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Cell[CellGroupData[{ Cell["DATA PROCESSING", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[{ \(Clear[T, Tau, Xi, sf, SXi, Alpha, AlphaXi, ximin, ximax]\n\), \(Len = Length[data]; \ Sinfty = kappa/\((1 + kappa)\); \n T = Table[data[\([i, 1]\)], {i, 1, Len}]; \nTau = \ T\ *sigma^2/2; \n Xi = Log[\ \ Tau]; \n\nsf\ = Table[\ data[\([i, 2]\)]/e, {i, 1, Len}]; \n Alpha = Log[sf]^2/\((4\ Tau)\); \n\n\ ximin = Xi[\([1]\)]; \ ximax = Xi[\([Len]\)]; \n\ taumin = \ Tau[\([1]\)]; taumax = Tau[\([Len]\)]; \ \n\ \ Tmin = T[\([1]\)]; Tmax = T[\([Len]\)]; \n\n\nSXi = Interpolation[Table[{Xi[\([i]\)], sf[\([i]\)]}, {i, 1, Len}]]; \n AlphaXi = Interpolation[\n\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Table[{Xi[\([i]\)], Alpha[\([i]\)]}, {i, 1, Len}]]; \n\n Print["\", r, \ "\< \[Sigma]=\>", sigma, \ "\< \[Kappa]=2r/\[Sigma]^2= \>", \ kappa, \n \t\ \ \ \ \ \ \ \ \ \ \ \ \ \ "\< S(\[Infinity])=\[Kappa]/(1+\[Kappa])=\>", Sinfty, \n \ \ \ \ \ \ \ \ \ \ \ \ "\< s(\[Infinity])=Log[\[Kappa]/(1+\[Kappa])]=\>", Log[Sinfty]\ ]; \n Print[\ \ "\< Tmin=\>", \ Tmin, "\< (year), Tmax=\>", Tmax, "\< (year)\>"\ ]; \n Print["\", ximin, \ "\< ximax=\>", ximax, \n \t\t\ \ \ \ \ \ \ \ \ \ \ "\< \[Tau]min=\>", taumin, "\< \[Tau]max=\>", \ taumax]; \n\t\ \ \ \ \ \ \ \ \ \ \ \n (*\npSXi = \(ListPlot[Table[{Xi[\([i]\)], sf[\([i]\)]}, {i, 1, Len}], PlotRange -> All, PlotStyle -> AbsolutePointSize[2]]\n pAlphaXi = ListPlot[Table[{Xi[\([i]\)], Alpha[\([i]\)]}, {i, 1, Len}], PlotRange -> All, PlotStyle -> AbsolutePointSize[2]]\)\ *) \n\n \)}], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{"\<\"r=\"\>", "\[InvisibleSpace]", StyleBox["0.09`", StyleBoxAutoDelete->True, PrintPrecision->1], "\[InvisibleSpace]", "\<\" \[Sigma]=\"\>", "\[InvisibleSpace]", StyleBox["0.6`", StyleBoxAutoDelete->True, PrintPrecision->1], "\[InvisibleSpace]", "\<\" \[Kappa]=2r/\[Sigma]^2= \"\>", "\[InvisibleSpace]", "0.499999999999999911`", "\[InvisibleSpace]", "\<\" S(\[Infinity])=\[Kappa]/(1+\[Kappa])=\"\>", "\[InvisibleSpace]", "0.333333333333333259`", "\[InvisibleSpace]", "\<\" s(\[Infinity])=Log[\[Kappa]/(1+\[Kappa])]=\"\>", "\[InvisibleSpace]", \(-1.09861228866811`\)}], SequenceForm[ "r=", 0.089999999999999997, " \[Sigma]=", 0.59999999999999998, " \[Kappa]=2r/\[Sigma]^2= ", 0.49999999999999994, " S(\[Infinity])=\[Kappa]/(1+\[Kappa])=", 0.33333333333333326, " s(\[Infinity])=Log[\[Kappa]/(1+\[Kappa])]=", -1.09861228866811], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[ \(" Tmin="\[InvisibleSpace]3.5762786865234375`*^-7 \[InvisibleSpace]" (year), \ Tmax="\[InvisibleSpace]9.99999999999999822`\[InvisibleSpace]" (year)"\), SequenceForm[ " Tmin=", 3.5762786865234375*^-07, " (year), Tmax=", 9.9999999999999982, " (year)"], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[ \("ximin="\[InvisibleSpace]\(-16.5585712923025596` \)\[InvisibleSpace]" ximax="\[InvisibleSpace]0.587786664902118793` \[InvisibleSpace]" \ \[Tau]min="\[InvisibleSpace]6.4373016357421875`*^-8 \[InvisibleSpace]" \[Tau]max="\[InvisibleSpace]1.79999999999999964` \), SequenceForm[ "ximin=", -16.55857129230256, " ximax=", 0.58778666490211884, " \[Tau]min=", 6.4373016357421879*^-08, " \[Tau]max=", 1.7999999999999996], Editable->False]], "Print"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["COMPARISON WITH ODE & ITERATIONS", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ \(Clear[GreenF, z, \[Tau], dsdxi, s, \[Xi], d\[Alpha]d\[Xi], \[Alpha], \n\txiini, xiend, \[Alpha]ini, sini, \n\tAlphaode, \ Sode, erode]\), "\n"}], RowBox[{ RowBox[{ \(GreenF[z_, \[Tau]_] = Exp[\ \(-\((z + \((kappa - 1)\) \[Tau])\)^2\)/\((4 \[Tau])\) - kappa\ \ \[Tau]]/Sqrt[4\ Pi\ \[Tau]]\), ";", "\n", "\n", \(dsdxi[0, s_, \[Xi]_] = \ s\ \ \ GreenF[s, \ E^\[Xi]]\ \ /\((2\ kappa)\)\), ";", "\n", "\n", \(d\[Alpha]d\[Xi][0, \[Alpha]_, \[Xi]_] = \[Alpha] \((\(-1\) + \ \ \ Exp[\(-\[Alpha]\) - \((\[Xi] + Log[4 Pi\ kappa^2])\)/2 + \n \t\t\t\t\t \((kappa - 1)\) Sqrt[\ \[Alpha]]\ *Exp[\[Xi]/2] - \((1 + kappa)\)^2\ Exp[\[Xi]]/4])\)\), ";", "\n", "\n", \(xiini = ximin - 10\), ";", " ", \(xiend = ximax + 5\), ";", "\n", " ", \(\[Alpha]ini = \((\(-xiini\) - Log[4\ Pi\ kappa^2])\)/2 - \n\t\t 1/\((xiini + Log[4\ Pi\ kappa^2])\)\), ";", "\n", \(sini = \ \(-\ 2\)\ \ Sqrt[\ \ E^xiini\ \ \ \ \ \[Alpha]ini]\), ";", "\n", "\n", \(Alphaode[0, \[Xi]_] = Evaluate[ A[\[Xi]] /. \(NDSolve[{\ \(A'\)[\[Xi]] == d\[Alpha]d\[Xi][0, A[\[Xi]], \[Xi]], A[xiini] == \ \[Alpha]ini}, A, {\[Xi], xiini, xiend}, AccuracyGoal -> Infinity, WorkingPrecision -> 20]\)[ \([1]\)]]\), ";", "\n", RowBox[{ RowBox[{"Sode", "[", RowBox[{"0", ",", StyleBox[ RowBox[{"\[Xi]", StyleBox["_", FontSize->11]}]]}], "]"}], "=", " ", \(\(-\ 2\)\ Sqrt[\ E^\[Xi]\ \ Alphaode[0, \[Xi]]]\)}], ";", "\n", " ", "\n", \( (*\ Sode[0, \[Xi]_] = Evaluate[ ss[\[Xi]] /. \(NDSolve[{\ \(ss'\)[\[Xi]] == dsdxi[0, ss[\[Xi]], \[Xi]], ss[xiend] == \ Sinfty}, ss, {\[Xi], xiend, \(-5\)}]\)[ \([1]\)]]; *) \), "\n", "\n", \(erode[0, \[Xi]_] = Log[10, Abs[Exp[Sode[0, \[Xi]]] - SXi[\[Xi]]]]\), ";", "\n", "\n", "\t", \(Clear[nn, \[Delta], xi, RE, re, x, y]\), ";"}], "\n"}]}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\nRE[x_, y_, t_, \[Tau]_] = 2\ kappa\ \((\((1 - y/x)\)/\((1 - \[Tau]/t)\) - 1/2)\)*\n\t\t\ GreenF[x - y, t - \[Tau]]/GreenF[x, t]; \n\n\t\ \[Delta] = 0.00001; \n Do[\ nn = 32*\((3/2)\)^n; Print["\", n, "\< Integration Points=\>", nn]; \n\ \ \t Do[xi[i] = ximin + i\ \((xiend - ximin)\)/nn, {i, 1, nn}]; \n\ \ \ \ Do[xi[j - nn] = xiini + j\ \((ximin - xiini)\)/nn, {j, 0, nn}]; \n \ \ \ \ Do[ re[n, i] = kappa*Sode[n, xiini] + \n\t\t\ \ \ NIntegrate[ RE[Sode[n, xi[i]], Sode[n, \[Eta]], \n\t\t\t\t\t\tE^xi[i], E^\[Eta]]*dsdxi[n, Sode[n, \[Eta]], \[Eta]], {\[Eta], xiini, xi[i] - \[Delta]}, MaxRecursion -> 10] + \n\ \ \ \ \ 2\ kappa\ Sqrt[\((1 - E^\((\(-\[Delta]\))\))\)/Pi]\ E^\((\(-xi[i]\)/2)\)*\n\t\t\t \((dsdxi[n, Sode[n, xi[i]], xi[i]]/Sode[n, xi[i]] - 1/2)\)*\n \ \ \ \ \ dsdxi[n, Sode[n, xi[i]], xi[i]]/ GreenF[Sode[n, xi[i]], E^xi[i]], \n\t{i, 1, nn}]; \n\t\n Do[re[n, j] = 2/\((xi[j] + Log[4\ Pi\ kappa^2])\)^3, {j, \(-nn\), 0}]; \n\nwei[n] = Table[{xi[i], re[n, i]}, {i, \(-nn\), nn}]; \n weight[n] = Interpolation[Table[{xi[i], re[n, i]}, {i, \(-nn\), nn}]]; \n\nd\[Alpha]d\[Xi][n + 1, \[Alpha]_, \[Xi]_] = \(-\[Alpha]\) + \t \[Alpha]\ \((1 + \(weight[n]\)[\[Xi]])\)\ \ Exp[\(-\[Alpha]\) - \((\[Xi] + Log[4 Pi\ kappa^2])\)/2 + \n \t\t\t\t\t\((kappa - 1)\) Sqrt[\ \[Alpha]]\ *Exp[\[Xi]/2] - \((1 + kappa)\)^2\ Exp[\[Xi]]/4]; \n dsdxi[n + 1, s_, \[Xi]_] = \((1 + \(weight[n]\)[\[Xi]])\)\ \ s\ \ *\ GreenF[s, \ E^\[Xi]]\ \ /\((2\ kappa)\); \n\ Alphaode[n + 1, \[Xi]_] = Evaluate[ A[\[Xi]] /. \(NDSolve[{\ \(A'\)[\[Xi]] == d\[Alpha]d\[Xi][n + 1, A[\[Xi]], \[Xi]], A[xiini] == \ \[Alpha]ini}, A, {\[Xi], xiini, xiend}, AccuracyGoal -> Infinity, WorkingPrecision -> 20, MaxSteps -> 3000]\)[\([1]\)]]; \n Sode[n + 1, \[Xi]_] = \ \(-\ 2\)\ Sqrt[\ E^\[Xi]\ \ Alphaode[n + 1, \[Xi]]]; \n\t erode[n + 1, \[Xi]_] = Log[10, Abs[Exp[Sode[n + 1, \[Xi]]] - SXi[\[Xi]]]], \n\t{n, 0, 4}] \)\)], "Input"], Cell[BoxData[ InterpretationBox[ \("n="\[InvisibleSpace]0 \[InvisibleSpace]" Integration Points="\[InvisibleSpace]32\), SequenceForm[ "n=", 0, " Integration Points=", 32], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[ \("n="\[InvisibleSpace]1 \[InvisibleSpace]" Integration Points="\[InvisibleSpace]48\), SequenceForm[ "n=", 1, " Integration Points=", 48], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[ \("n="\[InvisibleSpace]2 \[InvisibleSpace]" Integration Points="\[InvisibleSpace]72\), SequenceForm[ "n=", 2, " Integration Points=", 72], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[ \("n="\[InvisibleSpace]3 \[InvisibleSpace]" Integration Points="\[InvisibleSpace]108\), SequenceForm[ "n=", 3, " Integration Points=", 108], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[ \("n="\[InvisibleSpace]4 \[InvisibleSpace]" Integration Points="\[InvisibleSpace]162\), SequenceForm[ "n=", 4, " Integration Points=", 162], Editable->False]], "Print"] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["COMPARISON WITH IMPLICIT FORMULAE", "Subtitle"], Cell[BoxData[{ \(\nClear[F, \[Alpha], t, aimp, Alimp, erimp, Simp]\n\ \), \(F[1, \[Alpha]_, t_] = \ \[Alpha]^2\ \ E^\((2 \[Alpha])\)\ - \ 1/\((9 Pi\ kappa^2\ \ t)\); \n \n\t\t\tbb[t_] = 1 - \ \(\(kappa^2/\((1 + kappa)\)^2\)/2\)\ / \((1 + \((1 + kappa)\)^2\ t/2)\); \n F[2, \[Alpha]_, t_] = Log[E^\((2 \[Alpha])\) \[Alpha]]\ - \ 2 \((kappa - 1)\)\ Sqrt[\[Alpha]\ t\ ] + \n\t\t\ \((1 - bb[t])\) \((kappa + 1)\)^2\ \ t/2 + \ Log[4\ kappa^2\ t/bb[t]]; \n\n F[3, \[Alpha]_, t_] = E^\((2 \[Alpha])\) \((\ 2 \((\ 1 - E^\((\(-kappa\)\ t)\))\) + E^\((\(-kappa\)\ t)\)\ Erfc\ [Sqrt[\[Alpha]] - \((kappa - 1)\) Sqrt[t]/2]\ - \n\ \ Erfc[Sqrt[\[Alpha]] - \((kappa + 1)\) Sqrt[t]/2]\ \ E^\((\(-2\) Sqrt[\[Alpha]\ t])\)\ \((1 + \n\t\t\t\t\t 2/\ \((\ \ kappa - 1\ + \ Sqrt[\((kappa - 1)\)^2\ + \ 4\ kappa/\((1 - E^\((\(-kappa\)\ t)\))\)])\))\)) \); \n\t\t\t\t\t\t\t\n F[4, \[Alpha]_, t_] = \ \ \ E^\((2 \[Alpha])\)*\n\t\t\t\ \((\ 1 - 1/\((2 \((1 + \[Alpha])\))\) - 1/\((2 \((1 + \[Alpha])\)^2)\))\)^2\ - \ 1/\((4\ Pi\ kappa^2\ t)\); \n\t\n F[5, \[Alpha]_, t_] = \ \ \ \ \((\ E^\[Alpha] + E^\((1/\[Alpha])\))\)\ \ *\ Erf[Sqrt[\[Alpha]]]\ *\ E^\[Alpha]\ /\n\t\t\t \((E^\[Alpha] + 2\ kappa\ Log[\((1 + 1/kappa)\)]\ E^\((1/\[Alpha])\))\)\ - \ \ \ \ \n\t\t\ \ \ \ \ \ \ \ \ \ \ 1/Sqrt[4\ Pi\ kappa^2\ t]; \)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Do[\n\t Do[\n\taimp[i] = \ \[Alpha]\ /. \ FindRoot\ [ F[k, \[Alpha], Tau[\([i]\)]\ ] == 0, {\[Alpha], Log[sf[\([i]\)]]^2/\((4\ Tau[\([i]\)])\)}]\ , \n \t{i, 1, Len}]; \n\t\n\t Alimp[k] = Interpolation[\ Table[\ {Xi[\([i]\)], aimp[i]}, {i, 1, Len}]]; \n\t \(Simp[k]\)[\[Xi]_] = Exp[\(-2\) Sqrt[\(Alimp[k]\)[\[Xi]] E^\[Xi]]]; \n \t\t\(erimp[k]\)[\[Xi]_] = \ Log[10, Abs[\(Simp[k]\)[\[Xi]] - SXi[\[Xi]]]], \n\t{k, 1, 5}]\)], "Input"], Cell[BoxData[ \($Aborted\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["COMPARISON WITH EXPLICIT FORMULAE", "Subtitle"], Cell[BoxData[{ \(Clear[Alexp, \[Xi], \[Xi]0, \[Xi]1, \[Xi]2, \[Xi]3, Sexp, erexp]\), \(\[Xi]0 = Log[4\ Pi\ kappa^2]; \n\[Xi]1 = \ Log[9\ Pi\ kappa^2\ ]; \n \[Xi]2 = \ Log[4\ E\ \ \ kappa^2/\((2 - kappa^2/\((1 + kappa)\)^2)\)\ ]; \n\[Xi]3 = \[Xi]0 - 1.93242; \n\n\n Alexp[1, \[Xi]_] = If[\[Xi] + \[Xi]1 < 0, \ \(-\((\[Xi] + \[Xi]1)\)\)/2, 0]; \n Alexp[2, \[Xi]_] = If[\[Xi] + \[Xi]2 < 0, \ \(-\((\[Xi] + \[Xi]2)\)\)\ /2, 0]; \n Alexp[3, \[Xi]_] = If[\[Xi] + \[Xi]0 < 0, \ \(-\ \((\[Xi] + \[Xi]0)\)\)/2, 0]; \n Alexp[4, \[Xi]_] = If[\[Xi] + \[Xi]0 < 0, \ \(-\((\[Xi] + \[Xi]0)\)\)/2\ - \ 1/\((\[Xi] + \[Xi]0)\), 10]; \n Alexp[5, \[Xi]_] = If[\[Xi] + \[Xi]0 < 0, \ \(-\((\[Xi] + \[Xi]0)\)\)/2\ - 1/\((\[Xi] + \[Xi]0)\) + \n \t\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(1/2\)/\((\[Xi] + \[Xi]0)\)^2, 10]; \n Alexp[6, \[Xi]_] = If[\[Xi] + \[Xi]3 < 0, \ \(-\((\[Xi] + \[Xi]0)\)\)/2\ - \ 1/\((\[Xi] + \[Xi]3)\) + \n \t\t\t\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \((0.5 + 1.93242)\)/\((\[Xi] + \[Xi]3)\)^2, 10]; \n\n Do[\(Sexp[k]\)[\[Xi]_] = Exp[\(-2\) Sqrt[Alexp[k, \[Xi]]*E^\[Xi]]]; \n\t\t \(erexp[k]\)[\[Xi]_] = \ Log[10, Abs[\(Sexp[k]\)[\[Xi]] - SXi[\[Xi]]]], \n\t{k, 1, 6}]\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["COMPARISON WITH SSC ITERATIONS ", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[{ \(Clear[F, Ssc, xi1, xi2, nn, niteration, x, y, t, \[Tau], ingrand, erSSC, Fdis]\n\t\), \(xi2 = \(-Log[4\ Pi\ kappa^2]\); xi1 = Min[ximin, xi2 - 15]; nn = 50; niteration = 6; \ntt[\(-1\)] = 0.0; \n Do[xi[i] = xi1 + i*\((xi2 - xi1)\)/nn\ ; \n\t tt[i] = Exp[xi[i]], {i, 0, nn}]; \n\n ingrand[x_, y_, t_, \[Tau]_] = \t Sqrt[t/Pi]*\n\t\t \((\ \(-kappa\) - 1\ - \ \((x - y)\)/\((t - \[Tau])\))\)*\n\t\t Exp[\ \(-\((x - y + \((kappa - 1)\) \((t - \[Tau])\))\)^2\)/ \((4 \((t - \[Tau])\))\) - kappa \((t - \[Tau])\)]; \n \(F[0]\)[t_] = \(-Erf[\((kappa + 1)\) Sqrt[t]/2]\); \n \(SscO[0]\)[t_] = \ \((1 - kappa)\)\ \ t\ - \ 2\ Sqrt[\ \(-\ \ kappa\)\ t^2\ - t*Log[Sqrt[\ Pi\ kappa^2\ \((t + 10. ^\((\(-15\))\))\)] \((1 + \ \(F[0]\)[t])\)]]; \n (*\(Ssc[0]\)[t_] = 0.0; *) \n \(erSSCO[0]\)[\[Xi]_] = Log[10, Abs[\ Exp[\(SscO[0]\)[E^\[Xi]]] - SXi[\[Xi]]]]; \)}], "Input"], Cell[BoxData[ \(\(\n\n Do[Print["\", n]; \nFdis[\(-1\)] = 1. ; \n Do[Fdis[i] = \n\ \ NIntegrate[\ ingrand[\(SscO[n]\)[tt[i]], \(SscO[n]\)[tt[i] \((1 - \[Theta]^2)\)], \n\t\ttt[i], tt[i] \((1 - \[Theta]^2)\)]\ , {\[Theta], 0, 1}], {i, 0, nn}]; \nF[n + 1] = Interpolation[Table[{tt[i], Fdis[i]}, {i, \(-1\), nn}]]; \n \(SscO[n + 1]\)[t_] = \ \((1 - kappa)\)\ \ t\ - \ 2\ Sqrt[\ \(-\ \ kappa\)\ t^2\ - t*Log[Sqrt[\ Pi\ kappa^2\ \((t + 10. ^\((\(-15\))\))\)] \((1 + \ \(F[n + 1]\)[t])\)]]; \n \(erSSCO[n + 1]\)[\[Xi]_] = Log[10, Abs[\ Exp[\(SscO[n + 1]\)[E^\[Xi]]] - SXi[\[Xi]]]], \n \t{n, 0, niteration}]\n\)\)], "Input"], Cell[BoxData[{ \(xi2r = \(-Log[4\ Pi\ kappa^2]\) + 0.7; xi1 = Min[ximin, xi2r - 15]; nn = 50; niteration = 6; \ntt[\(-1\)] = 0.0; \n Do[xi[i] = xi1 + i*\((xi2r - xi1)\)/nn\ ; \n\t tt[i] = Exp[xi[i]], {i, 0, nn}]; \n\n ingrand[x_, y_, t_, \[Tau]_] = \t Sqrt[t/Pi]*\n\t\t \((\ \(-kappa\) - 1\ - \ \((x - y)\)/\((t - \[Tau])\))\)*\n\t\t Exp[\ \(-\((x - y + \((kappa - 1)\) \((t - \[Tau])\))\)^2\)/ \((4 \((t - \[Tau])\))\) - kappa \((t - \[Tau])\)]; \n \(F[0]\)[t_] = \(-Erf[\((kappa + 1)\) Sqrt[t]/2]\); \n \(Ssc[0]\)[t_] = \ \((1 - kappa)\)\ \ t\ - \ 2\ Sqrt[\ \(-\ \ kappa\)\ t^2\ - t*Log[Sqrt[\ Pi\ kappa^2\ \((t + 10. ^\((\(-15\))\))\)] \((1 + \ \(F[0]\)[t])\)]]; \n (*\(Ssc[0]\)[t_] = 0.0; *) \n \(erSSC[0]\)[\[Xi]_] = Log[10, Abs[\ Exp[\(Ssc[0]\)[E^\[Xi]]] - SXi[\[Xi]]]]; \n\n \[Lambda] = 0.6\), \(Do[Print["\", n]; \nFdis[\(-1\)] = 1. ; \n Do[Fdis[i] = \n\ \ NIntegrate[\ ingrand[\(Ssc[n]\)[tt[i]], \(Ssc[n]\)[tt[i] \((1 - \[Theta]^2)\)], \n\t\ttt[i], tt[i] \((1 - \[Theta]^2)\)]\ , {\[Theta], 0, 1}, MaxRecursion -> 10], {i, 0, nn}]; \n F[n + 1] = Interpolation[Table[{tt[i], Fdis[i]}, {i, \(-1\), nn}]]; \n \(Ssc[n + 1]\)[t_] = \ \((1 - kappa)\)\ \ t\ - \ 2\ Sqrt[\ \(-\ \ kappa\)\ t^2\ - t*Log[Sqrt[\ Pi\ kappa^2\ \((t + 10. ^\((\(-15\))\))\)] \((1 + \ \(F[n + 1]\)[t])\)]]; \n\t \(Ssc[n + 1]\)[t_] = \ \[Lambda]\ \(Ssc[n + 1]\)[t] + \ \((1 - \[Lambda])\)\ \(Ssc[n]\)[t]; \n\(erSSC[n + 1]\)[\[Xi]_] = Log[10, Abs[\ Exp[\(Ssc[n + 1]\)[E^\[Xi]]] - SXi[\[Xi]]]], \n \t{n, 0, niteration}]\)}], "Input"], Cell[BoxData[ \(\(\tpSssca = Plot[{SXi[x], Exp[\(Ssc[0]\)[E^x]], \n\t\t\tExp[\(Ssc[1]\)[E^x]], Exp[\(Ssc[2]\)[E^x]], Exp[\(Ssc[3]\)[E^x]], Exp[\(Ssc[4]\)[E^x]], Exp[\(Ssc[5]\)[E^x]]}, \n \t\t{x, ximin, xi2}, (*PlotPoints -> 500, *) \n\t\t PlotRange -> {{ximin, xi2}, {SXi[xi2] - 0.05, 1}}, \n\t\t AxesOrigin -> {ximin, 1}, \n\t\tTicks -> tickmarkSf, \n\t\t GridLines -> gridlineSf, \ \n\t PlotStyle -> {style[0], style[1], style[2], style[3], style[4], style[5], style[6]}, \n\t\t PlotLegend -> {"\", "\", "\", "\", "\", "\", "\"}, \n\t\t\ LegendPosition\ -> \ {\(-0.8\), \ \(-0.5\)}, \n\t\t\t\t LegendSize -> {0.3, 0.5}, \n\ \ \ \ \ LegendShadow\ -> \ {0.0, \ 0.0}, \n\t\tPlotLabel -> la]; \n\n pFssca = \t Plot[{\(F[0]\)[E^x], \(F[1]\)[E^x], \(F[2]\)[E^x], \(F[3]\)[E^x], \(F[4]\)[E^x], \(F[5]\)[E^x]}, {x, ximin, xi2}, \n\t PlotRange -> All, \n (*\tPlotPoints -> 500, *) \n\t\t PlotStyle -> {style[1], style[2], style[3], style[4], style[6]}, \n \t\tPlotLegend -> {"\", "\", "\", "\", "\", "\"}, \n\t\tLegendSize -> {0.3, 0.5}, \n\t\t\ LegendPosition\ -> \ {\(-0.75\), \ \(-0.5\)}, \n\t\t\t\t\t LegendSize -> {0.3, 0.5}, \n\ \ \ \ \ LegendShadow\ -> \ {0.0, \ 0.0}, \n\tPlotLabel -> la]; \n\n\t\t perSssca = Plot[{\(erSSC[0]\)[x], \(erSSC[1]\)[x], \(erSSC[2]\)[x], \(erSSC[3]\)[x], \(erSSC[4]\)[x], \(erSSC[5]\)[x]}, \n \t\t{x, ximin, xi2}, (*PlotPoints -> 500, *) \n\t\t PlotRange -> {{ximin, xi2}, {\(-7\), \(-1.5\)}}, \n\t\t AxesOrigin -> {ximin, \(-7\)}, \n\t\tTicks -> tickmark, \n\t\t GridLines -> gridline, \ \n\t PlotStyle -> {style[1], style[2], style[3], style[4], style[5], style[6]}, \n\t\t PlotLegend -> {"\", "\", "\", "\", "\", "\"}, \n\t\t\ LegendPosition\ -> \ {\(-0.7\), \(-\ 0.1\)}, \n\t\t\t\t LegendSize -> {0.3, 0.6}, \n\ \ \ \ \ LegendShadow\ -> \ {0.0, \ 0.0}, \n\t\tPlotLabel -> la]; \n\n\t pSsscb = Plot[{SXi[x], Exp[\(Ssc[6]\)[E^x]], \n\t\t\t Exp[\(Ssc[7]\)[E^x]], Exp[\(Ssc[8]\)[E^x]], Exp[\(Ssc[9]\)[E^x]], Exp[\(Ssc[10]\)[E^x]]}, \n \t\t{x, ximin, xi2}, (*PlotPoints -> 500, *) \n\t\t PlotRange -> {{ximin, xi2}, {SXi[xi2] - 0.05, 1}}, \n\t\t AxesOrigin -> {ximin, 1}, \n\t\tTicks -> tickmarkSf, \n\t\t GridLines -> gridlineSf, \ \n\t PlotStyle -> {style[0], style[1], style[2], style[3], style[4], style[5], style[6]}, \n\t\t PlotLegend -> {"\", "\", "\", "\", "\", "\"}, \n\t\t\ LegendPosition\ -> \ {\(-0.8\), \ \(-0.5\)}, \n\t\t\t\t LegendSize -> {0.3, 0.5}, \n\ \ \ \ \ LegendShadow\ -> \ {0.0, \ 0.0}, \n\t\tPlotLabel -> la]; \n\n pFsscb = \t Plot[{\(F[6]\)[E^x], \(F[7]\)[E^x], \(F[8]\)[E^x], \(F[9]\)[E^x], \(F[10]\)[E^x]}, {x, ximin, xi2}, \n\tPlotRange -> All, \n (*\tPlotPoints -> 500, *) \n\t\t PlotStyle -> {style[2], style[3], style[4], style[6]}, \n\t\t PlotLegend -> {"\", "\", "\", "\", "\"}, \n\t\tLegendSize -> {0.3, 0.5}, \n\t\t\ LegendPosition\ -> \ {\(-0.75\), \ \(-0.5\)}, \n\t\t\t\t\t LegendSize -> {0.3, 0.5}, \n\ \ \ \ \ LegendShadow\ -> \ {0.0, \ 0.0}, \n\tPlotLabel -> la]; \n\n\t\t perSsscb = Plot[{\(erSSC[6]\)[x], \(erSSC[7]\)[x], \(erSSC[8]\)[x], \(erSSC[9]\)[x], \(erSSC[10]\)[x]}, \n \t\t{x, ximin, xi2}, (*PlotPoints -> 500, *) \n\t\t PlotRange -> {{ximin, xi2}, {\(-7\), \(-1.5\)}}, \n\t\t AxesOrigin -> {ximin, \(-7\)}, \n\t\tTicks -> tickmark, \n\t\t GridLines -> gridline, \ \n\t PlotStyle -> {style[2], style[3], style[4], style[5], style[6]}, \n \t\tPlotLegend -> {"\", "\", "\", "\", "\"}, \n\t\t\ LegendPosition\ -> \ {\(-0.7\), \(-\ 0.1\)}, \n\t\t\t\t LegendSize -> {0.3, 0.6}, \n\ \ \ \ \ LegendShadow\ -> \ {0.0, \ 0.0}, \n\t\tPlotLabel -> la]; \)\)], "Input"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["LONG TIME ASYMPTOTICS", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[ \(\(sinfty = Log[kappa/\((1 + kappa)\)]; \n\n rho[x_] = Integrate[\ y^\((\(-3\)/2)\)\ E^\((\(-y\))\), {y, \((kappa + 1)\)^2\ E^x/4, Infinity}]; \n\n Do[mhat[n] = \(\(\((kappa + 1)\)/4\)/Sqrt[Pi]\)\ /sinfty* Exp[\(-\((kappa - 1)\)\)/2\ *sinfty]\n\t\t NIntegrate[\ Sode[n, x]*\n\t\t\t\t\t Exp[\((kappa - 1)\)\ Sode[n, x]/2 + \((kappa + 1)\)^2\ E^x/4]*\n \t\t\t\tdsdxi[n, Sode[n, x], x], {x, xiini, xiend}], \n \t{n, 0, 5}]; \n Do[\n\t\ SLong[n, x_] = \ sinfty\ *Exp[mhat[n]\ rho[x]], {n, 0, 4}]; \n Table[mhat[n], {n, 0, 5}]\n\t\)\)], "Input"], Cell[BoxData[ \({\(-0.167501214973333656`\), \(-0.205369623668917489`\), \(-0.210155542528187666`\), \(-0.210772075509186329`\), \(-0.210855828243070542`\), \(-0.210864687223039215`\)}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["OVERALL COMPARISON", "Subtitle"], Cell[CellGroupData[{ Cell[BoxData[{ \(Clear[nn, n, i, TTau, si, XXi, aimp]\n\), \(erNum[x_] = If[x < ximax, \ Log[10, Abs[SXi[x] - Exp[Sode[5, x]]]], 0]; \n\nDo[\terLong[n, x_] = \ Log[10, Abs[\ Exp[Sode[5, x]] - Exp[SLong[n, x]]]]; \n\t erode[n, x_] = Log[10, Abs[Exp[Sode[n, x]] - Exp[Sode[5, x]]]], \n{n, 0, 4}]; \n\tnn = 100; \n Do[XXi[i] = \ xiini + i*\((xiend - xiini)\)/nn; \n\t TTau[i] = Exp[XXi[i]]; \n\tsi[i] = Exp[Sode[5, XXi[i]]], {i, 0, nn}]; \n Do[\n\tDo[\n\t aimp[i] = \ \[Alpha]\ /. \ FindRoot\ [ F[k, \[Alpha], TTau[i]\ ] == 0, {\[Alpha], Log[si[i]]^2/\((4\ TTau[i])\)}]\ , \n\t{i, 0, nn}]; \n\t\n\t Alimp[k] = Interpolation[\ Table[\ {XXi[i], aimp[i]}, {i, 0, nn}]]; \n\t \(Simp[k]\)[\[Xi]_] = Exp[\(-2\) Sqrt[\(Alimp[k]\)[\[Xi]] E^\[Xi]]]; \n \t\t\(erimp[k]\)[\[Xi]_] = \ Log[10, Abs[\(Simp[k]\)[\[Xi]] - Exp[Sode[5, \[Xi]]]]], \n\t{k, 1, 5}] \n\)}], "Input"], Cell[BoxData[ \(FindRoot::"frmp" \( : \ \) "Machine precision is insufficient to achieve the accuracy \ \!