Mdot .68081 0 Mdot .68213 0 Mdot .68346 0 Mdot .68478 0 Mdot .68611 0 Mdot .68743 0 Mdot .68875 0 Mdot .69008 0 Mdot .6914 0 Mdot .69273 0 Mdot .69405 0 Mdot .69538 0 Mdot .6967 0 Mdot .69803 0 Mdot .69935 0 Mdot .70068 0 Mdot .702 0 Mdot .70332 0 Mdot .70465 0 Mdot .70597 0 Mdot .7073 0 Mdot .70862 0 Mdot .70995 0 Mdot .71127 0 Mdot .7126 0 Mdot .71392 0 Mdot .71525 0 Mdot .71657 0 Mdot .7179 0 Mdot .71922 0 Mdot .72054 0 Mdot .72187 0 Mdot .72319 0 Mdot .72452 0 Mdot .72584 0 Mdot .72717 0 Mdot .72849 0 Mdot .72982 0 Mdot .73114 0 Mdot .73247 0 Mdot .73379 0 Mdot .73511 0 Mdot .73644 0 Mdot .73776 0 Mdot .73909 0 Mdot .74041 0 Mdot .74174 0 Mdot .74306 0 Mdot .74439 0 Mdot .74571 0 Mdot .74704 0 Mdot .74836 0 Mdot .74969 0 Mdot .75101 0 Mdot .75233 0 Mdot .75366 0 Mdot .75498 0 Mdot .75631 0 Mdot .75763 0 Mdot .75896 0 Mdot .76028 0 Mdot .76161 0 Mdot .76293 0 Mdot .76426 0 Mdot .76558 0 Mdot .76691 0 Mdot .76823 0 Mdot .76955 0 Mdot .77088 0 Mdot .7722 0 Mdot .77353 0 Mdot .77485 0 Mdot .77618 0 Mdot .7775 0 Mdot .77883 0 Mdot .78015 0 Mdot .78148 0 Mdot .7828 0 Mdot .78412 0 Mdot .78545 0 Mdot .78677 0 Mdot .7881 0 Mdot .78942 0 Mdot .79075 0 Mdot .79207 0 Mdot .7934 0 Mdot .79472 0 Mdot .79605 0 Mdot .79737 0 Mdot .7987 0 Mdot .80002 0 Mdot .80134 0 Mdot .80267 0 Mdot .80399 0 Mdot .80532 0 Mdot .80664 0 Mdot .80797 0 Mdot .80929 0 Mdot .81062 0 Mdot .81194 0 Mdot .81327 0 Mdot .81459 0 Mdot .81591 0 Mdot .81724 0 Mdot .81856 0 Mdot .81989 0 Mdot .82121 0 Mdot .82254 0 Mdot .82386 0 Mdot .82519 0 Mdot .82651 0 Mdot .82784 0 Mdot .82916 0 Mdot .83049 0 Mdot .83181 0 Mdot .83313 0 Mdot .83446 0 Mdot .83578 0 Mdot .83711 0 Mdot .83843 0 Mdot .83976 0 Mdot .84108 0 Mdot .84241 0 Mdot .84373 0 Mdot .84506 0 Mdot .84638 0 Mdot .84771 0 Mdot .84903 0 Mdot .85035 0 Mdot .85168 0 Mdot .853 0 Mdot .85433 0 Mdot .85565 0 Mdot .85698 0 Mdot .8583 0 Mdot .85963 0 Mdot .86095 0 Mdot .86228 0 Mdot .8636 0 Mdot .86492 0 Mdot .86625 0 Mdot .86757 0 Mdot .8689 0 Mdot .87022 0 Mdot .87155 0 Mdot .87287 0 Mdot .8742 0 Mdot .87552 0 Mdot .87685 0 Mdot .87817 0 Mdot .8795 0 Mdot .88082 0 Mdot .88214 0 Mdot .88347 0 Mdot .88479 0 Mdot .88612 0 Mdot .88744 0 Mdot .88877 0 Mdot .89009 0 Mdot .89142 0 Mdot .89274 0 Mdot .89407 0 Mdot .89539 0 Mdot .89672 0 Mdot .89804 0 Mdot .89936 0 Mdot .90069 0 Mdot .90201 0 Mdot .90334 0 Mdot .90466 0 Mdot .90599 0 Mdot .90731 0 Mdot .90864 0 Mdot .90996 0 Mdot .91129 0 Mdot .91261 0 Mdot .91393 0 Mdot .91526 0 Mdot .91658 0 Mdot .91791 0 Mdot .91923 0 Mdot .92056 0 Mdot .92188 0 Mdot .92321 0 Mdot .92453 0 Mdot .92586 0 Mdot .92718 0 Mdot .92851 0 Mdot .92983 0 Mdot .93115 0 Mdot .93248 0 Mdot .9338 0 Mdot .93513 0 Mdot .93645 0 Mdot .93778 0 Mdot .9391 0 Mdot .94043 0 Mdot .94175 0 Mdot .94308 0 Mdot .9444 0 Mdot .94572 0 Mdot .94705 0 Mdot .94837 0 Mdot .9497 0 Mdot .95102 0 Mdot .95235 0 Mdot .95367 0 Mdot .955 0 Mdot .95632 0 Mdot .95765 0 Mdot .95897 0 Mdot .9603 0 Mdot .96162 0 Mdot .96294 0 Mdot .96427 0 Mdot .96559 0 Mdot .96692 0 Mdot .96824 0 Mdot .96957 0 Mdot .97089 0 Mdot .97222 0 Mdot .97354 0 Mdot .97487 0 Mdot .97619 0 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@00<000I@00V@0`000`<00`I@0`V@0`cP0`o`1U001U<01UI@1UV@1UcP1Uo`2I002I<02I I@2IV@2IcP3><03>I@3>V@3>o`3o<03oI@3oV@3ocS000300<300IC00VC00cS00oc0`030`<30`VC0` cS0`oc1U031U<31UIC1UVC1UcS1Uoc2I032I<32IIC2IVC2IcS2Ioc3>033><33>IC3>VC3>cS3>oc3o 033o<33oIC3ocS3oofD006D0<6D0IFD0VFD0cVD0ofD`0?l18@400?l18@4002H100<00@400P4202`1 10030@80G@4400<10P0]0@03004100810P0T0@009P401@010@40008100<00@40:@400`010@030@04 004105`100<00@400`4010010@0/0@0500410@000P400`010@0Q0@008`45008100@00@40;0400`01 0@020@04004105d100<00@400P4010010@0Y0@D00P4010010@0S0@007P4400050@010@000`401001 0@0U0@@010401@010@40008100<00@40G0401@010@40008100<00@409`4010010@030@04004102<1 000T0@03004000<100@00@40;P4010010@020@03004105d100@00@400P400`010@0X0@03004000<1 00@00@408`4002D10P030@04004102/100@00@400P4010010@1L0@040041008100@00@40:`4200<1 00@00@408`4002H100<00@400P4202d10P040@80GP4200@10P0]0@03004100810P0T0@00o`4Q0@00 o`4Q0@004`5Z02D1JP0D0@003@7o00H03P4001T100<00@402P400`010@0:0@03004100X100<00@40 2`400`010@0:0@03004100X100<00@402P400`010@040@L030400`010@0:0@P01@400`010@0;0@03 004100X100<00@402P400`010@0:0@03004100X100<00@402P400`010@0:0@03004101P100210@<0 2`400`010@090@@0P@4008<10P0:0@03004100P110220@00P`4300T100<00@40204308<100240@80 2@400`010@070@<0Q04008@10`080@03004100L10P250@00Q@4200P100<00@401P4308D100260@03 004100H10P080@03004108@100250@8020400`010@060@80QP4008H10P070@03004100H10P260@00 QP4200L100<00@401@4308H100270@03004100D100<00@401P400`010@250@00QP4200L100<00@40 1@4208L100270@03004100D100<00@401P400`010@250@00Q`4200H100<00@401@4208L100280@03 004100@10P070@03004108D100270@801P400`010@040@80R04008P100<00@4010400`010@050@03 004108H1002?0@03004108h100270@801P400`010@040@80R04008P100<00@4010400`010@050@03 004108H1002?0@03004108h100280@801@400`010@040@80R04008T100<00@400`4200H100<00@40 QP4008l100<00@40SP4008P10P050@03004100<10P290@00R@400`010@030@03004100@100<00@40 Q`4008l100<00@40SP4008P10P050@03004100<10P290@00O04200@100<00@400P4400@100<00@40 10400`010@270@00N`4010010@080@03004100D100<00@40SP4007/100@00@402@400`010@040@<0 SP4007/100@00@402P400`010@030@03004108h1001k0@04004100X10P040@03004100<10P290@00 N`4010010@080@04004100@100<00@4010400`010@270@00O04200X10P050@03004108h1002?0@03 004108h100290@8010400`010@020@80RP4008X100<00@400P400`010@030@03004108P1002?0@80 S`4008l100<00@40SP4008l100<00@40SP4008X10P030@03004100810P2:0@00R`401@010@4000D1 00<00@40R04008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l10P2?0@00RP4200<1 00@00@410P2;0@00R`401@010@4000@100<00@40R@4008l100<00@40SP4008l100<00@40SP4008l1 00<00@40SP4008l100<00@40SP4008l100<00@40SP4008X10P030@800P4208/1002;0@0500410@00 10400`010@290@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00 O04200@100<00@4010400`010@030@03004108h1001k0@04004100X100@00@000P4010010@4208/1 001k0@04004100L11@0010400@43008100<00@40R@4007/100@00@401`4010010@050@03004108h1 001k0@04004100P100<00@001@400`010@2>0@00N`4010010@090@801@400`010@2>0@00O04200/1 