Content-Type: multipart/mixed; boundary="-------------0312120425797" This is a multi-part message in MIME format. ---------------0312120425797 Content-Type: text/plain; name="03-540.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="03-540.keywords" Restricted 3-body problem, periodic solutions, linear stability ---------------0312120425797 Content-Type: text/plain; name="arioli.nb" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="arioli.nb" (*********************************************************************** 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[ 66486, 1407]*) (*NotebookOutlinePosition[ 67595, 1442]*) (* CellTagsIndexPosition[ 67551, 1438]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Branches of periodic orbits for the planar restricted 3-body \ problem\ \>", "Title"], Cell["\<\ Gianni Arioli Dipartimento di Matematica Politecnico di Milano via Bonardi 9 20133 Milano Italy\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Instructions", "Subsection", FontColor->GrayLevel[1], Background->GrayLevel[0.500008]], Cell["\<\ The following 4 subsections of the notebook contain all necessary \ definitions for the program to run. \ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Definition of the potential and the gradient", "Subsubsection", FontSize->14, FontWeight->"Bold", Background->GrayLevel[0.900008]], Cell[BoxData[{ \(\(c1 := \(-m2\)/\((m1 + m2)\)^\((2/3)\);\)\), "\[IndentingNewLine]", \(\(c2 := m1/\((m1 + m2)\)^\((2/3)\);\)\), "\[IndentingNewLine]", \(\(Omega[x1_, x2_] := x1\^2\/2 + x2\^2\/2 + m1 \((\((x1 + c1)\)\^2 + x2\^2)\)\^\(\(-1\)/2\) + m2 \((\((x1 + c2)\)\^2 + x2\^2)\)\^\(\(-1\)/2\) - m1 \((c1\^2)\)\^\(\(-1\)/2\) - m2 \((c2\^2)\)\^\(\(-1\)/2\);\)\), "\[IndentingNewLine]", \(\(Omega1[x1_, x2_] := x1 - \(m1 \((x1 + c1)\)\)\/\((\((x1 + c1)\)\^2 + x2\^2)\)\^\(3/2\) - \ \(m2 \((c2 + x1)\)\)\/\((\((c2 + x1)\)\^2 + x2\^2)\)\^\(3/2\);\)\), "\ \[IndentingNewLine]", \(\(Omega2[x1_, x2_] := x2 - \(m1\ x2\)\/\((\((x1 + c1)\)\^2 + x2\^2)\)\^\(3/2\) - \(m2\ x2\)\ \/\((\((c2 + x1)\)\^2 + x2\^2)\)\^\(3/2\);\)\), "\[IndentingNewLine]", \(\(V[x1_, x2_] := \(-m1\) \((\((x1 + c1)\)\^2 + x2\^2)\)\^\(\(-1\)/2\) - m2 \((\((x1 + c2)\)\^2 + x2\^2)\)\^\(\(-1\)/2\);\)\), "\ \[IndentingNewLine]", \(\(V1[x1_, x2_] := m1 \((x1 + c1)\) \((\((x1 + c1)\)\^2 + x2\^2)\)\^\(\(-3\)/2\) + m2 \((x1 + c2)\) \((\((x1 + c2)\)\^2 + x2\^2)\)\^\(\(-3\)/2\);\)\), "\ \[IndentingNewLine]", \(\(V2[x1_, x2_] := m1\ x2 \((\((x1 + c1)\)\^2 + x2\^2)\)\^\(\(-3\)/2\) + m2\ x2 \((\((x1 + c2)\)\^2 + x2\^2)\)\^\(\(-3\)/2\);\)\)}], "Input",\ InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["Graphic definitions", "Subsection", FontSize->14, FontWeight->"Bold", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(TestInt[l_, i_] := Block[{a, b, c, d, j, p}, \[IndentingNewLine]p = Length[l]; j = If[i < p, i + 1, 1]; \[IndentingNewLine]a = l[\([i]\)]; b = l[\([j]\)]; \[IndentingNewLine]c = Interval[{a[\([1]\)], b[\([1]\)]}]; d = Interval[{a[\([2]\)], b[\([2]\)]}]; {c, d}];\)\), "\n", \(\(TestIntOpp[l_, i_] := Block[{a, b, c, d, j, p}, \[IndentingNewLine]p = Length[l]; j = If[i < p, i + 1, 1]; \[IndentingNewLine]a = l[\([i]\)]; b = l[\([j]\)]; \[IndentingNewLine]c = Interval[{a[\([1]\)], b[\([1]\)]}]; d = \(-Interval[{a[\([2]\)], b[\([2]\)]}]\); {c, d}];\)\), "\n", \(\(Averint[a_] := .5 \((Max[a] + Min[a])\);\)\), "\n", \(WidthInt[a_] := Max[a] - Min[a]; PlotBox[a_] := Block[{x = a[\([1]\)], y = a[\([2]\)], xc, yc, sizex, sizey}, \[IndentingNewLine]xc = Averint[x]; yc = Averint[y]; \[IndentingNewLine]sizex = WidthInt[x]/2; sizey = WidthInt[y]/2; \[IndentingNewLine]MakePar[xc, yc, sizex, sizey, 0. , \[Pi]/2, 40]];\), "\n", \(Draw2[set1_, set2_] := Block[{len = Length[set1], whole1, i}, \[IndentingNewLine]whole1 = PlotBox[set1[\([1]\)]]; Do[AppendTo[whole1, PlotBox[set1[\([i]\)]]], {i, 2, len}]; \[IndentingNewLine]whole1 = Partition[Flatten[whole1], 2]; \[IndentingNewLine]ListPlot[ Join[set2, whole1], PlotRange \[Rule] All]]\), "\n", \(\(RotationMatrix[ alpha_] := {{Cos[alpha], \(-Sin[alpha]\)}, {Sin[alpha], Cos[alpha]}};\)\[IndentingNewLine]\), "\n", \(\(MakePar[x_, y_, lx_, ly_, alpha_, beta_, p_] := Block[{sidep = p/4, dx = 8. /p, data1, data2, data3, data4}, \n data1 = Table[{x + lx\ Cos[alpha] - ly\ Cos[ beta] \((\(-1. \) + dx\ i)\), \[IndentingNewLine]y + lx\ Sin[alpha] - ly\ \((\(-1. \) + dx\ i)\) Sin[beta]}, {i, 0, sidep - 1}]; \[IndentingNewLine]data2 = Table[{x - lx\ \((\(-1. \) + dx\ i)\) Cos[alpha] - Cos[beta] ly, \[IndentingNewLine]y - lx \((\(-1. \) + dx\ i)\)\ Sin[alpha] - ly\ Sin[beta]}, \[IndentingNewLine]{i, 0, sidep - 1}]; \n data3 = Table[{x - lx\ Cos[alpha] - Cos[beta] \((\(-1. \) + dx\ i)\) ly, \[IndentingNewLine]y - lx\ Sin[alpha] - \((\(-1. \) + dx\ i)\) ly\ Sin[beta]}, {i, sidep, 1, \(-1\)}]; \[IndentingNewLine]data4 = Table[{x + lx\ \((\(-1. \) + dx\ i)\) Cos[alpha] + Cos[beta] ly, \[IndentingNewLine]y + lx \((\(-1. \) + dx\ i)\)\ Sin[alpha] + ly\ Sin[beta]}, {i, 0, sidep - 1}]; \n Join[data1, data2, data3, data4]];\)\)}], "Input", InitializationCell->True], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(sizey\)\" is similar to \ existing symbol \"\!\(sizex\)\"."\)], "Message"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Poincar\[EAcute] definitions", FontSize->14]], "Subsection", FontSize->12, Background->GrayLevel[0.900008]], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{\(OrbitPlot[x10_, h_, M1_, M2_, T_]\), ":=", RowBox[{"Block", "[", RowBox[{\({x, y, x1, x2, y1, y2, x2p, x1p = 0. , x20 = 0. , \[IndentingNewLine]m1 = M1, m2 = M2}\), ",", "\[IndentingNewLine]", RowBox[{\(x2p = \@\(2. Omega[x10, x20] + h - x1p\^2\)\), ";", "\[IndentingNewLine]", RowBox[{\({x, y}\), "=", RowBox[{\({x1, x2}\), "/.", RowBox[{"First", "[", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x1", "\[Prime]\[Prime]", MultilineFunction->None], "[", "t", "]"}], "+", RowBox[{"2", " ", RowBox[{ SuperscriptBox["x2", "\[Prime]", MultilineFunction->None], "[", "t", "]"}]}]}], "\[Equal]", \(Omega1[x1[t], x2[t]]\)}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x2", "\[Prime]\[Prime]", MultilineFunction->None], "[", "t", "]"}], "-", RowBox[{"2", " ", RowBox[{ SuperscriptBox["x1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}]}]}], "\[Equal]", \(Omega2[x1[t], x2[t]]\)}], ",", "\[IndentingNewLine]", \(x1[0] \[Equal] x10\), ",", \(x2[0] \[Equal] x20\), ",", \(\(x1'\)[0] \[Equal] x1p\), ",", \(\(x2'\)[0] \[Equal] x2p\)}], "}"}], ",", "\[IndentingNewLine]", \({x1, x2}\), ",", \({t, 0, T}\), ",", \(MaxSteps \[Rule] 30000\)}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", \(ParametricPlot[{x[t], y[t]}, {t, 0, T}, PlotRange \[Rule] All]\)}]}], "]"}]}], ";"}], "\[IndentingNewLine]"}], "\n", RowBox[{ RowBox[{\(HalfPoin[x10_, x1p_, M1_, M2_, h_]\), ":=", RowBox[{"Block", "[", RowBox[{\({T = 5. , x, y, xp, yp, x20 = 0. , x2p, x1, x2, t, \[IndentingNewLine]m1 = M1, m2 = M2}\), ",", "\[IndentingNewLine]", RowBox[{\(x2p = \ \@\(2. Omega[x10, 0. ] + h - x1p\^2\)\), ";", "\[IndentingNewLine]", RowBox[{\({x, y, xp, yp}\), "=", RowBox[{\({x1, x2, x1', x2'}\), "/.", RowBox[{"First", "[", RowBox[{"NDSolve", "[", RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x1", "\[Prime]\[Prime]", MultilineFunction->None], "[", "t", "]"}], "+", RowBox[{"2", " ", RowBox[{ SuperscriptBox["x2", "\[Prime]", MultilineFunction->None], "[", "t", "]"}]}]}], "\[Equal]", \(Omega1[x1[t], x2[t]]\)}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox["x2", "\[Prime]\[Prime]", MultilineFunction->None], "[", "t", "]"}], "-", RowBox[{"2", " ", RowBox[{ SuperscriptBox["x1", "\[Prime]", MultilineFunction->None], "[", "t", "]"}]}]}], "\[Equal]", \(Omega2[x1[t], x2[t]]\)}], ",", "\[IndentingNewLine]", \(x1[0] \[Equal] x10\), ",", \(x2[0] \[Equal] x20\), ",", \(\(x1'\)[0] \[Equal] x1p\), ",", \(\(x2'\)[0] \[Equal] x2p\)}], "}"}], ",", "\[IndentingNewLine]", \({x1, x2}\), ",", \({t, 0, T}\), ",", \(MaxSteps \[Rule] 30000\), ",", \(StoppingTest \[Rule] \((x2[t] < 0)\)\)}], "]"}], "]"}]}]}], ";", "\[IndentingNewLine]", \(T = x[\([1, 1, 2]\)]\), ";", \(T = t /. FindRoot[y[t] \[Equal] 0. , {t, {T, .9 T}}]\), ";", "\[IndentingNewLine]", \({x[T], xp[T], T}\)}]}], "]"}]}], ";"}]}], "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Lohner definitions", FontWeight->"Bold"]], "Subsubsection", FontSize->14, Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(d = 4;\)\[IndentingNewLine]\), "\n", \(\(f[x_] := {x[\([2]\)], x[\([1]\)] - 2 x[\([4]\)] - V1[x[\([1]\)], x[\([3]\)]], \[IndentingNewLine]x[\([4]\)], x[\([3]\)] + 2 x[\([2]\)] - V2[x[\([1]\)], x[\([3]\)]]};\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(dftemp = {D[f[{x, v, y, w}], x], D[f[{x, v, y, w}], v], D[f[{x, v, y, w}], y], D[f[{x, v, y, w}], w]};\)\), "\n", \(\(df[a_] := Block\ [{x, v, y, w, e}, dftemp /. {x \[Rule] a[\([1]\)], y \[Rule] a[\([3]\)]}];\)\), "\[IndentingNewLine]", \(\(df2temp = {D[dftemp, x], D[dftemp, v], D[dftemp, y], D[dftemp, w]};\)\), "\n", \(\(df[a_] := Block\ [{x, v, y, w, e}, \[IndentingNewLine]dftemp /. {x \[Rule] a[\([1]\)], y \[Rule] a[\([3]\)]}];\)\), "\n", \(\(df2[a_] := Block\ [{x, v, y, w, e}, \[IndentingNewLine]df2temp /. {x \[Rule] a[\([1]\)], y \[Rule] a[\([3]\)]}];\)\n\), "\n", \(\(incl[z_, y_] := Block[{inc = True}, \[IndentingNewLine]vectbool = IntervalMemberQ[z, y]; \[IndentingNewLine]Do[ inc = inc && vectbool[\([i]\)], {i, d}]; \[IndentingNewLine]inc];\)\[IndentingNewLine] \ (*\[IndentingNewLine]recurse[i_] := Block[{}, x\_i = v\_\(i - 1\)/ i; \[IndentingNewLine]v\_i = \((x\_\(i - 1\) - 2 w\_\(i - 1\) - fxm\_\(i - 1\) - fxp\_\(i - 1\))\)/ i; \[IndentingNewLine]y\_i = w\_\(i - 1\)/ i; \[IndentingNewLine]w\_i = \((y\_\(i - 1\) + 2 v\_\(i - 1\) - fym\_\(i - 1\) - fyp\_\(i - 1\))\)/ i; \[IndentingNewLine]xmc\_i = x\_i; \ (*\ \((x + c1)\)\ *) \[IndentingNewLine]xpc\_i = x\_i; \ (*\ \((x + c2)\)\ *) \[IndentingNewLine]xmcq\_i = \[Sum]\+\(j = 0\)\%i\( xmc\_j\) xmc\_\(i - j\); \ (*\ \((x + c1)\)\^2\ \ *) \[IndentingNewLine]xpcq\_i = \[Sum]\+\(j = 0\)\%i\( xpc\_j\) xpc\_\(i - j\); \ (*\ \((x + c2)\)\^2\ \ *) \[IndentingNewLine]xymc\_i = \[Sum]\+\(j = 0\)\%i\( xmc\_j\) y\_\(i - j\); \ (*\ \((x + c1)\) y\ *) \[IndentingNewLine]xypc\_i = \[Sum]\+\(j = 0\)\%i\( xpc\_j\) y\_\(i - j\); \ (*\ \((x + c2)\) y\ *) \[IndentingNewLine]yq\_i = \[Sum]\+\(j = 0\)\%i\( y\_j\) y\_\(i - j\); \ (*\ y\^2\ *) \[IndentingNewLine]xmcy\_i = xmcq\_i + yq\_i; \ (*\ \((x - c)\)\^2 + y\^2\ *) \[IndentingNewLine]xpcy\_i = xpcq\_i + yq\_i; \ (*\ \((x + c)\)\^2 + y\^2\ *) \[IndentingNewLine]dp\_i = 1/\((i\ xpcy\_0)\) Sum[\((j/2 - 3 i/2)\) \(dp\_j\) xpcy\_\(i - j\), {j, 0, i - 1}]; \[IndentingNewLine] (*\ \((\((x + c)\)\^2 + \ y\^2)\)\^\(\(-3\)/2\)\ *) \[IndentingNewLine]dm\_i = 1/\((i\ xmcy\_0)\) Sum[\((j/2 - 3 i/2)\) \(dm\_j\) xmcy\_\(i - j\), {j, 0, i - 1}]; \[IndentingNewLine] (*\ \((\((x - c)\)\^2 + \ y\^2)\)\^\(\(-3\)/2\)\ *) \[IndentingNewLine]ddp\_i = 1/\((i\ xpcy\_0)\) Sum[\((3 j/2 - 5 i/2)\) \(ddp\_j\) xpcy\_\(i - j\), {j, 0, i - 1}]; \[IndentingNewLine] (*\ \((\((x + c)\)\^2 + \ y\^2)\)\^\(\(-5\)/2\)\ *) \[IndentingNewLine]ddm\_i = 1/\((i\ xmcy\_0)\) Sum[\((3 j/2 - 5 i/2)\) \(ddm\_j\) xmcy\_\(i - j\), {j, 0, i - 1}]; \[IndentingNewLine] (*\ \((\((x - c)\)\^2 + \ y\^2)\)\^\(\(-5\)/2\)\ *) \[IndentingNewLine]fxm\_i = \[Sum]\+\(j = 0\)\%i\( xmc\_j\) dm\_\(i - j\); fxp\_i = \[Sum]\+\(j = 0\)\%i\( xpc\_j\) dp\_\(i - j\); \[IndentingNewLine]fym\_i = \[Sum]\+\(j = \ 0\)\%i\( y\_j\) dm\_\(i - j\); fyp\_i = \[Sum]\+\(j = 0\)\%i\( y\_j\) dp\_\(i - j\); \[IndentingNewLine]fxxm\_i = \[Sum]\+\(j = 0\)\ \%i\( xmcq\_j\) ddm\_\(i - j\); \ (*\ \((\(-c\) + x)\)\^2\/\((\((\(-c\) + x)\ \)\^2 + y\^2)\)\^\(5/2\)\ *) \[IndentingNewLine]fxxp\_i = \[Sum]\+\(j = \ 0\)\%i\( xpcq\_j\) ddp\_\(i - j\); \ (*\ \((c + x)\)\^2\/\((\((c + x)\)\^2 + \ y\^2)\)\^\(5/2\)\ *) \[IndentingNewLine]fxym\_i = \[Sum]\+\(j = 0\)\%i\( xymc\_j\) ddm\_\(i - j\); \ (*\ \(\((\(-c\) + x)\) y\)\/\((\((\(-c\) + \ x)\)\^2 + y\^2)\)\^\(5/2\)\ *) \[IndentingNewLine]fxyp\_i = \[Sum]\+\(j = 0\)\ \%i\( xypc\_j\) ddp\_\(i - j\); \ (*\ \(\((c + x)\) y\)\/\((\((c + x)\)\^2 + \ y\^2)\)\^\(5/2\)\ *) \[IndentingNewLine]fyyp\_i = \[Sum]\+\(j = 0\)\%i\( yq\_j\) ddp\_\(i - j\); \ (*\ y\^2\/\((\((c + x)\)\^2 + y\^2)\)\^\(5/2\)\ \ *) \[IndentingNewLine]fyym\_i = \[Sum]\+\(j = 0\)\%i\( yq\_j\) ddm\_\(i - j\); \ (*\ y\^2\/\((\((\(-c\) + x)\)\^2 + y\^2)\)\^\(5/2\)\ \ *) \[IndentingNewLine]DF\_i = Transpose[{{0, 3 fxxm\_i - dm\_i + 3 fxxp\_i - dp\_i, 0, 3 fxyp\_i + 3 fxym\_i}, \[IndentingNewLine]{0, 0, 0, 0}, \[IndentingNewLine]{0, 3 fxyp\_i + 3 fxym\_i, 0, 3 fyym\_i - dm\_i + 3 fyyp\_i - dp\_i}, \[IndentingNewLine]{0, 0, 0, 0}}]; \[IndentingNewLine]\[Xi]\_i = \[Sum]\+\(j = 0\)\%\(i \ - 1\)DF\_j . \[Xi]\_\(i - 1 - j\)/ i\[IndentingNewLine]]; \[IndentingNewLine]\[IndentingNewLine]\ \[CapitalPhi][a_, order_, t_] := Block[{i}, \[IndentingNewLine]x\_0 = a[\([1]\)]; v\_0 = a[\([2]\)]; y\_0 = a[\([3]\)]; w\_0 = a[\([4]\)]; \[IndentingNewLine]xmc\_0 = x\_0 + c1; xpc\_0 = x\_0 + c2; \[IndentingNewLine]xmcq\_0 = xmc\_0\^2; xpcq\_0 = xpc\_0\^2; yq\_0 = y\_0\^2; \[IndentingNewLine]xmcy\_0 = xmcq\_0 + yq\_0; xpcy\_0 = xpcq\_0 + yq\_0; \[IndentingNewLine]dm\_0 = xmcy\_0\^\(\(-3\)/2\); dp\_0 = xpcy\_0\^\(\(-3\)/2\); \[IndentingNewLine]fxm\_0 = \(xmc\_0\ \) dm\_0; fxp\_0 = \(xpc\_0\) dp\_0; \[IndentingNewLine]fym\_0 = \(y\_0\) dm\_0; fyp\_0 = \(y\_0\) dp\_0; \[IndentingNewLine]Do[ recurse[i], {i, 1, order}]; \[IndentingNewLine]{\[Sum]\+\(i = 0\)\%order\( x\_i\) t\^i, \[Sum]\+\(i = 0\)\%order\( v\_i\) t\^i, \[Sum]\+\(i = 0\)\%order\( y\_i\) t\^i, \[Sum]\+\(i = 0\)\%order\( w\_i\) t\^i}]; \[IndentingNewLine]\[IndentingNewLine]d\[CapitalPhi][ a_, order_, t_] := Block[{i, j, f, d2, \[Xi], d}, \[IndentingNewLine]x\_0 = a[\([1]\)]; v\_0 = a[\([2]\)]; y\_0 = a[\([3]\)]; w\_0 = a[\([4]\)]; \[IndentingNewLine]xmc\_0 = x\_0 + c1; xpc\_0 = x\_0 + c2; \[IndentingNewLine]xmcq\_0 = xmc\_0\^2; xpcq\_0 = xpc\_0\^2; yq\_0 = y\_0\^2; \[IndentingNewLine]xymc\_0 = \(xmc\_0\) y\_0; \ (*\ \((x - c)\) y\ *) \[IndentingNewLine]xypc\_0 = \(xpc\_0\) y\_0; \ (*\ \((x + c)\) y\ *) \[IndentingNewLine]\[IndentingNewLine]xmcy\_0 = xmcq\_0 + yq\_0; xpcy\_0 = xpcq\_0 + yq\_0; \[IndentingNewLine]dm\_0 = xmcy\_0\^\(\(-3\)/2\); dp\_0 = xpcy\_0\^\(\(-3\)/2\); \[IndentingNewLine]ddm\_0 = xmcy\_0\^\(\(-5\)/2\); ddp\_0 = xpcy\_0\^\(\(-5\)/2\); \[IndentingNewLine]fxm\_0 = \(xmc\_0\) dm\_0; fxp\_0 = \(xpc\_0\) dp\_0; \[IndentingNewLine]fym\_0 = \(y\_0\) dm\_0; fyp\_0 = \(y\_0\) dp\_0; \[IndentingNewLine]fxxm\_0 = \(xmcq\_0\) ddm\_0; \ (*\ \((\(-c\) + x)\)\^2\/\((\((\(-c\) + x)\)\^2 + \ y\^2)\)\^\(5/2\)\ *) \[IndentingNewLine]fxxp\_0 = \(xpcq\_0\) ddp\_0; \ (*\ \((c + x)\)\^2\/\((\((c + x)\)\^2 + \ y\^2)\)\^\(5/2\)\ *) \[IndentingNewLine]fxym\_0 = \(xymc\_0\) ddm\_0; \ (*\ \(\((\(-c\) + x)\) y\)\/\((\((\(-c\) + x)\)\^2 + \ y\^2)\)\^\(5/2\)\ *) \[IndentingNewLine]fxyp\_0 = \(xypc\_0\) ddp\_0; \ (*\ \(\((c + x)\) y\)\/\((\((c + x)\)\^2 + y\^2)\)\^\ \(5/2\)\ *) \[IndentingNewLine]fyyp\_0 = \(yq\_0\) ddp\_0; \ (*\ y\^2\/\((\((c + x)\)\^2 + y\^2)\)\^\(5/2\)\ \ *) \[IndentingNewLine]fyym\_0 = \(yq\_0\) ddm\_0; \ (*\ y\^2\/\((\((\(-c\) + x)\)\^2 + y\^2)\)\^\(5/2\)\ \ *) \[IndentingNewLine]DF\_0 = Transpose[{{0, 1 + 3 fxxm\_0 - dm\_0 + 3 fxxp\_0 - dp\_0, 0, 3 fxyp\_0 + 3 fxym\_0}, \[IndentingNewLine]{1, 0, 0, 2}, \[IndentingNewLine]{0, 3 fxyp\_0 + 3 fxym\_0, 0, 1 + 3 fyym\_0 - dm\_0 + 3 fyyp\_0 - dp\_0}, \[IndentingNewLine]{0, \(-2\), 1, 0}}]; \[IndentingNewLine]\[Xi]\_0 = Interval[0. ] + IdentityMatrix[4]; \[IndentingNewLine]Do[ recurse[i], {i, order}]; \[IndentingNewLine]\[Sum]\+\(i = 0\)\%order\( \[Xi]\_i\ \) t\^i]; \[IndentingNewLine]\n Enclosure[x_, t_, ff_] := Block[{i, x00 = x, y, z, zeroh = Interval[{0. , t}], \[IndentingNewLine]thickness = Interval[{\(-ff\), ff}]}, z = x00 + zeroh\ f[x00]\ + Table[thickness, {i, 4}]; \[IndentingNewLine]y = x00 + zeroh\ f[z]; \[IndentingNewLine]While[\(! incl[z, y]\), \[IndentingNewLine]\((Do[\[IndentingNewLine]If[\(! \ IntervalMemberQ[z[\([i]\)], y[\([i]\)]]\), z[\([i]\)] = z[\([i]\)] + thickness, ]\ \[IndentingNewLine], {i, 4}]; \ (*\ end\ do\ *) \[IndentingNewLine]y = x00 + zeroh\ f[ z])\)\[IndentingNewLine]]; \[IndentingNewLine]y];\ \[IndentingNewLine]*) \), "\n", \(\(Averint[a_] := .5 \((Max[a] + Min[a])\);\)\), "\n", \(\(TestInt[l_, i_, div_] := Block[{a, b, c, d, j, p}, \[IndentingNewLine]p = Length[l]; j = If[i < p, i + 1, 1]; \[IndentingNewLine]a = l[\([i]\)]; b = l[\([i]\)] + div \((l[\([j]\)] - l[\([i]\)])\); \[IndentingNewLine]c = Interval[{a[\([1]\)], b[\([1]\)]}]; d = Interval[{a[\([2]\)], b[\([2]\)]}]; {c, d}];\)\ \[IndentingNewLine]\), "\n", \(\(Int2Array[x_] := {Min[x[\([1]\)]], Max[x[\([1]\)]], Min[x[\([2]\)]], Max[x[\([2]\)]], Min[x[\([3]\)]], Max[x[\([3]\)]], Min[x[\([4]\)]], Max[x[\([4]\)]]};\)\n\), "\[IndentingNewLine]", \(\(Mat2Array[x_] := Block[{e1, e2}, \[IndentingNewLine]e1 = Flatten[x]; \[IndentingNewLine]e2 = Table[{Min[e1[\([i]\)]], Max[e1[\([i]\)]]}, {i, 16}]; \[IndentingNewLine]Flatten[ e2]\[IndentingNewLine]];\)\[IndentingNewLine]\), "\n", \(\(Array2Int[x_] := {Interval[{x[\([1]\)], x[\([2]\)]}], Interval[{x[\([3]\)], x[\([4]\)]}], Interval[{x[\([5]\)], x[\([6]\)]}], Interval[{x[\([7]\)], x[\([8]\)]}]};\)\[IndentingNewLine]\), "\n", \(\(Array2Mat[ x_] := {{Interval[{x[\([1]\)], x[\([2]\)]}], Interval[{x[\([3]\)], x[\([4]\)]}], Interval[{x[\([5]\)], x[\([6]\)]}], Interval[{x[\([7]\)], x[\([8]\)]}]}, \[IndentingNewLine]{Interval[{x[\([9]\)], x[\([10]\)]}], Interval[{x[\([11]\)], x[\([12]\)]}], Interval[{x[\([13]\)], x[\([14]\)]}], Interval[{x[\([15]\)], x[\([16]\)]}]}, \[IndentingNewLine]{Interval[{x[\([17]\)], x[\([18]\)]}], Interval[{x[\([19]\)], x[\([20]\)]}], Interval[{x[\([21]\)], x[\([22]\)]}], Interval[{x[\([23]\)], x[\([24]\)]}]}, \[IndentingNewLine]{Interval[{x[\([25]\)], x[\([26]\)]}], Interval[{x[\([27]\)], x[\([28]\)]}], Interval[{x[\([29]\)], x[\([30]\)]}], Interval[{x[\([31]\)], x[\([32]\)]}]}};\)\[IndentingNewLine]\), "\n", \(\(Error2[y_, order_, t_] := \[IndentingNewLine]Block[{e1, e2, e3, o = order + 1}, \[IndentingNewLine]e1 = Int2Array[Enclosure2[y, t, .001]]; \[IndentingNewLine]e2 = error[e1, {Min[m1], Max[m1], Min[m2], Max[m2], Min[c1], Max[c1], Min[c2], Max[c2]}, o, t]; \[IndentingNewLine]e3 = Array2Int[ e2]; \[IndentingNewLine]t\^o\ e3\[IndentingNewLine]];\)\ \[IndentingNewLine]\), "\[IndentingNewLine]", \(\(Enclosure2[y_, t_, f_] := Array2Int[ Encl[Int2Array[y], {Min[m1], Max[m1], Min[m2], Max[m2], Min[c1], Max[c1], Min[c2], Max[c2]}, t, f]];\)\[IndentingNewLine]\), "\n", \(\(\[CapitalPhi]2[y_, order_, t_] := Block[{e1, e2}, \[IndentingNewLine]e1 = Int2Array[y]; \[IndentingNewLine]e2 = Phi[e1, {Min[m1], Max[m1], Min[m2], Max[m2], Min[c1], Max[c1], Min[c2], Max[c2]}, order, t]; \[IndentingNewLine]Array2Int[ e2]\[IndentingNewLine]];\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(Errord\[CapitalPhi][v_, order_, t_] := Block[{d, i, j, k, Qdf = df[v], lognorm, temp, \[IndentingNewLine]y = Table[Interval[0. ], {k, order + 2}, {i, 4}, {j, 4}], w = Interval[0. ] + IdentityMatrix[4]}, \[IndentingNewLine]lognorm = Max[Table[ Qdf[\([k, k]\)] + \[Sum]\+\(i = 1\)\%4 If[i \[Equal] k, 0, Abs[Qdf[\([i, k]\)]]], {k, 4}]]; \[IndentingNewLine]\[IndentingNewLine]temp = Exp[lognorm\ t]; \[IndentingNewLine]temp = Interval[{\(-temp\), temp}]; \[IndentingNewLine]Do[ y[\([1, i, j]\)] = temp, {i, 4}, {j, 4}]; \[IndentingNewLine]w += Interval[{0, t}]\ Qdf . y[\([1]\)]; \[IndentingNewLine]Do[ y[\([1, i, j]\)] = IntervalIntersection[w[\([i, j]\)], y[\([1, i, j]\)]], {i, 4}, {j, 4}]; \[IndentingNewLine]d = Transpose[Qdf]; \[IndentingNewLine]Do[ y[\([i + 1]\)] = d . y[\([i]\)]/i, {i, 1, order + 1}]; \[IndentingNewLine]\(t\^\(order + 1\)\) y[\([order + 2]\)]];\)\[IndentingNewLine]\), "\n", \(\(d\[CapitalPhi]2[y_, order_, t_] := Block[{e1, e2}, \[IndentingNewLine]e1 = Int2Array[y]; \[IndentingNewLine]e2 = dPhi[e1, {Min[m1], Max[m1], Min[m2], Max[m2], Min[c1], Max[c1], Min[c2], Max[c2]}, order, t]; \[IndentingNewLine]{Array2Int[ Take[e2, 8]], Array2Mat[ Take[e2, \ \(-32\)]]}\[IndentingNewLine]];\)\[IndentingNewLine]\), "\n", \(pos[a_] := Min[a] \[GreaterEqual] 0; neg[a_] := Max[a] \[LessEqual] 0; WidthInt[a_] := Max[a] - Min[a];\), "\n", \(\(hull[a_, b_] := Interval[{Min[a, b], Max[a, b]}];\)\), "\n", \(\(SignRot[x_] := Max[\((\(-2\) x[\([2]\)] + Omega2[x[\([1]\)], x[\([3]\)]])\) x[\([3]\)] - \((x[\([4]\)])\)^2];\)\), "\n", \(\(id = Interval[0. ] + IdentityMatrix[4];\)\[IndentingNewLine]\), "\n", \(\(go[t_] := Block[{order = 25, i, j, temp}, \[IndentingNewLine]temp = \[CapitalPhi]2[xreal, order, t] + Error2[x00, order, t]; \[IndentingNewLine]xrealold = xreal; x00old = x00; rtilde2old = rtilde2; \[IndentingNewLine]newCold = newC; Cmold = Cm; Bold = B; \[Xi]old = \[Xi]; \[IndentingNewLine]xreal = Table[Interval[Averint[temp[\([i]\)]]], {i, d}]; \[IndentingNewLine]z = temp - xreal; \[IndentingNewLine]Areal = \(d\[CapitalPhi]2[x00, order, t]\)[\([2]\)]; \[IndentingNewLine]If[ der, \[Xi] = \((Areal + Errord\[CapitalPhi][x00, order, t])\) . \[Xi], Null]; \[IndentingNewLine]AC = Areal . Cm; \[IndentingNewLine]newC = Table[Averint[AC[\([i, j]\)]], {i, d}, {j, d}]; \[IndentingNewLine]AB2 = Areal . B; \[IndentingNewLine]AB = Table[Interval[Averint[AB2[\([i, j]\)]]], {i, d}, {j, d}]; \[IndentingNewLine]{Bt, RR} = QRDecomposition[AB]; \[IndentingNewLine]B = Transpose[Bt]; \[IndentingNewLine]rtilde = AB2 . rtilde2 + z + \((AC - newC)\) . r0; \[IndentingNewLine]rtilde2 = \((Bt . AB2)\) . rtilde2 + Bt . z; \[IndentingNewLine]r = newC . r0 + rtilde; \[IndentingNewLine]Cm = newC; \[IndentingNewLine]\(x00 = xreal + r;\)\[IndentingNewLine]];\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(Section[t_] := Block[{}, \[IndentingNewLine]ok11 = Min[x00[\([3]\)]] > 0; \[IndentingNewLine]ok12 = Max[x00[\([3]\)]] < 0; \[IndentingNewLine]go[ t]; \[IndentingNewLine]ok21 = Min[x00[\([3]\)]] > 0; \[IndentingNewLine]ok22 = Max[x00[\([3]\)]] < 0; \[IndentingNewLine]new = SafeHull[x00old, x00, t]; \[IndentingNewLine]If[ der, \[IndentingNewLine]new\[Xi] = SafeHulld\[CapitalPhi][x00, \[Xi], \[Xi]old, t]; \[IndentingNewLine]\[Xi] = new\[Xi] . \[Xi]0; \[IndentingNewLine]\[Xi]\[Xi] = \ {{\[Xi][\([1, 1]\)] - \[Xi][\([3, 1]\)]\ new[\([2]\)]/ new[\([4]\)], \[Xi][\([2, 1]\)] - \[Xi][\([3, 1]\)]\ \(f[new]\)[\([2]\)]/ new[\([4]\)]}, {\[Xi][\([1, 2]\)] - \[Xi][\([3, 2]\)]\ new[\([2]\)]/ new[\([4]\)], \[Xi][\([2, 2]\)] - \[Xi][\([3, 2]\)]\ \(f[new]\)[\([2]\)]/ new[\([4]\)]}}; \[IndentingNewLine]{\((ok11 && ok22)\) || \((ok12 && ok21)\), {new[\([1]\)], new[\([2]\)]}, \[Xi]\[Xi]}, \[IndentingNewLine]{\((ok11 && ok22)\) || \((ok12 && ok21)\), {new[\([1]\)], new[\([2]\)]}}]];\)\[IndentingNewLine]\), \ "\[IndentingNewLine]", \(\(SafeHulld\[CapitalPhi][x0_, \[Xi]0_, \[Xi]1_, t_] := Block[{i, j, \[Xi]2 = Table[Interval[0. ], {i, 4}, {j, 4}], e, e\[Xi], force}, \[IndentingNewLine]e = Enclosure2[x0, t, .0001]; \[IndentingNewLine]e\[Xi] = Encd\[CapitalPhi][x0, t]; \[IndentingNewLine]force = Transpose[df[e]] . e\[Xi]; \[IndentingNewLine]g = \((df2[e] . f[e])\) . e\[Xi] + Transpose[df[e]] . force; \[IndentingNewLine]Do[\[Xi]2[\([i, j]\)] = hull[\[Xi]0[\([i, j]\)], \[Xi]1[\([i, j]\)]]; \[IndentingNewLine]g[\([i, j]\)] = Max[g[\([i, j]\)]], {i, 4}, {j, 4}]; \[IndentingNewLine]g = Interval[{\(-1\), 1}] \(t\^2\/2\) g; \[IndentingNewLine]Do[\[IndentingNewLine]If[ pos[force[\([i, j]\)]] || neg[force[\([i, j]\)]], Null, \[IndentingNewLine]\[Xi]2[\([i, j]\)] += g[\([i, j]\)]], \[IndentingNewLine]{i, 4}, {j, 4}]; \[IndentingNewLine]\[Xi]2];\)\[IndentingNewLine]\), "\n", \(\(Encd\[CapitalPhi][v_, t_] := Block[\[IndentingNewLine]{i, j, k, Qdf = df[v], lognorm, temp, \[IndentingNewLine]y = Table[Interval[0. ], {i, 4}, {j, 4}], w = Interval[0. ] + IdentityMatrix[4]}, \[IndentingNewLine]lognorm = Max[Table[ Qdf[\([k, k]\)] + \[Sum]\+\(i = 1\)\%4 If[i \[Equal] k, 0, Abs[Qdf[\([i, k]\)]]], {k, 4}]]; \[IndentingNewLine]\[IndentingNewLine]temp = Exp[lognorm\ t]; \[IndentingNewLine]temp = Interval[{\(-temp\), temp}]; \[IndentingNewLine]Do[ y[\([i, j]\)] = temp, {i, 4}, {j, 4}]; \[IndentingNewLine]w += Interval[{0, t}]\ Qdf . y; \[IndentingNewLine]Do[ w[\([i, j]\)] = IntervalIntersection[w[\([i, j]\)], y[\([i, j]\)]], {i, 4}, {j, 4}]; \[IndentingNewLine]w];\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(SafeHull[x0_, x1_, t_] := Block[{i, x2 = Table[Interval[0. ], {i, 4}], e, g = x0, force}, \[IndentingNewLine]e = Enclosure2[x0, t, .0001]; \[IndentingNewLine]force = f[e]; \[IndentingNewLine]e = Abs[Transpose[df[e]] . force]; \[IndentingNewLine]Do[ x2[\([i]\)] = hull[x0[\([i]\)], x1[\([i]\)]]; g[\([i]\)] = Interval[{\(-1. \), 1. }] \(t\^2\/2\) Max[e[\([i]\)]], {i, 4}]; \[IndentingNewLine]Do[\[IndentingNewLine]If[ pos[force[\([i]\)]] || neg[force[\([i]\)]], Null, x2[\([i]\)] += g[\([i]\)]], \[IndentingNewLine]{i, 4}]; \[IndentingNewLine]x2];\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(HalfA[temp_, mass_, energy_, div_, thick_, derivative_] := \[IndentingNewLine]Block[{x = temp[\([1]\)], px = temp[\([2]\)], t1, t2, y, py, der}, \[IndentingNewLine]m1 = mass[\([1]\)]; m2 = mass[\([2]\)]; \[IndentingNewLine]der = derivative; \[IndentingNewLine]t1 = \(HalfPoin[Averint[x], Averint[px], Min[m1], Max[m2], Min[energy]]\)[\([3]\)]/\((div - 1)\); \[IndentingNewLine]t2 = \(HalfPoin[Averint[x], Averint[px], Max[m1], Min[m2], Max[energy]]\)[\([3]\)]/\((div - 1)\); \[IndentingNewLine]t = \((1. - 10^\((\(-thick\))\))\) Min[t1, t2]; \[IndentingNewLine]zeroh = Interval[{0. , t}]; \[IndentingNewLine]y = Interval[0. ]; \[IndentingNewLine]py = Sqrt[2 Omega[x, y] + energy - px\^2]; \[IndentingNewLine]x00 = {x, px, y, py}; \[IndentingNewLine]\[Xi] = Interval[0. ] + IdentityMatrix[4]; \[IndentingNewLine]\[Xi]0 = Transpose[\[IndentingNewLine]{{Interval[1. ], Interval[0. ], Interval[0. ], Omega1[x, y]/py}, {Interval[0. ], Interval[1. ], Interval[0. ], \(-px\)/py}}]; \[IndentingNewLine]rtilde2 = Table[Interval[0. ], {i, d}]; \[IndentingNewLine]rtilde = Table[Interval[0. ], {i, d}]; \[IndentingNewLine]B = IdentityMatrix[d]; \[IndentingNewLine]Bt = B; \[IndentingNewLine]xreal = Table[Interval[Averint[x00[\([i]\)]]], {i, d}]; \[IndentingNewLine]r0 = x00 - xreal; \[IndentingNewLine]Cm = IdentityMatrix[d]; \[IndentingNewLine]Do[ go[t], {i, div - 1}]; \[IndentingNewLine]t = 1.2 Max[ Abs[x00[\([3]\)]/x00[\([4]\)]]]; \[IndentingNewLine]Section[ t]];\)\)}], "Input", InitializationCell->True], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(df2temp\)\" is similar \ to existing symbol \"\!\(dftemp\)\"."\)], "Message"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(dPhi\)\" is similar to \ existing symbol \"\!\(Phi\)\"."\)], "Message"], Cell[BoxData[ \(General::"spell" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(Bold\)\" is similar to \ existing symbols \!\({Fold, Hold}\)."\)], "Message"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(ok21\)\" is similar to \ existing symbol \"\!\(ok12\)\"."\)], "Message"], Cell[BoxData[ \(General::"spell1" \(\(:\)\(\ \)\) "Possible spelling error: new symbol name \"\!\(\[Xi]2\)\" is similar \ to existing symbol \"\!\(\[CapitalPhi]2\)\"."\)], "Message"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Test", "Section"]], "Subsubsection", Background->GrayLevel[0.666667]], Cell[BoxData[ \(\(Uninstall[link];\)\)], "Input"], Cell[BoxData[ \(\(link = Install["\"];\)\)], "Input", InitializationCell->True], Cell[CellGroupData[{ Cell["S1", "Subsubsection", Background->GrayLevel[0.900008]], Cell[BoxData[{ \(\(graph = {};\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .95 - 1.09 m1 + .4 m1^2, .97 - 1.09 m1 + .4 m1^2}]; \[IndentingNewLine]AppendTo[ graph, {m1, x}];\[IndentingNewLine], {m1, .5, 2, .01}];\)\), "\[IndentingNewLine]", \(\(x =. ;\)\), "\[IndentingNewLine]", \(Fit[ graph, {1, \ x\ , x^2, x^3, x^4, x^5, x^6, x^7, x^8, x^9, x^10, x^11, x^12, x^13}, x]\)}], "Input"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(pl = Table[{h, x /. FindRoot[\(HalfPoin[x, 0. , 1, 1, h]\)[\([2]\)] \[Equal] 0, \[IndentingNewLine]{x, f2[h] - .01, f2[h] + .01}]}, {h, .0, .2, .01}];\)\), "\ \[IndentingNewLine]", \(Fit[pl, {1, x, x^2, x^3, x^4, x^5, x^6}, x]\)}], "Input"], Cell[BoxData[ \(\(\(0.3157623860476379`\)\(\[InvisibleSpace]\)\) - 0.2220753775654798`\ x - 1.963658718090979`\ x\^2 + 43.52719223284639`\ x\^3 - 501.93419261351386`\ x\^4 + 2634.332116161491`\ x\^5 - 5256.625843576617`\ x\^6\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(6.5\ \( .14/ .00002\)/\((3600\ 24)\)\)], "Input"], Cell[BoxData[ \(0.5266203703703703`\)], "Output"] }, Open ]], Cell[BoxData[ \( (*\ 550\ h\ \ 16 h\ 20 h\ *) \)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(S1[True]\)], "Input"], Cell[BoxData[ \("S1"\)], "Print"], Cell[BoxData[ InterpretationBox[\(0.`\[InvisibleSpace]" "\[InvisibleSpace]True\), SequenceForm[ 0.0, " ", True], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\(0.1`\[InvisibleSpace]" "\[InvisibleSpace]True\), SequenceForm[ 0.10000000000000001, " ", True], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\(0.2`\[InvisibleSpace]" "\[InvisibleSpace]True\), SequenceForm[ 0.20000000000000001, " ", True], Editable->False]], "Print"] }, Open ]], Cell[BoxData[{ \(\(S1s := Block[{\[Delta] = .001, div = 5000, h = .299999, dh = .000002, M1, M2 = Interval[1. ], zero = .2712}, \ \[IndentingNewLine]Print["\"]; \ \[IndentingNewLine]Do[\[IndentingNewLine]ok = True; \[IndentingNewLine]M1 = Interval[{1. + 5\ 10^\((\(-8\))\) i, 1. + 5\ 10^\((\(-8\))\) \((i + 1)\)}]; \[IndentingNewLine]Do[ res = HalfA[{Interval[{zero + i\ \[Delta]/div, zero + \((i + 1)\)\ \[Delta]/div}], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4.5, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && Max[res[\([3, 1, 2]\)]] < 0 && Max[\((res[\([3, 1, 1]\)] + res[\([3, 2, 2]\)])\)^2 - 4 Det[res[\([3]\)]]] < 0, {i, \(-div\), div - 1, 500}]; \[IndentingNewLine]out1 = HalfA[{Interval[zero - \[Delta]], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4, False]; \[IndentingNewLine]out2 = HalfA[{Interval[zero + \[Delta]], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4, False]; \[IndentingNewLine]ok = ok && out1[\([1]\)] && out2[\([1]\)] && Min[out1[\([2, 2]\)]] > 0 && Max[out2[\([2, 2]\)]] < 0; \[IndentingNewLine]Print[ i, "\< \>", ok]\[IndentingNewLine], {i, \(-20\), 19, 5}]];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(fS1[x_] := 0.315762386\[InvisibleSpace] - 0.111037689\ x - 0.49091467\ x\^2 + 5.4408987\ x\^3 - 31.370887\ x\^4 + 82.322875\ x\^5 - 82.1347787\ x\^6;\)\), "\[IndentingNewLine]", \(\(S1[def_] := Block[{\[Delta] = .0004, div = 4000, dh = .00004}, \[IndentingNewLine]Print["\"]; \ \[IndentingNewLine]Do[ ok = True; \[IndentingNewLine]If[def, Do[res = HalfA[{Interval[{fS1[h] + i\ \[Delta]/div, fS1[h] + \((i + 1)\)\ \[Delta]/div}], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 30, 6, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && Max[res[\([3, 1, 2]\)]] < 0, {i, \(-div\), div - 1, 100}], Null]; \[IndentingNewLine]out1 = HalfA[{Interval[fS1[h] - \[Delta]], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 30, 6.2, False]; \[IndentingNewLine]out2 = HalfA[{Interval[fS1[h] + \[Delta]], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 30, 6.2, False]; \[IndentingNewLine]ok = ok && out1[\([1]\)] && out2[\([1]\)] && Min[out1[\([2, 2]\)]] > 0 && Max[out2[\([2, 2]\)]] < 0; \[IndentingNewLine]Print[ h, "\< \>", ok], {h, .0, .28, .001}];];\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(fS1m[x_] := \(-41.574879356136236`\) + 484.3571878257467`\ x - 2433.0717893606798`\ x\^2 + 7057.589279350295`\ x\^3 - 13035.908229731202`\ x\^4 + 15787.641399328304`\ x\^5 - 12175.192055110192`\ x\^6 + 4981.477603030709`\ x\^7 + 327.8412528980341`\ x\^8 - 1739.8021748698598`\ x\^9 + 1076.0895457941758`\ x\^10 - 343.99721755971774`\ x\^11 + 59.16891660039077`\ x\^12 - 4.347672451969145`\ x\^13;\)\[IndentingNewLine]\), "\ \[IndentingNewLine]", \(\(S1m[def_] := Block[{\[Delta] = .0005, width = 10. ^\((\(-8\))\), M2 = 1. , div}, \[IndentingNewLine]Print["\"]; \[IndentingNewLine]Do[ ok = True; \[IndentingNewLine]If[\((M1 > .72)\) && \((M1 < 1.17)\), div = 1000, div = 300]; \[IndentingNewLine]If[ def, Do[x0 = Interval[{fS1m[M1] + \[Delta]\ i/div, fS1m[M1] + \[Delta]\ \((i + 1)\)/ div}]; \[IndentingNewLine]res = HalfA[{x0, Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 30, 4, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && \((Max[res[\([3, 1, 2]\)]] < 0)\), {i, \(-div\), div - 1, 10}], Null]; \[IndentingNewLine]res1 = HalfA[{Interval[fS1m[M1] - \[Delta]], Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 25, 4.6, False]; \[IndentingNewLine]res2 = HalfA[{Interval[fS1m[M1] + \[Delta]], Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 25, 4.6, False]; \[IndentingNewLine]ok = ok && res1[\([1]\)] && res2[\([1]\)] && Max[res2[\([2, 2]\)]] < 0 && Min[res1[\([2, 2]\)]] > 0; \[IndentingNewLine]Print[{M1, ok}], \[IndentingNewLine]{M1, .5, 2. , .01}]];\)\)}], "Input", InitializationCell->True], Cell[BoxData[ \(End\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["S2", "Subsubsection", Background->GrayLevel[0.900008]], Cell[BoxData[{ \(\(pl = Table[{h, x /. FindRoot[\(HalfPoin[x, 0. , 1, 1, h]\)[\([2]\)] \[Equal] 0, \[IndentingNewLine]{x, \(- .44\), \(- .35\)}]}, {h, .0, 1, .01}];\)\), "\[IndentingNewLine]", \(Fit[pl, {1, x, x^2, x^3}, x]\)}], "Input"], Cell[BoxData[{ \(\(fS2[x_] := \(-0.439928\) + 0.033243\ x + 0.00522087\ x\^2 + 0.00115673\ x\^3;\)\), "\[IndentingNewLine]", \(\(S2s := Block[{\[Delta] = .001, div = 1000, h = .299999, dh = .000002, M1, M2 = Interval[1. ], zero = \(- .4294\)}, Print["\"]; \[IndentingNewLine]Do[ ok = True; \[IndentingNewLine]M1 = Interval[{1. + 10^\((\(-7\))\) i, 1. + 10^\((\(-7\))\) \((i + 1)\)}]; \[IndentingNewLine]Do[ res = HalfA[{Interval[{zero + i\ \[Delta]/div, zero + \((i + 1)\)\ \[Delta]/div}], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && Min[res[\([3, 1, 2]\)]] > 0 && Max[\((res[\([3, 1, 1]\)] + res[\([3, 2, 2]\)])\)^2 - 4 Det[res[\([3]\)]]] < 0, {i, \(-div\), div - 1, 100}]; \[IndentingNewLine]out1 = HalfA[{Interval[zero - \[Delta]], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4, False]; \[IndentingNewLine]out2 = HalfA[{Interval[zero + \[Delta]], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4, False]; \[IndentingNewLine]ok = ok && out1[\([1]\)] && out2[\([1]\)] && Max[out1[\([2, 2]\)]] < 0 && Min[out2[\([2, 2]\)]] > 0; \[IndentingNewLine]Print[ i, "\< \>", ok], {i, \(-10\), 9}]];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(S2[def_] := Block[{\[Delta] = .00025, div = 20, dh = .0004}, Print["\"]; \[IndentingNewLine]Do[ ok = True; \[IndentingNewLine]If[def, Do[res = HalfA[{Interval[{fS2[h] + i\ \[Delta]/div, fS2[h] + \((i + 1)\)\ \[Delta]/div}], Interval[0. ]}, \[IndentingNewLine]{Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 20, 3.5, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && Min[res[\([3, 1, 2]\)]] > 0, {i, \(-div\), div - 1}], Null]; \[IndentingNewLine]out1 = HalfA[{Interval[fS2[h] - \[Delta]], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 50, 6, False]; \[IndentingNewLine]out2 = HalfA[{Interval[fS2[h] + \[Delta]], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 50, 6, False]; \[IndentingNewLine]ok = ok && out1[\([1]\)] && out2[\([1]\)] && Max[out1[\([2, 2]\)]] < 0 && Min[out2[\([2, 2]\)]] > 0; \[IndentingNewLine]Print[ h, "\< \>", ok]\[IndentingNewLine], {h, .0, 1, .1}]];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(fS2m[x_] := \(-0.00291\) - 0.47163657\ x + 0.1915079897\ x\^2 - 0.2901520463215257`\ x\^3 + 0.19646214\ x\^4 - 0.059698935\ x\^5 + 0.006974198\ x\^6; S2m[def_] := Block[{\[Delta] = .0009, width = \ 10. ^\((\(-7\))\), M2 = 1. , div = 120}, \[IndentingNewLine]Do[If[M1 > 1.8, div = 170, Null]; ok = True; \[IndentingNewLine]If[def, Do[x0 = Interval[{fS2m[M1] + \[Delta]\ i/div, fS2m[M1] + \[Delta]\ \((i + 1)\)/ div}]; \[IndentingNewLine]res = HalfA[{x0, Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 25, 3.8, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && \((Min[res[\([3, 1, 2]\)]] > 0)\), {i, \(-div\), div - 1, 5}], Null]; \[IndentingNewLine]res1 = HalfA[{Interval[fS2m[M1] - \[Delta]], Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 30, 3.6, False]; \[IndentingNewLine]res2 = HalfA[{Interval[fS2m[M1] + \[Delta]], Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 30, 3.6, False]; \[IndentingNewLine]Print[{M1, ok, res1[\([1]\)], res1[\([2, 2]\)], res2[\([1]\)], res2[\([2, 2]\)]}], \[IndentingNewLine]{M1, .0, .5, .01}]];\)}], \ "Input", InitializationCell->True], Cell[BoxData[{ \(\(graph = {};\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , {x, \(- .4\) m1 - .05, \(- .4\) m1 + .1}]; \[IndentingNewLine]AppendTo[ graph, {m1, x}];\[IndentingNewLine], {m1, .5, 2. , .01}];\)\), "\[IndentingNewLine]", \(\(x =. ;\)\), "\[IndentingNewLine]", \(Fit[graph, {1, \ x\ , x^2, x^3, x^4, x^5, x^6}, x]\)}], "Input"], Cell[BoxData[ \(End\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["L ", "Subsubsection", Background->GrayLevel[0.900008]], Cell[BoxData[{ \(\(Ls := Block[{\[Delta] = .0001, div = 2, h = .29999, dh = .00002, M1, M2 = Interval[ 1. ]}, \[IndentingNewLine]Print["\"]; \ \[IndentingNewLine]Do[\[IndentingNewLine]ok = True; zero = .0487323; \[IndentingNewLine]M1 = Interval[{1. + 10^\((\(-6\))\) j, 1. + 10^\((\(-6\))\) \((j + 1)\)}]; \[IndentingNewLine]Do[ res = HalfA[{Interval[{zero + i\ \[Delta]/div, zero + \((i + 1)\)\ \[Delta]/div}], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 3. , True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && Min[res[\([3, 1, 2]\)]] > 0 && Min[\((res[\([3, 1, 1]\)] + res[\([3, 2, 2]\)])\)^2 - 4 Det[res[\([3]\)]]] > 0, {i, \(-div\), div - 1}]; \[IndentingNewLine]out1 = HalfA[{Interval[zero - \[Delta]], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4, False]; \[IndentingNewLine]out2 = HalfA[{Interval[zero + \[Delta]], Interval[0. ]}, {M1, M2}, Interval[{h, h + dh}], 30, 4, False]; \[IndentingNewLine]ok = ok && out1[\([1]\)] && out2[\([1]\)] && Min[out2[\([2, 2]\)]] > 0 && Max[out1[\([2, 2]\)]] < 0; \[IndentingNewLine]Print[ j, "\< \>", ok]\[IndentingNewLine], {j, \(-10\), 9}]];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(fLm[x_] := \(-4956.5495880717\) + 48949.415066511\ x - 217113.4293986\ x\^2 + 569528.5197618\ x\^3 - 978391.3559863\ x\^4 + 1.1500743572324*^6\ x\^5 - 936768.61024923\ x\^6 + 522067.566952 x\^7 - 190515.2886975 x\^8 + 41108.1614863\ x\^9 - 3982.73784599 x\^10;\)\), "\[IndentingNewLine]", \(\(Lm[def_] := Block[{\[Delta] = .0001, width = 10. ^\((\(-5\))\), M2 = 1. , div = 2}, \[IndentingNewLine]Do[ ok = True; \[IndentingNewLine]If[def, Do[x0 = Interval[{fLm[M1] + \[Delta]\ i/div, fLm[M1] + \[Delta]\ \((i + 1)\)/ div}]; \[IndentingNewLine]res = HalfA[{x0, Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 50, 2, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && Min[res[\([3, 1, 2]\)]] > 0, {i, \(-div\), div - 1}], Null]; \[IndentingNewLine]res1 = HalfA[{Interval[fLm[M1] - \[Delta]], Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 50, 2.4, False]; \[IndentingNewLine]res2 = HalfA[{Interval[fLm[M1] + \[Delta]], Interval[0. ]}, {Interval[{M1, M1 + width}], Interval[M2]}, Interval[ .3], 50, 2.1, False]; \[IndentingNewLine]Print[ M1, "\< \>", \(\(ok && res1[\([1]\)]\) && \((res1[\([2, 2]\)] < 0)\)\) && res2[\([1]\)] && \((res2[\([2, 2]\)] > 0)\)], \[IndentingNewLine]{M1, .8, 1.3, .05}]];\)\[IndentingNewLine]\), "\[IndentingNewLine]", \(\(fL[x_] := 0.004211937 + 0.48222802136\ x - 6.380933773\ x\^2 + 75.892622876\ x\^3 - 610.3549445\ x\^4 + 3305.8152457\ x\^5 - 12179.4838735\ x\^6 + 30508.61849\ x\^7 - 50813.218311\ x\^8 + 52633.664\ x\^9 - 27527.3442721\ x\^10 - 89.535844141\ x\^11 + 5514.005414 x\^12 + 579.953994\ x\^13 - 990.673304258\ x\^14 - 529.2037065\ x\^15 - 65.1681811664\ x\^16 + 75.371141329\ x\^17 + 68.4138686 x\^18 + 36.981639385\ x\^19 + 15.9614499604\ x\^20;\)\), "\[IndentingNewLine]", \(\(L := Block[{\[Delta] = .0002, div = 5, dh = .0002}, \[IndentingNewLine]Print["\"]; \ \[IndentingNewLine]Do[ok = True; \ Do[res = HalfA[{Interval[{fL[h] + i\ \[Delta]/div, fL[h] + \((i + 1)\)\ \[Delta]/div}], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 30, 1.6, True]; \[IndentingNewLine]ok = ok && res[\([1]\)] && Min[res[\([3, 1, 2]\)]] > 0, {i, \(-div\), div - 1}]; out1 = HalfA[{Interval[fL[h] - \[Delta]], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 50, 5. , False]; \[IndentingNewLine]out2 = HalfA[{Interval[fL[h] + \[Delta]], Interval[0. ]}, {Interval[1. ], Interval[1. ]}, Interval[{h, h + dh}], 50, 5. , False]; \[IndentingNewLine]ok = ok && out1[\([1]\)] && out2[\([1]\)] && Max[out1[\([2, 2]\)]] < 0 && Min[out2[\([2, 2]\)]] > 0; \[IndentingNewLine]Print[ h, "\< \>", ok]\[IndentingNewLine], {h, .01, .8, .1}]];\)\)}], "Input", InitializationCell->True], Cell[BoxData[{ \(\(graph = {};\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , h]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .001, .01}]; \ \[IndentingNewLine]AppendTo[ graph, {h, x}];\[IndentingNewLine], {h, .01, .02, .001}];\)\), "\ \[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , h]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .01, .03}]; \ \[IndentingNewLine]AppendTo[ graph, {h, x}];\[IndentingNewLine], {h, .02, .2, .002}];\)\), "\ \[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , h]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .038, .05}]; \ \[IndentingNewLine]AppendTo[ graph, {h, x}];\[IndentingNewLine], {h, .2, .4, .002}];\)\), "\ \[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , h]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .05, .06}]; \ \[IndentingNewLine]AppendTo[ graph, {h, x}];\[IndentingNewLine], {h, .4, .6, .002}];\)\), "\ \[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , h]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .07, .08}]; \ \[IndentingNewLine]AppendTo[ graph, {h, x}];\[IndentingNewLine], {h, .6, .8, .002}];\)\)}], "Input"], Cell[BoxData[ \(x =. ; xx = Fit[graph, Table[x^i, {i, 0, 20}], x]; fL[a_] := xx /. x \[Rule] a;\)], "Input"], Cell[BoxData[{ \(\(x =. ;\)\), "\[IndentingNewLine]", \(xx = Fit[graph, Table[x^i, {i, 0, 10}], x]; fLm[a_] := xx /. x \[Rule] a;\)}], "Input"], Cell[BoxData[{ \(\(graph = {};\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .1, .12}]; \ \[IndentingNewLine]AppendTo[ graph, {m1, x}];\[IndentingNewLine], {m1, .8, .87, .01}];\)\), "\ \[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .08, .1}]; \ \[IndentingNewLine]AppendTo[ graph, {m1, x}];\[IndentingNewLine], {m1, .88, .92, .01}];\)\), "\ \[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .04, .06}]; \ \[IndentingNewLine]AppendTo[graph, {m1, x}];\[IndentingNewLine], {m1, .93, 1. , .01}];\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .0, .04}]; \ \[IndentingNewLine]AppendTo[graph, {m1, x}];\[IndentingNewLine], {m1, 1.01, 1.05, .01}];\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .0, .02}]; \ \[IndentingNewLine]AppendTo[graph, {m1, x}];\[IndentingNewLine], {m1, 1.06, 1.1, .01}];\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .05\), .0}]; \ \[IndentingNewLine]AppendTo[graph, {m1, x}];\[IndentingNewLine], {m1, 1.11, 1.2, .01}];\)\), "\[IndentingNewLine]", \(\(Do[ x = x /. FindRoot[\(HalfPoin[x, 0. , m1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .11\), \(- .06\)}]; \ \[IndentingNewLine]AppendTo[graph, {m1, x}];\[IndentingNewLine], {m1, 1.21, 1.3, .01}];\)\), "\[IndentingNewLine]", \(\(ListPlot[graph];\)\)}], "Input"], Cell[BoxData[ \(End\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Pictures", "Subsubsection", Background->GrayLevel[0.666667]], Cell[BoxData[ \(\(Plot[\(HalfPoin[x, 0. , 1, 1, .1]\)[\([2]\)], \[IndentingNewLine]{x, .2, .4}];\)\)], \ "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(FindRoot[\(HalfPoin[x, 0. , .8, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .12, .13}]\)], "Input"], Cell[BoxData[ \({x \[Rule] 0.12870658673625612`}\)], "Output"] }, Open ]], Cell[BoxData[ \(\(Plot[fS1[ .5 h], {h, 0, .28}, AxesLabel \[Rule] {"\", "\"}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[fS2[ .5 h], {h, 0, 1}, AxesLabel \[Rule] {"\", "\"}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[fL[ .5 h], {h, 0, .8}, AxesLabel \[Rule] {"\", "\"}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[fS1m[m], {m, .5, 2}, AxesLabel \[Rule] {\*"\"\<\!\(M\_1\)\>\"", "\"}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[fS2m[m], {m, .5, 2}, AxesLabel \[Rule] {\*"\"\<\!\(M\_1\)\>\"", "\"}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[fLm[m], {m, .8, 1.3}, AxesLabel \[Rule] {\*"\"\<\!