\(1.00000000000000066`*^-6\)."\)], "Message"], Cell[BoxData[ \(FindRoot::"frmp" \( : \ \) "Machine precision is insufficient to achieve the accuracy \ \!\(1.00000000000000066`*^-6\)."\)], "Message"], Cell[BoxData[ \(FindRoot::"frmp" \( : \ \) "Machine precision is insufficient to achieve the accuracy \ \!\(1.00000000000000066`*^-6\)."\)], "Message"], Cell[BoxData[ \(General::"stop" \( : \ \) "Further output of \!\(FindRoot :: \"frmp\"\) will be suppressed during \ this calculation."\)], "Message"], Cell[BoxData[ \(FindRoot::"cvnwt" \( : \ \) "Newton's method failed to converge to the prescribed accuracy after \!\ \(15\) iterations."\)], "Message"], Cell[BoxData[ \(FindRoot::"cvnwt" \( : \ \) "Newton's method failed to converge to the prescribed accuracy after \!\ \(15\) iterations."\)], "Message"], Cell[BoxData[ \(FindRoot::"cvnwt" \( : \ \) "Newton's method failed to converge to the prescribed accuracy after \!\ \(15\) iterations."\)], "Message"], Cell[BoxData[ \(General::"stop" \( : \ \) "Further output of \!\(FindRoot :: 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.16831 .24391 L .16849 .24399 L .16917 .24433 L .17171 .2459 L .17692 .24993 L .17946 .25192 L .18178 .25359 L Mistroke .18293 .25434 L .18354 .25472 L .18387 .25491 L .18418 .25509 L .18445 .25524 L .18474 .25531 L .18507 .25535 L .18536 .25538 L .18589 .25543 L .18645 .25548 L .18679 .2555 L .18709 .25552 L .1874 .25553 L .18768 .25554 L .18801 .25554 L .18819 .25555 L .18837 .25555 L .18868 .25555 L .18885 .25555 L .18902 .25555 L .18934 .25554 L .18963 .25553 L .1899 .25552 L .1902 .25551 L .19085 .25548 L .19146 .25544 L .19264 .25534 L .19391 .2552 L .19621 .2549 L .20145 .25431 L .21192 .25314 L .21714 .25242 L .222 .25157 L .22441 .25101 L .2256 .25077 L .22669 .25059 L .22729 .2505 L .22795 .25043 L .22827 .2504 L .22861 .25038 L .2288 .25036 L .22898 .25035 L .22914 .25035 L .22931 .25034 L .22962 .25033 L .2299 .25033 L .23023 .25039 L .23054 .25052 L .2317 .25112 L .23702 .25478 L Mistroke .24191 .25845 L .24438 .26008 L .24559 .26079 L .24612 .26107 L .24641 .26122 L .24669 .26126 L .24728 .26133 L .24785 .26138 L .24845 .26143 L .24879 .26145 L .24909 .26146 L .24941 .26147 L .24974 .26148 L .25004 .26149 L .25035 .26149 L .25051 .26149 L .25069 .26149 L .25101 .26148 L .2512 .26148 L .25139 .26147 L .25173 .26146 L .25234 .26143 L .25291 .2614 L .25421 .26129 L .25548 .26115 L .25683 .26098 L .26153 .26034 L .27205 .25916 L .28218 .2577 L .28681 .25665 L .28808 .25641 L .28875 .2563 L .28945 .2562 L .29007 .25613 L .29039 .2561 L .29074 .25607 L .29106 .25605 L .29135 .25604 L .29165 .25603 L .29193 .25602 L .29222 .25612 L .29254 .25626 L .29318 .25657 L .29434 .2572 L .29695 .25888 L .3023 .2627 L .30483 .26439 L .30724 .26579 L .30788 .26612 L .30807 .26621 L Mistroke .30824 .26629 L .30857 .26634 L .30932 .26643 L .31001 .2665 L .31032 .26652 L .31065 .26654 L .31093 .26655 L .31123 .26656 L .31156 .26657 L .31186 .26658 L .31205 .26658 L .31222 .26658 L .31255 .26658 L .31284 .26658 L .31316 .26657 L .31345 .26656 L .31372 .26655 L .31435 .26652 L .31501 .26647 L .31626 .26636 L .31762 .26619 L .32231 .26545 L .33264 .2643 L .34258 .26285 L .34765 .26177 L .35032 .26123 L .35166 .26103 L .35243 .26094 L .35277 .26091 L .35314 .26088 L .3535 .26086 L .35383 .26084 L .35414 .26095 L .35448 .2611 L .3557 .26168 L .35844 .26329 L .36332 .26657 L .36595 .26824 L .36733 .26905 L .36879 .26981 L .3694 .27011 L .36974 .27026 L .37006 .27041 L .37024 .27045 L .37044 .27048 L .37079 .27053 L .37146 .2706 L .37208 .27065 L .37242 .27068 L .37274 .27069 L Mistroke .37304 .27071 L .3733 .27072 L .3736 .27072 L .37392 .27073 L .37425 .27073 L .37456 .27073 L .37483 .27072 L .37513 .27071 L .37546 .2707 L .37581 .27069 L .37643 .27065 L .37753 .27056 L .37875 .27042 L .38148 .27 L .3828 .26976 L .38338 .26964 L .38371 .26958 L .38402 .26953 L .38432 .26951 L .38464 .26949 L .3853 .26944 L .38668 .26932 L .3892 .26906 L .39392 .26842 L .40439 .26682 L .40961 .26571 L .41215 .26519 L .41336 .26499 L .41447 .26484 L .41503 .26478 L .41532 .26475 L .41562 .26473 L .41593 .26479 L .41622 .26491 L .41688 .26519 L .41915 .26634 L .42416 .26941 L .42674 .27098 L .42955 .27249 L .43083 .27309 L .43154 .27339 L .4317 .27345 L .43188 .27352 L .4322 .2736 L .4325 .27364 L .43282 .27369 L .43349 .27376 L .4341 .27381 L .43466 .27384 L .43498 .27386 L Mistroke .43516 .27386 L .43533 .27387 L .43562 .27387 L .43594 .27388 L .43611 .27388 L .43629 .27388 L .43661 .27387 L .43678 .27387 L .43695 .27387 L .43733 .27385 L .43766 .27384 L .43797 .27382 L .43855 .27378 L .43985 .27366 L .44103 .2735 L .44212 .27334 L .44457 .27288 L .44518 .27276 L .44549 .27269 L .44576 .27263 L .44609 .27261 L .44643 .27259 L .44704 .27255 L .44935 .27235 L .4519 .27206 L .45461 .27168 L .46522 .27003 L .47054 .26892 L .47288 .26841 L .47411 .26817 L .47543 .26794 L .4761 .26784 L .47673 .26776 L .4773 .26769 L .47762 .26767 L .47791 .26777 L .48022 .26875 L .48527 .27154 L .48776 .27295 L .49044 .27433 L .49173 .27492 L .49297 .27542 L .4935 .27561 L .4938 .27571 L .49407 .27577 L .4944 .27582 L .4947 .27586 L .49528 .27592 L .49584 .27597 L .49645 .27601 L Mistroke .49676 .27603 L .49709 .27604 L .49741 .27605 L .49769 .27605 L .49797 .27605 L .49824 .27605 L .49852 .27605 L .49883 .27604 L .49909 .27604 L .49934 .27603 L .49991 .276 L .50052 .27595 L .50116 .27589 L .50232 .27576 L .50491 .27535 L .51461 .27412 L .52493 .27256 L .5297 .27166 L .53487 .27054 L .53625 .27028 L .5377 .27003 L .5383 .26994 L .53894 .26985 L .53913 .26983 L .53931 .26981 L .53947 .2698 L .53964 .26984 L .5403 .27006 L .54543 .27241 L .55087 .2752 L .55344 .27632 L .55456 .27674 L .5552 .27696 L .55551 .27706 L .55579 .27714 L .55609 .27718 L .55637 .27722 L .55699 .27729 L .5576 .27734 L .55826 .27739 L .55858 .2774 L .55893 .27742 L .55911 .27742 L .5593 .27743 L .55948 .27743 L .55965 .27743 L .55995 .27744 L .56027 .27743 L .56044 .27743 L .56061 .27743 L Mistroke .56093 .27742 L .56126 .27741 L .56156 .27739 L .56223 .27735 L .56283 .27731 L .56346 .27725 L .56576 .27695 L .57542 .27575 L .5857 .27428 L .5956 .27241 L .59818 .2719 L .59954 .27168 L .60029 .27158 L .60066 .27153 L .601 .27149 L .60129 .27146 L .6016 .27152 L .60192 .2716 L .60226 .2717 L .60365 .27218 L .60611 .27319 L .61152 .27572 L .61407 .27684 L .61643 .27773 L .61704 .27793 L .61734 .27803 L .61762 .27811 L .61791 .27815 L .61822 .27818 L .61888 .27825 L .61953 .2783 L .61987 .27832 L .62024 .27834 L .62059 .27835 L .62091 .27836 L .62123 .27837 L .62154 .27837 L .62182 .27837 L .62212 .27837 L .62244 .27837 L .62274 .27836 L .62302 .27836 L .62328 .27835 L .62385 .27832 L .62447 .27829 L .62514 .27824 L .62636 .27813 L .63674 .27702 L .64674 .27579 L .65636 .27423 L Mistroke .65876 .27377 L .66128 .27339 L .66192 .27331 L .66261 .27324 L .66281 .27323 L .663 .27321 L .66317 .2732 L .66336 .27321 L .66353 .27325 L .66372 .27329 L .66405 .27336 L .66659 .27407 L .67164 .27602 L .67624 .27791 L .67746 .27836 L .6781 .27859 L .67878 .27882 L .67912 .27893 L .67944 .27903 L .67973 .27907 L .68003 .27909 L .68119 .27917 L .68184 .2792 L .68254 .27922 L .6829 .27923 L .6831 .27924 L .68328 .27924 L .68345 .27924 L .68364 .27924 L .68397 .27925 L .68427 .27925 L .68445 .27925 L .68461 .27924 L .68494 .27924 L .68512 .27924 L .68529 .27924 L .68592 .27922 L .68651 .2792 L .68779 .27915 L .68895 .27909 L .69155 .2789 L .69623 .27857 L .70643 .27774 L .71623 .27665 L .71863 .27623 L .72121 .27586 L .72268 .27569 L .72403 .27557 L .72468 .27554 L .72486 .27553 L Mistroke .72504 .27552 L .72521 .27552 L .72538 .27554 L .72667 .27566 L .7273 .27574 L .72797 .27584 L .72916 .27605 L .73185 .27666 L .73671 .27808 L .73914 .27883 L .74048 .27923 L .74079 .27933 L .74113 .27942 L .74142 .2795 L .74174 .27951 L .74291 .27954 L .74418 .27957 L .74641 .27961 L .75136 .2797 L .75278 .27973 L .75348 .27975 L .75413 .27976 L .75472 .27977 L .75505 .27978 L .75535 .27977 L .75568 .27975 L .75603 .27973 L .75667 .2797 L .7593 .27958 L .76176 .27949 L .76299 .27946 L .76431 .27943 L .76577 .27941 L .76641 .2794 L .76675 .27939 L .76694 .27939 L .76712 .27938 L .76744 .27936 L .76777 .27933 L .76838 .27928 L .76971 .27917 L .77253 .27896 L .77501 .27882 L .77637 .27875 L .77704 .27872 L .77733 .2787 L .77766 .27868 L .77798 .27865 L .77827 .27862 L .77892 .27854 L Mistroke .78029 .2784 L .78269 .27818 L .78493 .278 L .78611 .27792 L .7864 .2779 L .78671 .27788 L .78688 .27787 L .78705 .27785 L .78737 .27776 L .78874 .27737 L .79002 .277 L .79254 .27628 L .79482 .27569 L .79726 .27516 L .79856 .27494 L .79975 .27479 L .80032 .27473 L .80094 .27467 L .80207 .2746 L .80457 .27441 L .80526 .27436 L .80564 .27433 L .806 .27431 L .80633 .2743 L .80651 .27429 L .80669 .27429 L .80702 .27428 L .80733 .27428 L .8075 .27428 L .80767 .27428 L .80799 .27428 L .80816 .27429 L .80832 .27429 L .8087 .27431 L .80902 .27432 L .80932 .27434 L .80998 .27439 L .81121 .27451 L .81238 .27466 L .81498 .27509 L .81566 .27522 L .8164 .27537 L .81674 .27543 L .81692 .27547 L .8171 .27548 L .8174 .27546 L .81773 .27544 L .819 .27535 L .82014 .2753 L .82081 .27527 L Mistroke .82143 .27525 L .82177 .27524 L .82209 .27524 L .82244 .27523 L .82261 .27523 L .8228 .27523 L .82312 .27523 L .82341 .27523 L .82368 .27523 L .82397 .27523 L .82429 .27524 L .82462 .27524 L .82523 .27526 L .82584 .27528 L .82642 .2753 L .82749 .27535 L .82807 .27538 L .82838 .2754 L .82868 .27542 L .82885 .27543 L .82903 .27542 L .82936 .27539 L .82998 .27533 L .83126 .27521 L .83261 .2751 L .83378 .27502 L .83439 .27499 L .83506 .27496 L .83567 .27494 L .83623 .27493 L .83676 .27492 L .83732 .27491 L .83763 .2749 L .83798 .2749 L .8383 .2749 L .8386 .2749 L .83887 .27489 L .83916 .27489 L .83947 .27489 L .83976 .27491 L .84045 .27495 L .84111 .27498 L .84176 .27501 L .84204 .27502 L .84235 .27503 L .84262 .27503 L .84288 .27503 L .84315 .27504 L .84344 .27503 L .84373 .27503 L Mistroke .84405 .27502 L .84432 .27501 L .84461 .27499 L .84522 .27494 L .84556 .27491 L .84587 .27487 L .84703 .27466 L .84762 .27451 L .84827 .27431 L .84859 .27419 L .84877 .27412 L .84894 .27396 L .84926 .27342 L .84957 .27287 L .85191 .26783 L .85444 .26047 L .8572 .24979 L .85983 .23621 L .86222 .21967 L .86357 .20751 L .86431 .19961 L .86467 .19533 L .865 .19114 L .8653 .18817 L .86559 .18624 L .86622 .18207 L .86756 .17394 L .86815 .17084 L .86878 .16801 L .86932 .16602 L .8699 .16443 L .87023 .16379 L .87053 .16338 L .87082 .16314 L .87112 .16304 L .87145 .16312 L .87176 .16335 L .87194 .16356 L .8721 .16378 L .87246 .16443 L .87314 .16612 L .87377 .1681 L .87519 .17359 L .87643 .17887 L .87776 .18446 L .87808 .18573 L .87842 .18708 L .87875 .18832 L .87905 .18857 L .87935 .18802 L Mistroke .87962 .18753 L .88023 .18642 L .88254 .18251 L .88384 .18064 L .88525 .17898 L .88589 .17836 L .88658 .17781 L .8878 .17706 L .88845 .17678 L .88906 .17657 L .88962 .17642 L .89022 .17629 L .89053 .17624 L .89071 .17621 L .89087 .17602 L .89121 .17502 L .89156 .17392 L .89281 .17002 L .89748 .15506 L .90005 .1472 L .90141 .14295 L .90286 .13781 L .90357 .1348 L .90425 .13148 L .9049 .1276 L .90551 .12321 L .90608 .11799 L .90669 .11077 L .9073 .10063 L .90765 .09268 L .90797 .08276 L .90829 .06874 L .90859 .04696 L Mfstroke .90859 .04696 m .90881 0 L s .9091 0 m .90924 .03524 L .90943 .05671 L .90962 .0717 L .90978 .08146 L .90996 .09024 L .91031 .10377 L .91063 .1136 L s .91063 .1136 m .9109 .61803 L s 0 g .4 Mabswid [ 8 3 ] 0 Mabsdash 0 .44526 m .00983 .44698 L .02056 .44884 L .03063 .45057 L .04032 .45222 L .05063 .45395 L .06056 .4556 L .07111 .45733 L .08127 .45898 L .09105 .46054 L .10145 .46218 L .11147 .46373 L .1211 .4652 L .13135 .46673 L .14122 .46818 L .15172 .46969 L .16182 .47112 L .17155 .47245 L .18189 .47384 L .19185 .47514 L .20244 .47649 L .21263 .47774 L .22245 .4789 L .23288 .48008 L .24294 .48118 L .2526 .48218 L .26289 .4832 L .2728 .48412 L .28332 .48504 L .29347 .48585 L .30322 .48656 L .3136 .48725 L .3236 .48783 L .33321 .4883 L .34344 .48871 L .35329 .48901 L .35839 .48912 L .36099 .48917 L .36376 .48921 L .36639 .48924 L .36879 .48926 L .36994 .48927 L .37055 .48927 L .37119 .48928 L .37175 .48928 L .37237 .48928 L .37264 .48928 L .37294 .48928 L .37321 .48928 L .37346 .48928 L Mistroke .37363 .48928 L .3738 .48928 L .37411 .48928 L .37428 .48928 L .37447 .48928 L .3748 .48928 L .37511 .48928 L .37539 .48928 L .37571 .48928 L .37604 .48928 L .3768 .48928 L .37751 .48928 L .37885 .48927 L .38013 .48926 L .3813 .48925 L .38397 .48922 L .38643 .48918 L .38873 .48914 L .39398 .48901 L .39912 .48885 L .40384 .48866 L .41394 .48811 L .42365 .48739 L .43399 .48639 L .44394 .48516 L .45452 .48353 L .46471 .48157 L .47451 .47927 L .48494 .47627 L .49498 .47269 L .50464 .46842 L .51492 .46268 L .52482 .45545 L .52986 .45086 L .53534 .44487 L .54015 .43842 L .54547 .42938 L .5505 .41783 L .55326 .40942 L .55585 .39925 L .55834 .38581 L .5596 .37669 L .56098 .36336 L .56154 .35623 L .56214 .34693 L .56245 .34102 L .56279 .3333 L .56311 .32456 L .5634 .31443 L .56369 .30061 L Mistroke .56397 .28068 L .56429 .22673 L .56458 .24669 L .56484 .28178 L .56511 .30118 L .56541 .31542 L .56569 .32505 L .56633 .34143 L .5667 .34839 L .56703 .35389 L .5683 .36981 L .56945 .38039 L .57067 .38924 L .57321 .40327 L .576 .41471 L .58097 .42977 L .5863 .44174 L .59683 .45905 L .60698 .47146 L .61674 .48113 L .62713 .48985 L .63713 .49715 L .64674 .50342 L .65698 .50947 L .66683 .51479 L .67731 .52001 L .6874 .52469 L .69711 .5289 L .70743 .53313 L .71738 .53699 L .72795 .54088 L .73813 .54445 L .74793 .54774 L .75835 .55111 L .76838 .55424 L .77803 .55714 L .7883 .56014 L .79819 .56295 L .8087 .56585 L .81883 .56858 L .82857 .57115 L .83893 .57381 L .84891 .57633 L .85952 .57895 L .86973 .58141 L .87956 .58374 L .89002 .58615 L .90009 .5884 L .90977 .59053 L .92008 .59271 L Mistroke .93 .59473 L .94055 .5968 L .95071 .5987 L .96049 .60044 L .97089 .60219 L .9809 .60377 L .99053 .60518 L 1 .60648 L Mfstroke [ 6 5 ] 0 Mabsdash 0 .4722 m .00983 .47419 L .02056 .47635 L .03063 .47837 L .04032 .4803 L .05063 .48235 L .06056 .48432 L .07111 .4864 L .08127 .48839 L .09105 .49029 L .10145 .49231 L .11147 .49424 L .1211 .49608 L .13135 .49803 L .14122 .4999 L .15172 .50187 L .16182 .50375 L .17155 .50555 L .18189 .50745 L .19185 .50926 L .20244 .51117 L .21263 .51299 L .22245 .51472 L .23288 .51655 L .24294 .51829 L .2526 .51994 L .26289 .52168 L .2728 .52333 L .28332 .52506 L .29347 .5267 L .30322 .52826 L .3136 .52989 L .3236 .53143 L .33321 .53288 L .34344 .5344 L .35329 .53583 L .36376 .53732 L .37385 .53872 L .38355 .54003 L .39387 .54139 L .40381 .54266 L .41437 .54396 L .42455 .54517 L .43434 .54629 L .44476 .54744 L .45479 .54849 L .46443 .54946 L .4747 .55043 L .48458 .55131 L .49509 .55218 L Mistroke .50521 .55295 L .51495 .55363 L .52531 .55429 L .53528 .55484 L .54588 .55534 L .55609 .55574 L .56592 .55603 L .571 .55615 L .57637 .55625 L .57878 .55628 L .58137 .55631 L .58382 .55634 L .58604 .55635 L .58727 .55636 L .58794 .55636 L .58857 .55636 L .58911 .55636 L .58969 .55636 L .59 .55636 L .59033 .55636 L .59061 .55636 L .59091 .55636 L .59108 .55636 L .59127 .55636 L .59145 .55636 L .59161 .55636 L .59191 .55636 L .59224 .55636 L .59259 .55636 L .59291 .55636 L .59365 .55636 L .5943 .55636 L .59488 .55636 L .5962 .55635 L .59742 .55634 L .59872 .55633 L .60105 .55631 L .60356 .55628 L .60633 .55623 L .61125 .55613 L .61656 .55598 L .62702 .55558 L .6371 .55505 L .64679 .55438 L .65711 .5535 L .66704 .55245 L .6776 .55111 L .68776 .54957 L .69755 .54782 L .70796 .54564 L Mistroke .71798 .54317 L .72761 .54041 L .73787 .53695 L .74775 .53303 L .75825 .52805 L .76836 .52222 L .77809 .51531 L .78844 .50592 L .7984 .49368 L .80386 .48476 L .80899 .47391 L .81148 .46732 L .81411 .4589 L .81635 .44995 L .81881 .43706 L .82014 .42781 L .82141 .4165 L .82254 .40262 L .82319 .39194 L .82378 .37864 L .82408 .36958 L .82441 .35678 L .82472 .3392 L .82501 .31103 L .82532 .22979 L .8255 .30069 L .82567 .3236 L .826 .3489 L .82619 .35822 L .82636 .36514 L .82704 .38469 L .82742 .39258 L .82777 .39869 L .8291 .41585 L .8303 .42671 L .83157 .4358 L .83388 .44829 L .83663 .45933 L .83914 .46726 L .84399 .47911 L .84927 .48884 L .85963 .5026 L .86961 .51195 L .88021 .51935 L .89043 .5247 L .90026 .52857 L .90525 .53013 L .91072 .53155 L .91593 .53261 L .92078 .53336 L Mistroke .92345 .53368 L .92598 .53392 L .92823 .5341 L .92951 .53418 L .93071 .53424 L .9319 .53429 L .93251 .53431 L .93317 .53433 L .93354 .53434 L .93387 .53435 L .93422 .53435 L .93454 .53436 L .93485 .53436 L .93514 .53436 L .93545 .53437 L .93579 .53437 L .93608 .53437 L .93636 .53436 L .93666 .53436 L .93698 .53436 L .93731 .53435 L .93763 .53435 L .93823 .53434 L .93931 .53431 L .94048 .53426 L .94172 .53419 L .94287 .53412 L .94551 .5339 L .94809 .53362 L .95086 .53324 L .95586 .53237 L .96133 .53123 L .97141 .52825 L .9764 .52633 L .98173 .52391 L .99229 .51833 L 1 .51334 L Mfstroke [ 3 3 ] 0 Mabsdash 0 .29959 m .00983 .30367 L .02056 .3081 L .03063 .31227 L .04032 .31627 L .05063 .32053 L .06056 .32462 L .07111 .32896 L .08127 .33314 L .09105 .33716 L .10145 .34143 L .11147 .34553 L .1211 .34947 L .13135 .35366 L .14122 .35769 L .15172 .36196 L .16182 .36607 L .17155 .37001 L .18189 .3742 L .19185 .37822 L .20244 .38249 L .21263 .38659 L .22245 .39052 L .23288 .3947 L .24294 .39871 L .2526 .40256 L .26289 .40664 L .2728 .41056 L .28332 .41471 L .29347 .4187 L .30322 .42252 L .3136 .42658 L .3236 .43047 L .33321 .43419 L .34344 .43815 L .35329 .44194 L .36376 .44595 L .37385 .4498 L .38355 .45349 L .39387 .4574 L .40381 .46115 L .41437 .46512 L .42455 .46892 L .43434 .47256 L .44476 .47642 L .45479 .48012 L .46443 .48366 L .4747 .48742 L .48458 .49101 L .49509 .49482 L Mistroke .50521 .49847 L .51495 .50196 L .52531 .50567 L .53528 .50922 L .54588 .51297 L .55609 .51658 L .56592 .52004 L .57637 .5237 L .58643 .52722 L .59611 .53059 L .60641 .53416 L .61633 .5376 L .62687 .54123 L .63703 .54473 L .6468 .54809 L .65719 .55165 L .6672 .55507 L .67682 .55835 L .68707 .56183 L .69693 .56518 L .70741 .56872 L .71751 .57213 L .72723 .57539 L .73757 .57885 L .74752 .58216 L .75809 .58566 L .76828 .58901 L .77809 .59221 L .78852 .59558 L .79856 .5988 L .80822 .60186 L .8185 .60508 L .8284 .60813 L .83892 .61132 L .84905 .61435 L .8588 .6172 L Mfstroke .8588 .6172 m .86171 .61803 L s [ 1 2 ] 0 Mabsdash 0 .40599 m .00983 .4087 L .02056 .41164 L .03063 .41441 L .04032 .41707 L .05063 .4199 L .06056 .42262 L .07111 .42551 L .08127 .42829 L .09105 .43095 L .10145 .43379 L .11147 .43652 L .1211 .43913 L .13135 .44191 L .14122 .44458 L .15172 .44741 L .16182 .45013 L .17155 .45274 L .18189 .45552 L .19185 .45817 L .20244 .46099 L .21263 .4637 L .22245 .46629 L .23288 .46904 L .24294 .47167 L .2526 .47419 L .26289 .47687 L .2728 .47943 L .28332 .48213 L .29347 .48473 L .30322 .48721 L .3136 .48983 L .3236 .49234 L .33321 .49473 L .34344 .49727 L .35329 .49969 L .36376 .50224 L .37385 .50468 L .38355 .507 L .39387 .50945 L .40381 .51178 L .41437 .51424 L .42455 .51658 L .43434 .5188 L .44476 .52114 L .45479 .52336 L .46443 .52547 L .4747 .52768 L .48458 .52978 L .49509 .53198 L Mistroke .50521 .53406 L .51495 .53602 L .52531 .53807 L .53528 .54001 L .54588 .54203 L .55609 .54393 L .56592 .54571 L .57637 .54756 L .58643 .5493 L .59611 .55092 L .60641 .5526 L .61633 .55416 L .62687 .55576 L .63703 .55725 L .6468 .55862 L .65719 .56002 L .6672 .5613 L .67682 .56248 L .68707 .56366 L .69693 .56474 L .70741 .5658 L .71751 .56676 L .72723 .5676 L .73757 .56843 L .74752 .56915 L .75809 .56984 L .76828 .57042 L .77809 .57091 L .78852 .57134 L .79856 .57169 L .80822 .57194 L .81318 .57204 L .8185 .57212 L .82109 .57215 L .8239 .57218 L .82519 .57219 