00<00@400`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00R`42008100<00@400P2<0@00 S0400`010@02008100<00@40RP4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l1 00<00@40SP4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008/10P020@8000<10000 S04008`100@00@400`400`010@2:0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00 S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`4208l1002<0@8000@100410P2<0@00 S@400`0100030@03004108X1002?0@03004108h1002?0@03004108h1002?0@03004108h1001l0@80 10400`010@030@801@400`010@2>0@00N`4010010@080@04004100@100<00@40SP4007/100@00@40 204010010@040@<0SP4007/100@00@40204300D100<00@40SP4007/100@00@4020400`010@050@03 004108h1001k0@04004100P100<00@400P4200030@010080S@4007`10P0:0@<00P400`0100020@03 004108/1002?0@03004108h1002?0@03004108h1002?0@03004108h1002?0@80S`4008l100<00@40 SP4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008`10P000`40 0@0208d1002=0@030040008100<00@40R`4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00 S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00 S@4608d1002>0@800P400`010@2;0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00 S`400`010@2>0@00O04200@100<00@400`4200D100<00@40SP4007/100@00@40204010010@040@03 004108h1001k0@04004100P100@00@40104308h1001k0@04004100T10P050@03004108h1001k0@04 004100P100@00@400P4508h1001k0@04004100P100@00@400`4200030@0108d1001l0@802P4200D1 00<00@40SP4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l10P2?0@00S`400`01 0@2>0@00S`400`010@2>0@00S`400`010@2>0@00S@4508h1002>0@8000<10040S@4008l100<00@40 SP4008l100<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00 SP4408h1002?0@03004008h1002?0@03004108h1002?0@03004108h1002?0@80S`4008l100<00@40 SP4008h10`2?0@00S`4208l1002?0@03004108h1002?0@03004108h100270@@00`4308l100290@03 004100<10P2?0@00R@400`010@030@<0SP4008T100<00@40U04008T100<00@40U04008L10`2F0@00 R@400`010@2D0@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-54.7756, -0.0764114, 0.381256, 0.00624232}}], Cell[BoxData[ \(4.`\)], "Print"], Cell[BoxData[ \({16.849999999999966`\ Second, Null}\)], "Output"] }, Open ]], Cell[BoxData[{ \(\(n\ \ = \ 32;\)\), "\[IndentingNewLine]", \(\(L\ = \ 30\ \[Pi];\)\), "\[IndentingNewLine]", \(\(Tend\ = \ 10;\)\), "\[IndentingNewLine]", \(\(b\ = \ 1;\)\), "\[IndentingNewLine]", \(xmin\ = \ \(-L\)/2; xmax\ = \ L/2;\), "\[IndentingNewLine]", \(\(grid\ = \ N[Discretize[x, {x, xmin, xmax}, n], prec];\)\), "\[IndentingNewLine]", \(\(u0\ = \(Soliton[1, b]\)[grid\ + \ 10, 0] + \(Soliton[1, \(-b\)]\)[grid\ - \ 10, 0];\)\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Timing[ \(sol\ = \ SplitStepSolve[u0, {x, xmin, xmax}, \ {{0, Tend, 1}, Automatic}, \ Order \[Rule] 4];\)]\)], "Input"], Cell[BoxData[ \(10.`\)], "Print"], Cell[BoxData[ \({49.96`\ Second, Null}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(prec\ = \ 16;\)\)], "Input"], Cell[BoxData[{ \(\(n\ \ = \ 720;\)\), "\[IndentingNewLine]", \(\(L\ = \ 30\ \[Pi];\)\), "\[IndentingNewLine]", \(\(Tend\ = \ 4;\)\), "\[IndentingNewLine]", \(\(b\ = \ 1;\)\), "\[IndentingNewLine]", \(\(alp\ = \ 1/2;\)\), "\[IndentingNewLine]", \(xmin\ = \ \(-L\)/2; xmax\ = \ L/2;\), "\[IndentingNewLine]", \(\(grid\ = \ N[Discretize[x, {x, xmin, xmax}, n], prec];\)\), "\[IndentingNewLine]", \(\(u0\ = \ \(LinearPotentialSoliton[1, b, \ alp]\)[grid, 0];\)\), "\[IndentingNewLine]", \(\(uend\ = \ \(LinearPotentialSoliton[1, b, alp]\)[grid, Tend];\)\)}], "Input"], Cell[BoxData[ \(<< SplitStep.m\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Timing[ \(sol\ = \ SplitStepSolve[u0, {x, xmin, xmax}, \ {{0, Tend, 1}, Automatic}, \ Order \[Rule] 4, \ Potential \[Rule] alp\ grid, \ WorkingPrecision \[Rule] prec, \ Output \[Rule] {Centroid, \ {Plot, PlotRange \[Rule] {{\(-5\), 5}, {\(-1\), 1}}}}];\)] \)], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.1 0.309017 0.309017 [ [.1 .29652 -6 -9 ] [.1 .29652 6 0 ] [.3 .29652 -6 -9 ] [.3 .29652 6 0 ] [.7 .29652 -3 -9 ] [.7 .29652 3 0 ] [.9 .29652 -3 -9 ] [.9 .29652 3 0 ] [.4875 0 -12 -4.5 ] [.4875 0 0 4.5 ] [.4875 .07725 -30 -4.5 ] [.4875 .07725 0 4.5 ] [.4875 .15451 -24 -4.5 ] [.4875 .15451 0 4.5 ] [.4875 .23176 -30 -4.5 ] [.4875 .23176 0 4.5 ] [.4875 .38627 -24 -4.5 ] [.4875 .38627 0 4.5 ] [.4875 .46353 -18 -4.5 ] [.4875 .46353 0 4.5 ] [.4875 .54078 -24 -4.5 ] [.4875 .54078 0 4.5 ] [.4875 .61803 -6 -4.5 ] [.4875 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .1 .30902 m .1 .31527 L s [(-4)] .1 .29652 0 1 Mshowa .3 .30902 m .3 .31527 L s [(-2)] .3 .29652 0 1 Mshowa .7 .30902 m .7 .31527 L s [(2)] .7 .29652 0 1 Mshowa .9 .30902 m .9 .31527 L s [(4)] .9 .29652 0 1 Mshowa .125 Mabswid .15 .30902 m .15 .31277 L s .2 .30902 m .2 .31277 L s .25 .30902 m .25 .31277 L s .35 .30902 m .35 .31277 L s .4 .30902 m .4 .31277 L s .45 .30902 m .45 .31277 L s .55 .30902 m .55 .31277 L s .6 .30902 m .6 .31277 L s .65 .30902 m .65 .31277 L s .75 .30902 m .75 .31277 L s .8 .30902 m .8 .31277 L s .85 .30902 m .85 .31277 L s .05 .30902 m .05 .31277 L s .95 .30902 m .95 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 0 m .50625 0 L s [(-1)] .4875 0 1 0 Mshowa .5 .07725 m .50625 .07725 L s [(-0.75)] .4875 .07725 1 0 Mshowa .5 .15451 m .50625 .15451 L s [(-0.5)] .4875 .15451 1 0 Mshowa .5 .23176 m .50625 .23176 L s [(-0.25)] .4875 .23176 1 0 Mshowa .5 .38627 m .50625 .38627 L s [(0.25)] .4875 .38627 1 0 Mshowa .5 .46353 m .50625 .46353 L s [(0.5)] .4875 .46353 1 0 Mshowa .5 .54078 m .50625 .54078 L s [(0.75)] .4875 .54078 1 0 Mshowa .5 .61803 m .50625 .61803 L s [(1)] .4875 .61803 1 0 Mshowa .125 Mabswid .5 .01545 m .50375 .01545 L s .5 .0309 m .50375 .0309 L s .5 .04635 m .50375 .04635 L s .5 .0618 m .50375 .0618 L s .5 .09271 m .50375 .09271 L s .5 .10816 m .50375 .10816 L s .5 .12361 m .50375 .12361 L s .5 .13906 m .50375 .13906 L s .5 .16996 m .50375 .16996 L s .5 .18541 m .50375 .18541 L s .5 .20086 m .50375 .20086 L s .5 .21631 m .50375 .21631 L s .5 .24721 m .50375 .24721 L s .5 .26266 m .50375 .26266 L s .5 .27812 m .50375 .27812 L s .5 .29357 m .50375 .29357 L s .5 .32447 m .50375 .32447 L s .5 .33992 m .50375 .33992 L s .5 .35537 m .50375 .35537 L s .5 .37082 m .50375 .37082 L s .5 .40172 m .50375 .40172 L s .5 .41717 m .50375 .41717 L s .5 .43262 m .50375 .43262 L s .5 .44807 m .50375 .44807 L s .5 .47898 m .50375 .47898 L s .5 .49443 m .50375 .49443 L s .5 .50988 m .50375 .50988 L s .5 .52533 m .50375 .52533 L s .5 .55623 m .50375 .55623 L s .5 .57168 m .50375 .57168 L s .5 .58713 m .50375 .58713 L s .5 .60258 m .50375 .60258 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid 0 .31319 m .00258 .31329 L .01567 .31389 L .02876 .31457 L .04185 .31534 L .05494 .31623 L .06803 .31724 L .08112 .31839 L .09421 .3197 L .1073 .32119 L .12039 .32289 L .13348 .32483 L .14657 .32704 L .15966 .32955 L .17275 .33241 L .18584 .33567 L .19893 .33939 L .21202 .34361 L .22511 .34841 L .2382 .35386 L .25129 .36005 L .26438 .36707 L .27747 .37502 L .29056 .38399 L .30365 .39409 L .31674 .40543 L .32983 .4181 L .34292 .43217 L .35601 .44768 L .3691 .46459 L .38219 .48281 L .39528 .50212 L .40837 .52213 L .42146 .54231 L .43455 .56191 L .44764 .58003 L .46073 .59565 L .47382 .60774 L .48691 .61541 L .5 .61803 L .51309 .61541 L .52618 .60774 L .53927 .59565 L .55236 .58003 L .56545 .56191 L .57854 .54231 L .59163 .52213 L .60472 .50212 L .61781 .48281 L .6309 .46459 L Mistroke .64399 .44768 L .65708 .43217 L .67017 .4181 L .68326 .40543 L .69635 .39409 L .70944 .38399 L .72253 .37502 L .73562 .36707 L .74871 .36005 L .7618 .35386 L .77489 .34841 L .78798 .34361 L .80107 .33939 L .81416 .33567 L .82725 .33241 L .84034 .32955 L .85343 .32704 L .86652 .32483 L .87961 .32289 L .8927 .32119 L .90579 .3197 L .91888 .31839 L .93197 .31724 L .94506 .31623 L .95815 .31534 L .97124 .31457 L .98433 .31389 L .99742 .31329 L Mfstroke .99742 .31329 m 1 .31319 L s 1 0 0 r 0 .31019 m .00258 .31012 L .01567 .30965 L .02876 .30902 L .04185 .30819 L .05494 .30715 L .06803 .30587 L .08112 .30433 L .09421 .30252 L .1073 .30041 L .12039 .29801 L .13348 .29532 L .14657 .29237 L .15966 .28918 L .17275 .28582 L .18584 .28236 L .19893 .27891 L .21202 .2756 L .22511 .27262 L .2382 .27018 L .25129 .26853 L .26438 .26797 L .27747 .26884 L .29056 .27153 L .30365 .27646 L .31674 .28406 L .32983 .29478 L .34292 .30902 L .35601 .32712 L .3691 .34928 L .38219 .37553 L .39528 .40557 L .40837 .43875 L .42146 .47398 L .43455 .50965 L .44764 .54372 L .46073 .57383 L .47382 .59756 L .48691 .61278 L .5 .61803 L .51309 .61278 L .52618 .59756 L .53927 .57383 L .55236 .54372 L .56545 .50965 L .57854 .47398 L .59163 .43875 L .60472 .40557 L .61781 .37553 L .6309 .34928 L Mistroke .64399 .32712 L .65708 .30902 L .67017 .29478 L .68326 .28406 L .69635 .27646 L .70944 .27153 L .72253 .26884 L .73562 .26797 L .74871 .26853 L .7618 .27018 L .77489 .27262 L .78798 .2756 L .80107 .27891 L .81416 .28236 L .82725 .28582 L .84034 .28918 L .85343 .29237 L .86652 .29532 L .87961 .29801 L .8927 .30041 L .90579 .30252 L .91888 .30433 L .93197 .30587 L .94506 .30715 L .95815 .30819 L .97124 .30902 L .98433 .30965 L .99742 .31012 L Mfstroke .99742 .31012 m 1 .31019 L s 0 1 0 r 0 .31301 m .00258 .31314 L .01567 .31385 L .02876 .31457 L .04185 .31529 L .05494 .31598 L .06803 .31661 L .08112 .31713 L .09421 .31749 L .1073 .31762 L .12039 .31746 L .13348 .31692 L .14657 .31591 L .15966 .31433 L .17275 .31207 L .18584 .30902 L .19893 .30505 L .21202 .30006 L .22511 .29394 L .2382 .28659 L .25129 .27795 L .26438 .26797 L .27747 .25666 L .29056 .24409 L .30365 .23042 L .31674 .21589 L .32983 .20087 L .34292 .18586 L .35601 .17154 L .3691 .15874 L .38219 .14845 L .39528 .14179 L .40837 .13994 L .42146 .14406 L .43455 .15507 L .44764 .17351 L .46073 .19933 L .47382 .2317 L .48691 .26903 L .5 .30902 L .51309 .34901 L .52618 .38633 L .53927 .41871 L .55236 .44452 L .56545 .46297 L .57854 .47398 L .59163 .47809 L .60472 .47625 L .61781 .46959 L .6309 .45929 L Mistroke .64399 .44649 L .65708 .43217 L .67017 .41717 L .68326 .40215 L .69635 .38762 L .70944 .37394 L .72253 .36138 L .73562 .35007 L .74871 .34009 L .7618 .33144 L .77489 .32409 L .78798 .31797 L .80107 .31298 L .81416 .30902 L .82725 .30596 L .84034 .3037 L .85343 .30212 L .86652 .30111 L .87961 .30057 L .8927 .30041 L .90579 .30054 L .91888 .3009 L .93197 .30142 L .94506 .30205 L .95815 .30274 L .97124 .30347 L .98433 .30419 L .99742 .30489 L Mfstroke .99742 .30489 m 1 .30502 L s 0 0 1 r .025 w .00258 .31329 Mdot .01567 .31389 Mdot .02876 .31457 Mdot .04185 .31534 Mdot .05494 .31623 Mdot .06803 .31724 Mdot .08112 .31839 Mdot .09421 .3197 Mdot .1073 .32119 Mdot .12039 .32289 Mdot .13348 .32483 Mdot .14657 .32704 Mdot .15966 .32955 Mdot .17275 .33241 Mdot .18584 .33567 Mdot .19893 .33939 Mdot .21202 .34361 Mdot .22511 .34841 Mdot .2382 .35386 Mdot .25129 .36005 Mdot .26438 .36707 Mdot .27747 .37502 Mdot .29056 .38399 Mdot .30365 .39409 Mdot .31674 .40543 Mdot .32983 .4181 Mdot .34292 .43217 Mdot .35601 .44768 Mdot .3691 .46459 Mdot .38219 .48281 Mdot .39528 .50212 Mdot .40837 .52213 Mdot .42146 .54231 Mdot .43455 .56191 Mdot .44764 .58003 Mdot .46073 .59565 Mdot .47382 .60774 Mdot .48691 .61541 Mdot .5 .61803 Mdot .51309 .61541 Mdot .52618 .60774 Mdot .53927 .59565 Mdot .55236 .58003 Mdot .56545 .56191 Mdot .57854 .54231 Mdot .59163 .52213 Mdot .60472 .50212 Mdot .61781 .48281 Mdot .6309 .46459 Mdot .64399 .44768 Mdot .65708 .43217 Mdot .67017 .4181 Mdot .68326 .40543 Mdot .69635 .39409 Mdot .70944 .38399 Mdot .72253 .37502 Mdot .73562 .36707 Mdot .74871 .36005 Mdot .7618 .35386 Mdot .77489 .34841 Mdot .78798 .34361 Mdot .80107 .33939 Mdot .81416 .33567 Mdot .82725 .33241 Mdot .84034 .32955 Mdot .85343 .32704 Mdot .86652 .32483 Mdot .87961 .32289 Mdot .8927 .32119 Mdot .90579 .3197 Mdot .91888 .31839 Mdot .93197 .31724 Mdot .94506 .31623 Mdot .95815 .31534 Mdot .97124 .31457 Mdot .98433 .31389 Mdot .99742 .31329 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@00<000I@00V@0`000`<00`I@0`V@0`cP0`o`1U001U<01UI@1UV@1UcP1Uo`2I002I<02I I@2IV@2IcP3><03>I@3>V@3>o`3o<03oI@3oV@3ocS000300<300IC00VC00cS00oc0`030`<30`VC0` cS0`oc1U031U<31UIC1UVC1UcS1Uoc2I032I<32IIC2IVC2IcS2Ioc3>033><33>IC3>VC3>cS3>oc3o 