\(M\_1\)\>\"", "\"}];\)\)], "Input"], Cell[BoxData[{ \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , .8, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .12, .13}];\)\), "\ \[IndentingNewLine]", \(\(p1 = OrbitPlot[x, .15, .8, 1. , 2.3];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , .8, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .35\), \(- .34\)}];\)\), "\ \[IndentingNewLine]", \(\(p2 = OrbitPlot[x, .15, .8, 1. , .55];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , .8, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .35, .36}];\)\), "\ \[IndentingNewLine]", \(\(p3 = OrbitPlot[x, .15, .8, 1. , 1.5];\)\), "\[IndentingNewLine]", \(\(Show[p1, p2, p3, \ AspectRatio \[Rule] Automatic, AxesLabel \[Rule] {"\", "\"}];\)\[IndentingNewLine]\)}], \ "Input"], Cell[BoxData[{ \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .046, .049}];\)\), "\ \[IndentingNewLine]", \(\(p1 = OrbitPlot[x, .15, 1, 1. , 2.3];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .35\), \(- .34\)}];\)\), "\ \[IndentingNewLine]", \(\(p2 = OrbitPlot[x, .15, 1, 1. , .55];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .35, .36}];\)\), "\ \[IndentingNewLine]", \(\(p3 = OrbitPlot[x, .15, 1, 1. , 2];\)\), "\[IndentingNewLine]", \(\(Show[p1, p2, p3, \ AspectRatio \[Rule] Automatic, AxesLabel \[Rule] {"\", "\"}];\)\[IndentingNewLine]\)}], \ "Input"], Cell[BoxData[{ \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1.3, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .11\), \(- .10\)}];\)\), "\ \[IndentingNewLine]", \(\(p1 = OrbitPlot[x, .15, 1.3, 1. , 2.3];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1.3, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .35\), \(- .34\)}];\)\), "\ \[IndentingNewLine]", \(\(p2 = OrbitPlot[x, .15, 1.3, 1. , .55];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1.3, 1. , .15]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .35, .36}];\)\), "\ \[IndentingNewLine]", \(\(p3 = OrbitPlot[x, .15, 1.3, 1. , 2];\)\), "\[IndentingNewLine]", \(\(Show[p1, p2, p3, \ AspectRatio \[Rule] Automatic, AxesLabel \[Rule] {"\", "\"}];\)\[IndentingNewLine]\)}], \ "Input"], Cell[BoxData[{ \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .005]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .001, .01}];\)\), "\ \[IndentingNewLine]", \(\(p1 = OrbitPlot[x, .005, 1, 1. , 2.3];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .005]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .44\), \(- .43\)}];\)\), "\ \[IndentingNewLine]", \(\(p2 = OrbitPlot[x, .005, 1, 1. , .55];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .005]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .3, .32}];\)\), "\ \[IndentingNewLine]", \(\(p3 = OrbitPlot[x, .005, 1, 1. , 2];\)\), "\[IndentingNewLine]", \(\(Show[p1, p2, p3, \ AspectRatio \[Rule] Automatic, AxesLabel \[Rule] {"\", "\"}];\)\[IndentingNewLine]\)}], \ "Input"], Cell[BoxData[{ \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .4]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .015, .017}];\)\), "\ \[IndentingNewLine]", \(\(p1 = OrbitPlot[x, .4, 1, 1. , 2.6];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .4]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, \(- .44\), \(- .43\)}];\)\), "\ \[IndentingNewLine]", \(\(p2 = OrbitPlot[x, .4, 1, 1. , 1];\)\), "\[IndentingNewLine]", \(\(x = x /. FindRoot[\(HalfPoin[x, 0. , 1, 1. , .4]\)[\([2]\)] \[Equal] 0. , \[IndentingNewLine]{x, .3, .32}];\)\), "\ \[IndentingNewLine]", \(\(p3 = OrbitPlot[x, .4, 1, 1. , 3];\)\), "\[IndentingNewLine]", \(\(Show[p1, p2, p3, \ AspectRatio \[Rule] Automatic, AxesLabel \[Rule] {"\", "\"}];\)\[IndentingNewLine]\)}], \ "Input"], Cell[BoxData[ \(End\)], "Input"] }, Closed]], Cell[BoxData[ \(End\)], "Input"] }, Open ]] }, FrontEndVersion->"4.0 for X", ScreenRectangle->{{0, 1024}, {0, 768}}, AutoGeneratedPackage->Automatic, CellGrouping->Manual, WindowSize->{675, 600}, WindowMargins->{{117, Automatic}, {Automatic, 14}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PrintingMargins"->{{54, 54}, {72, 72}}, "PaperSize"->{597.562, 842.375}, "PaperOrientation"->"Portrait", "PrintCellBrackets"->False, "PrintRegistrationMarks"->True, "PrintMultipleHorizontalPages"->False, "PostScriptOutputFile":>FrontEnd`FileName[{$RootDirectory, "home", "gianni"}, \ "pippo.ps", CharacterEncoding -> "ISO8859-1"], "Magnification"->1} ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1717, 49, 95, 3, 174, "Title"], Cell[1815, 54, 126, 6, 125, "Subsubtitle"], Cell[CellGroupData[{ Cell[1966, 64, 96, 2, 61, "Subsection"], Cell[2065, 68, 128, 3, 32, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[2230, 76, 142, 3, 45, "Subsubsection"], Cell[2375, 81, 1420, 28, 251, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[3832, 114, 114, 3, 45, "Subsection"], Cell[CellGroupData[{ Cell[3971, 121, 2933, 52, 555, "Input", InitializationCell->True], Cell[6907, 175, 183, 3, 70, "Message"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[7139, 184, 137, 3, 45, "Subsection"], Cell[7279, 189, 5818, 108, 398, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[13134, 302, 136, 3, 45, "Subsubsection"], Cell[CellGroupData[{ Cell[13295, 309, 23322, 423, 5045, "Input", InitializationCell->True], Cell[36620, 734, 186, 3, 70, "Message"], Cell[36809, 739, 180, 3, 70, "Message"], Cell[36992, 744, 185, 3, 70, "Message"], Cell[37180, 749, 181, 3, 70, "Message"], Cell[37364, 754, 193, 3, 70, "Message"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[37606, 763, 95, 1, 56, "Subsubsection"], Cell[37704, 766, 53, 1, 27, "Input"], Cell[37760, 769, 110, 2, 27, "Input", InitializationCell->True], Cell[CellGroupData[{ Cell[37895, 775, 62, 1, 58, "Subsubsection"], Cell[37960, 778, 626, 13, 139, "Input"], Cell[CellGroupData[{ Cell[38611, 795, 333, 7, 59, "Input"], Cell[38947, 804, 264, 4, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[39248, 813, 69, 1, 27, "Input"], Cell[39320, 816, 53, 1, 27, "Output"] }, Open ]], Cell[39388, 820, 65, 1, 27, "Input"], Cell[CellGroupData[{ Cell[39478, 825, 41, 1, 27, "Input"], Cell[39522, 828, 37, 1, 23, "Print"], Cell[39562, 831, 156, 3, 23, "Print"], Cell[39721, 836, 173, 3, 23, "Print"], Cell[39897, 841, 173, 3, 23, "Print"] }, Open ]], Cell[40085, 847, 5382, 94, 937, "Input", InitializationCell->True], Cell[45470, 943, 36, 1, 27, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[45543, 949, 62, 1, 44, "Subsubsection"], Cell[45608, 952, 302, 6, 59, "Input"], Cell[45913, 960, 4583, 79, 753, "Input", InitializationCell->True], Cell[50499, 1041, 518, 10, 139, "Input"], Cell[51020, 1053, 36, 1, 27, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[51093, 1059, 62, 1, 44, "Subsubsection"], Cell[51158, 1062, 5243, 91, 911, "Input", InitializationCell->True], Cell[56404, 1155, 1508, 35, 347, "Input"], Cell[57915, 1192, 117, 2, 27, "Input"], Cell[58035, 1196, 157, 3, 43, "Input"], Cell[58195, 1201, 2267, 48, 491, "Input"], Cell[60465, 1251, 36, 1, 27, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[60538, 1257, 68, 1, 44, "Subsubsection"], Cell[60609, 1260, 133, 3, 43, "Input"], Cell[CellGroupData[{ Cell[60767, 1267, 146, 2, 43, "Input"], Cell[60916, 1271, 66, 1, 27, "Output"] }, Open ]], Cell[60997, 1275, 116, 2, 27, "Input"], Cell[61116, 1279, 113, 2, 27, "Input"], Cell[61232, 1283, 114, 2, 27, "Input"], Cell[61349, 1287, 126, 2, 27, "Input"], Cell[61478, 1291, 126, 2, 27, "Input"], Cell[61607, 1295, 127, 2, 27, "Input"], Cell[61737, 1299, 933, 18, 187, "Input"], Cell[62673, 1319, 921, 18, 187, "Input"], Cell[63597, 1339, 941, 18, 187, "Input"], Cell[64541, 1359, 925, 18, 187, "Input"], Cell[65469, 1379, 911, 18, 187, "Input"], Cell[66383, 1399, 36, 1, 27, "Input"] }, Closed]], Cell[66434, 1403, 36, 1, 24, "Input"] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************) ---------------0312120425797 Content-Type: application/postscript; name="arioli.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="arioli.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: r3bb.dvi %%Pages: 12 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX10 CMCSC10 CMR8 CMBX8 CMR10 CMMI10 CMMI7 CMSY10 %%+ CMR7 CMEX10 CMR5 CMMI5 CMTI8 CMSY7 CMTI10 MSBM10 Courier CMMI8 CMR6 %%+ CMTT8 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips r3bb -oarioli.ps %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2003.12.12:1119 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: f7b6d320.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmb10 cmbx10 cmbx12 cmbx5 cmbx6 cmbx7 cmbx8 cmbx9 cmbxsl10 % cmdunh10 cmr10 cmr12 cmr17cmr6 cmr7 cmr8 cmr9 cmsl10 cmsl12 cmsl8 % cmsl9 cmss10cmss12 cmss17 cmss8 cmss9 cmssbx10 cmssdc10 cmssi10 % cmssi12 cmssi17 cmssi8cmssi9 cmssq8 cmssqi8 cmvtt10 % /TeXf7b6d320Encoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /exclamdown /equal /questiondown /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: 0ef0afca.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmr5 % /TeX0ef0afcaEncoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: aae443f0.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmmi10 cmmi12 cmmi5 cmmi6 cmmi7 cmmi8 cmmi9 cmmib10 % /TeXaae443f0Encoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /omega /epsilon /theta1 /pi1 /rho1 /sigma1 /phi1 /arrowlefttophalf /arrowleftbothalf /arrowrighttophalf /arrowrightbothalf /arrowhookleft /arrowhookright /triangleright /triangleleft /zerooldstyle /oneoldstyle /twooldstyle /threeoldstyle /fouroldstyle /fiveoldstyle /sixoldstyle /sevenoldstyle /eightoldstyle /nineoldstyle /period /comma /less /slash /greater /star /partialdiff /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /flat /natural /sharp /slurbelow /slurabove /lscript /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /dotlessi /dotlessj /weierstrass /vector /tie /psi /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /alpha /beta /gamma /delta /epsilon1 /zeta /eta /theta /iota /kappa /lambda /mu /nu /xi /pi /rho /sigma /tau /upsilon /phi /chi /psi /tie /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: bbad153f.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmsy10 cmsy5 cmsy6 cmsy7 cmsy8 cmsy9 % /TeXbbad153fEncoding [ /minus /periodcentered /multiply /asteriskmath /divide /diamondmath /plusminus /minusplus /circleplus /circleminus /circlemultiply /circledivide /circledot /circlecopyrt /openbullet /bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal /precedesequal /followsequal /similar /approxequal /propersubset /propersuperset /lessmuch /greatermuch /precedes /follows /arrowleft /arrowright /arrowup /arrowdown /arrowboth /arrownortheast /arrowsoutheast /similarequal /arrowdblleft /arrowdblright /arrowdblup /arrowdbldown /arrowdblboth /arrownorthwest /arrowsouthwest /proportional /prime /infinity /element /owner /triangle /triangleinv /negationslash /mapsto /universal /existential /logicalnot /emptyset /Rfractur /Ifractur /latticetop /perpendicular /aleph /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /union /intersection /unionmulti /logicaland /logicalor /turnstileleft /turnstileright /floorleft /floorright /ceilingleft /ceilingright /braceleft /braceright /angbracketleft /angbracketright /bar /bardbl /arrowbothv /arrowdblbothv /backslash /wreathproduct /radical /coproduct /nabla /integral /unionsq /intersectionsq /subsetsqequal /supersetsqequal /section /dagger /daggerdbl /paragraph /club /diamond /heart /spade /arrowleft /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /minus /periodcentered /multiply /asteriskmath /divide /diamondmath /plusminus /minusplus /circleplus /circleminus /.notdef /.notdef /circlemultiply /circledivide /circledot /circlecopyrt /openbullet /bullet /equivasymptotic /equivalence /reflexsubset /reflexsuperset /lessequal /greaterequal /precedesequal /followsequal /similar /approxequal /propersubset /propersuperset /lessmuch /greatermuch /precedes /follows /arrowleft /spade /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: 74afc74c.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmbxti10 cmff10 cmfi10 cmfib8 cmti10 cmti12 cmti7 cmti8cmti9 cmu10 % /TeX74afc74cEncoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /exclam /quotedblright /numbersign /sterling /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /exclamdown /equal /questiondown /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /quotedblleft /bracketright /circumflex /dotaccent /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /endash /emdash /hungarumlaut /tilde /dieresis /suppress /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /ff /fi /fl /ffi /ffl /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /suppress /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: 8r.enc % File 8r.enc as of 2002-03-12 for PSNFSS 9 % % This is the encoding vector for Type1 and TrueType fonts to be used % with TeX. This file is part of the PSNFSS bundle, version 9 % % Authors: S. Rahtz, P. MacKay, Alan Jeffrey, B. Horn, K. Berry, W. Schmidt % % Idea is to have all the characters normally included in Type 1 fonts % available for typesetting. This is effectively the characters in Adobe % Standard Encoding + ISO Latin 1 + extra characters from Lucida + Euro. % % Character code assignments were made as follows: % % (1) the Windows ANSI characters are almost all in their Windows ANSI % positions, because some Windows users cannot easily reencode the % fonts, and it makes no difference on other systems. The only Windows % ANSI characters not available are those that make no sense for % typesetting -- rubout (127 decimal), nobreakspace (160), softhyphen % (173). quotesingle and grave are moved just because it's such an % irritation not having them in TeX positions. % % (2) Remaining characters are assigned arbitrarily to the lower part % of the range, avoiding 0, 10 and 13 in case we meet dumb software. % % (3) Y&Y Lucida Bright includes some extra text characters; in the % hopes that other PostScript fonts, perhaps created for public % consumption, will include them, they are included starting at 0x12. % % (4) Remaining positions left undefined are for use in (hopefully) % upward-compatible revisions, if someday more characters are generally % available. % % (5) hyphen appears twice for compatibility with both ASCII and Windows. % % (6) /Euro is assigned to 128, as in Windows ANSI % /TeXBase1Encoding [ % 0x00 (encoded characters from Adobe Standard not in Windows 3.1) /.notdef /dotaccent /fi /fl /fraction /hungarumlaut /Lslash /lslash /ogonek /ring /.notdef /breve /minus /.notdef % These are the only two remaining unencoded characters, so may as % well include them. /Zcaron /zcaron % 0x10 /caron /dotlessi % (unusual TeX characters available in, e.g., Lucida Bright) /dotlessj /ff /ffi /ffl /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef % very contentious; it's so painful not having quoteleft and quoteright % at 96 and 145 that we move the things normally found there down to here. /grave /quotesingle % 0x20 (ASCII begins) /space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash % 0x30 /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question % 0x40 /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O % 0x50 /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore % 0x60 /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o % 0x70 /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /.notdef % rubout; ASCII ends % 0x80 /Euro /.notdef /quotesinglbase /florin /quotedblbase /ellipsis /dagger /daggerdbl /circumflex /perthousand /Scaron /guilsinglleft /OE /.notdef /.notdef /.notdef % 0x90 /.notdef /.notdef /.notdef /quotedblleft /quotedblright /bullet /endash /emdash /tilde /trademark /scaron /guilsinglright /oe /.notdef /.notdef /Ydieresis % 0xA0 /.notdef % nobreakspace /exclamdown /cent /sterling /currency /yen /brokenbar /section /dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen % Y&Y (also at 45); Windows' softhyphen /registered /macron % 0xD0 /degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered /cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown % 0xC0 /Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla /Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis % 0xD0 /Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply /Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls % 0xE0 /agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla /egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis % 0xF0 /eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide /oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis ] def %%EndProcSet %%BeginProcSet: 09fbbfac.enc % Thomas Esser, Dec 2002. public domain % % Encoding for: % cmsltt10 cmtt10 cmtt12 cmtt8 cmtt9 /TeX09fbbfacEncoding [ /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /visiblespace /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright /parenleft /parenright /asterisk /plus /comma /hyphen /period /slash /zero /one /two /three /four /five /six /seven /eight /nine /colon /semicolon /less /equal /greater /question /at /A /B /C /D /E /F /G /H /I /J /K /L /M /N /O /P /Q /R /S /T /U /V /W /X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore /quoteleft /a /b /c /d /e /f /g /h /i /j /k /l /m /n /o /p /q /r /s /t /u /v /w /x /y /z /braceleft /bar /braceright /asciitilde /dieresis /visiblespace /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /space /Gamma /Delta /Theta /Lambda /Xi /Pi /Sigma /Upsilon /Phi /Psi /.notdef /.notdef /Omega /arrowup /arrowdown /quotesingle /exclamdown /questiondown /dotlessi /dotlessj /grave /acute /caron /breve /macron /ring /cedilla /germandbls /ae /oe /oslash /AE /OE /Oslash /visiblespace /dieresis /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef ] def %%EndProcSet %%BeginProcSet: texps.pro %! TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0 ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{ pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type /nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[ exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if} forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def end %%EndProcSet %%BeginProcSet: special.pro %! TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N /vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N /rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N /@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{ /hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B /@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{ /urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known {userdict/md get type/dicttype eq{userdict begin md length 10 add md maxlength ge{/md md dup length 20 add dict copy def}if end md begin /letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{ itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack} if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1 -1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{ noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop 90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr 1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr 2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4 -1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{ Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale }if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState save N userdict maxlength dict begin/magscale true def normalscale currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts /psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def @MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N /@beginspecial{SDict begin/SpecialSave save N gsave normalscale currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N} N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N /setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{ pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B /rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1 setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc savematrix setmatrix}N end %%EndProcSet %%BeginFont: CMTT8 %!PS-AdobeFont-1.1: CMTT8 1.0 %%CreationDate: 1991 Aug 20 16:46:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-5 -232 545 699}readonly def /UniqueID 5000830 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA17D1AFFF95F4224CF7ECEE45C BFB7C8C77C22A01C345078D28D3ECBF804CDC2FE5025FA0D05CCC5EFC0C4F87E CBED13DDDF8F34E404F471C6DD2E43331D73E89BBC71E7BF889F6293793FEF5A C9DD3792F032E37A364C70914843F7AA314413D022AE3238730B420A7E9D0CF5 D0E24F501451F9CDECE10AF7E14FF15C4F12F3FCA47DD9CD3C7AEA8D1551017D 23131C09ED104C052054520268A4FA3C6338BA6CF14C3DE3BAF2EA35296EE3D8 D6496277E11DFF6076FE64C8A8C3419FA774473D63223FFA41CBAE609C3D976B 93DFB4079ADC7C4EF07303F93808DDA9F651F61BCCF79555059A44CBAF84A711 6D98083CEF58230D54AD486C74C4A257FC703ACF918219D0A597A5F680B606E4 EF94ADF8BF91A5096A806DB64EC96636A98397D22A74932EB7346A9C4B5EE953 CB3C80AA634BFC28AA938C704BDA8DC4D13551CCFE2B2784BE8BF54502EBA9AF D49B79237B9C56310550BC30E9108BB06EAC755D6AA4E688EFE2A0AAB17F20FE 00CD0BFF1B9CB6BDA0FA3A29A3117388B6686657A150CE6421FD5D420F4F7FB5 B0DAA1BA19D638676E9CF159AC7325EF17B9F74E082BEF75E10A31C7011C0FFA 99B797CE549B5C45238DD0FADD6B99D233AC69282DF0D91EA2DBD08CE0083904 A6D968D5AE3BD159D01BDFF42D16111BC0A517C66B43972080D9DD4F3B9AE7FB 11B035CE715C1218B2D779761D8D7E9DEBE277531BD58F313EBD27E33BEF9DC5 50C7821A8BBC3B9FDF899D7EAA0B94493B97AFEAC503EB5ED7A7AB663529DD50 29E1FF043619C3969739047DCBE0806C6E7ED2CEE445EBA23109D4EA1AF26BFE 9CEFB8F80C4E811C7CB9E4F964F4A095E6456D80CFAB4E4FEBC91333683E769C BF12AB4D9AFF9738E8F5FD33E5E64D2DA80D00B697A2DB83F44297B501AAD801 C73389133F28E171C5F7E84A39D16BCF374986988FA525A8F0D6A7024E39331B CF80BB9CB9682EF2C3899C12B3D8F196F45636CBFB6B23FA38222B2B3D667736 DC4E61B7CDB4BA8F06ECAD6E279560B467C1C808146FF3B2EDB14ED971A023F5 2E2F1306654A905BAF872411E832B345DD3BCBE7D4A30B128B2A06BA7ACD95E1 A451AF157431B3AC6B429A8883ECB107615C9B79C0866560AF39B2D4 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-24 -250 1110 750}readonly def /UniqueID 5087383 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D251491EBF65A98C9FE2B1CF8D725A70281949 8F4AFFE638BBA6B12386C7F32BA350D62EA218D5B24EE612C2C20F43CD3BFD0D F02B185B692D7B27BEC7290EEFDCF92F95DDEB507068DE0B0B0351E3ECB8E443 E611BE0A41A1F8C89C3BC16B352C3443AB6F665EAC5E0CC4229DECFC58E15765 424C919C273E7FA240BE7B2E951AB789D127625BBCB7033E005050EB2E12B1C8 E5F3AD1F44A71957AD2CC53D917BFD09235601155886EE36D0C3DD6E7AA2EF9C C402C77FF1549E609A711FC3C211E64E8F263D60A57E9F2B47E3480B978AAF63 868AEA25DA3D5413467B76D2F02F8097D2841FE9D089F27B314C2B7095381853 3E28E2A3EA5E789DA4343DB3BE83B18FE9D7725C3A96CFD8038B3518C10A68BC 9A67AF6D30543F6C7CBF40C7875E5E2AE8A0AA5E69E169CDDEB9958F11724338 CFDE66C32301830F03E70A616154272F44852FA676325FC549F4F72A9258C6E9 BC0300564DE4476FC6E96A65C301EFF7827822A1913CD5A9134F3D7D08B53C4F 96C88207893E4C13BE3851571DC30259CE9E5E4C8411D7A846487981FC98C842 39CA32CE6FAF47A5BE62763084F2C685A03485461C76113177197A13A04D72C0 7331A7877AE53B0C72912A2921B4EE13A0DDB78AB4FFDD01D4D5561CE5D50047 1B9538207AB1BBA0D3284F10BB08FB2BB869721475FE64741612EE4FAA3D6562 AE017C988C91D4A4633C853D3EF2833F860221D2EA75F311FF475CEF44332F64 1AC85A32292359626FB5A39842A7636E9364BF6C0013040858EB300D5DD225C9 4D45DA6D7560F2A9624EDF15CABE9411CB4C109BEC7315EB37A7468481937181 F2BF275A13BF54C7A9633924C00DD150E2FC3C94BBCFDA 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI8 %!PS-AdobeFont-1.1: CMTI8 1.0 %%CreationDate: 1991 Aug 18 21:07:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-35 -250 1190 750}readonly def /UniqueID 5000826 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 32 /parenleftBigg put dup 33 /parenrightBigg put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 990CD249827D9648574955F61BAAA11263A91B6C3D47A5190165B0C25ABF6D3E 6EC187E4B05182126BB0D0323D943170B795255260F9FD25F2248D04F45DFBFB DEF7FF8B19BFEF637B210018AE02572B389B3F76282BEB29CC301905D388C721 59616893E774413F48DE0B408BC66DCE3FE17CB9F84D205839D58014D6A88823 D9320AE93AF96D97A02C4D5A2BB2B8C7925C4578003959C46E3CE1A2F0EAC4BF 8B9B325E46435BDE60BC54D72BC8ACB5C0A34413AC87045DC7B84646A324B808 6FD8E34217213E131C3B1510415CE45420688ED9C1D27890EC68BD7C1235FAF9 1DAB3A369DD2FC3BE5CF9655C7B7EDA7361D7E05E5831B6B8E2EEC542A7B38EE 03BE4BAC6079D038ACB3C7C916279764547C2D51976BABA94BA9866D79F13909 95AA39B0F03103A07CBDF441B8C5669F729020AF284B7FF52A29C6255FCAACF1 74109050FBA2602E72593FBCBFC26E726EE4AEF97B7632BC4F5F353B5C67FED2 3EA752A4A57B8F7FEFF1D7341D895F0A3A0BE1D8E3391970457A967EFF84F6D8 47750B1145B8CC5BD96EE7AA99DDC9E06939E383BDA41175233D58AD263EBF19 AFC27E4A7E07D09FB08355F6EA74E530B0743143F2A871732D62D80F35B19FD2 C7FDF08105847F13D50934419AC647CBA71DF74F4531DC02BBDA22AEEA3FBBBB 407E0ACC52BDC60D01A29407CC4F93EB8BF6D4813E9BA858D54F38918AC82720 4956D50291F0546E50FCAFA6DBD0099123F5ECD4AB338DB310DB4CAE11337A89 8ED99B6F483940C97544F888EAF0CBEB11094A13C073D0061808662A04A82BA0 AD35E8782F854AF66C20C0FEF18D0ECDD1646321B93D327E53D88CA0E825FA95 05AA57BD70E52EA0396B20ECDCB589689BC5EE0D3592A8CF6D7BFB179C014570 6C2C01AD768D8F4A5F27ED79FECC719C556F53F878BFD8F7E39B0554072E039A 24569CD4DB9CD7EED07979ADBB32CF8B31A34EE1D6300ECD62C790841F3EFB65 EE3C2158F1DD2E54039F1D8DCC9D4065F9B86F9EDA7271E670BFDBB7A2EE8C78 B47E0A09F38FD8D6917B85933461BBB19AD706D235817E5612433BC4983C0FA7 AF49D700B4F936A769B5FCBBD60B1927AAD38ADED99582E848174BE7F6DD9ED6 0841C9C31FB06A06ABEE9A6A877FE80CF9AC1C482A6CBFA450C9F927A20430FA 6C6D0BC4EE617618D596C0EC475A0C3E36A25DA34FEF9F584D9A6BDF838C80DD 4B9D07B84926EE873D1AA31826D66BB93B2F4FE7B06F6E641DC49FC20AB6F52A F6AC1ECDB744E03BB1E06E81D25D0CCDA4A22C0F11043C81110B2F7D966B6D30 C2C1107D4FA6B413420313C129F83B5E946258EF7E5CD04C42C409BEAD91E661 D15E9A035AE31AC62E2394AEFF59444CF214F6EFF686F333B06B7B9EE253BB39 3F660949B193ED6A030ABB318E368FAF73D55256A6AB1A686EC2173D7F8AA649 66A4D29C5CAAC78D662E7FB5D0BE169F2E3D3A46FECAE553B922E7CD27655A2A D233F5AB1AFF3C125483C21E060196A0D2D9F02AB57CFD178E19A491EED373C4 0A29394846A9C9170C71A9435838C891B3CDFC54A6CBD1AFE0EB614F0E56FFEC AB67BB568F4B4C618C1396EA5B390ECB49245E5E13396618626333E444EFC028 105061D0E0EF77D05C2A15B4F3EE01948D5B894928EFE3E14758A11CD48B4104 53F244B0A585C1C2011B2F08F9A2A0F5C89D215BC2315D84026F060A61D75422 959BA6F31DD9210846FA9E5E28F5B35DAA2DA7E53CE506D276C39075909AFACB 845746F74330C5602D3EFDF144F614761AA3C01378A8E521A244453270260FE8 F23EFB4448AA44AA59E02E619D91A32751B579CA22E07C5C312C030139CA5412 A81894C7CA76DC9AD1D6DB818417723EE2104F048B5EF98BEEF072478A492662 94439E7AD79B88D1C12E8E007CB4EDF601972B287AD56D134778D9447B0D69B5 47D99B068066C74C656BFFF0238980ABCC09C85856177AC217D984326847777F 1472E3B33EA7DC3EDBCAF966E9134214D35EE394082B2AF65BC0209DCED5BE74 221B79C6FD09B93AE5B782684C60B54901BFF59A99EE590522D1965FEA3431FC E512A6619083CF46AA4A51AAB8BE759550E611D42F506923F29BD5CB48BEF8AC 182B5D204D7C05DC7433C8F6FF0D74710683B5E4B763FAF3F3D65A9C350CF1A2 A3494B26D95993F3EED4FCAE02452234B23E475EFD0A04809881515F231D4161 66CDFCA87E51DA5DF15C61881E6C49414322BA77A85A5224CCBE320191B55AF2 9423A63F103DC28AA69184C1AB6FBDB820A490A9D1DE7D34955BC90E879F1787 8E0EA920CC20E71A6959BDB8FF9F1148B99E6C841B976667F4B3FE1057B73C32 3E8E8613957E1543B9AC5DC1F796DB7443C962338DBB090BCDB483FAC0C0B2D4 F16FAE01DCEE04D85A5700C2647C7AEBDDB4C3A0CF7DE04F3A11FF53576DD60B 2FF3910CF0204EF98AD25CC9CA4D01A9E7FE02C7FC45F1FF4B8579C54FCDA251 70077470407818D597D12580F462283A09AB245FC3BADB3CB76D58F3FA9F244E 04AF59C37740D9A6F12F60493D03211BC92A627EED957CB692D11BBF0A30F8D8 041AE13DDC34A05003C371ACB0940F8E1BA21D920671E9B2D4470E3BA7DE0DA6 05DFB148F81BB6938EBAC9787A46F93E7DFAC0007570F1765350BCABAF5C84E9 6798202977E5534174EA4B94005DA2C885CE16F69CF7883B8F5409444AB100D1 6FE551DD1DD5901832802F3DD85DD0B07BFB0BDDB27E17ECEAAE1C940388B173 8914E164FF0DCF11B09CEAC7B8681DF8F62F028AC91EBD5E49603EEC2B488F5D 5ADB84A7EF5F409F08E83F0FC54CBA29C2B27B5DB9931DA907B9D530AD7470E8 12A0D50C5475AFB62E01B8075B9A9C005373CC5D9298B5744B71CCC920395909 BCE10431C5F621D18DCFF29DBECCE2F33916F29DB0CFB634036E359CB02D2007 41227CDA049DE0D8FCBBA9E520F672C494219A8CCD567FD7936CD27FB88FD699 485A0D5D55FB999A56C6EDEF19D00B12E7E44B679C3DA660DA4D3E0A4DA43AAC 99458FAC9F6ADABE144CB74D9CC8C1A62CDB8AD43285A990FAD9712775436BF0 7B64B106B49E373DA32F2ABFB17F57E7B840012E1AA560BD539D6A50CCF5D924 6C15070B65EECF85D8AE61DB4179642F55D4637803D8A7FB5F2D2F3037F57254 9ABB3EA43E25D9770036235C4FAD1CF5F91BDF171A0F2F02EF974BB48FC389AF F619B45EEB7176B829F96C027CC06E489BE4AEC4025844C8F0FD00971F7CC7BE 1810B1A04359351F3D41110AAD7755F269680CF783B320FFBF65229FB6148FEC 4D13DE4CE4D65C4C07B875DC10AB0BCE9A1A504F19FEEE42EFF3E53B3FA301C2 6AB0F26FA86ACE53BB51208332A01905AD21B20FE97459DE9EFC3F337BBAE7ED 9648E17B73EB811C7E9D42C85BC10F02A410F2A05DEFBCA59770CC0DC0F30575 5876386D44521FFBDAB5854655CD69D1E8D0D06F5B82A52484BBF3418634914A F62DD592C00B1D70BB5ECBE29231883227FB79530F040E7A7A8E65226FF610DC 4B362AE0B3228B62BD5C47DDFBA9B80405A58C9EABB21C032E5B119964F30EA7 C8731624870E92009591EB9C12AF8A8E2B96DB37862FA69170611CEB82972BF1 FF34C2750F82A551036C374267550B2F2879930A9BDDF69CB846E089B819188D CA0558346161B706C64D6E09821DB1625F38526BD67A8DDA0B335B40E259FB9A D173BE65649E2ED09E904DD475A0EBF13A2FAAB3408C1023B93533630017E256 25447989BA2A7FFAC4F086F02F5FE6FCD025244C5D6DCB9BA7DEF12B4EA1E24C 2C395E326D2FD11670202D783F9C8C0906EFB43E7AC139F5B3B6A6270E1E7738 E92DDCC65F530716D9736DE33DA1BF56AB25DEA0207A20E2679098FB313C3898 621B7E51D0A03B8CC152B5EE875A4DFCAEBAE38E7E770590A8623D38441BF41E 6D2FD76D78CA1683A9D301661AD8CF97E884DD653F3C6F0A2D30EEDBDB5F8A27 89CE14DD2D67C992412900B0444B97833BC8506D13A8449F6DC1CBD38F1E4E57 062DEB78F60D5EAEC4B49DA3767CDED1D10F970EE72A4EA59342DE856A5FE7F8 1130D6B9CFF7942D4B74BDCBE34CA0E11EACAC660ACA47A5E346F85FE9EB88DE 02276A81C156AAB60BFF634BD75093FA78B46B91280A756A3A73EDD81C82079D C458C0646F9CB1A13AEFA4359B1F205E2CBDC713A7BFC3552155221A70352278 EB492BBDEFB52768210C6A9A73860E67E0198580133771BD769A05942FDF2797 7878D6EE4219A1A10F08E7C586F7CFF7C5D1C58446AFC75A7C05C14799099891 8729B735C36F46767183E37D97995EC1BC7652FB0B219EFEC033CEEA19F06CDE C5F2B87DB244CD3A70E3BA8B13461EE95401301DBEFF46C41189A673AB2B9121 72386EA64FB1E71F7DF5B3CBB1D8E74833B164C7558C06303D9680CC29679BF2 289F48A97CD9879559C79561A949B9923B0011B5E8143B725C0C5CF16581A064 D42C0428393F3F25A512BFD6784288B4D89C58C7B247184C54FEAD0E80250FD2 A621DF6CBEE49A27394123405395217707F7FBF8E8ACAD450BF8C9F46BEC1751 D73A332E7CA1A7BE3914532EC5AEE591C7AA12B55FDC2D5F98FC744960B67736 11D6E4B495AAFEAE11F9A02FEFF0F2DBC48B3D40AA9FF870829BDC853AABF485 A9CEDB88CC06D6FC7FBAEAE6F4642BD7C9357F3C76EA1EED56394BCF62E4FF99 FDA4722C4833D832608D0B945DA95E7FF5CA8B62B31ADA9C076F76AAB29D2DBD ACCFE6C3CE4E62ECA37874AA29436FDEA68BC966FB85956D927879762293B1A3 D2B0AB4F326A38AABA79270975B4D10FC810788AEE3645CE24E4898FB1E0B634 CAB39CCA2740558B7DF9CA089D9287962183A10D6468062D91C271BD292B708E 71D5E95A640D8C4FAACBDDE251A70F4E8A0D3FD44288635C85758C982427F1F0 FB98B21838B589E87955ABBF41DA395E4321645C3E6A4C7F02A88BD01721BAC8 BD70095132B3BE5E35B9BB3B68A50404251C1833EE9944E5900103832C8FF57E 43E003DD1FC051E44321D9342F3C11D2C46B8E943A30A351AC43DC18DF8B56E3 04A8B9CFE763E2F554C91531F5B5FC29EA7F6342BB204457F639DB1348D84310 64291AA4233793A89143871EF229D213D075C9E4F693BBF40D702B4BB4E5072E FC7C40696B172007CBAC57B9A85C1369B4F206BB73B1202A0B019DD1A0B20551 3011DD8CD49F551850189E6A2C83AB801EEB629B9D6968A778E76A305A176611 682AED48EE7476BB1C5B785123B7C916F4694B49D04EBC7FDA8F3ACEFEC6314B A757BB319A250D984DBC453E2591E955CD4752334EA453219600531F0B581490 BEFAFA9F7429FE397C94321E916D2A7218F6758B6E142AEAE947FBEA978218C1 53D6890C6EA7018E4A78EBE4024F47BF65C1AE379725A01710F891BF56F1D6CE 2B01ACC2A345B631110DB733765662B37660490C2710AC80045A6651D89CBDBE A02F48044D920BAD399B6E016BDE4B6483D60766C69524B796D0CF4828A36E81 C48527CC0F48A9DAB991A1CC11C0547D851EF7084B862287AE36152AD7610563 6C000F883A6BB4A5FDD4208C8A5CCABF7231E18E7771D790316E5050B7E9268C D95EA30C9548476CA476EB1CA68CD48681EB037D24F8E5F7FF7C4A273845E727 EF6EAA74DFEEFFB5ED7447B62314894B21EFF3347596A7FB47ED6D111CF01212 BD6D6DA2706E3CDD05CF1BF7EB0A164E56E90F848AD3D0E7D6BB6CE309B9C414 27261DD2257B078BA489AB3DCB87B9CD8E3A4596CF44C9957433F2C0A1EC4E9D 973B644C9BBB09A1126343F6EE426C7BC021F6E0B50441FE4654670E85148EC6 54EEB873206930186CAC99EEE836176838E80EB88E1340084F45D646BF7A4FC9 4C3EDB1F66EF897C31856207B5B83D79C04EDADFAE2E12CFC10DEB1C1A14BEFD 50F230963F3E463ACA1524BCF62611EF2BDAFAD3DF0E7871D9D18984A47C1654 7F250AB0E71052F999D5BEFA3FDDC94A18E5F7665E9EC11FB00BA867084816B5 078BAD40EBA825BDCD3F743E0B96F337758FB083A2B08FCAC069F68551FD11B4 67F69823895F18E426B5FEDD03632C5149D75B414A291BA1C1750F2937985662 1BE41E9B01DF8CA44DB7F92BECFB85B5616FE351820867F60C15DFCB71086A81 B495758A5FCC1D59E78FA390223FB5969AE7884C2F16850635D5243B18ABBA88 2A20E278063D0A7A590EEFD8AA16942BE71B55A1C7EDE1229D953BF88EA50AB7 B789B398DAF168D4EDA9D63B046DC46393EBA52B212E269465A70DD027D613E4 4D85B08464494FD309CD501E02FDC9AEE97AF99432D69135ED266EACA15F13D7 C2E6D9AFEEB4E022D88B157E62EE4B441C3C94A5CCDE4534B225B9927ADE2C0B B054800709B7C2B9C69623FC6854456807EAFAD0282E325EBE8E1FC0C34FAB26 D53F8634BE05CE9AB18F092316012263C0B16130982D9080FE66424BF19A46A5 7F7E148205236EE6DD911374B1BE187812F9503B5E6D33B56B5A5EFF1739BB69 19597026A1AA1E4CC3B8477B0DBB64E495A644009292AAAF6D2B4C9CEC919967 765F3E273B71544CC64520B17DF782D6A22593225E9DAF109FA2C28367C1819D CE68B2D86ABF47E366A311F566F957B1E5FD60310FD69F76F43B9BA536AD45DF 174A4AFFB67328182A99EF34F67ACD52ED19DFCD01B7C9B8DAA040F1E6BCFC8A DAF7CDA1E65D1D9AAB5A6AAC1CBA9C3667A9190112694B5370C3D501EF2FA57F D57E6C4E521B4EE0EE3A27D3DB6261DBE1FA741DF27CC193D338C03C648E88E9 8388BB9C089B949C0B30F1D13BD2FDE78D6A4E0AB061E5F78E3149A6ABFA0798 F8A767FC5421D15262EAD7FC60FF5A96A294634EAE289B7E7D83F9E3756FD3BD F09D3072EDB32445B5C8311D5ABE6E024BF03C5F2A3A2E417C9314FFC1081C39 1F70BB4AF5CFE0285087577E4E3E2265F1F9AD72FBABDAEBA4D74E58E43302CE BE4479D8A91A5C094FA9725358FFEC7263BFB05EA22229D9DDA68B385D26FCC8 2719754EE2013F5FDD991CC67688360096C2007F02FD20076842E275D7AD4EF8 CD3F143BD0BD2ABE761F741FA68CBCDD54C246A49B2AED7F6F94837456B82433 636644A5B63ADD9C404E7BB2E146F2F71CF9F2EF42F1A834CF501AD1B756D63D 0472F55C357128DEF3036700C2F20B513836D6A7DB7D09087AAA7B15AFAEA898 597C806E6AFFF211032A8AD6244B9EE9A5EF665638ED41DD7ACE631DFF68AB9F 802DB02965803FBC40488021E1BC1C07FD09D1092793B2AEE3982F07A9BFC908 8357026731C0F26EA830DD5E9AE33389C701009670A89B4D73DA2B8739DBA082 5E7138107F06A07E99255779DE958E6BBFA1DC9297E470455454C9A1C3DE1D95 C5704CD1B50827FEA2EC369658E4A06ED69A3D682954ECC02123384F13208B89 3B978EB3985E674D0A9A33DCD7C2129E120F9A3F92A9CE675A838394854F277C 4506305C46878F4C49E30F2D62BECF34FC62EB6A91ECA2B534F36E02FFC184C8 89E30FB399334276B6CC452290793AA04163C8CB7A706B0C175560FFC20C14F8 D017994D551DE7C7DF3A54F1E5750E4119E91739B05EB9C2CD741DA19B5E0EE8 9CD30A98A06C1458B3CF69018972E5FC07B21B142CFEA567C2339640E2EFE677 A0EED87B050B0F5EFAAB1B9B4F847889610A852A6C74AB795FEDF3521789D937 EBBC400787B8F99FF40E2EDF874A9ACA970E4002C2A9AC8AEBF076DA7F0CAFEB E432EAAFC3474B8FBF3381E3338F7899369518C5A242396B73FAED5996849BD9 3490412EF3F199C691E3CA723593486125EFDCF56B45189D8583D1D833A74E38 FE0025A79ABC4FF7C4BB1C01F221C03A51F21C1294BA65C359E2C09901EDA7C3 54ACB412A66AFB8FA519A7C0111676B2238D5F1CEEAAF9C119E2DA9BCB295D31 54233F5680D9EF32C134AEB3E7B77F9FB89BBF9B0ECEC579B199BE88D0E4E503 4A7D1B6D58F2C188010D37B9BC5A962F08E7368A32972176941C21AC41AC1561 A9166E1D39190663A183FA8188328725D04804DC01A6F083468D601C9B2C4998 10EF8E7D9F41A6FC0CEB09978514C1D8D5BE21A74BF03D336B3D979113A74B80 71C4321B3D1C3A144AD42B8E000D13063C2B4654DB08982E52D51AD8C6540E9D CC5F734BF44CEC901539DB0A208D9C54401A325DBD706E1ECA8C636AE99DEE49 DD3C608186AF211188B20C85F31BC4B02F24944065DAE818EFF8E511906B6F74 FB6B721E257EB5D85ACF95D7D64EFF6A502AACB32DAC071FA8D17A5237C78225 8C3AF1E6702313D229E9E103F2BC122251C8149AE45DC45AC264705A9111B7FF DEF0BECC18D76DA0B47454235BAAE90915A45DEE73C1B918A6530382029C37CE C56914F700A602919A783BE98F12AA76855550A5B300CA51CFD9FA804642CA67 C8647627F1B0CF23653EDC626204BAA961AF0B50E9EE936FEEAE514F64684324 D8684E2D5CC50702A50CA028093960BBA43687DC91B3F046F85177F0F0E0A387 46EB51687750EBA848B7550FDC511FBD85920F5C347CF7D41B66E38A006E123B D104F1A5A9F1183C4563A2AEBB73228ABBB4460466BCA4BD7A97F21EABD05E10 51A0191E45B482B24E08EFBCF543EDDD62D8FBA25406C6A027529873A7062526 28368CEEFD1AFF885460D2ED47 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX8 %!PS-AdobeFont-1.1: CMBX8 1.0 %%CreationDate: 1991 Aug 20 16:36:07 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-59 -250 1235 750}readonly def /UniqueID 5000766 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-36 -250 1070 750}readonly def /UniqueID 5000791 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMCSC10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMCSC10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{14 -250 1077 750}readonly def /UniqueID 5000772 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378 77B9F65C23E3BAB41EFAE344DDC9AB1B3CCBC0618290D83DC756F9D5BEFECB18 2DB0E39997F264D408BD076F65A50E7E94C9C88D849AB2E92005CFA316ACCD91 FF524AAD7262B10351C50EBAD08FB4CD55D2E369F6E836C82C591606E1E5C73F DE3FA3CAD272C67C6CBF43B66FE4B8677DAFEEA19288428D07FEB1F4001BAA68 7AAD6DDBE432714E799CFA49D8A1A128F32E8B280524BC8041F1E64ECE4053C4 9F0AEC699A75B827002E9F95826DB3F643338F858011008E338A899020962176 CF66A62E3AEF046D91C88C87DEB03CE6CCDF4FB651990F0E86D17409F121773D 6877DF0085DFB269A3C07AA6660419BD0F0EF3C53DA2318BA1860AB34E28BAC6 E82DDB1C43E5203AC9DF9277098F2E42C0F7BD03C6D90B629DE97730245B8E8E 8903B9225098079C55A37E4E59AE2A9E36B6349FA2C09BB1F5F4433E4EEFC75E 3F9830EB085E7E6FBE2666AC5A398C2DF228062ACF9FCA5656390A15837C4A99 EC3740D873CFEF2E248B44CA134693A782594DD0692B4DBF1F16C4CDECA692C4 0E44FDBEF704101118BC53575BF22731E7F7717934AD715AC33B5D3679B784C9 4046E6CD3C0AD80ED1F65626B14E33CFDA6EB2825DC444FA6209615BC08173FF 1805BDFCCA4B11F50D6BD483FD8639F9E8D0245B463D65A0F12C26C8A8EE2910 757696C3F13144D8EA5649816AAD61A949C3A723ABB585990593F20A35CD6B7E 0FA0AD8551CEE41F61924DC36A464A10A1B14C33FAFB04862E30C66C1BC55665 6D07D93B8C0D596E109EE2B1AAB479F7FAA35279ADB468A624BE26D527BFF5ED E067598E1B8B781EB59569E3D0D54D8EFAE0F3EDE26279776ABA15341E42E636 6E02817082BE6FE0B04249A4840C11F95F8ADEFF72173E9A5F2AB2F62C427E5B DC010E18641EAC906A5EF0F9BC2108062134A7F10956219C5847C0D82F0E8663 12D963E012DF0DD899911EC5D8096F80B49CA3444CF1294FBFAB57DFACC9D01C 46F3BA2F3D1C14EC30CBF83E5729F1C074D4F1665405C9AAFADB8BE41EEE43AA 16966E2C0CCC853C4C09F245ABFD4603C4AA55EADC0A59AA6E9F5895FAF3D3FA 83EDC6E2540417530AE7DDA8EF33DEB81444316FB3F93EF944D9FB06745BACE4 848398BEB747E58310BBA39C64E341185C82CB77E9D4439EC15BEFF1335F22F8 F036517C436225F4125ED67ACA7A84230D4E2B6CA713FD6B3CA54BEB540D4604 D58A8335BC20052440C4903786FE3E335E331CCE36A13F05F71126F680077AAD ECAE10CB7C057C2D55F384723D58EF3AAE83E9E0B39D6A522667CC5B3257DAFA AC1C3C981B9415967F7F4DECD492A52D35BDFF8A83E40438B3B35576A12BE3AD BAB149D495329FFE2ED1F3587EB4BF6B7C1209F279EC564EB9E63BE5CD767D04 E2D4193954C813AC49CEB1E84CE72CCAEEC6FEE3C2E374A2F9BDAA5DB3CE37C1 09585F829065A21C7A4F56C391CC4105490C90F3EDF580FFF16F3C96BF68C5AE 59C8AB53850981130A09EDDBCBD1504F5CDB92BDC42B61087878F2B3469B54AC 0EC5B2468083435A70A2721669277E9FF8E163F1B98A99D91E3D6EEF2D9B8A6F 25D17AC90BB9DB45E58E8D42A42352B860C295991CB99350A274CE08D3347955 3602C6B2684140261C2C653362971E9665D12306F0F4CD8882D55E03D84998CB 068B9614E3A111ED8A52C42248B4E15D2B5FC3CD8BCC8FBFB63074EB64FDE98B F0F62DE284B766C80DAF632607506ED39F3337E30D7B378CE805E6C111089C24 9EEADE9B0CE8839AE349A5475C5C9BE67D3EDF6BA2E11F7AEFA7CA9A88813084 6F94D78467DA5940D26031CDBDABF617F21D556A9B6781C450DB9D4AE3361211 E1BA46BCBE7C5EF77CCCAB7252004D9C1F6D5BD63F7629B956772E358CDEA9FB A4EC8EA1AD5F2680B25DC232DE9D3951E8AD6700511F613A3AA1554C208F5F11 3AF63F0ED48C723C249E2405110F84EB5F03411CAF6FD54DDF7FF201E8AC4230 0841787F5C04DA51180F3A8407A6ADE13A3BDB4D791F82A5CDCA61D2A1E672DD 62E29FD0EC18E55193B117F8EDB9584A6E8A5B2772C354CE9369D5B87FD63081 82FFDBAE549AF3A498CDAC796F15B3EE7D9C08099AB4374902EA90231780E38D A260BD105AAA1F1469D006B3DCA5AEBAF74F9CD2FBDBA2C523DC1ADBE3418053 05319C58811EA8D041261E2FD14D5F00B6A1EDDF6A014134EE8A23DB11B44604 A9BC9B79428DC24D9CA5E80E10F3B6A5A5AE9679354CDA6E6A9F4CBE452D2D6C 03B6B9B69B69CE3E50826A1EF7767B273E55C6A350E444A7F201B20F79EADFA8 8CC587C64ED6EF9978258F603349F24F97C68F0D02DE85F229A3780EA816A93A 7B9402BC07CB5E51DFE12C1C81416DB336A9241B3ED11C6D47380BADA58224F1 38975A2B29C50B827941F1C71CB8627476F294C19EA53E1F15037C60331F8BED 0A185A6FE822B8757079F023041A09CC9BB83BF2862E7DA1B57BF08C7D07F16E F0062171CC869A00E61A89F233D1DF2406C33BBFCBA72B3406153234CB5F0FE3 A94C7C57516EE111DB01605F483F85278F20D05AC176709FA3288515CE69ED24 5AA1E307367729A6768C5C3E38AD8693C3EF4FE75F2CDC2CFE069F003608AF8F 62D798E34126D95D7E055A36B8A2B3E204A0FDB7C994580EFC9731AB1663661E E581FC76B7FA1C581D9F159E35F693591698A9E01B9B8317B2B91A6DF5B79975 38813C6B9C2539FF668EBBE8D853170E4865E9D92D0642F9AADDA0D51F91B281 B5798C38DE0EEDC3F943D4B05B32C00E9E5E223C199D93313DEA9A70D8F7A328 52B0E6849ED230BB21FD5DA3A89535F793F36ADC3A6B636970C76FC643B609A2 596EFDEE7646F142DD208193EEF18DBCC17147795D1C6A329B98B3DCC18855D3 93DA530D966D7E93BFACF753F3544BAD20AE225E12B68B3E917770267C584798 08103923C774F3B6FDD56CA8AD1395F46E18E2A3DAF28F739D905A5C54F80512 EC4D4AF6CF33C2DFE909C667B9A85B69CD94C3F0F6DC64E882001B4C02F2CE2F 90AC2AAEBF56FF7B9D51663B33A9C5BED99E50894956E429092EE4BD62A6B63E 8748285EE32600DC8F311965EDDFB1D6C0E2CA6C3917497CEA6D5575DE5C4A3A 642A953D25F0F5A411C99C0DCC844EEA18E596241987FDC5D39E7F7D24D150C1 E422CEBC7F20D408C24512E966B82809897FFE2D12FEF9E20D1CE1CA140CC601 4313DB4010B67D580301185AB19D741221D47BBBDFA7AF56E594349815C335AC C9FAA02A92DDFF5C454A6396CF2786E2D5F982ABC0666A90685F1C09F744AA6C C35699EAC700C9781F3E797E6FDC4BF91608F5A83A352170A7D892EF6A1A69D0 C68462DDEE9EFF57C9D53D08D46A9135E3A9368C09C482B190E7E77013628159 4E3CC180E360CF9065639CF0408B70FC7D0DDDBB41A3F56A1AF6E2E2407FF719 62432C6044B16177639B4299F476D79CE7229C814D0B16C6D6B61DDC9B6BCADC A87A32F075F5B57FB0DAF6B63FABED6C8915753077CC7B4F064DB55DFC66E10E FE00A9E40C1BB2949CF561216130E52D90F1E0CA58278FB392E1357E9F7A80CE 804442457820B64CF6B9C735B3CB278A2DA5EBB4CDDC0CFEB5F87EE8B360D96E 26E3B83FB5ADE4E18B004D84B8E20B47DE3493B4905B1665416262747AA07855 FB6F01ACC088A9CECC819859807509819AC310DD300DED7D66198D1CEB8412A6 E0B3BC1094067C85FD98156591DE6E71C4143B28064CAE0B68652842F522619A 2028D9F267C52A66FD761B81E69A3E3FD053077EC6AEF3E507735935BE65C8A8 CA3B37CB18C4C8A9936A8FA9977CB8267C7EA56CC7F7892A51A321704E8FAB99 1F86CFFAF9488F0BEEC3BF46845D481E5B03FEA89E97E9CA3A88103E1BBCC581 632D101F751AE1B6723D2059B294EE0BE7151DC0B79894B24E79EBA34BF301A5 DB5B9A00F2AF242A5D15431BF5EA470CC24BA063DC4AD44704A6E3AE56B33FAE 7283BAFC35D3ABC0170740E95B05CA18008291BA6B26A1C9507A33B72626344B CDD1482D1A59D3BFBD103DAFBDE5F7793CC0250881238FA5292E64E1BE452A21 27B2BFD7CBB6F7758E6C6CD0853A21B4E53B3998A94ACAFCAE1AB340A6FFF34E E9F2A71E377B86A395C75756EAC9183C08ACB1AFA2C6659AFBF9A8670F2F5EC8 BADEDD89778672C4A1FC04BEBD35843C774CA652EDE39FDDBB7CD04BD7D892E3 F62B2AE03DA20BB2D709929868E2929DDA9497E6F00D797481B421766F1A1D33 4242A15EA56A3531C0CDD28CB4ECA588041FA1A4BBD87D8E357603A76BCC680E 671D6BF218C46FA595219D42CDDF0A8139FD4A446F2FEF3F2B7818390F432A30 F24B72BF4726C9A5A54631D0663FD519274BC5F0BDB16E54A337B5837C2F68B0 7F3EB87E229AAA924724C5B6D2EB6D0D56988C6115A4EE0D81E9ACCC7EAA911A D2229F1643B7590A5DA22250EE8D0CC0AB3A656B9B72ACFFBCBB10FFCB6B0A4D 9F2658E3BC211BA7718780AD87141E3E992567E99669D6C6C71D7E39909D8536 D6AB0D5D42ED7109C87C1D863A26E120F655D6959EC202D069B4E9C18DFB9EDD 7BDCD0320FC59110FE3D4F4966AB31256F2C89A6ABC2E7902D9F1BE60F23D963 62B1154C0AEF5872591ADB670378F893629909902DA44C34E6619910FFBD07D4 B8EEFAA392A9A25330B69E497A79F97A485166C043A508B6CAE3540258379831 7EBC915505B97F5C4F3C2C89A910451F502749F81A49D1BE6D25525AE69DA6DA 8175E7B27D8BAA4043D9FF1A9EF62CAF14C573A749EDCC6DA5C8992F982EC3BB 7ECE29DD5E8CB57F9CE3BF0F9F43415955F3D8C10488AFF5EC7AADAA7D5EC352 C84497EE590887A38C6D7CE9999E5809DF2B1D0ABDE6427A7DEB8B0806221F09 8B74CFAFE7E92D78E4A35D3359FDE7283C71759D91BD47B87138DDEE62856582 D41FE08CC0BF0FB69B8C178BB4647D8EF7C879A20D768331B97D7FFA470E87FB D35774C072C29FD55AECA8BB21671F4CB866D92BAD08FD9A63D35CB0738F2C0E B113D5840F082F702B494CC397C036886C58DD2246E543D60738BA4C321C9498 68E20C10C49A6CEC1E5F30327A78273CDAD602A0CF17DF00CF6A4FA4E6A24AFD 8717CD4922315516326FE44DE6AF1294B266806C9043F871AAB055A91F3F96E2 EC68637914FA430124E0D995CDC9AA768493A96A25A5DEC8AEC05A1A9548B195 7A2FFCA2322046BA2893A155B052C6320287DCFD5952BE7A9227683549973514 6E08EE43DE6DED8DB380EDEA8341E3508DE1064D1D5A4A7603F9CF9B693394B0 80A8F968EC1879A3A3C324506D83BC08354DD316A5CCE6EE94F28CE344258E27 9131C89E5B9270D926E07D54A00DC1371D40EE7C3BE39419F73CB6CA62B754E1 2606805F37273AA55065F048D674D7088D3B8F06EAC3D4546148E14FBECBC341 78B1EA58DB6E55DFF0EBE36AA45D609AA661000CBD16F1A738A1BCFED92B32D2 5F70E847668621CE34FFEE1654037C8EF339C6CC7EF5163F9A8448541AE17813 F3E767F5C51DD830006EAE8A94053108D7788F98E6C58BB64B16C83A45727FDC 254E08CC739C553584CF974F8C1AD1220E59D22729719F79711F2E4B73160B02 A96814387F8C29E454215A204D56790176AD9045C5F13F0D1D6443C4AA021551 248E7283F7A24DFF78E89D0C7D7922FA183FAB1CD5D5DA0BAF8912D1FDFA130E 218198EF93E69D151CA87CAA1FC268BE93F5EDE049D72B294ADE419210D0BB68 98D30F4486704807E0C573B364B346293973B4BF30F522136637013DE0EE9D80 1BD39A6B92F6E2A515DA1C2365D2AF759B5E565685CEC9A3C418897C135961C4 67276CDF15D175C335B24E1FF10FC5661C0BE662F0C630A168943996D0BC50A9 733CBF5315749A23D5FDF90BAB8CD120826F11FE4F014A4D2C2636637E055EDB 02E84295BEEA86C5C3E165A48CD33A449937BEC27642F5E5A10DB202B3A0E0E0 0682A5490DB436F8A12251E1DAEAEC4FC7253FD9BB048528052FB2BC2879CA74 DD83F72EE0C5B32352951345750FD3F4A1AAD399820EA5A75A873981D86664E5 26F36DF7173948423B3C2D40B3DAC469C9E6C9D21A8737943069CA45E5A4C0E4 E19462483A46F51DC9FBF6AB0F518F251340BD94D66CF5F02C8A8E75F8A8FA50 E80CA1460E986BB7AF9F13E4CBE61C519352FAF7ABAA4AAF4765B06E4CBF4F1E 0AF496B5E1D42815F4B810BFBAFA0493D5065E57D6A671BA728AF8876E5130B3 139873EC37E6F33F6DEC14C09B3E94D20C36396ED16EC8760F57DC37C4AB072B FC65B4364A789FABE59460C45A6DC38E6C9320D9CC68ECDCF4D6CE871B0E8B1F 1EB62AA7EE5F0C4783F9973F42AE0C8C37E31D75E8711CEE41B47739C27580B3 50B2FB98A6AC4339D0C31588D24AFD5CC99D48AE1AFFDAA0D07A1881C000DAC7 57F489E14EBB40AEA39C4A25DEBEA22053C0AA3311B4A67F61D005716D09F923 36F75432DC5230389433C048CE103A5F65E4B4EFBC7B5ECA62F7F22646B55161 F5332A49F56289FF3BAC0DBCE6AA024B3868AECD29D78C34FA129B8B8E06237F 881CE5A9F048A040D7F1D1F58F65B53FD8D83CDEDEC1984657538DFE11995816 3B4971A7EBEB6496F6F9E92D5CDB9A250CD05164EB10B9BC379A0BC3D6FEA7F1 DD9DCF712AE9F4B9FF487C20833A14D617316E632446F03F5746C6F92EF6B9CA 90C92BF9368E7DA09CDA1FFE54DD4E3A950650FB4C56D4D395E7D515F0520D45 268B974A52043AF734DF66945BA2F500964701B4EF9D3B4EC060E4DB3D77F556 5458D5B4E74B19FC9EC722787D09A1E40CC108836B039F45AE06D3517A01EDCF 7B0D81488002694AACF37721971C92913FC309E66B77F9D191D2CF97CC034B2D 05D9D1FD652A9AE2F776D7CB3CE2D9C8446058227A66A9FA58F1F3BF5D91CD11 E2547BEFA267AE298E9BE236E519F42576FDDADBA01AADEE6EA6F0DA6EFF4D77 5E1209FF55F442EAEE1BC683509F98E358587313BC822EDB2538C0AE88210A2A D217941C0A55C6E8D43401FD4963D50FD1C2A3E1D4806AFE1C4E4019D2867C0C 4B874B1CA5D63C4D73208D67144CDC66B94BC7749E0AA9BEECC4A8AA41710E8A C2E180C1CFC2A83EC34CBFA134AC2F257AC8BCD360011821A051191B71A7C13A E56367627FB1B8AC1309B865007EEE8F3F5F16003259DC09048F34846286B9AA 0F633F0CE53C272EECE6ECC7162ADBD08575CCD03981192E8B7B64706FBDA3E2 62DB27C57AFC20B9CA9BE4DE0113DF32929A69648DE6EFBC8D2F4F4590327AD7 B63C4365911ADD0DFD7210FF8825F0D729C7210969DE27C184800A19A02EC5E3 AA2066CBB5CFE5F765D992EB1E26577EBEC9B19CF200ED15565394437C3A1251 E0A578F873B11158FEC23C6E35E0240A2D20318FE14935ECC5CD073A2D4795A3 850733A549292EEDA3A16BF22B5F1618F19A0F4419C2C3287FBC9E72BE0AEBB8 5FBCBC9680E4883813F3BED6C17400598DA5323CDC992CFC304D62587475FDA8 C4B35ACD517B07851596A979193936B033AD79A8D523D12971151ABF13DD7BAE 