L .82656 .5722 L .82784 .5722 L .82902 .57221 L .83018 .57221 L .83076 .57221 L .8314 .57221 L .83174 .57221 L .83204 .57222 L .83221 .57222 L .8324 .57222 L .83273 .57222 L .83304 .57222 L .83338 .57222 L .83366 .57222 L Mistroke .83397 .57221 L .83428 .57221 L .83458 .57221 L .83513 .57221 L .83572 .57221 L .83637 .57221 L .83754 .5722 L .83862 .5722 L .83992 .57219 L .84131 .57218 L .84385 .57215 L .84859 .57207 L .85367 .57196 L .85903 .57181 L .8687 .57144 L .87367 .57118 L .87899 .57086 L .88953 .57009 L .89968 .56916 L .90944 .56802 L .91982 .56659 L .92982 .56498 L .93944 .56317 L .94968 .561 L .95953 .55865 L .97001 .55588 L .9801 .55294 L .9898 .54991 L 1 .54649 L Mfstroke 1 Mabswid [ 5 2 ] 0 Mabsdash 0 .217 m .00983 .21843 L .02056 .2198 L .03063 .22088 L .04032 .22171 L .0453 .22205 L .05063 .22233 L .05323 .22243 L .05605 .22252 L .05735 .22255 L .05872 .22258 L .05989 .2226 L .06056 .22261 L .06118 .22261 L .06181 .22262 L .06215 .22262 L .06232 .22262 L .0625 .22262 L .06268 .22262 L .06284 .22262 L .06316 .22262 L .06345 .22262 L .06376 .22262 L .06404 .22262 L .06434 .22262 L .06463 .22262 L .06489 .22262 L .06552 .22261 L .06612 .22261 L .06744 .22259 L .06867 .22257 L .07001 .22253 L .07144 .22249 L .07382 .22239 L .07639 .22226 L .08104 .22193 L .08615 .22142 L .09152 .2207 L .09654 .21983 L .10122 .21882 L .11116 .21589 L .11659 .21372 L .12172 .21119 L .13151 .20458 L .13657 .19985 L .14193 .19334 L .14691 .18516 L .15157 .17441 L .15422 .16601 L .15673 .15534 L Mistroke .15899 .14175 L .16027 .13093 L .16145 .11693 L .16213 .10576 L .16275 .09153 L .16307 .08128 L .16343 .06574 L .16361 .05473 L .1638 .0381 L .16398 .01131 L Mfstroke .16398 .01131 m .16401 0 L s .16438 0 m .16447 .02979 L .16477 .05768 L .1651 .07534 L .16527 .082 L .16545 .08826 L .16609 .1047 L .16669 .1158 L .16788 .13182 L .16897 .1426 L .17143 .16015 L .17393 .17302 L .17625 .1825 L .18153 .1991 L .19148 .22121 L .20205 .23852 L .21224 .25209 L .22205 .2634 L .23248 .27416 L .24252 .28361 L .25218 .29207 L .26246 .30053 L .27236 .30825 L .28288 .31608 L .29301 .32332 L .30276 .33003 L .31313 .33695 L .32312 .34341 L .33272 .34946 L .34294 .35575 L .35278 .36166 L .36325 .36782 L .37333 .37362 L .38302 .3791 L .39333 .38483 L .40327 .39024 L .41382 .3959 L .42399 .40127 L .43377 .40635 L .44418 .41167 L .4542 .41671 L .46384 .42149 L .4741 .42651 L .48397 .43126 L .49447 .43625 L .50458 .44098 L .51431 .44546 L .52466 .45016 L .53463 .45461 L .54522 .45927 L Mistroke .55542 .46369 L .56524 .46788 L .57568 .47225 L .58574 .4764 L .59541 .48032 L .6057 .48441 L .61561 .48828 L .62614 .49232 L .63629 .49613 L .64605 .49971 L .65644 .50345 L .66644 .50697 L .67605 .51027 L .68629 .5137 L .69615 .51692 L .70662 .52025 L .71671 .52337 L .72642 .52627 L .73675 .52927 L .74669 .53206 L .75726 .53492 L .76744 .53756 L .77724 .54001 L .78766 .54249 L .7977 .54478 L .80734 .54687 L .81762 .54898 L .82751 .5509 L .83802 .55281 L .84814 .55453 L .85788 .55606 L .86825 .55757 L .87823 .55889 L .88883 .56017 L .89905 .56127 L .90888 .56221 L .91933 .56309 L .9294 .56382 L .93909 .56442 L .9494 .56495 L .95932 .56537 L .96986 .56573 L .98002 .566 L .9898 .5662 L 1 .56635 L Mfstroke [ 5 2 1 2 ] 0 Mabsdash 0 .05991 m .00983 .06983 L .02056 .07969 L .03063 .08841 L .04032 .09648 L .05063 .1048 L .06056 .1126 L .07111 .12048 L .08127 .12772 L .09105 .13451 L .10145 .14161 L .11147 .14837 L .1211 .1548 L .13135 .16147 L .14122 .16769 L .15172 .17419 L .16182 .18039 L .17155 .18631 L .18189 .19258 L .19185 .19852 L .20244 .20468 L .21263 .21053 L .22245 .21612 L .23288 .22203 L .24294 .2277 L .2526 .2331 L .26289 .23873 L .2728 .24409 L .28332 .24973 L .29347 .25514 L .30322 .26031 L .3136 .26578 L .3236 .27094 L .33321 .27585 L .34344 .28102 L .35329 .28597 L .36376 .29119 L .37385 .29617 L .38355 .30089 L .39387 .30584 L .40381 .31054 L .41437 .31549 L .42455 .32021 L .43434 .3247 L .44476 .32939 L .45479 .33382 L .46443 .33802 L .4747 .34242 L .48458 .34658 L .49509 .35093 L Mistroke .50521 .35503 L .51495 .35888 L .52531 .36289 L .53528 .36664 L .54588 .37053 L .55609 .37415 L .56592 .37754 L .57637 .38101 L .58643 .38422 L .59611 .38717 L .60641 .39017 L .61633 .39289 L .62687 .39561 L .63703 .39806 L .6468 .40023 L .65719 .40232 L .6672 .4041 L .67682 .40558 L .68707 .40688 L .69693 .40786 L .70204 .40826 L .70464 .40842 L .70741 .40857 L .71005 .40869 L .71245 .40878 L .71361 .40881 L .71486 .40884 L .71595 .40886 L .71713 .40888 L .71778 .40889 L .71838 .40889 L .71866 .4089 L .71898 .4089 L .71927 .4089 L .71954 .4089 L .71986 .4089 L .72016 .4089 L .72048 .4089 L .72066 .4089 L .72083 .4089 L .72115 .4089 L .7215 .4089 L .72186 .40889 L .7222 .40889 L .7229 .40888 L .72355 .40887 L .72479 .40885 L .72612 .40882 L .72756 .40878 L .72996 .40868 L Mistroke .73261 .40855 L .73796 .40816 L .74291 .40766 L .74823 .40697 L .75325 .40616 L .75872 .40508 L .76884 .40245 L .77919 .39872 L .78915 .3938 L .79424 .39064 L .79974 .38656 L .80995 .37654 L .81503 .36981 L .82039 .36065 L .8228 .35553 L .82539 .34903 L .82782 .34163 L .83006 .33311 L .83265 .32001 L .83402 .31072 L .83547 .29754 L .83667 .28177 L .83728 .27057 L .83762 .26245 L .83794 .25304 L .83812 .2465 L .83829 .23915 L .83861 .22017 L .83879 .20326 L .83898 .17069 L .83914 .06535 L .83932 .1797 L .83964 .21881 L .83993 .23723 L .84025 .2507 L .84059 .26142 L .84123 .27599 L .84192 .28752 L .84319 .30262 L .84441 .31338 L .84555 .32133 L .84781 .33365 L .85021 .34369 L .85567 .3603 L .86081 .3716 L .87064 .38728 L .8811 .39924 L .89117 .40807 L .90085 .41488 L .91116 .4208 L Mistroke .92108 .42548 L .93163 .42956 L .94179 .43277 L .95156 .43529 L .96196 .43744 L .97198 .43907 L .9816 .44029 L .99186 .44127 L 1 .44186 L Mfstroke [ 5 2 1 2 1 2 ] 0 Mabsdash 0 .00431 m .00983 .01057 L .02056 .01725 L .03063 .02324 L .04032 .02875 L .05063 .03477 L .06056 .04071 L .07111 .04697 L .08127 .05287 L .09105 .05872 L .10145 .06511 L .11147 .07119 L .1211 .07685 L .13135 .08279 L .14122 .08846 L .15172 .09434 L .16182 .09982 L .17155 .10507 L .18189 .11078 L .19185 .11627 L .20244 .122 L .21263 .12755 L .22245 .13301 L .23288 .13879 L .24294 .14424 L .2526 .14939 L .26289 .15484 L .2728 .16 L .28332 .16533 L .29347 .17038 L .30322 .17531 L .3136 .18053 L .3236 .18547 L .33321 .19017 L .34344 .19522 L .35329 .20005 L .36376 .20508 L .37385 .20982 L .38355 .21433 L .39387 .21906 L .40381 .22347 L .41437 .22803 L .42455 .2324 L .43434 .23655 L .44476 .24085 L .45479 .24486 L .46443 .24866 L .4747 .25263 L .48458 .25631 L .49509 .26004 L Mistroke .50521 .26352 L .51495 .26675 