033o<33oIC3ocS3oofD006D0<6D0IFD0VFD0cVD0ofD`0?l18@400?l18@4008L1102E0@00R@400`01 0@2D0@00R@400`010@030@<0SP40084110040@03004100<100<00@40SP4008T100<00@400`400`01 0@2>0@00Q`4300D100<00@40SP4008T100<00@400`4208l1002?0@03004108h1002?0@03004108h1 002?0@03004108h1002?0@80S`4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l1 00<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`4208l1 002?0@03004108h1001f0@8010400`010@030@03004100810`050@03004108h1001e0@04004100T1 00<00@401@400`010@020@03004108h1001e0@04004100X100<00@4010400`010@020@<0SP4006l1 10020@04004100X100@00@410`050@03004108h1001e0@04004100/100@00@401`400`010@2>0@00 M@4010010@080@040041008100<00@401@400`010@2>0@00MP4200T110020@@0104208l1002?0@03 004108h1002?0@03004108h1002?0@03004108h1002?0@80S`4008l100<00@40SP4008l100<00@40 SP4008l100<00@40SP4008l100<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00 S`400`010@2>0@00M@433AL10P2?0@00L@443@<10`dD0@03004108h1001_0@8=2P400`d000040@03 004100810`050@03004108h1001]0@8=3040100=0@0;0@030041008100<00@40SP4006`100<=0@40 304010013@0;0@03004100810`2>0@00J`400`d10@070@@00P4010010@d80@<01@400`010@2>0@00 JP400`d10@0>0@05004100d01`400`010@050@03004108h1001Z0@033@4100h100D00@403@070@03 004100D100<00@40SP4006T100<=0@404042008100<=0@40104400@10P2?0@00J0400`d10@0F0@03 3@4100/100<00@40SP4006L100<=0@405`400`d10@0;0@03004108h1001V0@033@4101T100<=0@40 2P400`010@2>0@00I@400`d10@0J0@033@4100X10P2?0@00I0400`d10@0L0@033@4100T100<00@40 SP4006<100<=0@407@400`d10@090@03004108h1001S0@033@4101h100<=0@4020400`010@2>0@00 HP400`d10@0O0@033@4100P100<00@40SP40064100<=0@4080400`d10@080@80S`40060100<=0@40 8P400`d10@070@03004108h1001O0@033@4102<100<=0@401`400`010@2>0@00GP400`d10@0U0@03 3@4100H100<00@40SP4005d100<=0@409P400`d10@060@80S`4005`100<=0@40:0400`d10@050@03 004108h1001L0@033@4101L10P040@030041008110020@033@0000D100<00@40SP4005/100<=0@40 5`4010010@080@03004100@100<=0@0010400`010@2>0@00FP400`d10@0H0@04004100T100<00@40 0`400`d100040@<0SP4005P10PdE0@@00P4010010@0:0@0700410@0=00050@03004108h1001G0@03 3@4101/100@00@402`401P010@013@D100<00@40SP4005H100<=0@40704010010@080@0400410081 00<00@d01@400`010@2>0@00E@400`d10@0N0@802P4200<10P000`d00@030@80S`4005D100<=0@40 <@400`d10@030@03004108h1001D0@033@4103<100<=0@400P400`010@2>0@00D`400`d10@0d0@03 3@41008100<00@40SP4005410Pdg0@033@4100810P2?0@00D0400`d10@0h0@053@410@00T04004H1 2@`00`d<300333H100D=0@41000j0@h0@@<80400`010@0Q0@009@400`010@0G0@@<2@400`d10@090@<<<@4010d10@0c0@03 00`<01H10``M0@0300410241000R0@D05@4330`100<=0@403@4232l100<=0@400P0a0@8<00<00@40 604431H11@0R0@007@4400050@010@004P4430d10Pd90@@010400`0<0@0]0@043@41034100D<0@41 000M0@<<4`4010010@0S0@008`400`01000?0@<<3`423A@100<03040;@400`d1000_0@8<1@400`01 0@0M0@@<40400`01000S0@00904200/110`@0@8=4`401@010@01008<;0400`d1000^0@0330410081 00@00@408`4330h10P0S0@009@400`010@020@L<4`400`d10@0D0@8010400``10@0Z0@033@0002`1 00<<0@40104202L120`70@0300410241000V0@@<60423Ah100<<0@40:@400`d00@0[0@03304103H1 0``X0@007`4731T10`dP0@03304102T100<=0040:`400``10@0^0B0=4`4000H130l60@L<7@433B@1 00<<0@40:@400`d10@0Y0@03304102P11`dB0@L<1`4<3`L100060AX?60043BP000<<0000:0000`d0 000X0003300002H00`dI01X?1`4000D18Pl90@0300d=00D=1@400`010@0;0@03004100/100<00@40 2@400``00@0<0@03004100X100<00@402`400`d10@0;0@03004100X100<00@402`400`0<0@0:0@03 004100/100<00@402@443@/100<00@401`4Q3`L100060BT?0PdX0@03004100X100<<0@409P400`0= 0@0V0@03304100X100<00@405@423A81:0l70@001P4`3c0100<<0@409P400`0=0@0V0@0330410201 0Pd=0Bl?1`4000P100D?0@413`020@033`4?02L?;P400``10@0U0@0300d102D100<<0@407`423@/1 :Pl30@043`413`T1000C0@043`413`<100D?0@4?0@0N3b/100<<0@4090400`013@0T0@03304101h1 0Pd90Ah?00<13`400P4010l10@l30@033`410141000Q0@053`413`406PlX0@03304102@100<00@d0 90400``10@0M0@033@4100H16Pl01@4?0@4?0281000X0@043`410AP?9@400``10@0S0@0400413B81 00<<0@4070423@D15`l01@4?0@4?02T1000_0@043`410A4?9@400``10@0S0@8000<13@408@400``1 0@0K0@033@4100D140l01@4?0@4?0301000f0@033`4?00h?8`400``10@0R0@0400413B4100<<0@40 6P423@D13`l00`4?0@0f0@00>P4A3al100<<0@408P401@010@4=020100<<0@406@4010d10@4A3c/1 000m0@033`4?00/?80400``10@0Q0@0500410@d07`400``10@0I0@033@41008130l00`4?0@0m0@00 @@4>3ad100<<0@4080401@010@4=01h100<<0@4060423@813@m20@00@P4=3ad100<<0@40804200<1 00<=0@406`400``10@0G0@033@41008130m30@00A0400`l13`0;3a/100<<0@407`400`010@020@03 3@4101X100<<0@405`400`d13`0;3`030@l104@100180@033`4?00L?6`400``10@0O0@0300410081 00<=0@406P400``10@0F0@033@4100X?B@4004X130lH0@03304101h100<00@400P400`d10@0I0@03 304101L130m:0@00C04:3aP100<<0@407P4200@100<=0@4060400``10@0F0@033@l?00H?00<13`40 B`4004d130lF0@03304101d100<00@400`400`d10@0G0@03304101@130m>0@00C`400`l13`073aH1 00<<0@40104200@100<00@400P4400810`050@03004100<100<=0@405`400``10@0D0@X?D0400541 20lG0@033041008100@00@4020400`010@060@030041008100<00@4010400`d10@0E0@03304101@1 2PmA0@00D`4:3a<100<<0@400P4010010@090@03004100D100<00@400P4300@100<=0@405@400``1 0@0A0@T?00<13`40DP4005@12@lD0@0530410@000P400`010@080@0400410@<01@400`010@040@03 3@4101@100<<0@404P493eD1001F0@L?50401@`10@40008100<00@402@4010010@070@03004100D1 00<=0@404`400``10@0A0@H?00<13`40EP4005P120lB0@043041008100<00@401P4010010@020@03 004100D100<00@401@400`d10@0B0@033041010120mI0@00F0483a8100@<0@410P0:0@800`4400@1 0P070@033@41014100<<0@4040483eT1001J0@H?4`400``10@0I0@03004100H100<=0@4040400``1 0@0@0@L?F`4005/11@lC0@03304101T100<00@401`400`d10@0?0@03304101411@mL0@00F`493a01 00<<0@4060400`010@070@033@4100h100<<0@403P493e`1001M0@033`4?00@?40400``10@0H0@80 2@400`d10@0=0@03304100h11@l00`4?0@1M0@00GP463a0100<<0@4060400`010@080@033@4100d1 00<<0@403@463f01001O0@P?3P400``10@0G0@03004100P100<=0@4030400``10@0<0@P?H04005l1 20l>0@03304101L100<00@402@400`d10@0;0@03304100`120mP0@00H@463`h100<<0@405`400`01 0@090@033@4100/100<<0@402`473f81001R0@D?3`400``10@0F0@802`400`d10@090@03304100d1 1@mS0@00HP453`l100<<0@405P400`010@0:0@033@4100T100<<0@403@453f<1001T0@033`4?00@? 