596DBA855D36582146F0640D534002AF6000795824FEC874D0F15DA79128D651 CBDE0436BE319C04A1EC30358B0B51A0E7D97626DDF5804CEB5FCEF01B2EE778 655360E55B15550AE2E4292C5AFF080C9D43A664BE04091A03DA5D5C9C164E91 198A92E205CB815CE3F7A60BE3793A7140C217572342B2BE7CCD2E8D7758122D 461D6EF97F5A98F3C17C7A45CE9D0216C1B1EDC035C4F2243C02CE2FB58237C0 CB60978161D226A5565D39FA5D9BD8B48C32E18C901B3E5DE0FC0FF597E89A59 AEC581C8C6CA399C420FEE389FC842DA754A0E3E57B7F70134F68BDF6AF40590 05C56CCE481B6FAF6258B9FEC1951CFCB5CF6516664FDCC9F8E9436297A549BA 94748F5AF5D0B95837389058BE3E23BC429170BDFA39EA7E3376035B9BB8B0CC 249F320911C70C926648262867F98AD3E8CD388FDBC2868EBAC72AD6DE148209 D8009B526D916288824F75F07F8F7F547201A722529878913CD8B83F6AF4E4C7 460D673742EA9024147A0BF5F1C6E348A27732DBEAD1AB0ECA378C98E89BF73D B4D7814B9BE2D7CBB873FE52EC6BB21197FE86E51808A937E656D5858A7ABBE3 0C85703F582A74F740F1D58174FC164DED05BF108337F84B12CE4688300A00EC 0D63F03221BD6534323D6377433A2D11E9E4D98A489A357FE0F1376853E980A7 896E0414EEAEA1545D7A33A867CDA8C1DB6A84E302A54F3685FE91FF859C9276 281360788A5B7801DC35FC8DF2F2D9ADCD271EC3047D1BF75B0BF374DF891E14 0003B0D0A7EC5D70AC634A69F320BE8C042A2ED5BA8E7ECC6BB0B81D45CC4A51 138517E4DF97A5FDE6D305EADB826D342BC82BF9262FE0D5A4EA05335A750F98 943B46C01BF69699CC1989F6F1C5C1DD3AECD2C0ED446DC92D229C3CC19ADD7E FD8851377189AC7DB0DD125FDB2D71B2688CD63BB019BA7D3D4A745E437F8009 EACE0A7DB891D78089D4C4CA45CFA6F06EDB7C0570236F3021FAB94F306455D8 A1927DE5E8170A0CEF1CDE7E7EA274908E15CA5171025349EEE82FE0608F6323 B6B62545DF098A83F95E137D22C6652935FA778DBD1723C8E65484DCB7B31A52 59257D26D5E6E23516B408059E4680AD4468586627CEF2EF0BF8752691DB734D A63BA327A07BCFCEC7B9925674F24D5E0E7B8D626DA1398F98FDCCE5AF3268E0 C57642AD99BC25BABBEFB755CD172BDA15BE8ACADA40396848436C52D2B033B1 0F6696168D90909654E6C4D05981D0B0210DDEF6C07A7836FCFD538FBEFAE1CD A4B7FBA5BCD65B8C44EEA3269EAF27FBFFA1ADA1DDFEC0C056FD96EA3173AD36 D7B5EB857827B548D9EA93AB826C88F4110CE04E7C43879F5CB517ED86CD6BDA D06EE4ABE754E7400E5F702AF8A99D2EBD4B936A3B1A7D5FCC8FCBBC6797266D 47614C9634E02F0E079A23265F21CDA7B07992C401CC0A6916D5A9F0850D44AE DBFB54BF56AEEC67B5894F0DC857926D11BF1E627DF7BFA4B966F9E7DA657858 B22B8BC34CA72E977C22C76378B50C452C5B49C972307D1FE70F1EB77F445E3B 3DFB5EE224AECAC57598BC38211C1238554ECD898330554265455CC642EAD78A F1D036E4A809959D4632B280BACA2DFDB544CA0C28B1C11ACFF8758822DF4381 144BD85CAEC10CBAEE0E0D6278A8BCC7662FA77412461E9DF2A5AF34C35598C0 37817C3A279F32F59167733206DA39C87E409E828EEC5EA080AD12AD9EA20469 3525ECD2A8A32DBFC2A29DA8A7E78D25498790EA0353E7B8E547A84D23086EB0 AD2B414E1D3834B00FC2513CCC6A432DA12F56D6DD18D4EBD5EE976D876DD801 7C629DEBB7C579D12FEC25C8FDF16268DF320DF621FF56E94A17589E13E7AE73 A81DD1171543A975D75BADE1553D2F8F03F7906AA3971C797875F1EB664FE69F 0B772BD5E20CEA1B42F1BE02C11A3842E739DFBB185105D21F94F325F91B4BC5 5E44DEC5BD49635221324E419DD417134D3357DDA4A2376C49A8C08B2F920CFB 9E6064996A7AAB5A97C7CE6CD541D4EBD8D5BA6C33DF056ECC2D2CA29F7801E8 79ADA07F643F9CC7AA899D3A1AF9A411E8CCB953DB30049B87FCFA72D8289E40 00ACBA9C185EE3CE90D105D38F67A23EA485AD237E7258DF400D60C37C26860B 40AC2D1FD4BC97419CB749538A0EB309D15C258DA4121554531DE87B41E026F1 9E8F33D0E6CD952C3BB0CB37DE741B3322DC03A9B5D8C008676DDBF85BDD75E4 FC27826DE4259C03D8E79C0A8A32807253A8B8D63ABA11F352B3142447EC6D29 26A4D6E66AA9A9008F6D42725D7D45997252F96FFB675BC3A5CDD616DD5287D6 0438C4CE43A0806F43FD225435B6D23B254A6F732F3381009ED96303FB00D3D0 E6CCD8797D33DD122B12B4C57082B1D78B89B6AC82C38D0267C300D4CC8CC9AC 44826A3DA4305E0BCA13D24C1AB7A82C38B765E212381EA8A605F6F76E0BC440 965D2C7C59F4EF58DB0BCD6AEB597FA8A03487A1182400BAD570A570410A3F08 57DB8ED3EF237117736D41AA58B643DC8AED1AA97981B146F3AD1B4A68C11FE9 4E47604D12549195712A9F3B5F9E7D4AD9E76C629DA314DF377D6ECE3201DA52 445A4983A8C20677D713F286E165B893877E39B9A4B49AA2C768BEC4C2168140 0FBB2EB39A1BAE80B051C99C648509D18BA1DE273DD78B36D7EF2D85E9F2A85F 2D8C3AE97CC8421B5BFEADB6F8EFFC2B40A999ECF5F639A63B4703B277DB09C9 746AEB6FEA4A6789D85B7935BA46AFFE6927DE2E917CB581CA91B0B950C458FB E5D6706F7B98D9689AA30FE1664C941E76E3C68FB7420FB877F4AF5759687498 0876D403702BF65827F45D4881E5B6427E301196005171B0CF18E42E8A59201B 81CBB2B8D020B90ADA3F9BA945154C82A310A644C61351244AE4BC2ABDD58448 159AEC33A4CF0AC89891058AB4709DBD3737592364414CE541EE15664F528E95 494291DFDD5EA8939D749EFAA401598F87FF7C719AE754FC0F949D15A9A805D7 F7EA12FD9801EB9104ED30AC0DB7AB4ED59A98A0371CAE39A9E82B409434F661 91AA382B05CE5D2B3024AE1DA01FC415478B4AFF5495E49EC69F17DAE0FF3908 D5136D2A630C30DAA33D73217ECB1F04AAFF88B5C3D106F0005714150DFD48B8 2CE8803F9CB93C36A96378A11326127203C233A7A2C91C9F95B1262C6CF39F92 C903AF2DDCD26EA53CE5A6EE497446B9ED94710422290481232A57BAE982AA6A 6E372D73622F4F6AC9438AA92D63E3A49C94553B64CAE1E95A9EF828F0E77864 5794003DDD79A1994BC7462A3F9AB0B9EAB3ED5DD9A9C230A03E86FCD991A507 30E0DF7142CBB89C2F8CC8E57D8385105719B39893774E644B7726A577B06307 5A53F83AE5BB0ED259A7E938A205404BA9FE4741DB1C5625DF9561C4BA321000 0F5454ED6C6D535626E0E4A6BE716CD3FBBF88FB5B5E9E6127299178DF7243F0 E80CF062019B09D77B55EB722BA46058C1D58112202C6C32AE98956B195F2503 74D2C47C98DFD71E43FF2492100EBB7E1A9F25DAE494B9A212BD2A5FC0C5AAA6 7A5890680ECE806FD8B4EA97A7050CA736C1BB0C24D4FB7D041612408A5A2D57 F57EC9A6368423B131D05BFA4F4B1BD72DC81D4A66BEEF7AB42D224BB1F04467 B4BC295F28D512FFCE945B189B91F9E2C358774E80954DA346D273701FDD6595 C9AEE13A172C480A59F444F831D524D9D46B76E81C679762EFAC71522C05A849 1783AED5FE4C5ADD2DA678AB71D597B35757D198D13A9DE39F9575E7D206F28C A152715174FDDA21D9A6520F37DF414C4475D94EACCDCC490C62BD37FF57378E 94A95E38B3D82BE6062E99D3825862B5696EA6C5FD557E154C144C1E5A8ECF29 6AD61F74F6B88E02AAC1664671956C10DB548065FDCFEB6D08E678E2132375B0 88A4D892C5035EDF8365D1CC23304EBD4A3C20D869EB4530EA0699FBCAE62032 CA19D073D24440DA27AF9629555FD2A48BBF4D1F991ECECCBF8477CA407301A2 DA97207C4781BEF67FB1F89DC6CC475F64530F266D4C4FBE6C1D55CDB31FF9FB BFE9D0833F6475BB2923F19D9AD715A647198C65CD073A69BAF97EC74C5AF102 8DFCDC3494EAB9655A880A655CAEAB2839CDD6B1F7CCDEA4CDA1294018C4CD49 FABD1C2EBF5E0878E22F95C6B71B7834B15FC934BED7EAD61A72D276ED1F9BBF 7CA950AF8762067160715A843F838D3334DD91B71E8AA581A06DAC2734B12990 2F4004B305B02BE74ED0A484ABC598572E2DBA7E0CC6FA429CC31657D8623525 46EE0BDAFBD0BCA5D3297A31B9A27FCC19EC009C617B883505399AE877C51868 A23E2CDEE4BF4A3E4C8B0A1A61053EE810B6C458AC1E8DDF4D38F6FDD37DCC19 C789546F6FCFA8636FF26BDF7442DDF1E791698B747C5CBDC2FB9A48528777EA 4F5C70280F4B49219BAF6BBA52F7B573B0DED378238DC8CE00A3F3D496BBC67E CE6DFA77E3F8EE7F1857B2EF25E791ACB89C42A4B7635AA802A79C26BC130E99 0FE97326481C02E042793D2B143BF0DD5F4409C1C6F1409979A0B445D8A9EDB3 947FE7839ABBCA7B86FCDC45D7FF77C28B3A4A5F9A429B2D14E80320E0CAB7F4 72819D6B909ED62A0D05A836020D351171F6E9739B61E938D8E04CEAC0810EBB E8A3BA621AE9AC6F18753BEBB98137F73BD2012461B64B6CAD6B208379FCEC87 FDB1580B7ECE2A92E6949B6C0BC41777094692764D459D57E2CF3F64BEA8BC7B AADDC4919C0EEF86FB0064ED573FF9ED1FCD70DD220D22EF8B5F6709952CB16A 93E44BE0DEE35B6E0519C020D32043C95F9C303949A37CDB64AE60BA10A9962A 9912427392E5B7696C449DA43C1ED1EFA44DAA158FB45B6AC775CFD1710FE1D5 C93A2CD6E43E045BB5F13BC47E4935356C4981DC94E40C5A50AF6C794EDFF905 68DBC2731726378743D26B3378FE46BD645AB7D88E7CDD3E2C7998B1858BDD96 9286C25F0CEB6FB3D7EC777415A1CE5FDAB682DE9EF586605BC65D7271654E20 B90513B621EB05E622B469142B7496BA2A68D0A775EBB36EF12D0C296A688DDD C74994755984B1B3BB17BA4F3FDDF6EECC54696F0847313E9F5B1E5E846E03EE 43B87BB7C97773129F27B2906B40DBF9062F12E5B477D7F143C3AD15BAFB92CF A44BF5166417AF207A21BB3BC6358EC3FA4C216F09E403B7819C4D339174BDB1 02B503E1F13CE0F997495C5E0B26EED386639C3AA3715B40FDEB953572BA9CB3 A56DBCA6610E6B2EDD074806BF0D2D8742CD2A4837CCCCCA50819190B989AD18 831E78DD5963DE320918213D3784C094CEB68C348184FCC8696EA5EE1654C178 8D2DA880DB03E702349FAF486D40CE13B9E7CAC3E7213F6C6B683E22064834DB 89E432238FAA5FD2CC20AAB752A35855B48F0F837F2210FC816410DCB3562C6E 9FDBA411B56E204777620AA76CDACF441357D58C3FB4B5AD4671866DAEAA239E 80E278A4D9D3835E00D33EA04F0DA34FD773763A2DBF72A8EA670972980A963D A873D8FDDAC22AF64AC54E246D82CF6C5F2CECE2CB4BDA763F3EAC87B50C29CB 618A30C1F52BFA4C63431B9830043019E0D1BB2A6A6A0C3D3C23887F9B20CFD5 AE9341D50738C7B58A99077B23690E5CB5EDB528E813F91D1D4B7BFC723A5CAC 469E2068DDA88CBF551D2FBD9EE3B1EF58BDBEEA74F7BE52CDE1B5786900ED86 F96BBC1D1F9FD33C736652434D8D93DED135746812DA799C78E28305F4859E40 C258BDB8FE2B41C95875BD004EBAF310A2C9D8C21E6E33DF8DCC1CBEF7AB9BD9 EF06ECD3D6A0B3B2816C8CC3EB377029D66776280B091437534B77268E558625 EBEC166AA9103DA8DAC0E4FF7239A820FEA387150EF15442352F532AD8616CFD 8043B3EF8B5C442F41EA89963547090BB7E883F91A369DCA4BD984583D9E69B6 38D134C30C4D0FFDF35A85F1C08E9DEB408A57AFEA4009BF9DE28B744624FFC5 1D1DDC1AD149913FC2EA7FE7E99CA9FB7CF6526E8CB030091B9F762BC663330C 9C8ABB260793EA14BD236F655BAD2F4BC2C8DD95A711EDE9F641EE8F28EBE248 D37874BD7951F9E2781F4B90ADEFFACC14116F4FBEABAFC847822AEF6F36E1AB A627D28EB413D8F639A8B14DF756A5F5214476573FE07AC3B907012695B0D1EE 3E15E766A26A907AF7104F94D5745538EEDF667DC820CCFBD9D32923F283E5DC 22857729CAD670F44107DAAF7620040F94C5373BAFC16FA5D8551D6572C57A80 5161B9CBEBC49476C9C75FAB569E4F2138D014F0DEF1AC7FBBA4AE8B12043AA0 2D3D94E222485CE9CCE237176ACBBEBAE9DBA452AD229BD84EC35CD56116994C F5EA20506184066BDEDAE63E4A83C779E006F602EAE30EC9C925A05C06B92A60 E3F83CAE6B4AE4F7CAFD8BE6A52931523A00C9826E3FBA85D2737CDE6CD18131 CBEA3AE215B038739764F382D0CB1D46E0B65610383180772B19D8A3530C7804 494B3EA3AE5E697F456746 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont TeXDict begin 39158280 55380996 1000 600 600 (r3bb.dvi) @start /Fa 139[35 3[35 35 35 35 35 2[35 1[35 1[35 3[35 32[35 17[35 46[{ TeX09fbbfacEncoding ReEncodeFont }12 66.4176 /CMTT8 rf /Fb 206[30 49[{ TeXf7b6d320Encoding ReEncodeFont }1 49.8132 /CMR6 rf /Fc 188[50 67[{ TeXaae443f0Encoding ReEncodeFont }1 66.4176 /CMMI8 rf /Fd 173[60 82[{}1 83.022 /MSBM10 rf /Fe 134[40 39 55 38 45 28 34 35 38 42 42 47 68 21 1[25 25 42 38 25 38 42 38 38 42 12[59 47 6[52 1[44 2[64 54 2[59 1[62 5[25 2[42 42 42 42 42 42 42 42 2[25 30 25 2[34 34 40[{ TeX74afc74cEncoding ReEncodeFont }46 83.022 /CMTI10 rf /Ff 206[66 48[52{ TeXbbad153fEncoding ReEncodeFont }2 58.1154 /CMSY7 rf /Fg 133[29 35 1[47 33 38 24 29 30 1[36 36 40 58 18 33 22 22 36 33 22 33 36 33 33 36 10[53 2[40 52 1[48 55 53 64 45 55 1[27 53 55 46 48 54 51 50 14[36 4[22 26 22 4[22 19[36 6[40 12[{ TeX74afc74cEncoding ReEncodeFont }48 66.4176 /CMTI8 rf /Fh 135[33 58[31 61[{ TeXaae443f0Encoding ReEncodeFont }2 41.511 /CMMI5 rf /Fi 201[28 2[28 28 28 49[{ TeX0ef0afcaEncoding ReEncodeFont }4 41.511 /CMR5 rf /Fj 143[83 78[66 66 12[61 61 18[{}5 83.022 /CMEX10 rf /Fk 171[47 37 48 1[45 51 49 1[41 2[24 49 51 43 45 50 47 46 49 3[51 3[33 33 33 33 33 33 33 33 33 33 4[51 1[26 26 6[19 33[{ TeXf7b6d320Encoding ReEncodeFont }31 58.1154 /CMR7 rf /Fl 149[23 2[42 42 10[55 35[0 0 3[55 16[83 6[65 19[65 4[23 65{ TeXbbad153fEncoding ReEncodeFont }12 83.022 /CMSY10 rf /Fm 134[34 38 7[34 2[59 3[23 39 20[41 50 5[46 3[54 7[35 4[20 30[31 28[{ TeXaae443f0Encoding ReEncodeFont }13 58.1154 /CMMI7 rf /Fn 134[41 47 3[30 3[42 2[73 3[29 48 1[41 17[49 51 63 1[53 3[57 2[36 69 3[69 59 4[65 1[65 23 23 18[54 10[36 2[47 36 2[48 6[37 14[{ TeXaae443f0Encoding ReEncodeFont }27 83.022 /CMMI10 rf /Fo 128[42 42 3[37 44 44 60 44 46 32 33 33 44 46 42 46 69 23 44 25 23 46 42 25 37 46 37 46 42 1[23 42 23 42 23 51 2[85 62 62 60 46 1[65 57 65 62 76 52 1[43 30 62 65 54 1[63 60 59 62 1[39 1[65 1[23 23 42 42 42 42 42 42 42 42 42 42 42 23 28 23 65 1[32 32 5[42 11[42 2[42 4[69 46 46 48 60 10[{ TeXf7b6d320Encoding ReEncodeFont }83 83.022 /CMR10 rf /Fp 139[32 32 34 14[36 45 40 31[61 18[23 46[{ TeXf7b6d320Encoding ReEncodeFont }8 66.4176 /CMBX8 rf /Fq 129[35 2[35 31 37 37 51 37 39 27 28 28 37 39 35 39 59 20 37 22 20 39 35 22 31 39 31 39 35 3[20 35 20 43 2[72 53 53 51 39 52 55 48 55 53 65 44 55 36 25 53 55 46 48 54 51 50 53 1[33 4[20 35 1[35 35 35 35 35 35 35 35 35 20 24 20 2[27 27 5[35 14[35 7[41 11[{ TeXf7b6d320Encoding ReEncodeFont }75 66.4176 /CMR8 rf /Fr 137[51 51 49 38 50 1[46 53 51 1[43 2[25 51 1[44 46 52 49 1[51 12[65 1[66 1[62 6[34 1[71 4[64 68 65[{ TeX0ef0afcaEncoding ReEncodeFont }23 83.022 /CMCSC10 rf /Fs 134[50 1[69 1[53 37 38 39 50 53 48 53 80 27 50 29 27 53 48 29 44 53 42 53 46 7[72 4[66 53 72 1[65 72 75 91 57 2[36 75 1[60 63 73 69 68 72 7[48 48 48 48 48 48 48 48 48 48 1[27 32 45[{ TeXf7b6d320Encoding ReEncodeFont }52 83.022 /CMBX10 rf end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 652 780 a Fs(BRANCHES)40 b(OF)h(PERIODIC)g (ORBITS)h(F)m(OR)f(THE)g(PLANAR)1169 897 y(RESTRICTED)g(3-BOD)m(Y)g(PR) m(OBLEM)1666 1200 y Fr(Gianni)31 b(Arioli)1507 1326 y Fq(Dipartimen)n(to)25 b(di)e(Matematica)1622 1409 y(P)n(olitecnico)i (di)e(Milano)1505 1492 y(Piazza)h(Leonardo)h(da)f(Vinci)f(32)1649 1575 y(20133)i(Milano,)e(Italy)744 1807 y Fp(Abstract.)50 b Fq(W)-6 b(e)32 b(describ)r(e)e(a)h(metho)r(d)g(for)f(studying)h(the)g (existence)h(and)f(the)g(linear)744 1890 y(stabilit)n(y)19 b(of)f(branc)n(hes)i(of)e(p)r(erio)r(dic)h(solutions)f(for)g(a)h (dynamical)g(system)g(with)f(a)h(param-)744 1973 y(eter.)32 b(W)-6 b(e)24 b(apply)g(the)g(metho)r(d)g(to)g(the)g(planar)f (restricted)h(3-b)r(o)r(dy)g(problem)f(extending)744 2056 y(the)29 b(results)e(of)g([A].)42 b(More)27 b(precisely)-6 b(,)28 b(w)n(e)g(pro)n(v)n(e)g(the)g(existence)h(of)e(some)h(con)n(tin) n(uous)744 2139 y(branc)n(hes)g(of)f(p)r(erio)r(dic)g(orbits)g(with)g (the)h(energy)g(or)e(the)i(masses)f(of)g(the)h(primaries)e(as)744 2222 y(parameters,)e(and)f(pro)n(vide)h(an)f(appro)n(ximation)h(of)f (the)h(orbits)f(with)g(rigorous)f(b)r(ounds.)744 2305 y(W)-6 b(e)25 b(pro)n(v)n(e)f(the)h(linear)e(stabilit)n(y)g(or)h (instabilit)n(y)f(of)h(the)g(orbits.)1615 2496 y Fo(1.)41 b Fr(Intr)n(oduction)555 2646 y Fo(The)26 b(literature)e(ab)r(out)i(p)r (erio)r(dic)f(solutions)g(for)f(the)i(planar)e(restricted)h(3-b)r(o)r (dy)g(problem)456 2745 y(is)35 b(extremely)f(ric)n(h,)j(so)d(that)i(an) n(y)e(attempt)i(to)f(mak)n(e)f(a)h(list)g(of)h(references)e(is)h (futile.)60 b(W)-7 b(e)456 2845 y(only)25 b(cite)h(the)g(w)n(ell)f(kno) n(wn)g(b)r(o)r(oks)h([MH,)g(SM,)g(S])g(as)f(standard)g(references.)35 b(By)25 b(a)g(standard)456 2944 y(deriv)-5 b(ation,)25 b(see)g(e.g.)36 b([A],)26 b(it)g(can)f(b)r(e)h(sho)n(wn)f(that)g(when)h (the)g(primaries)e(orbit)h(around)f(eac)n(h)456 3044 y(other)29 b(clo)r(c)n(kwise)f(with)j(p)r(erio)r(d)e(2)p Fn(\031)s Fo(,)i(then)f(the)g(motion)f(of)h(the)g(third)g(b)r(o)r(dy)g (is)g(describ)r(ed)f(in)456 3144 y(a)c(rotating)f(reference)g(frame,)i (i.e.)36 b(in)26 b(syno)r(dical)f(co)r(ordinates,)f(b)n(y)h(the)h (follo)n(wing)e(system)i(of)456 3243 y(second)h(order)f(di\013eren)n (tial)h(equations:)456 3431 y(\(1\))1732 3380 y(\177)-47 b Fn(x)19 b Fo(+)f(2)c(_)-37 b Fn(y)25 b Fo(=)e(\012)2132 3392 y Fm(x)1722 3480 y Fo(\177)-48 b Fn(y)21 b Fl(\000)d Fo(2)c(_)-37 b Fn(x)23 b Fo(=)g(\012)2121 3492 y Fm(y)2161 3480 y Fn(;)456 3618 y Fo(where)456 3793 y(\(2\))222 b(\012\()p Fn(x;)14 b(y)s Fo(\))24 b(=)1158 3737 y Fn(x)1205 3706 y Fk(2)p 1158 3774 85 4 v 1179 3850 a Fo(2)1271 3793 y(+)1364 3737 y Fn(y)1408 3706 y Fk(2)p 1364 3774 81 4 v 1383 3850 a Fo(2)1473 3793 y(+)1819 3737 y Fn(m)1892 3749 y Fk(1)p 1566 3774 617 4 v 1566 3790 a Fj(p)p 1649 3790 534 4 v 71 x Fo(\()p Fn(x)19 b Fl(\000)f Fn(R)1893 3873 y Fk(1)1931 3861 y Fo(\))1963 3837 y Fk(2)2019 3861 y Fo(+)g Fn(y)2146 3837 y Fk(2)2211 3793 y Fo(+)2557 3737 y Fn(m)2630 3749 y Fk(2)p 2304 3774 617 4 v 2304 3790 a Fj(p)p 2387 3790 534 4 v 71 x Fo(\()p Fn(x)h Fo(+)f Fn(R)2631 3873 y Fk(2)2668 3861 y Fo(\))2700 3837 y Fk(2)2756 3861 y Fo(+)g Fn(y)2883 3837 y Fk(2)2949 3793 y Fo(+)g Fn(C)q(;)456 3995 y(m)529 4007 y Fk(1)605 3995 y Fo(and)38 b Fn(m)850 4007 y Fk(2)926 3995 y Fo(are)g(the)h(masses)e(of)i(the)g (primaries,)h Fn(C)45 b Fo(is)39 b(an)g(arbitrary)d(constan)n(t,)41 b Fn(R)3301 4007 y Fk(1)3380 3995 y Fo(=)608 4061 y Fm(m)667 4069 y Fi(2)p 466 4076 377 4 v 466 4127 a Fk(\()p Fm(m)551 4135 y Fi(1)583 4127 y Fk(+)p Fm(m)693 4135 y Fi(2)725 4127 y Fk(\))751 4110 y Fi(2)p Fh(=)p Fi(3)852 4095 y Fo(,)29 b Fn(R)967 4107 y Fk(2)1029 4095 y Fo(=)1271 4061 y Fm(m)1330 4069 y Fi(1)p 1129 4076 V 1129 4127 a Fk(\()p Fm(m)1214 4135 y Fi(1)1246 4127 y Fk(+)p Fm(m)1356 4135 y Fi(2)1388 4127 y Fk(\))1414 4110 y Fi(2)p Fh(=)p Fi(3)1544 4095 y Fo(and)f Fn(P)1759 4107 y Fk(1)1822 4095 y Fo(=)c(\()p Fn(R)2006 4107 y Fk(1)2043 4095 y Fn(;)14 b Fo(0\),)29 b Fn(P)2259 4107 y Fk(2)2321 4095 y Fo(=)c(\()p Fl(\000)p Fn(R)2571 4107 y Fk(2)2608 4095 y Fn(;)14 b Fo(0\))28 b(are)g(the)h(co)r(ordinates)456 4212 y(of)e(the)h(primaries.)36 b(F)-7 b(or)27 b(con)n(v)n(enience)f(w) n(e)h(c)n(ho)r(ose)g Fn(C)i Fo(=)23 b Fl(\000)2331 4178 y Fm(m)2390 4186 y Fi(1)p 2330 4193 92 4 v 2334 4240 a Fm(R)2384 4248 y Fi(1)2450 4212 y Fl(\000)2543 4178 y Fm(m)2602 4186 y Fi(2)p 2543 4193 V 2547 4240 a Fm(R)2597 4248 y Fi(2)2644 4212 y Fo(,)28 b(so)f(that)h(\012\(0)p Fn(;)14 b Fo(0\))22 b(=)h(0.)555 4319 y(In)32 b(the)h(recen)n(t)e(pap)r (er)h([A],)i(p)r(erio)r(dic)e(and)f(c)n(haotic)g(solutions)h(of)g(the)g (planar)f(restricted)456 4419 y(3-b)r(o)r(dy)39 b(problem)h(w)n(ere)g (in)n(v)n(estigated)f(b)n(y)h(means)g(of)g(computer)g(assisted)g(metho) r(ds)h(and)456 4518 y(top)r(ological)27 b(theorems;)h(a)g(rigorous)e (pro)r(of)i(of)g(the)h(existence)f(of)h(a)f(class)f(of)i(p)r(erio)r (dic)f(orbits)456 4618 y(at)f(di\013eren)n(t)h(energy)e(lev)n(els)h (with)h(a)f(v)n(ery)g(narro)n(w)e(estimate)j(of)f(the)h(lo)r(cations)f (of)g(the)h(in)n(ter-)456 4718 y(section)c(of)h(suc)n(h)f(p)r(erio)r (dic)h(orbits)f(with)h(the)h(line)f(connecting)f(the)h(primaries)f(w)n (as)f(pro)n(vided.)456 4817 y(Here)35 b(w)n(e)g(extend)g(those)g (results)g(in)h(t)n(w)n(o)f(directions.)59 b(First,)38 b(w)n(e)d(pro)n(v)n(e)f(the)h(existence)h(of)456 4917 y(con)n(tin)n(uous)30 b(branc)n(hes)h(of)h(solutions,)g(with)g(either)g (the)g(energy)f(or)g(the)h(ratio)f(b)r(et)n(w)n(een)h(the)p 456 5011 499 4 v 555 5105 a Fq(2000)27 b Fg(Mathematics)f(Subje)l(ct)f (Classi\014c)l(ation.)37 b Fq(34C25,35B10,37J45.)555 5188 y Fg(Key)25 b(wor)l(ds)i(and)g(phr)l(ases.)37 b Fq(Restricted)24 b(3-b)r(o)r(dy)g(problem,)f(p)r(erio)r(dic)h (solutions,)f(linear)h(stabilit)n(y)-6 b(.)555 5269 y(Researc)n(h)22 b(partially)f(supp)r(orted)h(b)n(y)f(MIUR)g(pro)t(ject)g(\\Meto)r(di)h (v)l(ariazionali)f(ed)g(Equazioni)h(Di\013erenziali)456 5352 y(Non)h(Lineari".)1933 5451 y Fk(1)p eop end %%Page: 2 2 TeXDict begin 2 1 bop 456 315 a Fk(2)1208 b(GIANNI)23 b(ARIOLI)456 515 y Fo(masses)28 b(of)h(the)h(primaries)e(as)h(a)g (parameter.)41 b(Second,)30 b(w)n(e)f(study)g(the)h(\(linear\))f (stabilit)n(y)h(of)456 614 y(some)d(orbits.)555 714 y(More)22 b(precisely)-7 b(,)23 b(w)n(e)g(describ)r(e)f(three)h(con)n(tin)n(uous) f(branc)n(hes)g(of)h(p)r(erio)r(dic)f(orbits)h(with)g(the)456 814 y(energy)h(as)h(a)g(parameter)e(and)j(three)f(con)n(tin)n(uous)f (branc)n(hes)g(of)i(p)r(erio)r(dic)f(orbits)g(with)h Fn(m)3308 826 y Fk(1)3370 814 y Fo(as)456 913 y(a)k(parameter.)44 b(Moreo)n(v)n(er,)28 b(w)n(e)i(conjecture)g(that)h(the)g(solutions)e (on)i(t)n(w)n(o)e(of)i(suc)n(h)f(branc)n(hes)456 1013 y(\(in)25 b(b)r(oth)h(cases\))e(are)g(linearly)g(stable,)i(while)f(the) h(other)e(one)h(is)g(unstable.)36 b(F)-7 b(urthermore)24 b(w)n(e)456 1112 y(pro)n(vide)k(explicit)h(functions)35 b(^)-48 b Fn(x)q Fo(\()p Fn(h)p Fo(\))29 b(and)35 b(^)-48 b Fn(x)q Fo(\()p Fn(m)1911 1124 y Fk(1)1948 1112 y Fo(\))30 b(describing)e(the)h(in)n(tersection)g(of)g(the)g(orbits)456 1212 y(with)f(the)g Fn(x)p Fo(-axis)f(in)g(dep)r(endence)i(of)e(the)h (energy)f(or)f Fn(m)2251 1224 y Fk(1)2316 1212 y Fo(resp)r(ectiv)n(ely) -7 b(.)555 1312 y(F)g(or)33 b(three)h(of)g(these)f(six)h(branc)n(hes,)g (w)n(e)f(pro)n(vide)g(a)g(computer)h(assisted)f(pro)r(of)g(of)h(their) 456 1411 y(existence)g(and)g(w)n(e)g(pro)n(vide)f(a)h(rigorous)e Fn(L)1874 1381 y Ff(1)1978 1411 y Fo(b)r(ound)j(on)f(the)h(accuracy)d (of)i(the)h(functions)461 1511 y(^)-47 b Fn(x)p Fo(\()p Fn(h)p Fo(\))27 b(and)32 b(^)-47 b Fn(x)q Fo(\()p Fn(m)956 1523 y Fk(1)993 1511 y Fo(\).)37 b(F)-7 b(or)26 b(the)i(other)e(three)h (branc)n(hes)e(w)n(e)i(can)f(only)h(pro)n(vide)e(a)i(partial)f(pro)r (of.)456 1611 y(Although)32 b(in)h(principle)g(w)n(e)g(could)f(pro)n (vide)g(a)g(full)h(pro)r(of)g(for)f(all)g(branc)n(hes,)h(this)g(has)f (not)456 1710 y(b)r(een)26 b(p)r(ossible)g(b)r(ecause)g(it)g(w)n(ould)g (ha)n(v)n(e)f(required)g(an)h(extremely)g(long)f(computation)h(time.) 555 1810 y(Concerning)39 b(the)h(linear)e(stabilit)n(y)-7 b(,)43 b(w)n(e)c(pro)n(vide)f(a)h(rigorous)f(pro)r(of)h(only)g(for)g(a) g(small)456 1910 y(section)30 b(of)h(the)g(branc)n(h.)46 b(As)31 b(ab)r(o)n(v)n(e,)f(a)g(pro)r(of)h(for)f(all)g(branc)n(hes)g(w) n(ould)g(require)g(to)r(o)h(m)n(uc)n(h)456 2009 y(computation)c(time.) 555 2109 y(These)c(results)g(highligh)n(t)h(some)f(imp)r(ortan)n(t)g (features)g(of)g(computer)g(assisted)g(pro)r(ofs.)35 b(On)456 2208 y(the)k(p)r(ositiv)n(e)f(side,)k(the)d(tec)n(hnique)g(is) g(extremely)f(v)n(ersatile)g(and)h(ma)n(y)f(b)r(e)h(applied)g(to)g(a) 456 2308 y(large)29 b(class)h(of)g(problems)g(for)g(whic)n(h)h(no)f (analytical)g(tec)n(hnique)h(is)f(a)n(v)-5 b(ailable.)45 b(Their)31 b(main)456 2408 y(dra)n(wbac)n(k,)39 b(b)r(esides)g (aesthetic)f(considerations,)h(consist)g(in)f(the)h(di\016cult)n(y)g (of)g(pro)n(viding)456 2507 y(results)27 b(when)g(the)h(parameters)e (en)n(tering)h(the)h(problem)f(assume)g(an)g(arbitrary)f(v)-5 b(alue.)555 2607 y(W)e(e)32 b(p)r(oin)n(t)f(out)g(that,)i(although)d(w) n(e)h(feel)h(that)f(these)g(results)g(are)f(in)n(teresting)h(in)g (them-)456 2707 y(selv)n(es,)24 b(the)i(main)f(purp)r(ose)g(of)g(the)h (pap)r(er)e(is)h(to)g(describ)r(e)g(the)h(computer)f(assisted)f(metho)r (ds)456 2806 y(and)31 b(to)h(sho)n(w)f(ho)n(w)g(their)h(application)f (leads)g(to)h(results)f(otherwise)g(una)n(v)-5 b(ailable.)49 b(All)32 b(the)456 2906 y(pro)r(ofs)19 b(can)h(b)r(e)h(easily)e(repro)r (duced)h(on)g(an)n(y)f(recen)n(t)h(computer.)34 b(T)-7 b(o)20 b(this)g(purp)r(ose,)i(in)e(the)h(last)456 3005 y(section)30 b(w)n(e)h(pro)n(vide)e(all)i(necessary)e(information,)i (mostly)g(b)n(y)g(referring)e(to)i(other)f(pap)r(ers,)456 3105 y(and)d(w)n(e)g(also)g(pro)n(vide)f(on)h(the)h(w)n(eb)g(the)g (Mathematica-C++)e(program)f(w)n(e)i(used.)555 3205 y(The)39 b(la)n(y)n(out)f(of)h(the)g(pap)r(er)g(is)f(as)h(follo)n(ws:)58 b(in)39 b(Section)g(2)g(w)n(e)f(in)n(tro)r(duce)h(some)f(basic)456 3304 y(facts)29 b(concerning)f(the)h(system;)h(in)g(Section)f(3)g(w)n (e)f(summarize)h(some)g(result)f(obtained)h(in)h(a)456 3404 y(previous)g(pap)r(er)h(whic)n(h)g(are)g(relev)-5 b(an)n(t)31 b(to)g(the)h(follo)n(wing)e(sections;)j(in)f(Section)f(4)h (w)n(e)f(state)456 3504 y(our)26 b(results)h(and)h(in)g(section)f(5)g (w)n(e)g(explain)h(the)g(computer)f(assisted)g(pro)r(ofs.)1764 3907 y(2.)41 b Fr(Basics)555 4057 y Fo(It)d(is)g(w)n(ell)f(kno)n(wn)g (that)h Fn(H)7 b Fo(\()p Fn(x;)28 b Fo(_)-37 b Fn(x;)14 b(y)s(;)29 b Fo(_)-38 b Fn(y)s Fo(\))40 b(=)53 b(_)-37 b Fn(x)2014 4026 y Fk(2)2077 4057 y Fo(+)39 b(_)-38 b Fn(y)2210 4026 y Fk(2)2272 4057 y Fl(\000)25 b Fo(2\012\()p Fn(x;)14 b(y)s Fo(\))38 b(is)f(an)g(in)n(tegral)g(of)g(the)456 4156 y(motion)26 b(called)g(the)g Fe(Jac)l(obi)k(inte)l(gr)l(al)p Fo(,)d(therefore)e(the)i(motion)f(tak)n(es)f(place)h(on)g(the)g (manifold)456 4256 y Fn(H)7 b Fo(\()p Fn(x;)28 b Fo(_)-37 b Fn(x;)14 b(y)s(;)29 b Fo(_)-38 b Fn(y)s Fo(\))36 b(=)f Fn(h)p Fo(.)59 b(With)36 b(some)f(abuse)g(of)g(language,)g(w)n(e)g (call)g(the)g(Jacobi)f(in)n(tegral)g(the)456 4355 y Fe(ener)l(gy)h Fo(of)27 b(a)h(solution.)555 4455 y(This)h(system)f(admits)h(\014v)n(e) f(equilibrium)h(p)r(oin)n(ts.)40 b(Three)28 b(suc)n(h)h(p)r(oin)n(ts)f (are)g(aligned)g(with)456 4555 y(the)34 b(primaries)e(and)h(are)g (called)g Fn(L)1586 4567 y Fk(1)1623 4555 y Fo(,)i Fn(L)1738 4567 y Fk(2)1809 4555 y Fo(and)e Fn(L)2033 4567 y Fk(3)2104 4555 y Fo(\(the)h(collinear)e(equilibrium)i(solutions\).)456 4654 y(One)c(of)g(the)h(collinear)e(p)r(oin)n(ts)h(lies)g(b)r(et)n(w)n (een)g(the)h(primaries;)f(call)g(that)h(p)r(oin)n(t)f Fn(L)3085 4666 y Fk(1)3122 4654 y Fo(.)45 b(All)31 b(the)456 4754 y(collinear)24 b(p)r(oin)n(ts)i(are)g(saddles)f(for)g(\012.)37 b(The)26 b(remaining)f(t)n(w)n(o)h(equilibrium)g(p)r(oin)n(ts)g(are)f (called)456 4854 y Fn(L)513 4866 y Fk(4)583 4854 y Fo(and)34 b Fn(L)808 4866 y Fk(5)845 4854 y Fo(;)j(they)e(are)e(the)h(absolute)f (minima)i(of)f(\012)g(and)f(they)i(b)r(oth)f(sit)g(at)g(the)h(v)n (ertices)456 4953 y(of)c(an)h(equilateral)f(triangle)f(with)j(the)f (primaries)e(at)i(the)g(other)f(v)n(ertices)g(\(the)i(equilateral)456 5053 y(equilibrium)27 b(solutions\).)555 5152 y(In)22 b(order)d(to)i(study)h(the)f(system)g(at)g(some)g(\014xed)g(energy)f Fn(h)h Fo(w)n(e)g(consider)f(the)h(half)h(P)n(oincar)n(\023)-39 b(e)456 5252 y(return)33 b(map)h Fn(H)976 5264 y Fk(1)1048 5252 y Fo(:)g Fn(D)r Fo(\()p Fn(H)1277 5264 y Fk(1)1314 5252 y Fo(\))h Fl(\032)e Fd(R)1539 5222 y Fk(2)1610 5252 y Fl(!)i Fd(R)1788 5222 y Fk(2)1859 5252 y Fo(de\014ned)g(as)e(follo)n (ws.)56 b(Giv)n(en)34 b(\()p Fn(x;)14 b(p)2990 5264 y Fm(x)3032 5252 y Fo(\))34 b(suc)n(h)g(that)456 5352 y Fn(x)26 b Fl(6)p Fo(=)g Fl(f)p Fn(R)725 5364 y Fk(1)p Fm(;)801 5352 y Fl(\000)20 b Fn(R)949 5364 y Fk(2)986 5352 y Fl(g)29 b Fo(and)g(2\012\()p Fn(x;)14 b Fo(0\))20 b(+)f Fn(h)h Fl(\000)f Fn(p)1810 5322 y Fk(2)1810 5372 y Fm(x)1878 5352 y Fn(>)26 b Fo(0,)k(there)f(exists)g(a)g(unique)h(p)r (ositiv)n(e)f(v)-5 b(alue)30 b(of)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 1381 315 a Fk(BRANCHES)29 b(OF)g(PERIODIC)g (ORBITS)892 b(3)456 515 y Fn(p)498 527 y Fm(y)560 515 y Fo(=)23 b Fn(p)690 527 y Fm(y)730 515 y Fo(\()p Fn(x;)14 b(p)888 527 y Fm(x)930 515 y Fo(\))23 b(=)1073 444 y Fj(p)p 1156 444 627 4 v 71 x Fo(2\012\()p Fn(x;)14 b Fo(0\))k(+)g Fn(h)h Fl(\000)f Fn(p)1741 491 y Fk(2)1741 535 y Fm(x)1810 515 y Fo(suc)n(h)27 b(that)h Fn(H)7 b Fo(\()p Fn(x;)14 b(p)2411 527 y Fm(x)2453 515 y Fn(;)g Fo(0)p Fn(;)g(p)2611 527 y Fm(y)2650 515 y Fo(\))23 b(=)g Fn(h)p Fo(.)37 b(W)-7 b(e)28 b(let)1216 833 y Fn(H)1285 845 y Fk(1)1323 833 y Fo(\()p Fn(x;)14 b(p)1481 845 y Fm(x)1523 833 y Fo(\))23 b(=)g(\()p Fn(')1752 845 y Fk(1)1790 833 y Fo(\()p Fn(x;)14 b(p)1948 845 y Fm(x)1990 833 y Fo(;)g Fn(T)2076 845 y Fk(1)2112 833 y Fo(\))p Fn(;)g(')2235 845 y Fk(2)2273 833 y Fo(\()p Fn(x;)g(p)2431 845 y Fm(x)2473 833 y Fo(;)g Fn(T)2559 845 y Fk(1)2596 833 y Fo(\)\))p Fn(;)456 1150 y Fo(where)24 b Fn(')p Fo(\()p Fn(x;)14 b(p)905 1162 y Fm(x)947 1150 y Fo(;)g Fl(\001)p Fo(\))24 b(:)f Fd(R)g Fl(!)g Fd(R)1358 1120 y Fk(4)1420 1150 y Fo(is)i(the)g(solution)f(of)h(the)g(equation)g(\(1\))g(with)g(initial)g (conditions)456 1250 y Fn(x)p Fo(\(0\))40 b(=)f Fn(x;)52 b Fo(_)-37 b Fn(x)p Fo(\(0\))40 b(=)f Fn(p)1200 1262 y Fm(x)1241 1250 y Fn(;)f(y)s Fo(\(0\))h(=)g(0,)54 b(_)-38 b Fn(y)s Fo(\(0\))40 b(=)f Fn(p)2035 1262 y Fm(y)2112 1250 y Fo(and)e Fn(')2337 1262 y Fm(i)2365 1250 y Fo(,)j Fn(i)f Fo(=)g(1)p Fn(;)14 b(:)g(:)g(:)f(;)h Fo(4)37 b(are)g(its)g(comp) r(o-)456 1350 y(nen)n(ts.)f(By)27 b(de\014nition)g Fn(')1259 1362 y Fk(3)1297 1350 y Fo(\()p Fn(x;)14 b(p)1455 1362 y Fm(x)1497 1350 y Fo(;)g(0\))23 b(=)g(0)j(and)h Fn(')2002 1362 y Fk(4)2040 1350 y Fo(\()p Fn(x;)14 b(p)2198 1362 y Fm(x)2240 1350 y Fo(;)g(0\))23 b Fn(>)f Fo(0,)27 b(therefore)f Fn(')2955 1362 y Fk(3)2993 1350 y Fo(\()p Fn(x;)14 b(p)3151 1362 y Fm(x)3193 1350 y Fo(;)g Fn(t)p Fo(\))23 b Fn(>)g Fo(0)456 1449 y(for)35 b(all)g(p)r(ositiv)n(e)h(and)g(small)f Fn(t)p Fo(.)62 b(If)36 b(there)g(exists)f(a)h(time)g Fn(T)47 b Fo(suc)n(h)36 b(that)g Fn(')2898 1461 y Fk(3)2935 1449 y Fo(\()p Fn(x;)14 b(p)3093 1461 y Fm(x)3135 1449 y Fo(;)g Fn(T)e Fo(\))36 b(=)h(0)456 1549 y(and)c Fn(')677 1561 y Fk(3)715 1549 y Fo(\()p Fn(x;)14 b(p)873 1561 y Fm(x)915 1549 y Fo(;)g Fn(t)p Fo(\))34 b Fn(>)g Fo(0)f(for)h(all)g Fn(t)f Fl(2)h Fo(\(0)p Fn(;)14 b(T)e Fo(\),)35 b(then)g(w)n(e)f(ha)n(v) n(e)e(\()p Fn(x;)14 b(p)2572 1561 y Fm(x)2615 1549 y Fo(\))34 b Fl(2)g Fn(D)r Fo(\()p Fn(H)2942 1561 y Fk(1)2979 1549 y Fo(\))h(and)f(w)n(e)f(set)456 1649 y Fn(H)525 1661 y Fk(1)562 1649 y Fo(\()p Fn(x;)14 b(p)720 1661 y Fm(x)762 1649 y Fo(\))23 b(=)g(\()p Fn(')991 1661 y Fk(1)1029 1649 y Fo(\()p Fn(x;)14 b(p)1187 1661 y Fm(x)1229 1649 y Fo(;)g Fn(T)e Fo(\))p Fn(;)i(')1450 1661 y Fk(2)1487 1649 y Fo(\()p Fn(x;)g(p)1645 1661 y Fm(x)1687 1649 y Fo(;)g Fn(T)e Fo(\)\).)555 1748 y(By)41 b(insp)r(ection)h(it)f(is)g (easy)g(to)g(see)g(that,)k(if)c(\()p Fn(x)p Fo(\()p Fn(t)p Fo(\))p Fn(;)14 b(y)s Fo(\()p Fn(t)p Fo(\)\))43 b(is)e(a)g(solution)g (of)g(\(1\),)k(then)456 1848 y(\()5 b(~)-47 b Fn(x)p Fo(\()p Fn(t)p Fo(\))p Fn(;)20 b Fo(~)-48 b Fn(y)s Fo(\()p Fn(t)p Fo(\)\))25 b(:=)e(\()p Fn(x)p Fo(\()p Fl(\000)p Fn(t)p Fo(\))p Fn(;)14 b Fl(\000)p Fn(y)s Fo(\()p Fl(\000)p Fn(t)p Fo(\)\))28 b(is)g(also)f(a)g(solution.)37 b(As)28 b(it)g(is)g(w)n(ell)f(kno)n(wn,)h(if)g(there)g(exist)456 1947 y Fn(x)503 1959 y Fk(1)540 1947 y Fo(,)f Fn(x)637 1959 y Fk(2)701 1947 y Fo(suc)n(h)f(that)h Fn(H)1135 1959 y Fk(1)1172 1947 y Fo(\()p Fn(x)1251 1959 y Fk(1)1289 1947 y Fn(;)14 b Fo(0\))23 b(=)f(\()p Fn(x)1589 1959 y Fk(2)1627 1947 y Fn(;)14 b Fo(0\),)27 b(then)f(there)h(exists)e(a)h (p)r(erio)r(dic)h(orbit)e(of)i(\(1\))f(whose)456 2047 y(in)n(tersections)h(with)h(the)h Fn(x)p Fo(-axis)f(o)r(ccur)f (orthogonally)f(at)i(\()p Fn(x)2401 2059 y Fk(1)2439 2047 y Fn(;)14 b Fo(0\))28 b(and)g(\()p Fn(x)2819 2059 y Fk(2)2857 2047 y Fn(;)14 b Fo(0\),)28 b(resp)r(ectiv)n(ely)456 2147 y(with)34 b(p)r(ositiv)n(e)g(and)g(negativ)n(e)f Fn(y)s Fl(\000)p Fo(v)n(elo)r(cit)n(y)-7 b(.)56 b(On)34 b(the)g(other)g(hand,)i(if)f(the)f(system)g(admits)456 2246 y(a)g(p)r(erio)r(dic)i(orbit)f(whic)n(h)g(crosses)e(orthogonally)g (the)j Fn(x)p Fo(-axis)e(at)i(some)e(p)r(oin)n(ts)i Fn(x)3118 2258 y Fk(1)3191 2246 y Fo(and)f Fn(x)3407 2258 y Fk(2)456 2346 y Fo(\(resp.)43 b(with)30 b(p)r(ositiv)n(e)f(and)h(negativ)n(e)f Fn(y)s Fl(\000)p Fo(v)n(elo)r(cit)n(y\),)g(then)h Fn(H)2430 2358 y Fk(1)2467 2346 y Fo(\()p Fn(x)2546 2358 y Fk(1)2584 2346 y Fn(;)14 b Fo(0\))27 b(=)f(\()p Fn(x)2892 2358 y Fk(2)2930 2346 y Fn(;)14 b Fo(0\).)43 b(It)30 b(follo)n(ws)456 2446 y(that,)24 b(in)f(order)e(to)i(study)g(the)g(p)r(erio)r(dic)g (orbits)f(of)h(\(1\))g(it)h(is)e(con)n(v)n(enien)n(t)g(to)h(study)g (the)g(second)456 2545 y(comp)r(onen)n(t)k(of)g Fn(H)1043 2557 y Fk(1)1081 2545 y Fo(\()p Fn(x;)14 b Fo(0\))28 b(as)f(describ)r(ed)g(in)h(Section)g(5.)1539 3238 y(3.)41 b Fr(Previous)31 b(resul)-6 b(ts)555 3388 y Fo(The)36 b(case)e(considered)h(in)h([A])g(is)f(usually)g(referred)f(to)i(as)f (\\the)g(Cop)r(enhagen)g(orbits",)456 3487 y(from)24 b(the)i(results)f(of)g(the)g(Observ)-5 b(atory)23 b(of)i(Cop)r(enhagen) g(\(see)g([S])g(and)g(references)f(therein\).)456 3587 y(W)-7 b(e)31 b(recall)e(that,)j(b)n(y)e(our)g(c)n(hoice)g(of)g(the)h (constan)n(t)f Fn(C)37 b Fo(in)31 b(\(2\),)h Fn(h)c Fo(=)f(0)k(is)f (the)h(energy)f(of)g(the)456 3687 y(stationary)36 b(solution)h(at)h (the)g(Lagrangian)d(p)r(oin)n(t)j Fn(L)2179 3699 y Fk(1)2253 3687 y Fo(\(the)h(origin\).)66 b(Since)38 b(the)g(problem)456 3786 y(has)27 b(the)h(additional)f(symmetry)g(consisting)g(in)h(switc)n (hing)f(the)h(primaries,)f(w)n(e)g(only)g(lo)r(ok)n(ed)456 3886 y(for)i(orbits)g(that)h(cross)e(the)i(p)r(ortion)f(of)h(the)g Fn(x)p Fo(-axis)f(b)r(et)n(w)n(een)g(the)h(primaries)f(with)h(p)r (ositiv)n(e)456 3985 y(sp)r(eed)36 b(in)h(the)g Fn(y)i Fo(direction.)63 b(The)37 b(lo)n(w)n(est)e(v)-5 b(alue)36 b(of)h Fn(h)f Fo(w)n(e)g(considered)g(w)n(as)f(0,)j(when)f(the)456 4085 y(admissible)26 b(region)g(is)h(split)h(in)f(t)n(w)n(o)g(parts)f (touc)n(hing)h(at)g(the)g(origin)f(and)h(no)g(tra)5 b(jectory)26 b(can)456 4185 y(en)n(ter)32 b(b)r(oth)i(regions.)52 b(The)33 b(highest)g(v)-5 b(alue)33 b(of)g Fn(h)g Fo(w)n(e)f (considered)g(is)h(0)p Fn(:)p Fo(8,)h(since)f(at)g(sligh)n(tly)456 4284 y(larger)27 b(v)-5 b(alue)28 b(the)h(b)r(ounded)h(admissible)e (region)g(touc)n(hes)g(the)h(un)n(b)r(ounded)g(part)f(and)h(some)456 4384 y(tra)5 b(jectory)18 b(starting)i(close)f(to)h(the)h(primaries)e (ma)n(y)h(b)r(e)g(un)n(b)r(ounded.)35 b(A)21 b(subset)f(of)g(the)h (results)456 4484 y(on)27 b(p)r(erio)r(dic)g(orbits)g(giv)n(en)g(in)h ([A])g(is)g(the)f(follo)n(wing)g(Theorem:)456 4738 y Fs(Theorem)44 b(3.1.)k Fe(L)l(et)40 b Fn(m)1299 4750 y Fk(1)1378 4738 y Fo(=)i Fn(m)1558 4750 y Fk(2)1638 4738 y Fo(=)g(1)p Fe(.)71 b(F)-6 b(or)41 b(al)t(l)g(ener)l(gy)g(values) g(displaye)l(d)i(in)e(c)l(olumn)456 4837 y Fn(h)35 b Fe(of)i(\(3\),)h(system)e(\(1\))g(admits)g(at)g(le)l(ast)g(a)g(p)l (erio)l(dic)i(solution)e(for)h(e)l(ach)g(value)f(printe)l(d)g(in)456 4937 y(the)j(r)l(emaining)g(c)l(olumns.)66 b(Such)39 b(solution)g(cr)l(osses)g(the)g Fn(x)p Fe(-axis)g(ortho)l(gonal)t(ly)j (twic)l(e)d(and)456 5037 y(only)32 b(twic)l(e.)44 b(The)33 b Fn(x)p Fe(-c)l(o)l(or)l(dinate)f(of)h(the)e(interse)l(ction)h(with)g (p)l(ositive)h Fn(y)s Fe(-velo)l(city)f(lies)h(in)e(the)456 5136 y(interval)24 b(c)l(enter)l(e)l(d)e(in)i(the)f(p)l(osition)i (given)f(in)f(the)g(table)h(with)g(width)g Fo(10)2702 5106 y Ff(\000)p Fk(3)2790 5136 y Fe(.)37 b(The)24 b(orbits)g(in)f(the) 456 5236 y(c)l(olumn)30 b Fn(S)794 5248 y Fk(2)862 5236 y Fe(ar)l(e)h(r)l(etr)l(o)l(gr)l(ade)g(ar)l(ound)g Fn(P)1725 5248 y Fk(2)1762 5236 y Fe(;)h(the)f(orbits)g(in)g(the)g(classes)g Fn(S)2756 5248 y Fk(1)2824 5236 y Fe(ar)l(e)g(dir)l(e)l(ct)g(ar)l(ound) 456 5336 y Fn(P)509 5348 y Fk(1)546 5336 y Fe(;)f(the)g(orbits)h(in)e (the)h(class)h Fn(L)e Fe(ar)l(e)h(r)l(etr)l(o)l(gr)l(ade)g(ar)l(ound)g Fn(L)2361 5348 y Fk(1)2398 5336 y Fe(.)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 456 315 a Fk(4)1208 b(GIANNI)23 b(ARIOLI)456 1064 y Fo(\(3\))1403 665 y Fn(h)162 b(S)1664 677 y Fk(1)1959 665 y Fn(S)2010 677 y Fk(2)2341 665 y Fn(L)1406 765 y Fo(0)94 b(0)p Fn(:)p Fo(3158)80 b Fl(\000)p Fo(0)p Fn(:)p Fo(4399)1394 864 y Fn(:)p Fo(1)j(0)p Fn(:)p Fo(3028)d Fl(\000)p Fo(0)p Fn(:)p Fo(4365)h(0)p Fn(:)p Fo(02697)1394 964 y Fn(:)p Fo(2)i(0)p Fn(:)p Fo(2883)d Fl(\000)p Fo(0)p Fn(:)p Fo(4330)h(0)p Fn(:)p Fo(03894)1394 1064 y Fn(:)p Fo(3)i(0)p Fn(:)p Fo(2712)d Fl(\000)p Fo(0)p Fn(:)p Fo(4294)h(0)p Fn(:)p Fo(04873)1394 1163 y Fn(:)p Fo(4)i(0)p Fn(:)p Fo(2443)d Fl(\000)p Fo(0)p Fn(:)p Fo(4257)h(0)p Fn(:)p Fo(05751)1394 1263 y Fn(:)p Fo(5)396 b Fl(\000)p Fo(0)p Fn(:)p Fo(4218)81 b(0)p Fn(:)p Fo(06575)1394 1362 y Fn(:)p Fo(6)396 b Fl(\000)p Fo(0)p Fn(:)p Fo(4178)81 b(0)p Fn(:)p Fo(07369)1394 1462 y Fn(:)p Fo(8)396 b Fl(\000)p Fo(0)p Fn(:)p Fo(4093)81 b(0)p Fn(:)p Fo(08922)555 1780 y(In)30 b([A])g(w)n(e)f(left)h(op)r(en)f(a)g(few)h(questions:)39 b(are)29 b(the)g(orbits)g(unique)h(in)f(the)h(in)n(terv)-5 b(al)29 b(of)g(the)456 1879 y Fn(x)p Fl(\000)p Fo(axis)f(of)i(width)g (10)1156 1849 y Ff(\000)p Fk(3)1273 1879 y Fo(men)n(tioned)g(ab)r(o)n (v)n(e?)41 b(Do)30 b(orbits)e(describ)r(ed)i(b)n(y)f(the)h(same)e (column)456 1979 y(b)r(elong)j(to)g(a)g(con)n(tin)n(uous)f(branc)n(h)g (of)h(p)r(erio)r(dic)h(solutions)e(as)h(the)g(n)n(umerical)g(exp)r (erimen)n(ts)456 2078 y(hin)n(t?)37 b(Are)27 b(the)h(orbits)f(linearly) g(stable?)1734 2355 y(4.)41 b Fr(Resul)-6 b(ts)555 2504 y Fo(In)42 b(order)e(to)h(simplify)h(the)g(statemen)n(ts)f(of)g(the)h (result)f(w)n(e)g(in)n(tro)r(duce)g(the)h(follo)n(wing)456 2604 y(notation:)h(if)31 b Fn(x)e Fl(2)g Fd(R)i Fo(and)f Fn(\016)i(>)c Fo(0)i(let)i Fn(x)21 b Fl(\006)f Fn(\016)32 b Fo(:=)c([)p Fn(x)21 b Fl(\000)f Fn(\016)o(;)14 b(x)20 b Fo(+)h Fn(\016)s Fo(].)47 b(The)30 b(\014rst)h(results)f(concern)456 2703 y(branc)n(hes)c(of)h(orbits)g(for)g(v)-5 b(arying)27 b(energy)-7 b(.)456 2928 y(4.1.)40 b Fs(Branc)m(hes)35 b(of)f(Cop)s(enhagen)f(orbits)g(with)h(the)f(energy)h(as)g(a)h (parameter.)41 b Fo(In)456 3027 y(this)c(subsection)g(w)n(e)g(pro)n(v)n (e)f(that)h(the)h(v)-5 b(alues)37 b(prin)n(ted)g(in)h(the)f(columns)h Fn(L)p Fo(,)h Fn(S)3065 3039 y Fk(2)3139 3027 y Fo(of)f(T)-7 b(able)456 3127 y(\(3\))30 b(actually)g(b)r(elong)g(to)g(single)g (branc)n(hes)f(of)h(solutions)g(and)g(w)n(e)g(pro)n(vide)f(a)h(partial) g(result)456 3227 y(concerning)c Fn(S)922 3239 y Fk(1)959 3227 y Fo(.)37 b(Let)706 3399 y(^)-47 b Fn(x)748 3411 y Fm(L)798 3399 y Fo(\()p Fn(h)p Fo(\))23 b(=)g(0)p Fn(:)p Fo(00421194)14 b(+)k(0)p Fn(:)p Fo(964456)c Fn(h)h Fl(\000)j Fo(25)p Fn(:)p Fo(5237)c Fn(h)2333 3364 y Fk(2)2385 3399 y Fo(+)k(607)p Fn(:)p Fo(141)c Fn(h)2805 3364 y Fk(3)929 3538 y Fl(\000)k Fo(9765)p Fn(:)p Fo(68)c Fn(h)1349 3503 y Fk(4)1401 3538 y Fo(+)k(105786)c Fn(h)1798 3503 y Fk(5)1850 3538 y Fl(\000)19 b Fo(779487)14 b Fn(h)2248 3503 y Fk(6)2300 3538 y Fo(+)k(3)p Fn(:)p Fo(9051)c(10)2710 3503 y Fk(6)2762 3538 y Fn(h)2810 3503 y Fk(7)929 3677 y Fl(\000)k Fo(1)p Fn(:)p Fo(30082)c(10)1381 3642 y Fk(7)1432 3677 y Fn(h)1480 3642 y Fk(8)1535 3677 y Fo(+)k(2)p Fn(:)p Fo(69484)c(10)1987 3642 y Fk(7)2038 3677 y Fn(h)2086 3642 y Fk(9)2142 3677 y Fl(\000)k Fo(2)p Fn(:)p Fo(8188)c(10)2552 3642 y Fk(7)2603 3677 y Fn(h)2651 3642 y Fk(10)2740 3677 y Fl(\000)k Fo(183369)p Fn(:)c(h)3160 3642 y Fk(11)929 3816 y Fo(+)k(2)p Fn(:)p Fo(25854)c(10)1381 3781 y Fk(7)1432 3816 y Fn(h)1480 3781 y Fk(12)1568 3816 y Fo(+)k(4750983)c Fn(h)2007 3781 y Fk(13)2092 3816 y Fl(\000)k Fo(16231191)c Fn(h)2573 3781 y Fk(14)2658 3816 y Fl(\000)k Fo(17340947)c Fn(h)3139 3781 y Fk(15)929 3955 y Fl(\000)k Fo(4)p Fn(:)p Fo(27086)c(10)1381 3920 y Fk(6)1432 3955 y Fn(h)1480 3920 y Fk(16)1568 3955 y Fo(+)k(9)p Fn(:)p Fo(87905)c(10)2020 3920 y Fk(6)2071 3955 y Fn(h)2119 3920 y Fk(17)2208 3955 y Fo(+)k(1)p Fn(:)p Fo(79343)c(10)2660 3920 y Fk(7)2711 3955 y Fn(h)2759 3920 y Fk(18)929 4093 y Fo(+)k(1)p Fn(:)p Fo(9389)c(10)1339 4059 y Fk(7)1390 4093 y Fn(h)1438 4059 y Fk(19)1527 4093 y Fo(+)k(1)p Fn(:)p Fo(67368)c(10)1979 4059 y Fk(7)2030 4093 y Fn(h)2078 4059 y Fk(20)2148 4093 y Fn(;)678 4232 y Fo(^)-47 b Fn(x)720 4244 y Fm(S)761 4252 y Fi(1)798 4232 y Fo(\()p Fn(h)p Fo(\))23 b(=)g(0)p Fn(:)p Fo(315762)15 b Fl(\000)j Fo(0)p Fn(:)p Fo(222075)c Fn(h)h Fl(\000)j Fo(1)p Fn(:)p Fo(96366)c Fn(h)2250 4198 y Fk(2)2302 4232 y Fo(+)k(43)p Fn(:)p Fo(5272)c Fn(h)2722 4198 y Fk(3)929 4371 y Fl(\000)k Fo(501)p Fn(:)p Fo(934)c Fn(h)1349 4337 y Fk(4)1401 4371 y Fo(+)k(2634)p Fn(:)p Fo(33)c Fn(h)1821 4337 y Fk(5)1874 4371 y Fl(\000)k Fo(5256)p Fn(:)p Fo(63)c Fn(h)2294 4337 y Fk(6)2328 4371 y Fn(;)678 4510 y Fo(^)-47 b Fn(x)720 4522 y Fm(S)761 4530 y Fi(2)798 4510 y Fo(\()p Fn(h)p Fo(\))23 b(=)g Fl(\000)p Fo(0)p Fn(:)p Fo(439928)14 b(+)k(0)p Fn(:)p Fo(0664862)c Fn(h)h Fo(+)j(0)p Fn(:)p Fo(0208835)c Fn(h)2440 4476 y Fk(2)2491 4510 y Fo(+)k(0)p Fn(:)p Fo(00925382)c Fn(h)3037 4476 y Fk(3)3070 4510 y Fn(:)555 4683 y Fo(The)28 b(follo)n(wing)e(theorems)h(hold:)456 4854 y Fs(Theorem)k(4.1.)39 b Fe(L)l(et)29 b Fn(m)1266 4866 y Fk(1)1327 4854 y Fo(=)22 b Fn(m)1487 4866 y Fk(2)1547 4854 y Fo(=)h(1)p Fe(,)30 b(let)f Fn(I)1884 4866 y Fm(h)1951 4854 y Fo(=)g([)p Fn(:)p Fo(01)p Fn(;)14 b(:)p Fo(8])28 b Fe(and)i(let)f Fn(\016)d Fo(=)d Fn(:)p Fo(0002)p Fe(.)36 b(Ther)l(e)31 b(exists)456 4953 y(a)j(c)l(ontinuous)f(function)g Fn(x)1331 4965 y Fm(L)1411 4953 y Fo(:)e Fn(I)1501 4965 y Fm(h)1574 4953 y Fl(!)f Fo([)p Fn(:)p Fo(008)p Fn(;)14 b(:)p Fo(09])32 b Fe(such)i(that)f(for)i(al)t(l)f Fn(h)c Fl(2)h Fn(I)2883 4965 y Fm(h)2960 4953 y Fe(ther)l(e)j(exists)f(a)456 5053 y(p)l(erio)l(dic)39 b(orbit)e(of)h(\(1\))f(of)h(ener)l(gy)f Fn(h)g Fe(cr)l(ossing)g(the)g Fn(x)p Fl(\000)p Fe(axis)g(at)g Fn(x)g Fo(=)e Fn(x)2788 5065 y Fm(L)2838 5053 y Fo(\()p Fn(h)p Fo(\))i Fe(with)h(p)l(ositive)456 5152 y Fn(y)s Fe(-velo)l(city.)h(Such)29 b(orbit)h(is)g(r)l(etr)l(o)l(gr)l(ade)g(ar)l (ound)g Fn(L)2071 5164 y Fk(1)2108 5152 y Fe(.)38 b(F)-6 b(urthermor)l(e)30 b Fn(x)2698 5164 y Fm(L)2748 5152 y Fo(\()p Fn(h)p Fo(\))23 b Fl(2)29 b Fo(^)-47 b Fn(x)3009 5164 y Fm(L)3059 5152 y Fo(\()p Fn(h)p Fo(\))18 b Fl(\006)g Fn(\016)32 b Fe(for)456 5252 y(al)t(l)e Fn(h)23 b Fl(2)h Fn(I)760 5264 y Fm(h)803 5252 y Fe(.)39 b(F)-6 b(or)30 b(al)t(l)g Fn(h)23 b Fl(2)h Fn(I)1326 5264 y Fm(h)1399 5252 y Fe(and)30 b(for)h(al)t(l)36 b Fo(\026)-48 b Fn(x)24 b Fl(2)29 b Fo(^)-48 b Fn(x)2007 5264 y Fm(L)2057 5252 y Fo(\()p Fn(h)p Fo(\))19 b Fl(\006)f Fn(\016)s Fe(,)36 b Fo(\026)-48 b Fn(x)24 b Fl(6)p Fo(=)e Fn(x)2571 5264 y Fm(L)2622 5252 y Fo(\()p Fn(h)p Fo(\))30 b Fe(ther)l(e)f(is)h(no)g (orbit)h(of)456 5352 y(ener)l(gy)f Fn(h)f Fe(cr)l(ossing)h(the)g Fn(x)p Fl(\000)p Fe(axis)g(ortho)l(gonal)t(ly)j(at)i Fo(\026)-48 b Fn(x)q Fe(.)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 1381 315 a Fk(BRANCHES)29 b(OF)g(PERIODIC)g (ORBITS)892 b(5)1050 1632 y @beginspecial 91 @llx 3 @lly 322 @urx 146 @ury 2160 @rwi 1440 @rhi @setspecial %%BeginDocument: L.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 146 %%HiResBoundingBox: 91.5625 3.1875 321.938 145.5 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:12:15) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 148.688 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 145.500 moveto 321.938 145.500 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 145.500 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 145.500000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 142.312500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 1.19048 0.0147151 6.59563 [ [.2619 .00222 -9 -9 ] [.2619 .00222 9 0 ] [.5 .00222 -9 -9 ] [.5 .00222 9 0 ] [.7381 .00222 -9 -9 ] [.7381 .00222 9 0 ] [.97619 .00222 -9 -9 ] [.97619 .00222 9 0 ] [1.025 .01472 0 -4.90625 ] [1.025 .01472 10 4.90625 ] [.01131 .14663 -24 -4.5 ] [.01131 .14663 0 4.5 ] [.01131 .27854 -24 -4.5 ] [.01131 .27854 0 4.5 ] [.01131 .41045 -24 -4.5 ] [.01131 .41045 0 4.5 ] [.01131 .54237 -24 -4.5 ] [.01131 .54237 0 4.5 ] [.02381 .64303 -5 0 ] [.02381 .64303 5 9.8125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .2619 .01472 m .2619 .02097 L s [(0.2)] .2619 .00222 0 1 Mshowa .5 .01472 m .5 .02097 L s [(0.4)] .5 .00222 0 1 Mshowa .7381 .01472 m .7381 .02097 L s [(0.6)] .7381 .00222 0 1 Mshowa .97619 .01472 m .97619 .02097 L s [(0.8)] .97619 .00222 0 1 Mshowa .125 Mabswid .08333 .01472 m .08333 .01847 L s .14286 .01472 m .14286 .01847 L s .20238 .01472 m .20238 .01847 L s .32143 .01472 m .32143 .01847 L s .38095 .01472 m .38095 .01847 L s .44048 .01472 m .44048 .01847 L s .55952 .01472 m .55952 .01847 L s .61905 .01472 m .61905 .01847 L s .67857 .01472 m .67857 .01847 L s .79762 .01472 m .79762 .01847 L s .85714 .01472 m .85714 .01847 L s .91667 .01472 m .91667 .01847 L s .25 Mabswid 0 .01472 m 1 .01472 L s gsave 1.025 .01472 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (h) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .14663 m .03006 .14663 L s [(0.02)] .01131 .14663 1 0 Mshowa .02381 .27854 m .03006 .27854 L s [(0.04)] .01131 .27854 1 0 Mshowa .02381 .41045 m .03006 .41045 L s [(0.06)] .01131 .41045 1 0 Mshowa .02381 .54237 m .03006 .54237 L s [(0.08)] .01131 .54237 1 0 Mshowa .125 Mabswid .02381 .04769 m .02756 .04769 L s .02381 .08067 m .02756 .08067 L s .02381 .11365 m .02756 .11365 L s .02381 .17961 m .02756 .17961 L s .02381 .21258 m .02756 .21258 L s .02381 .24556 m .02756 .24556 L s .02381 .31152 m .02756 .31152 L s .02381 .3445 m .02756 .3445 L s .02381 .37747 m .02756 .37747 L s .02381 .44343 m .02756 .44343 L s .02381 .47641 m .02756 .47641 L s .02381 .50939 m .02756 .50939 L s .02381 .57534 m .02756 .57534 L s .02381 .60832 m .02756 .60832 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .0425 m .03279 .06429 L .04262 .08398 L .06244 .11473 L .08426 .1404 L .10458 .16029 L .14357 .19305 L .18502 .22332 L .22495 .24938 L .26336 .27244 L .30423 .29555 L .34358 .3168 L .38141 .33642 L .4217 .35655 L .46047 .37531 L .5017 .39479 L .54141 .41323 L .5796 .4307 L .62025 .44897 L .65938 .46629 L .70096 .48453 L .74102 .50202 L .77957 .51878 L .82058 .53645 L .86007 .55335 L .89804 .5697 L .93846 .58706 L .97619 .60332 L s % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1670 1732 a Fe(Gr)l(aph)31 b(of)36 b Fo(^)-47 b Fn(x)2067 1744 y Fm(L)2117 1732 y Fo(\()p Fn(h)p Fo(\))555 1876 y(Next)28 b(w)n(e)f(consider)g(the)h(orbits)f(in)h(the)g(class)e Fn(S)2068 1888 y Fk(1)p Fm(;)p Fk(2)2158 1876 y Fo(.)456 2021 y Fs(Conjecture)e(4.2.)34 b Fe(L)l(et)23 b Fn(m)1332 2033 y Fk(1)1392 2021 y Fo(=)g Fn(m)1553 2033 y Fk(2)1613 2021 y Fo(=)g(1)p Fe(,)h(let)g Fn(I)1939 2033 y Fm(h)2005 2021 y Fo(=)f([0)p Fn(;)14 b(:)p Fo(28])22 b Fe(and)i(let)g Fn(\016)i Fo(=)d Fn(:)p Fo(0004)p Fe(.)34 b(Ther)l(e)25 b(exists)456 2121 y(a)34 b(c)l(ontinuous)g(function)g Fn(x)1333 2133 y Fm(S)1374 2141 y Fi(1)1442 2121 y Fo(:)d Fn(I)1532 2133 y Fm(h)1607 2121 y Fl(!)h Fo([)p Fn(:)p Fo(27)p Fn(;)14 b(:)p Fo(32])32 b Fe(such)i(that)h(for)g(al)t(l)g Fn(h)c Fl(2)h Fn(I)2881 2133 y Fm(h)2959 2121 y Fe(ther)l(e)i(exists)g (a)456 2220 y(p)l(erio)l(dic)j(orbit)f(of)g(\(1\))f(of)h(ener)l(gy)g Fn(h)f Fe(cr)l(ossing)h(the)f Fn(x)p Fl(\000)p Fe(axis)h(at)f Fn(x)e Fo(=)g Fn(x)2764 2232 y Fm(S)2805 2240 y Fi(1)2842 2220 y Fo(\()p Fn(h)p Fo(\))i Fe(with)h(p)l(ositive)456 2320 y Fn(y)s Fe(-velo)l(city.)j(Such)28 b(orbit)h(is)g(dir)l(e)l(ct)g (ar)l(ound)g Fn(P)1903 2332 y Fk(2)1941 2320 y Fe(.)38 b(F)-6 b(urthermor)l(e)29 b Fn(x)2530 2332 y Fm(S)2571 2340 y Fi(1)2607 2320 y Fo(\()p Fn(h)p Fo(\))24 b Fl(2)29 b Fo(^)-48 b Fn(x)2868 2332 y Fm(S)2909 2340 y Fi(1)2946 2320 y Fo(\()p Fn(h)p Fo(\))16 b Fl(\006)g Fn(\016)32 b Fe(for)d(al)t(l)456 2420 y Fn(h)d Fl(2)h Fn(I)648 2432 y Fm(h)692 2420 y Fe(.)44 b(F)-6 b(or)32 b(al)t(l)h Fn(h)27 b Fl(2)g Fn(I)1232 2432 y Fm(h)1307 2420 y Fe(and)32 b(for)h(al)t(l)38 b Fo(\026)-47 b Fn(x)27 b Fl(2)32 b Fo(^)-47 b Fn(x)1929 2432 y Fm(S)1970 2440 y Fi(1)2007 2420 y Fo(\()p Fn(h)p Fo(\))20 b Fl(\006)f Fn(\016)s Fe(,)38 b Fo(\026)-47 b Fn(x)27 b Fl(6)p Fo(=)f Fn(x)2533 2432 y Fm(S)2574 2440 y Fi(1)2611 2420 y Fo(\()p Fn(h)p Fo(\))32 b Fe(ther)l(e)g(is)g(no)g(orbit)h(of)456 2519 y(ener)l(gy)d Fn(h)f Fe(cr)l(ossing)h(the)g Fn(x)p Fl(\000)p Fe(axis)g(ortho)l(gonal)t(ly)j(at)i Fo(\026)-48 b Fn(x)q Fe(.)973 3775 y @beginspecial 91 @llx 3 @lly 322 @urx 146 @ury 2344 @rwi 1457 @rhi @setspecial %%BeginDocument: S1.