L .52531 .27 L .53528 .27292 L .54588 .27585 L .55609 .27849 L .56592 .28082 L .57637 .28303 L .58643 .2849 L .59611 .28644 L .60641 .28775 L .61117 .28823 L .61633 .28865 L .61915 .28883 L .62175 .28898 L .62439 .2891 L .62687 .28918 L .62799 .28922 L .62916 .28924 L .62978 .28925 L .63045 .28926 L .63106 .28927 L .63163 .28928 L .63196 .28928 L .63232 .28928 L .63265 .28928 L .63295 .28928 L .63327 .28929 L .63346 .28929 L .63363 .28929 L .63381 .28929 L .63398 .28929 L .63417 .28928 L .63435 .28928 L .63466 .28928 L .63498 .28928 L .63556 .28928 L .63619 .28927 L .63688 .28926 L .63813 .28924 L .63944 .2892 L .6418 .28912 L .64433 .289 L .6471 .28883 L .65209 .2884 L .65742 .28777 L .66285 .28693 L .66798 .28591 L .67776 .28329 L .68817 .27937 L Mistroke .69819 .27415 L .70782 .26717 L .71277 .2625 L .71808 .25634 L .72347 .24846 L .72858 .23866 L .73103 .23279 L .73363 .22528 L .73831 .20626 L .73959 .19886 L .74078 .19038 L .74203 .17893 L .74269 .17114 L .7434 .16062 L .74377 .15376 L .74417 .14464 L .74455 .13353 L .74473 .12689 L .7449 .11945 L .74521 .10034 L .74538 .08458 L .74556 .05518 L Mfstroke .74556 .05518 m .74566 0 L s .74582 0 m .74593 .06281 L .74626 .10227 L .74658 .12081 L .74676 .12836 L .74692 .13418 L .74752 .15076 L .74786 .15774 L .74823 .16415 L .7489 .1737 L .75013 .18694 L .75148 .1978 L .75421 .21358 L .75674 .2242 L .7591 .23212 L .76427 .24535 L .76899 .25441 L .77425 .26237 L .77912 .26834 L .78886 .27764 L .79884 .2847 L .8043 .28768 L .80944 .28995 L .81456 .29173 L .81927 .29294 L .82176 .29343 L .82407 .29379 L .82662 .29411 L .82803 .29425 L .82934 .29435 L .8306 .29443 L .83124 .29446 L .83194 .29448 L .8323 .29449 L .83264 .2945 L .83283 .29451 L .83303 .29451 L .83322 .29451 L .8334 .29451 L .83357 .29451 L .83374 .29451 L .83391 .29452 L .8341 .29451 L .83427 .29451 L .83445 .29451 L .83476 .29451 L .83508 .29451 L .83537 .2945 L .83602 .29448 L .83663 .29446 L Mistroke .8372 .29443 L .83849 .29435 L .83989 .29423 L .84228 .29395 L .84492 .29351 L .84767 .29292 L .85026 .29222 L .8554 .29038 L .86011 .2881 L .86492 .2851 L .87019 .28093 L .87518 .27592 L .88051 .269 L .88312 .26482 L .88594 .25948 L .88839 .25398 L .89107 .24662 L .89369 .23755 L .89613 .2263 L .89748 .21823 L .89871 .20895 L .89939 .20267 L .90013 .19441 L .90084 .18458 L .90149 .17255 L .90181 .16472 L .90216 .15433 L .90246 .14262 L .90278 .1239 L .90296 .10784 L .90313 .08259 L Mfstroke .90313 .08259 m .90322 0 L s .90342 0 m .90351 .08002 L .90383 .12113 L .90401 .13353 L .90418 .14236 L .90448 .1545 L .90477 .1633 L .90541 .1782 L .90604 .18883 L .90672 .19783 L .90792 .21016 L .90919 .22005 L .91146 .23337 L .91389 .24408 L .91649 .25309 L .92117 .26554 L .92661 .27639 L .93174 .28441 L .94154 .296 L .95197 .3049 L .96201 .3113 L .97166 .31598 L .98194 .31972 L .99183 .32239 L 1 .32406 L s [ 5 2 1 2 1 2 1 2 ] 0 Mabsdash .13973 0 m .14122 .00082 L .15172 .00667 L .16182 .01211 L .17155 .01717 L .18189 .02269 L .19185 .02776 L .20244 .03332 L .21263 .03894 L .22245 .04448 L .23288 .05066 L .24294 .05638 L .2526 .06161 L .26289 .06709 L .2728 .07193 L .28332 .07693 L .29347 .0818 L .30322 .08643 L .3136 .09156 L .3236 .09652 L .33321 .10116 L .34344 .10616 L .35329 .11078 L .36376 .11557 L .37385 .12018 L .38355 .12439 L .39387 .12881 L .40381 .13297 L .41437 .13711 L .42455 .14101 L .43434 .14457 L .44476 .14818 L .45479 .15161 L .46443 .15472 L .4747 .15791 L .48458 .16088 L .49509 .16366 L .50521 .1661 L .51495 .16814 L .52531 .16986 L .53528 .17122 L .54074 .17178 L .54588 .17218 L .54837 .17233 L .551 .17246 L .55346 .17256 L .5557 .17263 L .55686 .17266 L .55812 .17268 L .55881 .17269 L Mistroke .55945 .1727 L .56006 .17271 L .5604 .17271 L .56071 .17271 L .56098 .17271 L .56126 .17271 L .56155 .17271 L .56186 .17271 L .56213 .17271 L .56242 .17271 L .56269 .17271 L .56293 .17271 L .56354 .1727 L .56419 .17269 L .56538 .17265 L .56663 .17261 L .5678 .17255 L .57045 .17239 L .57304 .17218 L .57581 .17188 L .58121 .17113 L .58633 .17019 L .59139 .169 L .59608 .16759 L .60123 .16564 L .60607 .16339 L .61567 .15748 L .6208 .15325 L .62551 .14839 L .63032 .14212 L .63558 .13305 L .64057 .12096 L .64336 .11158 L .6446 .10648 L .6459 .10013 L .64711 .09307 L .64844 .0833 L .64902 .07806 L .64965 .07147 L .65023 .06404 L .65078 .05558 L .65146 .04158 L .65181 .0315 L .652 .02512 L .6522 .01684 L .65239 .00687 L Mfstroke .65239 .00687 m .65248 0 L s .65363 0 m .65387 .01552 L .65417 .02812 L .65452 .03902 L .65485 .0472 L .65543 .05862 L .65607 .06825 L .65731 .08231 L .65847 .09224 L .66111 .10879 L .66368 .12049 L .66646 .13039 L .67156 .14438 L .67693 .1556 L .68664 .17086 L .69697 .18306 L .70691 .19231 L .71748 .20025 L .72766 .20659 L .73746 .21152 L .74788 .21573 L .75791 .21901 L .76756 .22126 L .77293 .22221 L .77784 .22295 L .78027 .22328 L .78291 .22359 L .78541 .22382 L .78772 .22398 L .78902 .22405 L .79042 .22411 L .79175 .22416 L .79296 .22419 L .79406 .22421 L .79469 .22421 L .79527 .22422 L .79559 .22422 L .79589 .22422 L .79615 .22423 L .79645 .22423 L .79676 .22423 L .7971 .22423 L .79739 .22423 L .7977 .22423 L .79803 .22423 L .79834 .22422 L .79903 .22422 L .79963 .22421 L .80028 .22421 L .80264 .22417 L Mistroke .80543 .22411 L .80796 .22405 L .8092 .22401 L .81051 .22395 L .81285 .22381 L .81538 .22362 L .81815 .22336 L .82844 .22218 L .83834 .22109 L .84886 .21983 L .85142 .21955 L .85413 .21929 L .85664 .21909 L .85787 .21901 L .859 .21894 L .86009 .2189 L .86123 .21886 L .86183 .21884 L .86238 .21883 L .8627 .21883 L .86299 .21883 L .86364 .21882 L .86396 .21882 L .86425 .21882 L .86456 .21881 L .8649 .21881 L .86524 .21881 L .86544 .21881 L .86561 .21881 L .86577 .21881 L .86595 .21881 L .86627 .21881 L .8666 .21881 L .8669 .21881 L .86706 .21881 L .86724 .21881 L .86756 .21882 L .86818 .21882 L .86876 .21883 L .86938 .21884 L .86996 .21885 L .87124 .21888 L .87243 .21892 L .87356 .21896 L .87608 .2191 L .87882 .21932 L .88122 .21957 L .88386 .21991 L .88921 .22083 L .89945 .2233 L Mistroke .90931 .2263 L .91979 .23001 L .92989 .23379 L .9396 .23737 L .94993 .24093 L .95988 .24405 L .97046 .24691 L .98064 .24918 L .99045 .25095 L 1 .2523 L Mfstroke [ ] 0 setdash 0 .58343 m .00983 .58535 L .02056 .58744 L .03063 .5894 L .04032 .59128 L .05063 .59328 L .06056 .59519 L .07111 .59722 L .08127 .59917 L .09105 .60103 L .10145 .60302 L .11147 .60492 L .1211 .60674 L .13135 .60867 L .14122 .61052 L .15172 .61248 L .16182 .61437 L .17155 .61617 L s .17155 .61617 m .18166 .61803 L s .67234 .61803 m .67594 .61633 L 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