2`400``10@0F0@03004100/100<=0@4020400``10@090@D?00<13`40I04006H11@l<0@03304101D1 00<00@402`400`d10@070@03304100X11@mW0@00I@463``100<<0@405@4200d100<=0@401P400``1 0@090@H?I`4006H11@l=0@03304101@100<00@403@400`d10@040@03304100/11@mW0@00IP493`T1 00@<0@410P040@03004100810`050@03004100d100<=0@4010400``10@080@P?I`4006P1000@03304100@11@me0@00M0453`H1 00<<0@403@400`010@0=0@03304100@11@me0@00MP400`l03`043`<100<<0@00104300D100<00@40 304010`10@453`030@l107H1001e0@03004100D?0`400``100070@030041008100<00@40304010`1 0@453gT1001e0@03004?00D?10400``100060@03004100810`0;0@0430410@H?N@4007D100<00@40 1@l40@03304000<10`050@03004100/100<<0@400P453gT1001e0@03004100D?104010`10@020@03 004100D100<00@402`400``10@020@D?N@4007D100L00@400@l000D100@030400P400`010@050@03 004100X100<<0@4010400`0?0@1j0@00MP4200<11@l00`403002008110040@802`400``10@053g`1 001k0@D?0P400``10@0:0@03004100X100<<0@401@ml0@00NP463`<100<<0@402@400`010@090@03 304100H?O04007/11@l30@03304100T100<00@402@4010`10@453g`1001k0@D?10400``10@080@80 2@400``10@020@D?O04007d100"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-5.28102, -1.0536, 0.0368016 , 0.0119092}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.1 0.309017 0.309017 [ [.1 .29652 -6 -9 ] [.1 .29652 6 0 ] [.3 .29652 -6 -9 ] [.3 .29652 6 0 ] [.7 .29652 -3 -9 ] [.7 .29652 3 0 ] [.9 .29652 -3 -9 ] [.9 .29652 3 0 ] [.4875 0 -12 -4.5 ] [.4875 0 0 4.5 ] [.4875 .07725 -30 -4.5 ] [.4875 .07725 0 4.5 ] [.4875 .15451 -24 -4.5 ] [.4875 .15451 0 4.5 ] [.4875 .23176 -30 -4.5 ] [.4875 .23176 0 4.5 ] [.4875 .38627 -24 -4.5 ] [.4875 .38627 0 4.5 ] [.4875 .46353 -18 -4.5 ] [.4875 .46353 0 4.5 ] [.4875 .54078 -24 -4.5 ] [.4875 .54078 0 4.5 ] [.4875 .61803 -6 -4.5 ] [.4875 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .1 .30902 m .1 .31527 L s [(-4)] .1 .29652 0 1 Mshowa .3 .30902 m .3 .31527 L s [(-2)] .3 .29652 0 1 Mshowa .7 .30902 m .7 .31527 L s [(2)] .7 .29652 0 1 Mshowa .9 .30902 m .9 .31527 L s [(4)] .9 .29652 0 1 Mshowa .125 Mabswid .15 .30902 m .15 .31277 L s .2 .30902 m .2 .31277 L s .25 .30902 m .25 .31277 L s .35 .30902 m .35 .31277 L s .4 .30902 m .4 .31277 L s .45 .30902 m .45 .31277 L s .55 .30902 m .55 .31277 L s .6 .30902 m .6 .31277 L s .65 .30902 m .65 .31277 L s .75 .30902 m .75 .31277 L s .8 .30902 m .8 .31277 L s .85 .30902 m .85 .31277 L s .05 .30902 m .05 .31277 L s .95 .30902 m .95 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 0 m .50625 0 L s [(-1)] .4875 0 1 0 Mshowa .5 .07725 m .50625 .07725 L s [(-0.75)] .4875 .07725 1 0 Mshowa .5 .15451 m .50625 .15451 L s [(-0.5)] .4875 .15451 1 0 Mshowa .5 .23176 m .50625 .23176 L s [(-0.25)] .4875 .23176 1 0 Mshowa .5 .38627 m .50625 .38627 L s [(0.25)] .4875 .38627 1 0 Mshowa .5 .46353 m .50625 .46353 L s [(0.5)] .4875 .46353 1 0 Mshowa .5 .54078 m .50625 .54078 L s [(0.75)] .4875 .54078 1 0 Mshowa .5 .61803 m .50625 .61803 L s [(1)] .4875 .61803 1 0 Mshowa .125 Mabswid .5 .01545 m .50375 .01545 L s .5 .0309 m .50375 .0309 L s .5 .04635 m .50375 .04635 L s .5 .0618 m .50375 .0618 L s .5 .09271 m .50375 .09271 L s .5 .10816 m .50375 .10816 L s .5 .12361 m .50375 .12361 L s .5 .13906 m .50375 .13906 L s .5 .16996 m .50375 .16996 L s .5 .18541 m .50375 .18541 L s .5 .20086 m .50375 .20086 L s .5 .21631 m .50375 .21631 L s .5 .24721 m .50375 .24721 L s .5 .26266 m .50375 .26266 L s .5 .27812 m .50375 .27812 L s .5 .29357 m .50375 .29357 L s .5 .32447 m .50375 .32447 L s .5 .33992 m .50375 .33992 L s .5 .35537 m .50375 .35537 L s .5 .37082 m .50375 .37082 L s .5 .40172 m .50375 .40172 L s .5 .41717 m .50375 .41717 L s .5 .43262 m .50375 .43262 L s .5 .44807 m .50375 .44807 L s .5 .47898 m .50375 .47898 L s .5 .49443 m .50375 .49443 L s .5 .50988 m .50375 .50988 L s .5 .52533 m .50375 .52533 L s .5 .55623 m .50375 .55623 L s .5 .57168 m .50375 .57168 L s .5 .58713 m .50375 .58713 L s .5 .60258 m .50375 .60258 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid 0 .30995 m .00258 .30997 L .01567 .3101 L .02876 .31026 L .04185 .31043 L .05494 .31063 L .06803 .31085 L .08112 .31111 L .09421 .3114 L .1073 .31173 L .12039 .31211 L .13348 .31255 L .14657 .31304 L .15966 .3136 L .17275 .31424 L .18584 .31498 L .19893 .31581 L .21202 .31676 L .22511 .31784 L .2382 .31907 L .25129 .32048 L .26438 .32208 L .27747 .32391 L .29056 .32599 L .30365 .32835 L .31674 .33105 L .32983 .33413 L .34292 .33762 L .35601 .3416 L .3691 .34613 L .38219 .35127 L .39528 .35711 L .40837 .36374 L .42146 .37125 L .43455 .37973 L .44764 .38931 L .46073 .40007 L .47382 .41211 L .48691 .42553 L .5 .44038 L .51309 .45665 L .52618 .4743 L .53927 .49314 L .55236 .51288 L .56545 .53307 L .57854 .55303 L .59163 .57196 L .60472 .58885 L .61781 .60269 L .6309 .61248 L Mistroke .64399 .61748 L .65708 .61726 L .67017 .61185 L .68326 .6017 L .69635 .58757 L .70944 .57047 L .72253 .55143 L .73562 .53141 L .74871 .51125 L .7618 .49156 L .77489 .47281 L .78798 .45527 L .80107 .43911 L .81416 .42439 L .82725 .41108 L .84034 .39914 L .85343 .38848 L .86652 .379 L .87961 .3706 L .8927 .36317 L .90579 .35661 L .91888 .35083 L .93197 .34574 L .94506 .34126 L .95815 .33732 L .97124 .33386 L .98433 .33082 L .99742 .32815 L Mfstroke .99742 .32815 m 1 .32769 L s 1 0 0 r 0 .30856 m .00258 .30856 L .01567 .30856 L .02876 .30857 L .04185 .3086 L .05494 .30864 L .06803 .3087 L .08112 .30879 L .09421 .30892 L .1073 .30908 L .12039 .30929 L .13348 .30956 L .14657 .3099 L .15966 .31031 L .17275 .31082 L .18584 .31143 L .19893 .31217 L .21202 .31305 L .22511 .31409 L .2382 .31533 L .25129 .31678 L .26438 .31847 L .27747 .32044 L .29056 .32272 L .30365 .32535 L .31674 .32836 L .32983 .3318 L .34292 .3357 L .35601 .34011 L .3691 .34508 L .38219 .35065 L .39528 .35684 L .40837 .36369 L .42146 .37123 L .43455 .37945 L .44764 .38834 L .46073 .39787 L .47382 .40793 L .48691 .41842 L .5 .42914 L .51309 .43983 L .52618 .45013 L .53927 .45961 L .55236 .46774 L .56545 .47388 L .57854 .47738 L .59163 .4776 L .60472 .474 L .61781 .46627 L .6309 .45441 L Mistroke .64399 .43878 L .65708 .42012 L .67017 .39946 L .68326 .37797 L .69635 .3568 L .70944 .33692 L .72253 .31907 L .73562 .30369 L .74871 .29096 L .7618 .28086 L .77489 .27322 L .78798 .26779 L .80107 .26426 L .81416 .26233 L .82725 .26169 L .84034 .2621 L .85343 .2633 L .86652 .26509 L .87961 .26732 L .8927 .26982 L .90579 .27249 L .91888 .27525 L .93197 .27801 L .94506 .28072 L .95815 .28334 L .97124 .28584 L .98433 .28821 L .99742 .29042 L Mfstroke .99742 .29042 m 1 .29083 L s 0 1 0 r 0 .30821 m .00258 .30818 L .01567 .30803 L .02876 .30786 L .04185 .30767 L .05494 .30745 L .06803 .30721 L .08112 .30694 L .09421 .30664 L .1073 .3063 L .12039 .30593 L .13348 .30553 L .14657 .30509 L .15966 .30462 L .17275 .30411 L .18584 .30357 L .19893 .303 L .21202 .30241 L .22511 .3018 L .2382 .30119 L .25129 .30058 L .26438 .3 L .27747 .29947 L .29056 .29901 L .30365 .29866 L .31674 .29846 L .32983 .29845 L .34292 .29871 L .35601 .29929 L .3691 .30027 L .38219 .30177 L .39528 .30388 L .40837 .30675 L .42146 .31051 L .43455 .31533 L .44764 .3214 L .46073 .32891 L .47382 .33808 L .48691 .3491 L .5 .36218 L .51309 .37747 L .52618 .39506 L .53927 .41495 L .55236 .43696 L .56545 .46074 L .57854 .48565 L .59163 .5108 L .60472 .53504 L .61781 .55703 L .6309 .57539 L Mistroke .64399 .58886 L .65708 .59654 L .67017 .59803 L .68326 .59346 L .69635 .58345 L .70944 .56898 L .72253 .55122 L .73562 .53135 L .74871 .51044 L .7618 .48938 L .77489 .46885 L .78798 .44934 L .80107 .43117 L .81416 .41451 L .82725 .39945 L .84034 .38596 L .85343 .37401 L .86652 .3635 L .87961 .35433 L .8927 .34638 L .90579 .33953 L .91888 .33367 L .93197 .32868 L .94506 .32446 L .95815 .32092 L .97124 .31797 L .98433 .31553 L .99742 .31352 L Mfstroke .99742 .31352 m 1 .3132 L s 0 0 1 r .025 w .00258 .30997 Mdot .01567 .3101 Mdot .02876 .31026 Mdot .04185 .31043 Mdot .05494 .31063 Mdot .06803 .31085 Mdot .08112 .31111 Mdot .09421 .3114 Mdot .1073 .31173 Mdot .12039 .31211 Mdot .13348 .31255 Mdot .14657 .31304 Mdot .15966 .3136 Mdot .17275 .31424 Mdot .18584 .31498 Mdot .19893 .31581 Mdot .21202 .31676 Mdot .22511 .31784 Mdot .2382 .31907 Mdot .25129 .32048 Mdot .26438 .32208 Mdot .27747 .32391 Mdot .29056 .32599 Mdot .30365 .32835 Mdot .31674 .33105 Mdot .32983 .33413 Mdot .34292 .33762 Mdot .35601 .3416 Mdot .3691 .34613 Mdot .38219 .35127 Mdot .39528 .35711 Mdot .40837 .36374 Mdot .42146 .37125 Mdot .43455 .37973 Mdot .44764 .38931 Mdot .46073 .40007 Mdot .47382 .41211 Mdot .48691 .42553 Mdot .5 .44038 Mdot .51309 .45665 Mdot .52618 .4743 Mdot .53927 .49314 Mdot .55236 .51288 Mdot .56545 .53307 Mdot .57854 .55303 Mdot .59163 .57196 Mdot .60472 .58885 Mdot .61781 .60269 Mdot .6309 .61248 Mdot .64399 .61748 Mdot .65708 .61726 Mdot .67017 .61185 Mdot .68326 .6017 Mdot .69635 .58757 Mdot .70944 .57047 Mdot .72253 .55143 Mdot .73562 .53141 Mdot .74871 .51125 Mdot .7618 .49156 Mdot .77489 .47281 Mdot .78798 .45527 Mdot .80107 .43911 Mdot .81416 .42439 Mdot .82725 .41108 Mdot .84034 .39914 Mdot .85343 .38848 Mdot .86652 .379 Mdot .87961 .3706 Mdot .8927 .36317 Mdot .90579 .35661 Mdot .91888 .35083 Mdot .93197 .34574 Mdot .94506 .34126 Mdot .95815 .33732 Mdot .97124 .33386 Mdot .98433 .33082 Mdot .99742 .32815 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@00<000I@00V@0`000`<00`I@0`V@0`cP0`o`1U001U<01UI@1UV@1UcP1Uo`2I002I<02I I@2IV@2IcP3><03>I@3>V@3>o`3o<03oI@3oV@3ocS000300<300IC00VC00cS00oc0`030`<30`VC0` cS0`oc1U031U<31UIC1UVC1UcS1Uoc2I032I<32IIC2IVC2IcS2Ioc3>033><33>IC3>VC3>cS3>oc3o 033o<33oIC3ocS3oofD006D0<6D0IFD0VFD0cVD0ofD`0?l18@400?l18@4008L1102E0@00R@400`01 0@2D0@00R@400`010@030@<0SP40084110040@03004100<100<00@40SP4008T100<00@400`400`01 0@2>0@00Q`4300D100<00@40SP4008T100<00@400`4208l1002?0@03004108h1002?0@03004108h1 002?0@03004108h1002?0@80S`4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l1 00<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`4208l1 002?0@03004108h1001f0@8010400`010@030@03004100810`050@03004108h1001e0@04004100T1 00<00@401@400`010@020@03004108h1001e0@04004100X100<00@4010400`010@020@<0SP4006l1 10020@04004100X100@00@410`050@03004108h1001e0@04004100/100@00@401`400`010@2>0@00 M@4010010@080@040041008100<00@401@400`010@2>0@00MP4200T110020@@0104208l1002?0@03 004108h1002?0@03004108h1002?0@03004108h1002?0@80S`4008l100<00@40SP4008l100<00@40 SP4008l100<00@40SP4008l100<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00 S`400`010@2>0@00S`4208l1002?0@03004108h1001l0@8010400`010@020@<01@400`010@2>0@00 N`4010010@0;0@030041008100<00@40SP4007/100@00@402`400`010@020@<0SP4007D110020@04 004100P10`050@03004108h1001k0@04004100P100<00@401@400`010@2>0@00N`4010010@080@03 004100D100<00@40SP4007`10P090@@0104208l1002?0@03004108h1002?0@03004108h1002?0@03 004108h1002?0@80S`4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l100<00@40 SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`4208l1002?0@03 004108h1001f0@8010400`010@020@@00P4300D100<00@40SP4007D100@00@4020400`010@060@03 0041008100<00@40SP4007D100@00@402@400`010@050@03004100810`2>0@00K`44008100@00@40 2P4010010@4300D100<00@40SP4007D100@00@402`4010010@070@03004108h1001e0@04004100P1 00@00@400P400`010@050@03004108h1001f0@802P4200<110040@80S`4008l100<00@40SP4008l1 00<00@40SP4008l100<00@40SP4008l10P1B0@X<<`4008l100<00@40C@4430X120`[0@00S`400`01 0@1:0@<<5P4732@1000U0@0300410381100a0@0300410341100B0@<<80433241000U0@0300410381 00<00@400@001@523c400`eC0003300004L0204000H1C0l70@03004100X100<00@40 2`400`010@040@8=10400`010@0;0@03004100/100<00@402P400`010@0;0@03004100X100<00@40 1@400``10@030@03004100/100<00@402P400`010@0;0@03004100X100<00@402@433@P100060E0? 0`400`010@0Q0@8=40400`010@0c0@03004100@100<<0@40;@400`010@0>0@P=2`4000P100D?0@41 3`020@053`410@l00P401@l10@4?0081003aL1001/0@d?50423@80<`400``10@0^0@033@4100`?00<13`406@4006l1 00@4008X120l:0@033@4101P100<<0@409@463c/1002<0@H?00<<0@4020400`d10@0F0@03304102D1 1Pll0@00S0463`030@`100T100<=0@4050400``10@0W0@D??04008d11@l20@8<20400`d10@0D0@03 304102H100<=3`l00`ll0@00S@493`03304100H100<=0@404P400``10@0T0@D?00<13`40?