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 146 %%HiResBoundingBox: 91.5625 3.1875 321.938 145.5 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:10:36) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 148.688 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 145.500 moveto 321.938 145.500 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 145.500 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 145.500000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 142.312500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 3.40136 -3.94514 14.4047 [ [.19388 .36377 -12 -9 ] [.19388 .36377 12 0 ] [.36395 .36377 -9 -9 ] [.36395 .36377 9 0 ] [.53401 .36377 -12 -9 ] [.53401 .36377 12 0 ] [.70408 .36377 -9 -9 ] [.70408 .36377 9 0 ] [.87415 .36377 -12 -9 ] [.87415 .36377 12 0 ] [1.025 .37627 0 -4.90625 ] [1.025 .37627 10 4.90625 ] [.01131 .08817 -24 -4.5 ] [.01131 .08817 0 4.5 ] [.01131 .23222 -24 -4.5 ] [.01131 .23222 0 4.5 ] [.01131 .52031 -24 -4.5 ] [.01131 .52031 0 4.5 ] [.02381 .64303 -5 0 ] [.02381 .64303 5 9.8125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .19388 .37627 m .19388 .38252 L s [(0.05)] .19388 .36377 0 1 Mshowa .36395 .37627 m .36395 .38252 L s [(0.1)] .36395 .36377 0 1 Mshowa .53401 .37627 m .53401 .38252 L s [(0.15)] .53401 .36377 0 1 Mshowa .70408 .37627 m .70408 .38252 L s [(0.2)] .70408 .36377 0 1 Mshowa .87415 .37627 m .87415 .38252 L s [(0.25)] .87415 .36377 0 1 Mshowa .125 Mabswid .05782 .37627 m .05782 .38002 L s .09184 .37627 m .09184 .38002 L s .12585 .37627 m .12585 .38002 L s .15986 .37627 m .15986 .38002 L s .22789 .37627 m .22789 .38002 L s .2619 .37627 m .2619 .38002 L s .29592 .37627 m .29592 .38002 L s .32993 .37627 m .32993 .38002 L s .39796 .37627 m .39796 .38002 L s .43197 .37627 m .43197 .38002 L s .46599 .37627 m .46599 .38002 L s .5 .37627 m .5 .38002 L s .56803 .37627 m .56803 .38002 L s .60204 .37627 m .60204 .38002 L s .63605 .37627 m .63605 .38002 L s .67007 .37627 m .67007 .38002 L s .7381 .37627 m .7381 .38002 L s .77211 .37627 m .77211 .38002 L s .80612 .37627 m .80612 .38002 L s .84014 .37627 m .84014 .38002 L s .90816 .37627 m .90816 .38002 L s .94218 .37627 m .94218 .38002 L s .97619 .37627 m .97619 .38002 L s .25 Mabswid 0 .37627 m 1 .37627 L s gsave 1.025 .37627 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (h) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .08817 m .03006 .08817 L s [(0.28)] .01131 .08817 1 0 Mshowa .02381 .23222 m .03006 .23222 L s [(0.29)] .01131 .23222 1 0 Mshowa .02381 .52031 m .03006 .52031 L s [(0.31)] .01131 .52031 1 0 Mshowa .125 Mabswid .02381 .11698 m .02756 .11698 L s .02381 .14579 m .02756 .14579 L s .02381 .1746 m .02756 .1746 L s .02381 .20341 m .02756 .20341 L s .02381 .26103 m .02756 .26103 L s .02381 .28984 m .02756 .28984 L s .02381 .31865 m .02756 .31865 L s .02381 .34746 m .02756 .34746 L s .02381 .40508 m .02756 .40508 L s .02381 .43389 m .02756 .43389 L s .02381 .46269 m .02756 .46269 L s .02381 .4915 m .02756 .4915 L s .02381 .05936 m .02756 .05936 L s .02381 .03055 m .02756 .03055 L s .02381 .00174 m .02756 .00174 L s .02381 .54912 m .02756 .54912 L s .02381 .57793 m .02756 .57793 L s .02381 .60674 m .02756 .60674 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .58435 L .10458 .56226 L .14415 .5407 L .18221 .51954 L .22272 .49675 L .26171 .4747 L .30316 .45119 L .34309 .42845 L .3815 .40645 L .42237 .38284 L .46172 .35984 L .49955 .33739 L .53984 .31306 L .57861 .28917 L .61984 .26321 L .65954 .23764 L .69774 .21251 L .73838 .18521 L .77751 .15839 L .81909 .12936 L .85916 .10087 L .89771 .073 L .93871 .04283 L .97619 .01472 L s % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1657 3875 a(Gr)l(aph)31 b(of)k Fo(^)-47 b Fn(x)2053 3887 y Fm(S)2094 3895 y Fi(1)2131 3875 y Fo(\()p Fn(h)p Fo(\))555 4020 y(In)28 b(principle)g(w)n(e)f(ha)n(v)n(e) f(the)i(means)g(to)f(pro)n(v)n(e)f(Conjecture)h(4.2,)g(and)h(w)n(e)f(b) r(eliev)n(e)g(it)i(to)e(b)r(e)456 4119 y(true.)41 b(But)30 b(a)f(full)h(pro)r(of)f(with)g(our)g(metho)r(d)h(w)n(ould)f(require)f (ab)r(out)h(10)f(y)n(ears)g(of)h(computa-)456 4219 y(tional)g(time.)44 b(This)29 b(is)h(due)g(to)f(the)i(fact)e(that)h(this)g(orbit)g(app)r (ears)e(to)i(b)r(e)g(v)n(ery)e(sensitiv)n(e)i(to)456 4319 y(the)g(v)-5 b(alue)31 b(of)f Fn(h)p Fo(,)h(therefore)f(with)h(a)f (single)g(step)h(w)n(e)f(can)g(only)g(pro)n(v)n(e)f(the)h(statemen)n(t) h(for)f(a)456 4418 y(v)n(ery)25 b(narro)n(w)g(in)n(terv)-5 b(al)26 b(in)h Fn(h)p Fo(.)37 b(With)28 b(ab)r(out)f(a)f(w)n(eek)g(of)h (computation)g(time)g(w)n(e)f(could)h(pro)n(v)n(e)456 4518 y(the)h(follo)n(wing:)456 4662 y Fs(Theorem)k(4.3.)41 b Fe(The)32 b(statement)e(of)i(Conje)l(ctur)l(e)e(4.2)j(hold)f(if)g Fn(I)2560 4674 y Fm(m)2654 4662 y Fe(is)f(substitute)l(d)f(with)h(the) 456 4763 y(set)595 4742 y Fo(~)585 4763 y Fn(I)621 4775 y Fm(m)708 4763 y Fo(:=)22 b Fl([)873 4733 y Fk(28)873 4785 y Fm(i)p Fk(=0)985 4763 y Fo([10)1092 4733 y Ff(\000)p Fk(2)1181 4763 y Fn(i;)14 b Fo(10)1331 4733 y Ff(\000)p Fk(2)1418 4763 y Fn(i)k Fo(+)g Fn(:)p Fo(00004])p Fe(.)555 4908 y Fo(F)-7 b(or)27 b(the)h(orbits)f Fn(S)1134 4920 y Fk(2)1199 4908 y Fo(w)n(e)g(could)h(get)f(a)g(full)h(result)g(in)g(a) f(reasonable)e(time:)456 5053 y Fs(Theorem)33 b(4.4.)41 b Fe(L)l(et)31 b Fn(m)1272 5065 y Fk(1)1335 5053 y Fo(=)26 b Fn(m)1499 5065 y Fk(2)1562 5053 y Fo(=)g(1)p Fe(,)32 b(let)f Fn(I)1906 5065 y Fm(h)1976 5053 y Fo(=)g([0)p Fn(;)14 b Fo(1])30 b Fe(and)i(let)f Fn(\016)e Fo(=)d Fn(:)p Fo(00025)p Fe(.)41 b(Ther)l(e)33 b(exists)456 5152 y(a)h(c)l(ontinuous)f(function)g Fn(x)1331 5164 y Fm(S)1372 5172 y Fi(2)1440 5152 y Fo(:)d Fn(I)1529 5164 y Fm(h)1603 5152 y Fl(!)g Fo([)p Fl(\000)p Fn(:)p Fo(44)p Fn(;)14 b Fl(\000)p Fn(:)p Fo(4])32 b Fe(such)i(that)f(for)i (al)t(l)g Fn(h)30 b Fl(2)h Fn(I)2959 5164 y Fm(h)3036 5152 y Fe(ther)l(e)j(exists)456 5252 y(a)d(p)l(erio)l(dic)i(orbit)e(of) h(\(1\))f(of)h(ener)l(gy)f Fn(h)f Fe(cr)l(ossing)i(the)f Fn(x)p Fl(\000)p Fe(axis)g(at)g Fn(x)25 b Fo(=)g Fn(x)2773 5264 y Fm(S)2814 5272 y Fi(2)2850 5252 y Fo(\()p Fn(h)p Fo(\))32 b Fe(with)f(p)l(ositive)456 5352 y Fn(y)s Fe(-velo)l(city.)53 b(Such)34 b(orbit)h(is)f(r)l(etr)l(o)l(gr)l(ade)h(ar)l(ound)g Fn(P)2105 5364 y Fk(1)2142 5352 y Fe(.)53 b(F)-6 b(urthermor)l(e)34 b Fn(x)2751 5364 y Fm(S)2792 5372 y Fi(2)2829 5352 y Fo(\()p Fn(h)p Fo(\))d Fl(2)37 b Fo(^)-47 b Fn(x)3106 5364 y Fm(S)3147 5372 y Fi(2)3184 5352 y Fo(\()p Fn(h)p Fo(\))22 b Fl(\006)f Fn(\016)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 456 315 a Fk(6)1208 b(GIANNI)23 b(ARIOLI)456 515 y Fe(for)34 b(al)t(l)g Fn(h)29 b Fl(2)h Fn(I)912 527 y Fm(h)955 515 y Fe(.)49 b(F)-6 b(or)33 b(al)t(l)i Fn(h)29 b Fl(2)g Fn(I)1507 527 y Fm(h)1584 515 y Fe(and)34 b(for)g(al)t(l)39 b Fo(\026)-47 b Fn(x)30 b Fl(2)35 b Fo(^)-48 b Fn(x)2215 527 y Fm(S)2256 535 y Fi(2)2293 515 y Fo(\()p Fn(h)p Fo(\))22 b Fl(\006)e Fn(\016)s Fe(,)40 b Fo(\026)-47 b Fn(x)29 b Fl(6)p Fo(=)g Fn(x)2829 527 y Fm(S)2870 535 y Fi(2)2907 515 y Fo(\()p Fn(h)p Fo(\))k Fe(ther)l(e)h(is)f(no)456 614 y(orbit)d(of)h(ener)l(gy)f Fn(h)f Fe(cr)l(ossing)h(the)g Fn(x)p Fl(\000)p Fe(axis)g(ortho)l(gonal) t(ly)j(at)h Fo(\026)-47 b Fn(x)q Fe(.)973 2019 y @beginspecial 91 @llx 3 @lly 322 @urx 146 @ury 2344 @rwi 1457 @rhi @setspecial %%BeginDocument: S2.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 146 %%HiResBoundingBox: 91.5625 3.1875 321.938 145.5 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:12:25) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 148.688 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 145.500 moveto 321.938 145.500 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 145.500 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 145.500000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 142.312500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 6.55027 14.856 [ [.21429 .59538 -9 -9 ] [.21429 .59538 9 0 ] [.40476 .59538 -9 -9 ] [.40476 .59538 9 0 ] [.59524 .59538 -9 -9 ] [.59524 .59538 9 0 ] [.78571 .59538 -9 -9 ] [.78571 .59538 9 0 ] [.97619 .59538 -3 -9 ] [.97619 .59538 3 0 ] [1.025 .60788 0 -4.90625 ] [1.025 .60788 10 4.90625 ] [.01131 .01365 -30 -4.5 ] [.01131 .01365 0 4.5 ] [.01131 .1622 -30 -4.5 ] [.01131 .1622 0 4.5 ] [.01131 .31076 -30 -4.5 ] [.01131 .31076 0 4.5 ] [.01131 .45932 -30 -4.5 ] [.01131 .45932 0 4.5 ] [.02381 .64303 -5 0 ] [.02381 .64303 5 9.8125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .21429 .60788 m .21429 .61413 L s [(0.2)] .21429 .59538 0 1 Mshowa .40476 .60788 m .40476 .61413 L s [(0.4)] .40476 .59538 0 1 Mshowa .59524 .60788 m .59524 .61413 L s [(0.6)] .59524 .59538 0 1 Mshowa .78571 .60788 m .78571 .61413 L s [(0.8)] .78571 .59538 0 1 Mshowa .97619 .60788 m .97619 .61413 L s [(1)] .97619 .59538 0 1 Mshowa .125 Mabswid .07143 .60788 m .07143 .61163 L s .11905 .60788 m .11905 .61163 L s .16667 .60788 m .16667 .61163 L s .2619 .60788 m .2619 .61163 L s .30952 .60788 m .30952 .61163 L s .35714 .60788 m .35714 .61163 L s .45238 .60788 m .45238 .61163 L s .5 .60788 m .5 .61163 L s .54762 .60788 m .54762 .61163 L s .64286 .60788 m .64286 .61163 L s .69048 .60788 m .69048 .61163 L s .7381 .60788 m .7381 .61163 L s .83333 .60788 m .83333 .61163 L s .88095 .60788 m .88095 .61163 L s .92857 .60788 m .92857 .61163 L s .25 Mabswid 0 .60788 m 1 .60788 L s gsave 1.025 .60788 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (h) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .01365 m .03006 .01365 L s [(-0.44)] .01131 .01365 1 0 Mshowa .02381 .1622 m .03006 .1622 L s [(-0.43)] .01131 .1622 1 0 Mshowa .02381 .31076 m .03006 .31076 L s [(-0.42)] .01131 .31076 1 0 Mshowa .02381 .45932 m .03006 .45932 L s [(-0.41)] .01131 .45932 1 0 Mshowa .125 Mabswid .02381 .04336 m .02756 .04336 L s .02381 .07307 m .02756 .07307 L s .02381 .10278 m .02756 .10278 L s .02381 .13249 m .02756 .13249 L s .02381 .19192 m .02756 .19192 L s .02381 .22163 m .02756 .22163 L s .02381 .25134 m .02756 .25134 L s .02381 .28105 m .02756 .28105 L s .02381 .34048 m .02756 .34048 L s .02381 .37019 m .02756 .37019 L s .02381 .3999 m .02756 .3999 L s .02381 .42961 m .02756 .42961 L s .02381 .48904 m .02756 .48904 L s .02381 .51875 m .02756 .51875 L s .02381 .54846 m .02756 .54846 L s .02381 .57817 m .02756 .57817 L s .25 Mabswid .02381 0 m .02381 .61803 L s gsave .02381 .64303 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .06244 .03488 L .10458 .05717 L .14415 .07839 L .18221 .09908 L .22272 .1214 L .26171 .14319 L .30316 .16668 L .34309 .18964 L .3815 .21205 L .42237 .23623 L .46172 .25986 L .49955 .28291 L .53984 .30781 L .57861 .33213 L .61984 .35837 L .65954 .38405 L .69774 .40911 L .73838 .43618 L .77751 .46264 L .81909 .4912 L .85916 .51915 L .89771 .54646 L .93871 .57595 L .97619 .60332 L s % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1655 2119 a Fo(Graph)27 b(of)33 b(^)-48 b Fn(x)2055 2131 y Fm(S)2096 2139 y Fi(2)2133 2119 y Fo(\()p Fn(h)p Fo(\))555 2338 y(The)31 b(follo)n(wing)e(pictures)h (displa)n(y)f(the)i(orbits)f(b)r(elonging)f(to)h(the)h(classes)e Fn(S)3014 2350 y Fk(2)3051 2338 y Fo(,)i Fn(L)f Fo(and)g Fn(S)3407 2350 y Fk(1)456 2437 y Fo(\(from)d(left)h(to)g(righ)n(t\))f (at)h Fn(h)22 b Fo(=)h Fn(:)p Fo(01)k(and)g(at)h Fn(h)23 b Fo(=)f Fn(:)p Fo(8.)973 3320 y @beginspecial 91 @llx 3 @lly 322 @urx 89 @ury 2344 @rwi 881 @rhi @setspecial %%BeginDocument: h005.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 89 %%HiResBoundingBox: 91.5625 3.1875 321.938 88.1875 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:19:30) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 91.375 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 88.188 moveto 321.938 88.188 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 88.188 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 88.187500 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 85.000000 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .36932 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 0.473456 0.546862 0.18466 0.546862 [ [.06331 .17216 -15 -9 ] [.06331 .17216 15 0 ] [.20002 .17216 -12 -9 ] [.20002 .17216 12 0 ] [.33674 .17216 -15 -9 ] [.33674 .17216 15 0 ] [.61017 .17216 -12 -9 ] [.61017 .17216 12 0 ] [.74689 .17216 -9 -9 ] [.74689 .17216 9 0 ] [.8836 .17216 -12 -9 ] [.8836 .17216 12 0 ] [1.025 .18466 0 -4.90625 ] [1.025 .18466 10 4.90625 ] [.46096 .0206 -24 -4.5 ] [.46096 .0206 0 4.5 ] [.46096 .07529 -24 -4.5 ] [.46096 .07529 0 4.5 ] [.46096 .12997 -24 -4.5 ] [.46096 .12997 0 4.5 ] [.46096 .23935 -18 -4.5 ] [.46096 .23935 0 4.5 ] [.46096 .29403 -18 -4.5 ] [.46096 .29403 0 4.5 ] [.46096 .34872 -18 -4.5 ] [.46096 .34872 0 4.5 ] [.47346 .39432 -5.03125 0 ] [.47346 .39432 5.03125 9.8125 ] [ 0 0 0 0 ] [ 1 .36932 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .06331 .18466 m .06331 .19091 L s [(-0.75)] .06331 .17216 0 1 Mshowa .20002 .18466 m .20002 .19091 L s [(-0.5)] .20002 .17216 0 1 Mshowa .33674 .18466 m .33674 .19091 L s [(-0.25)] .33674 .17216 0 1 Mshowa .61017 .18466 m .61017 .19091 L s [(0.25)] .61017 .17216 0 1 Mshowa .74689 .18466 m .74689 .19091 L s [(0.5)] .74689 .17216 0 1 Mshowa .8836 .18466 m .8836 .19091 L s [(0.75)] .8836 .17216 0 1 Mshowa .125 Mabswid .09065 .18466 m .09065 .18841 L s .118 .18466 m .118 .18841 L s .14534 .18466 m .14534 .18841 L s .17268 .18466 m .17268 .18841 L s .22737 .18466 m .22737 .18841 L s .25471 .18466 m .25471 .18841 L s .28205 .18466 m .28205 .18841 L s .3094 .18466 m .3094 .18841 L s .36408 .18466 m .36408 .18841 L s .39143 .18466 m .39143 .18841 L s .41877 .18466 m .41877 .18841 L s .44611 .18466 m .44611 .18841 L s .5008 .18466 m .5008 .18841 L s .52814 .18466 m .52814 .18841 L s .55549 .18466 m .55549 .18841 L s .58283 .18466 m .58283 .18841 L s .63751 .18466 m .63751 .18841 L s .66486 .18466 m .66486 .18841 L s .6922 .18466 m .6922 .18841 L s .71954 .18466 m .71954 .18841 L s .77423 .18466 m .77423 .18841 L s .80157 .18466 m .80157 .18841 L s .82892 .18466 m .82892 .18841 L s .85626 .18466 m .85626 .18841 L s .03597 .18466 m .03597 .18841 L s .00862 .18466 m .00862 .18841 L s .91095 .18466 m .91095 .18841 L s .93829 .18466 m .93829 .18841 L s .96563 .18466 m .96563 .18841 L s .99297 .18466 m .99297 .18841 L s .25 Mabswid 0 .18466 m 1 .18466 L s gsave 1.025 .18466 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .47346 .0206 m .47971 .0206 L s [(-0.3)] .46096 .0206 1 0 Mshowa .47346 .07529 m .47971 .07529 L s [(-0.2)] .46096 .07529 1 0 Mshowa .47346 .12997 m .47971 .12997 L s [(-0.1)] .46096 .12997 1 0 Mshowa .47346 .23935 m .47971 .23935 L s [(0.1)] .46096 .23935 1 0 Mshowa .47346 .29403 m .47971 .29403 L s [(0.2)] .46096 .29403 1 0 Mshowa .47346 .34872 m .47971 .34872 L s [(0.3)] .46096 .34872 1 0 Mshowa .125 Mabswid .47346 .03154 m .47721 .03154 L s .47346 .04248 m .47721 .04248 L s .47346 .05341 m .47721 .05341 L s .47346 .06435 m .47721 .06435 L s .47346 .08622 m .47721 .08622 L s .47346 .09716 m .47721 .09716 L s .47346 .1081 m .47721 .1081 L s .47346 .11904 m .47721 .11904 L s .47346 .14091 m .47721 .14091 L s .47346 .15185 m .47721 .15185 L s .47346 .16279 m .47721 .16279 L s .47346 .17372 m .47721 .17372 L s .47346 .1956 m .47721 .1956 L s .47346 .20653 m .47721 .20653 L s .47346 .21747 m .47721 .21747 L s .47346 .22841 m .47721 .22841 L s .47346 .25028 m .47721 .25028 L s .47346 .26122 m .47721 .26122 L s .47346 .27216 m .47721 .27216 L s .47346 .28309 m .47721 .28309 L s .47346 .30497 m .47721 .30497 L s .47346 .31591 m .47721 .31591 L s .47346 .32684 m .47721 .32684 L s .47346 .33778 m .47721 .33778 L s .47346 .00966 m .47721 .00966 L s .47346 .35966 m .47721 .35966 L s .25 Mabswid .47346 0 m .47346 .36932 L s gsave .47346 .39432 -66.0312 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 69.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .5 Mabswid .47804 .18466 m .47803 .18482 L .47803 .18497 L .47803 .18515 L .47803 .18531 L .47803 .1856 L .47803 .18591 L .47802 .18626 L .47801 .18662 L .478 .18728 L .47797 .18795 L .47795 .18858 L .47787 .18999 L .47777 .1914 L .47766 .19266 L .47733 .19536 L .47698 .1975 L .47652 .19959 L .47603 .20128 L .47545 .20274 L .47515 .20332 L .47482 .20384 L .4745 .20422 L .47419 .20449 L .47405 .20458 L .47396 .20462 L .47389 .20466 L .47381 .20469 L .47374 .20471 L .47366 .20473 L .47363 .20473 L .4736 .20474 L .47356 .20474 L .47352 .20475 L .47348 .20475 L .47345 .20475 L .4734 .20475 L .47337 .20474 L .47334 .20474 L .47332 .20474 L .47328 .20473 L .47319 .20471 L .4731 .20469 L .47294 .20462 L .47279 .20453 L .47264 .20443 L .47232 .20412 L .47201 .20372 L .47168 .20319 L .47108 .20185 L Mistroke .47056 .20023 L .4701 .19834 L .46973 .19635 L .46939 .1939 L .46915 .19152 L .46905 .19019 L .46898 .18894 L .46895 .18822 L .46892 .18755 L .4689 .18684 L .4689 .18646 L .46889 .18606 L .46888 .1857 L .46888 .18552 L .46888 .18532 L .46888 .18515 L .46888 .18497 L .46888 .18479 L .46888 .18464 L .46888 .18455 L .46888 .18445 L .46888 .18428 L .46888 .18417 L .46888 .18407 L .46888 .18388 L .46888 .1835 L .46889 .18309 L .46891 .18238 L .46893 .18164 L .46899 .18031 L .46906 .17903 L .46916 .17768 L .4694 .17535 L .46975 .17283 L .47016 .17068 L .47063 .16883 L .47112 .16738 L .47165 .1662 L .47196 .16567 L .47227 .16526 L .47257 .16495 L .47272 .16483 L .4729 .16472 L .47304 .16465 L .47312 .16463 L .4732 .1646 L .47327 .16459 L .47331 .16458 L .47335 .16458 L .47338 .16458 L Mistroke .47341 .16457 L .47345 .16457 L .47348 .16457 L .47352 .16457 L .47355 .16458 L .47357 .16458 L .4736 .16458 L .47364 .16459 L .47372 .16461 L .47381 .16463 L .47398 .1647 L .47413 .16479 L .47441 .16501 L .4747 .16533 L .47499 .16573 L .47529 .16625 L .47581 .16742 L .47636 .16913 L .47683 .17106 L .47722 .17323 L .47753 .17543 L .47776 .17782 L .47787 .17924 L .47794 .18059 L .47797 .18129 L .47799 .18195 L .47801 .18263 L .47802 .183 L .47803 .18339 L .47803 .18372 L .47803 .18391 L .47803 .18408 L .47803 .18423 L .47803 .1844 L .47803 .18458 L .47803 .18474 L .47803 .1849 L .47803 .18505 L .47803 .18519 L .47803 .18533 L .47803 .18566 L .47803 .18597 L .47802 .18634 L .47801 .18668 L .47799 .18744 L .47797 .18811 L .47794 .18881 L .47787 .19001 L .47778 .1913 L Mfstroke .23306 .18466 m .23306 .18559 L .23305 .18643 L .23302 .1874 L .233 .18832 L .23293 .18996 L .23282 .19173 L .23268 .19368 L .23248 .19574 L .23202 .19944 L .23142 .20323 L .23073 .20675 L .22872 .21468 L .22604 .22258 L .22305 .2296 L .21453 .24447 L .20527 .25611 L .19342 .26715 L .18074 .27581 L .17315 .27981 L .16601 .28287 L .15912 .28526 L .15169 .28725 L .14775 .28807 L .14339 .2888 L .14147 .28906 L .13941 .28929 L .13764 .28947 L .13568 .28962 L .13369 .28974 L .1326 .28979 L .13158 .28982 L .13062 .28985 L .12975 .28986 L .12879 .28987 L .12778 .28987 L .12724 .28986 L .12675 .28985 L .12618 .28984 L .12565 .28983 L .1247 .2898 L .12367 .28976 L .12134 .28962 L .11919 .28945 L .11559 .28906 L .11165 .2885 L .10378 .28689 L .09618 .28472 L .0894 .28225 L .07488 .27501 L Mistroke .06276 .26653 L .05105 .25543 L .04161 .24333 L .0336 .22907 L .0305 .22165 L .02779 .21339 L .02678 .20952 L .02587 .20541 L .02516 .20152 L .02465 .19796 L .02444 .19615 L .02424 .19417 L .0241 .19246 L .02397 .19057 L .02393 .18961 L .02388 .18857 L .02386 .188 L .02385 .18747 L .02382 .18644 L .02381 .18556 L .02381 .18458 L .02382 .18357 L .02383 .18263 L .02385 .18173 L .02388 .18076 L .02396 .179 L .02407 .17728 L .02419 .17571 L .02455 .17213 L .02507 .16837 L .02647 .16111 L .02852 .15346 L .03098 .1464 L .03366 .14012 L .04086 .12713 L .05068 .1143 L .06174 .10363 L .07506 .0942 L .08144 .09069 L .08856 .08741 L .09545 .08484 L .10201 .08288 L .10925 .08125 L .11313 .08059 L .1173 .08006 L .1194 .07985 L .12169 .07967 L .12274 .07961 L .12386 .07955 L .12481 .07952 L Mistroke .12535 .0795 L .12586 .07948 L .12687 .07946 L .1278 .07945 L .1288 .07945 L .12937 .07945 L .12989 .07946 L .13085 .07948 L .13172 .0795 L .13272 .07954 L .13367 .07958 L .13554 .07969 L .13728 .07982 L .14124 .08023 L .14507 .08078 L .14916 .08152 L .15647 .08328 L .16302 .08534 L .17666 .09126 L .18396 .09546 L .19039 .09985 L .2015 .10932 L .21212 .12147 L .2203 .13427 L .22406 .14195 L .22696 .14924 L .22928 .15661 L .23094 .1636 L .23169 .16767 L .23222 .17139 L .23246 .17345 L .23268 .1757 L .23284 .17782 L .2329 .17882 L .23295 .17978 L .23298 .1807 L .23302 .18171 L .23304 .18262 L .23305 .18347 L .23306 .18447 L .23306 .18538 L .23305 .18589 L .23304 .18644 L .23302 .18743 L .233 .18829 L .23296 .18924 L .23286 .19115 L .23274 .19292 L .23259 .19456 L .23213 .19865 L Mistroke .23157 .20235 L .22984 .21058 L .22764 .2181 L .22512 .22487 L .21777 .23944 L .2103 .2502 L .2006 .26086 L Mfstroke .64548 .18466 m .64549 .18667 L .64552 .1885 L .64557 .19061 L .64564 .1926 L .64582 .19615 L .64609 .19999 L .64647 .20421 L .64698 .20867 L .64814 .21663 L .64969 .22477 L .65146 .2323 L .65659 .24906 L .66337 .26542 L .67086 .27961 L .68106 .29507 L .69183 .30822 L .71412 .32866 L .72717 .33759 L .74191 .34558 L .75678 .35171 L .76483 .35431 L .77348 .35657 L .78117 .35814 L .78528 .35882 L .78971 .35941 L .7938 .35985 L .79755 .36016 L .79936 .36027 L .80133 .36037 L .80319 .36044 L .80491 .36049 L .80678 .36052 L .80874 .36053 L .81042 .36051 L .81226 .36048 L .81425 .36041 L .81638 .36032 L .81838 .3602 L .82021 .36007 L .82376 .35976 L .82761 .35933 L .8346 .3583 L .84286 .35667 L .85156 .35445 L .86696 .34922 L .88131 .34272 L .89619 .33412 L .92107 .31445 L .93341 .30142 L Mistroke .94544 .2856 L .95524 .26927 L .96279 .2531 L .96614 .24423 L .96924 .23443 L .97151 .22563 L .97343 .2162 L .97474 .20758 L .9753 .20265 L .9757 .19805 L .97585 .19586 L .97596 .1938 L .97605 .19192 L .97612 .18992 L .97617 .18775 L .97619 .18575 L .97619 .18359 L .97616 .18121 L .9761 .1789 L .97602 .17676 L .9759 .17441 L .97575 .1719 L .97531 .16679 L .9748 .16216 L .97346 .15327 L .97181 .14498 L .96676 .12691 L .96313 .11705 L .95929 .10821 L .94189 .07865 L .92982 .06382 L .91733 .05141 L .90323 .04003 L .88906 .03082 L .8759 .02395 L .86094 .01785 L .84582 .01335 L .83744 .01153 L .8336 .01086 L .82955 .01025 L .82604 .00981 L .82219 .00942 L .8187 .00914 L .81714 .00905 L .81545 .00896 L .81347 .00888 L .8116 .00883 L .80978 .0088 L .80811 .00879 L .8063 .00881 L Mistroke .80431 .00884 L .80224 .00891 L .8003 .009 L .79833 .00911 L .79624 .00926 L .79249 .0096 L .78804 .01012 L .78404 .0107 L .7762 .01215 L .76891 .01388 L .75562 .01802 L .74173 .02383 L .72858 .03088 L .71493 .04005 L .70151 .05129 L .69028 .06283 L .67158 .08848 L .66324 .10417 L .65673 .11988 L .65188 .13542 L .64993 .14346 L .64819 .15244 L .64704 .16015 L .64656 .16422 L .64615 .16852 L .64588 .17231 L .64576 .17432 L .64565 .17646 L .64558 .17844 L .64553 .18024 L .6455 .18205 L .64548 .18375 L .64548 .18573 L .64551 .18785 L .64555 .18985 L .64561 .19168 L .6457 .19382 L .64582 .19614 L .64612 .20037 L .64653 .20478 L .64708 .20945 L .64834 .21779 L .64999 .22612 L .65186 .23385 L .65621 .24798 L .66233 .26319 L .67016 .27841 L .6874 .30313 L .69774 .3144 L .70978 .32525 L Mistroke .73375 .3414 L .74814 .34837 L .75597 .35142 L .76445 .3542 L .77198 .35622 L .78039 .358 L .78411 .35863 L .78813 .35921 L .79196 .35967 L .79545 .35999 L .79944 .36027 L .80163 .36038 L .8037 .36046 L .80563 .3605 L .8074 .36052 L .80935 .36052 L .81141 .36049 L .81349 .36044 L .81466 .36039 L .81573 .36034 L .81977 .3601 L .82203 .35992 L .82449 .35968 L .82896 .35915 L .83701 .35787 L .84553 .35604 L .86068 .35156 L .87509 .34574 L .89015 .33785 L .91563 .31942 L .92775 .30773 L .93982 .29345 L .951 .27682 L .95958 .26048 L .96653 .24311 L .97143 .22598 L .97341 .21636 L .97477 .20737 L .9753 .20265 L .97574 .19743 L .97591 .1948 L .97599 .19335 L .97605 .19197 L .97609 .19069 L .97613 .1893 L .97618 .18685 L .97618 .18685 L Mfstroke 0 0 m 1 0 L 1 .36932 L 0 .36932 L closepath clip newpath % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1637 3420 a(Orbits)27 b(at)h Fn(h)23 b Fo(=)f Fn(:)p Fo(01)973 4492 y @beginspecial 91 @llx 3 @lly 322 @urx 114 @ury 2344 @rwi 1133 @rhi @setspecial %%BeginDocument: h8.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 114 %%HiResBoundingBox: 91.5625 3.1875 321.938 114 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:19:50) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 117.188 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 114.000 moveto 321.938 114.000 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 114.000 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 114.000000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 110.812500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .48113 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 0.429019 0.474712 0.240565 0.474712 [ [.19166 .22807 -12 -9 ] [.19166 .22807 12 0 ] [.66638 .22807 -9 -9 ] [.66638 .22807 9 0 ] [.90373 .22807 -3 -9 ] [.90373 .22807 3 0 ] [1.025 .24057 0 -4.90625 ] [1.025 .24057 10 4.90625 ] [.41652 .05068 -24 -4.5 ] [.41652 .05068 0 4.5 ] [.41652 .14562 -24 -4.5 ] [.41652 .14562 0 4.5 ] [.41652 .33551 -18 -4.5 ] [.41652 .33551 0 4.5 ] [.41652 .43045 -18 -4.5 ] [.41652 .43045 0 4.5 ] [.42902 .50613 -5.03125 0 ] [.42902 .50613 5.03125 9.8125 ] [ 0 0 0 0 ] [ 1 .48113 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .19166 .24057 m .19166 .24682 L s [(-0.5)] .19166 .22807 0 1 Mshowa .66638 .24057 m .66638 .24682 L s [(0.5)] .66638 .22807 0 1 Mshowa .90373 .24057 m .90373 .24682 L s [(1)] .90373 .22807 0 1 Mshowa .125 Mabswid .23913 .24057 m .23913 .24432 L s .28661 .24057 m .28661 .24432 L s .33408 .24057 m .33408 .24432 L s .38155 .24057 m .38155 .24432 L s .47649 .24057 m .47649 .24432 L s .52396 .24057 m .52396 .24432 L s .57143 .24057 m .57143 .24432 L s .6189 .24057 m .6189 .24432 L s .71385 .24057 m .71385 .24432 L s .76132 .24057 m .76132 .24432 L s .80879 .24057 m .80879 .24432 L s .85626 .24057 m .85626 .24432 L s .14419 .24057 m .14419 .24432 L s .09672 .24057 m .09672 .24432 L s .04925 .24057 m .04925 .24432 L s .00178 .24057 m .00178 .24432 L s .9512 .24057 m .9512 .24432 L s .99867 .24057 m .99867 .24432 L s .25 Mabswid 0 .24057 m 1 .24057 L s gsave 1.025 .24057 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .42902 .05068 m .43527 .05068 L s [(-0.4)] .41652 .05068 1 0 Mshowa .42902 .14562 m .43527 .14562 L s [(-0.2)] .41652 .14562 1 0 Mshowa .42902 .33551 m .43527 .33551 L s [(0.2)] .41652 .33551 1 0 Mshowa .42902 .43045 m .43527 .43045 L s [(0.4)] .41652 .43045 1 0 Mshowa .125 Mabswid .42902 .07442 m .43277 .07442 L s .42902 .09815 m .43277 .09815 L s .42902 .12189 m .43277 .12189 L s .42902 .16936 m .43277 .16936 L s .42902 .19309 m .43277 .19309 L s .42902 .21683 m .43277 .21683 L s .42902 .2643 m .43277 .2643 L s .42902 .28804 m .43277 .28804 L s .42902 .31177 m .43277 .31177 L s .42902 .35924 m .43277 .35924 L s .42902 .38298 m .43277 .38298 L s .42902 .40671 m .43277 .40671 L s .42902 .02694 m .43277 .02694 L s .42902 .00321 m .43277 .00321 L s .42902 .45419 m .43277 .45419 L s .42902 .47792 m .43277 .47792 L s .25 Mabswid .42902 0 m .42902 .48113 L s gsave .42902 .50613 -66.0312 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 69.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .5 Mabswid .47137 .24057 m .47137 .24204 L .47137 .24338 L .47137 .24493 L .47136 .2464 L .47135 .249 L .47132 .25182 L .47129 .25493 L .47125 .25821 L .47115 .26408 L .47101 .27011 L .47086 .27571 L .47039 .28828 L .46975 .30078 L .46901 .31185 L .46796 .32414 L .46676 .33526 L .46549 .34477 L .46395 .35435 L .46068 .37001 L .45858 .37784 L .45609 .38554 L .45377 .39152 L .45106 .39737 L .44552 .40631 L .4423 .41002 L .4392 .41273 L .43765 .41379 L .43594 .41474 L .43432 .41545 L .43354 .41572 L .43281 .41593 L .4321 .41611 L .43144 .41623 L .43072 .41634 L .43034 .41638 L .42994 .41641 L .42957 .41643 L .42918 .41644 L .42881 .41644 L .42848 .41643 L .42808 .41641 L .42786 .41639 L .42765 .41637 L .42688 .41628 L .42648 .41621 L .4261 .41614 L .42539 .41598 L .42379 .41548 L .42242 .4149 L Mistroke .42094 .41412 L .41762 .41177 L .41463 .40886 L .41153 .40498 L .40874 .40062 L .40389 .39063 L .39927 .3772 L .39566 .36254 L .39264 .34542 L .39123 .33481 L .3901 .32437 L .3891 .3129 L .38833 .30161 L .38778 .29117 L .38731 .27954 L .38697 .26798 L .38684 .26134 L .38675 .25507 L .38672 .25185 L .3867 .25009 L .38669 .24845 L .38668 .24693 L .38667 .24555 L .38667 .24402 L .38666 .24238 L .38666 .24153 L .38666 .24062 L .38666 .239 L .38667 .2381 L .38667 .23726 L .38667 .23634 L .38667 .23534 L .38668 .23356 L .38669 .23188 L .38672 .22872 L .38675 .22576 L .38679 .223 L .3869 .2167 L .38704 .21061 L .38722 .20409 L .38766 .19249 L .38818 .18208 L .38891 .17085 L .38973 .16075 L .39087 .14945 L .39213 .1393 L .39529 .12041 L .39885 .10543 L .40337 .09181 L .40811 .08163 L Mistroke .41079 .07722 L .4134 .0737 L .41637 .07049 L .41806 .06901 L .41964 .06783 L .4213 .0668 L .42281 .06605 L .4245 .06541 L .42544 .06514 L .42632 .06495 L .4271 .06482 L .42749 .06478 L .42772 .06475 L .42792 .06474 L .42829 .06471 L .42869 .0647 L .42906 .06469 L .4294 .0647 L .42981 .06471 L .43001 .06473 L .43023 .06474 L .43063 .06478 L .431 .06483 L .43184 .06497 L .43274 .06518 L .43431 .06568 L .43577 .0663 L .43749 .06724 L .43904 .06828 L .44216 .07096 L .44538 .07463 L .45074 .08313 L .45354 .08905 L .45596 .09521 L .46005 .10859 L .46211 .11731 L .4638 .1259 L .4666 .14454 L .46784 .15568 L .46883 .16676 L .4696 .17766 L .47025 .18964 L .47073 .20126 L .47104 .21197 L .47118 .21803 L .47123 .22135 L .47128 .22446 L .47131 .22734 L .47134 .22997 L .47136 .2329 L Mistroke .47137 .2345 L .47138 .23603 L .47138 .23753 L .47139 .23919 L .47139 .24002 L .47139 .24092 L .47138 .24255 L .47138 .24416 L .47138 .24569 L .47137 .24706 L .47136 .24856 L .47133 .25197 L .4713 .2556 L .4712 .26211 L .4712 .26224 L Mfstroke .23467 .24057 m .23466 .24195 L .23464 .24322 L .23459 .24467 L .23453 .24605 L .23438 .24849 L .23415 .25114 L .23382 .25406 L .23339 .25713 L .23239 .26261 L .23106 .26819 L .22954 .27336 L .22515 .28477 L .21936 .29579 L .21299 .30521 L .20445 .31514 L .19527 .32351 L .18623 .33006 L .1759 .33594 L .16562 .34038 L .15596 .34343 L .15046 .34472 L .14742 .3453 L .14458 .34576 L .14194 .34611 L .13953 .34638 L .13684 .3466 L .13536 .3467 L .13396 .34677 L .13257 .34682 L .13105 .34686 L .13028 .34687 L .12946 .34687 L .12796 .34686 L .12655 .34683 L .12507 .34678 L .1238 .34672 L .12242 .34664 L .11929 .34639 L .11595 .34601 L .10998 .34506 L .10395 .34374 L .09848 .34221 L .08646 .33768 L .07638 .3325 L .06638 .32586 L .05797 .31885 L .04979 .31039 L .04301 .30168 L .03756 .29301 L Mistroke .03235 .28244 L .0299 .27615 L .02803 .27033 L .02665 .26505 L .02546 .25928 L .02494 .25608 L .02455 .25313 L .02425 .25029 L .02413 .24885 L .02402 .24729 L .02393 .24575 L .02387 .24432 L .02384 .24295 L .02381 .2415 L .02381 .2402 L .02382 .23899 L .02385 .23765 L .0239 .23622 L .02397 .23478 L .02406 .23321 L .02433 .23004 L .02466 .22712 L .02503 .22442 L .02599 .21908 L .02709 .21428 L .03035 .20375 L .03495 .19305 L .04019 .1837 L .04699 .17411 L .05527 .16487 L .06345 .15755 L .07301 .15069 L .08268 .14523 L .09195 .14117 L .09718 .13933 L .10285 .13767 L .10781 .1365 L .11323 .13551 L .11626 .13508 L .11906 .13477 L .12174 .13454 L .12309 .13445 L .12457 .13437 L .12542 .13433 L .12622 .13431 L .12772 .13427 L .12857 .13426 L .12934 .13426 L .13019 .13426 L .1311 .13427 L Mistroke .13259 .13431 L .13399 .13436 L .13552 .13444 L .13717 .13455 L .1401 .13481 L .14321 .13518 L .14878 .13608 L .15532 .13753 L .16117 .13922 L .17238 .14352 L .18244 .14873 L .19192 .15502 L .20114 .16275 L .21528 .17906 L .22119 .1885 L .2264 .19925 L .22849 .20466 L .2302 .20989 L .23159 .21502 L .23266 .2199 L .23357 .22524 L .23395 .2281 L .23426 .23118 L .23449 .23425 L .23457 .2358 L .2346 .23669 L .23463 .23749 L .23466 .23894 L .23467 .24049 L .23466 .24193 L .23464 .24328 L .2346 .24454 L .23454 .24592 L .23446 .24736 L .23436 .24871 L .23415 .25111 L .23387 .25369 L .23298 .25953 L .2319 .26482 L .22866 .276 L .22459 .28598 L .21901 .29638 L .21186 .30667 L .20387 .31572 L .19417 .32439 L .18412 .33139 L .17424 .33675 L .16375 .34105 L .15362 .34402 L .14769 .34525 L Mistroke .14223 .34607 L .1392 .34641 L .1376 .34655 L .1359 .34667 L .13441 .34675 L .13363 .34678 L .13278 .34681 L .13129 .34685 L .12989 .34687 L .1291 .34687 L .12835 .34687 L .12696 .34684 L .12546 .3468 L .12461 .34676 L .12383 .34672 L .1211 .34654 L .11822 .34628 L .1151 .34589 L .1122 .34545 L .10565 .34415 L .09998 .34266 L .09488 .34103 L .08377 .33643 L .07372 .33089 L .06501 .32481 L .05566 .31664 L .04779 .30802 L .04113 .29889 L .03589 .28993 L .03112 .27943 L .02909 .27376 L .02728 .26759 L .02593 .26176 L .02499 .25641 L .02463 .25381 L .02432 .25099 L .02409 .24831 L .024 .24702 L .02394 .24584 L .02388 .24445 L .02384 .24296 L .02381 .24157 L .02381 .24026 L .02383 .23874 L .02386 .23732 L .02389 .23651 L .02392 .23578 L .024 .23413 L .02411 .23253 L .02423 .23106 L Mistroke .02458 .22776 L .02497 .22486 L .02547 .22181 L .02797 .21103 L .02985 .20513 L .03186 .19985 L .04191 .18106 L .04885 .17184 L .05611 .16404 L .07515 .14936 L .07707 .14823 L Mfstroke .59287 .24057 m .59289 .24392 L .59296 .24697 L .59309 .25049 L .59327 .25381 L .5937 .2597 L .59434 .26606 L .59526 .27302 L .59646 .28032 L .59918 .29318 L .60271 .30607 L .60661 .31772 L .61733 .34252 L .63025 .36513 L .64325 .38337 L .67447 .41643 L .70197 .4373 L .71739 .44647 L .73105 .45324 L .74382 .4585 L .75723 .46293 L .76442 .46485 L .77093 .46632 L .777 .46745 L .7834 .4684 L .78653 .46877 L .78948 .46906 L .79232 .46929 L .79493 .46945 L .79738 .46956 L .79861 .46961 L .79996 .46964 L .80131 .46966 L .80275 .46967 L .80411 .46967 L .80535 .46966 L .80671 .46963 L .80815 .46959 L .80951 .46954 L .81073 .46949 L .81372 .4693 L .81651 .46908 L .82201 .46847 L .82785 .46759 L .83762 .46554 L .84799 .46254 L .85841 .45861 L .86779 .45424 L .88547 .44358 L .90042 .43173 L Mistroke .91572 .41631 L .9286 .40006 L .95027 .36248 L .95947 .33986 L .96617 .31818 L .97138 .29477 L .97349 .28126 L .97424 .27521 L .97491 .2687 L .97543 .26223 L .97579 .25632 L .97592 .25347 L .97604 .25037 L .97608 .24895 L .97611 .24744 L .97614 .24612 L .97616 .24473 L .97618 .2431 L .97619 .24161 L .97619 .24001 L .97619 .2391 L .97618 .23826 L .97617 .23672 L .97615 .23532 L .97611 .23371 L .97608 .23219 L .97596 .22874 L .97583 .22556 L .97539 .2184 L .97491 .21246 L .97426 .20611 L .97276 .19474 L .97044 .18138 L .96781 .1694 L .9614 .14692 L .95256 .12374 L .94245 .10316 L .93002 .0831 L .90372 .05242 L .88838 .03964 L .87044 .02828 L .85184 .01993 L .84196 .01674 L .83624 .01526 L .83072 .01407 L .82556 .01317 L .81987 .0124 L .81732 .01213 L .81459 .01189 L .81225 .01173 L Mistroke .80965 .01159 L .80809 .01153 L .80732 .01151 L .8066 .01149 L .80526 .01147 L .80379 .01146 L .80296 .01146 L .80217 .01146 L .8007 .01148 L .79987 .01149 L .7991 .01151 L .79737 .01157 L .79596 .01163 L .79464 .0117 L .79163 .0119 L .78866 .01215 L .78545 .01248 L .77906 .01335 L .77304 .01439 L .75907 .01768 L .74633 .02172 L .73239 .02729 L .70514 .04181 L .67871 .06106 L .6496 .08999 L .62487 .12475 L .6135 .14661 L .60466 .16899 L .60054 .18266 L .59749 .1955 L .59611 .20276 L .59489 .21073 L .59399 .21832 L .59366 .22194 L .59339 .22538 L .5932 .22859 L .59303 .23211 L .59294 .2353 L .59288 .23827 L .59288 .2418 L .59292 .24499 L .59302 .24867 L .59317 .25213 L .59335 .25517 L .59359 .25838 L .59412 .26409 L .59486 .2702 L .59586 .27685 L .59856 .29053 L .60231 .30474 L Mistroke .61104 .32891 L Mfstroke 0 0 m 1 0 L 1 .48113 L 0 .48113 L closepath clip newpath % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1658 4592 a(Orbits)27 b(at)h Fn(h)23 b Fo(=)f Fn(:)p Fo(8)456 5148 y(4.2.)40 b Fs(Branc)m(hes)d(of)f(orbits)g(with)g (the)g(mass)f(of)h(a)h(primary)g(as)f(a)g(parameter.)42 b Fo(W)-7 b(e)456 5248 y(describ)r(e)19 b(ho)n(w)g(the)i(p)r(erio)r (dic)e(orbits)h(v)-5 b(ary)19 b(when)h(the)g(ratio)f(of)h(the)g(masses) f(of)h(the)g(primaries)f(is)456 5352 y(c)n(hanged.)33 b(More)19 b(precisely)-7 b(,)21 b(w)n(e)e(v)-5 b(ary)19 b Fn(m)1727 5364 y Fk(1)1784 5352 y Fo(while)h(k)n(eeping)f Fn(m)2358 5364 y Fk(2)2415 5352 y Fo(\(and)h Fn(h)p Fo(\))h(\014xed.)34 b(Let)3082 5330 y(^)3073 5352 y Fn(\030)3109 5364 y Fm(L)3159 5352 y Fo(\()p Fn(m)3264 5364 y Fk(1)3301 5352 y Fo(\))24 b(=,)p eop end %%Page: 7 7 TeXDict begin 7 6 bop 1381 315 a Fk(BRANCHES)29 b(OF)g(PERIODIC)g (ORBITS)892 b(7)810 856 y Fo(^)801 877 y Fn(\030)837 889 y Fm(L)887 877 y Fo(\()p Fn(m)992 889 y Fk(1)1030 877 y Fo(\))23 b(=)g Fl(\000)p Fo(4956)p Fn(:)p Fo(55)15 b(+)j(48949)p Fn(:)p Fo(4)c Fn(m)1973 889 y Fk(1)2025 877 y Fl(\000)k Fo(217113)c Fn(m)2447 843 y Fk(2)2447 898 y(1)2500 877 y Fo(+)k(569529)c Fn(m)2922 843 y Fk(3)2922 898 y(1)1080 1016 y Fl(\000)k Fo(978391)c Fn(m)1502 982 y Fk(4)1502 1037 y(1)1555 1016 y Fo(+)k(1150070)c Fn(m)2019 982 y Fk(5)2019 1037 y(1)2071 1016 y Fl(\000)k Fo(936769)c Fn(m)2493 982 y Fk(6)2493 1037 y(1)2545 1016 y Fo(+)k(522068)c Fn(m)2967 982 y Fk(7)2967 1037 y(1)1080 1155 y Fl(\000)k Fo(190515)c Fn(m)1502 1121 y Fk(8)1502 1176 y(1)1555 1155 y Fo(+)k(41108)p Fn(:)p Fo(2)c Fn(m)2000 1121 y Fk(9)2000 1176 y(1)2052 1155 y Fl(\000)k Fo(3982)p Fn(:)p Fo(74)c Fn(m)2497 1121 y Fk(10)2497 1176 y(1)2565 1155 y Fn(;)782 1280 y Fo(^)773 1302 y Fn(\030)809 1314 y Fm(S)850 1322 y Fi(1)887 1302 y Fo(\()p Fn(m)992 1314 y Fk(1)1030 1302 y Fo(\))23 b(=)g Fl(\000)p Fo(41)p Fn(:)p Fo(5749)15 b(+)j(484)p Fn(:)p Fo(357)c Fn(m)1973 1314 y Fk(1)2025 1302 y Fl(\000)k Fo(2433)p Fn(:)p Fo(07)c Fn(m)2470 1268 y Fk(2)2470 1323 y(1)2523 1302 y Fo(+)k(7057)p Fn(:)p Fo(59)c Fn(m)2968 1268 y Fk(3)2968 1323 y(1)1080 1441 y Fl(\000)k Fo(13035)p Fn(:)p Fo(9)c Fn(m)1525 1407 y Fk(4)1525 1462 y(1)1578 1441 y Fo(+)k(15787)p Fn(:)p Fo(6)c Fn(m)2023 1407 y Fk(5)2023 1462 y(1)2075 1441 y Fl(\000)k Fo(12175)p Fn(:)p Fo(2)c Fn(m)2520 1407 y Fk(6)2520 1462 y(1)2573 1441 y Fo(+)k(4981)p Fn(:)p Fo(48)c Fn(m)3018 1407 y Fk(7)3018 1462 y(1)1080 1580 y Fo(+)k(327)p Fn(:)p Fo(841)c Fn(m)1525 1546 y Fk(8)1525 1601 y(1)1578 1580 y Fl(\000)k Fo(1739)p Fn(:)p Fo(8)c Fn(m)1981 1546 y Fk(9)1981 1601 y(1)2034 1580 y Fo(+)k(1076)p Fn(:)p Fo(09)c Fn(m)2479 1546 y Fk(10)2479 1601 y(1)2565 1580 y Fl(\000)k Fo(343)p Fn(:)p Fo(997)c Fn(m)3010 1546 y Fk(11)3010 1601 y(1)1080 1719 y Fo(+)k(59)p Fn(:)p Fo(1689)c Fn(m)1525 1685 y Fk(12)1525 1740 y(1)1611 1719 y Fl(\000)k Fo(4)p Fn(:)p Fo(34767)c Fn(m)2056 1685 y Fk(13)2056 1740 y(1)2123 1719 y Fn(;)782 1844 y Fo(^)773 1866 y Fn(\030)809 1878 y Fm(S)850 1886 y Fi(2)887 1866 y Fo(\()p Fn(m)992 1878 y Fk(1)1030 1866 y Fo(\))23 b(=)g Fl(\000)p Fo(0)p Fn(:)p Fo(00291)15 b Fl(\000)j Fo(0)p Fn(:)p Fo(471637)c Fn(m)2015 1878 y Fk(1)2067 1866 y Fo(+)k(0)p Fn(:)p Fo(191508)c Fn(m)2554 1832 y Fk(2)2554 1887 y(1)2606 1866 y Fl(\000)k Fo(0)p Fn(:)p Fo(290152)c Fn(m)3093 1832 y Fk(3)3093 1887 y(1)1080 2005 y Fo(+)k(0)p Fn(:)p Fo(196462)c Fn(m)1567 1971 y Fk(4)1567 2026 y(1)1619 2005 y Fl(\000)k Fo(0)p Fn(:)p Fo(0596989)c Fn(m)2148 1971 y Fk(5)2148 2026 y(1)2200 2005 y Fo(+)k(0)p Fn(:)p Fo(0069742)c Fn(m)2729 1971 y Fk(6)2729 2026 y(1)2762 2005 y Fn(:)456 2290 y Fs(Theorem)38 b(4.5.)43 b Fe(L)l(et)35 b Fn(m)1283 2302 y Fk(2)1353 2290 y Fo(=)e(1)p Fe(,)j(let)f Fn(I)1712 2302 y Fm(m)1809 2290 y Fo(=)f([)p Fn(:)p Fo(8)p Fn(;)14 b Fo(1)p Fn(:)p Fo(3])34 b Fe(and)i(let)f Fn(\016)h Fo(=)c Fn(:)p Fo(0001)p Fe(.)53 b(Ther)l(e)36 b(exists)f(a)456 2389 y(c)l(ontinuous)c(function) g Fn(\030)1240 2401 y Fm(L)1317 2389 y Fo(:)c Fn(I)1403 2401 y Fm(m)1494 2389 y Fl(!)f Fo([)p Fl(\000)p Fn(:)p Fo(11)p Fn(;)14 b(:)p Fo(13])30 b Fe(such)i(that)g(for)g(al)t(l)h Fn(m)2686 2401 y Fk(1)2750 2389 y Fl(2)27 b Fn(I)2868 2401 y Fm(m)2964 2389 y Fe(ther)l(e)32 b(exists)f(a)456 2489 y(p)l(erio)l(dic)d(orbit)f(of)g(\(1\))f(of)i(ener)l(gy)e Fn(h)d Fo(=)g Fn(:)p Fo(3)i Fe(cr)l(ossing)i(the)g Fn(x)p Fl(\000)p Fe(axis)f(at)g Fn(x)e Fo(=)e Fn(\030)2809 2501 y Fm(L)2860 2489 y Fo(\()p Fn(h)p Fo(\))k Fe(with)h(p)l(ositive)456 2598 y Fn(y)s Fe(-velo)l(city.)44 b(Such)31 b(orbit)h(is)g(r)l(etr)l(o) l(gr)l(ade)g(ar)l(ound)f Fn(L)2085 2610 y Fk(1)2122 2598 y Fe(.)43 b(F)-6 b(urthermor)l(e)32 b Fn(\030)2708 2610 y Fm(L)2758 2598 y Fo(\()p Fn(m)2863 2610 y Fk(1)2900 2598 y Fo(\))26 b Fl(2)3048 2576 y Fo(^)3040 2598 y Fn(\030)3076 2610 y Fm(L)3126 2598 y Fo(\()p Fn(m)3231 2610 y Fk(1)3268 2598 y Fo(\))20 b Fl(\006)f Fn(\016)456 2706 y Fe(for)31 b(al)t(l)g Fn(m)781 2718 y Fk(1)842 2706 y Fl(2)24 b Fn(I)957 2718 y Fm(m)1021 2706 y Fe(.)40 b(F)-6 b(or)30 b(al)t(l)i Fn(m)1434 2718 y Fk(1)1495 2706 y Fl(2)24 b Fn(I)1610 2718 y Fm(m)1704 2706 y Fe(and)30 b(for)h(al)t(l)37 b Fo(\026)-47 b Fn(x)24 b Fl(2)2277 2684 y Fo(^)2268 2706 y Fn(\030)2304 2718 y Fm(L)2354 2706 y Fo(\()p Fn(m)2459 2718 y Fk(1)2497 2706 y Fo(\))19 b Fl(\006)f Fn(\016)s Fe(,)36 b Fo(\026)-47 b Fn(x)24 b Fl(6)p Fo(=)g Fn(\030)2923 2718 y Fm(L)2973 2706 y Fo(\()p Fn(m)3078 2718 y Fk(1)3115 2706 y Fo(\))31 b Fe(ther)l(e)f(is)456 2806 y(no)f(orbit)i(of)f(ener)l (gy)g Fn(h)23 b Fo(=)g Fn(:)p Fo(3)29 b Fe(cr)l(ossing)i(the)e Fn(x)p Fl(\000)p Fe(axis)i(ortho)l(gonal)t(ly)h(at)j Fo(\026)-48 b Fn(x)q Fe(.)973 4176 y @beginspecial 91 @llx 3 @lly 322 @urx 146 @ury 2344 @rwi 1457 @rhi @setspecial %%BeginDocument: Lm.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 146 %%HiResBoundingBox: 91.5625 3.1875 321.938 145.5 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:15:58) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 148.688 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 145.500 moveto 321.938 145.500 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 145.500 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 145.500000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 142.312500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%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 -1.5 1.90476 0.277691 2.53014 [ [.02381 .26519 -9 -9 ] [.02381 .26519 9 0 ] [.21429 .26519 -9 -9 ] [.21429 .26519 9 0 ] [.59524 .26519 -9 -9 ] [.59524 .26519 9 0 ] [.78571 .26519 -9 -9 ] [.78571 .26519 9 0 ] [.97619 .26519 -9 -9 ] [.97619 .26519 9 0 ] [1.025 .27769 0 -4.90625 ] [1.025 .27769 15.5 4.90625 ] [.39226 .02468 -24 -4.5 ] [.39226 .02468 0 4.5 ] [.39226 .15118 -30 -4.5 ] [.39226 .15118 0 4.5 ] [.39226 .4042 -24 -4.5 ] [.39226 .4042 0 4.5 ] [.39226 .53071 -18 -4.5 ] [.39226 .53071 0 4.5 ] [.40476 .64303 -5 0 ] [.40476 .64303 5 9.8125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 .27769 m .02381 .28394 L s [(0.8)] .02381 .26519 0 1 Mshowa .21429 .27769 m .21429 .28394 L s [(0.9)] .21429 .26519 0 1 Mshowa .59524 .27769 m .59524 .28394 L s [(1.1)] .59524 .26519 0 1 Mshowa .78571 .27769 m .78571 .28394 L s [(1.2)] .78571 .26519 0 1 Mshowa .97619 .27769 m .97619 .28394 L s [(1.3)] .97619 .26519 0 1 Mshowa .125 Mabswid .0619 .27769 m .0619 .28144 L s .1 .27769 m .1 .28144 L s .1381 .27769 m .1381 .28144 L s .17619 .27769 m .17619 .28144 L s .25238 .27769 m .25238 .28144 L s .29048 .27769 m .29048 .28144 L s .32857 .27769 m .32857 .28144 L s .36667 .27769 m .36667 .28144 L s .44286 .27769 m .44286 .28144 L s .48095 .27769 m .48095 .28144 L s .51905 .27769 m .51905 .28144 L s .55714 .27769 m .55714 .28144 L s .63333 .27769 m .63333 .28144 L s .67143 .27769 m .67143 .28144 L s .70952 .27769 m .70952 .28144 L s .74762 .27769 m .74762 .28144 L s .82381 .27769 m .82381 .28144 L s .8619 .27769 m .8619 .28144 L s .9 .27769 m .9 .28144 L s .9381 .27769 m .9381 .28144 L s .25 Mabswid 0 .27769 m 1 .27769 L s gsave 1.025 .27769 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (M) show 69.000 12.750 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 7.125 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 74.500 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .40476 .02468 m .41101 .02468 L s [(-0.1)] .39226 .02468 1 0 Mshowa .40476 .15118 m .41101 .15118 L s [(-0.05)] .39226 .15118 1 0 Mshowa .40476 .4042 m .41101 .4042 L s [(0.05)] .39226 .4042 1 0 Mshowa .40476 .53071 m .41101 .53071 L s [(0.1)] .39226 .53071 1 0 Mshowa .125 Mabswid .40476 .04998 m .40851 .04998 L s .40476 .07528 m .40851 .07528 L s .40476 .10058 m .40851 .10058 L s .40476 .12588 m .40851 .12588 L s .40476 .17649 m .40851 .17649 L s .40476 .20179 m .40851 .20179 L s .40476 .22709 m .40851 .22709 L s .40476 .25239 m .40851 .25239 L s .40476 .30299 m .40851 .30299 L s .40476 .32829 m .40851 .32829 L s .40476 .3536 m .40851 .3536 L s .40476 .3789 m .40851 .3789 L s .40476 .4295 m .40851 .4295 L s .40476 .4548 m .40851 .4548 L s .40476 .4801 m .40851 .4801 L s .40476 .5054 m .40851 .5054 L s .40476 .55601 m .40851 .55601 L s .40476 .58131 m .40851 .58131 L s .40476 .60661 m .40851 .60661 L s .25 Mabswid .40476 0 m .40476 .61803 L s gsave .40476 .64303 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .58671 L .10458 .56693 L .14415 .54718 L .18221 .52736 L .22272 .50554 L .26171 .48395 L .30316 .46046 L .34309 .43737 L .3815 .41479 L .42237 .39046 L .46172 .36664 L .49955 .34341 L .53984 .31841 L .57861 .2941 L .61984 .26794 L .65954 .24238 L .69774 .21744 L .73838 .19048 L .77751 .16408 L .81909 .13543 L .85916 .10704 L .89771 .07864 L .93871 .04658 L .97619 .01472 L s % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1645 4276 a(Gr)l(aph)31 b(of)2003 4254 y Fo(^)1994 4276 y Fn(\030)2030 4288 y Fm(L)2080 4276 y Fo(\()p Fn(m)2185 4288 y Fk(1)2223 4276 y Fo(\))555 4556 y(Concerning)c(the)h(orbits)f(in)g(the)h(classes)f Fn(S)1928 4568 y Fk(1)1992 4556 y Fo(and)h Fn(S)2205 4568 y Fk(2)2270 4556 y Fo(w)n(e)f(ha)n(v)n(e)f(the)i(follo)n(wing:)456 4836 y Fs(Conjecture)37 b(4.6.)43 b Fe(L)l(et)34 b Fn(m)1365 4848 y Fk(2)1434 4836 y Fo(=)d(1)p Fe(,)k(let)f Fn(I)1789 4848 y Fm(m)1884 4836 y Fo(=)g([)p Fn(:)p Fo(5)p Fn(;)14 b Fo(2])33 b Fe(and)i(let)f Fn(\016)h Fo(=)30 b Fn(:)p Fo(0001)p Fe(.)51 b(Ther)l(e)35 b(exists)f(a)456 4935 y(c)l(ontinuous)g(function)i Fn(\030)1248 4947 y Fm(S)1289 4955 y Fi(1)1359 4935 y Fo(:)e Fn(I)1452 4947 y Fm(m)1549 4935 y Fl(!)g Fo([)p Fn(:)p Fo(2)p Fn(;)14 b(:)p Fo(62])34 b Fe(such)i(that)f(for)i(al)t(l)f Fn(m)2661 4947 y Fk(1)2732 4935 y Fl(2)e Fn(I)2857 4947 y Fm(m)2956 4935 y Fe(ther)l(e)i(exists)f (a)456 5035 y(p)l(erio)l(dic)26 b(orbit)f(of)g(\(1\))f(of)h(ener)l(gy)f Fn(h)f Fo(=)g Fn(:)p Fo(3)g Fe(cr)l(ossing)i(the)f Fn(x)p Fl(\000)p Fe(axis)h(at)f Fn(x)f Fo(=)g Fn(\030)2786 5047 y Fm(S)2827 5055 y Fi(1)2864 5035 y Fo(\()p Fn(h)p Fo(\))h Fe(with)h(p)l(ositive)456 5143 y Fn(y)s Fe(-velo)l(city.)39 b(Such)30 b(orbit)h(is)f(dir)l(e)l(ct)g(ar)l(ound)g Fn(P)1910 5155 y Fk(2)1948 5143 y Fe(.)39 b(F)-6 b(urthermor)l(e)29 b Fn(\030)2527 5155 y Fm(S)2568 5163 y Fi(1)2605 5143 y Fo(\()p Fn(m)2710 5155 y Fk(1)2747 5143 y Fo(\))24 b Fl(2)2890 5122 y Fo(^)2882 5143 y Fn(\030)2918 5155 y Fm(S)2959 5163 y Fi(1)2995 5143 y Fo(\()p Fn(m)3100 5155 y Fk(1)3138 5143 y Fo(\))19 b Fl(\006)f Fn(\016)32 b Fe(for)456 5252 y(al)t(l)d Fn(m)646 5264 y Fk(1)706 5252 y Fl(2)23 b Fn(I)820 5264 y Fm(m)884 5252 y Fe(.)38 b(F)-6 b(or)28 b(al)t(l)h Fn(m)1290 5264 y Fk(1)1350 5252 y Fl(2)24 b Fn(I)1465 5264 y Fm(m)1556 5252 y Fe(and)29 b(for)g(al)t(l)34 b Fo(\026)-47 b Fn(x)23 b Fl(2)2121 5230 y Fo(^)2113 5252 y Fn(\030)2149 5264 y Fm(S)2190 5272 y Fi(1)2226 5252 y Fo(\()p Fn(m)2331 5264 y Fk(1)2369 5252 y Fo(\))14 b Fl(\006)h Fn(\016)s Fe(,)34 b Fo(\026)-48 b Fn(x)24 b Fl(6)p Fo(=)f Fn(\030)2783 5264 y Fm(S)2824 5272 y Fi(1)2860 5252 y Fo(\()p Fn(m)2965 5264 y Fk(1)3003 5252 y Fo(\))28 b Fe(ther)l(e)g(is)g(no)456 5352 y(orbit)i(of)h(ener)l (gy)f Fn(h)22 b Fo(=)h Fn(:)p Fo(3)29 b Fe(cr)l(ossing)i(the)f Fn(x)p Fl(\000)p Fe(axis)g(ortho)l(gonal)t(ly)i(at)j Fo(\026)-48 b Fn(x)q Fe(.)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 456 315 a Fk(8)1208 b(GIANNI)23 b(ARIOLI)973 1646 y @beginspecial 91 @llx 3 @lly 322 @urx 146 @ury 2344 @rwi 1457 @rhi @setspecial %%BeginDocument: S1m.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 146 %%HiResBoundingBox: 91.5625 3.1875 321.938 145.5 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:14:07) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 148.688 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 145.500 moveto 321.938 145.500 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 145.500 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 145.500000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 142.312500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%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 -0.293651 0.634921 -0.25231 1.39406 [ [.0873 .014 -9 -9 ] [.0873 .014 9 0 ] [.21429 .014 -9 -9 ] [.21429 .014 9 0 ] [.46825 .014 -9 -9 ] [.46825 .014 9 0 ] [.59524 .014 -9 -9 ] [.59524 .014 9 0 ] [.72222 .014 -9 -9 ] [.72222 .014 9 0 ] [.84921 .014 -9 -9 ] [.84921 .014 9 0 ] [.97619 .014 -3 -9 ] [.97619 .014 3 0 ] [1.025 .0265 0 -4.90625 ] [1.025 .0265 15.5 4.90625 ] [.32877 .16591 -18 -4.5 ] [.32877 .16591 0 4.5 ] [.32877 .30531 -18 -4.5 ] [.32877 .30531 0 4.5 ] [.32877 .44472 -18 -4.5 ] [.32877 .44472 0 4.5 ] [.32877 .58412 -18 -4.5 ] [.32877 .58412 0 4.5 ] [.34127 .64303 -5 0 ] [.34127 .64303 5 9.8125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .0873 .0265 m .0873 .03275 L s [(0.6)] .0873 .014 0 1 Mshowa .21429 .0265 m .21429 .03275 L s [(0.8)] .21429 .014 0 1 Mshowa .46825 .0265 m .46825 .03275 L s [(1.2)] .46825 .014 0 1 Mshowa .59524 .0265 m .59524 .03275 L s [(1.4)] .59524 .014 0 1 Mshowa .72222 .0265 m .72222 .03275 L s [(1.6)] .72222 .014 0 1 Mshowa .84921 .0265 m .84921 .03275 L s [(1.8)] .84921 .014 0 1 Mshowa .97619 .0265 m .97619 .03275 L s [(2)] .97619 .014 0 1 Mshowa .125 Mabswid .11905 .0265 m .11905 .03025 L s .15079 .0265 m .15079 .03025 L s .18254 .0265 m .18254 .03025 L s .24603 .0265 m .24603 .03025 L s .27778 .0265 m .27778 .03025 L s .30952 .0265 m .30952 .03025 L s .37302 .0265 m .37302 .03025 L s .40476 .0265 m .40476 .03025 L s .43651 .0265 m .43651 .03025 L s .5 .0265 m .5 .03025 L s .53175 .0265 m .53175 .03025 L s .56349 .0265 m .56349 .03025 L s .62698 .0265 m .62698 .03025 L s .65873 .0265 m .65873 .03025 L s .69048 .0265 m .69048 .03025 L s .75397 .0265 m .75397 .03025 L s .78571 .0265 m .78571 .03025 L s .81746 .0265 m .81746 .03025 L s .88095 .0265 m .88095 .03025 L s .9127 .0265 m .9127 .03025 L s .94444 .0265 m .94444 .03025 L s .05556 .0265 m .05556 .03025 L s .02381 .0265 m .02381 .03025 L s .25 Mabswid 0 .0265 m 1 .0265 L s gsave 1.025 .0265 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (M) show 69.000 12.750 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 7.125 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 74.500 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .34127 .16591 m .34752 .16591 L s [(0.3)] .32877 .16591 1 0 Mshowa .34127 .30531 m .34752 .30531 L s [(0.4)] .32877 .30531 1 0 Mshowa .34127 .44472 m .34752 .44472 L s [(0.5)] .32877 .44472 1 0 Mshowa .34127 .58412 m .34752 .58412 L s [(0.6)] .32877 .58412 1 0 Mshowa .125 Mabswid .34127 .05438 m .34502 .05438 L s .34127 .08226 m .34502 .08226 L s .34127 .11014 m .34502 .11014 L s .34127 .13803 m .34502 .13803 L s .34127 .19379 m .34502 .19379 L s .34127 .22167 m .34502 .22167 L s .34127 .24955 m .34502 .24955 L s .34127 .27743 m .34502 .27743 L s .34127 .33319 m .34502 .33319 L s .34127 .36107 m .34502 .36107 L s .34127 .38896 m .34502 .38896 L s .34127 .41684 m .34502 .41684 L s .34127 .4726 m .34502 .4726 L s .34127 .50048 m .34502 .50048 L s .34127 .52836 m .34502 .52836 L s .34127 .55624 m .34502 .55624 L s .34127 .612 m .34502 .612 L s .25 Mabswid .34127 0 m .34127 .61803 L s gsave .34127 .64303 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .52783 L .10458 .44676 L .14415 .37448 L .18221 .3096 L .22272 .24786 L .26171 .19777 L .30316 .15547 L .34309 .12448 L .3815 .10187 L .42237 .08338 L .46172 .06938 L .49955 .05855 L .53984 .0494 L .57861 .04261 L .61984 .03712 L .65954 .03299 L .69774 .02968 L .73838 .02663 L .77751 .02416 L .81909 .02199 L .85916 .02008 L .89771 .01819 L .93871 .01643 L .97619 .01472 L s % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1619 1746 a Fe(Gr)l(aph)31 b(of)1978 1724 y Fo(^)1969 1746 y Fn(\030)2005 1758 y Fm(S)2046 1766 y Fi(1)2083 1746 y Fo(\()p Fn(m)2188 1758 y Fk(1)2225 1746 y Fo(\))p Fn(:)456 1903 y Fs(Conjecture)37 b(4.7.)43 b Fe(L)l(et)34 b Fn(m)1365 1915 y Fk(2)1434 1903 y Fo(=)d(1)p Fe(,)k(let)f Fn(I)1789 1915 y Fm(m)1884 1903 y Fo(=)g([)p Fn(:)p Fo(5)p Fn(;)14 b Fo(2])33 b Fe(and)i(let)f Fn(\016)h Fo(=)30 b Fn(:)p Fo(0001)p Fe(.)51 b(Ther)l(e)35 b(exists)f(a)456 2003 y(c)l(ontinuous)24 b(function)h Fn(\030)1227 2015 y Fm(S)1268 2023 y Fi(2)1327 2003 y Fo(:)e Fn(I)1409 2015 y Fm(m)1496 2003 y Fl(!)g Fo([)p Fl(\000)p Fn(:)p Fo(83)p Fn(;)14 b Fl(\000)p Fn(:)p Fo(21])22 b Fe(such)j(that)g(for)h (al)t(l)g Fn(m)2715 2015 y Fk(1)2775 2003 y Fl(2)d Fn(I)2889 2015 y Fm(m)2978 2003 y Fe(ther)l(e)i(exists)f(a)456 2103 y(p)l(erio)l(dic)i(orbit)f(of)g(\(1\))f(of)h(ener)l(gy)f Fn(h)f Fo(=)g Fn(:)p Fo(3)g Fe(cr)l(ossing)i(the)f Fn(x)p Fl(\000)p Fe(axis)h(at)f Fn(x)f Fo(=)g Fn(\030)2786 2115 y Fm(S)2827 2123 y Fi(2)2864 2103 y Fo(\()p Fn(h)p Fo(\))h Fe(with)h(p)l(ositive)456 2211 y Fn(y)s Fe(-velo)l(city.)38 b(Such)28 b(orbit)g(is)g(r)l(etr)l(o)l(gr)l(ade)g(ar)l(ound)f Fn(P)2056 2223 y Fk(1)2094 2211 y Fe(.)38 b(F)-6 b(urthermor)l(e)27 b Fn(\030)2670 2223 y Fm(S)2711 2231 y Fi(2)2748 2211 y Fo(\()p Fn(m)2853 2223 y Fk(1)2890 2211 y Fo(\))d Fl(2)3033 2189 y Fo(^)3024 2211 y Fn(\030)3060 2223 y Fm(S)3101 2231 y Fi(2)3138 2211 y Fo(\()p Fn(m)3243 2223 y Fk(1)3280 2211 y Fo(\))14 b Fl(\006)g Fn(\016)456 2320 y Fe(for)32 b(al)t(l)g Fn(m)783 2332 y Fk(1)846 2320 y Fl(2)27 b Fn(I)964 2332 y Fm(m)1027 2320 y Fe(.)44 b(F)-6 b(or)32 b(al)t(l)g Fn(m)1446 2332 y Fk(1)1509 2320 y Fl(2)27 b Fn(I)1627 2332 y Fm(m)1722 2320 y Fe(and)k(for)i(al)t(l)k Fo(\026)-47 b Fn(x)27 b Fl(2)2303 2298 y Fo(^)2294 2320 y Fn(\030)2330 2332 y Fm(S)2371 2340 y Fi(2)2408 2320 y Fo(\()p Fn(m)2513 2332 y Fk(1)2550 2320 y Fo(\))20 b Fl(\006)f Fn(\016)s Fe(,)38 b Fo(\026)-48 b Fn(x)27 b Fl(6)p Fo(=)f Fn(\030)2984 2332 y Fm(S)3025 2340 y Fi(2)3061 2320 y Fo(\()p Fn(m)3166 2332 y Fk(1)3204 2320 y Fo(\))31 b Fe(ther)l(e)456 2419 y(is)f(no)g(orbit)g(of)g(ener)l(gy)h Fn(h)22 b Fo(=)h Fn(:)p Fo(3)29 b Fe(cr)l(ossing)i(the)f Fn(x)p Fl(\000)p Fe(axis)g(ortho)l(gonal)t(ly)i(at)j Fo(\026)-48 b Fn(x)q Fe(.)973 3716 y @beginspecial 91 @llx 3 @lly 322 @urx 146 @ury 2344 @rwi 1457 @rhi @setspecial %%BeginDocument: S2m.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 146 %%HiResBoundingBox: 91.5625 3.1875 321.938 145.5 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:14:14) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 148.688 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 145.500 moveto 321.938 145.500 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 145.500 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 145.500000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 142.312500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%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 -0.293651 0.634921 0.81391 0.972268 [ [.0873 .0236 -9 -9 ] [.0873 .0236 9 0 ] [.21429 .0236 -9 -9 ] [.21429 .0236 9 0 ] [.46825 .0236 -9 -9 ] [.46825 .0236 9 0 ] [.59524 .0236 -9 -9 ] [.59524 .0236 9 0 ] [.72222 .0236 -9 -9 ] [.72222 .0236 9 0 ] [.84921 .0236 -9 -9 ] [.84921 .0236 9 0 ] [.97619 .0236 -3 -9 ] [.97619 .0236 3 0 ] [1.025 .0361 0 -4.90625 ] [1.025 .0361 15.5 4.90625 ] [.32877 .13332 -24 -4.5 ] [.32877 .13332 0 4.5 ] [.32877 .23055 -24 -4.5 ] [.32877 .23055 0 4.5 ] [.32877 .32778 -24 -4.5 ] [.32877 .32778 0 4.5 ] [.32877 .425 -24 -4.5 ] [.32877 .425 0 4.5 ] [.32877 .52223 -24 -4.5 ] [.32877 .52223 0 4.5 ] [.34127 .64303 -5 0 ] [.34127 .64303 5 9.8125 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .0873 .0361 m .0873 .04235 L s [(0.6)] .0873 .0236 0 1 Mshowa .21429 .0361 m .21429 .04235 L s [(0.8)] .21429 .0236 0 1 Mshowa .46825 .0361 m .46825 .04235 L s [(1.2)] .46825 .0236 0 1 Mshowa .59524 .0361 m .59524 .04235 L s [(1.4)] .59524 .0236 0 1 Mshowa .72222 .0361 m .72222 .04235 L s [(1.6)] .72222 .0236 0 1 Mshowa .84921 .0361 m .84921 .04235 L s [(1.8)] .84921 .0236 0 1 Mshowa .97619 .0361 m .97619 .04235 L s [(2)] .97619 .0236 0 1 Mshowa .125 Mabswid .11905 .0361 m .11905 .03985 L s .15079 .0361 m .15079 .03985 L s .18254 .0361 m .18254 .03985 L s .24603 .0361 m .24603 .03985 L s .27778 .0361 m .27778 .03985 L s .30952 .0361 m .30952 .03985 L s .37302 .0361 m .37302 .03985 L s .40476 .0361 m .40476 .03985 L s .43651 .0361 m .43651 .03985 L s .5 .0361 m .5 .03985 L s .53175 .0361 m .53175 .03985 L s .56349 .0361 m .56349 .03985 L s .62698 .0361 m .62698 .03985 L s .65873 .0361 m .65873 .03985 L s .69048 .0361 m .69048 .03985 L s .75397 .0361 m .75397 .03985 L s .78571 .0361 m .78571 .03985 L s .81746 .0361 m .81746 .03985 L s .88095 .0361 m .88095 .03985 L s .9127 .0361 m .9127 .03985 L s .94444 .0361 m .94444 .03985 L s .05556 .0361 m .05556 .03985 L s .02381 .0361 m .02381 .03985 L s .25 Mabswid 0 .0361 m 1 .0361 L s gsave 1.025 .0361 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (M) show 69.000 12.750 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 7.125 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 74.500 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .34127 .13332 m .34752 .13332 L s [(-0.7)] .32877 .13332 1 0 Mshowa .34127 .23055 m .34752 .23055 L s [(-0.6)] .32877 .23055 1 0 Mshowa .34127 .32778 m .34752 .32778 L s [(-0.5)] .32877 .32778 1 0 Mshowa .34127 .425 m .34752 .425 L s [(-0.4)] .32877 .425 1 0 Mshowa .34127 .52223 m .34752 .52223 L s [(-0.3)] .32877 .52223 1 0 Mshowa .125 Mabswid .34127 .05554 m .34502 .05554 L s .34127 .07499 m .34502 .07499 L s .34127 .09443 m .34502 .09443 L s .34127 .11388 m .34502 .11388 L s .34127 .15277 m .34502 .15277 L s .34127 .17221 m .34502 .17221 L s .34127 .19166 m .34502 .19166 L s .34127 .2111 m .34502 .2111 L s .34127 .24999 m .34502 .24999 L s .34127 .26944 m .34502 .26944 L s .34127 .28889 m .34502 .28889 L s .34127 .30833 m .34502 .30833 L s .34127 .34722 m .34502 .34722 L s .34127 .36667 m .34502 .36667 L s .34127 .38611 m .34502 .38611 L s .34127 .40556 m .34502 .40556 L s .34127 .44445 m .34502 .44445 L s .34127 .46389 m .34502 .46389 L s .34127 .48334 m .34502 .48334 L s .34127 .50278 m .34502 .50278 L s .34127 .54168 m .34502 .54168 L s .34127 .56112 m .34502 .56112 L s .34127 .58057 m .34502 .58057 L s .34127 .60001 m .34502 .60001 L s .34127 .01665 m .34502 .01665 L s .25 Mabswid .34127 0 m .34127 .61803 L s gsave .34127 .64303 -66 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .60332 m .06244 .57859 L .10458 .55145 L .14415 .52579 L .18221 .50097 L .22272 .47443 L .26171 .44878 L .30316 .42147 L .34309 .39517 L .3815 .36992 L .42237 .34318 L .46172 .31759 L .49955 .29319 L .53984 .26747 L .57861 .24302 L .61984 .21738 L .65954 .19307 L .69774 .17006 L .73838 .146 L .77751 .12327 L .81909 .0996 L .85916 .07726 L .89771 .05621 L .93871 .0343 L .97619 .01472 L s % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1617 3816 a Fo(Graph)28 b(of)1980 3794 y(^)1971 3816 y Fn(\030)2007 3828 y Fm(S)2048 3836 y Fi(2)2085 3816 y Fo(\()p Fn(m)2190 3828 y Fk(1)2227 3816 y Fo(\))p Fn(:)555 3940 y Fo(As)j(b)r(efore,)f(the)h(lac)n(k)e(of)h(the)h(pro)r (of)e(is)h(only)g(due)h(to)f(unreasonable)e(computation)i(time.)456 4040 y(In)d(ab)r(out)h(a)f(w)n(eek)g(w)n(e)g(could)h(pro)n(v)n(e)e(the) i(follo)n(wing:)456 4197 y Fs(Theorem)g(4.8.)37 b Fe(The)28 b(statements)e(of)i(Conje)l(ctur)l(es)f(4.6)h(and)f(4.7)i(hold)f(if)g Fn(I)2888 4209 y Fm(m)2978 4197 y Fe(is)g(substitute)l(d)456 4298 y(with)i(the)g(set)913 4277 y Fo(~)903 4298 y Fn(I)939 4310 y Fm(m)1026 4298 y Fo(:=)23 b Fl([)1192 4268 y Fk(200)1192 4320 y Fm(i)p Fk(=50)1337 4298 y Fo([)p Fn(:)p Fo(01)p Fn(i;)14 b(:)p Fo(01)p Fn(i)i Fo(+)i(10)1852 4268 y Ff(\000)p Fk(8)1940 4298 y Fo(])p Fe(.)555 4456 y Fo(The)28 b(follo)n(wing)e (pictures)i(displa)n(y)f(the)h(orbits)e(at)i(di\013eren)n(t)g(v)-5 b(alues)27 b(of)g Fn(m)2895 4468 y Fk(1)2933 4456 y Fo(.)973 5240 y @beginspecial 91 @llx 3 @lly 322 @urx 89 @ury 2344 @rwi 881 @rhi @setspecial %%BeginDocument: m08.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 89 %%HiResBoundingBox: 91.5625 3.1875 321.938 88.875 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:17:41) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 92.0625 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 88.875 moveto 321.938 88.875 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 88.875 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 88.875000 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 85.687500 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .37201 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 0.441861 0.565084 0.186006 0.565084 [ [.01805 .17351 -15 -9 ] [.01805 .17351 15 0 ] [.15932 .17351 -12 -9 ] [.15932 .17351 12 0 ] [.30059 .17351 -15 -9 ] [.30059 .17351 15 0 ] [.58313 .17351 -12 -9 ] [.58313 .17351 12 0 ] [.7244 .17351 -9 -9 ] [.7244 .17351 9 0 ] [.86567 .17351 -12 -9 ] [.86567 .17351 12 0 ] [1.025 .18601 0 -4.90625 ] [1.025 .18601 10 4.90625 ] [.42936 .01648 -24 -4.5 ] [.42936 .01648 0 4.5 ] [.42936 .07299 -24 -4.5 ] [.42936 .07299 0 4.5 ] [.42936 .1295 -24 -4.5 ] [.42936 .1295 0 4.5 ] [.42936 .24251 -18 -4.5 ] [.42936 .24251 0 4.5 ] [.42936 .29902 -18 -4.5 ] [.42936 .29902 0 4.5 ] [.42936 .35553 -18 -4.5 ] [.42936 .35553 0 4.5 ] [.44186 .39701 -5.03125 0 ] [.44186 .39701 5.03125 9.8125 ] [ 0 0 0 0 ] [ 1 .37201 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .01805 .18601 m .01805 .19226 L s [(-0.75)] .01805 .17351 0 1 Mshowa .15932 .18601 m .15932 .19226 L s [(-0.5)] .15932 .17351 0 1 Mshowa .30059 .18601 m .30059 .19226 L s [(-0.25)] .30059 .17351 0 1 Mshowa .58313 .18601 m .58313 .19226 L s [(0.25)] .58313 .17351 0 1 Mshowa .7244 .18601 m .7244 .19226 L s [(0.5)] .7244 .17351 0 1 Mshowa .86567 .18601 m .86567 .19226 L s [(0.75)] .86567 .17351 0 1 Mshowa .125 Mabswid .0463 .18601 m .0463 .18976 L s .07456 .18601 m .07456 .18976 L s .10281 .18601 m .10281 .18976 L s .13106 .18601 m .13106 .18976 L s .18757 .18601 m .18757 .18976 L s .21583 .18601 m .21583 .18976 L s .24408 .18601 m .24408 .18976 L s .27234 .18601 m .27234 .18976 L s .32884 .18601 m .32884 .18976 L s .3571 .18601 m .3571 .18976 L s .38535 .18601 m .38535 .18976 L s .41361 .18601 m .41361 .18976 L s .47012 .18601 m .47012 .18976 L s .49837 .18601 m .49837 .18976 L s .52662 .18601 m .52662 .18976 L s .55488 .18601 m .55488 .18976 L s .61139 .18601 m .61139 .18976 L s .63964 .18601 m .63964 .18976 L s .66789 .18601 m .66789 .18976 L s .69615 .18601 m .69615 .18976 L s .75266 .18601 m .75266 .18976 L s .78091 .18601 m .78091 .18976 L s .80917 .18601 m .80917 .18976 L s .83742 .18601 m .83742 .18976 L s .89393 .18601 m .89393 .18976 L s .92218 .18601 m .92218 .18976 L s .95044 .18601 m .95044 .18976 L s .97869 .18601 m .97869 .18976 L s .25 Mabswid 0 .18601 m 1 .18601 L s gsave 1.025 .18601 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .44186 .01648 m .44811 .01648 L s [(-0.3)] .42936 .01648 1 0 Mshowa .44186 .07299 m .44811 .07299 L s [(-0.2)] .42936 .07299 1 0 Mshowa .44186 .1295 m .44811 .1295 L s [(-0.1)] .42936 .1295 1 0 Mshowa .44186 .24251 m .44811 .24251 L s [(0.1)] .42936 .24251 1 0 Mshowa .44186 .29902 m .44811 .29902 L s [(0.2)] .42936 .29902 1 0 Mshowa .44186 .35553 m .44811 .35553 L s [(0.3)] .42936 .35553 1 0 Mshowa .125 Mabswid .44186 .02778 m .44561 .02778 L s .44186 .03908 m .44561 .03908 L s .44186 .05039 m .44561 .05039 L s .44186 .06169 m .44561 .06169 L s .44186 .08429 m .44561 .08429 L s .44186 .09559 m .44561 .09559 L s .44186 .10689 m .44561 .10689 L s .44186 .1182 m .44561 .1182 L s .44186 .1408 m .44561 .1408 L s .44186 .1521 m .44561 .1521 L s .44186 .1634 m .44561 .1634 L s .44186 .1747 m .44561 .1747 L s .44186 .19731 m .44561 .19731 L s .44186 .20861 m .44561 .20861 L s .44186 .21991 m .44561 .21991 L s .44186 .23121 m .44561 .23121 L s .44186 .25382 m .44561 .25382 L s .44186 .26512 m .44561 .26512 L s .44186 .27642 m .44561 .27642 L s .44186 .28772 m .44561 .28772 L s .44186 .31032 m .44561 .31032 L s .44186 .32163 m .44561 .32163 L s .44186 .33293 m .44561 .33293 L s .44186 .34423 m .44561 .34423 L s .44186 .00518 m .44561 .00518 L s .44186 .36683 m .44561 .36683 L s .25 Mabswid .44186 0 m .44186 .37201 L s gsave .44186 .39701 -66.0312 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 69.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .5 Mabswid .51459 .18601 m .51459 .18665 L .51459 .18724 L .51459 .18792 L .51458 .18856 L .51457 .1897 L .51456 .19094 L .51454 .1923 L .51451 .19374 L .51445 .19631 L .51437 .19896 L .51428 .20143 L .51401 .20698 L .51365 .21254 L .51325 .21749 L .51208 .22809 L .51079 .23654 L .5091 .24478 L .50725 .25151 L .50505 .2574 L .50389 .25977 L .5026 .26193 L .50133 .26359 L .50015 .26477 L .49956 .26522 L .49893 .26562 L .49833 .26592 L .49778 .26612 L .49744 .2662 L .49713 .26626 L .49697 .26628 L .49688 .26629 L .49679 .2663 L .4967 .26631 L .4966 .26631 L .49652 .26632 L .49643 .26632 L .49627 .26631 L .49611 .2663 L .49595 .26629 L .49581 .26627 L .49565 .26625 L .49547 .26621 L .49514 .26613 L .49484 .26604 L .49452 .26591 L .49393 .26563 L .49324 .26519 L .49262 .2647 L .49127 .26334 L Mistroke .49002 .26167 L .48769 .25743 L .48567 .25235 L .48362 .24546 L .48198 .23822 L .48053 .22983 L .47989 .22519 L .47927 .2199 L .4788 .21506 L .47838 .20973 L .47803 .20397 L .47779 .1985 L .4777 .19563 L .47764 .19296 L .47761 .19157 L .47759 .19003 L .47759 .18925 L .47758 .18841 L .47758 .18803 L .47757 .18763 L .47757 .1869 L .47757 .18621 L .47757 .18558 L .47757 .18523 L .47757 .18486 L .47758 .18417 L .47758 .18353 L .47758 .18285 L .4776 .18164 L .47762 .18022 L .47764 .1789 L .47771 .1759 L .4778 .1732 L .47792 .17027 L .4782 .165 L .47855 .15997 L .47894 .15541 L .47996 .14627 L .48139 .13695 L .483 .12908 L .485 .12171 L .48714 .11583 L .4883 .11332 L .48958 .11102 L .49083 .10921 L .492 .10788 L .49256 .10736 L .49318 .10686 L .49373 .1065 L .49431 .10619 L Mistroke .49464 .10605 L .49494 .10594 L .49524 .10585 L .49552 .10579 L .49569 .10576 L .49585 .10573 L .49602 .10571 L .49611 .10571 L .4962 .1057 L .49636 .1057 L .49651 .1057 L .49668 .1057 L .49676 .10571 L .49685 .10571 L .49703 .10573 L .4972 .10576 L .49752 .10583 L .49786 .10592 L .49823 .10605 L .4989 .10637 L .49951 .10675 L .50071 .10776 L .50181 .109 L .50299 .11068 L .50422 .11288 L .50641 .11801 L .50848 .12476 L .51018 .13223 L .51154 .14006 L .51276 .14965 L .51361 .159 L .51396 .16422 L .51422 .16913 L .51433 .17194 L .51442 .17459 L .51449 .17737 L .51452 .17896 L .51455 .18043 L .51456 .18157 L .51457 .18278 L .51458 .18347 L .51458 .18412 L .51458 .1847 L .51459 .18533 L .51459 .18589 L .51459 .18651 L .51458 .18716 L .51458 .18776 L .51458 .18832 L .51458 .18883 L Mistroke .51457 .18998 L .51455 .1911 L .51454 .19213 L .51449 .19445 L .51444 .19649 L .51438 .19865 L Mfstroke .24777 .18601 m .24777 .18695 L .24776 .18781 L .24774 .1888 L .24771 .18974 L .24764 .19141 L .24754 .19321 L .2474 .1952 L .24721 .19731 L .24676 .20107 L .24618 .20494 L .24551 .20855 L .24355 .21666 L .24094 .22475 L .23803 .23197 L .22972 .24734 L .22065 .25951 L .20901 .27124 L .19649 .28066 L .18187 .28865 L .1743 .29175 L .1659 .29447 L .16198 .29549 L .15779 .29642 L .15385 .29713 L .15023 .29767 L .1484 .29789 L .1464 .2981 L .14466 .29825 L .14275 .29838 L .14072 .29849 L .13961 .29853 L .13857 .29856 L .1376 .29858 L .13671 .29859 L .13573 .2986 L .1347 .29859 L .13379 .29858 L .13296 .29856 L .13201 .29853 L .13111 .29849 L .1295 .29841 L .12777 .2983 L .12383 .29794 L .12022 .29749 L .11266 .29615 L .10568 .29443 L .09817 .29203 L .09031 .28886 L .07555 .28089 L Mistroke .06278 .27134 L .05162 .26024 L .04275 .24863 L .03835 .24145 L .0347 .23441 L .02925 .22065 L .02712 .21316 L .02617 .20901 L .02544 .20511 L .02487 .20148 L .02446 .19816 L .02413 .19446 L .02399 .19242 L .02394 .19149 L .0239 .19049 L .02386 .1895 L .02384 .1886 L .02382 .18773 L .02381 .18682 L .02381 .18582 L .02381 .18489 L .02383 .18387 L .02384 .1833 L .02386 .18278 L .02389 .18173 L .02393 .18076 L .02405 .17858 L .0242 .17665 L .02438 .17462 L .02481 .17103 L .0253 .16769 L .0268 .16016 L .029 .15215 L .03161 .14473 L .03788 .13139 L .04647 .11813 L .056 .10704 L .06702 .09718 L .08057 .08809 L .09436 .08143 L .10247 .07854 L .11009 .07644 L .11376 .07563 L .1177 .07491 L .12112 .0744 L .12486 .07396 L .12714 .07376 L .12926 .07361 L .13128 .07351 L .1323 .07347 L Mistroke .13288 .07346 L .13343 .07344 L .13444 .07342 L .13537 .07342 L .13637 .07342 L .13694 .07342 L .13746 .07343 L .13842 .07345 L .13929 .07347 L .14029 .0735 L .14124 .07355 L .14315 .07365 L .14493 .07378 L .14896 .07419 L .15288 .07472 L .15705 .07545 L .16452 .07717 L .17122 .07918 L .18524 .08496 L .19278 .08905 L .19946 .09335 L .21109 .10263 L .22239 .11458 L .23132 .12722 L .23522 .13418 L .23892 .1421 L .24168 .14937 L .24408 .15733 L .24515 .1618 L .24597 .1659 L .24661 .16982 L .24713 .17399 L .24731 .17582 L .24747 .17779 L .24761 .17996 L .24766 .18093 L .2477 .18199 L .24773 .18302 L .24775 .18398 L .24776 .18489 L .24777 .18586 L .24777 .18681 L .24776 .18771 L .24774 .18852 L .24772 .18939 L .24768 .19044 L .24764 .19141 L .24751 .19363 L .24735 .19578 L .24712 .19808 L Mistroke .2466 .20224 L .24599 .206 L .24431 .21381 L .24226 .2209 L .23598 .23632 L .23547 .23733 L Mfstroke .64962 .18601 m .64962 .18739 L .64963 .18866 L .64966 .19012 L .64969 .1915 L .64977 .19395 L .64989 .1966 L .65007 .19953 L .6503 .20262 L .65083 .20816 L .65155 .21385 L .65236 .21916 L .65473 .23109 L .65788 .24302 L .6614 .25366 L .67144 .27644 L .6824 .29463 L .6965 .31247 L .71175 .32722 L .72975 .34038 L .73915 .34581 L .7497 .35088 L .75911 .35459 L .76971 .35792 L .77479 .35921 L .7803 .36039 L .78511 .36125 L .79038 .362 L .79348 .36236 L .79637 .36263 L .79914 .36284 L .80056 .36292 L .80209 .363 L .80346 .36306 L .80473 .3631 L .80594 .36312 L .80721 .36314 L .80861 .36315 L .80992 .36315 L .81067 .36314 L .81136 .36313 L .81215 .36312 L .81289 .3631 L .81414 .36306 L .81548 .36301 L .8179 .36289 L .82079 .36269 L .82343 .36246 L .82917 .36179 L .83462 .36096 L Mistroke .84423 .35901 L .85467 .35616 L .86579 .35226 L .87574 .34798 L .89734 .33575 L .91598 .32135 L .93423 .30251 L .94933 .28148 L .95593 .26975 L .96208 .25654 L .96694 .24351 L .97052 .23126 L .97195 .22525 L .97326 .21865 L .97422 .21283 L .97504 .20652 L .9754 .20304 L .97567 .19985 L .97587 .19679 L .97603 .19357 L .9761 .19185 L .97613 .19091 L .97615 .19002 L .97618 .18829 L .97619 .18672 L .97619 .18581 L .97619 .18485 L .97617 .18313 L .97615 .18217 L .97613 .18127 L .97607 .17924 L .97599 .17744 L .97589 .17549 L .97565 .17194 L .97502 .1653 L .97398 .1576 L .97273 .15053 L .96973 .13774 L .9661 .12601 L .96121 .11341 L .95511 .10069 L .94111 .07829 L .9259 .0602 L .90774 .04378 L .88946 .0313 L .87857 .0254 L .86807 .02066 L .85859 .01712 L .84806 .01396 L .83751 .01157 L Mistroke .83172 .01058 L .82631 .00986 L .82373 .00958 L .82127 .00936 L .81904 .0092 L .81667 .00906 L .81532 .00899 L .8141 .00895 L .81288 .00891 L .81173 .00888 L .81038 .00886 L .80914 .00886 L .80779 .00886 L .8071 .00887 L .80635 .00888 L .80495 .00891 L .80366 .00895 L .80224 .00901 L .80073 .00908 L .79821 .00924 L .79544 .00946 L .79036 .01001 L .78562 .01068 L .77517 .01272 L .76414 .01573 L .75464 .01909 L .74454 .02348 L .72523 .03457 L .70872 .04742 L .69289 .06365 L .67893 .08263 L .668 .1025 L .66356 .11269 L .65951 .12383 L .65632 .13455 L .65393 .14455 L .65194 .15545 L .65111 .16151 L .65048 .1673 L .65026 .16989 L .65006 .17265 L .64991 .17504 L .64979 .17762 L .64973 .17921 L .64969 .18067 L .64966 .18207 L .64963 .18354 L .64962 .18487 L .64962 .1861 L .64962 .18746 L Mistroke .64964 .18891 L .64966 .19016 L .64969 .19155 L .64974 .19299 L .64979 .19435 L .65006 .19936 L .65027 .20221 L .65049 .20481 L .65113 .21066 L .65269 .22107 L .65468 .23085 L Mfstroke 0 0 m 1 0 L 1 .37201 L 0 .37201 L closepath clip newpath % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1151 5339 a(Orbits)g(at)h Fn(h)23 b Fo(=)f Fn(:)p Fo(3)28 b(with)g Fn(m)2025 5351 y Fk(1)2085 5339 y Fo(=)23 b Fn(:)p Fo(8)k(and)g Fn(m)2499 5351 y Fk(2)2559 5339 y Fo(=)c(1.)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 1381 315 a Fk(BRANCHES)29 b(OF)g(PERIODIC)g (ORBITS)892 b(9)973 1259 y @beginspecial 91 @llx 3 @lly 322 @urx 100 @ury 2344 @rwi 992 @rhi @setspecial %%BeginDocument: m10.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 100 %%HiResBoundingBox: 91.5625 3.1875 321.938 99.1875 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:18:51) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 102.375 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 99.188 moveto 321.938 99.188 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 99.188 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 99.187500 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 96.000000 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .41701 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 0.472516 0.538845 0.208504 0.538845 [ [.06838 .196 -15 -9 ] [.06838 .196 15 0 ] [.20309 .196 -12 -9 ] [.20309 .196 12 0 ] [.3378 .196 -15 -9 ] [.3378 .196 15 0 ] [.60723 .196 -12 -9 ] [.60723 .196 12 0 ] [.74194 .196 -9 -9 ] [.74194 .196 9 0 ] [.87665 .196 -12 -9 ] [.87665 .196 12 0 ] [1.025 .2085 0 -4.90625 ] [1.025 .2085 10 4.90625 ] [.46002 .04685 -24 -4.5 ] [.46002 .04685 0 4.5 ] [.46002 .10073 -24 -4.5 ] [.46002 .10073 0 4.5 ] [.46002 .15462 -24 -4.5 ] [.46002 .15462 0 4.5 ] [.46002 .26239 -18 -4.5 ] [.46002 .26239 0 4.5 ] [.46002 .31627 -18 -4.5 ] [.46002 .31627 0 4.5 ] [.46002 .37016 -18 -4.5 ] [.46002 .37016 0 4.5 ] [.47252 .44201 -5.03125 0 ] [.47252 .44201 5.03125 9.8125 ] [ 0 0 0 0 ] [ 1 .41701 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .06838 .2085 m .06838 .21475 L s [(-0.75)] .06838 .196 0 1 Mshowa .20309 .2085 m .20309 .21475 L s [(-0.5)] .20309 .196 0 1 Mshowa .3378 .2085 m .3378 .21475 L s [(-0.25)] .3378 .196 0 1 Mshowa .60723 .2085 m .60723 .21475 L s [(0.25)] .60723 .196 0 1 Mshowa .74194 .2085 m .74194 .21475 L s [(0.5)] .74194 .196 0 1 Mshowa .87665 .2085 m .87665 .21475 L s [(0.75)] .87665 .196 0 1 Mshowa .125 Mabswid .09532 .2085 m .09532 .21225 L s .12227 .2085 m .12227 .21225 L s .14921 .2085 m .14921 .21225 L s .17615 .2085 m .17615 .21225 L s .23004 .2085 m .23004 .21225 L s .25698 .2085 m .25698 .21225 L s .28392 .2085 m .28392 .21225 L s .31086 .2085 m .31086 .21225 L s .36475 .2085 m .36475 .21225 L s .39169 .2085 m .39169 .21225 L s .41863 .2085 m .41863 .21225 L s .44557 .2085 m .44557 .21225 L s .49946 .2085 m .49946 .21225 L s .5264 .2085 m .5264 .21225 L s .55334 .2085 m .55334 .21225 L s .58029 .2085 m .58029 .21225 L s .63417 .2085 m .63417 .21225 L s .66111 .2085 m .66111 .21225 L s .68805 .2085 m .68805 .21225 L s .715 .2085 m .715 .21225 L s .76888 .2085 m .76888 .21225 L s .79582 .2085 m .79582 .21225 L s .82277 .2085 m .82277 .21225 L s .84971 .2085 m .84971 .21225 L s .04144 .2085 m .04144 .21225 L s .0145 .2085 m .0145 .21225 L s .90359 .2085 m .90359 .21225 L s .93053 .2085 m .93053 .21225 L s .95748 .2085 m .95748 .21225 L s .98442 .2085 m .98442 .21225 L s .25 Mabswid 0 .2085 m 1 .2085 L s gsave 1.025 .2085 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .47252 .04685 m .47877 .04685 L s [(-0.3)] .46002 .04685 1 0 Mshowa .47252 .10073 m .47877 .10073 L s [(-0.2)] .46002 .10073 1 0 Mshowa .47252 .15462 m .47877 .15462 L s [(-0.1)] .46002 .15462 1 0 Mshowa .47252 .26239 m .47877 .26239 L s [(0.1)] .46002 .26239 1 0 Mshowa .47252 .31627 m .47877 .31627 L s [(0.2)] .46002 .31627 1 0 Mshowa .47252 .37016 m .47877 .37016 L s [(0.3)] .46002 .37016 1 0 Mshowa .125 Mabswid .47252 .05763 m .47627 .05763 L s .47252 .0684 m .47627 .0684 L s .47252 .07918 m .47627 .07918 L s .47252 .08996 m .47627 .08996 L s .47252 .11151 m .47627 .11151 L s .47252 .12229 m .47627 .12229 L s .47252 .13307 m .47627 .13307 L s .47252 .14384 m .47627 .14384 L s .47252 .1654 m .47627 .1654 L s .47252 .17617 m .47627 .17617 L s .47252 .18695 m .47627 .18695 L s .47252 .19773 m .47627 .19773 L s .47252 .21928 m .47627 .21928 L s .47252 .23006 m .47627 .23006 L s .47252 .24083 m .47627 .24083 L s .47252 .25161 m .47627 .25161 L s .47252 .27317 m .47627 .27317 L s .47252 .28394 m .47627 .28394 L s .47252 .29472 m .47627 .29472 L s .47252 .3055 m .47627 .3055 L s .47252 .32705 m .47627 .32705 L s .47252 .33783 m .47627 .33783 L s .47252 .3486 m .47627 .3486 L s .47252 .35938 m .47627 .35938 L s .47252 .03607 m .47627 .03607 L s .47252 .0253 m .47627 .0253 L s .47252 .01452 m .47627 .01452 L s .47252 .00374 m .47627 .00374 L s .47252 .38093 m .47627 .38093 L s .47252 .39171 m .47627 .39171 L s .47252 .40249 m .47627 .40249 L s .47252 .41326 m .47627 .41326 L s .25 Mabswid .47252 0 m .47252 .41701 L s gsave .47252 .44201 -66.0312 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 69.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .5 Mabswid .49878 .2085 m .49877 .2094 L .49877 .21021 L .49877 .21115 L .49876 .21203 L .49875 .21361 L .49873 .21532 L .49871 .2172 L .49867 .21919 L .49859 .22275 L .49849 .2264 L .49836 .22981 L .498 .23749 L .49752 .24516 L .49698 .25201 L .4954 .26667 L .49365 .27837 L .49134 .28981 L .48879 .29923 L .48573 .30757 L .48413 .31098 L .48232 .31414 L .4807 .31643 L .47888 .31845 L .47801 .31923 L .47707 .31993 L .47625 .32043 L .47536 .32086 L .47483 .32106 L .47434 .32121 L .47388 .32132 L .47364 .32136 L .47338 .3214 L .47314 .32142 L .47293 .32144 L .47269 .32145 L .47258 .32145 L .47245 .32145 L .47223 .32145 L .47199 .32143 L .47177 .32141 L .47157 .32139 L .47115 .32132 L .4707 .32121 L .47022 .32107 L .46978 .32091 L .46898 .32054 L .46814 .32005 L .46623 .31852 L .46451 .31665 L Mistroke .46135 .31182 L .45965 .30837 L .45814 .30473 L .45527 .29593 L .45296 .28654 L .45091 .27553 L .4491 .26235 L .44778 .24867 L .44726 .24148 L .44682 .23342 L .44666 .22951 L .44653 .2258 L .44643 .2224 L .44635 .21878 L .44632 .2169 L .44629 .21483 L .44628 .21392 L .44627 .21295 L .44627 .21203 L .44626 .21118 L .44626 .21069 L .44626 .21017 L .44626 .20959 L .44626 .20907 L .44626 .20852 L .44626 .20793 L .44626 .20737 L .44626 .20686 L .44626 .20594 L .44627 .20542 L .44627 .20493 L .44628 .20395 L .44629 .2029 L .44631 .20094 L .44634 .19912 L .44642 .19501 L .44652 .19148 L .44665 .1876 L .44698 .18052 L .44736 .17399 L .44788 .167 L .44854 .15985 L .44998 .1477 L .45189 .13582 L .454 .12591 L .4567 .11636 L .45943 .10913 L .46249 .10323 L .4643 .10062 L .46602 .09868 L Mistroke .46683 .09794 L .46771 .09725 L .46848 .09675 L .46933 .0963 L .46984 .09608 L .47031 .09591 L .47081 .09577 L .47102 .09572 L .47126 .09567 L .47149 .09563 L .4717 .0956 L .4719 .09558 L .47212 .09557 L .47234 .09556 L .47255 .09555 L .47278 .09556 L .47291 .09557 L .47303 .09557 L .47325 .09559 L .47344 .09562 L .4739 .09569 L .47434 .0958 L .47482 .09594 L .47567 .09628 L .47646 .09669 L .47824 .09797 L .48009 .09984 L .48171 .10195 L .48339 .10467 L .48627 .11071 L .48932 .11953 L .49186 .1295 L .49402 .14084 L .49567 .1524 L .49699 .16508 L .49758 .17263 L .49802 .17986 L .4982 .18333 L .49836 .18714 L .49849 .19052 L .49859 .19414 L .49867 .19774 L .49873 .20102 L .49875 .2026 L .49876 .20343 L .49876 .20431 L .49877 .20508 L .49877 .20593 L .49878 .2067 L .49878 .20742 L Mistroke Mfstroke .24111 .2085 m .2411 .2094 L .24109 .21021 L .24107 .21116 L .24105 .21204 L .24099 .21363 L .24089 .21534 L .24076 .21723 L .24058 .21922 L .24018 .2228 L .23963 .22647 L .23901 .22989 L .2372 .23759 L .23479 .24528 L .23209 .25215 L .2244 .26682 L .21598 .27848 L .20516 .28981 L .19351 .299 L .17986 .30693 L .17279 .31007 L .16491 .31288 L .1573 .31497 L .15019 .3164 L .1467 .31692 L .14477 .31715 L .14294 .31735 L .14124 .3175 L .13939 .31763 L .1377 .31773 L .13614 .31779 L .13525 .31782 L .1343 .31784 L .13339 .31785 L .13257 .31785 L .13165 .31785 L .13113 .31784 L .13065 .31783 L .12967 .31781 L .12912 .3178 L .12863 .31778 L .12666 .31769 L .12452 .31755 L .12252 .31738 L .12067 .31719 L .11719 .31675 L .11347 .31615 L .10682 .31474 L .09904 .31252 L .0921 .31 L Mistroke .07924 .3038 L .06628 .29519 L .05521 .28536 L .045 .27334 L .03645 .25966 L .03322 .253 L .03032 .24575 L .02809 .23887 L .02617 .23118 L .02551 .22776 L .02492 .22407 L .02448 .22058 L .02417 .21739 L .02404 .21567 L .02394 .21376 L .02389 .2128 L .02386 .21177 L .02383 .2108 L .02382 .2099 L .02381 .20907 L .02381 .20829 L .02381 .20744 L .02383 .20653 L .02385 .20557 L .02388 .20467 L .02395 .20298 L .02406 .20108 L .02421 .19907 L .02458 .19548 L .02511 .19164 L .02585 .18744 L .02758 .17996 L .02962 .17325 L .03573 .15875 L .04305 .14641 L .05277 .13421 L .06354 .12401 L .07639 .11488 L .0825 .11143 L .08933 .10817 L .10221 .1035 L .10915 .10172 L .11318 .10091 L .11687 .1003 L .12079 .0998 L .12296 .09958 L .12501 .09942 L .12691 .09931 L .12866 .09923 L .12958 .0992 L Mistroke .13011 .09919 L .13059 .09918 L .1311 .09917 L .13164 .09916 L .13263 .09916 L .1336 .09916 L .13451 .09918 L .13533 .09919 L .13621 .09922 L .13718 .09926 L .1382 .09931 L .14002 .09942 L .14328 .09969 L .14685 .10011 L .15069 .10069 L .15478 .10147 L .16207 .10328 L .16936 .10563 L .17707 .10877 L .1904 .11596 L .20242 .1248 L .21375 .13591 L .22273 .14762 L .22967 .15963 L .23276 .16644 L .2355 .17382 L .23759 .1809 L .23907 .18744 L .23969 .19088 L .24023 .19463 L .24047 .19669 L .24066 .1986 L .24082 .20055 L .24093 .20237 L .24101 .20393 L .24104 .2048 L .24107 .2056 L .24109 .20648 L .2411 .20743 L .2411 .20833 L .2411 .20916 L .24109 .21011 L .24108 .21099 L .24106 .21179 L .24103 .21265 L .24094 .21458 L .24082 .21636 L .24056 .21943 L .24019 .2227 L .23926 .22857 L Mistroke .23775 .23547 L .236 .24165 L Mfstroke .61866 .2085 m .61867 .2103 L .61869 .21193 L .61872 .21381 L .61877 .21559 L .61888 .21876 L .61906 .22219 L .6193 .22596 L .61963 .22995 L .62039 .23708 L .62139 .2444 L .62254 .2512 L .62588 .26644 L .6303 .28156 L .63522 .29491 L .64913 .32296 L .66416 .34465 L .68331 .36507 L .7038 .38099 L .71612 .38834 L .72776 .394 L .73906 .39841 L .75135 .40212 L .75791 .40366 L .7652 .40502 L .76843 .40552 L .77191 .40597 L .77491 .4063 L .77824 .40659 L .78163 .40682 L .78349 .40692 L .78524 .40699 L .78688 .40703 L .78838 .40706 L .79003 .40708 L .79177 .40708 L .7927 .40707 L .79355 .40706 L .79453 .40704 L .79545 .40701 L .79709 .40695 L .79888 .40687 L .80294 .40662 L .8067 .40629 L .81303 .40555 L .82001 .40444 L .83415 .40125 L .84802 .39688 L .86059 .39178 L .87507 .38448 L Mistroke .88819 .37639 L .9118 .35762 L .92409 .34511 L .93484 .33208 L .94449 .31816 L .95373 .30195 L .96088 .28639 L .96641 .2712 L .97099 .25448 L .97285 .24543 L .9744 .23563 L .97499 .23066 L .97551 .22524 L .9757 .22275 L .97586 .22011 L .97598 .21782 L .97603 .21662 L .97608 .21536 L .97614 .21298 L .97618 .21081 L .97619 .20876 L .97618 .20654 L .97614 .2041 L .97611 .20273 L .97607 .20149 L .97598 .19908 L .97586 .19681 L .97556 .19239 L .97519 .18827 L .97406 .17895 L .97255 .16994 L .97049 .1604 L .96567 .14354 L .96009 .12873 L .94459 .09901 L .93404 .08387 L .9233 .07103 L .90128 .05028 L .8877 .04029 L .87483 .03239 L .86253 .02611 L .84886 .02044 L .83501 .01599 L .8275 .0141 L .8204 .01264 L .81369 .01155 L .81016 .01109 L .80643 .01069 L .8033 .01042 L .80164 .0103 L Mistroke .79986 .01019 L .79823 .0101 L .79675 .01004 L .79525 .00999 L .79384 .00996 L .79206 .00993 L .79046 .00993 L .78958 .00993 L .78862 .00994 L .78688 .00997 L .78526 .01002 L .78354 .01009 L .78048 .01026 L .77692 .01052 L .77362 .01085 L .76617 .01183 L .75971 .01298 L .75277 .01453 L .74042 .01813 L .72874 .02259 L .71828 .02753 L .69754 .04035 L .6768 .05818 L .65965 .07822 L .64409 .10303 L .63235 .12957 L .62774 .14374 L .62374 .15973 L .62223 .16755 L .62104 .17501 L .62017 .18184 L .61946 .18911 L .61918 .1929 L .61894 .19707 L .61886 .1989 L .61879 .20087 L .61874 .20273 L .6187 .20442 L .61869 .20545 L .61867 .20654 L .61867 .20851 L .61867 .20971 L .61868 .21084 L .61869 .21186 L .61871 .21295 L .61875 .21501 L .61882 .21717 L .619 .22104 L .61923 .22493 L .61952 .22861 L Mistroke .6202 .23547 L .62116 .24281 L .62245 .25072 L .62545 .26473 L .62897 .27738 L .63869 .30298 L .64552 .31663 L .65272 .32874 L .66951 .35102 L .68719 .36849 L .70479 .38164 L .72557 .39302 L Mfstroke 0 0 m 1 0 L 1 .41701 L 0 .41701 L closepath clip newpath % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1163 1358 a Fo(Orbits)27 b(at)g Fn(h)c Fo(=)g Fn(:)p Fo(3)k(with)h Fn(m)2036 1370 y Fk(1)2096 1358 y Fo(=)23 b(1)k(and)h Fn(m)2488 1370 y Fk(2)2548 1358 y Fo(=)23 b(1.)973 2182 y @beginspecial 91 @llx 3 @lly 322 @urx 95 @ury 2344 @rwi 942 @rhi @setspecial %%BeginDocument: m13.eps %!PS-Adobe-2.0 EPSF-1.2 %%BoundingBox: 91 3 322 95 %%HiResBoundingBox: 91.5625 3.1875 321.938 94.5625 %%Creator: (Mathematica 4.0 for X) %%CreationDate: (Sunday, December 15, 2002) (8:19:11) %%Title: Clipboard %%DocumentNeededResources: font Courier %%DocumentSuppliedResources: %%DocumentNeededFonts: Courier %%DocumentSuppliedFonts: %%DocumentFonts: Courier %%EndComments /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 97.75 translate 1 -1 scale gsave 0.000 0.000 0.000 setrgbcolor 1.000 setlinewidth gsave newpath 91.562 94.562 moveto 321.938 94.562 lineto 321.938 3.188 lineto 91.562 3.188 lineto 91.562 94.562 lineto closepath clip newpath gsave 150 dict begin /Mfixwid true def /Mrot 0 def /Mpstart { MathPictureStart } bind def /Mpend { MathPictureEnd } bind def /Mscale { 0 1 0 1 5 -1 roll MathScale } bind def /Plain /Courier findfont def /Bold /Courier-Bold findfont def /Italic /Courier-Oblique findfont def /MathPictureStart { /Mimatrix matrix currentmatrix def gsave newpath Mleft Mbottom translate /Mtmatrix matrix currentmatrix def Plain Mfontsize scalefont setfont 0 setgray 0 setlinewidth } bind def /MathPictureEnd { grestore } bind def /MathSubStart { Momatrix Mgmatrix Mtmatrix Mleft Mbottom Mwidth Mheight 9 -2 roll moveto Mtmatrix setmatrix currentpoint Mgmatrix setmatrix 11 -2 roll moveto Mtmatrix setmatrix currentpoint 2 copy translate /Mtmatrix matrix currentmatrix def /Mleft 0 def /Mbottom 0 def 3 -1 roll exch sub /Mheight exch def sub /Mwidth exch def } bind def /MathSubEnd { /Mheight exch def /Mwidth exch def /Mbottom exch def /Mleft exch def /Mtmatrix exch def dup setmatrix /Mgmatrix exch def /Momatrix exch def } bind def /Mdot { moveto 0 0 rlineto stroke } bind def /Mtetra { moveto lineto lineto lineto fill } bind def /Metetra { moveto lineto lineto lineto closepath gsave fill grestore 0 setgray stroke } bind def /Mistroke { flattenpath 0 0 0 { 4 2 roll pop pop } { 4 -1 roll 2 index sub dup mul 4 -1 roll 2 index sub dup mul add sqrt 4 -1 roll add 3 1 roll } { stop } { stop } pathforall pop pop currentpoint stroke moveto currentdash 3 -1 roll add setdash } bind def /Mfstroke { stroke currentdash pop 0 setdash } bind def /Mrotsboxa { gsave dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def grestore Msboxa 3 -1 roll /Mtmatrix exch def /Mrot 0 def } bind def /Msboxa { newpath 5 -1 roll Mvboxa pop Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Msboxa1 5 -3 roll Msboxa1 Mboxrot [ 7 -2 roll 2 copy [ 3 1 roll 10 -1 roll 9 -1 roll ] 6 1 roll 5 -2 roll ] } bind def /Msboxa1 { sub 2 div dup 2 index 1 add mul 3 -1 roll -1 add 3 -1 roll mul } bind def /Mvboxa { Mfixwid { Mvboxa1 } { dup Mwidthcal 0 exch { add } forall exch Mvboxa1 4 index 7 -1 roll add 4 -1 roll pop 3 1 roll } ifelse } bind def /Mvboxa1 { gsave newpath [ true 3 -1 roll { Mbbox 5 -1 roll { 0 5 1 roll } { 7 -1 roll exch sub (m) stringwidth pop .3 mul sub 7 1 roll 6 -1 roll 4 -1 roll Mmin 3 -1 roll 5 index add 5 -1 roll 4 -1 roll Mmax 4 -1 roll } ifelse false } forall { stop } if counttomark 1 add 4 roll ] grestore } bind def /Mbbox { 0 0 moveto false charpath flattenpath pathbbox newpath } bind def /Mmin { 2 copy gt { exch } if pop } bind def /Mmax { 2 copy lt { exch } if pop } bind def /Mrotshowa { dup /Mrot exch def Mrotcheck Mtmatrix dup setmatrix 7 1 roll 4 index 4 index translate rotate 3 index -1 mul 3 index -1 mul translate /Mtmatrix matrix currentmatrix def Mgmatrix setmatrix Mshowa /Mtmatrix exch def /Mrot 0 def } bind def /Mshowa { 4 -2 roll moveto 2 index Mtmatrix setmatrix Mvboxa 7 1 roll Mboxout 6 -1 roll 5 -1 roll 4 -1 roll Mshowa1 4 1 roll Mshowa1 rmoveto currentpoint Mfixwid { Mshowax } { Mshoway } ifelse pop pop pop pop Mgmatrix setmatrix } bind def /Mshowax { 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get show } for } bind def /Mshoway { 3 index Mwidthcal 5 1 roll 0 1 4 index length -1 add { 2 index 4 index 2 index get 3 index add moveto 4 index exch get [ 6 index aload length 2 add -1 roll { pop Strform stringwidth pop neg exch add 0 rmoveto } exch kshow cleartomark } for pop } bind def /Mwidthcal { [ exch { Mwidthcal1 } forall ] [ exch dup Maxlen -1 add 0 1 3 -1 roll { [ exch 2 index { 1 index Mget exch } forall pop Maxget exch } for pop ] Mreva } bind def /Mreva { [ exch aload length -1 1 {1 roll} for ] } bind def /Mget { 1 index length -1 add 1 index ge { get } { pop pop 0 } ifelse } bind def /Maxlen { [ exch { length } forall Maxget } bind def /Maxget { counttomark -1 add 1 1 3 -1 roll { pop Mmax } for exch pop } bind def /Mwidthcal1 { [ exch { Strform stringwidth pop } forall ] } bind def /Strform { /tem (x) def tem 0 3 -1 roll put tem } bind def /Mshowa1 { 2 copy add 4 1 roll sub mul sub -2 div } bind def /MathScale { Mwidth Mheight Mlp translate scale /yscale exch def /ybias exch def /xscale exch def /xbias exch def /Momatrix xscale yscale matrix scale xbias ybias matrix translate matrix concatmatrix def /Mgmatrix matrix currentmatrix def } bind def /Mlp { 3 copy Mlpfirst { Mnodistort { Mmin dup } if 4 index 2 index 2 index Mlprun 11 index 11 -1 roll 10 -4 roll Mlp1 8 index 9 -5 roll Mlp1 4 -1 roll and { exit } if 3 -1 roll pop pop } loop exch 3 1 roll 7 -3 roll pop pop pop } bind def /Mlpfirst { 3 -1 roll dup length 2 copy -2 add get aload pop pop pop 4 -2 roll -1 add get aload pop pop pop 6 -1 roll 3 -1 roll 5 -1 roll sub dup /MsaveAx exch def div 4 1 roll exch sub dup /MsaveAy exch def div } bind def /Mlprun { 2 copy 4 index 0 get dup 4 1 roll Mlprun1 3 copy 8 -2 roll 9 -1 roll { 3 copy Mlprun1 3 copy 11 -3 roll /gt Mlpminmax 8 3 roll 11 -3 roll /lt Mlpminmax 8 3 roll } forall pop pop pop pop 3 1 roll pop pop aload pop 5 -1 roll aload pop exch 6 -1 roll Mlprun2 8 2 roll 4 -1 roll Mlprun2 6 2 roll 3 -1 roll Mlprun2 4 2 roll exch Mlprun2 6 2 roll } bind def /Mlprun1 { aload pop exch 6 -1 roll 5 -1 roll mul add 4 -2 roll mul 3 -1 roll add } bind def /Mlprun2 { 2 copy add 2 div 3 1 roll exch sub } bind def /Mlpminmax { cvx 2 index 6 index 2 index exec { 7 -3 roll 4 -1 roll } if 1 index 5 index 3 -1 roll exec { 4 1 roll pop 5 -1 roll aload pop pop 4 -1 roll aload pop [ 8 -2 roll pop 5 -2 roll pop 6 -2 roll pop 5 -1 roll ] 4 1 roll pop } { pop pop pop } ifelse } bind def /Mlp1 { 5 index 3 index sub 5 index 2 index mul 1 index le 1 index 0 le or dup not { 1 index 3 index div .99999 mul 8 -1 roll pop 7 1 roll } if 8 -1 roll 2 div 7 -2 roll pop sub 5 index 6 -3 roll pop pop mul sub exch } bind def /intop 0 def /inrht 0 def /inflag 0 def /outflag 0 def /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def /Minner { outflag 1 eq { /outflag 0 def /intop 0 def /inrht 0 def } if 5 index gsave Mtmatrix setmatrix Mvboxa pop grestore 3 -1 roll pop dup intop gt { /intop exch def } { pop } ifelse dup inrht gt { /inrht exch def } { pop } ifelse pop /inflag 1 def } bind def /Mouter { /xadrht 0 def /xadlft 0 def /yadtop 0 def /yadbot 0 def inflag 1 eq { dup 0 lt { dup intop mul neg /yadtop exch def } if dup 0 gt { dup intop mul /yadbot exch def } if pop dup 0 lt { dup inrht mul neg /xadrht exch def } if dup 0 gt { dup inrht mul /xadlft exch def } if pop /outflag 1 def } { pop pop} ifelse /inflag 0 def /inrht 0 def /intop 0 def } bind def /Mboxout { outflag 1 eq { 4 -1 roll xadlft leadjust add sub 4 1 roll 3 -1 roll yadbot leadjust add sub 3 1 roll exch xadrht leadjust add add exch yadtop leadjust add add /outflag 0 def /xadlft 0 def /yadbot 0 def /xadrht 0 def /yadtop 0 def } if } bind def /leadjust { (m) stringwidth pop .5 mul } bind def /Mrotcheck { dup 90 eq { yadbot /yadbot xadrht def /xadrht yadtop def /yadtop xadlft def /xadlft exch def } if dup cos 1 index sin Checkaux dup cos 1 index sin neg exch Checkaux 3 1 roll pop pop } bind def /Checkaux { 4 index exch 4 index mul 3 1 roll mul add 4 1 roll } bind def /Mboxrot { Mrot 90 eq { brotaux 4 2 roll } if Mrot 180 eq { 4 2 roll brotaux 4 2 roll brotaux } if Mrot 270 eq { 4 2 roll brotaux } if } bind def /brotaux { neg exch neg } bind def /Mabsproc { 0 matrix defaultmatrix dtransform idtransform dup mul exch dup mul add sqrt } bind def /Mabswid { Mabsproc setlinewidth } bind def /Mabsdash { exch [ exch { Mabsproc } forall ] exch setdash } bind def /MBeginOrig { Momatrix concat} bind def /MEndOrig { Mgmatrix setmatrix} bind def /sampledsound where { pop} { /sampledsound { exch pop exch 5 1 roll mul 4 idiv mul 2 idiv exch pop exch /Mtempproc exch def { Mtempproc pop } repeat } bind def } ifelse % Here are the short operators /g { setgray} bind def /k { setcmykcolor} bind def /m { moveto} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /P { grestore} bind def /s { stroke} bind def /MFill { 0 0 moveto Mwidth 0 lineto Mwidth Mheight lineto 0 Mheight lineto fill } bind def /MPlotRegion { 3 index Mwidth mul 2 index Mheight mul translate exch sub Mheight mul /Mheight exch def exch sub Mwidth mul /Mwidth exch def } bind def /Mcharproc { currentfile (x) readhexstring pop 0 get exch div } bind def /Mshadeproc { dup 3 1 roll { dup Mcharproc 3 1 roll } repeat 1 eq { setgray } { 3 eq { setrgbcolor } { setcmykcolor } ifelse } ifelse } bind def /Mrectproc { 3 index 2 index moveto 2 index 3 -1 roll lineto dup 3 1 roll lineto lineto fill } bind def /_Mcolorimage { 7 1 roll pop pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index 9 index Mshadeproc Mrectproc } for pop } for pop pop pop pop } bind def /_Mimage { pop matrix invertmatrix concat 2 exch exp 1 sub 3 1 roll 1 1 2 index { 1 1 4 index { dup 1 sub exch 2 index dup 1 sub exch 7 index Mcharproc setgray Mrectproc } for pop } for pop pop pop } bind def /Mimage { 4 index 4 index mul 1600 gt { image } { _Mimage } ifelse } def /Mcolorimage { 6 index 6 index mul 1600 gt { colorimage } { _Mcolorimage } ifelse } def /Mnodistort true def 1.000000 1.000000 scale 91.562500 94.562500 translate 1.000000 -1.000000 scale -0.000000 -0.000000 translate /Mleft 0.000000 def /Mbottom 0.000000 def /Mwidth 230.375000 def /Mheight 91.375000 def 0 setgray 0 setlinewidth /Courier findfont 12 scalefont setfont /Mfontsize 12 def /Plain /Courier findfont def %! %%Creator: Mathematica %%AspectRatio: .3968 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 0.508937 0.517511 0.198401 0.517511 [ [.1208 .1859 -15 -9 ] [.1208 .1859 15 0 ] [.25018 .1859 -12 -9 ] [.25018 .1859 12 0 ] [.37956 .1859 -15 -9 ] [.37956 .1859 15 0 ] [.63831 .1859 -12 -9 ] [.63831 .1859 12 0 ] [.76769 .1859 -9 -9 ] [.76769 .1859 9 0 ] [.89707 .1859 -12 -9 ] [.89707 .1859 12 0 ] [1.025 .1984 0 -4.90625 ] [1.025 .1984 10 4.90625 ] [.49644 .04315 -24 -4.5 ] [.49644 .04315 0 4.5 ] [.49644 .0949 -24 -4.5 ] [.49644 .0949 0 4.5 ] [.49644 .14665 -24 -4.5 ] [.49644 .14665 0 4.5 ] [.49644 .25015 -18 -4.5 ] [.49644 .25015 0 4.5 ] [.49644 .3019 -18 -4.5 ] [.49644 .3019 0 4.5 ] [.49644 .35365 -18 -4.5 ] [.49644 .35365 0 4.5 ] [.50894 .4218 -5.03125 0 ] [.50894 .4218 5.03125 9.8125 ] [ 0 0 0 0 ] [ 1 .3968 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .1208 .1984 m .1208 .20465 L s [(-0.75)] .1208 .1859 0 1 Mshowa .25018 .1984 m .25018 .20465 L s [(-0.5)] .25018 .1859 0 1 Mshowa .37956 .1984 m .37956 .20465 L s [(-0.25)] .37956 .1859 0 1 Mshowa .63831 .1984 m .63831 .20465 L s [(0.25)] .63831 .1859 0 1 Mshowa .76769 .1984 m .76769 .20465 L s [(0.5)] .76769 .1859 0 1 Mshowa .89707 .1984 m .89707 .20465 L s [(0.75)] .89707 .1859 0 1 Mshowa .125 Mabswid .14668 .1984 m .14668 .20215 L s .17255 .1984 m .17255 .20215 L s .19843 .1984 m .19843 .20215 L s .22431 .1984 m .22431 .20215 L s .27606 .1984 m .27606 .20215 L s .30193 .1984 m .30193 .20215 L s .32781 .1984 m .32781 .20215 L s .35368 .1984 m .35368 .20215 L s .40543 .1984 m .40543 .20215 L s .43131 .1984 m .43131 .20215 L s .45719 .1984 m .45719 .20215 L s .48306 .1984 m .48306 .20215 L s .53481 .1984 m .53481 .20215 L s .56069 .1984 m .56069 .20215 L s .58656 .1984 m .58656 .20215 L s .61244 .1984 m .61244 .20215 L s .66419 .1984 m .66419 .20215 L s .69007 .1984 m .69007 .20215 L s .71594 .1984 m .71594 .20215 L s .74182 .1984 m .74182 .20215 L s .79357 .1984 m .79357 .20215 L s .81944 .1984 m .81944 .20215 L s .84532 .1984 m .84532 .20215 L s .87119 .1984 m .87119 .20215 L s .09493 .1984 m .09493 .20215 L s .06905 .1984 m .06905 .20215 L s .04318 .1984 m .04318 .20215 L s .0173 .1984 m .0173 .20215 L s .92295 .1984 m .92295 .20215 L s .94882 .1984 m .94882 .20215 L s .9747 .1984 m .9747 .20215 L s .25 Mabswid 0 .1984 m 1 .1984 L s gsave 1.025 .1984 -61 -8.90625 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (x) show 69.000 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .50894 .04315 m .51519 .04315 L s [(-0.3)] .49644 .04315 1 0 Mshowa .50894 .0949 m .51519 .0949 L s [(-0.2)] .49644 .0949 1 0 Mshowa .50894 .14665 m .51519 .14665 L s [(-0.1)] .49644 .14665 1 0 Mshowa .50894 .25015 m .51519 .25015 L s [(0.1)] .49644 .25015 1 0 Mshowa .50894 .3019 m .51519 .3019 L s [(0.2)] .49644 .3019 1 0 Mshowa .50894 .35365 m .51519 .35365 L s [(0.3)] .49644 .35365 1 0 Mshowa .125 Mabswid .50894 .0535 m .51269 .0535 L s .50894 .06385 m .51269 .06385 L s .50894 .0742 m .51269 .0742 L s .50894 .08455 m .51269 .08455 L s .50894 .10525 m .51269 .10525 L s .50894 .1156 m .51269 .1156 L s .50894 .12595 m .51269 .12595 L s .50894 .1363 m .51269 .1363 L s .50894 .157 m .51269 .157 L s .50894 .16735 m .51269 .16735 L s .50894 .1777 m .51269 .1777 L s .50894 .18805 m .51269 .18805 L s .50894 .20875 m .51269 .20875 L s .50894 .2191 m .51269 .2191 L s .50894 .22945 m .51269 .22945 L s .50894 .2398 m .51269 .2398 L s .50894 .2605 m .51269 .2605 L s .50894 .27085 m .51269 .27085 L s .50894 .2812 m .51269 .2812 L s .50894 .29155 m .51269 .29155 L s .50894 .31225 m .51269 .31225 L s .50894 .3226 m .51269 .3226 L s .50894 .33295 m .51269 .33295 L s .50894 .3433 m .51269 .3433 L s .50894 .0328 m .51269 .0328 L s .50894 .02245 m .51269 .02245 L s .50894 .0121 m .51269 .0121 L s .50894 .00175 m .51269 .00175 L s .50894 .364 m .51269 .364 L s .50894 .37435 m .51269 .37435 L s .50894 .3847 m .51269 .3847 L s .50894 .39505 m .51269 .39505 L s .25 Mabswid .50894 0 m .50894 .3968 L s gsave .50894 .4218 -66.0312 -4 Mabsadd m 1 1 Mabs scale currentpoint translate /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding ISOLatin1Encoding def currentdict end newfontname exch definefont pop } def 0 17.8125 translate 1 -1 scale 63.000 11.250 moveto %%IncludeResource: font Courier %%IncludeFont: Courier %%BeginResource: font Courier-MISO %%BeginFont: Courier-MISO /Courier /Courier-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (y) show 69.062 11.250 moveto %%IncludeResource: font Courier-MISO %%IncludeFont: Courier-MISO /Courier-MISO findfont 10.