@4008l1 000@00 MP4200@100<00@400`400`010@020@<01@400`010@0<0@H?1`400`d10@0O0@D?CP4007D100@00@40 2@400`010@050@030041008100<00@403@453`P100<=0@407P453dh1001e0@04004100X100<00@40 10400`010@020@<03@453`P100<=0@407P400`d13`1@0@00M@4010010@0:0@0400410@<01@400`01 0@0?0@H?1P400`d10@0J0@D?D@4007D100@00@402`4010010@070@03004101011@l70@033@4101T1 1@mA0@00M@4010010@080@040041008100<00@401@400`010@0?0@H?1`400`d10@0H0@H?D@4007H1 0P090@@00P4400@10P0A0@D?20400`d10@0H0@D?D@4008l100<00@4040453`T100<=0@405`453e41 002?0@0300410181003f0100290@03004100<1 0`0O0@l?H04008T100<00@409`4;3f8100290@03004102P12@mS0@00Q`4302`100D?0@413`1U0@00 R@400`010@2D0@00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-5.28102, -1.0536, 0.0368016 , 0.0119092}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.1 0.309017 0.309017 [ [.1 .29652 -6 -9 ] [.1 .29652 6 0 ] [.3 .29652 -6 -9 ] [.3 .29652 6 0 ] [.7 .29652 -3 -9 ] [.7 .29652 3 0 ] [.9 .29652 -3 -9 ] [.9 .29652 3 0 ] [.4875 0 -12 -4.5 ] [.4875 0 0 4.5 ] [.4875 .07725 -30 -4.5 ] [.4875 .07725 0 4.5 ] [.4875 .15451 -24 -4.5 ] [.4875 .15451 0 4.5 ] [.4875 .23176 -30 -4.5 ] [.4875 .23176 0 4.5 ] [.4875 .38627 -24 -4.5 ] [.4875 .38627 0 4.5 ] [.4875 .46353 -18 -4.5 ] [.4875 .46353 0 4.5 ] [.4875 .54078 -24 -4.5 ] [.4875 .54078 0 4.5 ] [.4875 .61803 -6 -4.5 ] [.4875 .61803 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .1 .30902 m .1 .31527 L s [(-4)] .1 .29652 0 1 Mshowa .3 .30902 m .3 .31527 L s [(-2)] .3 .29652 0 1 Mshowa .7 .30902 m .7 .31527 L s [(2)] .7 .29652 0 1 Mshowa .9 .30902 m .9 .31527 L s [(4)] .9 .29652 0 1 Mshowa .125 Mabswid .15 .30902 m .15 .31277 L s .2 .30902 m .2 .31277 L s .25 .30902 m .25 .31277 L s .35 .30902 m .35 .31277 L s .4 .30902 m .4 .31277 L s .45 .30902 m .45 .31277 L s .55 .30902 m .55 .31277 L s .6 .30902 m .6 .31277 L s .65 .30902 m .65 .31277 L s .75 .30902 m .75 .31277 L s .8 .30902 m .8 .31277 L s .85 .30902 m .85 .31277 L s .05 .30902 m .05 .31277 L s .95 .30902 m .95 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .5 0 m .50625 0 L s [(-1)] .4875 0 1 0 Mshowa .5 .07725 m .50625 .07725 L s [(-0.75)] .4875 .07725 1 0 Mshowa .5 .15451 m .50625 .15451 L s [(-0.5)] .4875 .15451 1 0 Mshowa .5 .23176 m .50625 .23176 L s [(-0.25)] .4875 .23176 1 0 Mshowa .5 .38627 m .50625 .38627 L s [(0.25)] .4875 .38627 1 0 Mshowa .5 .46353 m .50625 .46353 L s [(0.5)] .4875 .46353 1 0 Mshowa .5 .54078 m .50625 .54078 L s [(0.75)] .4875 .54078 1 0 Mshowa .5 .61803 m .50625 .61803 L s [(1)] .4875 .61803 1 0 Mshowa .125 Mabswid .5 .01545 m .50375 .01545 L s .5 .0309 m .50375 .0309 L s .5 .04635 m .50375 .04635 L s .5 .0618 m .50375 .0618 L s .5 .09271 m .50375 .09271 L s .5 .10816 m .50375 .10816 L s .5 .12361 m .50375 .12361 L s .5 .13906 m .50375 .13906 L s .5 .16996 m .50375 .16996 L s .5 .18541 m .50375 .18541 L s .5 .20086 m .50375 .20086 L s .5 .21631 m .50375 .21631 L s .5 .24721 m .50375 .24721 L s .5 .26266 m .50375 .26266 L s .5 .27812 m .50375 .27812 L s .5 .29357 m .50375 .29357 L s .5 .32447 m .50375 .32447 L s .5 .33992 m .50375 .33992 L s .5 .35537 m .50375 .35537 L s .5 .37082 m .50375 .37082 L s .5 .40172 m .50375 .40172 L s .5 .41717 m .50375 .41717 L s .5 .43262 m .50375 .43262 L s .5 .44807 m .50375 .44807 L s .5 .47898 m .50375 .47898 L s .5 .49443 m .50375 .49443 L s .5 .50988 m .50375 .50988 L s .5 .52533 m .50375 .52533 L s .5 .55623 m .50375 .55623 L s .5 .57168 m .50375 .57168 L s .5 .58713 m .50375 .58713 L s .5 .60258 m .50375 .60258 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid 0 .30958 m .00258 .3096 L .01567 .30968 L .02876 .30977 L .04185 .30987 L .05494 .30999 L .06803 .31013 L .08112 .31029 L .09421 .31046 L .1073 .31066 L .12039 .3109 L .13348 .31116 L .14657 .31146 L .15966 .3118 L .17275 .31219 L .18584 .31263 L .19893 .31314 L .21202 .31371 L .22511 .31437 L .2382 .31512 L .25129 .31597 L .26438 .31694 L .27747 .31805 L .29056 .31931 L .30365 .32075 L .31674 .32239 L .32983 .32426 L .34292 .32639 L .35601 .32882 L .3691 .33158 L .38219 .33472 L .39528 .3383 L .40837 .34238 L .42146 .34701 L .43455 .35227 L .44764 .35825 L .46073 .36503 L .47382 .3727 L .48691 .38138 L .5 .39115 L .51309 .40214 L .52618 .41443 L .53927 .4281 L .55236 .44321 L .56545 .45974 L .57854 .47761 L .59163 .49664 L .60472 .51651 L .61781 .5367 L .6309 .55655 L Mistroke .64399 .57518 L .65708 .5916 L .67017 .60478 L .68326 .61375 L .69635 .61783 L .70944 .61666 L .72253 .61035 L .73562 .59942 L .74871 .58468 L .7618 .56715 L .77489 .54787 L .78798 .52777 L .80107 .50765 L .81416 .4881 L .82725 .46955 L .84034 .45225 L .85343 .43635 L .86652 .42188 L .87961 .40883 L .8927 .39713 L .90579 .38669 L .91888 .37741 L .93197 .36919 L .94506 .36192 L .95815 .35551 L .97124 .34986 L .98433 .34489 L .99742 .34051 L Mfstroke .99742 .34051 m 1 .33975 L s 1 0 0 r 0 .30915 m .00258 .30915 L .01567 .30917 L .02876 .30919 L .04185 .30922 L .05494 .30925 L .06803 .30928 L .08112 .30932 L .09421 .30936 L .1073 .3094 L .12039 .30946 L .13348 .30952 L .14657 .30959 L .15966 .30967 L .17275 .30976 L .18584 .30987 L .19893 .30999 L .21202 .31012 L .22511 .31028 L .2382 .31045 L .25129 .31065 L .26438 .31088 L .27747 .31114 L .29056 .31144 L .30365 .31178 L .31674 .31216 L .32983 .3126 L .34292 .3131 L .35601 .31367 L .3691 .31432 L .38219 .31506 L .39528 .31591 L .40837 .31686 L .42146 .31795 L .43455 .31919 L .44764 .3206 L .46073 .32219 L .47382 .324 L .48691 .32604 L .5 .32834 L .51309 .33092 L .52618 .33381 L .53927 .33703 L .55236 .34058 L .56545 .34447 L .57854 .34868 L .59163 .35315 L .60472 .35783 L .61781 .36258 L .6309 .36725 L Mistroke .64399 .37163 L .65708 .37549 L .67017 .37859 L .68326 .3807 L .69635 .38166 L .70944 .38139 L .72253 .3799 L .73562 .37733 L .74871 .37386 L .7618 .36974 L .77489 .3652 L .78798 .36048 L .80107 .35574 L .81416 .35114 L .82725 .34678 L .84034 .34271 L .85343 .33897 L .86652 .33557 L .87961 .3325 L .8927 .32974 L .90579 .32729 L .91888 .32511 L .93197 .32317 L .94506 .32146 L .95815 .31995 L .97124 .31863 L .98433 .31745 L .99742 .31643 L Mfstroke .99742 .31643 m 1 .31625 L s 0 1 0 r 0 .30957 m .00258 .30958 L .01567 .30966 L .02876 .30975 L .04185 .30985 L .05494 .30997 L .06803 .3101 L .08112 .31025 L .09421 .31042 L .1073 .31062 L .12039 .31084 L .13348 .3111 L .14657 .31139 L .15966 .31172 L .17275 .3121 L .18584 .31253 L .19893 .31302 L .21202 .31358 L .22511 .31422 L .2382 .31495 L .25129 .31578 L .26438 .31672 L .27747 .3178 L .29056 .31903 L .30365 .32042 L .31674 .32202 L .32983 .32383 L .34292 .3259 L .35601 .32826 L .3691 .33094 L .38219 .334 L .39528 .33748 L .40837 .34144 L .42146 .34594 L .43455 .35106 L .44764 .35687 L .46073 .36346 L .47382 .37092 L .48691 .37935 L .5 .38885 L .51309 .39953 L .52618 .41147 L .53927 .42476 L .55236 .43944 L .56545 .45551 L .57854 .47288 L .59163 .49138 L .60472 .51068 L .61781 .53031 L .6309 .5496 L Mistroke .64399 .56771 L .65708 .58367 L .67017 .59648 L .68326 .6052 L .69635 .60916 L .70944 .60803 L .72253 .6019 L .73562 .59127 L .74871 .57694 L .7618 .55991 L .77489 .54116 L .78798 .52163 L .80107 .50207 L .81416 .48308 L .82725 .46505 L .84034 .44824 L .85343 .43278 L .86652 .41872 L .87961 .40603 L .8927 .39465 L .90579 .38451 L .91888 .37549 L .93197 .3675 L .94506 .36044 L .95815 .35421 L .97124 .34871 L .98433 .34388 L .99742 .33963 L Mfstroke .99742 .33963 m 1 .33889 L s 0 0 1 r .025 w .00258 .3096 Mdot .01567 .30968 Mdot .02876 .30977 Mdot .04185 .30987 Mdot .05494 .30999 Mdot .06803 .31013 Mdot .08112 .31029 Mdot .09421 .31046 Mdot .1073 .31066 Mdot .12039 .3109 Mdot .13348 .31116 Mdot .14657 .31146 Mdot .15966 .3118 Mdot .17275 .31219 Mdot .18584 .31263 Mdot .19893 .31314 Mdot .21202 .31371 Mdot .22511 .31437 Mdot .2382 .31512 Mdot .25129 .31597 Mdot .26438 .31694 Mdot .27747 .31805 Mdot .29056 .31931 Mdot .30365 .32075 Mdot .31674 .32239 Mdot .32983 .32426 Mdot .34292 .32639 Mdot .35601 .32882 Mdot .3691 .33158 Mdot .38219 .33472 Mdot .39528 .3383 Mdot .40837 .34238 Mdot .42146 .34701 Mdot .43455 .35227 Mdot .44764 .35825 Mdot .46073 .36503 Mdot .47382 .3727 Mdot .48691 .38138 Mdot .5 .39115 Mdot .51309 .40214 Mdot .52618 .41443 Mdot .53927 .4281 Mdot .55236 .44321 Mdot .56545 .45974 Mdot .57854 .47761 Mdot .59163 .49664 Mdot .60472 .51651 Mdot .61781 .5367 Mdot .6309 .55655 Mdot .64399 .57518 Mdot .65708 .5916 Mdot .67017 .60478 Mdot .68326 .61375 Mdot .69635 .61783 Mdot .70944 .61666 Mdot .72253 .61035 Mdot .73562 .59942 Mdot .74871 .58468 Mdot .7618 .56715 Mdot .77489 .54787 Mdot .78798 .52777 Mdot .80107 .50765 Mdot .81416 .4881 Mdot .82725 .46955 Mdot .84034 .45225 Mdot .85343 .43635 Mdot .86652 .42188 Mdot .87961 .40883 Mdot .8927 .39713 Mdot .90579 .38669 Mdot .91888 .37741 Mdot .93197 .36919 Mdot .94506 .36192 Mdot .95815 .35551 Mdot .97124 .34986 Mdot .98433 .34489 Mdot .99742 .34051 Mdot % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg00000c/h0cP3>c_[ZeT10@?l0003o0?oo0000ool0o`3ook:b/UUIFO[jn^kF][jn_W61TEeM G@00PG4LD000@4A4]SP<:9e4LHTLHLKFhXVI]P2AoonA05D0ZZX005FAE@3oZZZAoj[o0?lTEEGooj[o Z_nAZ_ooE@18EEE805E8ojY8ZP2A05GoE@2fEEFf05FfZZZfE@0TZUDTEJXTojY]0?m]o`2AZZX0EJ[o ool0Z_nAEOooZP3oEEE]ZUFAoeGo05GoZZY]EJZAZZZf0:[oEOnfo`00E@180018oeD005D0ojX0Z_m8 0?m8ZP1]E@2f002fZP2foeE8ZUE]05FfEEFfojY80:Y8EJZfZZZfoom8oonf0?nfEOnfZP00ZP0T000T E@0To`18ZP1]001]ZP1]o`2AE@3J003JE@3JZP3JoeD0EEDT05DTZUDToeE8EEE]EEE]oeFA05FAZUGJ 05GJEEGJZUGJojX0ojXT0:XTEJXTZZY8ojY]ZZY]ojZA0:ZAEJ[J0:[JEJ[JZZ[Jool0EOlT0?lTZ_lT oom8EOm]0?m]EOm]Z_nAoooJ0?oJEOoJZ_oJol;2`YT0IOooc^[ZjW5aLH40030`IFEUcX61PIVIob0P 88610021PD2IY@0d?0210?mUoooo_]KFokZj^X61oe1@^/jIIIUUVC3oV@2IoaQMI@00 kUDHRJFUY@00<000I@00V@0`000`<00`I@0`V@0`cP0`o`1U001U<01UI@1UV@1UcP1Uo`2I002I<02I I@2IV@2IcP3><03>I@3>V@3>o`3o<03oI@3oV@3ocS000300<300IC00VC00cS00oc0`030`<30`VC0` cS0`oc1U031U<31UIC1UVC1UcS1Uoc2I032I<32IIC2IVC2IcS2Ioc3>033><33>IC3>VC3>cS3>oc3o 033o<33oIC3ocS3oofD006D0<6D0IFD0VFD0cVD0ofD`0?l18@400?l18@4008L1102E0@00R@400`01 0@2D0@00R@400`010@030@<0SP40084110040@03004100<100<00@40SP4008T100<00@400`400`01 0@2>0@00Q`4300D100<00@40SP4008T100<00@400`4208l1002?0@03004108h1002?0@03004108h1 002?0@03004108h1002?0@80S`4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l1 00<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`4208l1 002?0@03004108h1001f0@8010400`010@030@03004100810`050@03004108h1001e0@04004100T1 00<00@401@400`010@020@03004108h1001e0@04004100X100<00@4010400`010@020@<0SP4006l1 10020@04004100X100@00@410`050@03004108h1001e0@04004100/100@00@401`400`010@2>0@00 M@4010010@080@040041008100<00@401@400`010@2>0@00MP4200T110020@@0104208l1002?0@03 004108h1002?0@03004108h1002?0@03004108h1002?0@80S`4008l100<00@40SP4008l100<00@40 SP4008l100<00@40SP4008l100<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00 S`400`010@2>0@00S`4208l1002?0@03004108h1001l0@8010400`010@020@<01@400`010@2>0@00 N`4010010@0;0@030041008100<00@40SP4007/100@00@402`400`010@020@<0SP4007D110020@04 004100P10`050@03004108h1001k0@04004100P100<00@401@400`010@2>0@00N`4010010@080@03 004100D100<00@40SP4007`10P090@@0104208l1002?0@03004108h1002?0@03004108h1002?0@03 004108h1002?0@80S`4008l100<00@40SP4008l100<00@40SP4008l100<00@40SP4008l100<00@40 SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@00S`400`010@2>0@00S`4208l1002?0@03 004108h1001f0@8010400`010@020@@00P4300D100<00@40SP4007D100@00@4020400`010@060@03 0041008100<00@40SP4007D100@00@402@400`010@050@03004100810`2>0@00K`44008100@00@40 2P4010010@4300D100<00@40SP4007D100@00@402`4010010@070@03004108h1001e0@04004100P1 00@00@400P400`010@050@03004108h1001f0@802P4200<110040@80S`4008l100<00@40SP4008l1 00<00@40SP4008l100<00@40SP4008l10P2?0@00S`400`010@2>0@00S`400`010@2>0@009@400`01 0@0b0@@0<@400`010@0a0@@0=@400`010@0Q0@009@400`010@0b0@030041038100<00@40<@400`01 0@0f0@0300410241000R0@D0=0400`010@0a0@80<`400`010@0b0@D08P4001d110001@400@4002h1 10040@030041030100<00@40<`400`010@0a0@04004102<1000S0@03004003L100<00@40;`400`01 0@0d0@030041034100<00@008`4002@10P0d0@040041034100<00@40<@4010010@0d0@808`4002D1 00<00@40<`4203810P0c0@80=P400`010@0Q0@00S`400`010@2>0@001P4Y3f0100<00@40SP4000H1 @@m80@03004108h100050E4?`P080@001P5G3a0<1`400`010@0:0@03004100/100<00@402`400`01 0@0:0@03004100/100<00@402P400`010@0;0@03004100/100<00@402P400`010@0;0@03004100X1 00<00@40504000H1GPl90@l<4`400`010@0c0@03004103@100<00@404P4730P100080@053`410@l0 0P401@l10@4?008100D?0@413`020@053`410@l00P401@l10@4?00<1?`lA0@L<30400`010@1d0@/< 3`4002l100D?0@413`020@053`410@l00P401@l10@4?008100`453`030@l103H1002?0@03004101011@lk0@D?>@4008l100<00@404P400`l1 3`043cH11Pli0