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .5 Mabswid .45513 .1984 m .45513 .19873 L .45513 .19903 L .45513 .19937 L .45513 .1997 L .45512 .20028 L .45512 .20091 L .45511 .2016 L .45509 .20233 L .45506 .20364 L .45501 .20499 L .45496 .20625 L .4548 .20907 L .4546 .2119 L .45437 .21442 L .45372 .21982 L .453 .22411 L .45208 .2283 L .45109 .23171 L .44992 .23466 L .44931 .23584 L .44864 .2369 L .44799 .2377 L .44738 .23825 L .44708 .23845 L .44676 .23862 L .4466 .23869 L .44645 .23874 L .44632 .23878 L .44618 .23881 L .44609 .23882 L .44602 .23883 L .44593 .23884 L .44589 .23884 L .44585 .23885 L .44577 .23885 L .4457 .23885 L .44562 .23884 L .44554 .23883 L .4455 .23883 L .44545 .23882 L .44537 .23881 L .44521 .23877 L .44502 .23872 L .44485 .23865 L .44455 .2385 L .44424 .23829 L .44367 .2378 L .443 .23701 L .44241 .23611 L Mistroke .44132 .23387 L .44022 .23074 L .43929 .22714 L .43842 .22273 L .4377 .21769 L .43743 .21523 L .43719 .21255 L .437 .21001 L .43683 .20716 L .43678 .20589 L .43673 .20452 L .43669 .20332 L .43666 .20204 L .43665 .20134 L .43664 .20056 L .43663 .20022 L .43663 .19985 L .43663 .19951 L .43663 .19919 L .43663 .19901 L .43662 .19882 L .43662 .19847 L .43662 .19825 L .43662 .19805 L .43662 .19787 L .43663 .19768 L .43663 .19749 L .43663 .19728 L .43663 .19685 L .43663 .19646 L .43664 .19609 L .43665 .19536 L .43666 .19467 L .43669 .19338 L .43674 .192 L .4368 .1905 L .43693 .18794 L .43711 .18517 L .43763 .17977 L .43825 .17516 L .43907 .17065 L .43999 .16686 L .44109 .16352 L .44162 .16225 L .4422 .16107 L .44277 .16013 L .44331 .1594 L .44394 .15875 L .44428 .15848 L .44464 .15825 L Mistroke .44479 .15818 L .44496 .15811 L .4451 .15806 L .44525 .15802 L .44535 .158 L .44543 .15798 L .44552 .15797 L .44556 .15797 L .44561 .15796 L .44565 .15796 L .44569 .15796 L .44578 .15795 L .44585 .15796 L .44593 .15796 L .44601 .15797 L .44609 .15798 L .44617 .15799 L .44625 .15801 L .44654 .15809 L .44669 .15815 L .44685 .15823 L .44719 .15842 L .44779 .15891 L .44834 .15951 L .44895 .16035 L .44957 .16143 L .45063 .16381 L .45167 .16697 L .45254 .17044 L .45339 .17483 L .45402 .17923 L .45453 .18411 L .45476 .18698 L .45492 .18968 L .45498 .19096 L .45503 .19234 L .45507 .19354 L .4551 .19486 L .45511 .19566 L .45512 .19605 L .45512 .1964 L .45513 .19675 L .45513 .19712 L .45513 .19732 L .45513 .19751 L .45513 .19787 L .45513 .1982 L .45513 .19851 L .45513 .19885 L .45513 .19921 L Mistroke .45513 .1994 L .45513 .19959 L .45513 .19995 L .45512 .20063 L .45511 .20117 L .4551 .20175 L .45508 .2028 L .45504 .20404 L .455 .20518 L .45489 .20762 L .45475 .20991 L Mfstroke .22082 .1984 m .22082 .19928 L .22081 .20008 L .22079 .201 L .22076 .20188 L .22069 .20343 L .2206 .20511 L .22045 .20696 L .22027 .20892 L .21983 .21242 L .21926 .21601 L .2186 .21936 L .21667 .22688 L .21412 .23437 L .21127 .24102 L .20315 .25509 L .19431 .26609 L .18302 .2765 L .17095 .28463 L .16373 .28836 L .15694 .29122 L .1504 .29342 L .14334 .29525 L .1396 .29599 L .13547 .29664 L .13365 .29687 L .1317 .29708 L .13001 .29722 L .12816 .29735 L .12725 .2974 L .12627 .29744 L .12573 .29746 L .12524 .29748 L .12427 .2975 L .12343 .29751 L .12251 .29752 L .12156 .29752 L .12067 .2975 L .12016 .29749 L .11961 .29748 L .1186 .29745 L .11763 .2974 L .11673 .29736 L .11469 .29722 L .11253 .29702 L .10891 .29659 L .10555 .29606 L .09796 .29443 L .09062 .29223 L .08383 .28962 L Mistroke .07168 .28339 L .05975 .27493 L .04992 .26558 L .04055 .25365 L .03372 .2417 L .03074 .23489 L .02845 .22845 L .02646 .22122 L .02566 .21753 L .02495 .21345 L .02444 .20959 L .02424 .20768 L .02409 .20592 L .02398 .20432 L .0239 .20262 L .02386 .20174 L .02384 .20091 L .02382 .20001 L .02381 .19903 L .02381 .19805 L .02382 .19714 L .02382 .19662 L .02383 .19615 L .02386 .19509 L .0239 .19406 L .02396 .19295 L .02409 .19094 L .02425 .18908 L .02445 .18711 L .02492 .18358 L .0262 .1767 L .02811 .16943 L .03042 .16273 L .03293 .15677 L .03971 .14442 L .04899 .13224 L .05946 .12211 L .07209 .11317 L .07812 .10984 L .08488 .10674 L .09141 .10431 L .09763 .10246 L .1045 .10093 L .10817 .10032 L .11212 .09982 L .11411 .09963 L .11629 .09947 L .11728 .09942 L .11834 .09937 L .11924 .09933 L Mistroke .11975 .09932 L .12023 .09931 L .1212 .09929 L .12207 .09928 L .12302 .09929 L .12356 .09929 L .12405 .0993 L .12496 .09932 L .12579 .09934 L .12674 .09938 L .12763 .09942 L .1294 .09954 L .13105 .09967 L .1348 .10007 L .13843 .10061 L .1423 .10133 L .14922 .10303 L .15541 .10502 L .16831 .11072 L .1752 .11474 L .18126 .11896 L .19172 .12803 L .20167 .13964 L .2093 .15186 L .21279 .15919 L .21546 .16614 L .21757 .17315 L .21907 .17981 L .21973 .18367 L .22019 .18721 L .22039 .18917 L .22056 .1913 L .22063 .19228 L .22069 .19332 L .22073 .19428 L .22077 .19518 L .22079 .19608 L .22081 .19707 L .22082 .19794 L .22082 .19887 L .22081 .19978 L .22079 .20064 L .22077 .20141 L .22074 .20224 L .22065 .20416 L .22051 .20619 L .22016 .2098 L .21972 .21315 L .21921 .21626 L .21767 .22325 L Mistroke .21543 .23076 L .21277 .23766 L .20645 .24997 L .19784 .26206 L .18839 .27195 L .18685 .27331 L Mfstroke .62156 .1984 m .62157 .20042 L .6216 .20227 L .62165 .20439 L .62172 .2064 L .62188 .20997 L .62213 .21383 L .62249 .21809 L .62297 .22258 L .62406 .2306 L .62552 .23881 L .62718 .24643 L .63201 .2634 L .63839 .28007 L .64545 .29462 L .6551 .3106 L .66531 .32436 L .68652 .34621 L .699 .35606 L .71314 .36517 L .72746 .37253 L .74364 .37888 L .75126 .38122 L .75944 .38329 L .76719 .38485 L .77433 .38594 L .77797 .38638 L .78194 .38676 L .78376 .38691 L .7857 .38704 L .78752 .38714 L .78919 .38722 L .79108 .38728 L .79312 .38733 L .79492 .38735 L .79682 .38735 L .79891 .38733 L .80085 .38728 L .80197 .38725 L .80299 .38721 L .80527 .38709 L .80901 .38684 L .81246 .38654 L .82026 .38558 L .82712 .38443 L .83437 .38291 L .84919 .37874 L .86482 .37274 L .87919 .36564 L .89189 .35794 L Mistroke .91757 .33731 L .93062 .32342 L .94155 .30921 L .95176 .29286 L .9599 .27643 L .9659 .26093 L .96869 .25201 L .9709 .24356 L .97285 .23439 L .97424 .22596 L .97483 .22144 L .97535 .21651 L .97559 .2138 L .97577 .21129 L .97591 .2089 L .97603 .20634 L .97612 .20386 L .97617 .2016 L .97619 .19943 L .97619 .19715 L .97618 .19594 L .97616 .19464 L .9761 .19231 L .97605 .19089 L .97599 .18954 L .97586 .18703 L .9755 .18192 L .97504 .17723 L .9736 .1667 L .97198 .15804 L .9698 .14886 L .96478 .13266 L .95707 .11421 L .9485 .0983 L .92823 .07062 L .91494 .057 L .90165 .04583 L .87486 .02885 L .85875 .02152 L .85138 .0188 L .84324 .01622 L .83578 .01423 L .82775 .01249 L .8233 .01169 L .81925 .01108 L .81513 .01055 L .81133 .01016 L .80781 .00987 L .80408 .00965 L .80215 .00956 L Mistroke .80034 .00951 L .79836 .00946 L .79725 .00945 L .79623 .00945 L .79442 .00945 L .79274 .00948 L .79091 .00952 L .78895 .00959 L .78709 .00968 L .78533 .00979 L .78207 .01003 L .77829 .01039 L .77478 .0108 L .76686 .01201 L .75922 .01356 L .75114 .01562 L .73681 .02036 L .72417 .02581 L .69843 .04116 L .68508 .05186 L .67362 .06298 L .65477 .08669 L .64571 .1017 L .63842 .11665 L .63244 .1321 L .62752 .14897 L .62446 .16376 L .62321 .17226 L .62236 .18022 L .62201 .18473 L .62178 .18889 L .62169 .19107 L .62162 .19347 L .6216 .19468 L .62158 .19598 L .62157 .1972 L .62156 .19832 L .62158 .2005 L .62161 .20252 L .62166 .20474 L .6217 .20598 L .62175 .2071 L .62197 .21138 L .62226 .21541 L .62306 .22337 L .62407 .23064 L .62547 .23856 L .62728 .24683 L .63167 .26238 L .63769 .27844 L Mistroke .65176 .30546 L .66126 .31921 L .6728 .33294 L .68372 .34372 L .69667 .35436 L .70914 .36279 L .72326 .37055 L .73885 .37721 L .74665 .37985 L .754 .38196 L .76206 .38386 L .76945 .38523 L .77775 .38635 L .78233 .3868 L .7844 .38695 L .78667 .38709 L .78853 .38719 L .79052 .38726 L .79162 .3873 L .79263 .38732 L .7946 .38735 L .7964 .38735 L .79836 .38734 L .80021 .3873 L .80192 .38725 L .80389 .38716 L .80574 .38707 L .80996 .38676 L .81408 .38637 L .81851 .38583 L .82638 .38457 L .83368 .38307 L .85011 .37843 L .86582 .3723 L .88211 .36399 L .89598 .35513 L .91026 .34398 L .93358 .31984 L Mfstroke 0 0 m 1 0 L 1 .3968 L 0 .3968 L closepath clip newpath % End of Graphics MathPictureEnd %%PSTrailer end grestore %%EPS Trailer grestore grestore %%Trailer %%EOF %%EndDocument @endspecial 1131 2282 a(Orbits)k(at)g Fn(h)c Fo(=)g Fn(:)p Fo(3)k(with)h Fn(m)2004 2294 y Fk(1)2064 2282 y Fo(=)23 b(1)p Fn(:)p Fo(3)k(and)g Fn(m)2520 2294 y Fk(2)2580 2282 y Fo(=)c(1.)456 2434 y(4.3.)40 b Fs(Linear)25 b(stabilit)m(y)f(of)h(the)f(orbits.)41 b Fo(W)-7 b(e)21 b(ha)n(v)n(e)f(n)n(umerical)h(evidence)g(of)g(the)g(follo)n(wing:)456 2584 y Fs(Conjecture)33 b(4.9.)41 b Fe(A)n(l)t(l)31 b(p)l(erio)l(dic)i (orbits)f(in)f(obtaine)l(d)h(in)f(The)l(or)l(ems)g(4.1)i(and)e(4.5)h (ar)l(e)f(un-)456 2684 y(stable.)38 b(A)n(l)t(l)27 b(p)l(erio)l(dic)i (orbits)e(obtaine)l(d)h(in)f(The)l(or)l(ems)h(4.3,)h(4.4)f(and)f(4.8)h (ar)l(e)f(line)l(arly)h(stable.)555 2834 y Fo(Although)37 b(w)n(e)f(ha)n(v)n(e)f(a)h(meto)r(d)h(to)f(pro)n(v)n(e)f(the)i(ab)r(o)n (v)n(e)e(conjecture)h(b)n(y)g(computer)g(assis-)456 2934 y(tance,)d(it)f(is)g(not)g(really)g(practical)f(b)r(ecause)g(it)i(w)n (ould)f(require)f(a)g(v)n(ery)g(long)h(computation)456 3033 y(time.)51 b(Therefore)31 b(w)n(e)h(c)n(hose)g(to)g(pro)n(v)n(e)f (the)h(conjecture)g(only)g(for)g(a)g(small)g(in)n(terv)-5 b(al)32 b(of)g(the)456 3133 y(parameters)27 b Fn(m)960 3145 y Fk(1)1026 3133 y Fo(and)h Fn(h)p Fo(,)h(and)g(w)n(e)f(pro)n (vide)g(the)h(algorithm)e(for)h(the)i(v)n(eri\014cation)d(of)i(further) 456 3233 y(in)n(terv)-5 b(als.)456 3383 y Fs(Theorem)27 b(4.10.)37 b Fe(L)l(et)26 b Fn(m)1305 3395 y Fk(2)1365 3383 y Fo(=)d(1)p Fe(.)37 b(F)-6 b(or)27 b(al)t(l)g Fn(m)1897 3395 y Fk(1)1957 3383 y Fl(2)d Fo(1)12 b Fl(\006)g Fo(10)2251 3353 y Ff(\000)p Fk(5)2364 3383 y Fe(and)27 b(for)g(al)t(l)h Fn(h)23 b Fl(2)g Fn(:)p Fo(3)12 b Fl(\006)g Fo(10)3154 3353 y Ff(\000)p Fk(5)3267 3383 y Fe(ther)l(e)456 3483 y(exists)36 b(one)h(and)h(only)f(one)g(p)l(erio)l(dic)i(orbit)f(of)f(1) h(cr)l(ossing)f(the)g(the)g Fn(x)p Fl(\000)p Fe(axis)g(with)h(p)l (ositive)456 3582 y Fn(y)s Fe(-velo)l(city)30 b(in)g(the)g(interval)g Fn(:)p Fo(0487323)15 b Fl(\006)j Fo(10)1869 3552 y Ff(\000)p Fk(4)1987 3582 y Fe(and)30 b(such)g(orbit)h(is)f(unstable.)456 3732 y Fs(Remark)42 b(4.1.)k Fe(The)39 b(uniqueness)f(r)l(esult,)i(to)l (gether)f(with)g(the)f(estimate)h(on)f(the)g(lo)l(c)l(ation)456 3832 y(of)c(the)f(orbit,)i(imply)g(that)e(this)h(is)f(the)h(orbit)f (obtaine)l(d)i(in)e(The)l(or)l(ems)h(4.1)h(and)f(4.5)g(for)g(the)456 3932 y(c)l(ommon)c(values)g(of)g(the)g(p)l(ar)l(ameters,)h(ther)l(efor) l(e)g(the)f(orbit)g(is)g(r)l(etr)l(o)l(gr)l(ade)g(ar)l(ound)g Fn(L)3212 3944 y Fk(1)3249 3932 y Fe(.)456 4082 y Fs(Theorem)d(4.11.)37 b Fe(L)l(et)26 b Fn(m)1305 4094 y Fk(2)1365 4082 y Fo(=)d(1)p Fe(.)37 b(F)-6 b(or)27 b(al)t(l)g Fn(m)1897 4094 y Fk(1)1957 4082 y Fl(2)d Fo(1)12 b Fl(\006)g Fo(10)2251 4052 y Ff(\000)p Fk(6)2364 4082 y Fe(and)27 b(for)g(al)t(l)h Fn(h)23 b Fl(2)g Fn(:)p Fo(3)12 b Fl(\006)g Fo(10)3154 4052 y Ff(\000)p Fk(6)3267 4082 y Fe(ther)l(e)456 4181 y(exists)36 b(one)h(and)h(only)f (one)g(p)l(erio)l(dic)i(orbit)f(of)f(1)h(cr)l(ossing)f(the)g(the)g Fn(x)p Fl(\000)p Fe(axis)g(with)h(p)l(ositive)456 4281 y Fn(y)s Fe(-velo)l(city)33 b(in)g(e)l(ach)g(of)g(the)g(intervals)39 b Fo(^)-48 b Fn(x)1752 4293 y Fm(S)1793 4301 y Fi(1)1830 4281 y Fo(\()p Fn(:)p Fo(3\))21 b Fl(\006)f Fo(10)2149 4251 y Ff(\000)p Fk(3)2270 4281 y Fe(and)38 b Fo(^)-47 b Fn(x)2481 4293 y Fm(S)2522 4301 y Fi(2)2558 4281 y Fo(\()p Fn(:)p Fo(3\))21 b Fl(\006)f Fo(10)2877 4251 y Ff(\000)p Fk(3)2965 4281 y Fe(.)47 b(Such)33 b(orbits)456 4381 y(ar)l(e)d(line)l(arly)h(stable.)456 4531 y Fs(Remark)c(4.2.)37 b Fe(As)26 b(b)l(efor)l(e,)i(the)e(orbits)h(obtaine)l(d)h(in)e(The)l (or)l(em)h(4.11)h(have)g(to)e(c)l(oincide)i(with)456 4631 y(the)i(orbits)g(obtaine)l(d)h(in)f(The)l(or)l(ems)g(4.3,)i(4.4,)f (4.8.)1659 4804 y Fo(5.)41 b Fr(The)32 b(pr)n(oofs)456 4953 y Fo(5.1.)40 b Fs(The)i(tec)m(hnique.)f Fo(The)36 b(pro)r(ofs)f(of)g(existence)h(of)f(p)r(erio)r(dic)h(solutions)f(are)g (obtained)456 5053 y(b)n(y)29 b(a)h(com)n(bination)f(of)h(the)h(metho)r (d)f(of)g(rev)n(ersing)e(symmetries,)i(see)g([La1)o(,)g(La2)o(,)g(LQ],) h(and)456 5152 y(rigorous)24 b(computations;)i(w)n(e)h(summarize)f (here)g(the)h(pro)r(cedure,)f(see)g([A)q(])h(for)f(details.)36 b(Con-)456 5252 y(sider)f(at)g(\014rst)h(a)f(\014xed)h(v)-5 b(alue)35 b(for)g Fn(h)h Fo(and)f Fn(m)1921 5264 y Fk(1)1959 5252 y Fo(.)61 b(Let)36 b Fn(f)9 b Fo(\()p Fn(x)p Fo(\))36 b(b)r(e)g(the)g(second)f(comp)r(onen)n(t)h(of)456 5352 y Fn(H)525 5364 y Fk(1)562 5352 y Fo(\()p Fn(x;)14 b Fo(0\).)56 b(According)33 b(to)h(the)g(results)g(in)g(Section)g(2,)h(w) n(e)e(ha)n(v)n(e)g(to)h(lo)r(ok)f(for)h(zeros)e(of)i(the)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 456 315 a Fk(10)1175 b(GIANNI)23 b(ARIOLI)456 515 y Fo(function)k Fn(f)9 b Fo(,)26 b(therefore)g(w)n(e)g (\014rst)h(lo)r(ok)f(for)g(an)g(appro)n(ximate)f(zero,)h(call)g(it)32 b(\026)-47 b Fn(x)q Fo(.)36 b(W)-7 b(e)27 b(c)n(ho)r(ose)f Fn(x)3407 527 y Fk(1)456 614 y Fo(and)31 b Fn(x)668 626 y Fk(2)737 614 y Fo(suc)n(h)h(that)f Fn(x)1159 626 y Fk(1)1227 614 y Fn(<)j Fo(\026)-47 b Fn(x)30 b(<)g(x)1540 626 y Fk(2)1609 614 y Fo(and)h(b)r(oth)h Fn(x)2021 626 y Fk(1)2091 614 y Fo(and)f Fn(x)2303 626 y Fk(2)2372 614 y Fo(are)g(v)n(ery)f(close)h(to)37 b(\026)-47 b Fn(x)p Fo(.)49 b(Then)32 b(w)n(e)456 714 y(compute)g(the)h(rigorous)d(half)j (P)n(oincar)n(\023)-39 b(e)29 b(map)j Fn(H)2041 726 y Fk(1)2111 714 y Fo(at)g(\()p Fn(x)2296 726 y Fk(1)2334 714 y Fn(;)14 b Fo(0\))32 b(and)h(\()p Fn(x)2723 726 y Fk(2)2761 714 y Fn(;)14 b Fo(0\).)51 b(When)33 b(w)n(e)f(can)456 814 y(pro)n(v)n(e)22 b(that)i(the)h(second)e(comp)r(onen)n(t)h(of)g Fn(H)1837 826 y Fk(1)1874 814 y Fo(\()p Fn(x)1953 826 y Fk(1)1991 814 y Fn(;)14 b Fo(0\))24 b(has)g(opp)r(osite)f(sign)h (with)g(resp)r(ect)g(to)g(the)456 913 y(second)30 b(comp)r(onen)n(t)g Fn(H)1223 925 y Fk(1)1261 913 y Fo(\()p Fn(x)1340 925 y Fk(2)1378 913 y Fn(;)14 b Fo(0\))30 b(and)h(that)g(the)g(segmen)n(t)f (joining)h(the)g(t)n(w)n(o)f(p)r(oin)n(ts)h(b)r(elongs)456 1013 y(en)n(tirely)e(to)h(the)g(domain)g(of)g Fn(H)1471 1025 y Fk(1)1508 1013 y Fo(,)h(then)g(b)n(y)e(the)i(con)n(tin)n(uit)n (y)e(of)h(the)h(half)f(P)n(oincar)n(\023)-39 b(e)27 b(map)j(w)n(e)456 1112 y(ha)n(v)n(e)e(a)h(pro)r(of)f(that)i(there)f(exists)g(at)g(least)g (a)g(p)r(oin)n(t)g Fn(x)2200 1124 y Fk(1)2264 1112 y Fn(<)i Fo(~)-48 b Fn(x)27 b(<)e(x)2565 1124 y Fk(2)2632 1112 y Fo(suc)n(h)k(that)h Fn(H)3072 1124 y Fk(1)3109 1112 y Fo(\()5 b(~)-47 b Fn(x)q(;)14 b Fo(0\))29 b(lies)456 1212 y(on)22 b(the)i Fn(x)g Fo(axis.)34 b(F)-7 b(urthermore,)23 b(w)n(e)g(can)g(pro)n(v)n(e)e(the)j(uniqueness)f(of)g(the)g(orbit)g(in) h(the)f(in)n(terv)-5 b(al)456 1312 y([)p Fn(x)526 1324 y Fk(1)563 1312 y Fn(;)14 b(x)647 1324 y Fk(2)685 1312 y Fo(])28 b(b)n(y)f(sho)n(wing)f(that)i(for)f(all)h Fn(x)23 b Fl(2)g Fo([)p Fn(x)1808 1324 y Fk(1)1846 1312 y Fn(;)14 b(x)1930 1324 y Fk(2)1968 1312 y Fo(])28 b(the)g(deriv)-5 b(ativ)n(e)26 b(of)i(the)g(second)f(comp)r(onen)n(t)456 1411 y(of)i(the)h(map)f Fn(x)e Fl(7!)f Fn(H)1135 1423 y Fk(1)1173 1411 y Fo(\()p Fn(x;)14 b Fo(0\))30 b(do)r(es)f(not)g(c)n (hange)g(sign.)42 b(Note)30 b(that)f(the)h(computation)g(of)f(the)456 1511 y(deriv)-5 b(ativ)n(es)26 b(of)i(the)g(half-P)n(oincar)n(\023)-39 b(e)24 b(map)j(w)n(as)g(not)g(necessary)f(in)i([A].)555 1611 y(In)i(order)e(to)h(obtain)g(the)g(pro)r(of)g(with)h(the)g (parameters)d Fn(m)2446 1623 y Fk(1)2513 1611 y Fo(and/or)g Fn(h)i Fo(v)-5 b(arying)29 b(in)g(some)456 1710 y(range,)21 b(w)n(e)f(giv)n(e)h(to)g(suc)n(h)f(parameters)g(some)g(in)n(terv)-5 b(al)21 b(v)-5 b(alues.)34 b(More)21 b(precisely)-7 b(,)21 b(w)n(e)g(partition)456 1810 y(the)35 b(in)n(terv)-5 b(al)35 b Fn(I)950 1822 y Fm(h)1029 1810 y Fo(\(resp.)59 b Fn(I)1328 1822 y Fm(m)1392 1810 y Fo(\))35 b(in)h(a)f(certain)f(n)n (um)n(b)r(er)h(of)h(subin)n(terv)-5 b(als)34 b(of)h(equal)g(size)g (\(the)456 1910 y(actual)26 b(n)n(um)n(b)r(er)h(v)-5 b(aries)26 b(from)g(10)1518 1879 y Fk(3)1582 1910 y Fo(for)g(the)i(pro) r(of)e(of)h(Theorem)f(4.1)g(to)h(10)2829 1879 y Fk(7)2892 1910 y Fo(for)g(the)g(pro)r(of)g(of)456 2009 y(Theorem)i(4.8\).)44 b(Then)31 b(w)n(e)f(solv)n(e)f(the)h(di\013eren)n(tial)g(equation)g (with)h(the)f(Lohner)g(algorithm)456 2109 y(\(see)i(b)r(elo)n(w\))g (with)h(the)g(parameters)e Fn(h)h Fo(or)g Fn(m)1936 2121 y Fk(1)2006 2109 y Fo(ha)n(ving)f(an)h(in)n(terv)-5 b(al)32 b(v)-5 b(alue)32 b(and)h(w)n(e)f(rep)r(eat)456 2208 y(the)c(pro)r (cedure)e(for)h(all)h(subin)n(terv)-5 b(als.)555 2308 y(More)37 b(precisely)-7 b(,)40 b(consider)e(Theorem)f(4.1,)j(the)e (pro)r(of)g(of)g(the)g(other)g(theorems)f(b)r(eing)456 2408 y(similar.)42 b(Set)31 b Fn(I)949 2420 y Fm(h)1019 2408 y Fo(=)26 b Fl([)1165 2378 y Fk(3999)1165 2429 y Fm(i)p Fk(=50)1310 2408 y Fn(I)1353 2378 y Fm(i)1346 2431 y(h)1390 2408 y Fo(,)k(where)g Fn(I)1729 2378 y Fm(i)1722 2431 y(h)1792 2408 y Fo(=)c([)p Fn(:)p Fo(0002)p Fn(i;)14 b(:)p Fo(0002\()p Fn(i)i Fo(+)k(1\)].)43 b(F)-7 b(or)29 b(all)h Fn(i)f Fo(w)n(e)h(c)n(hec)n(k)f(b)n(y)456 2507 y(the)21 b(n)n(umerical)g(rigorous)e(pro)r(cedure)i(describ)r(ed)g (b)r(elo)n(w)g(that)h(the)g(second)e(comp)r(onen)n(t)i(of)f(the)456 2607 y(half)29 b(P)n(oincar)n(\023)-39 b(e)25 b(map)k(at)g(\()5 b(^)-47 b Fn(x)1330 2619 y Fm(L)1381 2607 y Fo(\()p Fn(:)p Fo(0002)p Fn(i)p Fo(\))17 b Fl(\000)i Fn(\016)o(;)14 b Fo(0\))28 b(is)h(negativ)n(e)f(and)h(and)f(at)h(\()5 b(^)-47 b Fn(x)2862 2619 y Fm(L)2913 2607 y Fo(\()p Fn(:)p Fo(0002)p Fn(i)p Fo(\))17 b(+)i Fn(\016)o(;)14 b Fo(0\))456 2707 y(is)36 b(p)r(ositiv)n(e)h(for)f(all)g Fn(h)i Fl(2)h Fn(I)1348 2676 y Fm(i)1341 2730 y(h)1385 2707 y Fo(.)64 b(Then)37 b(w)n(e)f(partition)h(the)g(segmen)n(t)f(\()5 b(^)-47 b Fn(x)2746 2719 y Fm(L)2796 2707 y Fo(\()p Fn(:)p Fo(0002)p Fn(i)p Fo(\))23 b Fl(\006)h Fn(\016)o(;)14 b Fo(0\))36 b(in)456 2806 y(10)d(subin)n(terv)-5 b(al,)35 b(and)f(w)n(e)f(c)n(hec)n(k)g(that)i(the)f(deriv)-5 b(ativ)n(e)33 b(with)i(resp)r(ect)e(to)h Fn(x)h Fo(of)f(the)g(second)456 2906 y(comp)r(onen)n(t)29 b(of)g(the)h(half)f(P)n(oincar)n(\023)-39 b(e)26 b(map)k(is)f(strictly)g(p)r(ositiv)n(e)g(in)h(eac)n(h)e(subin)n (terv)-5 b(al,)30 b(whic)n(h)456 3005 y(yields)f(the)h(result)f(of)g (existence)g(and)h(uniqueness)f(of)g(a)g(\014xed)h(p)r(oin)n(t)f(for)g (the)h(half)g(P)n(oincar)n(\023)-39 b(e)456 3105 y(map)30 b(in)i Fn(I)787 3075 y Fm(i)780 3129 y(h)823 3105 y Fo(.)47 b(The)31 b(existence)f(of)h(a)g(con)n(tin)n(uous)f(function)h Fn(x)2388 3117 y Fm(L)2469 3105 y Fo(satisfying)f(the)i(statemen)n(t)f (of)456 3205 y(the)k(theorem)g(follo)n(ws)f(b)n(y)h(the)g(con)n(tin)n (uit)n(y)g(of)g(the)h(half)f(p)r(oincar)n(\023)-39 b(e)33 b(map)i(and)g(the)h(implicit)456 3304 y(function)28 b(theorem.)555 3404 y(T)-7 b(o)27 b(pro)n(v)n(e)f(Theorems)h(4.10)f(and)i(4.11)e(w)n (e)h(compute)h(the)g(gradien)n(t)1134 3632 y Fn(D)r Fo(\()p Fn(x;)14 b(p)1363 3644 y Fm(x)1405 3632 y Fo(\))24 b(=)1548 3490 y Fj( )1665 3536 y Fm(@)t(H)1758 3544 y Fi(1)1791 3536 y Fk(\()p Fm(x;p)1909 3544 y Fh(x)1946 3536 y Fk(\))p 1665 3557 307 4 v 1780 3605 a Fm(@)t(x)1665 3650 y(@)t(H)1758 3658 y Fi(1)1791 3650 y Fk(\()p Fm(x;p)1909 3658 y Fh(x)1946 3650 y Fk(\))p 1665 3671 V 1763 3719 a Fm(@)t(p)1836 3727 y Fh(x)2023 3490 y Fj(!)2112 3632 y Fo(=)2200 3515 y Fj(\022)2302 3581 y Fn(D)2371 3593 y Fk(11)2524 3581 y Fn(D)2593 3593 y Fk(12)2302 3681 y Fn(D)2371 3693 y Fk(21)2524 3681 y Fn(D)2593 3693 y Fk(22)2705 3515 y Fj(\023)456 3860 y Fo(of)g(the)h(half)g(P)n(oincar)n(\023)-39 b(e)21 b(map)k(with)g(b)r(oth)g(the)g(energy)e(and)h Fn(m)2379 3872 y Fk(1)2441 3860 y Fo(taking)g(in)n(terv)-5 b(al)24 b(v)-5 b(alues)24 b(in)h(the)456 3960 y(region)k(where)i(the)g (\014xed)g(p)r(oin)n(t)g(has)g(b)r(een)g(pro)n(v)n(ed)f(to)h(exist.)47 b(It)31 b(is)g(easy)f(to)h(c)n(hec)n(k)f(that,)i(if)456 4059 y(\()p Fn(D)557 4071 y Fk(11)638 4059 y Fo(+)11 b Fn(D)783 4071 y Fk(22)852 4059 y Fo(\))884 4029 y Fk(2)933 4059 y Fl(\000)g Fo(4)p Fn(D)1120 4071 y Fk(11)1188 4059 y Fn(D)1257 4071 y Fk(22)1338 4059 y Fo(+)g(4)p Fn(D)1525 4071 y Fk(12)1594 4059 y Fn(D)1663 4071 y Fk(21)1756 4059 y Fn(>)23 b Fo(0,)h(then)h(the)f(eigen)n(v)-5 b(alues)22 b Fn(\025)2731 4071 y Fk(1)2769 4059 y Fn(;)14 b(\025)2854 4071 y Fk(2)2915 4059 y Fo(of)24 b Fn(D)r Fo(\()p Fn(x;)14 b(p)3235 4071 y Fm(x)3277 4059 y Fo(\))24 b(are)456 4159 y(real)f(and)g(satisfy)h Fl(j)p Fn(\025)1098 4171 y Fk(1)1136 4159 y Fl(j)f Fn(<)f Fo(1)i(and)g Fl(j)p Fn(\025)1564 4171 y Fk(2)1601 4159 y Fl(j)f Fn(>)g Fo(1)h(\(recall)f(that)h Fn(\025)2275 4171 y Fk(1)2313 4159 y Fn(\025)2361 4171 y Fk(2)2421 4159 y Fo(=)f(1\),)i(in)f(whic)n(h)g(case)f(the)h(orbit)456 4259 y(is)j(unstable,)g(while)h(if)g(\()p Fn(D)1288 4271 y Fk(11)1376 4259 y Fo(+)18 b Fn(D)1528 4271 y Fk(22)1598 4259 y Fo(\))1630 4228 y Fk(2)1686 4259 y Fl(\000)f Fo(4)p Fn(D)1879 4271 y Fk(11)1949 4259 y Fn(D)2018 4271 y Fk(22)2106 4259 y Fo(+)h(4)p Fn(D)2300 4271 y Fk(12)2369 4259 y Fn(D)2438 4271 y Fk(21)2531 4259 y Fn(<)23 b Fo(0,)k(then)h(the)g (eigen)n(v)-5 b(alues)456 4358 y(are)26 b(complex)h(conjugate)g(of)h (mo)r(dulus)g(1)f(and)g(the)h(orbit)f(is)h(linearly)f(stable.)456 4555 y(5.2.)40 b Fs(Computational)31 b(details.)40 b Fo(W)-7 b(e)28 b(describ)r(e)g(here)f(brie\015y)g(the)h(algorithm)f (used)g(in)h(the)456 4654 y(computer)k(assisted)f(pro)r(ofs.)51 b(Consider)32 b(\014rst)g(the)h(existence)f(result.)52 b(Since)32 b(no)h(analytical)456 4754 y(solution)28 b(of)g(equation)g (1)g(is)h(a)n(v)-5 b(ailable,)28 b(all)g(w)n(e)g(can)g(do)h(in)g(order) e(to)h(pro)n(v)n(e)f(that)i(the)g(second)456 4854 y(comp)r(onen)n(t)35 b(of)g Fn(H)1059 4866 y Fk(1)1097 4854 y Fo(\()p Fn(x;)14 b Fo(0\))36 b(is)f(p)r(ositiv)n(e)g(or)g(negativ)n(e)f(is)h(to)h (estimate)f(the)h(tra)5 b(jectories)34 b(and)456 4953 y(compute)26 b(the)h(in)n(tersections)e(with)i(the)g(P)n(oincar)n(\023) -39 b(e)24 b(plane)i(with)h(rigorous)d(error)g(b)r(ounds.)37 b(W)-7 b(e)456 5053 y(use)23 b(the)g(Lohner)g(algorithm)f(with)h(in)n (terv)-5 b(al)23 b(arithmetics.)35 b(W)-7 b(e)23 b(start)g(with)h(a)f (T)-7 b(a)n(ylor)21 b(metho)r(d)456 5152 y(of)31 b(order)e(25,)i(i.e.) 48 b(w)n(e)31 b(estimate)g(the)g(tra)5 b(jectory)29 b(of)i(an)g(in)n (terv)-5 b(al)31 b(b)n(y)g(using)f(the)i(T)-7 b(a)n(ylor)29 b(ex-)456 5252 y(pansion)i(of)h(order)f(25)g(and)h(w)n(e)g(estimate)g (the)g(error)e(b)n(y)i(the)g(Lagrange)e(remainder.)49 b(More)456 5352 y(precisely)-7 b(,)35 b(if)g Fn(\034)45 b Fo(is)34 b(the)h(time)g(step,)i(w)n(e)d(compute)g(a)h(rough)e(but)i (rigorous)d(enclosure)i Fn(D)j Fo(of)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 1381 315 a Fk(BRANCHES)29 b(OF)g(PERIODIC)g (ORBITS)859 b(11)456 515 y Fo(the)26 b(tra)5 b(jectory)24 b(at)i(times)g([0)p Fn(;)14 b(\034)9 b Fo(],)26 b(that)h(is)e(an)h(in)n (terv)-5 b(al)25 b(set)h Fn(D)i Fo(suc)n(h)e(that)g(the)g(solution)f (of)h(the)456 614 y(equation)e(lies)h(in)h Fn(D)h Fo(for)e(all)g(times) g(b)r(et)n(w)n(een)h(0)f(and)g Fn(\034)9 b Fo(,)26 b(and)f(b)n(y)g (Lagrange)e(theorem)i(w)n(e)g(esti-)456 714 y(mate)g(the)h(error)d(w)n (e)i(mak)n(e)f(neglecting)h(the)h(remaining)e(terms)h(of)g(the)h(T)-7 b(a)n(ylor)23 b(expansion)i(b)n(y)456 823 y(computing)j Fn(x)914 793 y Fk(\(26\))1036 823 y Fo(\()p Fn(D)r Fo(\))1181 790 y Fm(\034)1219 765 y Fi(26)p 1182 804 98 4 v 1189 852 a Fk(26!)1290 823 y Fo(,)h(where)e Fn(x)1629 793 y Fk(\(26\))1752 823 y Fo(\()p Fn(D)r Fo(\))i(\(whic)n(h)g(is)f(an)g (in)n(terv)-5 b(al)27 b(enclosing)h(all)g(p)r(ossible)456 923 y(v)-5 b(alues)24 b(assumed)h(b)n(y)g(the)g(26th)g(deriv)-5 b(ativ)n(e)24 b(of)h(the)h(tra)5 b(jectory)-7 b(,)24 b(therefore)g(enclosing)g(the)h(La-)456 1022 y(grange)e(remainder\))h (is)h(computed)h(using)f(a)f(recursiv)n(e)g(algorithm)g(for)g(the)i (time)g(deriv)-5 b(ativ)n(es)456 1122 y(of)27 b(the)h(solutions.)555 1221 y(The)k(computation)g(of)g(the)h(v)-5 b(ariational)30 b(equation)i(are)f(obtained)h(similarly)-7 b(,)32 b(see)g([Z])g(for)456 1321 y(details.)555 1421 y(The)44 b(round-o\013)g(errors)e(are)h(tak)n (en)g(care)h(directly)f(b)n(y)h(suitable)g(C++)g(libraries)f(\(see)456 1520 y([CAPD]\))22 b(and)g(b)n(y)g(Mathematica.)34 b(Suc)n(h)23 b(errors)c(ma)n(y)j(v)-5 b(ary)21 b(b)n(y)h(c)n(hanging)e(computer)i (and/or)456 1620 y(op)r(erating)d(system,)i(but)g(since)f(all)h(pro)r (ofs)e(go)g(through)h(with)h(a)f(relativ)n(ely)f(large)g(margin)g(with) 456 1720 y(resp)r(ect)31 b(to)h(the)g(round-o\013)f(errors,)f(w)n(e)h (exp)r(ect)h(that)g(all)g(the)g(pro)r(ofs)f(can)g(b)r(e)h(easily)f (repro-)456 1819 y(duced)c(on)h(an)n(y)f(recen)n(t)g(computer.)555 1919 y(T)-7 b(o)23 b(p)r(erform)g(the)h(pro)r(ofs)f(the)h(author)e (implemen)n(ted)i(a)g(v)n(ersion)d(of)j(the)g(whole)f(algorithms)456 2018 y(in)30 b(a)g(com)n(bination)f(of)h(Mathematica)g(and)f(C++)h (under)g(the)g(Lin)n(ux)g(O.S.)g(More)f(precisely)-7 b(,)456 2118 y(Mathematica)25 b(has)h(b)r(een)h(only)f(used)g(to)g (handle)g(all)g(the)h(data)f(and)g(to)g(p)r(erform)g(a)g(few)g(algo-) 456 2218 y(rithms)d(whic)n(h)g(are)f(less)g(demanding)h(for)g(the)g (CPU,)g(but)h(more)e(complicated)h(to)g(implemen)n(t.)456 2317 y(F)-7 b(urthermore)29 b(Mathematica)h(has)g(b)r(een)h(used)f(to)g (mak)n(e)g(all)g(n)n(umerical)f(exp)r(erimen)n(ts)i(used)456 2417 y(to)23 b(compute)g(the)h(appro)n(ximate)e(branc)n(hes)g(and)h(to) g(dra)n(w)f(the)i(pictures.)35 b(On)23 b(the)h(other)f(hand)456 2517 y(C++)d(has)h(b)r(een)g(used)g(for)g(the)g(hea)n(vy)f(in)n(terv)-5 b(al)21 b(arithmetic)g(computations,)h(where)e(it)i(o\013ered)456 2616 y(a)33 b(m)n(uc)n(h)h(b)r(etter)h(sp)r(eed.)57 b(The)34 b(connection)g(b)r(et)n(w)n(een)g(the)h(t)n(w)n(o)e(languages)g(is)h (obtained)g(b)n(y)456 2716 y(MathLink.)41 b(W)-7 b(e)29 b(wish)g(to)g(p)r(oin)n(t)g(out)g(that)h(the)f(full)h(pro)r(of)e(to)r (ok)h(almost)f(a)h(mon)n(th)g(of)g(CPU)456 2815 y(time)24 b(on)g(a)g(mac)n(hine)f(equipp)r(ed)i(with)g(a)f(1.5GHz)f(P)n(en)n (tium)h(IV)g(pro)r(cessor.)34 b(The)24 b(reader)f(who)456 2915 y(desires)g(to)i(repro)r(duce)e(the)i(computer)f(assisted)g(pro)r (ofs)f(in)i(this)g(pap)r(er)f(without)h(writing)f(the)456 3015 y(program)32 b(can)h(do)n(wnload)g(the)i(Mathematica)e(noteb)r(o)r (ok)h(and)g(the)g(C++)g(sources)e(for)i(the)456 3114 y(full)26 b(program)f(from)g(h)n(ttp://www1.mate.p)r (olimi.it/~gianni/r3b.tar.Z.)e(The)j(noteb)r(o)r(ok)g(is)456 3214 y(pro)n(vided)g(with)i(commen)n(ts)f(and)h(instructions.)1708 3475 y Fr(References)456 3608 y Fq([A])187 b(G.)26 b(Arioli,)f Fg(Perio)l(dic)k(orbits,)g(symb)l(olic)f(dynamics)h(and)g(top)l(olo)l (gic)l(al)i(entr)l(opy)e(for)f(the)g(r)l(estricte)l(d)736 3691 y(3-b)l(o)l(dy)e(pr)l(oblem)p Fq(,)f(Comm.)e(Math.)g(Ph)n(ys.)h (231)g(\(2002\))i(1-24)456 3774 y([A)n(GT])83 b(G.)28 b(Arioli,)f(F.)h(Gazzola,)j(S.)d(T)-6 b(erracini,)28 b Fg(Minimization)j(pr)l(op)l(erties)g(of)f(Hil)t(l's)g(orbits)g(and)g (appli-)736 3857 y(c)l(ations)d(to)f(some)g(N-b)l(o)l(dy)h(pr)l(oblems) p Fq(,)e(Ann.)f(Inst.)h(Henri)e(P)n(oincar)n(\023)-33 b(e,)25 b(Analyse)f(non)h(lin)n(\023)-33 b(eaire)24 b(17,)g(5)736 3940 y(\(2000\))h(617-650)456 4023 y([AZ])144 b(G.)26 b(Arioli,)f(P)-6 b(.)26 b(Zgliczy)r(\023)-37 b(nski,)27 b Fg(Symb)l(olic)i(dynamics)f(for)h(the)f(H)n(\023)-35 b(enon-Heiles)28 b(Hamiltonian)i(on)e(the)736 4106 y(critic)l(al)d (level)p Fq(,)e(J.)h(Di\013.)e(Eq.)i(171)g(\(2001\))i(173-202)456 4189 y([AZ2])109 b(G.)25 b(Arioli,)e(P)-6 b(.)25 b(Zgliczynski,)g Fg(Perio)l(dic,)j(homo)l(clinic)g(and)g(heter)l(o)l(clinic)g(orbits)e (for)i(H)n(\023)-35 b(enon)28 b(Heiles)736 4272 y(Hamiltonian)f(ne)l (ar)f(the)f(critic)l(al)h(ener)l(gy)f(level)p Fq(,)e(preprin)n(t)456 4355 y([CAPD])34 b(Computer)73 b(Assisted)g(Pro)r(ofs)f(in)h(Dynamics,) 85 b(a)73 b(pac)n(k)l(age)i(for)d(rigorous)g(n)n(umerics,)736 4438 y(h)n(ttp://lim)n(ba.ii.uj.edu.pl/~cap)r(d/)456 4521 y([GH])132 b(J.)27 b(Guc)n(k)n(enheimer,)i(P)-6 b(.)26 b(Holmes)h Fg(Nonline)l(ar)j(Oscil)t(lations,)f(Dynamic)l(al)h (Systems,)f(and)h(Bifur)l(c)l(a-)736 4605 y(tions)c(of)f(V)-5 b(e)l(ctor)25 b(Fields)56 b Fq(Springer-V)-6 b(erlag,)22 b(19??)456 4688 y([La1])126 b(J.S.W.)26 b(Lam)n(b,)i Fg(R)l(eversing)h(symmetries)f(in)h(dynamic)l(al)h(systems)p Fq(,)d(J.)g(Ph)n(ys.)g(A:Math.)g(Gen.)g(25,)736 4771 y(925{937)e(,)e(1992)456 4854 y([La2])126 b(J.S.W.)32 b(Lam)n(b,)k Fg(R)l(eversing)e(symmetries)g(in)g(dynamic)l(al)i (systems)p Fq(,)f(PhD)e(Thesis,)h(Amsterdam)736 4937 y(Univ)n(ersit)n(y)-6 b(,)23 b(1994)456 5020 y([LQ])141 b(J.S.W.)22 b(Lam)n(b)i(and)f(G.R.)f(Quisp)r(el,)h Fg(R)l(eversing)h (k-symmetries)g(in)h(dynamic)l(al)h(systems)p Fq(,)d(Ph)n(ysica)736 5103 y(D)g(73,)h(277{304,)h(1994)456 5186 y([L])196 b(R.J.)21 b(Lohner,)46 b Fg(Computation)26 b(of)e(Guar)l(ante)l(e)l(d)i(Enclosur) l(es)f(for)f(the)g(Solutions)h(of)f(Or)l(dinary)h(Ini-)736 5269 y(tial)f(and)i(Boundary)g(V)-5 b(alue)24 b(Pr)l(oblems)5 b Fq(,)24 b(in:)30 b(Computational)24 b(Ordinary)e(Di\013eren)n(tial)h (Equations,)736 5352 y(J.R.)g(Cash,)g(I.)h(Gladw)n(ell)f(Eds.,)g (Clarendon)h(Press,)f(Oxford,)g(1992.)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 456 315 a Fk(12)1175 b(GIANNI)23 b(ARIOLI)456 515 y Fq([MH])122 b(Mey)n(er)18 b(K.R.,)g(Hall)g(G.R.,)h (In)n(tro)r(duction)i(to)e(Hamiltonian)f(Dynamical)h(Systems)g(and)h (the)f(N-b)r(o)r(dy)736 598 y(problem,)k(Springer)g(V)-6 b(erlag,)23 b(1991)456 681 y([M])175 b(J.)31 b(Moser,)j(Stable)e(and)h (random)f(motions)g(in)g(Dynamical)g(Systems,)i(Princeton)f(Univ.)e (Press,)736 764 y(1973)456 847 y([SM])136 b(C.L.)23 b(Siegel,)g(J.K.)g (Moser,)g(Lectures)h(on)g(celestial)g(mec)n(hanics,)g(Springer)g(V)-6 b(erlag,)23 b(1971)456 930 y([MZ])132 b(M.)29 b(Mrozek,)j(P)-6 b(.)30 b(Zgliczy)r(\023)-37 b(nski,)32 b Fg(Set)f(arithmetic)h(and)h (the)f(enclosing)g(pr)l(oblem)h(in)e(dynamics)p Fq(,)i(in)736 1013 y(prin)n(t)23 b(on)h(Annales)g(P)n(olonici)g(Mathematici)456 1096 y([S])201 b(V.)23 b(Szeb)r(ehely)-6 b(,)25 b(Theory)f(of)f (orbits,)g(Academic)i(Press,)d(1967)456 1179 y([Z])197 b(P)-6 b(.)23 b(Zgliczy)r(\023)-37 b(nski,)24 b Fc(C)1261 1155 y Fb(1)1321 1179 y Fg(L)l(ohner)i(algorithm)p Fq(,)e(F)-6 b(ound.)25 b(Comp.)e(Math.)h(2)f(\(2002\))j(429-465)555 1276 y Fg(E-mail)g(addr)l(ess)5 b Fq(:)33 b Fa(gianni@mate.polimi.it)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0312120425797 Content-Type: application/x-gzip; name="arioli.tar.gz" Content-Transfer-Encoding: base64 Content-Disposition: inline; filename="arioli.tar.gz" H4sICH2W2T8AA3IzYi50YXIA7DzZctvGsnkNv2JsV2yABCUClCxfU1Aq99jJcSWxXdnOgyOr QBKURsJmABQB2vr32z07wMViEjl1cs1ySKB7prfp6e5ZlNk8mZQ0TfYmWfbFHX0G7mDweDD4 YgCfo8eHjd/BwBseDgF3dPh4cHB4eHAEcNc7GnpfkMFdCWR+5kUZ5IR8cU6DJKGb230M/1/6 eUCTSTSfhsdFOaXp3sVJx4REdNwAxUF5sQKIaHJlAu/TpAzz6yDau7hPOpM0KUoCIFLQZegf DEadznVKpyQPJ/O8CC1Epfk0zB3Zj8Su8ezp54kBn3hO50uCHwXqVhrdvTaea+N5YXfed4xO VTx5g5KdOlWmnuLJOw18p6G1horHkUlrGgv8NBMPsypWTwpWK1gtYfW7BjlCnUuwE2HSDU79 Cr56E3dEUEb17o14i3cIytJFmFu8vePZI0KY6BqTKUxtgGsB5JRqRpxT7LFmnA6HZyYcOoC6 ik7xLi8tQcF2+kMUAKzQwmcGHgigdThD+OkyciOEZoIdg2aCG5oNwHWjaZ1pmGqY5sSiPliL HvvMs+Cp17MJjjuo84ae+tdvaN893acjBrpGkFUxWN/rLvhD7HZRQP7sdVEsfLZlrxp7LRqE FoxQzWA9r3utCdUGobpFCPWnOKj0VACyNgCHBCDS06zBns0xTNlLfzC6PPbp6BLVFI17zK6X p11Gvn+pae9AKpOkMk4qM0nVtydUczI1EqlNadBjqPA5ynzLMAJHZSsoGOqPMRZ8Wcuev3fY tS77wy610U24IqYYnCD73rdoV/qpQMa35havcIvFCDS4MYLsm3GLTW7M5W5pVd5WDTRSVEyY u96aTmaOMtpB06l3kKeO9TA3pal3kKbODCpalpvOTaeZO7w/nzx2zR76uaJvDk7xHwvc/w1Z RYhWa9lqJdxUEZ9Kfo1es8rgqZlWmmtVa1EMWSS0QS0Q6LHkKX6ffWvalOWYdD6OQug5c4p5 ZqRH58qJnPj/QZKcbqFwyChsIXF4h3mWOZImW7OmzKU01VoSrZQI7xgRQZn5kjZbd6rFqLgc govRg8siGJk9aiF5k0MtZG/RDxCo4pG7Z/eGXZbxmaCYsxkBhGLuZ2Ji9lYExkhg2LVYJ8a5 x1oydnzkNrDgcrZZcDkbLGA6DE75v5XQyXHuaZuHxnlb+g034VzJL9AyuCt8Gu05n3GjfYt+ 31MdvC0KeVsYeVsU8lYYakMMJT9DwOEKH89sz/lMG+3XGIwQXWwORvT4YGRUmUZeO+BpjcMh fs2gvX9pYwKhp5Dj1gmOnzAqwvWNVPa8YWnxc8376WpeFo5uTYo3VlI1Kt8624VQNjFlqv/u KvwfXYZz7A7aGeoNu5f9Q8ZyvYZCxU067qCkoaXBdK2iQtPPK46dVhxCqZ2so83zjtFqGWgn C2kTCVoNI1W7WKkSZmIBaY1cu9iqEsZiMWlVrnqn0ZPDt85a9U4jKIdwja0CJKOrOypLL2pW d1SWXjLyjXkvVd9RXd9RNV81Za5KmzIXq0VZlXVrtVOF3RastxU73Ix1Jd/AlMbdys+V/Mat Plv4eFv187by87bq523lO5R8G7IOt/IbSn7TVp9NfDbXdgxzBZgrwFxxzJdQwkH9drWG2Jes fQTtI2gfifaCTAzgGKJ9zAoATaPng3TwEp2+iSHUU3xARN/tx6wo+/JGSHPDKlRZJd6IvZPX F9QSq+pu4ERpck6CsyhMHAmMOTBmQL3BItBla6cjdp3YcyauM/GcIIC1u1OJxfy13IUQv4uV Vf34zZNTRy/q+WK+UeniKsQJYPSY6a9bOA9xQ46rW7gDxB1y3KKFe4y4I46LXY3B1ZgTS26x Z2I8xAhek0afA8QITpNGn8eIORIlhTzv4NY0zVY5107tLBiBgK1LA1QZvz32PVz1QrXuWF/w Z2I7oHSocFpGuMfq626mQFCy47rABHksETZAQwAtFOimxf6gwRkmXpdLTU/3onBWno0te6RR PVcic3p+obBItEN+/OH1vPwpDKIfaFFa7AAquXLGzhNsk4flPE9GypHDPE/zu3Ll3Zz4s+d2 xIZI9Ya1ag79GL1ZYRrjPkYXv17faWhgWp0OcDNqbadDA9Pq9BiXrms7HRkYoxPgtnrkiktO /+LgygPqlG+KOs0d54+5qDlQDXc9GJhBl++k/oMdmCVBdWCw0YfBujqwrknuMBSXG4uBRsqf 8lS90rYdNz9x2N6tbhFKAGddeUg6N3eZBKj/ZNswrKuwuA5jXsIxYVs8GRJ5SnSDK35oz/ea ym2a+AeD9szvqOn6m6VPWfRBUb3z2RSbmK1QMHWdqcem6dQ19/qtqjdx7S7/6dXdWh8ceO12 Hm/nNdsVC1pOLizKTTkJipC4T5ktuJKSxdTtCSJTfhbCmnqNpnXXgmaAF+N5Y1hnpq1jnrXt bpM1Ag8aUlQyjqxRBoNc39vrVjA9+r+xV4ikXiNcOq69ScFKBSLEDVs4mISMtLuZdMs0MMCG WQLHOI8cKw+AKJ3OS+wGP77bqP9a+850RiyrMe1O2FpIvdofPnS+tJpz75g3Ue+2zRgN5JwU +gHM1rnueTKJdsh1MsPJh1nQTnYzAIG9DjCTwdeSfYV5erExkz3R92XYzPhUCYVJZcZ3p+S5 AzQwDj1QH1RTjFdzuKrGchDid5diaoSfnpB5pctSbpD3mADdmVU1XIvaPZRgbd96pe+y1Zdl 6wsa4Y0sQNa27w+MqLvO2YS7LZvuVrfdjTflzQyfq9s+t2SrW6kCd70/rMqtElS9JT/Vq+lp hxXK332v77Yf9MBo7+JOebD7nwcHG+5/DtzHh3j/04Ofo8OjI3h23cdHn+9/fpLPg2k4o0lI fnr168tnZz9+8/P3MAdevvqFDP41GFwQ+dnfJz8GxVWAoW9+GUwCMqYlKfN6PCfLIL3Kg/Mo SGjQadJ7+fybn57//AsjMSDGB+j9J8jTspggIU0jBBrk0QJCfPSoRevZq/+8lN1d8vO/fyDu 4I/S+vW1FsVbpVWmm2idp3n4iJV8EVLji75wcsZTkkqHM/t9Ryeqc787Y4lqZnVn5IQMbJ2r idW1LJYmu/bMtvt94vvQgPT7JqInCpIbPBOWnZHYsSImyPV6TYKCXBMsyTUIEmJ2JNCtkhN0 tNoASAAAGz0RrQRBJibLxg/oDIxOnj3/31+/++7Fy+806PufvvleK3Hin9t8M+d5RUvr/nN8 hKxuGPbp7wn5qgB/C5JiBk3DKSlTDrzvdEzH4u29i7Cyzu29osxpcm7ZjgGGwVFwZoUHYTKl M/1wo24op/NkepaEQR5CrEcQtDcw82wNcJoukjXgyVxR4OAiLM9Y8D2jcaP9JAKGK6i7mv+y Arnz+/8b4//QPRo8bsV/7+hg+Dn+f4qPvLRPzFv7nY6YqL++PmMBE2fvA6y0ddvr/jzL0Wvu dx5gEFnFFwuFZ/OqA8H1GUZhOrkMCJg9qicX5DxKx0GU4CMlZQ0rVpgh/I8GxmzmACwk5Oz1 C4g2P8LPiMfp4Z574B7+D7whkPTJkkV4mi4CCMwL8uM3v/x772IdJY+R8rqcGAj1eM974j1+ MlrXOErPz1hswli3x4IhqpFm82I5WaLgZBwFkASigMzmydXkkhLos45UWGU7k4I+JAkaEW7N B8ik0wkUonPypu867uk69gVN1rAnkGnIhw/43WAMrefFOjKTtNiBDLQ2COFKTX7O4qAC66YZ ZhFvMOIlxlVRx2CJgER0shwHZFHnwTJdkALqjvB8Top5nPY7mhxfOb54+dvZcwsc4Tnpu2Hf feLgY489EryoBbR/Bn8LoELP8nAZJiUvYhiXkIQddM7+rT/kW6ZeQNIxUggYrYJGCQ07LEGy 54DdTgb55iFf6RKGU0t4vrLBxau4t8Wa8mWKGHFoS7o+4Xem+OqCsJ2Azs0u8m7+rNdbqrdc 5KAZ0y7Ll+F0ScHYy2BBwxyhNZniXFOoWu/1kBcX8yiyWuP0kFDXIatAr7UTAJrCj9hmw5CE SzTfoi57gKKHeuzJ/ppI2FMJM3qxxRvrxp5OoAV74N3YI+vGnvSmnsW7Y6a++ahjCFcIG66Q pWV4HnLvqkVJ0hHFIN+SEy9sxB2+gxFJLxHjDA0tjkfUXzjkDUGUi35qKW4x49ZOM2Fb5XRz 7XRco6Z7PZTa6QikdVQ9+ZxkceK7aQ1R5woCcUKvODdKLqEAhEJuASF60FFVJomc3OF7FWIP SjxFwMKH/xRgmQRXOOk7okwHHJbuRG2ksAaihObd+5EkgE6IUB4flJOTXACE+yJov0umCzZZ 6yyYXlEQFMReLoIlW8Ag2ywAZFGGkG0hXKm37r6UDfmSr2BZxFYO7zlzZD8LxoUVyS3znL/n 8r4c7wurm1zvDpHSz+XaATpE6jnyxRYPv70qrZJYkFEcHjFtaARvpgXWFCWsL98h4jGUWc0M oSyIchthKM2luDDge9LgkkCjv1aia0huLPYelnZLCeTEQhXXjtdFXHm5YFDm2ir0epGNBYZ9 K8mlPFqBGy4Xr8f4iFvM93Cvb7v7zy/DOKmxz3ulLaRud19sTQsr3E2W0jM1g9xTpvnbz/P8 8zz/PM//YfP8FmRUUcBKAigIFnK/LlwuludROIX1kr5AAa7bDhRsbyVvh4YyjDOfo0bm1Ofu j1hecprI3EDyypJhVWPfio793P46epprhKhKoxMDYcwKIZ1tUJHTQ5gcEXexAlixbKyXY2uM zNZ50nxzRU4d733M8vJAkGmzYnDedKPJBbpldGnv/Gl0lwZj23T05yyipXF2S9W555QGsY27 HWi4+rKY0Dmh0DKblzb5vZiPixCsgsepDNKDRTt2gQf8OUXzGImnAFUi3+pSW6aEnL/JZUsB avdyex/PRrtUnykWaBiIpcmaYGrGKbUBygT3837BeBR9NCJ6JoMf5yxoiTb84sPqfFU+VOb1 eZqkcQgPkyWsEhvbM+g6qoJPFzstvpv8Cppgzi8cUgbJbqv49YIDQVLpAAKvK268FB6MuwoZ VAvBFNNuSIL8fB7j3gKmY71AIW8GjpfRUxLNxzDU8OgMThuxp4L4uoRcjFtTowYmEMWCAuAO kYAh+3mMKyICcXgKZQawVdsq5gZDgkegCVQiCjuyjQBPgp5vEYsvn/quk0D06cr3yvG6CR4Y QBGzTyy5tcGBRKU5kvR6MnmCYK8KiCA41mAWcOTpnCxIhhamuPAscgggNCaWijB1bOvOaPPX L/Y92/fdDpQ67CMufSRfebKlSn/yDgh5yrq7IDyQ0Fj9YftrPmFpQSnYP0NmDkG1QUOhIL6p 60FNInkYXI1azF2DObjjrZmTP8j3psMruS105bhp2mokjZHCQoBRSKfQleLApBD5o5r0mQ/n fBD5EjyUVoVygvc6NjcWdS1mCMvLBeD0OsVdPD5VjNmRMkLYJmABru/ju96UATB77jXgguar MXjUpEkQZsEyuMrDQu2GcoE5+eM+uC1/9PvuSOH4FhHD8QwtyniRQ4JPu/Xx0TAFPmaGKXj9 A2FK7tKuhCsCgUjFq9cvdohXuCu8GrEUdEtEIo2QhDGJtIJS1wxJMiBp17Z1MEKdE5KFgIJU B4kU/B4iUKqi0pxHJdncCF7cq7izbwteRvPXgCsVxiHnYMiQjRArqEFDGs9jB2qBJC0oGbCE ZQ1EeJOEVgOcGeGMEMfCzMYoo+KBGQ5I5STklmFmNcAZEQ55910WXyHC4HccSAXBShhIdxCK R14MgX9UOCMMrmfB4yBph8EGAzOY6eMNu7Oe7d8Tz/6J4UwXi0FyHiaFDmcA2BjOGlFIhSFi FvwWKyGggSxacL7x17s+Orm90pN0RW0A/Tm1tZ6iVkvuQO1b602eV1maQKaBdSIeigZ5Xcaw KAJhseTbSIh8F7EtuCA6T1kXWXzQAA9EGcmarSE+LD8cQxBVtqHJNTRYZ0M2uyAa0zjA/90h SWekvIDlJAZoaBZLQPV2P7nHW9OCnNPrECZLAXkrApmKpxxDfofC++w99ZObt+9/p8msrG+g J92n92BwqrcJ0FBtBhxlYem1twc/1CbHgs6Gtslbqum4+5YLtVi1n9iyV3kBssG/ANbjJUgv FYPV9EWQ4FcJNisDmoRTMsvTmPwS1BHEtCLMaVhIMnjdE0/gQcmChF3OTyLH4SSYFyEzCjOQ IQfyLnHRmJyTMoXMABZKsAes90gE9UXYed9pOO0SorKPkXlpmxFPlgKNturqsQYt2K4tk2zh CzkbDVjIxl6S6hS8RL7zW633EMTvZRG2qdXzF7Jg0Pl/0fWX+8lIsFq+tRIIsPvs+x6U9oDD 2kdaCj6cM6q2gHZuHzUFE43kdqfFs8mxcf6vMgsTUgTm26cVudvX9xk1I7Oo7cReE3Vn+3Vr pzB5nS9h8V+K5V9jVYz3GSieK6cTpiDOVghmtp7CG+avjIFkGTlLvmm2jHCvw1oam0TLXIDk xlDLC6NZ7vP2eGEkajrZMmdYvh8L6LzdnZ8Liz+qYHcOQBS7K4IOdrdHarOVcbkn6cm9WkUr Wkcs0sQiRoz1Mc/AI+NlZTPWOLi+42i/LUIbt2B4jK4+gPd7jSANuJVBrtYd1mzY/RBThUkR QJ1fAh8py1ztXxbgd+rmCKRDdLhlsAAIFOtZHiwQYDeXJRBnkuNNixLcCYdliV6TQEjvyl0E XKJAoFBlZXND5CWwAv+/ShMQbJpCOWmsRsJtGydLTFJLSHg/BOc5VgyPAtBFr0gq37PJOEU7 H/teh0f2ZjWstgSJXEAxUYXonsMXU/qPpbZ1VXqaPcwKWt+Y0hX0R6pnWBjRq3UhjpC+T1rl sz4z6TVxdxfl1tNpxblpwC6xwSCj55tBDr29GeTW+b8KchA8jgfc79B2EzDm8bG4FdvtdrGA ZP/LZkalsiFUTdMYcj1PRff1uinE67Subdi9uYJvzq0pvbbcvUNbz65pTaoT3yOLdAETClJ8 UJRhNr8Mn4oWsLz4Pk3ALQqoZyu2jZAWZTChjD5eHRnuo3dB4qxFF/BVY3WNlqrIZXCV4mSt YYWZdFEr6Ib74vhY27pSYNsI/JJ2++hqyBeePNUDzROfeHghrSLHPul7zXlckX0f9W1PVcM5 1cb9koUXfjb2VAYzgpsX5R4EEsBzTcF0qGmPVA1PTEB3EfCAIeLFW/WX1uRQkZUwx2LyUB6Q n5xYCkaTzPjDsofUVtl0csEUN274RZGTi0MpffpExSJSnkRxMz968+ieb03wL6GyvfOwtCCM PHwINO/5z199a8vFqHyX1ofW5OQEGBnRQ1Hw/UfOI32yKRvn+ny53fzUbM6wUYSDnucNuNIH +Ep1TKryz43Mp5uO/BKjCXyhBzumxn3qNLoO+aXXAudj0HszcMrTbibPeCbsL5DKjrY963IW zPBvEc5UT32K9ND8C8CHxBg2sKsYNrzmfw+W+JyJNcHg/b6z5rY9iwH6Xv2/giRJSyE1F0EL fx+GS5wDiQwiVBabCuYfCoCJsxM8SFZWETnCUopYE1H39PWfuAmIva9A8tTUNko4/v+9M7Zm suOPsmK9TU4M0GDEIQ0+nJPhI/JE0vX/nCKjVZKe/ycENui1zQCuULrHpUe+hl8In/Bk7mxJ B8bA9jEfbF/LDFZvamaroAm/N/hwSvOt7snE2eCjOzkpJyT/ZGOtX/4fe98CJcdVHVj6zKjd yCCwTQwYKI2R1DM9PT/97Jlpod/YEh5JgyzZ2JZo13TXTNdMf8b9mZ88sYzs2EJWEAkBAzYY Q4KzsHvIWU7ic9YblGDWhnWCkiVZ74mzESDvarAIIlGMEwSz9973qupV1av+zPSM5Kx6zptb 73ffvffd9391y6pSICpqvbwyT9rqeIPG0ldRq4CISHuJOqyJKk+9+XQZZEW66+ymnXUmk1eh XdwbdjMuEbgERYcDRdD5ILSaoPONJXbyz7GwWS4MbxrMy6AdmGf2wKXlERd/gpbvdOxbdKqr 8gcyNDityrMsUeHFprj49hKJUvpeEyvK+WrTVNC8mzQnymkOqnZ3qx7CGzA0TlFEP/nZJW0I 4rxQoDWBnzLHGSdJBXzHSpijjEJfw+jLpnH7gEjBoX/UftUYnu33hz3csXzQP9k5yGNnYbcY xCoeyDH5OeZRduCAdxqFkyw+z4LZQWjAWQEsBmbFODOmeVJBT6UG+fUwPrmhC4XYiw6LKSKQ AyMGogOhYcHmhDqAZFt3u+g3+/d/THbm8xXg0u9/dbSvbXO//9uxduP6K+9/LcTPs7a1NhCs X1LXEnpOHcD7otkBNZ7S8nl1jak4a7wYzDtHsZ279/XsvWNLb2xb75bbb7fewXWHB61Px6jd RpY1GfGDMmoDTCQK0Kjw1TTeWndu3RXECYWZD+Yl7PM1SL4dPIJr8HyesLEWY8d5v2+jWh+4 YT/ABcWpjOxECHuIWM/evXv23t7oLKdhIKeldSQPs7gKaqDLVpz84I1Fkk3ayFiP2ngwiGsv 9Ji2LawFGe17q45X5yC4COvRREYfNHeUhNchgkFWQ2YF0Y73SBEX3Z1su9saBhvVQ1NdziBh JRhjF3RhVondZ4h7m1lPbnpLY6ARRQwQLuzZOdw7IbBO7nJSutq69w2rbXl6n+ThaFXJI9Ul b6oueWt1ycPhUMlICC3BSaREZoh0ZMZpPR4XmZdIuBaON7L5vp3OnNS7VgG4syGkZC84O+9H rs65yIEmkGBvN5tZucXdnAENiEqzK10mOM+rZBhoTuxkWLprgmVTbWiRqXH1tNQEy8q5cGRk vH1Gs0zL2ZmquZSToLGT59NaKhUzRlUJImYICgOMLKiUA6dbgfg5gqX1JXoa30zh2cumAkwm IpcIVbVSZK6MMsLK4pLJZXYsyjDNmsVIDVlsqhmLMkyzZrGphiy21ozFVQuDSWC6AlTeF76c RKmG2ZTFzWy27hNGGfWQuYyi3QiVz16EPObyUJqJrWK5gRMvtb04UZIMjnLe9tJESppcmh4m ilIhVF4xaclt9uow4PV/veB5zbYEl5lsBiaqWsEY1fu0XFX8wgRBlppPiPFmCiRJ0LvMNKAN WAml+Po1ySvp0HrdQTknJz6ve4w63/fw4UHy/oCPnCRXeH1SSm7H+eL0XCjzI1R+dcoHb+Up 5Yf9PonlKaVJJa8XOZGWeA/Jp3Tp6+NCD+OTjaxrVlaCn1UEiU0Ev8LmdH5UFc4KzgNUz4EA lCIcCDjrjq/s7WVId3coax5RMigbZFxUu5GI55wmEvcEz212iuPybvYBRY7NPk9n4SSmut1C pzRuwR0DR8k8hLYSJEWP2id0sJ7PGaNaQe/0jHiqvckuhvLdVxy3WltvLPGjl+VSgDpPZ5f0 0lqEvamm+mQxP8po0lr57nJXtXvAXdKXziKCGY41zDLbGu/7ZsMpLT8h7luZRtzMkM5O86mS PYxO89CAbY7Qvnwz3xox986D7t2jRrySYAZYx2CNDttJwzltGHeKVHaWDXg3MXxuAdub8aQr uWIc50kUt7Khmcg2xSxYNmttvY2lHsbUw9kRA03hTJQQhqRJ4sY37fJHzd112p+mWzlRa4+9 i9m4NfEKuEtvNxyy97pD7CwhinGrV6uh8e6oyZMT93Z9UM9gU9IdCtQo4AKyrHLbWtpKoeAE rc6J+UO5aFSWz2ar3O6Ih7FNlvwYe8Rbd9QUoLsoc0g1y3PtoNjohQM6hihs+fnpXAfD3dq6 V09puKmIVg+y+bihRqMic7PaghEIUUOQil28ALY6BF4xnJ0PUQQ/dHRRlU9p/Zqazhj6UH6S yOuWk1fN3o5AnkVEt0Wd6qYBxygXDXIS5kiBJR6pDMYMfZgXv0kugmo2plwEUC9jV4OPCEQS 5BTMjQBbDVzFr4yqaohuiU1quNPNb4/lKBo1tlFKTjX7WhJ6VtoqAb22VU8rox4675wQ369L ZPHYr5g26DpsHAZPkzrPDEi1p0Cr1bx09kMnsJyyPJ2q3kPnqbzfoJBmM4TVHgYdbGDEiVMf TkW10x6bjIFqyu+yCXceWba28hfGPD2b3wK3TI1ZESGnLhF9H1TNMLQRZjYxp9FQ+tkt0VZE nps9s+zOfgoW1HJOfBba1XPSPRdOuivnZH9Gy00g3cW8hxtTT6QbqKKCWuRHTGVojpgDXKNl M0DdzjcRPAX57C5Y5biLsQbKiBgkFIc1lKDdAUkVuXcX3MVIygl7y7GHUmGnA83veIssvRVi Fc9uOVjXFOwrTeLOlnUX03UpguwLQ7QQxJK5NSzlvAzBVpxT1uU77LeoJbu5wm0W3t7ZJQ8j r8KaoTBxINNgfg/DybZk34V2Tb37LrKWgOocyTXadzjAH841Oikn+e8upvv1nGqfBzgmaZUd UwjarIZ4OmGahjMXHthtT3QtCqwZuR8NdlmVn3GY18LV0Eo7TFVFOk1kLa5ZJZJrxfHO2Um2 Kt639MNXCp1TCLWz9+VUIb+NVZnCmC2TLXfdmHw3XX1QWQO9jYuvDogm/pwQsyfEaTtPwIr1 T12JeciusqYbu4JzW3PajbfM9oSP/CjSO0mgVuqdKFjBbLJgzhUQB7+ZRTOGLvMBN33dd0cu 9f2ZN/vPECw1z1cZZex/b9zY7rn/tbG9/cr9r4X4OTts1+Wv21JaXlOtQW2SrhnBmmsSX3hK uz7/gKudFtfmHE339piLHTJXaOTxOxHwDOse22DwamFXw95y8DcgxqY99B50NKqu5uHsYMgu RmdXpbSoZUGb9zFNmJNNi9hrZlFVMDjG50t8N0s0NeaYSXEkU748Tqayk9nMhBqOluZTckdJ ZNRrDpDRHJYRLdr1spgIy7jgK0PXbXznliMXm3vjUd1jk666thoJtXU9v2pZRcrISnJBqxJZ RaT1KBVWRCLWmsgqUmtZNZWRleR2mm2Bz+QgxPfgcGeT9uXYXh16GyXNhT74JIpSyCmIjSMw 7+U7zBiaknYEeAritkCRRL5B14aFOKqx27RmGYpEGtFRDrkeuNZPZC6QkDR5FUOmHDbZZGnT oyIWm5ZBQ9Vfc3y1p7QGNUUtTiWa5NKmkmLFF3ZFsQrsOEPYhgjK2RJzuFoxiwJ7M0k5PFcp u5VXYAdEqtoyDZeVKTPvWqUQrQxOAc6LtMJzkpZdNheVqXfyNk9yC8+5yTvFctnqYrhGLd5H vBW0fVvgtqJK5S3uULV7G36zmuooUQWSGhAvZrV7KqJZzXWU6sWR6fZNqY5GVlGpDisGNz14 YLuYPNfenYPk/P1gV3oeameYn7qusCXJq7riuhZ6oPD890CuDPMiuLl1QY4pXamOJ3xpOh6X BBei5wnPuedxybSKqUY4XMlUg6QwG9EumGKGq2jRFSumSLtK5wOWzGzj8jKJORqxKCqvoKRi CpaWko+MykvIr+k65OPf4dkvqApmUrSCcFmC3Ytpof1HwMltTwgWUqpdfLWWWXxJ3vURzZ+D pMo3BEv5JeyhAZ28QbvJxqiR0NX+CfoucQsM1lEfIzBMm+STUhaEmuReUHn0yGEthLW+VodK 2bkshRLH8Rz1a62eBsiGY266nQ21zEBHTZbfrSUXT7aiubRsyldiVDhOjqqcxrfKZ+W+XVXr QnRVrZVO48v1VWXnHqaiqXOdxXsVqLQcfbTOqpf5HE1bazSPr2xmJwq3Mp1UZ62U87i0bK3J vK7E0Nk99xndnJRwYdeSrZXO6GYjT1Pv3NOQCrvCSsW3UGpXak5Sxayt0mmJSoP2rOYmiWxC G6OZSdj7lSzJO4dMfpKbSCyig+2jSw2CyXbXU9YJCbuaFOZoSp1J5IQ8JFork/eQxTqKJzLo noWHSz8mfV7LmzWHnMFRLVWWMZMvM+0suHG/E1jq2GNhmZFxozJ2amdx0VLwbEIfSmeZikck Ku69lFaRiktF5pGYR78jXlV1Sc6r3hFPm6hCHfzYK6XcVfPGWbO01Zcjk6FZ6LXf67wl9Loa PiBvxDOYSBkRUpavkHlQ6HQmyyzlNgnfyy3xfnEF6myf5om6Sh97sw/mrOv2wsGc+0IlfoGM Tu7cOzghUYddiDtmhdj7si7KvNncZBAOGtuta22uYnkwFlvp/kcqKuJs8o5W0q2QXNQhwibJ eDVl36NzkC4cVHpFhrfx8Jz1kOcQsyz5voSUYcCH7akS1Kvd7vomwTPaD3kOBj0/vLbl4HqT 2qZGmGH6kZw+amSLeVTuhFEwLUNUV3tz575U5fmwL+iduPafL8qd9e0m3SHm9krEnPdpZR5m ZYoanrWiVtzQqqwpOe12aOMhzxnWHGqqEBVLaHKwaqZB8grdqVQjopwTz3Z5JZs9FbgJhi1E KReXV1qHPBsFC6PAnp5TVF/WvtgneAW6O8T2eMizcl8QTSxBt9C7eQi3BH7Ic7gxX2T7y5sN sFJjrGQ9GXXIXLzPcmNd9Ww8U5Geu06SiaN35ug3JfKfApunoK4rSY5rSp45i5skmLAw6qc4 NkTOrzuVyICJ5fa0GQZzY9/nCN09K2+yl13yCnfNze30RLbZ/CsozZW9bHFO6kwjqv5rwxI1 W/Ga4Eq9XpJ6XcjlEX48jy4Tq62S1b7XytFcNrSsU7gO7zFcR6lzuJ0mYXa36HceV+IszkGC vVTw0NAtXr8ru0/tHjpaZUOHzx6rc9RrlYwe+POz4+0aPngYF5Vko1U8kOMaZRUh22INuTXQ I0q1lCzFPeoKj+tScnlUJUlnJcyrKNmW9RxF6VZLT8tot1qGv6ZWdKLiq6mVHAcsuKqGa6Sq s5SvQ3srO2GpvfZKj11qJNzaKK9UvH6qWsXp33zo6nxJMzyfquqjltWc/PnoZXWSXBjFDNdO MfGhVveUhI3VZtpUvRQfNVUlc7Z0NlFMZdVVkqmb1xgkTjJlEzf43yGs4siPq2eVqdl2Xppu loavpU3SbIu+WY2fl+rX1eKQns5ofJIs+Y6WRf2qVbP6hhYe1fPzBOvDuywQd6rNr5/xL1Kx cMaa/WE0DI1EKdCJoVuOoFsN4eeXORYnnrCJR5iws9sEksOYcpXBXzS2akKoCL6XfXnVQ5TX gihEsRZKV0NF9eCqiIgMR4k6mIfvMZLpQdWbxpKMxDShan1ozgphX41kH6Rg355jC2fPi+Sc VeE7JrtNwxDmRz4BKyt1vNH8WM+NwvecPHVvraOsj9rx3H6a4FhCWX0waYRzvOAfymS7AYRU +Cqoe2Sy09OOAk+OzxRpGn/lgipfl26TeJ2dXmvoKGTT8FmqeTzXTHdHxlNRcygbz0WtEZGR m9HxO+AFxqB99TkaGk+Fx3ONrR1dHs7Az3gaT0VMxC5BcRmN5yJWcZLxE+9AssGeZ/C9cUms NjTzNzRyltSt+jLNwOy9u2fb3XepfXu33Ll9T9+e7Xu27t7Zo27fo955196792/r2b1zi+sa rh4xMsM5HTUNLT+Vea02HPJ7KTQc9r+eEg57b6FYN2+qacU23dl8oQrCmWV/tLVS6p1W8+ui 0pdYrUgn+fOwW4N1ktArrhP8KoEPU5GIf51EIvNSJ5UTzj6YUK5OIpESdWJFzkudzPb9fwPt PxTyhUtn/6FtXUd7u9v+w4aNG67Yf1iIn/3pmwHZh3dMwzB2iNk2mLkYGuXQbGvMshvLLFIe onEmWyCrMS3bUjBysdZgGZor6OMwg7invbmjZf3Be9a2rG9eBw8NjfzLWHygNJqHukRUtHjC rNEDDbRIwmcKPNBABqhUFoKf1cJ/ktxbBgA3NEONvl9vqFomoQ6xY3LM2snRODMZMNNnxmuY 0ash7h1iZcuylKZSRpORyes5/NCReqDBiI6SmSk0an6gQS1kHcRZ+Ax2bdSYY/FkDzqh6wCi Aps88ZhmFLbStGNKrPOe8RF7RjPprHLKPslwTYq47IXu+Ah2PlH63DmphmkdCUJYqG0mqNFL M8wk0N474ulUs8WchRm/MQ9z4wLUq5ZDZKymeHk4scQwi6QpF0f+qussfx+kx6rSBSk0HsgQ Tqohhq69pY1NV82Atpabb3YF4EeXW5tgTMoYk/qQmu0f0sZgLZ2nb4BriWZVw+8uTqSGaYk1 oY5NoBGWbIbS5qFdTur4cfNEdnIsm2LBOG6hbUxakuG4w76EBSMfGlDqVUM7d+HXlNUxtd+A 4S+pprX8ML9lid8dz46pGZjR5ybik/hZ62BTK9mGsbjqaGGHaBLVyCezYzHzm1fMprPVJdjN HyayxZR5S0+Q65YCbWk4RGwi67TFK5sRc5zRkLPwRjQR06Z+UG3Yc1uD2qk2bN2ynS9OnDW6 l2dTOVb+eUOG1VaYoGz8L1F0ezVFI8pOnCaUKdq+0+hfcEc1BRdHOtl8vkzB8WIF0l5bTcmA sdO/ZNWtY7gopMkYrDnjzEB4Ez2P3nOwMdivDxrsQ0BGxijEBkaKAPgST7oraO3IWcGOvTf7 lQi3EXkrI4bI8tClzsytd4bUjRvamtff1NZ8546d+3qat/Zu2XYbowgaPQpNHdVzxsAEDUcD lraraR2Yyxj5tDqWzQ3nsQlDs05NqNAYVVkza7Rt3e/vi+3ds3/3dsamqDM2R2bp9JHqpO7s ydQBc0UeUY2CmtSofOga0vmVK1cyEqwu02Qmn4XKzQKuHMXl7WTC/ICljqeyeR2EAz4gqOuK IbdL86P5f3HkEtp/W7ehvX2jx/5b25Xvfy7Ir6T9N/OjCvzTCabpxTVqv+6wBaf5mIITcd05 kdYGtYymso9YpoxJMu3tzEi4xtTBbE5X3cTEqEMvjsTiWeiIQo0SW3PFTN4YzOjsi3IxqNiC HoOuMxFtY1/RxE3r21PZsSzNDov49QM+K9KqOvgQthGqM2n3JrFot9BnSXfzd+qzMrGWsZ5X xngeE4bUVB5JQ2oaL6HHY2wxElrNN4Fpu/lSWMy7rOqijHW+Usb5BNWUG+Oj6pAZ35vP2qjW Jt9lVRtl7P/N2fzfoaBfF+N5L6hqW4DmeQ7LV9oOICtK9bdaETVvbppXu5ocFzqqMvtnvaRd scEvH/3011FfPS2tq7Wz/jcb839cts0k3Oawv3RF2b0JhTtXM3aoqaqvdDfZqur62dINi9Il Yfm9JU96LH8jfqHlNseX5cW+u5zpEKcImdzCpJWVtnnXBbjLXCtrYv5vVj9Rtlwn52JG0Kyc uRkJvLwtAvprxmVqK7BiY4GOfsvWDElvJZndEQ2su/KJXegmVcMOq3wn5RZduMYdlkuWl7jH qrnZwEpnKE7huvSyrET9htkFF91c7c5UbSvQMclwrZBlUpnPFVlpi4C+KzPz8ndwlndsrXtl wct7zVfG7GAtrA6yhZr3VSeSmtpZ7kUn4YaepY6y6bB9CV/24wu5Vr6QYzRVYkSwvHVCU+NN U4NOW4PzqtyV2iCUKrdact22qeSAg0NNq3es9rP6RkK7xN1hxRYJLaqrNixeQhPNCU5rBaO0 nw04a5iu3Ojgggp37guLamaQLv20BezRSl9jhA61vDTr3drYJCw3e/Rty9YEp6Z6edmsdys2 UThL6ZbuKEXp+neVMmleBkp5OVksZB3DPE2jLELmwcghmxtUYNPQUbMp85pvRYYNy9d+5S+o hUNao1ry3bRq7GzUyI6iW4huS4PlZOcxN1hbifWXfJlvNvKam6XGy1xc8dLvPv77NAUZlHUD EtOPsrqpxP5jTesoAp1ArVS6NtYmXeJzWZcsIzS3ickay6p2zb8mBi1tUY3KDFj6y2pUYsWy xqIq3fTn3SZMdVdy+M+mv+ZmNj17EE6DlX72tBzvzjv6hQo2w1SYTzU0iyianSg8Owdl6OgQ 6eiogo4Oi44OkY4OGR1vRnOkDLEaqsLoKH5YWWLoU2hd/oYULcqsn7Apq3a5jYFWZLe0Attv jEfocICvXE4gwt7/4qhSQu8rGjCsmXGFJptd8FVoCYhZGbvsjJVWZh2xAkOPPrL1SrakXL1j nCDEmto6rZZxp2LWnnPvkOXh3FHJC2wqtTKrjgumJ4nZ6ImcdTtUaml1vq2qzqcN1VpJW69C 2l5hywy1zq31OVLVhsWBCppfDey8zqkZzQPbg9WwPWszsdVyPe+1nSzJNp8FSrcvKrA9W6Zs w1V2JVte87YDOQsDtarj9qxkFjt/dkwrt2RqKV4J06XS+pUs6P3sl0rKcKWvrBAnYVM1UjP3 TEr2PULJ3letTN361dKlsn97RUHKTTgv9/2Ry9nMrlnVfoanHKandpo000FVJ11GyePrqvw6 SoMwKNkGqPws+Hrz+9rtdY9yIn9lbPg6fva1DMdJbqXWeyszf+rTLi5XE75lBCk/vvW731KZ 9dMK7fQukCAvCwO+fpdfKjaBevnoZs0Moc7Vaq//hZe5qWmJCwfzJ9J501JfjXT8fO7AzFU9 F1yUtTPTW4Esfa6++N14qdBE72WjljW00xuUHBdcMbJ7xcjuFSO7/z8a2a38d+dEfszQC6yy +o1CdkxnBrHgOR8yTb3yirZMVaD9IrVppJCLhlxhjavHu3gdqEZzhp7j2SLZRhpnVug6VVZ7 aMEnZETbuozum7oMvkHMl1OZKPZjjaGmEBQSNsyuzkKV1AlZhmFssFfHZgJ2wW9elq01tmBs mZBj6hAkHVsZmtxk74YsqFHjOVs1VkuaMWbNwWWt2DnaYgIKpIMNalTQsVC2thZ66160e8zF NiuDx1XbO8bCfawd269ruUwbMzLpOtF4SgiJ2JdgLo054wW0ZizaLva5YOwwYcy1vna3jcPh 8peML7ndZKKCblKGS4qKXZ4Mz5uoqO+tWl6Xi6Fmok00zOwjRYd95ppLMRJZSIVzCqlyq9CW xpmGnktpnJlmHmR1STXuUpszu/Kr8gfTVG0+bf/hr4z97/a2tWvd9v/a1rVfsf+3ED/TsHcD KQLa9KaJXE4f1XN5PUQrkTwaVuUTbjXezE1yw5oDlxzNQ9F8IQeLnlC+MdLepRrd6hD8D4eb hyIR813iaP4e4yDrhvAJvEOWd+hgNN5Fs13LgjDSQj1rhtl3RQqa0Z8optMTNi1GMy6Y2PQ2 FMLnaKaR72BPaplsoTikTma0YbZInqACM9FIpsvqSGHehgZO+3XcXIHpaUIrwOoNETKbVIks W0+7fpBtUM/oOcAfnxjITajZxFguy7MSj+HwwWhGXdXepobVNW1rulhRWr6gj2Q0yoSL9Sm2 3lVDoUxrtL2tcVNbYxdDX8wXM+qQpvKpO/LWza+WcuxrImu6TGLGQInHGKtDej5l2NsBJO41 B9rWOHhm6YezQHAcVgPD+UKRlgKs0vNABFTGpVbNK78F+LFmP79llOn/0QSsq/9vX99+pf9f kF8l/e0V48z/fn+4GXWJ53/Y6qn9b2xv27B2XQfN/9Zesf+8ID9z/tedLySMrPjxFwxJGf2O oLRWSHoCUkZmGAODQX0clqUZlfoUtjLlG35au9ZsPfZbjx12aIcdulZrDl51lbVZqK21o9bZ Gdb1Uw+VzSX0nBnIlroOMhJ9SWMuVNSECB8ahILXaiJ6KFiKFjcjVMn3D9QmeB5ls/Sr+MJ+ V+8uTMgSYTTdS/TUP7X/Qnpedazc+g+aPrT/9Rva1q1fv76tHcf/DTANuNL+F+DXuRU/mNEZ 7DSPKvhXQFj7DXb2aQXUYzOUBd+jxXqNfKE5zQDpaQxPPQZBXwuxvbqWOhjs3MKPT/I88yGt Oc3SNhem7Oh9EyM6JjmE2Qif9WCixADIsZc0G9MzjLu0TFFLBTt7MglgoGdUSxW1AsQRjZ2d xbw2qONnmzjNdukHm/n2V56fwwSDvnLADsQrBgy9zKWAJApCYBQLMijFtJTny59lJ8fVMNwD 45mXYwx1scyYbB7QSnNbwBSV8Ur4qmQUCRM4ZXSaxQKjlbf/tDasDxgpff56mPL9/7q29dj/ r29fv25D2/p1OP+DHFf6/4X49e7cGlVbk9m03so4bMUpXStM/Hb1tmhqJJUOBnfu3nfHnq0f uh1UzTx4aMlanylqyVKCHaivQoKknSCp5vVCgT1hPEQGg4SQ5fnAIbOEqeCOW3b29twuBO+Y CgZ37ODF02wlq/JJCzyZHykCIiCVSQPtaQSD27aBZzAcViMjg2okrkZ2ehgNBnNr+zuhKFbE lIOWqygvcLq2X54CnkF+U+ybVC3ZTtVcTQWv+sChbdumbH/QIrnToj7uSEUBQZufTps3QCDI 1cwlRgMbVm102oLHjLYYeT4QhJjgKvuIC/Naz5TXEL4OxDz5MeaRYBWzIlasBcTITxjMahEy 8BhbOnFLOsGrvEqZHsnpI2YCrBhBcMGWvh17dt+ldqrxlK5lgvRf7QxeFcmlgVizusxKbPpN dTCNYi4WIO+lboSX8Ae6Pe9lYP8P3bu0/29vXw//1prz/40b2mj/D4Ou9P8L8Hugp/eWRYsW Wf7FyhIFfSNPLw2sA/hc01IKX6eoSr0SUt6nvAcg+sEdhjTgTsIzujpwmHoJuAvoIA7dNfB8 DY9bxB39IA7da3+3REGH+ZUVPP4VwJIKBNC9cb2iPP4ehcrF+MUA1AtLFPWhQADdy+BHV8/L QBcAJIEHlwbQqZheiMPRrTWViKSMTHG8JZ9t6WDhKzhtt+7ez2XBHNJ1BNwXwbVw0hs5fJtL njvBZcD9BrjfBbcJHOrxe4U0vwWuCC4Ozmx9vw0uBe5hcJvB5cB1gjO35j+O4uJ84O92DtvB xcD9HrgxcPeDu4nHTYHbxp/fDW4I3GPg9oC7G9xnwX2ex+8Gdy/yDm4Q3KfBrQJ3ENwBcJ9R vL9uDu/h8EmF6QX+PgYOJ5U3gxsHNwzuI+AawGF/ewdPlwWXBxcCh1J/FNxvgtsBbhm4x3m6 L4AzdymuBpdw0VIANwDuUwqrS3ND8zi4J4R0D3D4SXD7FKaXHwV3AtwxHvcJhdU3/raCGwX3 OXB94CYVpt/V/BaViV9RIZ53gruqinJv4BCajvIuITzAYZMrfUcJXCs5xLbwDv78VnDv489h Dj/oyvd+Dps5vBHcdv68gcNeVx5sc1EJDR8Wnt/O4S3gVoO7k/uxD/gQuLcIac1eey+4XeAi 4O4Ct1FShiYJw98HXP5rwS3nzz3gHuTPt4HbAu567l8LrtWVt4vDQ+CO8uf7wD0C7jpwE0La hzhcA249uN/xoW8jVszDgQDK+e2gKdgWTv/BssBHF2F9LVc2QmM68IWlAawnrL8jIKgU+L/Y w/x/Ckq9tHVZgNXvcuUTkP5+iO9YxOINiD+5vD7wLR6P7ePwg3WBGxcz/yuA7zFI/yLHPwn5 nwD/Ku5/GPKfemt9IMLp+TnAdf+3LvBL7sf6O//7ywI/5fh/AeFt03WBT/P4D0P+l99SH3iV x78I5X0d6eP4u4FwHAsU4v/nM3ko/zmIX83jPwP5+95RH5jh+Xsg/UsQv5zzF4X0r4B/M0// nwD/OUFerdjo/0td4D/Ws/zLoKSLEN/J478F+Zd/cWlgJ/dHQC43/awu8Puc/m0QfwPER3j8 IPibwX+K+7dCp/XKSCCwlOh/m/JnkO/k6brAA1y+/x3Sd0P6zy1m6e8A+nvBfzX374T0T5yq C/yQl/curG+I7+X4ByB9CvzPcz+2kc3PLOP0L1fqIf6CUL4OD6cF/9sh/g3BXwD//YDvWo7v f0B5j4H/eu7/FdDx4k/qAh8x6xfk9gTEv4vTey+k/zr4P8/l/yNwL/15XWCa8/sXIO+nbl/G 5blc+Q7WJ6QPcfxt4H8J/FHuX4r1B/5Bju8agI+/CPW1hOX/JuA9+0ZdYJDj/yWkefY7dYG/ 5/7HgZ91UJ8K4Qsqn4R86tvrA22c/u9BupHr6wNR7v8YlHdOKP9vIf05oPdqTm8X6nuwPlDP 0z8FgvsByC/A5Xcr4Dt9vi5wnMe/DvK5CPhGuHz+AsI3/7gu8CqPD6N+PWXr29+AW/GHdbx9 LVf+N5Q38sKyQITz+wXg5wZI/7dcHqvZNE5h9acoM0uc/lWoj5D+Ol7+NyB/N/i/rrAx+0XU N/DfwMvH+cv9oD838PL3o749ZcvjFODp+2WdRc9RiE89ZbfXCyif9was+O9B2NlnbH4KII/7 IX0rT38U+Lj+7+oC+3l9fR/7G4jfzPmLYf38U13gII+/DvDuWFwfWMrxn4M0j11VH9jC5bkH 4Cs/qAv8Lx7/x6ifgO9r9QzfT0Aw42eWBf6Y0/Ms+E8J+o/97CuH6wLv5fGroGLfEPqfxyBh 6h+XWfxgv7fjpbrAI5y+J6HcE/9cH9jP43+G7QHK/x7nF+cEzwn4z4D8n4P4n/D4nwOdL4F/ E/f/A+A9/Ou6wFnO378uxrljfeA0938F/M+9qz5Q4Pjuh/yvCPXRh/os1N8FKO+x3gBvD1cr i7C/g/jtXD/+BvIv/9LSwH08/V7w3wD+E9z/Dkjf/CUb3x+Buwn0tYGX/wLQ1XdNfSDL6fsR 5O+G9E9yffsa0NML/sM8/y9Ano9fFwgc4/mfRH2D+D/h9f80jmfg383Tn8HxC/x1PP59rvr5 N+Dv+Qdt/9Xw9Bikv8Dzt4P/8UfseBXHM5EfqL/TLcssfiJA30uCfvwKx6cv2fIdwknNO+sD vZzfaezPIP5mHv85rE8Bf72rvf4W5O/9jfrAjTz/cogI/bdlgSAv/08BHhDk+1nsD79k9xdf BddbVx84wOPPAv2bf2b3FytwvIP013F53QP+53tNft6q3Ab4Ln7J1rfXcHy6tp63v+XKStSH p+3xAPuxUxfqAj/j8XcAok9Be/gyL/+rED7y93WBXbz830P9edrm/0+wP3raHi/fgeOfEP8A 5Dt8dX1gD8d/CvCfFeQfAXxtwnwI1xEnnqwPfHQpS98B8b2A70Gub9jvnfhpXeAZji+D+vW0 PR8Yh3xnBPzHsP9cUR9QefrHIP/J16H/4u37dexDob2Z9SOuAVRwwxDw7Mt2fxUAqJ6rC6Q5 Puz3Q6/WBYI8XonFcMMKP2qcK8RiCm22ZbRUzDyBj2mpVDaOd8AlcQndjt3VuyWlA45ixhgH z179viJ+n517t2UzA0YubXr79Fza4JEJfUArpgqxHM+Bh8pKOpXRY7GEkR/RCvGkEs/HYv14 xqLQ/UigYaSYT9qe7Igyks2mGLHskdOmjBQLjDtIbT71a5lBZSCn65N6rH+ioOfx/eIse5SE A5nxbEI3YwCvGKvl44ahxEbaYwNmCp7BN7cjnuU3Y9ETyw5AkuFMdiwTi2eLmYIz1oE1NnAz lBsbuMkuXUjFaRvswDSDa/F/oZ3+Y0g8mx3mTNOjiVP0iJLxhvvnYCVTOCdibJ1ZpEAgQxwb Wy+JM5GDFsS1XCI2oiVwd9mTzsS/wcSRTSXyhZyV1PJ6eHHFOLhxxXF+QA8HtDjo+4QgPQ9e ie64wznRWaqN++h/jv7n6b+2Ef6j6vZnc7nsWEwfH0kZcaOgpIxCIaVzReceU9XTwzHWLugB 24QxosdwN1vJZ+PDoP70jC02xYMLCT2XQwCeXb292czgbi2t78tuS2o54FPPbUPiIT5bLCjZ TGoihleGtZSegFJHjbiugJwwDJKmY0ktk4BOQGFpLC9PAny7g7T+nB1G1PLeYMLQUwkLk1Va LK3n8XTSE+4sWUifH0TJGzrDntO1BASZ4jC92A9xkdKjKdCU0Q+sx8PhCDzFN7R0RDpwX2+t gu9mKrHtd+3esmvnNgXfZI3Fbtm7MQsao2tp6FRToCimN0E9T2yjIY3ts/PFBAz4VXp3ym1x CAGpQEeYB3nHBnJQV5ByIOvFudbI5mP03xUHSjcAyJXYrb17tm7pje255Zbbe/bF9m3Z2tsT g7S5vE3q3oSS1MeRNUKEb+5iCkn5IJ80imaDgq+NQg88psR27omRYsWKeT2BKeIsxZhmFEaM hDICrasAug6pcoVsImaOL0pOj49CYZmMHi9gjerpkcJEXodnTJhKmFlSdhaQMKIcAJhX0no6 PjKh6ON6PAVp4+MasqyljEnoTIojHUqaVa+R1wqFCcybBOH0T0D/kuOqoeT1FJUOdato0AgL pECKFo/rIwXICVwrYzmjAP0652PYSKWUfgPSA6mIJQsJkZSkqZYK6puSZl06JBoZzI2AXECW GSJ2FNNpdPqGdNqEZUDOpo+e87zM0YFsbhioyWgZ7P2zI4Aphm9vZbIxGpgRFb4FrMTY/xhW Ax/tqQcYiGcKKSWeyubZCIXFIPFUTExPaAUNcvXn83zojKFAbu3duXVbrKOlzXpqb1lLc5BF ymL4W0TOfDb/zHDFSrNYSLOY51as9ArFLBFwidgWCT67RIWnM2mxKXGnd2NSrFCbLrPspVaI G5sz3KbCxGljtGMURaRAccAd9WyNhnO5FYZxNe4Kb+Abq5hrqN7e182/37gKZ/KbAyyMpV9s pf/BxwKBehDFywhhXfIKQph/nkYIac4gfAvMbxHCVPAcQsBwHuFbYa2G8G2wvkF4DczTEeIB xBGA74aSEcJCMoDwfTBPR7gS6ED4AUW5FiEsVK9HuBrm4QjXAG8ImxTlAwhhIh5C2ALzcoSw sGlDCOq0DuE6WN8h3ADzdIQbYX2BEBY42xHCQmQHwi6YdyPshvUfQlhQ7EMIE+2PINwC826E 2xTlXoTbFSWBcAesZxF+CNZ5CHth/YBwl6IUEO6BOTrCD8O6D+FeWB8gvF1RHkK4T1EeRXgH rPMQ3gnzfYQfgXUJwrthvYfwHljnIYSF0lMIP6ooX0GoKcozCPthXYcwDvN7hMOK8k2EKZjP I8zCug7hOKwHEE7AOgrhIUV5EeFvwjoP4QOwPkIIC9wfIISFyMsIj0D9I3wI6h/ho1D/CD8O 9Y8QFsDnED4G9Y8QFtwXEH4S6h/h70L9I8QDIVjv1n8G6h8hLIACCD8L9Y/wc1D/CD8P9Y/w Cah/hLAAvwEhHrjA+gnXz7iOqvsdoBfWy8tg3fMDhLAQehkh7iMgBA0/jRAWPGcQgqKfRQiL p3MIYWF4HuF1QC/CdwK9CK8HehHiAQXo7bL3AL0IbwB6Eb4f6EUIDW0FQlisXYvwRqAXYQjo RdgI+oowDPqKEBZ+IYStoK8I24APhO2grwhvAn1FCAvKboQfBH1FuBX0FWEP6CvCW0BfEd4K +opwJ+grwttAXxHuBn1F2Af6inA/6CvCg6CvCGOgrwjvBX1FmAB9RaiDviIcBH1FmAR9RWhA tSEcAn1FmAZ9RZgBfUU4AvqK8D7QV4Q50FeERdBXhGOgrwgnQV8R3g/6inAK9BXhx0BfET4M +orwEdBXhEdBXxEeB31F+Nugrwg/AfqK8FNQ/wg/rSj7j7565Fzg7H5QgRNnX8OF9+jXlijf /fbM+hehJmdWvcT3VWZWocbQCeb06Rn4rULNSWLc9CnyowYlsUucPkl+1KQkbiFPf4P8qFFJ 7GKnnyI/alYSt4CnT5AfNSyJx6vTh8mPmpbE48/pEfKjxiVxCT99L/lR85J4tDjdR37UwCQe 601vJj9qYhKPKafbyI8ambwX/Sr5UTOTyND0CvKjhibxqHFaIT9qahKPO6fP/xr9qLHJw8Q/ +VFzk48S/+RHDU6eIP7Jj5qcfJz4Jz9qdPIp4p/8qNnJZ4h/8qOGJ79B/JMfNT35LPFPftT4 5Enin/yo+ckXiX/yYwtIniL+yY8tIfky8U9+bBHJ08Q/+bFlJM8S/+THFpI8T/yTH1tK8g3i /1foxxaTxDFz+jT5seUk8Wh++hT5sQUlV6D/JPmxJSWvR/83yI8tKolbLNNPkR9bVjKE/hPk xxaWxC366cPkx5aWvAn9I+THFpfELarpe8mPLS+5A/195McWmOxD/2byY0tM4pHFdBv5D1P9 o18l/0NU/+hfQf5Hqf7Rr5D/Map/9J+/iP4TVP/EP/k/RfVP/JP/cap/4p/8T1D9E//kf4rq n/gn/1eo/ol/8j9D9U/8k//rVP/EP/m/QfVP/JP/m1T/xD/5n6X6J/7J/xzVP/FP/pNU/8Q/ +Z+n+if+yf8i1T/xT/6XqP6J/1+i/xTV/2LkH/zYEbT/9KNHf3jkzPm+fXuTuL+cxEOXD9+R LHx5aeDse0CJLhx9HfqX2/tQy5R7Hvz26n9Yohw70gs4Hj5ZWDxz6tjBi9/99tHXT/Af64uO Xbc8FQg8/NfFnceuC8DTscWQ+N3HC6uV41uXfhlDZt7BY4IPf7f4k2fxaAOSrDhybnlSuS8Q OIv1feT5FSg75cuI7Oi5g98+Psr7OvLgUYCy/1ncNaRAyH8dgOSBh5FJRPLLXxMSTH3i+DdX U3pX/hMWzrNREAnAmeLymWLg7K0wkcO8J4+eJP7MdKGz10G6F3ouYu4j55Ye77nQd7znjT7M s+T/LGJ5Hj5ZrJ/Go70TlOIcpDhPKX74qp0iMI2XTAAvFHq85yzFN56y45e+dvDo6xR3muKi fyXGbcE4onTiD8XwRgxfOlM8M1M8PVM8O1M8N1M8P1O8MFN84+wjGvKkAvGLGPFmbOCsykin MEyLYctZ2LGei0wGJv//5sv/q2X5P1OG/++X4P+UD//PVMr/mgF//l+V8P+qnP9/9eX/TFn+ f1yG/78swf/3ffj/asX8f8Sf/zMS/s/I+X/Dl/8fl+X/R378Mx7vkvL/MuP/L334/wMX/zPF V2aKL5siEPifKfjz/2MJ/z+W8B84e90vsJ+gov/DRbOT6Ll4ZOqiUrhhSEme3IWdNPzDFI8u dqXALmpIwahVizyZF7HM6m6W+TZp5kUYhd2xK/Nilvlenvmt0syLMepr3sxLko/uxrGNZ/4r N22UeQlGZdyZr8dO93meccUnFzljr+Gi+s9FO4JLlMvzO/+C8lw6tDS5OcWQvLDI0fdSuuvP PvkvqHfnD+Ng8Pqx/cuP9yyfgTHmgaWvNYC/5/yRmxSo/3eyvvrY/vOgc0dgrd2pFP/ptVM8 fvmzNPv9R/h39HWuxC/04AxJgRRHe84d6znH8GxFnOeOKUd7zh7rOXsYwkLoB22ATvpoz4Vj +y8cBz1aQfCNRStAy6G0174FZUNjnlFe++4JFFkD8vPV+7giYQmEl5Wx21PGOkkZjStAJSF8 pm2meBHRJT5O6HiJf3SClfdfT3BJT59jkv5z4vXhv37bp0469Hf/BSbvJckXeaW98DBXfnPw +9BjdsAKDLhZCLgWA/Y9wgMo/ai8SHPMvP7sD/8Z6+4C6zMCZn/R9V2r5b7tIbxpeWTqDWX8 gWM9b3T1rJgaA3j05J+dXrqkZ/nRnvOsBse3UY9ysS/5PznxTS9YSArbMdH4UqUYhPoHLeta XGznQQUr6P73HesJfLkZ1Aioh1hAcmxzYOb/0XYt4FFU138hQVaNNVawq0QJGG14tI08JA8e 4bEQ5OEkgRCRlxowBkSERCJCBMMia1ibVjZSJYBK1c/+P1sfQeUTGzAlQYMN1EKqPC0f3hDE KMFGBPY/59x7Z+bemckOC36f37Jz557zO697zp05d2MDi87W0mWtrqLhtd6TVFpU8K1mHSQe 4v0AQ49/Vr/RWaXpgJF0UmVT68UtE3Ar/B1jk7NQn92NjW19SeBAKAey62O2lyJ//l7Lt2rO G5IAp3CLZjLqcyf05DeOjXn+Ja3Qfupn58Lo5t5qzHeKn0efBtnkxefoHgkYvMxgmv9Urs9j i1XfJ3X9nsZPh/xjzAhPl/LkqSah02xwoT7YQXPWdOPMs2wwgw+68y+woV1avOV3uJsObVmj kUblX8MGr7Hi1/aUifhxQ/ziQM1xA2E8m/X3pwyDiWzwDTO3Prp0A9iQx2/SodMa09D3ZcZV k7EAr/i6vW+P5LZu6ud1RZ2ar8caiXMCG5GkuZ5dL9toZPgtsVyGzG/TW1S/DUG3FrpxRvOi cr2QG/z53go9JCfQW6lMz/WGW/30hHHjanNgP/SIENjnaGCf0+TZ/a1JnsXlOsvRIS0wC0dq uY1Hq9FGUaKNHtog2uieDUYbffq1vY2iSYoqUxmkG+DeofA6+FzYHTAW39h8jYpR2wnWH6hC Vwh8M9SoH0+BTkm4RLuoiAUucsUu5tZXYJjf7Nw0pgNdz8l43R3M7Mov/mu0OzQQppCb/sbp YEbpslhX4S2Y+yB3xrJJwU/pJG9rc1w5vQVasrtjtLtl3lZmsaLfoInb2JTV/4Apbn+1wga6 0+TRFGB7syED0EFdgGrgACzQ58j8t3ESE57dTGY3t7/l0ux9jtT+oLvxt2zPdo70+ImNlrb9 sjCquWs5G//TT3o2+pyN/We3xo+K2FaLA7WdkliKQleyzCjG/EPfYK5STVLgUn2Rc4GHT7We X73fGPKrWhrSvDEL2Z7i3Ny66K3L1edJdVgt09HXlXrdUH3UcrsP99kFND1uP9KxE0xT8uGT fHveAKPV3YMnad5USdxIotY18BepNk5Xbc6eNafkZK842beHy0VeUSkDvnx1mt+Xp36WGT79 PniVUuubpn7CoeTSbfAtVNif2roK7pJXn4/CHQPOLXXFluGXABKF3Iyk6J8BX+NZ4DgNueuf HCNPw8gzY4ywwchjGHkcI7ctYoxDFQ4xGs9EjLHEKUbu6YgxbnCsR0vEGG8HnepxKmKMiU4x Gpsjxjix1qkeTRFjrHKK0Xg8YoyejvU4FjHGR8851eNoxBhTnWLkHo4Y44c/OsKARwlfxmH2 OK4+l8QppHsxFIcudFyhWVMhveazGmIk8CDBqcUiAaRAhbQ9rBEEGUFBR8Yti5x4RqSBlKaQ GmsaZJhFtkg0kKIUUv6wSTB4Rk9QyCoZA/4hs8wY7BaTIovcLCkEeUohv26HEEXJIscekyRs AcJT8zTCSi7h+UAw+TA4BHlnkRmrYE50wAejSjb5xC+JcAo4bTZwStY5ZSAnBMsiXTinDMpp OeeUzGRqBk5TdU7BZE2ZU7rDs8jMYpEQsoNCelgRIk/NT7dLhLDkFULm2iGqzsoi3y2W0I4B 0TtWRIiGRB9KRLAoFVJCiWhFh+1lOV04aV53SaemYzH0CZob8Eu8F8hLaDsYl8CsRmp/D8sn hl1ScnyOji8lsapRn1hmBDbcV5dDqEAPyGRcwZ8fskeaLiAFtiUyLQMecGoQbKexD0THAry6 ec0k2zHUVAgP0lW5OV3bIaADZ5npYjKJn9PBPCVQSahsKhL9YtAlEYigN5he4MoiC54AQo9q 5EOSytQkMUXMJMBRySHnCtk1SKZMISf5NWiohKrAKKT/Uhs7xivkvYf0YG+0tCAikW7PMgsS SbBEKtg/n2AYsuBqisjWMfC239fQDtJbASNSYFsbs13ATX111MZXXYuYzd3UVx7uq0Skg1C3 9NXBQkaHJtMiVks/clxqvqp5nPlKDt8EapLBC41mzyHKInbtob5K59cYJKEqMAp5eomNHRMV cnU+t6OwFgLB/POibgo58qDNVMge4tQqbSo+CBa4GDZJXBNliEXVgm0y6ZIHWQ6AsueiOQC+ puGsko7NC4xxFQignMFZmrS9GpCTW1Nhls48m4xaZDSFFX4qxaf1V33YWVFu1uL+MlELKCIi l3fnSFrAe9l29UAjWutB7SvosXShqIdZgoVzwuvxwjOSNw7LXE7ODqtHHugR4ElI1gAWqyY7 XGSS6kclH5hQt8wWZQ+UGzEsKCwcmUliH5FwTss4v5itJZF2mZusm0nemS85oEVm/laezRpI 8EvR0yyTPpbX3hpYekXTB7S/JMRPi138BGilcHMkQyCVBXFf2rDnSIcGStxrh79B+TI6Ifdg p1l3u92HdrFMmkl6CWUim/womdesxrcPCG5sGqR+sp6XJneQlzG6CxKydxapKmTpkNhgZJM3 isKJkfiAjSNefFoK/1My6Tf3S44I7weMsjB+oEAR+uGlRaIfHpUi0azFg/dfjB9wXyv54TeL RD+YMLJJz8JwYmy6z8YP16+S/NAkk86+rx0/mHMpYjuuCUkPS5Kb4G+/L3wuneiTVvVxk/6z LromNF9MTcifJ60EkwQzZoXXY9VKyRnHZC6NM8PqMc+hP4TKkE1enSt5woS9fqaowdM0jiUd dpRKvjgq8+kSTodfsDeErqbH1fUg51o7v0j67CuQPGKSo36GuDSLYWnObr13xszpH/P3oHEq F/Li/kt8D7rhqZ//PWiqDcblfA+6b8XP/x50oVOMS3gP+gvHekT+HvSN5T//e9DRTjEu4T3o V0/+/O9BS5xiXMJ70Jsc6xH5e9AtJT//e9AspxiX8B701DKnehyIGOMZpxi5X0SMcbtjPfZH jLFjqVM9/h0xxgynGI17I8Y4+4RTPRoixqhwitG4O2KMfo71+DRijM+WONWjLmKMAqcYuTsj xrjCsR4fR4zx8uNO9dgeMcZQpxiNH0WM8UWxU4yKcBhROsa1K/9D+/942+/7vAIIPkcWDRVA UF/BCeCbSrCCvpNowDl1OL8Ov9fg/OoKrgR8CxX2wzMOVXCT3MB1gCvUAb4EkAZ0wH9BB2C+ wrW8IzzsNeCUejYF/y1aTs2wAv+In6UlrvX1CtEnbt+6CqFTdmYa25jDuNYpC2Xp75Q1Atop q5EIaKfsM50gyAgMnbLqR0Qa2il7wZqGdWDWSDS0UzbHLBjrlE2TMbA1cacZQ+6Unb5XIsRO 2flMe0LWKdsqEdJOWY1OWMklPB8Irq4wdMoG4NNddMAHo+rT0ab5kgjYKVti4LRa57SuwtAp O1HAOK2jnHI4p9UVhk5ZkgWnnzgnJtMmiVOMxAkKpkKOK+1wYjLlSJx2PCzJtB84rdc5BVdr Bha6dy9Nk0TA7t0DVoRi9y5fIqTdu962iNiI6y+jYffuzN12aEh04V4JCbt31WYidbam1y6Z 6AAQldkQMZ3WSkSwEVNIjpV46Cotvu+V0fYC4c2Weu03xndPGbEBCI9NtEdERbJI01QJcTcQ /sWKkCGiMlnkbxIhbAoUsrAdRFyRWWSxjFgHhCntIVLCoTLiTiB06YR4w+9rDbKXgyzSaQDE ZpHz98BUt7Z0i3F6C5temU+XWANlXsF+WxSb73K50wtcCjk0g+Hn0rXyJmeXj+y2ZTCxg8mU EY3WmCzi4xOTcWJVIptY6aEC7kVEN0eM0RDncUQ3RRzMGQGhUgo/vXK1DIM3SG1BsMXyR9kb JLzMITU5jB4QlSmkcQq7BlGVUBWoTjbyScV0EMxH3pwiOelj4L92vGbrqrYgLVKVVO7oQJBq g3GA5n421yhtIJiouXU3t8zcXKOA2eR6lCWGKczskEPyprNpqBfd8CjkCl0avOH3neSed0ue j+KiuKk6HvQ84Z5PpJLvxHvJZs8f4+kmmYr57hTGLlHyfK7k+TI+MZd6Pp97vpgKWIeIq82e XygkuGwygjMqlj2PsUxWPcI8j5c55JNJjD6fev7QZNHzoDr5M5/koYNgPvLuZNHWsPFT6/9d prfgNOSuecQYcnQPp5C5xulSkH4530zRCTZMChlgh/KaFQ38KV11/dvRLLLE6Qw09WP1yMHI 5hyvgrtvjrXh2MOSYwzQLDFwxOjkHK+Fu9PGiuZwVetM6x+2YnodkN1mJ8g6Kxr4i7oK+S7D hibPEucGoNlmR5NkiXMj0Pgz7D384zwrqG5AlpVhY6db0P8SUzhdwJlutmQaD2Tnxxjc+ZGB 6a1w9/AYG+2yLDneBjR/GcNetMO+nv2OA/f4USWdm47T3yLhEwC/V4P3rmYPBK7mPepzBnxN w1lFOZZ22jPXKEBZEAj8DduPdOzQ4N++/eiVZcEafWT7kc6BaHeUt6+65qh0zZlmnUoiZLl1 tEt/vgm5mnqrn6Aj0Hdgz1moD55pWt3dRftwtAjEfIn3tNMrmGTJ6YIoQy6n5MYzTa/lGhON 4b764NJntJzaj7WD5BeQAts8Ffy8S4V+pomxN56T+SZTSONVyZwuo0I/0yTTxWSSKk6HyTRQ mcvTP0vvBl3EM03rsbx5WFY2qkxNkqwYdxg5JJFfJ9Ms7uHXLGGDUcjMKTZ2jFfIf0fpjwDt +WrMQza+YmeafsqxwVAf5p4cJfvqSDtIB/Pb99VRG18NV9r31TEbX12pOPaVeKapZZKNr9iZ pvwJoq+WThR9NW+i6CswCnlnso0dExUyaCS3o7AWePNX100hMXZTaX/VOPXoCJvsN+lBIfux oyhG0ldHsCTIE105feuRhrO0vi+LK36mCWZQPqb+dU2Foe+7YKLRFFb4c0YIOUnq+1Itnp0j akHPvBi5HBkuaYE90/b0oGeaLPWg9hX0eH2CqIdZgg3Dw+uxc7akxwGZiye8Hti/DjA9TBrA YrXwRCY5Pl7SwIR9IF3UQO5fUx06SjrAg6LIZ1L6ZdHB5IVM0lPSwYztcaTD0DxJh8Myn/Jh YXXIC6uDJj09W5Y3TpLehDp1mCg9O1vGY9ZMYbGgMsm7GRLOaRnn7aFaMm+XuSnKM8kUiTk9 W2ZkPnmoTS6qu1+K/maZ9Kah7eUi4UyTvo5b7NZxgD1rcyRDKPEtEz3TBDcMZ5ryxTNNu3kK Y4/nlWMlC5jUeG6IuM0ynmnSzO2uEM+WGapoFrlnIitLtH6aMbLJxLvDiVE/2MYRw+6Twv+U TPqHwZIjwvuBni1r3w8UKEI/eCeIfugqh7lJi6sHX4wf2NkywQ97xot+MGFkk50TwokxKs3G D+/NlBbEfpn0yrT2/bCN+6HKwXqo1NfDftkPeOHfseerDjvKAuiTOnh4qLNzRzbZMs7ojhyy arQUjyZllqaK7khiDRCHa8I7TloTMkA2SZVrnEmG91NsfNFnhrQm/i2TLku5aF/YrwndFxTo 0nzR+y7RF2dHSTFpUqYl2bEvrNbFB2OldSEDZJM37wonQ99kG19snCb5okkm/W5QO74w7/Xo GT+ne9YPR0qSm+DfHhR+r/fFvdLiPm7SX1Yi/J61+WL2rK0jpNVgkuDEneH1+KWkh/wMppC8 O53t9xz4Q9gxZZN+kgZm7ERJA+v93sSpki+Oynw2DbxYHWx9Iekwf7jkBRN23kAnOjxzj6TD XtP+fcDFxhOuSet4ovtKIZ42p0uamCR4YUD4eNqRK8VTg8yly0XrgXneZl2cMelxYJgUVSYJ 9vYPr8fZKZI/dstcxve/jP6gj2uCHl0kPcwSXOVAj36SHtDZEbms7HcZ/UEf2QQ9xg+V/GGS YES/8HoU5Ej+qJO5fHjH5Vwfh016rBwi+cMkwZI7wuvx8mTJHztlLq1Jl9MfZj0+HCz5wyTB 20kWevD3ggc4KrbnzM8l+KIvdzB7YSe9IKRNOvOStGzY9eeplTXsojhT9vaQN+wCuZSpvDPH V4efpTEi2ryr5M07c3qjbTmphfdXnhSLqQxPprHrfLoVG5fKrvHN5BTyqxTxhSFYi9yeKkXO x7LF4X+OaNuTDXiofvK6QUufSmX60f5sIFHTT04XaI6/c1FYr/ZB3KSZerXvyzl0uyzxxN/K L4wbnQTGsNT2A0OORcvAuGmYGBgnUiIIjKoUu8CQ17VlYFQMFQNjTooYGP2SxcC4cKcYGGAt ck2yFBgfyWb+uq/NJnpqppQPK2TS/7Mj7R6GlPVx59nRH1bC0NOebl87+o3h6Gl/92QfLcLM K8YKFfu+W/rYoPYKi4o94McMqKaot0LF3nC6Heo7d4dDxSaxy45+UTh62jCu7m1D3z8sPjaP l9vRn54YDh8byel29O+Eo6cdZVfvi7Q6dpo/6WWDOiQsKracn+lliDB56VmhYit6kh1q7YRw qNiW7tLLXN957/la3ntuyvqK9m7rKvT+dF0F60+zurzLYn8xQhBC6BSz3nFdhdQ79u+ImtxX zB0LEpmM9UYZ67mMdVTGAtZfbtBkpMdl2TuTq9ixWVdzjfG9iWVHsWy80FGsZHWhLFjvQP7t URP6lgUbTPsf6PFZWaBe5NDFTY8NdNhBxdd2Sn/sb8zZOWRrijFdR2rbSb9mu6sGasW6C8Lv 7lacTIb/ycntm1RtvHFlk+P93hb/5FYoTd5GhWSNi6LRp17WKWSk4fJ9hQwwXL6ukNvGsQPP +SH88V4ILKR/+n3w/wOo9U0L8TPW8E07Mw03yVd38XPfIX7uO4S/3QvR0874L577PofnvpG5 /skhAI6dLQ8JZ8sBo8QGI49h5HGM3LMRY9zkFKPxfxFjbBnrVI8zEWNkOcPAxBBd5nWXVrtD C6JDSepX/FcN3lbcP4zleQIuqfsUUpyg5zZK7eHUpdWxAoMbJQa5eCx9kIlBos4gXmDQmCFJ 8D8Y/eFWmUGyziBJYPC8xACsqpAqkUGsbgBR/ntEalhbS0ykXPtYWftuErW6FAebqBN1alH1 g2NEanXlXugpUyfr1KLeGyVqdaFXa9SgCJ+4YUyUNlqnjhIcXW0YfR/sjqMLDaOvq6N1ODpt jJZPqHmZm5i7Wdiw2YwVw2FChIo85NU31VCtSTIWK8o+OJppwughTanaKqSlB27OtaF41WbS kJpJPxGGFLK1B6tasJpYfxG+pnk9JZ2apsGftz4ZHaqiKas1VNRCkmlH8mBl7Bn60BWoa6Vb /aou6kioCsbVSn6Or1GtUVpyB6sFBtHV9dND77xacso9a+I0wIITqtcnHDNwhcTs6yQrZqr5 DsWHk+yMidkLlsxU9/whnpUwNKWrKaiWsHLd7LBXwZpSEtX8aDk9qBOSuJMPRmFosdS3Y/tX 0WqdVWU4GNfRhuJ5IwUMKm6NhIvS7CuHP/bJbiihgfAHp8myYfjXZ3fR+krUBwWyc511ff1+ pFBf/ztSqK+fjxTq6z9GsmSciL9eSsBmg/7p98Xjj57itB9WxZ031Fe4SZ7iLOL576ri8ddE cezXRHH8d1XrsPbFIXP9k0MkaBAJwm+3EOMWG4wEhpHAMTxtEWNsHeEQY92ZiDFynGG0U/sy sETMGMHSTgZNaYn4E6ylNzuofZTBzRKDdVj70kwMLGofZXBguMjAg7/POhvnoPZRBi9KDNbh 6Adx4WofpZ4uUkPcl5hILWofpe4uUavLJN1EbVH7KPXRdJFaXVUdTdQWtY9SvyJRq4uwpptY ++jEl9PF2peMo2vSxdqXiKOPpYu1D1MHmZWu1751Bjcxd7OwYbMZK4bDhIDa98ZrrPapKQ0I yrwens/eGxZFi0/uGfbqSZrwKp8wi08AZMOEIj4h32ZCHp+wgE8AFQwT+vMJxTYTevIJyzWI M8KE74ayCattJhzhE8pxAibnXENyPpLCkjP9+8vZK05OGqgm6NueExO06hq/d3MZ/uf3bqr1 rsdHlmXrQ4W3Yj4t2kQGUqiAdxNkB++mgHe9mhfUKUWHVK+pRcrvXV+G/yGHzZTD5lDhAnjH 7t3k9629ABkJPv0++J+L1frWXOAPR/AtVHgH5iO4R3YOYfkIrjAfwZcAkkA+wn/VnAfipKM4 m0GczaGi5wK+1fsAYw3i6Z8cda2GCt9C166sYs/X5ZoWsgoo/8p9wGkl8l6+Dzgt3cczKnzj 8sM9cgWXH65QfvgSQBKQH/9F+dmPYY0qlFO1+W9gqeZrmeZUaN8EfDRp+xdIsxQl0z+5fCs1 +VbK8s0ZbC3fSibfSiafr3jPxSDwmoIYHZ1itH0WMcaGNKd61EeMkeoMA7NZfj3kN3eaYW+P Iz+k6iMZOHLMMJKMI3v5iG2NbfwEa1kqS9R4SYNAIZ4bHNRYyuADiQH4WCH7uzqosZRBsSzB ZzBaYWJgUWMpg0GyBGiAyV3D1VhK/WOKSE2N/isTtUWZpQzelxhQH+3r4qDSUgaLJQbUpUET A4tiSxncKTGgETBJY8CU4tN/l6KVUSqs+uDw/8xdD3hU1ZWfmUySESckxAESwRr+SAGxQUFM /2lQn0YlMhAn0MIoIGhq1SLNrP8SiSZ8ZnaMTVVWbKXLumXNbm3dYqnx+8q36GITlW6DjTZC RqJiveNEnEAkA4TM3nPOve/dN+9NwLbffvvJF2fevfecc8/9nXPPufe+uVgwQSmooIJ2LDhV ZhSUUUEbFhxSCsBRSu2LURRoEKgSjQRRwVQIBVNw6U6cgjvQImR+Ap/hPaD/oO9KakoSnLhM 9J1oB9rIoOSktvgckWo2KTSb3hXrs1AzBfe5WOk+Z6IribqyyGdTGgQzFXKJFYo8q4kIPkvu XK61wmfKbSe7RG5LLhtz25WlIrdNvCly27Y3Rd43+CbkffC8ZTOokEjped9zU0XeR32HIOuf C4300ZYMDEgamRXpZDCrDZyOEoxwGqVxVko8pT37tDLttVDqmGKhxPPZV8eJ0ZQIkfjIF5Oh I/b4CK11jzbeb9CZWRtZIpuhinmtuMl4IlehAeqwCq2IXMV8JpFPg5ihAhNiYstSeCZWxQ3N 65Cb34W5OUBbYchKLhVpdp1BP/mmnpinV3eq1WVWLupL7cUjugxwc4hVz7mx34r38UbT775W fNdnVAWsma+I0+J7HTcvFPlP03zefFNvsqy9aXS4dO1+J4W/z+e+YyZVkiFtXindPAaXdLbK 39J7gUvCFjdDVOvj4bFccHh4HnIM75ZLDuuNB5ClhDfdlEqJn6Kob2sJbcF6zXhDGBf48Lm0 ja01+1u23pcShzprcIlrcirk9bOmIrHRjUtU3DVTJVm8rkjAC57D+fdz5cY2fK9mmijXtsDv cePehRtcQmonyMWqLxTF7ZRHLhhrzA7LcVHbr4u/CyRo2SmlNDoxS+lEkDrYlgqVoHyvTxRl bZAsouBU8MJEnXMV+6RYl7KaPTFR7cIytkBITRpI7QSJ2NbZar9R8w/koewRbXp40yIQchf8 ddaOpw+u/Ca8tPhlsR/W727ZCo0pwayRaiXpxkoZakit1xTL4wbITh8qSFm1ZmU83pkgetLM WxUUqz3B+7iw2Bu/tBVf19f5czpL2TMTVCbiErm9RdQiC3Mcj9hqes3t0POtnwMyd24CZJbQ LhHtIzhrq8SHjWPpg6P2gli5S25NcIVMc8ovWflNl8CVt1NcdE46onnB34MEEy5GRMdyXDTX uluCDK8HIgsYmot7fxiOeMGz42B8oD/l/cBlgj8qT3w4K+1SnhTB2LNfKE8mgw7ZM/KJ9w4n AoxXE2DyS81VsWV4w9VMuBDUGJvNYkxRrLnGW4U/wfWKIomnkLeKXTUhfaAupoGKjXMq+piL RTlzSR/HHFIfW4kTqoRIsA9KLVrhvXmr1KQV3uNXStO18nypSStcc5tLTVrh2m0s1bXiIi20 C61sQUZCiip2+UlSjPAewR6cA5jUivKuZdMk0gpXoZC4inl8Asx0l+h54wmKgENwjhyEeE9T dVVjfwGb14g3TeItX3RpYWtj/WDWQzmxX9PZe85yEA/eeritfo1WFYJwh2Mk0B/+7/C7Sg1u SMupRjjIwqH+qMb2xw72HduTzTFtIrTwtITOtyHUcEgb2dswXL4hOz4G5jYtgRONNshnhWtp zo1oiZZ1yRU3B+kuKrpXilsAu+ERXB+JBCaHtb5w4BC3ukhgeljrCQd65STw/YvESkZzWGuK 4L+w1sCn0JRcF4BPqdrZ4m6vBvZ12aIB1z4aWrAupvE4GfTwEBv9cR0urBt/ga7WROsITana qYJebE4aPa0JMv8mXEtJjpwBpem6bFsz08Lpio1gvjLHSDZ78Mk65UknPqlSnrTjk4XKkzZ8 UiqfZMzQlmO9ZXNEKI5fJc9Q7hlkaERgQhoBEnG+hYBNhkYE3rnQTIB6dDTnDDI0IvBUGgFS wA6VAF3ISykINbolrRFpv97cCO7yjWg9kUDvw0f4gDYs9cvmJebmgNaFOSJ+rkvJuK5O7P98 r1X0A8vI6PQBIdRACAbLB7UF7tT8AsnmldkmNoFmnQIGav+TLQLdOtr3aWk1uGOMm6K48nKn yO+IUHjToVNi4u2E33wZoS87yyAA3DpzhE5cEhRaNhURTmZL7ymGuGWTBwsuVwraqSCJWwkX KAVtQslY4KUCnqfhyhg7ZTQSRAVTmv6DSXC+XAczlZGqZicKxDRfZqeaZeyJsWIygu7BLwzA 5km9fEj63JwckWYrVfqg26TS2MsjMnew0esEXa+7mNDoTuhHy1aPrRILZ1mUiJ1ix2dalIjd Yn0zLUrE/rCOmSYlViiNdE0VieEYwUkM747G95lMetyRL/RIA2DR4/V5QmU0TpvLUukqq8gy q6wXNkLFO4jobqUMbMJxEKEALuWMrXFRrjOaXr12I7Tpq2IpvQs3zvDv5m7YPqNJy07EJdQm jG3CO6F2FFvK+fDeDMxm/hXMBmeMwkyZMy+Q94932iLxYpdZrVHaX7bT1xOYl585Dv9xRgYc 3jMjAw6Xz8iAwytmfFkctgza4nB23ug4fG3M6XC422HFoZ2+9P14K4lZF8jMN6WnxTUjxn68 tUWu2kJm/qKJ7pf1/fiaESM//ux8ukpbnHqju8N5jMTm3g+hEdwFGoLLP+MzMY7yRvzuiCNS 6Qk7w0vc+N0bKffAg4We8BIeq3mCmGdXwWWy/TxyjQQh3o5m9Tqik+DDVZ7eck90BSzGVbGX phNIe/T8HNv9Rm23yqM3LJHtHrS0a+yfyervQ5Gj5Z73Dr/3hsA5R3ltVnxKayTgibosz89q 5Q1irdmwo+K1NnTFr4bnDku7i4BehwuGtONKN74XWenpWIiXsXYs9OIDTviybHpnJF0oMj53 fA3cseq1L7sGy0DsKz29FZ5oMAlfKz1RZy8MSHQ5/5uMBIblYDTS9b6rphEUOPdX3HDuJhPv B4i3w1KUHb+FxlppB94pO36twACo8kuI9Iepukgz3OKOWXuZbkyTCdi64mUKT+BWbOgFv3/H IxitNRjtyhJ9t+vfg9APJGDu362WfmcajzPu+74pukg84BB9t5EpBhcp28gUSzgIm3Ztuh3p uKU2v6Pn1nFaiJIn9DIP5lqyCGr2RbVkVEtIahrH+jiux0QkMCh7Fh9r7inPw6Jan2IgTj5m vojWF+EJlXQM8ULULaR1+jOhol+V6CrKden2Yjdut2cYt8Vi3M4cNxVm4FxoiNDkdJj5E61V Z4yLPh0XFTowpCoUYLSfr7PEdQkbnndmss+qDPb5TcM+pW1k7vNlhgCtDts+L7LjcZnqA07D ovsrkkUcjhzW7P2ZG3+2rWGxx1PjgIuiZ9fCNOzzs4d/iEEZrg2x2lAqpdwpvn0D+HU7VdAY W2ScRjFNzTadz2sq+fGcfKsZR8p43mHjkwnTfr3f6802NRdtSrURw0JUpO85T1d5yDWab7b6 Qc2E57lpel9v1vtKg0+eaxQ/eG8Ge7L6f10HV6tMhStBsK/Xwa7qQQj01mRdoLp0+/rr7Ht0 fcw1qaPS4D7isPhgwvrKL9vfuaN0t3eSzrDFYW/bFTb9ma/ga9QO1U2yt6s+He9vrxd2NWu9 AvzJG3S74nGWjy36gYyzIoGCqKPXxTuICXnCz4okDywr9/ReCZMFCtCfCjHa2YQ9CqhWQpHY a26HiOGms8TdgnZBJOCjc0PY5V4tQXRgdZLtOFdyARZQ1IcsYKGEGFWxb6SxkPJPZ4/drcgv efjSedwoefgy83i32J6Hj82826yjNR5FSUeL05Q01U5H9xdn0NHeuzLoaJ0q/+PFqo7W2co/ IYP801nNXbY60hIQWBtMZhXrSuJFJXY8dhTZ8AD/nH2X1T9DmOyOL7D1pRBXTxab8fAfQDpA xGPPU9xWYBNzX4rPz4DWWYLWCqJliQsKTfTh2YIMs7srXmfhaY7dCRRjxHRAILgeIGKOo7Jr c2P/6iLfAw4jrLEwj4RwlpCDgkveWjIcGI7dJ+OgDDHH5UCnwNaHTpPzM8h1vccQDKVMxM5z 2eQ6ku430uiSvqbb0uMdRYJ7nbqsdvJcgWUZdDhV1yFRS5P1Hmfm2PfnGLPY6iDWLONfRWZu Yl7xjWHEmjR5eh7VgizGGJgkMY8ttVdi5NxYh5hXqD2MZ+w3jlH1knGcJIDi/2DF++n1Rk2/ mRkfJQZfc1vJFz1CEs5HydV88mOp0HAqlAT7+ncf2hefft7Q9y7BD5yqAT9Avkyo8G/yCQuJ T+yXMIfCgJkbZMcnYZxnapNHbeJ1Sn1AsTs+W8RUvZVJxYNf7FOdKxSx+Azlm17RY1QkEul+ Hrj/6BxVM61CLx/fjv4R/S/pxZdJL74z0cusc768Xr4oHFUvvnS9FJ+jTpq6XnwWvSQK9YqZ 9XJvoZ1e/nAb4iVTXK9i3xzXl/hlnPPp7Up48+3vQVyfybfdRjZhE+MtMizgEtWWNqjm4CnM ZA4/GUfD0Sb8ewb+ayy+VVN4O1TWXBAT78fGZeL9FcF7js7bzuY3ZsgXb7fzzRadbPBkVMrR gkyCbSogwZ50ps/B6eswNnLdKuQ6Q11doki0OqNER/NJIqfNfEXz3NovqwuVMcvPxPgBwbjZ YRkjPfew9LXCpPAMna3NyDOHeMYntqb5gc/G2vnuMrbwVjwpJ49IQkj4yNgseYogFSpgn+eL w1CbdsPOtKdmlW6Fa9cqVvjyOvnbj3iqhBP6l7HGLrAg3+Nn0yR5OHbDa8UV+pfgPgKeq+Al x42SkDs+wVT2RgxZx7vSqL+eZ6a+WqFeQfsd+k+ZJP4LfkZk8QlMmegIBm9RqnB1xX0Kz/ME z3akw/A8xa48mZKpeq1gsdXGnAhhAcQNtvO5WaOFtyoaXbeW7p6Vp3SW5Fn02elnf/KKHtNB GvZT0jrv70qqSRjBUyjPy7riqNjTsi7X79fkGVyl/r1p9asYaeDfTOd1oWZlWs1YnpTiNlmX ImB9Lxtkn5gm+0t5o8jD639ytrl+5BOS52e0/yTOuMzy2o1JEQuswn0CHhDSfMxtKawNwgBs 4gOAigY7qpkLI9G+CmER3u1n9auRizxhwjFen8h9CP1DIksbzP+tI6z1A5kwkoFZELJy73Nu D9G6c7VOa5/xcQaR5bNpyhF/Qebz1OIO5F4g9zjK2DO3iD1zjsN9Y+xw8NYYXTccMOwpr1Tl FFwS0yH24ioFYq41Yu+OO5rUev6PxzIkFrobeuxOzWX3y6d9KEWfn31OUsASsNlxZsfH4Xmc PtwU0Q7RpggshVL2o1jPxjHqSLWKc0hF7Bc385Gq9ESckSVukSYt9ESWeIkAZKo8Es/u4X16 /zisvPJ/oUPhnvARWnaTm1RRJ6TNRZGgV+5gEfrCWeEqLNdY72pYzeF6g1NCch9qzs2YO0ez 3mPvvxqdhFtPDtHdqzz4cIVHbELJNsmgtc3es0Zvs0dpExNttqhtYtY2rTZt1mZuw5XNgkE4 1TVMp7qSTpmfJOESCvSrEW04/0UwBjAJDsaPsHw4vNvYYysOGvhb4lFXPxxRV9q86cW5jo9L fIyIfXB/oU9sOuB8Bmt9yl5DnojfosGe+BiR//DPUa2HcCgBc6NHBYzoX/1Ks10f0ArEb5uQ QbNvBYU1SV/gYdfxNgc0r6h3QPOIT6zAXJfrfC2bvBL3seW1I6CDYK4QhMf2nR3aHiceuSpw 3O/lX+ggWudQkYSdPGUmtk3poFmET0V9Tm6gd3J7aliVu5H7L/gfaErrMbSTHf8qjgecBApr XeFAt7QmotIVCXQTAzq+CB6BfeyR/nes2RI7NEjcITbb+02tk49/YfgYGFQlaLpF28uH/1CH 1kVVu6HHogXKINpMhTZdvZV8SLsQFV1+djBHnDADEu+0SrnQ4uv3OELlMIzBNgGiRuMWFzhC OTZHOK8t/ir2zlExI7fRjLzuA+GxdBhcmyNhkLbutZat/65lrH6d/f97rL6e+389VvOy/4ax WuNWxmrWEfNYvXIwfax+6rYbK5jTXl8uf9MNm26QFWEx5eEPU6nURjkWGDiIJ6BIVe1KXnE2 7zf6ma54DrqOLt5zXLcxjxLs/2O9TlGvM6p1oqPRx2R7tjImjDTcj+fqjJ69mmUXZ5Swz5aR P8IJR0hNS30ewpR8KCYzPg1Z8mAPrDVxD5oTxYVrlDbJc3jDh5WxTQqfNA7mibJPTpQyoILl XQwa/smlBA0edjKKoyemxnV90SLOmFalyacrkpKvHxup9IrlL5h0cc7hc/ieBvZJNZyLZzUn pxSX1xRddPVNeLY+iudv4CiPHrIXukQ449ZjmZQTHwnzbOWYPOehnNgacY67JQTIxOhkz76+ cj/z4ckuL/50t/xVK0BqO5Lx4onqYDP+yBgdLHeLljCSS9l4zADksW8EwZ47Uuxtoqr/BviM wwLqzf5qdvHnCu55J5xREcztSSFE8BULZKoK+v2kvaD5iqCBNoyVFflCx3VeVaxdleIlPDPv FpKj6sp6pQGC2X644Nwrai66anJcnmnf7hBnOo0Wl7sE1PObnoSjQ1pP77ounHz7esF8wHai 2YxjKH3sO7QesoxeSKYgEmRqLmvyZokrlAj9UYe0HDqfTXM54ebFm+xws/2IBTf7U6503HTQ ozTc3GyLG47FY/aj8TBSyQgbMSoHh2xR8+yQGTWJuDJeJ/vNqHlr/2lR42cLMoi5f8RlAxoh 3cIhBTNN/YoMG09YMOPePypm7kFGJsyMceiYeTozZhJ/T8xUoRTpmOFz/nxWtxRjYitqfpCQ qGkJ9MBf1M2P4ZTiHvqtikAnPdNOklZ456rYTThmXn3HS/LxZeKTa8tn4ISVz/hTCp/+Ty18 8B0FOMfDnl9ChydhwcJN72Gh9+DzZXcq1IX4+fOwinfVEnYNS+PQp254L2XYbDIcRU9JEk+J c4r1Tzlqc2LXSZtBqHKCJT1mqMpXdA5oe/QfEqRfYLpymHCpvJuT9SkBUCKIi1LeowcKu8RL PsZ7aVvpDTm3SrwCiX98UhCvIErw5tD2mLBEfOdK9LeaHflQHPUkpnh8ElgvZXVDwgTK6O20 tTEhHr1hA2oZeHdUk7j5pNkkeIshUiSYBBxe5QqFSCz2AppHZ++6bRhmdPVq2zAQ88g598GT Bq7T3gtr7K9l2xbLTdb6/ojW/3vtM+97d/WHtf4DwUH+QSyjWsoS/AO9uHRAG4w63v9A9xwc NttOSBhgeYJTUCrwwd5IFVqC7QjpNsIh19x3penge0oYSyRqGh71ePzsjzIShLBwP4bsmHbD 9pue7YEfGCwPueKV+JahThtenRsZVmjT+3iDgvYPj+gOrIo9JGlviQSeDWvt4cDvxK/JgDrn nHCZw03SJdrVY/j+540ILX0aefK4ZRppOC7NyilsAueRDdIm6tvMwIfhX3Tc8MahZsVCYF6Q 7yZ6BDjRnA8fVFFXxR4fSJtQuD8v9/Mp5boBdUqpZls/1rWxjLX9xTyl3NdttlPzG5+q0M1+ 9nRSCC3f+gRZtbY0QbWDylzCEvowV7ML/6La9TI2bVAYVo0+U7T9KYMhkbMYnxSGZLT41XHd kBpt5xZlUrg8aTUemQvWsrWLLIvb24dcxuK2l10pedWej51eIlfJwpXKKlnvjaZE5Y0hxbcm rxA4umFIgKYbY4/fa0+LOybkBaywTDpDsm+ndOlwUvAPlRqVdwtvffyYqCzzYL2yK+7m9J0N 9U87+OcS+cNLUGm39NPdKUfs3pRYk9cNDeagzxRDC+JidmCLILGUdQ0T2Pj4HtC69TBm1kdi 2MnKdhwQNuhRzrbAyt3A9eiuYF+cT+LldESafy+nI9LlXpqo8DhT6AYUNawNN9YPr6jN4X9T oY/gb37TIzLVSiC/N/XhgG/fooaNyTmhoJKPbTdVmigrBUNltkmW2BOvFAvTtGioZzPyWLs4 NwXuA45LsoLrBRZ8gJ8HjskhyY3tcKX9jgUMx6VfKHgrYCPHdGw/SjN2C7zkVUBrrwj/rC+E TXbS6Hj1pVkExaFBUdzmxzKfLOM+qHPQZWTm8w7oI1bNHvlQhA7wUhloZytWLYidEj5Nlxni X4MMyHz4C8Mepcxt+pt8gGq/lImjOtgpRcZSbhiXyNIeXWIs4v5nouQEfv2R/fpGTDXb94EQ +IVUqA0E7j9KAi+CbTxwsG5FbVwve4/qerGojWv1l0d1rZrVxgX88VGX3DOqYsPvKWq7QU41 zZHAY2GtIRxoUnhjLzjrJbassZRznmflLDVTpDJuVBm/3acyRvca3lxH80lUa4jiE1NoDWuo ULJ1PS+Bz1iFvqZ21uJf/Mx1ue0I6tJ4Hz09B7vwWhXkm49KkOfE9rnS8ALrwUdMGD93UMfL j9D6izoczgxgn3BkVLAPDWQG+4EBBezX9CjK23wwDez/OUDY8eFvtJiwvnnAhHXXUavsKVJ7 OuhXDIwG+m8PZAT91AEF9C1/VkDf+34a6IcSJPgK2ru2w313YlTc70xkxv0zif9l733gmyqv xvEkTdu0BBIwQoECAZm0FJUqEwIItJIUmIG0I4nOP3ObMNa926uQ26ojULyN9PZ6sZu67d32 bs6p073uHf4B0YG2laXVMa3olCnT6qremk4jdiXU2vzOOc9zk5s2Rbb3+/t9v9/fRz6flOTe 5895zjnPec45z3nOo2M/86s6DH75jTPh+yuydq3x/bLRPWvIceo7ll/RdfzaX8fg++xMf66e QOwUWJJUHUTekx8yLp/domfBpNCYFBoofoO/N7aMmAO4jpWuHhW7I/uLtESlZrYniet1abVu 6xAflFfzTUBazhenNIrF7tTO34L019npr57Vqa/j0k8Xrs7Yj2Dn9OVLk0m+zPV/QKNIRaLz o4H4qpe9kq6OSwJuQGtWtjm2mJ8Lt6h/oDJmvs7TQEA+fMBIp22iWNV38STfYSc/Tc/3UHIB il1hK55wExaIYYtROBeHXPh07qot3wo6ZN03VOPVb1GzTtxW4j5gi9pWyfRibAQ0rXuS2r5n i+bnNKv/CWV++pfw8OZdm4aTH28WvcOGv3xnWNubMqvhzPe74L2ZCvD3V49+b9G/v2T0e2v6 /RJ1RiWac0eQrQ6g+vIkan2MLTLjOZmzOh1LiDFXuCGX21CNDljaBERvdCLDjwr20FN6r0ji aW3/QAscwHrpNnpJF47rHeDYxnPkS3mj9y+tWLpJ12MXwTEiVuxS8pXH/5rbUp3hpFnF9zDA VB1Vx0b7ukcwvUBsK5VJ6L03tGfPoUhB8IH+/QRpAOrj8bnYhWP0b0z3gzOW53Y4wvTII6k9 TWlVMqkWD7O49hb4B89lP+5XR44K5vLWWI5UaeV8lno+Dp4XKY+dS56OSvMllwMkdfkdlWb8 wviJNL7M/zej7NDmn/Y/a5OfAZQqLR2VpNlKXZq+iNvXID8EDAGJPBvyiAljaJyYMIXKYkuV 0LkGcak5NK7DhPVjpbgO50kVHKKzOioIolghFBJexzfWA4QMU3mrLAylZMGIPr6MzS+oz8eu 7DG3mMgJlcZW8PGKS3Pqtf7mY38V5thZ8LAuJldYYwUt+LVbBq03jxXK7JDh0W0BQylPXmWO 5bSUt2r4gWe58iorltVwaOXvrBm4FPtWgxlOmylX7nrmldk5BjlsAegjA6GJAfV3ML1WwRJw EYkaawDETvJVyX3wCygalE17wbpLwZG9/VTT38Om3Ux9sWM7Xanzohn0bdH9Y7IgDd5ibIMz TqhQfsQM+IgMCBZgoWuIfoncUK6YsAiTk4/gGb6A+u4skwFtmcOWWAHy+RDxbKAIGO8saEby OHFP3TOXYXaq4h4Ci83qqy1K1jmSR0HluLP1C3hYmCxZ3V51CqR7nTSsDneCyQrqALC/SG4h 6I6G5svrioAR5rG2E77aqcmtjuSLoLmBiTwE/00FURVzIPwwDqt4s9Ngu4v1Kl/dr+tTR6fz Wa+yYJXDaCgXar3RNPse63FJqsdpvMfQBDExCdhwCue/J2jUS8qfjXlasP8nUJzGSuRKJ8hK uXIuYo6BY9vf2VHppCFWzqUhPhuaBDySC7BLeZEkfhmS8qVOZVMfMUXLCDxtn0UQAwzzU5hx MjinpuAs1jCThyhBfiYMtOj56KJZxANQvUS+hRpqDc2U12BDU2pwp3B68npqRCMdzZerh1Lr mznVlDpTg2leCqYZDKbJqIoO+WqnaBDh+FhLiUy+/tXMz4Bn8mnhSbVz5cw0ghp4O07ZB5wa mspmDGvpaJaW9O2clWqnPNXOPNaOk7czfWQ7BZwfeHMZ+H5mBmM1vxUauiDV5BfYEGey+bzr OQMGkI01Ut183tWHSRl1rPwNbF+wRAZskQdwou1D1VG5y4ZKx9vxDjrcn4eykhIZ5NYXskcU OGOyPfT3YS7lOyrt7D/iUlk8jhkjKh2yeIS+FEExqlNpLqD/LNjoE/hdPFVQP5M1bxBg+bBP R9hn0t0+1HtdATwsJkTJ9ES62SJGbeK7cWlfH/zctQLhCE3s8NhnoHt5PZ51wfkkK/havMlu sEVc8FC+ySEd6seMEWuLJCUOX7ZsAaBApLL8K4fNwGmT5ENYq6PKju6ZXiPWo3Yw3OoQlpN2 Xwu1OnZfB39xTLKCbUobrDK1KW2wq19fCHJvN/pWg/IhfBhkhapVXwVUYM1UmUGmQ49FrP2O CtajiAde9hMWCZKBKqcx5JAVrNOB/Rlic7X3GU0ry0xa0/kgcTsiQ/B1FQFIdXfhjggqKh27 WlPfWsgrZTMkHyZP8PhpKfB247ESwknoYoXa8kmJXNwS8UnDu6Kd8CVQa5CpGKwmVCJqXkj2 wySOf2wouquTOIPySBA41H7ycerwwFRgj3bs5qit8dtGSouIXcmUH2ZXtADXEZnok4sM6uPf D9J3Qni1TEQNJo+yDqVdqJLK1A4ClImmLehGU986P4WrqhLx8NzMlragU0c9hGVYixULpE6x 9Tof/t1If1f7RmD/1UvSLYZQpU+IrTeOgFD1FGnUkHZhDDRPk5B8FF04qtWZ5g1H8tESfGaA Z1JVUfJRO/4anIW/ipOP3o2/hujX3OSjxfjrXfrl5PjBBhkOxahD6hh6Ihf6+fg+9ja2UDc/ gO8WpKmyWK1ZTuYPA7NarrAnu8pblfuOwa+0vgEWl06IzJyKeos1khTmb0GCoRJWASqG1IGE TQr55a29yAQd+ThhOqq4C9TesMQQylsFf4XBMoxEGopdq5j9BURarQl3gvHgQXmxcUBaKFeZ ZW8C9EI5aBbbLJK3X6m3SEIc5OvZsjfebJSF/qa8Cskb94CFt06IBaklGIQcxpbkKXK9GcpL XaVxl3uo/nbZOwSNyEJcCS3GhsC8BcF6NuKn2QQtNhkrsbWkt1/4EPQ+I9ROKJt6CBWabnC5 DheTinJAD9mLE7U8CRagwdZ4L0NJtbp7BV619h34K7kfQnez9ynJ+wC9cnbDw6givvwC7hrI 3oeqVby/BDFolz5q8j612ba/bbPkfkr2PlDN3gv8vVUcLttxljjssTViNs/eXCOXf+Lw/LAT JHvjxzjFb/s7zufhc2y399CXObbbXkeJ7z7gIwiO5mD6E1y5rpL9B6SuhqUp4pR2+X3qI2cD 8KznTz5lPTsU8dU0vO/Q06RwgP18RftJrR+wY+vO2A2RpK3xDgQzQp0/xjrPfcvAO1/hTwqP qe50Z3uydnYjPZXdj8nevcplFqPk3Ys5/CaBLrQkdh6Tj/B9QWx20rvXRqlU4ecMpcoCjBM1 m5DDoJlLilBEex8iDlE2/YzISuvkQ8aMdXLZZGRxRzTyC2jJwFLhG2jBxAcSpd6X9lGy/H1N 9LeR/m6njoU85RCCgPwgjOvIx0Wy9+cmmhHYiHI3FlZuhL/VikKJ/pXr2Q9qWPk39oPaV7aw H9SNch37Qb0p17IfDfTjKvZjO/3A/FrVTAEhhK+hfHALQFuIPGFAPwM9vXgaJwPzxQ9EkAeN wrYtBpLMezFbTu1ZirA3QMUXs0SgQLXqDvOtNKnZGGQGvczglhnEMoNVZlDKDD6ZQRZgbMBy xAFUwryO/NmIpJuMlJkXyqB+MRrD8l00vleAW4Wvs4T/yLLnDlAdY2hGkBr+wwSo3JGkKkH1 LBe0PB1abliBbppDWNQgnCNHGln1UP4BlMux3APUKTXFOgom99EtAkTvJEGTJGhY08l9WLSG upyDex/At3M5Fm2RB4knbY2/JH0KS5pskTtprcLKgMYC6NwW2UUssZfoFoK/zeJfgPGbCP3K Ha+9gJuXD8P3RrA8mk1NeZWexlZhIKhevxiB3UjGornZ0OSBNvGXdAJKFkkDsoK/mo1NpgqJ vlZCvfejlcnCKK50IaIHgj4PZp+UQP1RuQ8TSOnl/sYg0N6hCMmoO2l4+k9HjhxZL3WefK/t /RzF/ANja2lbQ9vCpgnSi5FnhXdl71wl/GbU/SaTRxsOYPGTb2WWtVHZv4HcJYlTiZQcLPPb JRBCJ4BA2qPSE5L/IdlfhKXGUXta0SLJ/5jsL86oXiz598p+p+6Z9GKZ1ykNNqw0hKxMPvB2 B2X3QznuAznux3JAbrcpGwvzJP/BZX7rzstx7fDbAcewCCCOpRPp7wCK/kexNKD/iftounqD bD1JvXcfVDbdm5I1CzNlzQsTc1Bd4hKmI9Kf+hYfZsmzxHCJQShQ7hpC6vpLZG9Jh5FcviBf QlPBHhJvNhtCdkWOvYBMhBm9AMd22V/SYXKSpdG7DBVb79xqgBz4tQj+d8D/dvjfWsOmu4Km gKT0IFuoBuwpChJ81zC+rJ8v34UvangWMYWAxEmcLFevWwTab6SP+NAe+04AfQaVOnVgAsFL yu42zN/lnws9F0PPRfC/A/63w//W6kBQbSa13Bkc0YvfkrxQHb5I6yW1xIMsEg/10WSuUghZ Pg4m6vkNyX0sqRs2goVx+2acTOViuUAvMJdotFGzxSB5HexuNmrvHFvjCYP2Y44tcoomrcql xXhuv3FNhp5LkW7sK2yV9xH2W2179qJIWWDbP1m6qwseue56Gf4K32o49CZCbGtEVTypYDVb YyN8r/LY9tsk5RjJASzbPKXpLizb1GX+xfKp9QViWzd/MaFJeQNfdNKLn6X6kLrE1m5XBMuE fiRTzrmGCDbxC9br1PocKNAQeYM9ekN75CyLYHXBARwx0GYMWdPsGFvLUSIsBEINtFtCyH7V o4loZWJQBsnb+7yBzvspWBGYUCrsvflT+lYjE00iAyELowsKHR+uLskbzOrJ+UyE2oFp5sgE Ai5NK6AuHeM726cRs3c+XVLkyNAoHWt8KdaLotSqVu+jpHZgde04G9hr3EVoXGARYh5rbDwW CqofX0jLIL1BnSTfF1R3f4jnb0qYBQYq4H2HNcHIfC0LdRN4wgTmKAsXd7h7cF4qW1fzo1I8 ZJoHUCviRy+Q4J8OU5A1LYOQMkr5AIhkFG8OwTSHyfoO5V+sddQaA+qJc4Dvb7TDD1NAfQd+ YNE1+DsnoP6ZfhfBb1h44JE5oLbTIycrkhtQH8H67bJ7gVSJT/IC6t3wRPHGU5XyA6pCj/pY JUtADdNvlf0uCKjf4Y3MhUZYpcKAejl/WAIPk8JCxd3jS9aZmdKhLnOg1tsddSeui7pPbYq6 B78edX8iRN1D34y6P10adQ+jfojz5CkScA6YEY8RPhyyEan+a0LbcfQbSB2KkIidDWzu8ncJ qxvCrxtCX016j4e+wuaM92XJ29Vsa/K+zmdEgex9GWcLPJ3Q5H2NP30aGlAqu13uLrAu3C83 uF//BTTF54T7NfjxGpsNpV3Cgs0d7gGA6xKyl4UC8RKiVmjCZtk9sBn9vepN85FDHKIxTwzH DaGJRFLSI85l640Y7oOlix6Tv98mhlVDqIAemMki6lY2HdbxlEPHU0+O444a9Lf2ooGK54MA wSXqASfgvQPmyHeVHQuVO04gSx0NzWgW8VuTZ6GyzqgEyklbwLW/klYgr5Wv4euzrspsBf+b 9BFbMQvT6226DTSEutO6wa4+XBnSEFvGpbykXhS1xQD7BGi08ECBIc/Q+yPUhlpBM46Qy8ln E9+Ou57flid1QqdRKGeSPhJP5dbnPvG/xtkkDhfUz4BmCzQX0xTxVF79OGmd5QCWihW2cDcT aj0Jmtwp/zhIMxpDyCq22ubGY/ktzF8MT4p3LUHIBId4o90A4zsaKgT7MU/ywaQsYrH/2IAX 9ySg+Dg2ULbeHIXSll1LyX2VfwCdV7F5IIsAK05owwz4sh54D9bp2ERmr1eCTJAri6S8jD0P 5m7MZ5CZCCgLAyo0njU6ifuLVmHTuQdmGnBrR9u/ANCwBofLlAEUr7+A1yfQZqF53OBCJXkm cXHDOqcxlg+wNHzdOZyxBzKJYOIIyoXuQaNGcTjCx/mmBRhFNMRIEhYmG9CxFpsmDeC+6xr2 NI89lagUOTV5PKjWxk+xjTuojaOhufItWFpZk5Sa8YuYMAn2GhWZpoNaoNFovtY0xwYsmjO0 cQ9yzA6zgS3FsfGIf5/6FcrvbMZQ2h8t4KaSoIKQUy8/H9r2kGMjebE6ocxEC8itB4nJQ2fx c+fJ5H70TTFNZUfIEHIontU+xbMRPtf51A+pmjVZt0A9UGwy4NzeC/8HZA9Zp4n0Hkja/53P 93WKUls7cgN3yY30Tdd/dlmxz6eTOR6oEHV/qK1WsN6X+a1tgybJf0Rxfyi5e3B/130cDyC5 u3AF8bZW02UFIPnxQKziPu5jUXgv+/CQFahDwRqKXUvg9jFFaJcPdLgPkmJxpew/iPPEMVHy d0rCgWXC4R0XyeGDxhekMOjyB5WNE4dQ0/c+Jhvl8F4pX+wYgjdi25DkfSzpPSD7D7v8B3a+ Kfs7ZfgVtkqO25Puw6L7oNmzTDgSLpO9rVBSirepuZKwV9y0dxa2Zd4le/e+pD5gFAq1ottf hz+2yL+hcho+DJNfMT8J+rrO55NC0Tl5iFMrIBR0DXtpu9TVljCxOzE+5JzK/O4NmX73WC76 E+y1TmVfA6guAZCCwyw0XP2PaVgSVZca9QZoRLkvNML3pt+LuieX+95CecyZQD4G/D2L+Rli U4LIe9TcnnnoZUKFaoC2qjYAO+Si3ukLqIUlGkMvhsrjAupvpxkN6Ek2axtEAXUH3SZtpY2z 0NNMB8M0C12xRwAvUlzbfsoC56CZrQZhexpU6AsBLeaAOghQn6qem4YS96e9XL8G5ATU94o1 MBcxMPNGg/nqHB2YT+nBfHgEjOn9HwAvvTkK5DtrKhcRmeUugnIUAwxlWHn16rN5SX25cSPb q5+mby+Nl7dzuMwJzQ6oS6cakRRfpVtgzD61Uvvy95NMNeZCYNRe2s9ydOLPkiTxFyuuNaiW dzFvMvnXQYjSc4nKIbYYaDVqPonDxMixVuWMGMPf+jhLj+q/eKz+m945bf/Q+Rt4jTV2PnLP stOUY9Boir0bZ+uoOk5HVd0+La07AqyPsVywN1ZZdLEJCADuOVdaaLdZ68+q49GAifbf+W4y sNeGoPpSCfpsnyhB7bWfuShdijAE1sNv/6T5LEvE8BCY27WTg+rGIiPuI6/G9SKAkAfVh+Pc 5qApNx9Alv39ya0L1LlTQG+Lwu+g+sUhSpWN2l3tlKA6AVpBTlU1fyRfNgnvo2TQL4xobtgV 0Qx4lSrNB/IMel4DOgUpLkKwro/mMZ8N6RNjO26w735ND03v/2M/4iKTbu1MvZtO7xxZ3yUN OZRwpWRW9rX7Tf7+x86M90E0zaQXQbiVD0idOsuutKth6TyhtGG7PTlPmAPa7ZN0wPf6pOvE tnGgnuZXVFW6Tmz9x1P4OJpPmEzQaFhMjNuJGkWH4RxS9rS4CfZsHn+Win9YpeOPiw3EH8od 5V3od+nDPSu8GUYRV3ah7m+VjIq4Ft9VmDHNSbVFEb9MP0H7s4pRe9SEaynLOjBEhiHwd1Cd jqa6uweZKRm6TtxZZAhdkzr0lWDlkJM+Rqe3+zhqFlVzaRIYg7hF0k0RkgnZexyM19c+ZQev wt2GUFHaHO+rCcpVRVhaBUZLCkOytwdKP6SVBktkFsDcbFruDJmXLxTyoFrUCEO7GgbQ+x7a G83idThMv6PJpMibcFze1krJfxgsi2mkn/pbccvkcJMRnrZWSN7D6F9U7vguYetYh/tlfosO jghxJxvodhoY2VQaWdcIDBxhGIgzDMSh3EdDWK5zFAaOEAbisrcTxnRsiI/pSAYGjqUw8DJh oF/2dkHp32Dp8MuGkFMRGxDSPDFq7sApZCgTrG3DJikeszP9229lec5RDj+ms9OK9Ps/wyaU 5/yuoKcRdCkcl8JDYthqYPEhSPSAeu4Q29dA0X+luMNhCPm5c0D2xyV/gi1lBhqwigP28AEH cAh9nOR+tQbWxE/4gMG+xOR+NaAxOrBUP5UaCgbUw5+gf6Rf2XR8DLi/8qkGtzEL3IUkM3vJ M03Qb/kkDf3XxB1AryuzQF/5yRlAX6qDfjJbb/gYivgY7GwMhs8aww+HaAygYzxJ8CMkDP58 KdG7IwX8f+Gt9UyaE+6Ls+O+cfAMoP/2oA73QQ54MXN2WnGa+fuhlBubSmiQa/uGevv+tU/0 fMOZXk5TAPdQb0uNoPcUghZnI/iquMNpCF3BRyCFOfh/OMVJlBV6wOfeU2nQp6esAj4EJ8e9 I1aQ4nsaThyGU3eKU6I7Yzx6fa+Qjac8qZN0AbWc4E4wuCdxwFCvYwizUA8J6AHPryPCdLpa uu3/HjSRfw1M8qPkH8P4F8onJqpGMWGu75PeKHtMvC0XpMq7GCR+EMW64Vqotho+c+Fjhk8P nnQ6ZQxZpHWOXgwLkG+5jHkSYvW0fwrvxknrimLf4vbvLT7mX4hd3qJ7Xxxbq73fSO+LY0v0 752xUu395fTeGSvS3gvj5FuuoodzYznSOhYIx5W8MWIvR/+fGa9Haz2PhCsfaHAttEXwmu7m CuPyG0OW5ZfbIvejldBmii1t6jJ3LS+ot9ieMiq+rthM+P308lz++9nYBHI059YX0e8HQfFq 6zYbgS2GKponNh4VWhsGtwtV9D20GtB8hs2dzZoDO6zbrCwysbaegc9EWOrPWTxOGJIWp0It dXrIrj5Dpg3164TJsLkjUkue6Y7Idaltkmv5N1yRaZuR7X+K4SKDkEd2atGTGP5ie7odnW9m FGuGzes2i4NJIUZ79nvOAZ3YtmdGPjUiF7D9ssiztsZCemSXFB9/gGEavWjVt8iHsJBMb+Ty 2GT0T96FZp0QbDi0AWEK7eBOfSsBhe+abU3KhrTv3ibTO3LtG7hrf3369UPcZUnWYuhBOWIl l/4G5r/foHPpr2eP1qdc+qVdwgR5H8IWm8n9kRH85WAAiy6DLbIUJmr5AEzNAJCi7BCiri1p kgbFt2cRRaQXX+pu+zAXkFZgfkLahxgnJ8ldrZtt+zs3SwrSYjNgJfIc3iPiYae64GvS0NsA /20WD9WyzQ58SORZQyjDnkrZ9334F5fdExm9fsB6fThFcLadLFeYxUSObfccaE/6S9lt4vYC mPRv0fza+pHJEBowGWb9w2T46oBJq1FtR5IaJVPv380p8q4mMOj9WoBqFY7s0GoG62toDACl j+ISiN5pbo/Kh1itVdnovTKD3pYMeq/MoLdlJL1XnIbeFqL3SkbclTp6r2CPVmTSm8FWbWbx dBH8ZWEPU/SmpRI4HzQHjlG7ZO89ituDdxEpBk3SK+K7s/AEd1L66KXWtveRFLPN3+9tz2H4 m5iqKRukyELcQovgzv8Cmf4bb3AWGL6QhD8S/eYkBOWSfvpqnYoSJwQtwL1GJYKHsnw1qlqA +9mLCMcL6P0S2lN04C5BeQ5O0DIKz8PHSMQSPiXPhqepTjSqwpSdS43YM0ntJFLPZaTOMzJS Y3J8xFDjP0hWWiTFTLVKqIVi+u5kZJ+eJnug4dB0IvtNyQiW8chU1LbfJR0i4hY0KdPTxC1Q NuioPi394rcZVP+NlGiITGfkna6j+DT2aJqe4gtkBmjF0MkumcZ7jlEysofjjOyJZOw9yu7z iuBjqxjBkVjZgIgtHMn0WBGEchAKMWcLl+8zZHpoe2qiYn5a2V7ZVcEHgXL8dVwTliUJcjn1 OHQezscs9fcroRH14TNOJhr1/g3nGIFczaCpVqeSyoIBKpEJGFWlA1JHZweHmXVES+DdfAn8 OiyBlbbI90n84VtTbDZYO+byo7GC5eXCbGZKmsM4v5XlpoyBGMGceWn5dmH1yKehi0neZGlH oHYWZWkHPjD3EdJzyguGpfJYRUtatGXKQJp4L8LE+4BNvIfT003BySZZYstIn6Brvswy/VcW wSnTljAtoxlku+3PQykcVaDTokyidTJ2Du5ZuQzbp5NUZPE4klFsM7NFE94mjaLbinkRyiJX 8TbdFtttf0vgZjq2odzXr3komV6bWqLNH6HF26cZcIq7z5d2J5VgA1erKQVG0yHBxAatt/xo c37V8jmhFTsLl+8PlQCWbbFLls8LlS6/KnR27CJ2TlmaWBYeUqqSdB+T+Jwx9kfxOVMsyte3 58yx34vPWWL72W/bU62ge5YPiK0nQUmsyxPDCaeQS14CWPK+Lz5nj92mbIrr4ud1ysbSuAn9 rPJiVGQBwqDqRbK0Y+C9OxFpFVzNtsZnQxdhFrVQgey2l8Zd7eHZTROSbouH639hS3N+U16V FLZgxE68F2M618S+J4cTJztw60Aop9pWpRLMaHvpR67O8JXRvHkeXUWsh4+ieYZeXI8ejOHJ PveoeudE8+aMrjeH6v0EeRL4Ran4FB3Wvd/nv7H4FCzcMDgntHhnfsPg/tDCWGHDICC9YfCq 0FzbU89x35hSQSjMFU85hXyeQRHQaQjZCJLcZYJ9W0407ypP+qepabIHJvdP6MlUeFLnQHzm L3NjUTS27WBpW9aj434xKn59I20l9GGVY52VUrgP94VdZWE76ifhoah7ULueF6w/yYVbOI8a +ZZrIXZpi3wHfpMfrfen7Oyo7anwJ2DjoloYuohHFk2wPQXcHQ9ZabPzBO7kgvHYxeNDQO7g YYyuWDHt/x2VwQRLMVMcmImmfeSoLWKgmM8hl7c//F3Z24dA2cQOsxS2x65pcn/isT2V0Lpe cJquzdC1Sddv0dh9hvIawoOG0JaG8CdX4fdP9guT4Mm8kLU5DyZPHvYaWwDP59HbOYITywuF zd5PmryDsXOlAfi21DsoWBCZlAMzPOQK94et8FwO9zXZgDX6sC2mN/DRTQGOk8MOyQZFovmG KiKNRSpPuvtxr/0TTyNog3gfIm+tAMprkQ59SGsbe7EjHwzKUhZ0tqknPQftwQDGBvDwCVLO I1cbKYTpW4hjwSIJCY8kgJURTkrhfkLpFzNQ2p9Gab9BKACUpvdvR9KzP43bfj0930d75Lom dxKms+2pTsnLOlrIO5qE9bN0lpV+2ftAqgwbQv6GcJLol9wvTIYn80AvEywYB2fBUTbnxcpo WkMBImRyjjANK8Irb7LJOxwDciWXeocFM6INiYU3P8uCwyXEw/NkISGH4yg4Fz0BtmNpHNrC /X3jGtkbl2EGmvdgtDNQEHQVbxJp9xOkHd4arabkuzUtFs+Jmfj5FKzt7pf8CQwPNONlPwZj HGxFdpSHfOHo61PPx3XIPVQah3WEJnl6juvOmv3xfXQf4Ck+xXxXqi26Opwas/oU3NB66xN9 Y/2pvZFUOyK0gxBYaQvh3EF2hFnnG3fq/f/vk19B6spxWzHzK4WGK14HYcSuLKJBwQgzg3gk f4/UAYu1axDkmAmWEtueEDxer3gTkrc7KHu7qxG5xuRC0WhWfwUajBGdMOR3AV3HnYganEl3 IlaCTlhhDmWh7amz4O41tNDpSmzLi2JwSELqUNYbJa8qxddHWnfeT/XHw3NWMroqiYVkbz8o fG5V2fTymL6m7/YS0WCIqYNzJDolPC5tlZfKfrtsApYpjeKwwvFtebI/TkPbEV6v+Ickfx/y exC9ylQWhmYyq50JHFqChpYw0Pk6GtpQ7Dzm78AZAeMbAikH4/Ml8bRwV2p8QzC+gFHy97Px /ZIagfENsZJsfEOY0taUxfek38fZo5q0s4B8gEhVvJvKKrtGDK4fBuftjxpxcP+2PohchRKN U+sfJ3FIQzSkIYLGQkOyoLwkAGfSzaD9deY1ktuSGouFjyXBxvJAqjbRysLGQul5TSRHLHRF WpE0EcnJt32Y/LtMN67975nofOjjTSj5VkjhxzrcdLiGvBlK+IgUPiidsj3dnunS+IC/7pbC B7K9zkQVnhcRDgdgmmQE01lXgdZzOKi+lGSbs9bIgODAzbLdtwEwGOYEEhmv74NBUVAy8CoP UOZBr0q4Uwq3onr3WFA9iNur0F4gqL6YxL0v5pHBjXvhsV1RPOrTgu6Z5bfOXr6LA/oh1JR3 H+CMuvsgfenn9Q7ioaQ7uVNndK17qfBxdiCjhlyrFplAFxOFIavu1BwMszVICt5liI2EMTRt Zx7oy+fGJomJqWBcormcKLU1WlkrDAHkHh8c1j3Bf9yd94COnvqzIu++Y6KzMk/gqT75YaSq JDwmS3h4VvIewFhxDPSSq4pAv1wiwbrv8G1BXPvUy4bxtI9VqrLQ1qKt8RA/WWOhQwX4t4qC pGKraafUkax38JhXW+SH6VM4SpXZp1RZfbUGKEDbIzK1KleZpXzeBKYMClth3b0HgQEAL5aE vYoXFkFrtSwcCICI21utPm818DwhkYuNGksK3ZLwELze1YYUlbwPIHWEB2TrrbLw0GzrrZxG vbKwV75Vo+ytesoq3iOS9yFGWkk4bX1OY9n7mNgGMvuB6i2rAJBq1fkp0xNuRSoRukLfwwBj n9ruMhpksQ/R7T4oi3YM2Xe3QgcSJv06SPHMD2Mt9baleH7FnLx+AbSU3E/PbtSelfAH39Qe OAJqPSAB8IcMgIcrDlSrX+uireHiSDJ0Fu5wgTwQHggk660B9XmYgHTkQDuCwnhlkT7+728m iooU8hRYb/wOCvOYAGtth9GJvPcKTT2L2O6Q/C/XqD8bYtMUg8hYKYq3xnNJHbciexZyqfhD kiXel6trS6rVgU/YLKHdalx8O0xU7d/JXyB7j3dUFNORR1gfKxyYPbqiqKOCTiR3VDjZf+zQ /x5iaYCk1l6j/uITFsdrZcHfGjD8nle50qysMUrrzFInshyxZUcVS45VxVp7Cq8ixYgifnvH Vqt66RNGAPUYeYNQsnbjhqup924SBsdg3dYsFXHvuZ8mKY97v0/5IU0tf1cNRRjb1dK4kXNE PtWPBTuIS5g8PIJfpThI9FVJ7xHhJMZ97XwmmeTxyckbLOrypJEfgTGD9RJIoQzDoHB/UX3v IyOLJT5Wo/4uSvyBtdeaETnBGvWlQRbVABSQ/cdrqtV29iCAT9TzPmG7ja1jrnX3vMXWBK9V 06q5eo3S4wpk+KdJGgkFQXXZDgonkR9HdILJO1720LZ3ECWDudYQVE+hr/ZieTcyBd58INDw MB2Bgz1EERTwqTMYkFil3cyCpXcjsqC15T71jsVGdnJUmJt8nGbGf8KTdAPsoU999RSJDGxl 0RcJTUSk3RZ6+1ugjazFXBT41Bv+wLD3I35WfJNcWYzL6bpiENJCkD2XK0FW4lFAO2hBu+nJ KgftzMemy1th0QpNyxjIxlMM/axy6k2NT13K3jBhjlGYwfRr9a5TOFf167Rej5zQjTSx8008 YPocBW09jMvqyMemeh/EM3rI+z8goe9XcRnYhT1J+ShBJewIp3JPjfpiIj2VoT5NnW+x+qo2 faEyDkC6lZ8Pz0muKpahMs6+2VifNE4878AboJXaq8oVZsWHWd6kLjDHJGNHBZt+Gdd3S3v4 TcC5RBhtEnXXqJv/rp0ZzJfye+83cFBo2tzKaPztL6ZFbL8mYhOY/91PUxIPCQTU2ReyIC4M MF3LBBT+o4ivTTnaOTmYXmpyqzm51aIe/kSbdwUw775K+iUbGk7Sdy8kuLhYNgMItQbUw9Ur PqD5ju2sM2MEBKqw1er6k4wL0uhbUxzA1+pDJ9kEfDm9D6mPxdERfeobtOEZkG9NcUnOKZR7 +icfAS2MCZaYcVQczKt/NWXm6LjerPafyoiJSXf3m7+a0okPiAkW8lqP0KBfv4hmC+65jgct wAL1CXC+uajv96t/NfErkVKBQ5lxsSv+auIxah75Vk1nmqjTmVYT/olaUzCRLChNk0hpKo4V gtIUsoHCFCpkdDWSqhibKA2k6azf9sy03545buL5FIp86r8jM7bDkK0skAsXoEqrFnun0/9Z JVlA6TbNpy7W6k2gnBmVVilPrrSMjKdj2CzApm9Bhs+Mr7bIDfiQpXTRYqcz8TglBevZPvWZ JAUuj8PUMBbm/8uW3+Fvr2t1Cn3q7VQHt/rJ3yRniaV6VF/+q59dXnw9ZZ+vMmO+H5TqtlNG jHevwe8dCePIWLF0/O/rJvK4hGpIH6Y9GjSG8Dz2Sh7PMhDDl/KPkAWVSoeP2w0FAI/OdMA3 6o8/TpsOGAizckxTQQ4PyUEMGXSQmq6Tyvd+jHbDkFRvxqiueNrnrD+Pvuc1WhNxBcQjJKS8 Nv4Gvm35sYHyPTBpamv8ISlB1pqgEgBZG69RHzzBH6jfeAokksfKZMzXZfEhTYK10JeEJJD4 Uqe/h+XsDCkXIEfm8Thw1k7HAL63MCmJOsK8ZJ1djbzHNMU6qxp4ir6CbLMmj2J4hXrZCSZz erLFPjzyF5qLyTr0nxsN2NiS9/B/q2qFlhQPIHocNBBIRYy3pHjYLI/gX8pd04DojZmlAR4L l8kDlX/hMTVWEC/BgPqhamQpfXA1WSoOG0MLtpVTMOdi9RftTObA14NtRlrKhELM3DKJ+9ti BfDqwUNGGl48mwx86RjxK4amksC87iMukUaU+68R5W4bo5yYLudTp2iFMmXMV/VlLtXK8Hwp CzNjDi46xkw2qRVlioLpSJR9uPsRjeBfb9Rj/FrUYwpFPTlboh6zM+rJvSzqyftW1JP/3ajH 8u2op8DQQUkY8NCJwjKGKJhcobq2IEAHMMEyUSMv0vImJgpstz1rZiwcmpV6/cpRWt+kCFaP TeT70R30k1iPvqEicRtucWvtK7T/JCkvU6fHKb+D1uSbz6d7DFIlLBWtKDA8jZDKd1GlfV0Y L0ipIgyhi5tpzEtob0sobkFH6JwNoVmVyQgWkxX822xcYgq902xiv5YaQYWJdPMMMrFvAIoA PbmAnjxATz6gx+J82kL9IXgZHdD54LM3hCZVeprzoNF4s2lpni3yG1APmmlffLkzZFleYIv8 GBUG6gSjllgWmZw6nrkGbcpo5AP45mwm8mHYq/IhwcvQZFL24es0MRIvcNQYbXuW53BiFKVe r31RT4zCbFTIw1qHCCLBteUkrtb7jlNuDh3Nb5igGdC3vWLC7FlddFjRHFurxRtoAKbrlP4p DdovTYgIBH2ujWXNcrjJAjK3NweM4ts2Y5fUsYywUZfHMung0cGbFkk3LRST0ACoSYYtGGMj a7xhqVYvteImPMuPg46G25aaUpBIbdWMTdJsdISx0TKqYbttvGkUuqZ1fSa6XkV5nzTZGn/F NErxCUyWAubuAcxU0ouuDpQno2D9nXEErHuMp4PVmQnr14yjYP3uC58Jaxkp0g5mc5HHQnpe jJppPwA9bZQWIcMRJwsOMVrEphK6M2hiZLrkwBxwNKwtauA8E/ou0edgmgdSEPYQNq2okBWI ifG2CB6ry0QML3n/OM5e2+spHlZDBuBtyjjNL3ItoD0UZMMYGA1/1oa949JYx+aLRzbflUtK NS75uXTWTrnvsG6/eFffdmPm+fejtOSI0RslyrbAzr0OwsJDV1HBK5Z+SBJ68BSsTIUC6l94 AZUKkL+I0jSIh4uika/hwflo5Fr8rzzJ9DEpgSeBTolvzZKpoGy+Fc8BsSNf0cjPMYJls20/ fdks0X+KQn/3YTs8DcUJZR+e2WbpKBoOUQ/Zz0vKVCQQVH+PgS1taDTf1aSrlDeyQpWY3Gm7 1U/Z6nEAktCHx3y1AavvsQHHacAF5D3sx0O/WoEOXiBBBcgDRykrCCNvDRNGEHbECMCrx8dt enyECB8/0/DxM4aPnxE+6K8OA9KJhkPU5ujhpMdvSY2fIW2MCmz8m2j8CC7pXN2+Wrx+VEZj Y+m7uPDiDlUhAvYTBthPCDDat/JbcecsI9+DDp6RLm7lPsxekubLnky+XNxlMihCl7SvhPl5 xY4bpUNLGIMaguoV7zJsdyn76Oz9Poy7wEC6ZP1CtTMftcaXGb8uIeqU8vLHlPBx6dBybBMP CZilfQuJRs5opJpxrS9JOWeKhzXhg9+AViy8COl1aCHRazejl0L0Wq/Raz1Dy3pCC/3d5yP+ ncv49xDlmDnkJFL4Tse/ThrRIew1qP4jL0XFubqqBawa5r9I1WThUCJVBIouQ4oewsHJ+3Dc 0goa9nKGSrOGIMs7iCCZUIOn/cw6LIH8XEBYskYjLzJORqTrsCQNZMPTAj2eIoSnyzQ8Xcbw dBnhCf/Kdy0ibLHkPgw/1MsY+CEUBuV9xQT+n3NT+Fmkq3oG+LmUOB6HxQe/ODV4PMMvE9MF VfVvhB+GQjy1wDP0IMstVgPYfV4KsbJgzxEc0j4KCDxEYVMUvqhE1lAdKhRQIvjMp1CkIDRk D6o/78EwnzUU5mMf1uU82NW3KHN+TPkTuiQwJyaBO0SzBL4XSYfwPDW5HyQKLotGpiOvSHT0 m4n6aKQIg0+RDvgF6ID/Kb+/D49kHMIsD5FkyFlbpITvlg5hSo1gTY363bewxSPDfOkJjy9v 7W3MSefP66dhWrDfQ3Ziuun03Urfi+i7OckmcED98dtgPx1C+Fh+BXgUgUf8hga2CoWojJ2V YZkPTAH1GnpqTdXMCahfokeW1CNzQF1Cj8z6urkBdQ49NaQKwiNbutdknVlmw5UPHSGq/+Q1 pIeDskLPFRPJUAEGl1QtkqoWsgQxNPR9BGJcVhAFzZOX3oF4FKyNR0PuVRXN9qUTQ/3NhqXG 0GIJN/t3teF62mwHobb0R/hVwHzDUHiCvrBQyDqgHYAI4fD3dtengEPMmqIcchI+SfaRRI9G iuHJgmhkBvwH0mwm0lw5VEzFjuNgap0ylQ/6fOrgm2laOsTf4hfjVr9MLSXZBMCv6pMm7g4V D9FoBTtIJAQg+Sozwoukj2Cqk0uJxQ0TJxaYH+eNbvsvmRGBENqw0mBrnIPbIpRLhiHPkom8 iYId5zvgY00G8pZy5OHSy5GHXwV+3j4b/vo4/pTfOwlzx2g6Mpy9PBbO5DS2XtaxQlCNvpEF Z19jpTjO8Kt6qzGFs74Uzo6dFmeJETjDO2jpYYOtQaZ5i7yHk13Kj01g56PCdvTT5nN33n2t mrTItm/xficqedaoexiXbvfwZsk9rPy+CWd7uB9zBpK4iIWU8LAUTjS7h5vyFG9SCaCnyM7w q89m0c9yRVm5cB31PnHa91KcEk3x44Wpg5ea/8+Od7fwYaVyrI8+U3mG5ykDMqVMHteiOBps +9uU1b6u5gmexmcpv2DWs9NPdVAwjBTPcTvWgDqnhIdiNmkACXDOMiEROq8pz0NHj+iQ94uH UyZBLpgEwjEAkGjFIuxyuRu4L+070/dVk6Wvs3g8Zfb+vqb1Z9mJ/e38rP5ktwXWZLHbqI01 bMm3/ZB5kjMSUI+KW9mPecrc0BOYhnjFa/0kjGNF47exAQ3Db2P6uITZ1ohrn+0Way7BbGu8 NA/TwubRLjDuDN1QXH6Uwi7Kh9tlEbO5ShVFcrhIzn/AFDI9kvOAOZTT8Jz5AQv+BzWKGlyG 8MSG5xpiVlk8SFFndskDNexNwbmw5CRyKZ6QjtmDVQQajGAJqJcktWD1yKu5FJcYVEvXkSlk Yb3G8nhzXtxIje0Dy1CmZqWqItlTLFUVy3liYtaOn4nqHDGxrv5OOuFw1VI84QD9hQ6bDDOj 2T9jvRv5/H9a7g9t6Xf4fSx48LPocOb/2sfxjMkwqX3sz1jt6GHQPvj73vb05xwo+xi0T/JJ cNj2ry+RvPFmCnZrWl8iu+MnjynbF/pYRKmy0eJrNslCHzA4GFuVSW9c+LAXI+yZfHM0V5UA sZoqSnpzSadyyHUlYJXAG7nKkuPZKLZeTalLjXTSjvKLCfbeIhO7fzg8JFdtxH22io14eA9Z 81GcV21XSSDABsX2q2Qh3myeLIf7m8wrxO/Ejds+YNG5PH7YIe8skbCVy8XWe0sT8oaNpW0w HExIC/0Cc+fxE37m1HUtONI+af1G6QRGWL0qRYeecBgwFSzy6lA1vAyASYLufYUC8/rE1qsk z+VQTzyVDE2R2kEoyfA7DIDlN5mnEFQxqEYTqaT3U6il+ac4fBSbW2HJqXKIrVNTYLVH6ISX PVp1jpGF4baZWBBohUOqdGgI+W8c7tYiSUiIbUUShoj2YV5Xs0sWEk3mctZ9L/qDWrCbtSVY xii2qqWd8g2O0ijmdo1Tv2GLnM/7xf3gaIXW71oTj3cGzK1z4FDyJJPsMUuVZtljwX0lj1Wq tCqVRZIJkTBTcvcz+vfJ+QQMZZnlwPTifA2W9PZjKKLXLraVyH672L5AdsPwS4D8HZ4S8s56 0Hll8NVUE7ZfoJ1GYULUo4H1CPMkia4rbZFff0LcBex6no5dz8MObbc044HZqBOMfcC42OEE jPPzyXGxfQJgtNlcSABeSACqvVd8QneeAaCusMPWuO4Tlj9NJ6u+P5iSVejQqkVaBum9id7f AO/ZnrG4xsRirEFE5YNwsu35BOuqG8VEkW33h3jOFYWUdSUJKcYY/PxlS6vJsPE0n9PJjmwf bE/7bIbPjlZaupJ1JUj7KjMmLo59lY80eUMJH+t97O5gGEOyvoRSB7KSXyS6gUiwi60LfDVU 9sHLabNyGtdvLEGtWd1+6thxiHmtlJ1NLoDpXZ6UnsOs/XKlVV5ngWnbaeyQJwFvflA+ILv7 cSM753qzjDxxUqmy+3DTjhIFYRhFAQ/Ri13IbpGTrjdz+0C6EVc0eWLkaMgsmWIWFviA8Q5i K2ZUZvsvdQx+ryP2JVCF5GqLOGird+I+2vNi1C75+6F6WUtzXlO+pwozHf8jNoXuwUpAIzU+ lBPq994YpmuIqLoRoxUTOK4EqDcPsZMjMNCJco1V8lnpN1TN1KMy9Yz3n0JiFWGk8dq5TdCY 12LbX+GE5Ts0b+fZtMTj0tj7C1PqvB1oGLZGzETQ22xi8UhW2dXsTQy0mUPTKb+f5pMkt6MA hXo3mSjTdCm2L1fbXe1CKdUwhWaPrvGSBWpclMq/TgUt2ZoeNEPBQhMvYspW5MpKKPIejAC6 zPK6C193GjGmYeSrt/DVb43saJ1xbCCesGMWZYqh4omHMImvfJPd1SHM5YCtHF3tGgcqQxg/ MjbwJxCE+VCmbdDoejUb/NdeygO4Rr+6AV/93cDgd6H7/ia7IVwJOv1sOvuRpbX5k6HKk8jO 4aFalKLVuKOo/uqE0XCyC48TVIC9bB0b3kkzof7NaZIVjS4yqwimz1c4t2R5vwGgji2NJENT R79bhu9mtox+sf5SyhKsV3BTd97reH3497TBKLZiyDW5O0B4J3CG47X0/ahGrKBfdubMlSev Ewfn2nb/HjFyrKzxjstWgzTt7gfTNwYf8+//v/9gvx3wOR8+E+DjhGcO+CTd/b2lfD9GdPeb eiuMqfnKlrVnjCn9RYiL0RxYtpaFi7ZOlnHgQ1IeXt9icOKsFlmUUfMqc1N+FZTZtkMM96/c Ob7Z3W9dBY96f0lM1S+eWlk/GdQBMXqBJKj0FpUDzwWxC0lkXUB7AImo5wJn0qvq0hsu+oFx oPQjsMtkt9pkIdPsjWa3au5qcvc1uxPz3X3UjiU2nclLPYSzEcK3aBQJWJYtSkWXdKK0HcC0 iajENZua8iur1gofjB4c5pmh4KgolMDXU+D1GvZesHTkYfxkL+6zAPTNq4x88FOkwSoxHF+5 0wLLf8Ozq2Kmh51NhbFpdH5kOF37C7gufInB65CW0OtP+Wvgc7eDn7ij9ezUWoyEiV04YnyJ pjUWamwOQYHNPHo9o4Z0fdEB3EYdeZ5ggT7//xN6/kbHuB1sdnriRP7mjB5HBXGxxuh9uEjb 1oqnzrPtfpszury8Chmd80/P4ybDq/Dp/z/sgzA9Ch8HfE7sNxmsgCDzAfbu+v04J+K96BoV 3XFTr2/kfPhG+n4Pd59idtNemzu+TCC2ieOinE9sgzpT7yxTak7keaCMTcQ0JsQX9mZ3HOZF nqf3PgOzL1BnX1kPBmS/2HGBFO6hAmhMVF0QW4T5MfppcvTAo2gVTo4e3eRY/gNjsvQUTY6e 9OTowcmBc2w+zClsyRIryoASdVvK0o7nxfpt+4MWpbJLOgUKzgCBW2UkR0tehWcdzA0Y5NSM 6vOx+lIjwR/NuxSHiNMjvoYVCVs68suwyBTixn6cHoSHbUXSRx4x3LdyZ0Gzv6/huVWxnJZH nE0TcX7EcX6kqtOWMV4l1wL0+BRP/2BO79Lnlvn7wjl4U52/qPQErJ7qLGM7LHepx+E+Y1IK q9AcKA8MXniYKM1HdxnNn2iewcOGlvT24WmcnX/HubOQnWoDSbTEsKOMYDgfqS1iEmpQm5d5 7dvyn6QMsLlsp7UrVs31y458ExW9lhVlaTAWafZVCnH9TT4LlS7l83Wh/PstfL7eqM3Xzoz5 ukR//mffyPXIztajkfMVFqaLwQ7WpqyKuVzhQQ8+sIuDptDMnYXioDH0hdjZeP528AJb41nI +IMLbY0eo8bxnxg1e0vl/AkSYgMIXpTblibPBk0e0XM8YrNqA+ZP35BNdKfyxTNmqEoqVcOS +1i0argC94Yx7FroCah3LjFQLuJ+yX28NHxcFo4rGy+8EDMCvSgeBvV3Zf1EseNTNkGEY02e ZOz8FnggQ0urkk42P0/bv1KVhG751KxKNruP4Uw5TjPlOFpfHgs0Vorb1d1GIQ6Q2Pb7LMpW sM+PlQrHmPwtcrn7bCJdAeA+1mwgx0PSfQx9D0lvfJ3wV0ZbLsdTg3v8IyMMrtQPzKkao0QP KxZzyHll7j48AiHES6No7y/EE2ELywRVWhgZ2HENTbmF2N2jmIsLZDtMdjyAO5If+XoC66ED 14c4XyeI73CduIC4lNrwMH6LFbXQGx3/eop4XOfBMeKk331k5Lrh1NaNEuRDfLJACseR3Xwl YCuN5yfvYjaWD9cKRoaxnc1WsWOhFO6m85WyBSytwpacarNcALQ6CTQHvrMDJdbDQiqHu5s2 IL3xt+zuRoKzfHjZpKGWCZmvzZ6ksmMY+ol6hivKn8W+7GA7ncX492ZL2c1W4yky605Ay0CM 0jbs+myta3d305pk7CJNH4L+oamqM+lfWZ/kzOZJlnlp8dxZDIAQCPJWK3ReetJ1Spgjm0AO U+hdARCO2Ys10I2800ze/liu8XlpqzUN/ISRcA9JmTli0V2BxqbUnhEHLfbN1dFy2sM8aMNC /jCAzoK0ZBKEkZJcQ1hkAahtvXg2Qa6xlD4Hk1IOF+FQhP5SoRtAdQ3a9qCuJyZt9cWScFxq kwZBM5+Dt/scR3kLz9YJH8UmQtkgTIn+gHr8BWaegkUZdkiLQUkrw6aG4CvH1HF09EyW11nl Sktpp8vdLcySTVIe4SmssgBzMPqPyx6w8GMYv5rj7ZbWWUnOBoir13CpjDze+xJbh231JQAA ASn78RqiCwHK8HFMQgh9ApTYLcrM2FQ5HOfQns+hBXyshHUaVf71xTJ8CVrlKktpl8sdB0Lm o+cuE0Cc/uSvQEIW5CDmeiSoJMSNiLwEne+lQffJUyR/D8BjgyErqwvpYBZFdYTR4JBWjDlb uzLWjRJ9/sPfjZyvJdp8XcDn607zfFsEVRS5qoSmoSDfZFW2u+w4jSssmCo4WnaDtfyo60R4 I/Bns9nU5I4tT4bMy531K0pfQWEWPlZ6UrrJIsVLK8zk2Shn86Wjkk4lyMaOVSzAtkA2knvv XSYPKl0ntj9EM16GhVq2Sd5j5QPkdeHzs9JSVmk1RhmfK4EuMXzMgL4Vumg2Nk6uIHnSBvWk F2FVAPsCYEFNifX/GfIBZJRZbH9DHCyoF6Q3yw7eYa0BZfa9dP6xI781GZ6Bz51jfB6Dz73w UQLJqCf55dgy9uWK2IWsf/azJnaO5laj32tjZ6V/p0SEhgAAzVI+wPJXs/Epiyyg77xCa3ox qeHHUmwXBa5z4UnjJWCtA9f1M66rxpVgFee6XOMJqRrFB/QwhcQHQ2sbFx/AfrYM8eG2+NQ/ YSJAEB9HxrQhXnvof2JDLLbtTmo2xPYvkw1RZ2j8L5OhHj53/F/6Qdi/DJ/HfmMy/AA+98L3 n/F39t8wO2OBZmesSalbW03a/Yenty/KUYpd8H+6fXEhQimNbV8ET29fLMLq605rX3wRi8z7 l+2Li7G6Otq+0NsS/4KJMUMa2CxPFNtMUtfmNtUCUDVNTtkZ74yyMy4iWJaQOG9N2xlWptcV Ej9oyt3G1H7NP21vXJS2N1rP3N4YfuD/JXvDpdkbS22NlakJ8OL/BnsjUfZ/i72xLZzd1ngr u60x7920raEs8pyZpbFzKU0+4q1Hr2WWBuOtJagOUUejjQqXge54xa9LiSt9prR9oVkRGn8V 6/jr5/fToQy6DzKh+VdVTQntxz0R3EEDXioFzMCEw8c9tE8rJr4d+uZOfj/4KjHxb7bGb+DO /BdR3glxprpK9Raef0auKpb9/WL71TW4OUM5m3F/5mxgtWhFDt/Ie1DjP6Gnw7ORzTQV2sCM PuxiPUqaR8rjMigkezYq2/OuAklAsgKVyArGv32o8ap0n2UfEEpdJ8RQS6zaGHPS/kxPzqqN YutVIJira3zqscNcB8YWc9ykG1ZtjK5echWlUvFapXJQQUtR/+vHiJhyTMixo5gm9rcJ4Xu5 GEBB0fs2AdpDu9Oq5B2SOqHlHM/G2qSPvPO5r5N3HtBTZcfznAn97jJU7DAixTsqLJTJFhjj hstTwRaUGxd1BDYcGIMx4cMrUy/38STN7TK0Sp5/UE2kCgsGOA3iffGDeF/8aoZfi+xBtTlI ykk2bTbmxGSoxn9Lj66Cm6v50gD32x8b02/vufdf8NuvtO2ea+R+e+tVqIq0cHn68j0mQwd8 /vb/8w+O8VfwMcPn7V+aDP3wf989bK+A6Sv9en3lOWNKX4mn9JUsewTLkCl3j9gj0PSVftJX +D5BSl/pZ/I/21YB6Sv/SzYLijKgXG7g+wTQfsZOAegrCO7vDCP2CqZmVF+B1e9h8EfzL822 XbASi+w0jNguKNK2Cwr4dkFOS/b9glXI/Zey+dMvRj/lwht9/iD7fTql/ciFtFlwXpZ9gksM qX2CEtNp9wn0esDA3Wk5fQxFNVfzXyYhDc+dGMzi7dIkdx/fPCdRXm9nqVq9PaBOlflVpk/h rqcrHjZJUUx0wSzzlL8R5F+4k5JinC/hjnXctr9ivLLIroBWEz7eAuuCy9tpa7wTeSrcyVPl dXoCmEhfXfoXPOiIieUxmO0lMTGMme6OfJqkXEVi64kylLDQZHB8aVcOKL246R6tGg9vj7Ql QF1SgTLN3iNNtio8ZuUCaS62gd6YwIxn/UkbLj9rARHdzKLBX7BMdUreIzp1kYbXCdqiu1MM d6auRDtS5u1EwbvBjlFldApHPmaki7QtkaPhOnEQgH0SQY3VMn+Iv4tCQ6yyEd19k2m+NRua TBgrnl9JWfi2ftjUZT4x390le7uaKsbLCNkxBBbrAx69LxtdJE0vJWm6mktTWiuamP7bPYzb 0ClllcF8++WUKIda6cbcHC68jc1l2LGSVp5Kai2uc63ELuHnc+IIThwvYUZw7KTvUn+x6afx l2f6G/U+qrqfZ5fnDu0UjTwZl5fiHWeLg6thUfeglO81avKJ1h8ms3bgM3Lb2FHEjJdOgiYJ s65p/YbY/Ay98jOUyoROqexhSiWoAInSQQwxBB0GzAlDKUooVdk4+UJMjvUiKpMOUiZJmvWg MllO8KE+2fPP6JM9On1Ss8QS80kgkj7ZU4pSrs8I+oI7kdIne0qFnpQ+Gd+2BsqhPhlHfbIH 1BS8LDulT6ZkRxHokw7QLe0+PLpDAuZScipm2BvM35yWN1w1XE1Uvs2o1we7xtQH9/xspD5o R0WOTzjNzOjR5lwfqoZ5EibyVDFnAWbIQxHT43p1h0l6lcIr4Gue9GrMVJ7EU+U/h36WhePh 8yi/5DyY2tXoik/Q0NS+F1Fy9GGyshWlmPYmZmX5KZjzGr2a81FhcoN4UiPJUJE2fm8Pu5zX 21MJa5HwoeTviZ0VZHr4J0+ScmccRsARdgdoc5THGrrBIfRLE0oxtR8MLyFNQMBse/6bsIr3 5eTCBBdmEi7dhMvLmW7di4cKef+Yp4hHXpTCEECvnTG6AhOxeHNHC/PYM/maEi0TSaoI1mRe pZyXkirSqZLOpqrxQNZSPLoVL0N9NIEjAHniofaLoeHY+agj75w6hm8yNoXK6+Dh8kdT4rL4 pW/5CecFO17zjgsLuSIZ5hLapkMfFSlhSw1tOvR0uI9jE+UDy4R4+GKmj9ur8QozddZLPO1J uBDXhqkHUNLizVWDh40GI13Q4oFa258ncyOO0emUkfSPBpYgpQKMiONiu70mS4TX0pERXnL4 OAV59ZArdJxkitlS9nsPXhSqarFelGRuaQ722Q/CFnMBwpJEUvIrhLK5TEoCu6SNFV0+c1oW uylt4XEmX7uDbMzHg2oZO3LuUydTuLdlvdBNSHS57XUe2d8Hy0ua/KMXFUBwH0pxBOZKAmaB ztbg+YuR9tO4XcBxTWE223qTSdxfGjUSTvwunbzX+6tv/XEm7YnUca5G9GkO7B4qsoBW4j4p fGxMhYH0hWO2xh7C/TGuLxzj+kIhzXp1hL6gMtYAbSCoHm+HElHGAJjrKDCCAShfVczFGKBj lZnMJx7md70FF0/0txYAB4zn8XzdSF5gAqJ/ghLw1qaVEwS/mpQTSrSaH60Yb8A0nMAy1eoG AIb0kCz4fnwI8L2yRVt/w3GcumGyIF2MXnNY/zAZdcTEGPp4tIpzlubs5XNSn5/jgx/SXpGy HqTxkLIDHb3KeifSaIeFCISRhHliYk1o2g6bmFhri3wKFQHX8ViZmKiyRT5A+esv2uroyFtD /V/FpAQMObYK7yDqb6owVkKJbbOaTZUPrArlS23iWytjhcudggvdmFwRiy3oyFs7ooG15MFG fWUKk3V4mlKLn5QmarWpTH9z/gPm0PRovpmu0OYxs4jHgDphFuBp4wOW0EzKLwn0KwpSABnX 2AJqP5a48AETlAj3R/NNo9t40gkl7I2tIX4aRgs169Hl2tbff3MX5T1RghZMrlSPTjYl6MTE l/UWWJZlv0MuxKDddaEZOyaJiS/ZIhjSiyt27Hz0pyFq0Y2+zIuozV9HmNloYkLDH4/VNBtl f39TpbECSmwrbzZWAGqtoHW+vRIXnckxN+C3gsK8YJnqw5sWZxnjGJfoTwDXzuvI/9KIJtfh Qj8ZV/0JaWRjJrZCCmYe5q/7m/MAkbOieRa6zgn1CLwkHBbboDoB140rkD6ESX9/1GQiLxZe aI4HnSgNSwteo3oREAvWwP5onnl0O3SZ6UTAtYXhOq8la3yvXs84904Ty7mH+E7vWeATwjo3 YwjxF+KvDXi7jjwJ1nVx5Xpb4yc02P7mGlOT/0PaA1VLUedTAW858Bd0/zbQQNpAaSpz97Dv itmLvZfSvJT9Q9JSVBfxztmy5jxP8+Qm/wceMnxUmC89MJyCZveHsXzS990fyH61ybRW+DNt D6HvxW/FBhzShZFnd/hIwHqJREs0Etld/h6hkGn5P0XeEIpCzuY85qsHEDYQDB5qg+qvh0JM jf93wESHiS3jGMsrVfJlPMD0U2zqzyMhBnw03GwxhHKbK02xHAQZDakMUJOg4/jJNT1lLU3j 3sfx/NyApgWMotOOH/wP6OSzNX5MdMo0ynSESf3U0YbDh958G9DmC4R/pI9H6tjc9p5ls21/ ewGmQdssmcR2E/S0VngzK1WuIKxuICwuN+qpwmyh3t9o8gn3Qxox/8PpyONDAgj8vEB28lzF 9QGkz5eQPh8CffoB4irL5rZuBN3/YQEY6QB7vthhkjSA0cRD2iAiLdLNlrXSOnsvXpOuxb+Z dKqaNp/093e90pLW23X7BNwz0I/2Vh0JMsz9Tr/IRoL3rmttjX/iVBrUUcmt7sghBw/IAcpW qsJMv67LaMCDIiq/nwHphY0OSeXGDmarQ695ZW4Vd993XEXr3FcJT018nfNi/gHXBFvjAbIE ikLnlYaLxHCRkd2u1JzPPfJCfD21y10AqNZeq2GCblOjtnU0qOA02AL4wXb/DA3Z9nssgHfb /il4+VJfFWqaTYeNtN+Ai3KZEbQJV/vOC+g0j/odeEXdIS3QHLBI6y1gT6CmCObqYUvvK8N0 HoRrT2PfSea5PTOmg88bbjj3p900oD9MSOvWeOBHbH1CTFhtu2lQb5YdFItvoM1wtpHN9sP3 7jEZVimf/cFydfyDS1Mp4bGakPYYX7eFPh734JBsDLsibQwSHYwVSW8fLlnfSaJLHVets55G N9rsDoC3F9N9aP7kybCCTRAHv2yLmKD+SVj0vgW/QnivRy5M6pNHzV2K4wc8vY4P2rQ1vgPf WbtQt1uCKhen7nvoyK9JgwkTF3E1hLEXqQXveFr/1tLosyJhMuRWsMXPFJoTzTORCoGLFqoQ aERjZM5TeBYBE5m1wBI5m1Y3S9aC38GF8npYAufxJTBbocsNFE3Mzi+3hpaztXApyYuTR2mV p2F9OeuwwkUUWsLEf27W9TMj/us27QwIn/IpFktN+ZRoZp7APo3LurkWD1zd37zW1OR9D+zy PV2ERbsrrNpEvF2aIvbV6//AXWO7BpFutlvvMOCe4XCIP9hRABLtvd4wI4Gc74rbGt+lIknh StrumeCKb5vYQqYNXodSCWZPfGucWTb9JGvHk28rIbnKkBPjpSdx2rtwrwmVZprl1xHKcFOs F714fP+hF8UWw3cSLRC1Ca/gUPH6TtvtC8lzxhpGDBgxoow0e6aAorlqlWxYeMdUosvXqBOn SWdb/TvaVaGagF75ZLQ+B95Wfzbguja13ZOR/reDGf63l3X2mH4dHmj+l+ndo9EbyYz3gmrn 2YDSh1KUvvWZlBPUpiiMykIhOULp+scUecuNjLxfT5F3kjTwGfTt+Qw0bSJMWHRooqhlRuXx RqRvD1TYLE2hRRNI3AMkXkwk7vlsEvcYdswkjH+d+lmtI3Hv74if2P7ibbSqEPZ6pHgp+onl IC4PTuNzZMFouZUzSRf7VktpO/qUgxbyLXXkf5Ne4221sXJu//SQuoUo8MZLP8oAMAtoxClT xljhTrfv9nxTet1JbRLoln+kIvPgkgbQx++EUWnDthsD8YpKn3O9Aku/v5surVdd/m76RdOq 8bfECt0UedfnOglvMOqsJ1h7VbV60f3DLHuYkIf7q9gLuiS9Q6Wdpe6+0AyQdSAtuxXzBB/a amrykJFn15VRZ3HIK0pfAPGETr5zMEEvEOFUJBmaRPvJPc15TSawt3oq1wofSX41Nhl9LKSW qNN+nXLwobuXrsFJjTRMDj5YDLrRpYQoSEiLmY/vfm2l+Qbh+N8YOWuNaAORL+/qQ0Z25jys usJ2TZdHAQdFXMIQPCFmfZmpIzARuUsPO1/mLtqm+SeZZ8/BPXtFzLVT0klunSHQf2BelOEK kODBhZsJoBuNmn1Gcugr2KxNdhcBZwL9AsiZxcYXJVuHh7Flno5XPEWx5Smu5IsLNZ3mTX38 8ZnII72+uflWvb6Zij/2WuQbLAjmShRERjCLQw4xsdHWKKemMyboa8GzixVOWHXzohVOS2w6 rNIYLRqtcppiE4DesNTmQxl4CWttwrY/Hw83Tts5gQ434rFuurdUTFhCnt5WA48KAMyUueOu qO124lK3HcPybLffbcCM3bbGO4ja8eb85Sdtu/HMUJOpEh0j64Xe2M04D6ZoDey8niqjFhzd eV1kIDQdjy4bl5+sn0TqCzM88LaX9cI7yG1TYisyINh5Ae9957lQewbGX2G/O+onLZ9VN2H5 VaHCVN/v0FVcpIFFBoTzccpX0NUBJMYcXDqMJk0vJegjh5gSmMpjKvqZQwyaS6AzqbcZtFUu f/o7KhxMU0pIGywaoGB6RfE4Kjr3+8VhW/15coVD2W5EexrPeHv7pBMwgkUwi5rRX9pkxFuK YOQYTxHD3dWcVQ6xFQ8Fxqt96vd/xYNz++Uqh5G8txUO6TmxvShqtuOIjB/xMQ3J+aVxDLXe UUxSbiMN8F5dmEEvEzX9wRr1679jieC9wAlGPMq6GyU16cYLtqNu3HIBsONG0WQIiez/vfx/ 7XOniOya6SMifx0qYzFPy0gPEy3yeIAoNp/jL0vdN3NS8WFcXzs+ply+WOR2tB0DVSh8S9tD UenimOY1qInJ11uw1NIttsbzjalrcmQPXtvX+Gxa310Wtm+7UtxhNu7Ml/Ns+w2xgoBqISyZ QYJWXYJcWpfT7H5P9nY3GfGiUaFYzsOUbfmYtHyy1IX5WiZxwYG1ax9kKeKxK+FuEHrXQB/C Fbi5E8cD/rCYByx4RZEH7/eJHA2tSLpVupbmHNkdx5YteBUBZlTApqdpPtmJhB+8wU7NZ13Q 3S/tuPj5+9BZBfYv2OoziA22EBt06/dHcbZTvvfK4gAFq4xl931b3GExhH6NqLkHbLYR2Hn/ t9mw4+9uMhF2ZmrYgTFMYEPYq2Hn19JAQF33ANWP/YSNhwvGUXra+l16OuspjC4Rko8loutb tsYLRpG3Db+Se2Lbl2FJFd09JhoDmISb+SC+wAaBzoMMkqaB1pP0R7/WkfQ+ysXMvB9fGZuq K7k+zWk7Mxttz9ZoayWyLvx1mqwdKbJ6ybNRiBcz7ZhN7pJvEcl6uLuEaIvXU/H5hYKM03cM 3wqj789pK6Fn2w/RLA/3KEF0ABGexnE8WWH+BdTB/8pA1WfSt/b+TPrq/GH6efzdnel9kT6d H4WHV8CDHSXiilpb49M6+gZRqW68kuJvesRW3Nvb9jVxJ8BcKOfb9mMkQ8waVKsYyJSnEy+x 6K5Wjz+Ku2I9uDOykwiez0ZxvVFaLMUZwas4wYPq/fcxgmN/wp3YJx75J/1hVGev/UbrrBZP 0wTUGx7lbpEy6s/VvuMaVKDieJ0NsEmQ2KSKsYmtcY+OSeZkY5KpGpPY0/P/vjSjPBPbkBrk yUcyBnnO6EFO1QZp5/IvqD55L2tsJ95qN4OFyWF+mPLIAPAbiohaYqEDellSmoqXovi3zOC3 g7rt0t6kRrfQr9l+vUa3q8gdZK0mjFoQo7gGBNVmJtx8aukj/wzJPv6VjmT/gZhdBGNpGU2v +Q+OoFfbwyPoZbv9FKYlY+AF1F8+nAHHjNFwnKXBgfDX/iqFT2FX7+/QzZWWcboJ8J3ttFFS a0nlgqeE9OeDdum2Sh4z5SkYJ4tLjCTNJFNSKGb7ZOrfQAFR63DljmvXOLB8YKnG7dvZlXND Pn7Pac+TRrq57OrEqLI93xtR9vgTGWUpPmPuXCNPjkV7aZimvSVzPP/5PbahtsOZmWwG2KN2 VWqPMZTeWmT/Wdl/FjoRGFiAFytIJsmzAHOTYT5YzwLJUyIm4sK41K5ebJL+bEdAPZaHCnYK DymIxgFE+pI4Nsrrnc7RroP/rzf/74J/S34G/DqY1p4ZTF/8TJgsDKb8ljOBx2LJjs/f3/TP 4FO56X8bPjPh13g1BdnHN/4z4/jDjWc0jkWfOY58No689BAmpYcwlcvjzJE88leUHv36PWx9 /pr5N/J7ERxKwCn5h8QVptAEZhwWaPGHHvMXBgxo4c0RLsXjeAnZX+TyJ7aVyP5Es8ncatvf yVMuyv6hpkpzcj0ozolKaUpHXhWKNCezIZ7g6x8UilaaG9jLJ/BkltQJNrCYyLPtbsFfr5Xd KW5vAlvibaLXonqT4Tr4bICPWfeZVc/zofmLaoK0Aeq31gRUfzfgwjfi4Y/fgofLuD8789Wf 3oNXzpHl4/BwHCufNS+KXs98t06/L8cVEtyXk2vYdY3kxcLdJPlmeypsA4zSTlcHGH0d3ACk 78zhImD8PF7ISYFVs1lEFYbP93gooio2IYhXbGDAlvrgXcNJI0b+9JGSh4bdKbb17O0vPYX7 ZqDXJ2RTaUIygYlXQuvxVbTKNvBtINRE+7blMwfETOZu/SyHF+clvR/iDWGMfRbyd/Uzj0lK TWNGvmba7yjscMdZzLRKXhXc88JnJv5MUJVFWyWhz3Vimx1USyPY/RVg+C/z922Nk9lPmxGy 0F+GbdMeSkLOx80vMGx3TteFYul1i9gU9AeAUX81vVrINwLwnthM+1F/l8hAiOhN1B1im3jw a6sd4U5wO96PhF42sW5+TXUgqP7pEdyqA1qUnsDDANUW40m2k4amlB2M70o7Rv7uWERIv4Zg KWJIx8jpQtyo81tdhUI+I845jFTFp9v/1G4mGe0vujiUtot0PmsckR1PMVO+I8FeOgyQn5XA y3L6mM1Hdn8fsHd1loiv5aMivsD28FnI7lqAHu9nQ4WSEbdUKxfECuhMxAKpooTFfFF0n/AF GoqfhrLAREPBoBMtyCu2ncaLrkOcTQmpMMfdR4c4ANDah9kVb6kgkw2AY7Rn0V23o4wQq2sZ EWvXWH4uw+oMbm+xSCKUBeh9wNygBa1pj8Lo/YB3t/J4FcSnsoGQGdQwSXMdkPl8oFqdZmW8 XEWY9KtnHDvnVaU1Fjm4gB2FngCrQNWC2Hgu7+G7VJWBxxkd+UEaqlOLlNMhcVMG/lSGP7w/ TP3FzzUUWvX7ZTnoJ7fiMZu4YedZaexUB9VftkMpx4jeMkIZs8nL/TecCb7aho2Asm/+A/nv M1G2+DNQNo6hjPKdZ8XX5TSCVabR+Lp8THy9RE4emOh9ivUGbmHrUOS1V9cE1ecPMRRldJCB olH4+eH1Z46fjwvOiKX+x/i5gsAPZeGnLWPiZ/p/juCnS7h/4XT4Wt/K8JXR4Wh8Zfi///0z 119NQjMExkEWXcsWYCat04Ib/a5z0eEajsNiExkITWppzqdwo6pKya8mvX14E68aG09e1qBa tgdW35N4UtHfT+fRKRwYFt0L+WmJOA0UZHsJCbdzaViLmJzGhfdFTQjNYkKoqEW38F6bsfAe H8v//92R/v+xNyPLtZ1IFQMeRgQDJfCEhopuIlvjIwhAuK8Mfc8W6SZ7Kmq49/70CY2Q7oTG FhbLTRuRuLhj2Ow2B94PQPuRVtqP1IXSpjYk42wPkkWCA+ITRuZn153P0PaAv83ys8Uzz2cw iG//SpLdBFSe2nQMJ8SVhp2zxkCoJu/HOL6RiW+932ng3/Rx+al9Pe3kT5ZjP7Sv14Pb/aOD clto/7eb3ewme7u5pteNp6RrjWzv62v38NzUxtCLwFxi+4kykAaoNqqu9h08BOM2Tb9mx3JU jATGGMYJmD0DY6m6MS8mAIHZPHC3HPlzVJQtHdzWzgFldcVvfAFm6Jysp1pQCcWtVT5fdX5Z fTzz/m//a/hDb+MLgp25j943pPMJq6cJd+6G+VRE8c50S54u3hnwy3xeU+41suuCKeS5C0Oe C+lI1AaT5D0+JorwdiNUaHqS7p5d4ePo2tiZ2+w+HsvDHaYqEwaQ9/B99f5kQVZc7v1rFlwW sX0ZDZeMGY9kx2VtbVr2JdJB4jwmMK4dFunDmMBJdEGrdvgMRI+2idrGsEjVz6czbUNgXtj2 V46XnjdGFZie3m6M4rqZcMcQh/emvnGPHnF/5bHixzPPlmFD68aXdoJkLDUi1vCCYtl/HIya zRJmBuBmC6IIo1kRRXrdK/xGVhQxC6ePlp0MFI2er55v/Yvz1TvGfC2i+frrsefrwz/POl8p /BXnK2FdypyvPZ85X62nma+cGYHHqjP2xb75ph57PAS+iM19HHFCcmU576i/GzbT9hn8Jrs4 EA/7oZUHK2dcrkYPtbO0HQwbWSiSFncYdRvbWqyNMwdWxSnalbxZLct4Fv+V9E26YAHj9icD YuaCvcbSHeVpuY546mP03OZRHp03TuPvWMrgBwVgBruXvY7db4ZBjKn7wRoK9tANat9QxP/G mxzaG36P/2fclwOjhfHQ4RQ8lQ6w7SgR3zduLQb+SMA8wc3ZREVja2gcPN0Wi5mjRkOF1LUO jNF/4JarYHetAIVjheZY0HCdgrRl8wifquGOMf2v140se3dmWd34N2t34BazO3BBO5ssJgqF 8QH1d02YURr1RvQiz8Sm2M3DAyAgJF5auyyX38o58j7f1zaN3f6Gsdr/4We1ryPgTZu0izyh jzniU+xW8KlB3tTfnjPwq5wLWYvQ08WR5M7z6ML1/ZjqN7nfTH+pvO3g6K5juZwfU/4/Hf9f p42vgPdNF8Kdx92Aozv479+fMe5+nr3t+dkbLhgbaSPuWvVcN5om0zhNfn+rRhO8zON8fv9x lu6ef/aMx/HKNxiJ3FZmdYwcULGPt7n/zNu85RujcIP3Bc+HclmAfWLshkfgZv7odhHEeVka nds5ZqMZvuFXv86O5x7AooVCoU8NROiC4zxoGPM1YC/8btbU/SDLgwG853kgtE1Zn2zYkXTW 5a1tcDnrB3HJcltK3QlYlF1tdXhMQvJ3Jb1omoFm7X5h+eq6Gcs3hWYvd4dmLL8mZF5+rTBe dnf1fjGVP8lvcfmH6o/AOucKDwk50FBFA0aaP2zgYfcYAWSEpiqWr66fuNxZf0KpToJ0i/mp fkP4hU2hPPjrFuYqNyWl8BDFCNct1uKp8Ff9qdg8/htKXhMaB3+vFR6M5UgDFTSOMrAiOnvv pp0oSyWMqtSfoE6hpYlYODSuonlik/+FhkFn/YfS8/DIWUfy1tOwAuo33AQ4MUkYrdew0mm7 FZNKR/PmR/OvkYSu0nBX6fPoYnR3rZLch/EoEO7i32pg0UYYMynFy4+eFA7DErJN9h+mwI8+ eDKAB3xeiQygAdcH+lH5gOuVbdWS0Cm7D2MFFU9HDDWb85rc72nxzf7OHPTOdkpd1CR8oyKm JncXxjGEh5rMS5vdXVBjrXDUs0zo2/o79MCG+5XLphgBCXj+RBK6S73dZcKQJBy2NYoGTP7Q bQiFZXc3QgVgbpWE47LQjfkdjjNAj2uAHpf8xwjQ9WSvp4A9lgb2VYKyeywoX9VB+SqD8vjW /bI7kePuVjYdTOtRFu1+IO5JKE+6PrI1rsVJMCCcBWRyAacyCrG/zRMbBstCuQ2D5wk5SNAu c9fygrpxDYPnC7OZvo5fc6piOUn3ULrA+/A09D7eD3p7HyFjyGDb8zaV3oStuYV5FSOabmjv ahgssO3Go7/phv4B/GPbjZdEVgCkIkasYL1rhZv4JngF+4ktuD7a5kg1WQgPoIiRBslHCwWc LbzhXIR7Uibwro+2vgUw71xOZ1bHwddQOW2pl0Hf2moyGyCqmxbLRVSdBUBtZRIgVsD5iS6R 1vvKUBa48Wy/tl8x1DxJegVbuaJh0FW3oWHwGlvjdsLNtSFPCkGL6YLwyNUosTDWEudJ3Xhp IElunIYlzvp/wNQr9eOv3gnp+wjgfeynaIPHm9x/ZLPxj9fw2fhHmo04T18jjehsjqHYxSiB GGCxZ6T48mttd7bb9rfjTUvVRslvhTawpZuMzrpxSTeob1aApv4fDeHXrrFFMF4watwUrUji PUhlAJ/fWvocztxKvMQBZi7a6bgBfznqh1185jK+A16nLAcw2eNsXsS1eQGTsg/nhY25IoUj fF70pedFDOaT/0iOv1/yH0nNjCO6mRHTzYwYmxnxrY/1vmBIn29AJFoB8F4MAsP9AysYC6Wg wA/DfLY13kv822OwNf7EQFEmbELbGmU27+EJjJRNdOGwHD4MKr7kh/EJMSl8vMN9mDgvfHjb NVp+bRjwESa/jtNIQIARuK/z/F9HctC5cERKED4yhvO6bjivrxVeSkLP/m6X//DWB/DIDdhA yK7GtVInn/ZpnRldZvp5f8LWeLY2719pWOqs4/eR8nlf2HCqLHRuw6nzhLmxWU2dfM6cOl+Y in8Kq2KFaX6rbC50ndj6Gk33ttR0fxzHfSJ0U8Opa4Xv8dlKJbc58VEO++7AfnKxn0J4MGrG ntiW0fkk/MMnLOuVJuyG9IRdTRhY4Toh5LN5WdNwar5wPhUOzWs4dY0wh32fnuqYQRKCEV+A vbjqCmBln46/rAxGevghYCylJsR1uF2Na72FZmvjLlp+rXgW123dLN447KwrgB+bRVgzT+Iq KSTawgkjLv4f1V2CDoEB0T00DFNvszxps+RvB4tldd0s+LspNBP+ukNF8PeaUB78vVbIlxK9 LTDTXcJQfSfGSOPiDyb3Zjpphuf4e59Bpvxos2zcLLnb6VVidf0E+Ousf1+pHkY14MubxXD7 plA+/ucWnErFMMgmltUPenHWXQS1WU1nfX/sC1jsmpAV/7tWuD+Ww/qD4ZR+1HYK179hPLUQ NaVHx3vHBuqKWqhiyI7V5Il8iM76XslLTYJIE91WE2ELRNrHm8WbAGc5aIYBTsSloBq8TpPG uhnTsm/uMF1jkNwHS/0H28IHjaWdEua2O9wWPmyU/Qcr0UXiPrwKL7mCCdpsIN2u8RbkKJht mMLsJhIrKuV7U5m8UTV5o0r+HpgYr27biNmH3J0830v4IBNNQg/O1s7N8kLoKgfVi4NM5ECD UARQaPZtJlEwtFla5JOFw2uFP4vuTlPVsrC69UBbuB9PHMtu0BvsiLeogZ8XsZaFmciUcIU/ 3hY+bmyDqdT4U5pKxw0sLJvpDSdxYLcQWMcwnR/mWzvGxnFMG8cxyf9yh7uL5o+/a1uQRnNE 9nchxChUhJdxJEdgJFgfB3NcG8zJscfyiug+Ykq6u6ADaHbr79rC3UZNxXhshKwZrWP8B5M1 06TnkXtgVkSBjUDSnEx9QfYQYflGXj9PyGMMI3VtFlvhkyiow+fnC2X0N1P+jCr6OhYKvU4C CdcOJpAmwzeaWdiSW1jCWXJUn5vFdmgGdRHMqTCq8Q+QgW27O9k71EqQT1hL19oieMCHS7tU B9dqTYMGMlXX4Xj2NIueUjJq4JPpL5d9Wmtbj6H4W5UWf18k8XeBTl/5Ak3qGan9RUL/BIJ8 68dMRJpG6SyrNJ0F11fghqWbRdDXr4O/rroa+Asay53UVvLa0Hr4SzhNuoWLmdKCB1JBrpmQ fWBa4xyHH2xC139MBtBQW3jIiKrLYhMrG/shXx+9wHLhKHU4DeABKRG9hsuP8s2SAG+GQX7A D1JhnJoK49buY9Lk6dLYY7ieIoyADNv+Ltx+qzBJKGrCUWedA2SNSZM/fiuDDRoHjeY1HBue ndrcUTGMKoK1zD/UNgjwWks72xJG1GtAysRxMm5iFmQjKmo4t/rxoY80m37casesl1lNE5A0 NpFleIX52SWFW6FGykjpgtnJ7b1Wsk9ambABTac1PUE7UxO0k4RNFwqbvq2PMgVnf1q/aQtb jZqOwyWO24pJk7w9beEevbzpScmbnkx50y0LPSRvutlourXRoNDi6apd/mNc3rxMcqiVyRvS c17W5A2Mp0cbz8mxhwPy5mWQN8dIwTkGRhcpOLDm6HScA5+p43yVyR1QbJHAdYUtOnlTuFkE HaAc/p4nlMdKubzv1E88UDem019LVcxC9MDZ1w68iMrHSyRhhlIqzwlSWWyNv6C5cQqkwc91 0oDX2laKr0AiaL+nEhh5BMZ49jSLHqTlo/pn4dt5bVo6+Al1G0A5KuAHuqUBqD1fWK5VCV0I v68RFqR+z9EBlwIZ1QFQj/Cpq64QtCUn/banhsTevD9KZcp251pdtQnQZzGEpqJ7/knmtZla o9Z/oPmyrOWtlH1Q83/Ij6AHR/4BenMofs0iP0n+HcEehCW2JqB+uN/A9qqFr9SeE1DNv+Vu ROFLJDSm15pqkzABMGyX36/rw0ix2CxpIOoeugzY8AvJb20LjTfAH5CCUNysuIf8vloD7+Dt B2lmSbeMdCDp48rSY/yBT/NLTdb8UlMC6l1/10aIOLxIi1cZw/U4/ZExHVYZfZ07uq+JAbX0 73pv7cIt7VjbbfVl6eiRh8/Yj/fkhmx9Heo74748Z97X+tF9nRVQq1N9oT/uQmlgyzNj93Zs 72l9fum+3l6fjV7vxPT04ufptxwdu78tZ9rf1qz9Cf9sf4nfnWF/pqz95Wbt76Wx+2s60/5+ 4GU+ZL9ddjtGemcvrLX4FHOlryY739fff2Z8f/7p+iivNfuMXWN14Ri7i8xxPHdZVv/yRSAg cOLWjuFtf+y+M2y/9jJtDCO7uLjWlBSKpK4ct2OsUawfu5dR+y5G3lEYO9qsdTQ+oBp7OQ+E fLVzeMN/+LUmPi+uteAV24r5Zl9N1g2Y5+7NsgFj0fZusse0C1/SwbJFB4ugarDUpGBxpWBZ UmsGVcOK+Q1BdGeFZvkZQZNlX/Ttddq2lJRoWJm+hD2BZ3QGQt/UAdn1ngZkdQrIO+/XgFxM K41/SDEv9QWzwvjjX50exvhYMK5IwQirkurux8i6Iew1k6AL30sTdD7vs/8+HUEBuhrFHBwD vFP3nAl42eJqf75WD99H748BX8u7o+HbqIPPzOAbC31X/BPw6fl/7Vj8rwPnHI3/7z1z/v/l v8D/a8bi/3fS/K/B4rr3n+H/M4ImG/9XnTn/96T5XwPyzl/9E/x/9xnzfxq+yqqs+4eYH5+J YuC52mSW3uZn6W0MfeMND5fF1pGyeBH2gaLYPgYXHP7FaeV9Jq7rPBQfijkMhCLtzEJQXfCQ psLW1p4TVCvu0VB6JYAzH9EqxRtWpPXXQK0hXfnSX2ASP3Yf4On12XQd2y90UebpfwDvrj7M jacD+Rm3ydAROfhpEgdmUBRDEia3cgB+oyJva7zbxJI2PMFVwmr1N29zLrE1iibMPUkXYFMV vLRW3oUug+T1VvUf8zHWxoFxBhjotwtbwBiT3stM2v0Zdkl57FMMDrQkHyZ0R8By9SlK66cI xUP0dy82rN74E0SaVQ4XbRDDRYYdX0b7kyony8U2M2tHDDuAkSnLCT7zOtAf4uOwIZCsrdWY zS2KoA3YIouhWymxIdK6c6/23vdTAx03hMF8n/wf7Q48sCfYZG+RYl6rmCOYLjhWSD//RKmD vZZqMRHalnsgZMAr2NXxV0OrUczzMRAqU9avltZbsPTqPaslz1xpguxGbjArq5+H32YGoLTe GZuUiShM78LtqTQJiqvVeW9p2p0tTbte1CYDhEri4oeJixla54DVJLVjvOj3sRFkxqPkSemU FKwfeZZnfthhpf4ceEUEhSkd7Na6Kk93Ffsas9+IQtWq8yeEAelh1rY59nWmbwbpVKN1DJie e5TV2sVqFdP8SkEUUPd8kKICsZTY6qgO+NScqxgjMKKqx0qNBpkAU+67G/5mXyP+WpmKTUmG po2wcf7ypt7GKQlmkQJv/1c2KdCfTZ5trcyq/7+p18ddmn3ooAjrMazEB8e2Ekf0OVyRzZ4y vqm3pxZLA9Dfll8aTmOXLj5Du3RP1v6+/0aW/tpO11/H2CZjRn8zs/Y3O1t/7afrL3iG/f33 qmz9PfzXLP09c7r+3hvbaMzob0XW/iqy9ffi6fqrP8P+nl+Zrb8Xj2fp7+jp+ss/w/6uydrf 17L199Lp+vvR2EaqPs7nwxUmA2f0zIOgnyRgrcH4Hpo/qfJPY/m2LOX/mL387Vi+PUv5n2Yv /1Us/0yW8t/OXv4CLH80S/ll2csnL4HyL2YpPy57+Rew/EtZyr9+Ul9ef/77Eh44ZhcTO3d+ szwJ6kZAHSIngxUWeC+Qdq1Ok7z1NU2TvAhap0y5Yym2z/w2TVMhFxNCwHIcm8b8g46aWiOG T9p97PTn0pMjzszqYDy1XA/jdRzGy1MwrgcY1+lgfPsvGoyLAEai55hAzswK5BSqlAnhjwfS EGbCd0VW+A68PxZ8lZnwHT0dfDseyg7f0VHwJf6RAV+m/3b/srT5wnahdcvkI8dSet/DpPJY d7UhIJJ3qFr9jy9hwHkC1+sfcpVJMe8McFUpQzU68WUDHVOxRo4KmPayWFm3WlpnUVY/uVqq nCstVVYPwhczRkCvc+IdD3iH7JIaGbrBwyqkQlRni4PM4vmJWTtu1bQptED6RseNti/Ntl7/ 4dWs63URaTQ0Y7LY1785/XqtQ7R3KTcU0E6cFlDveYfpOru5ohMERWca4Ckj3HVEToYC1gZe F4GhguLTnFJB1fJqilJ4bBu1YhZyBxNK88qPr1H/I586BQb7DporbkcuDgn4xJF8BIdVg8N8 nIb5OA3zcRrmPb/Bak6othInqHrxHlR1+ct9t2OEjEOwSo8TIgaEibECPBLwCN2tsZsH/vJ8 UBmjaxltT53r0mhTm4qPnb79GjFRGMoXE+OEjTGYJz+4UpsnbmRx5SmEOMgoE1CXtGu212x4 Ky417CzFaGy0WVJlFjxKLdtTccna+XIG3wi/SBq83Us08L6kA29lCrwvIngff0UD71zsWLmV kKx1fdfTbMqCWTfCmk/Zl+n+ppxJf+Jp+3P/9p/o79eLz6C/s07b365/ZnyLz6S/X11x2v6e On1/OuZ69mItwQI7rwDdbkh1O3v7pdjteOzWFTuL8UNAPTfV+dwgWzZH9P/WXqqeDnHPjFgf KQfco2FID30GG3oBG7oN8y/df/ln9P+1M+g/3X30ixrC3TqEu1IIvwARfmGqT+fo/q5oHaO/ rH6YwJn01x48TX+lT392fzr8vrNIs/tS+HXr8OtK4fcChl9Pqu+ZwRE9f+kQVRqX6jmvJQO1 rO9Uz99exFIRuHGZQ/32EmmAyd7C0Dyfcgtrm8lZdVlrxqI1ie8PsyD9dFR6Bi4LF2m4rNTh 8uIULhcgLusC2nhmjBhOA0OkNTUcLf49m/7+84u0vtam+pq1/RLsaxz2dVFsIsrzgJoXOA3t fnkGtMuQB/O0boVcKB1uSfV9CZ7fKseDEhfJe7BxuRo9FmdxyX5WjVxRlOxCGbCGbY5XpPMP xr44AqylT6CCYg9xcRErZCqDgfQWu+0unbU/co/n1gs1vLhSsE1CsOYH1E82joX6G56gghNT eLBq+esz8Z/qZtaFjJf4DnWoePvkFJmtsQk16u0b6RiDOYVTdogh8/xPuQbrah2/LEk1dD7y iycF9Kxa4wiwb3n0dOT7/LzE5+clPj8v8fl5ic/PS3x+XuLz8xKGz89LfH5e4vPzEp+fl/j8 vMTn5yU+Py/x+XmJz89LfH5egsmXy/X5j5x04UYHuZv4eCk31kN0SfJenmVVDjuDirvfVzu5 liKNVPH/Ie5Zw5uqss1JQ4mQkgAtFKhSeQooUlCkgDPlkYI6gSROE3W8vgXs9aqDCeBcgzAh 6uFwgPHBwxHR6ziD8/lARsUn0yK3kRk/L6IXcS56izzcNVWKUyADvc1da+1zTvZJTwr1z/xI Hzlrn/Xcj7X32mtNpHCeWKncH6OY9kZLap2Ylok9FeFhR87UQ4APljy1lFQevAR1ertfib0U VnxbTTU6WPIx3qQ8cRIryZbDt6WZKwjNgUqs4kQK3OVKXbKWRHhhPFZmi7gxV1F3LMuTVHxl lP4IJvWGKgm8wR2sgAyve0Vd01QHNG4viI7gby4LW9YIOTYI1m+9AXR5O7Z1J47bqQZLPFks x7bI6fp0gZSEv5JeRvLwlSpYDGbU5+Ar4ItVb7Nf8W6J19n9QcreddvlPN6pVO6dFRBy+8D9 moCa6DzM95H0CSwkUUoMpNScV0rP/QazOX7Iz71GmsX0xiRdTNB5UVJj9fH4XORVcVJnug0H RF9adeA8apO8W4Al5NwLfDdyOyhV+mOlKKB5FzeKw1m+kZTay3IMo0wzjOULdb5XC/4frB1B hMR+I7B/mNj3vQS8bTVlRGP/sRbZr+PsX4SoQbaZCpL1m1fYskasROtQAhev5fWYusY/Db3A f5Xi26K6psm+LfKHKIB6+AtG2VwRvMdFcMAsgvkTckQwQBPB0l/qIkD3lfub7xn87wf+D+Tn fw3y/5Y1/xNN/L/1I/mPdJdbqIqb6vtM9r3O6ymQMGJb1KmzcvrBnmw/iLaN2scpej1g6gT/ Mj5PJ4jcp0tiDRraPjlKItgDIvgsrwg2r86OEyPMEnj9ckECyL6Wz5v4H31W/o39bxo4NGtY kcEgzRb1zqfz1F7vMchOebWISOymSGSf57XTXnfijxIOqa1O7pYGsC557TCykDuxk2BhToTM RHvsoFjLv3Prq2dSvA7cQgYS8bXKvsaAVAeLBSntV7HS04GA6muWffsDJrRx1ZCNO7GRXtQy Kk11qZulPciwlNi79B6ExRGcqTN72KU6Px/83hyH5KCGMtEiKnF2mChKXav4DqvFleDZYaPG AKZn5QWApZ1BLAmv5NJxZpVBR7QEaJiXpNVcFcXwlsqVqcsQjKPNTOBxlIbl+sr4H1TIlvnv 0YOU78DUdunRaMjleN/ORopnZ45h/jXkrXfqMk3fdfviaWlxBdqlBE/AAUg6/OU2Wgj3BH+/ zk6u7imii6AQgG8cijkChwl6HjLAQs+jnzP0rHI9O0Q99yMOY+NNeu7N9cyE8c+Xjte3U41P mENQ24cDqB1HJVd2I1f2AbOQ1ymCsmVd2SZN32nStKbnj8fm6plxPc/mOHEvEOcVIAKzZ3ON 5+AemMUd7Q14tT7UQblDxneq3Pvv1pUb1JQ7KB4bZouU6ModfzSr3GGaWodn1drgsJcvA51i wHr54tMNmjLha1LlHvEugthnQ/0tdHnTZkOXN3CHdag74c3be/8wzqTVnlyrp2xY/+pHdt9d sqDRp/N133utu++pi7Nq7SV239DaLvffKVlCov0t+i8sNydnlXzluE6VvLoWiOhZW8Dn/9rc PJxiH9tRYqGXhk2GXuYYeqm06G19iBr3pVaj6rc/uptd+qiglMcsu9k8q242f0yuPrRuFlh7 7v1s2yNZRQzI6WeghGm6v66rYtvYTlVRcBeGoq3VdHFiAepij6ALl6CL8cX6Oe2VQjDgd3rE f2QkRb2so8i7mtagfjpb+rSmLeGA9hegs9HRa9RYGt52THjbZuNtX2B0IN6DCirZlykPa2Fo fvZvp+lk+SXuM/XgMYRO8mpYNoZQrOm9sK9Gv3vFOzZTAOGog0ZY2rMoo9WEpb4Y0+LSKb7s a+HRW5TYthmNK4zJvENs8m/1KK6bYVFRHe1RWxBiL88HkuaGsNaGpgkAVXytAfb4D0T1BBgQ tMFrBG6rSljghA9dS88D/whHr4f46OXSRy/LE+7GPPUFHu6DIXgeJVrMax3wfveU0W+KaIuj tNLbFumrKT89D3rFCRvf/9R6EPp2IUwPC5a0/zgKCS9DJP6LllBlNhgKADATbSWAWTDeNGEO cDxPbQVjLvCmZW9zg+1GsNOVnmWnb4wM1ec3b9lkT3RIlewtU2pa1OkSQK8MSgASPTzF2xyF dXF5pa8s8iyIsEGyUWc8rELn8jE9Hzx1E7bmasmGJTCx17AAW4b/QhfzVLZHHYmTsc9F+v4w hrpCZXvEo7HcbR5m7gR+cW4w1SgR7WZyb/2OVhLXtnTcvd1sQOwrw4A2IXt6pCmmkl/HMwjo BlTTJtc0B6kWS4i1bRCsp606WsGzC+CjjYZhzVSyDTLr9W/H4rAXIXP7yZ1YgyWECqNbVgSK vYYNayFzs3dqPbr/L/Jc7cnXV/7vS3NfMSU4EBhP6z2nlTOOg1uNBxNKN6NJhqHvtBvMzCXu R+AoF0bCQ+wp3VajE7DY74PFCtZj9EzpzVm+5g5geQD2K4o8HhrG3hXCtAmspQ15towfys9v yG2ErNIecjZktSjL7yvIb40nacdoHY1xXh9K436NMW6klfVc7a3qdp17n4cqMVCHDIaZrQP3 NZ4gjRJh9vTGXO4xbbVnSg/kPsx8txP3VM4H5pmhpGwQQTrAfjhD3PcyAlrPE+JZGy3zRtzQ y4gVEkbiEv0ORGSoZTzfP9Z2Jb7uZJGOY4qA47X/0XEM12455GJ5nGNxG1hM8bkW938s8Vwl 4NlpiWdMp9yY45VGW+I48rcsjg8scSTXnDuOBpcVjuUCjk8scdy+pmvyuskSzwABz15LPGdW nzsvp3ta4XjjiyyOTy1xrD8rDvMdgcd66ncEkt42XAnItLyYJSCtMpBW8NzXirdYdczy49DZ kYDqpTkE9IEBZtRpmDfrT0uyR6PGlItbpMcu0uOwpGfrfoOeTLQMCZLTmHzBmp43Yzn0YDFx IimHmI6yWdRDoMVu0FIt0DLMoGUcl01npIw5V1Jy4nq/P8+IsxVQv6hfC4hcWmuzGm2EdZ/6 PQ1wRQZmJ4w1ee17qYFvtoCv0sA3vtZm3DPKi9JOs2g+QzTh62XJ3+59Wf6ksyB7+buu8PeM 04q/6/dl+ZPOzt+QY+fM31gD3wwBX9N/6/guOQuqOBflOY9PO7rr+ERTfcDAN+7s3G05nnc9 oOMzrwWuNnAuFXB2M3AuOOvyjvsHtGAbuEafyUeCfzA0OoDqHAG9wipt6dFMJuXEZU3kF53e 92i0iuf+bSHlDscUAnWRksTeSG9/UFlmsP9aeTZG22gzv/M2Mas2Ezpvc5VVm0y3TtuUWLX5 a+dtDg62aLO+8zYvC20ERd/aTagLMEec/z7VdT3JlJrCH64dktfOlvyQpxdZ3pE64hBwBwTc m/bquKdw3Jo/yNEPzYv+H8c7RW8xP91GJLjUWFuY34OE5SerXaXb6724KuWr7S+vg/XmzTBD ZeFOr9bhZgmtb1H0byuy7slmbH1hJlrOp5JSAxwvdv76kO6hCHfgzHet3inQynmAD1DOF9/k QXCUbxsop2YJvhhRXgzgQQ3qGoPcfrygMboMOg07WvDmYUs+OU0uwNxxpaAJpaaUu4C0dNDY QAeE/esqvrfjSWQifWjXgm0JgzuMQbKgP2pO9NTyMjd2PxWqiZTx3RxP4mTUjVlyoN190C51 f8VJLq22kAnPoBjHU4o1PsFyeuM7Q/SuD8vIveXIx+BLxgIAzMvpBsc4PEBomFkokdseccJ/ Sk2ZbCe6ugFb8visAvR8HFgcShDDBLvdlvSSnareR/1ado1YceYK9mKTjRfP3rIfD3bkmpfo WMe9IoBDoneFX42tkt+PgOLCdHaJJzcxVziIb2CtzwvbaVjBMh5bJUWKdlDBGxpTMb6hTPau VWPL5NgT6vsPYiaQ2FZFf6MrzE5pL0GPNfEp+Wkb5CeXIOAnid3u1f+OvCje8njjLfF0VWSY Eis/lcQ1InSYdLzR4361PlWh+Mrrm6T4wQJ5z6eNqSH04okhYk3ntjyMVWMAPIHv9qP1vDeA Dv/k7nRZNnq+dpT1Yo1+4D0J41dL+TmsytvRKRUd03aUCjv0O96yTHvILqAsLY5M9CU2/wi6 3I9ij5Fb1BcWZEx5JZY3b5VMOnvIhuOii+8EJRN3tPMsGfL7t8BfGJjxGI4f8pM34pFWYgn8 TCYe1ICSiWXaXyo98avqCgRTr4OfgcxCDztaJNmUeDO+IXE3vjDuwVqFifu0l6/U3WE1gvXI CcYfZJ//nFsLWe0O/R/codmt/aM+Sclenvw5NAiykUG61jk3TlTbIrNAngCtJhbg+0LxBofy JNKEfUvFJgG6kmKMjAVnkDnknbavMGJzLvx61wBnr12L2WK0t7BL3VSDMP4+iStyVUZFvJWE fekURUVhEVd+5EqP5wnGG9oyExX6MsCmDKDOKDZ96G8KEaG+gFle8tTl+7hdsvH0NjM7pLeJ f2TsRIykKASn8mdafMSwgqF+5RmrVQkbEa3hBUvg7wAr6Y+7EM0YSY2WitsKGJVDW6ZNf5Xw gLgZRYnFWpdQiavm5CwHqOEheU45N/+AkS6FbT+i9fg/HsLXMsqm407cJaEjVxZSYukwXYuO OcOZRdScvfeEBlmOkBMQo69ZCTjAcZA9yjRHPF24GEbA5vjO2akLsGF9Y4GfNk1v6Gfcy3av OI32G3IqP1Ed76PQpJ1yiM5fjG94o+H9UEQerVvy0ltU377YFhlqAX+iBOGLNfjIvBBZ5ObN GtGUZ4oaX0BjHqgaN5/wkDneRvVG+fTSg2bdpkdt6CXduYWkRM1KCCc2JXT7SrSsQU4M5cDj 6tYwq+dfqtUzlZCzcieM7tAmSI9+r8EDUrb0EL+TTW2bA/T84RLaLNY3+Rk8lNfol0zNdYnF Pf2b2nR7myPl2lvfvxj2ViFxe8vaVVu4NhJgdcU4VClejzyOMgqhRbUah9bJQjQfsLjlSbJN MArWwyWBGsphBsZgRu1eN5oVvzy/qBzATZe68YRF9rbGdw1Ds8EYEaUf3b2Pn3Ys7q6GZqYu 5OOBUqg6quobYWaFBQ0bUWzYTORGtJdeevQK2gv+cGhWql/cZzOe0TChHov4ucKVvH8LGgGh 041/VlxsaDBEXxQUowRbTZJnQj8XfYyjpyVc/oG0+PBRHqTwI5zqfZ4AbRGy/z2D8i/FEaui rmmXREGJyhKP4H60JDJLMTQqXjk22i/EvB/gwFsO8zpX21xJ26cfDDC4+VgG8Lev2P2gm98k pCl2NPwBX/8sxL4uh/GUfQg/temupizoZ6//0J4JuV9N+sn2Pu5DQsICfIDlonis1RYdmE1l 0HTARvv/hiViJTsHuES03+Be8XubaTN5a9IwMSpFiTvYvrIAekVo2TmbDn/ZpKVjEvzH67L+ I3x/NS2uYFhK/Q4Ntk2dNRteXznLFekbyix2ocvFbuyj6Q2eLvGzikZ4NayziLuqPpqvlboO OQMSOSnwaLjWTKg3iKsz9kIPoeNRT8esAnyZCLrUxaAtHNEmsmc2Qv2rtGTh5/6moQt+7uyT nXnxOfsw8wx84r7BhQa+8UK6orwY9504532Dk6es8L32n1l8e8+Ob97Z8GXzHyC6/P7g9R4L H/LaztsMt2ozuPM2x93ZNmaf5uhJKev+iTuCz+wydgTJyTELI7OYz6V1GyiZgBMvEvfEeMqc TIYm2f/qpC77UQKiyw1EfTETGntjQ1f280cY76wS3nnwA/2do1Vvsd9IIZbTj+1PdYbKvP9z QsczXdz/MfBcjHiE1GE5mDZs7HQ/pSO+OZb4zsvBV58P30VdxfdVqxW+jTvN+PL1RfbWhi7i u8cS36gcfB/kwze7q/ja/26F7+16M75P8uHbv76L+FZb4rsqB1++sYYt6Cq+CyzxfVFnxvdp PnzpdV3E98oPOr6fCvjuMvCNEjMB5SBT1p39PEUco6YjLkoFJK77QmzNJn1BhHPrzkgvbUFU 0JNvQPDV0IkeQqbPGnPtUXZc0iqPluUm+tp7EhN9pXPqI26HBpZ5057PWOYRewTh6y3g77eG DyO8Vd60GdbwIxHeKm9aX2v4Uy2Sdd60Q+2W8EmEt8qb9idr+PUIb5U3LW4NPx/gc0GnStpk lbO/PMUC1pMH1m0Bi/e1rGAPHesI+1Ye2O0WsKvywCoWsLfkgb3ZAvayPLATLGCdZlhz/7Ef k2jzJVpKmUsjpi0RXxumbAn6A+wjSnbloqVjpdwyB1O8wApSnbpNi+LvS9nSnXJLPNkGT6MM dxv4GrQtyFS9ucfG/UVeCRt64P3dO+aIEn2/276n/s0vyVJsA16SdeAWAv6xBKOfhI5PBA7G Y75xqd6UyTZz2dawlj/dSYQDaRiDcM/GrNvbB2O1wb1Fgr4u1HYovZ7MOPpmTyGFNsfrZkJD JeDE8JzsgLKtUPN5wV9e+Rlu4GGBb3yyoTAb56Xl9xDrP3+HjGFC1Vv0QI6iMJv5rj5IXo36 iI6pldRH+ABJ/maYTb6X3xrDm0I8fiI12Njf0dOTFQfZ9JV6CjbMB/0A5oPOeRXAZ7ZRfjLK o5OhWiJs4lO6/1IVZhunkeuMgPSwZIbNNiXmjBZjxY9tWoqyZ1O9yL/hOcuMWiCpRzvN3SQ3 6/z30/kvB/7f0anuG2aDpmVznjUdtdloEyB6vphUjQ1NAUNhtnWcxK8wmx4WpvQN10zkVkHK X72tS/kaQWhFQVYkC2euoXMR1xXP6OncZoRZbZVZXEencXGViOLqn3Jr98XM8upwGpKT/zBl dITIXZiLLUu122DHD4z+TGD0Sr0ydWQinVlDT9ez1Ln0LHUdU9TdvklIUecKssd/KqSo6zMN kxK4or2NFHX9NP2ju23OU9eBH3BD4K1OZRkZCH/cYQy791sJpZLYGy0CvWOommbfJKbZ8XT/ xQ/KX4xZFf+oBCaOg/JJ9b2R+PxWaPdRU/4PPv+sk+dn+wTZPFcmk3Inf60nODLlliKSIwM1 vWB8uYsrlvvqBWsr6kzpxDvutyxqkijHIN2EpZhdLAGPQanDlElTYp6F5wMCuzw5XufAbZlq D7ZrQhRa/gdPPFkQ/6aNQ6lzYZRsTuyOdk96m4nQaDPdr5aopjx0sXJ4C/hYDlx3raGf1zu0 waw5oBRm9uA4cwkqdBKgbBqK1hp1xRva5GirHKUK8dPapng9i0oII97Fb2q3GfcDQIEFag1W hJejzYj4ATx4GqR0r2xZqLWIJwVOUtcrPk+8viB+EMNXCaCHEmsGGC0nZxid0UKd+vND7FcF SPRn9POZAm3c5gByEnA5gRHZDS+Av+cpQHG/+m/tQDa8Xo61RAbgZf5CxdciS/EGBxBJE0vL 1dFvEFHIAwz0hHFdnuNJXYTnO1GXUt1WaV9Egz2CVDtSRQoFbsq/hPlsmiOzR06Leyfc7cZE 7R55tiNZhVOxLVnl4r+I65y188JvaO0cYvfg7nm1I7u+FvNffqMtenE3s9sOlE1I6a4LZmCY 3YpZ6tm79DNhJ8EQgHjOmz3/Pkr7A7BaUKqAA4sz6C+P8o2AatxBOC9ZTfSnxvx5LY2LhkYG hhijRfx0O/502bMaEcaA7Pr3qL4vEV8CgxosFxB9qkD2uyxouJ5oQFniEmW6h1YgkypPLSxN 7AZLqcROUeNMTtdMCc8zGwriR9voaYW6FGzAMCN4gV0negSd8IzjI3GQPaL/QUH7dFJJwICu mzwOkOTJBfjOEUmrDQ+Go86GPhjthobTV6lCkykIpBzwbxA0isKw0OkD2guqnVzGzrwyXoHq Zl/RTzy67UzGQ49kZQzLO5cm4+40X/udupxpaDLx8+1hzQ77EZ776OdkW/76V4cF8gv9xKfG hGW83Uod3iPCe/LC33BYMEED3pUDL8hzFG/AFvWF8evU8m/wkFBuGW6D3/UMk+KV8isLLrq2 wOb3plVGLxgAK5PuxHYc9dKXoDcXT493P/Iw/o9zztQynHNovG39WrLN+Sd+voLPLvi88iPb PwGfpfC5Az48Xl24wpEphakF995N3xYNwEspRv0J4clgfLLHngNfgd++YwU/A588mwv/HN5k XmkF/yd8ch8NaHd7qJX7VclvPH5Qas+A+ubi0e4/Vux2q3jGvKLOrW5BxZ1e/i1p8jRoUtU0 +bjrAtQkItLWD8MOSrZY4z/vUwT4W+H3lz+y/S74vAyfJxqz+sxKaN1AEOClki3n6//n7mmg m7rOk2TZFrawBDjGBBYDgwTh0JqMJRgMWJQnA4lB9pBNKWnoSpzMBzqSPoWuRbao7ETPr8qh PUlOd5Y1607as6xN0jUOIxnBsqdYIjXUOJzGQhZ4xAvPPA/U4IDNcXj7vnvfk55k+We0GTvz OddP977v3vvd7333u993f757EOmKGxpwPUT94vwCeCFpUuEr7pEPAabCv1EEL347Dn7uIkg+ lga+YTG8QCOGuJUcfFFDJotzawVfHrzA4+VNftfKfzKzhQofEMvKLvw99FTxr8j5j6T0FbPx lNKNIMoQ9iH5Be3hwjq9srMGfQ7cr5w/UoPUmNB1aHJalnnc3qRylYjpvED0NdlLg7xMFmRi RLl3DLXoylY4FYcMYuaRsmJnhsQMoU5SKVgcAjnTW8wInhGd6fkHtJh1IIPgBQB+31uBbtA2 55qOFpQ6As4tbtfHGnavVDnAPiYxfhvv8puOmjg87BxoMXkrP/aG9K+UzTs4g3ed9QT7OVeg Jc9beVFOfRdK8W3sL2UC7L/yzFk38/ErUN68gxkef7+buQiRiySy0NJNVkcR48E3SWv6CEou UJgApRCidI+s3yUwixDM+pIx65YxiyQw605gdi4tZt1uJgLIRBTMzkHkXByzPKAtoWWhrO/K +1WO4aoV6fu8SwAVmJwzO+wy4FyWqQkNx8Y5EMWpKnbB4DzFHyYkfUggPFDooA61FVxO247n rtnlyLOad+V/MfKvkWNCnKMryoTCj46FmbFw/2AjVj8ZpLjL44pBHW9q6YFu1pIOPHwlnuH8 yXC/uJSsF04JSLAATg3PG6SrqIC+feJaEuj3g+UdLRq8W5see1SRtVyVfnAUpSbB/6rmj48/ VBOdR3q+fN4/jv69U6Mf2SB+fSLcFcBIqbgG0WdXTQcXgDZSH7fZBB9cqWpV932zqu9/EJH1 PbyeYR1yGrud+rBbh3xmakYRE9ZFHSOeIUN0wRJh+cjnZAoK7BLnHMk5JjlHhGdGP5fQxkJ/ Y51ZWrBS1qCzlYfFXVh/FHLH5NxDNxK5TZJzWHLGhNUkN2snOZ2zOm3abZ02nbXTlrHNB5aJ BYoiqVsgFd5k2DB1DiSsgIQtCNZp00NiZqdGY4ltJh+dGO1k8+LjA0lzcmq5d/qcVj5S5ZwP ZgjthMEKPD2AOlSbPH4LT0CTuY74ZsR6jZ1sHSuBtkQfHSbr1GPuNcBc2CUtN4nDQtwz4eoC +mXq4rLUvWGFM1tiYhWcC4TTEBVIRiKQiIxcQOU5yqMzzofdLlHD1kmVQ+w34uIom2P6uPaW bC8jepkuN9MFcqUL5Up7f0uWl7msTjwmS6R29m2+ss/NiJAsUlg3cxkil0lkoeWMcy9hrmWy q8YgE4o/YvKjMcoEkF0N0SJxyWRwoKQDaLSQd8VQggEdVgMpWdWogF6XFBFM7veIt/dj0t6B 5Pb20vZ+7GUCbiYAaAcS7b2oTkxqb69qaGhXDw2kvftJe++fsr3hK9ChSJvvnQw2fKWvMoAN L+SZmMefQXY2QavRTS+eJ0DGEVlh4XXg/dUadk9yWSewJM4ZeofIhspQlBlGCg5e6HcPMO6x cva+ZHgAJVCA3zkCtMk9XO7MFXXR3mPIwWIOoLzSj8UUKR3/iOKnMc77PR/Feb8olfeDFcTe GfyJjuAvPPFZEv9T7v/1MCZWR/RLwKCLuGK4+SRgIN3gUy3tBiG5G4SgG5wnHDCk6gZDtBsI 8W5wXO4GBXGGuEQYQkCGOA4McVzNEJe8TMjNhOC7hhIM8Yk6MZUhLkHyJYUhPoHIJ3GGqMQd ehNJ6y7O0R1lumCURPcC3PV0UNX2KBLCMHiWfKj+OKcflzk90agLpFH9yY06Sxt1IV2jzk/Y KFCALkDyBaVR5yFyPt6oJ0ij/nSKRoWviIsmGlUUoJOkG0Q2kFks2qkHD2uU+UzK388I5dco f/9lkPFTfg2o+Dsg83cgyvgj+2PR/1D4OxpGDlfnAGAKNyGHQwEEIRzafpUk3xfU1sgetGBU w8k9xshrtMzIypMtBV7HVfSOPLdxpvvmQnaZ4u/M7bq6gs0T59s6mRsaJPhVcQ7+1pIcYrZN DOAbcvffN92uGxp2RQtzlQuCWdYUArb2wXhzkrvpuWiynLG1ZOELpzj4hlahT4vjKvdRU4+p 6e+0pD8BPG6DNvmMm20tBfjKOTTYqI3PN+JSjnM7qciC8hEqQ/+vpue+RivzGStLcJg4wVy1 tNsokpE40IMUCN/6HtncLb/vJ8XddeyJurq6G/vN3Eftkg7GfHEOyieamC8n5nOM0O4Siopd Asl0n5Kp/SZmkd/yjGDp4BwDvvwfaXuwpKVKMQQsPz1YvqWbYwbQxV5DLu8Y8HSUcI6YOBPG xxLSYQYsTIxUWiK352B96WhjrvMRbM5aJtb4FZ8e2s+Ma3+3Ar+mdPRQrnOBAj/Hly+Twt4t FtDvAfxBuMgk09tGv/l7xBFxIadb6xz59t3FyD0CLgU84HEJGucMnikMashhvpDv8b609yY1 9KBvCIPvrQj0eOA9Lub+N/wZP9JSjGf0x95F4WBq6wjqsQ9p6rbWeW5KzivuLXrd4S2GPE2e hiyOgGwgU9NOM1/Q3NNQ7LmsfbqI2gsjICu0ID5HrE1+NhdefFsU9Z1ajZXr3trsb/yMd+Fs den6Bh23PulsYBzVD8+Q+bTMx0BFIhNDeWg6nyt+wbP7S7ck6aK8E7MN/5/tBnv8DoZTEAJy uJ38mO89CK3ddD6BrmMspmJrPshzHPTE2cdw0BNzIY6zcegSNLGWn37N+fluZV+ZWn0uacwj qjM7V2SJ/r0OrTO2VKyT+Q2H0LCOKsT1M8Rcsjnjab30QP0sn6erGzf/27R24YexzyVxEcoL 8t5AQfJ9ng/jIN8CEODaZr9rFujcWbIVSVT/XEjQcdmgU09yZ/Kp39L5d0c+MtrKw7dwnqQh 8wSZLmHM8rThYtNzuHWbTBseKiGTTXJD6HzT8Gmtpv8OhqsQBuRA9cnZ4nxT22ylv/OzFXto CfkePv16e7XwIO6tHV0W8mYT94zllk40HFYmLlFOmYf96WnSuXlcMy5sySpjDuZ61mgbFrsb tMwzC4iD7oLqGuVcSZXw0hWocDexz0cJX1gacw6PEsbIEzccHiVMca/459z1asxUQ5QqB4gG 8T5VwuZrqDuoEv7sOiQopk269dXRU2Q9GtcXANV4F19MffmSLl72AHbx+HrjKsgx3HXnwhKo Px+C/pQ83+corK6qqRXI7boPof9dGm/F+H2J+DJce52biP8Y43jeVE0cpd+qbd7fdVG2r5T7 rWekmM30jGxxLsOu5lmjawB+wcoU+9le766uEl6+IUnebNwFulSewKm2V/mcwzXCPxJvLTgt l4t+NgEXewbOuA0kztip66+ZqP77af16rL9RXf+TGrckAQrzAIU6Li0O94zDYe9kOPT8ZgIc 7lNwMCAdG8l6L9QPahLU/7fAfemrfyWWWr1LVf2RcfVXT1H/jLT1z5uw/qJx9fvG1b8gUf2H H2hVZ9GZYbtwnjiya+4xNeP2C7Cewn55dswPlivVGwSVPivI+qwQZQaSjTU1MDpXJyBJqmwt qrITAEYvx8sqmbCsBBBozyZFLZ4ZDVN/kYZwoXwSRVnfw2GKktoMusSMFq03y2rb6rwBg5xT uSMoGcZEnNij125Pp26r8/cypLxelgw7k9cipN7Tqd/qvDZxmbPpfGcaYFxjriRrzACqafY3 zIQRskMfngeAmxEqnd+lvJOEh+TZFcxZ0ny9YZeYsY39Ouj90gG9VOLxGzjGKPhhTIcPik6f x1rBLBsO7x++4BoI7x8jt1cMtTBD3mywxOzUngVLruJc4qO+CVUghZuvs5lQjaUE7PxJfBg9 E0qH11fFGXQ82sbWpmC3GLFLwi3iGCK4DUFv/3ECKU9Qp0LraFq0Jva7cz5IhoYUvKqQXg7p oF56yBM0CC/lUlwcY0eNnEOFC94wZODM1Qlk/HqOMajwOabGx2G2PDAFPtumg0/WF4lPMs/J 9/tFgfMMUeA8g8x56WBnRpZHSj0dRk+7UcWfqsY91UmVQ7zHAcZhc+YGMg7Ppvf7cBeKj3uO l8I4fOnI8Pugu0A4C+GF2wgBCK0QXn2fjp8wGAr7ckAefI22B+NNGH84EX8Z42sT8VaMFyfi ZzE+PxEfxriyX3r8+Kpe/38/pd1xE2OTVmn3Gmx3XP9gAzD+3+GwF8KO28y7CcIqCEsCCfoP z0im/+oU+ttT6H8ghf4vpNC/ddr0H/33KelfVpZE/+EO4KM7GAbk59nbzB+A0Arh1Y4E/VtT 6D8yI5n+ZSn035FC/30p9HdPn/87pub/dcn83w58dAfDXgg7/oD8myCsgrCkPUH/Qyn0P55C f00K/ctT6L87hf4Hps///qn5f0My/7cBH93BMADhLITAH1BGK4RX21Tyfwr+d6fQX5ObTH93 bjL9X86dNv+3Tc3/5cn8fwL46A6GvRB2QNh0m/lXyc8lJxL0t38GZrqK/r0YV9F/D5rxKvr3 Y7w4ZXxQ0T80ff5/Ly39V5qeWxXn/41J9B87DrxzB8OnEAYgnL3N/AEIrRCQTgHk87/AXx8g xbYo3yOUm8zvAWMyvwdmJtPbnjcpvck8IO6odBmbe1yruDM3wr6DUmeFpGk71dXVtY0L3bjU fjnDp/+R1m9pd7eXePPQNYrzE1+D1Jm9ghsRLdwZzJE1VQb0fT+ssjOWxD+0GZocdt2q45lb 7oFr7i5DHQfG6v6xKJh/8LxFJxh37sILwhwjxKDte9wQ9Qx0S1LvGaIks+vOh2VtWcsWh/1R zxC8DJ8Mj1zo/8l3R6Ph6KN9UaYv6hmGZJVinRMWzg+K+mhvtJd/tDe9jZlXZzqKBqSVmI+f Juy8VNvxCMARMDAHhye2HY1pwNLVm4/lyRZT+B4K/1/ThI8ivGH68JH1AG9Mgae8QfIoK1EO M7+mWWpYTPerbmcXo/1tOtptasN75mylHawoL0o0S9RUWQO2oPzh09AiDzLKprl+MtrOIfZ2 WuC0dvzdCnycfko2ccI6Co4k4KMU3jBd+Mh6Am9Mgp+YfosU+i2S6YfX9OmRfEMTk2+Kb7JI zNjOLqVzHaY2WiJwLJQpTFHmdOdAku1GE3c9ogvP83ToEzMb6e1LXZRCGVT2ZVp7NaJDS1Sf sETVMipdm/8E2/x/goa0zESBTjO/nnQUKPBevNTEwBXIxek5J/oEuaQu0Wm2rE+UODF9/pfo rZ6bevpoujmgx8RM7vo29hs8YwxrqIAmsxZGoegmCN7bnqD65SQTVOPP5/zu7XS47U7MT+0a j1/jKOD3P5+iemuSKapxeK1/O9180A6cD9oZzpbRCeqFayMUl9uYEnp7kimhcfi80To9fL75 heGTlv/CqZyalp/DqVw6/sz56be0xOe9y7zyOj8XZNi2qGcMRvqoR38G1NH58jKfvD0TZ5Up /lvZFVHolIbeHqpFGGV1ArQIZw8qBdHeE6RRPazBMpfqCajHJM6np+AaJbgaUnFdqL7/5a00 PGt6/jRExEp5c2HkutKHEl/igqufcGk/x/S3OPq9c01HO8b1ITIp37jN1OQlUs0YWa4oTx7G CN+/H+uMT8YP0K1fA3QjjcA5hqKMEGX6VasAKyfLA6BhGRgrNjWvA/0S1wPScMJZ9Ryzmh6z f52WHni7obhZpsdvPhvPlzI1oM+CpK4e32vvMCk2TkUKRdaqaZH1L2n6qUyLR7jrMjXeG56A Go7+SXopocf3gB54Winy5Tgxgl88LTbdDi1uvpmWFqeQFnb5fiZKj9ev/X+lh3qd8fIbKhmX jTeW+ht2RT3GMyjm8lHMFcjyzWEI303cZxmkyhj7lYgl3rZ2Y9yGSify2lQij2wszeUdMbXc G0geh+mJR0XlgS9kQKeZeIWUaCb7pYs8QcMWU5MbKfylOBadRnn/pPxtySMmPxrjGEaZIRWF V0yWB0DVFHY+i9Sl2tVJSt0col0NKCf/4+d9gUFS9x0cfl3eDFOITpaCtu9I/nc1NcJf42mG bM62l6/Qc7Yn+QoDZ9uHOyNtO6ECrmY378jnavago6UadIKGrlfzpZ6g7RCWm/ac59zXyd4l vBQJT5/SLavlBrTSg+VG+jDTR75E3tkpyA76OEAfLD6wXnu9Vjqwmy/fk/bM6Gu/pAxktfNV O9DdXIWdq93BjXCnx97JB5BrP4PBLGglpRG/EAXoADSbs5IWW0mLrfvEHAK1l3xyl5Gv2ImH ba07+YrdnHU3X7GHswINaqvqddJBjAIqINwrCBGDFYQWiZ0p4+Z8MqeBo5nXkjd7eaueq3iS t8LvfSTTTq5iZ72mqrY+Q3pqN2+FuoMVbHKNKWtbL/5C2fhEv5teemY3b8OMtu8gCCjns3jb Xi6btz3JVeh52z6uwqAuix7l5OwHuG7lPD1ffkB+5yBm1ca9nJbf+CRn1fMb93GAbUgeBwns 7kQ55XtUv3fGf/9R2EPxz5uG33/4z2Q/UPAwDpS4EyFoXU1yWsvoo5zUYd1EH5vp4xFyfDME /Z8Ljr2Tp/CP52/yNc4isjGQOw22jqmtw1P2rIbVr/SLlfIGQRHlRu39oFTdxY14/IX2eg0+ V8NTOrhM6iHI/EBD/4KHj8B/069OvBs8/IKcluTEQNYZ6Xc4gtnwUyh0dP+ANF6hd/wbub1J 6fwRjPu2ajmvl7RLXa78Tkp9p1r/fY2yUQ02apbPhk3y2aBBwE/QoOCzR2TMlZOxKn8DZerx /zW65clh8Hx3tY411WdWC0V4GE+vo+f1DPxTZZ5bNufM+swqIRPfXKbHo/nqctymjh9gk6Tc 1FvX7GczuKpNvCNU6ihsKEC/zQ3m+iziHyZ4C3JDd0MoU9N/Yss+beox+Voo2y/ns32bJc7U fPJQDvR8r1mqMIg7uOwalGy1AvNzcsyZY7pEG3ZJq5m3mzlHYK19gdNcUyU8+hK5ka+00zlX vIf7Pe8IeHOkcjMXI4iVdrIzgkwX2aeYDT/o+NEF6O6hLn2XI3ImuWm6pciXDngTqhJ2mtGT ZECqDHCf8pUB7yzE4orltI/pstdUUeS+81OsPL80xs6SnF2kwPDnUOAJ/AIAh/usJGc+OVoo PEyB1zKFFBqPmv8CofGb8ZWFlkogawidgmwtbz7p/F5wI+kPQKISIJFd4sDeOJQLJOrU5CCN tnPZ9Tm06IU/I0Rq9jtXiKvJfdlmfqOZP2Bee2CBc3Z9TrXw4IuETJ6RHGeOeFdnFtJInFmv JTgvBSzEmeQyHmq/oBg7ptaj1ecgPvg53dZnXe0Z0bJLGrPwPh9xh2dEx35ZrCTzYfWZxPPs qTFo3fdxOGMWZjD5RH5v5pklXuvOTutXG8SF6NWksVwiDkR3ARzkQ3xexHxbyak8o4adTaS/ gWP6+IP6jING0XwEGaEKm4iJTy/wufrwJnTgyfbVXGXI5yrkXN01fKVfvji5G56hWoKzXerm mOPEHTAb5R198Rq4WkNxrZHfrrec4UziDByRKsyc3exxHdeZmjVaGZm74hcbD/0DoSjH9CJn 9VLO6kUnsN9SgAvJYEEwf0qf8dR/s/c+8FFU1+L4zmaTLGHJLrBAgAhRoxKImigiIahJZDdA XdhEsqsVW62KNq+1gDv8sWwSnCxkMo7mqai1PrVV+2y1r7bKn1qBhNIsWlojWv+02KKlOnGi BoxhiSH7O+fcO7uzm6C8tu/93nufr+2Q2Zk7955777nn3z33HIc+MZE/2KUEk/DLvbM8B6XY dOfd1Wg39x2iw50H5Y/V8FtyeK/qy5N9+0EIag9S9NHw/iBiKBK36tT++PbWKJ6Dszyv+5Xw 68kczK8+Qvls6Q2i6x6WrR67JhYR5zENb/evMSZX6gB3/wxjSodfFMQNxGQJMamLcygDnLou LpdF4htyobeInZX27plUi0MWAEfDrmCNtuGHdMx3dreL108rGZcxICjM+T3oOJsjurt7ARs7 rYig3X+D26T/cTlAkBG6sD5OyLVyAJB2BpPP2Vr+Gj6ZSPnMxbeozBX4xCb3Jw89pMciOvF4 wiHZS/g8quEWxGSffr3inV8WC10oDzQfCE/jh4uzpdjMULbulGKzxJz6zID24XFoYZEUP0PM PavfQr6/IrKgOfjyd/iyGNZjQNuUQzGnMMCDP6A9jy/GR71zsV9yw/yol5hduryysQcZkQna pY9zT1Uiz+vnCqITiHSoQBryh6ZKQ5WhiXwFXQkNdHcnzlPAHM9Oklma7iMtdiQiV7P4TUBt iZC8+RijthGMYW8iuAa1/aTNoLZupLZppNYRpe+I2uawe8J2usOwuGyetsUAuCsEFuRGIJqr qhQ0X8WA8nV+IJna2zkUth2fdhd1yOpKxLi9Dum44Iz8lHXp0mSXxilBu6Ji6VahxYod+xaI UvQA9x5Y5wYe5Z3DGPd6nfG6jCP7alf56nzRDag6ivcyKk7RC8n/zqg6K17lggrLotjXdaa+ rjP6SkH9IwcMzgjTj/7TPKw+9aKG1cYOsGsXUR49N/tOoQGQx5ZHsGAoL74Vh4UGbeMxOvxn 5N+1J6SluVZGsJ+8zgi2b7ITh0lYGVI8eVL7nzGd4wq4fcoW+jqwEh8FQHMf29MOH4qOppcr WgLxJfo8jNf6Kt+b4+0t2YFbbsfeHWm/7a9QrkC3LenMKliiePJbsuCusuiYPJBR52Ih1ngL OUYLs9ug/oZ4pzdR/9IR63fy+r3xAnloSasnryUrdW9vY8+Dqevj/McESxLvopEQvyvtV5F4 1rlrNfG3jBGG91lCt3jrgQjuFRqdiqfduQ2VSQZPUJuynweQ/+XrgJ9UEX211yKeAYUxtZ5d 9QtyXbvchQdVfsaPGuo/wvkOard30vf6A/x8s+tKMWfHGViA8iWdCXf1DZRtZAvWXRtQxbag hpH35Q51Cy2GLYgltWplV1FnoIYlGgWJIZOC1xUba8oZOYGyRrhLHpJ3IgqpdU3yFsSeWuru ppd5d1t4ED2VZZ3YcguhG31R0yXHirqkWGbj6QprtOgIJivkLd4LgyxvXUcjAHiKH9ZK4Wah cZTiaaJRa1NYi9rhl/moSa/xZptpvJqS49XExis/6mmh8RpP64t/v+A3PDIfQBv5GkLI4FFo /RRR1iIO1YkHDMKiPrncwHzCibZUnJj6COq+eR1ahnQIw2NL701HurPAbpNffU17SnA230QS Sh7PvXGWIuYd68R1HbLLx6QPXPpMkDfyWOYNiiL02gf6JB6BHIOiY2gaN6XdkKP8QUC7/zgh DBC9K2FgnZFnUJppmAvE64fYWmA+lOzvcIVypIGZodxuFV8PzHJGmq2U6gGruPtTXoWz+dcY puCbVlP+bTvXnYgJV2B0pCykhblEC732Vl8e0HevnctjqDxlMdhcLLHuxxTrz6Gfy9+7FG+C HWPBgGajxDV2it+M1SGpp9ZEaq0otr5ApfH3s6gZRs03gkBehGmE9a+zZpfYGV1XRLe8FedZ HgDl5XRGDFsFZSu+bMmqZDTeK9PvxeJf2AuUIVbZ9XMTjWifRFgDFEDQRCG/fhTYygIWzwQj iyWFlAompKyMy6WRfhgfQ0jRb06MJxNUiMe99j1DmC7RvYl4IWniyvuySZ4uYOKKnkdyip9m 79UjAA1+zM4jdD9NBAnRuIlNoFLjjhwAooBQdmPof4NJiO6AGm4KYigLxvWexH8BVeR9Tftn 6qMo30xe0/5Z/vgB5r9fK+3EIiCe7Jhpoeh6sxJwjDnGsUgsrrexdeR3bqtrEgaEPbXObZ4m Ieavp4AoMFssqUROHy6qG+MpuVuS+a8eomPQKPTHRZdfO8w0C50lcR1NOWde7wVmZRwH4/ot qZoCgJiJIOaiQatqIZ6OrLrC2L9Ixn99KBm7CoScHGndfG/IFjkQBpnLr63B2h2yvyJawZmf qR3T/sdDJNrVewOavd8YBGfiCENAe6gfnVRMMa0Sn37wPYpDSEaVuZH2DVOAdTbyWPmoKvd9 AhCciXJiDv78G/50K1UVUiwessmCnsWKms/DmeJffY/HsyJ5003606V6MdY2Wj+L60/66VJD hWVDFtxNkvtBUiSG5iXTiO665QMKfPftT6hbfOhz6ifoboav9deyPmrZQCVB3lzwSaKnqfHf HmT9rCJQXI3ZGMxSv6ANYXHoM7Fvo7BvpdLtAAz19Tge0jo9WsUAqmIAOQmgWu3gx4a8TR0f MU+T8iB1H1C8js2F9jEKwR1qZVNRlPEwlPPiQCrvt5DVuhRoGygYl4KC4VACdpLwgLRdL2eR bAcaTkCbdj+KiyS1Xin3O7eVopgMKtbtLpbYqfx2FGBJG5q1CYVVcaJeAMSHXrZkc7Hu5CIs sWQS65zb9umnc8qnELjBGgZD/b9iP1hRyhpTTvzVEAVN6ZBS/KEYVU1ISUtRTJokx/RzE1JY 25fKX6lyUYDjrohxDMcj5QIpPYv+5uu5SD+q7PC7ypZR5Uj6nOA3+ME4PAAOH7w8y++SF7rk Ln2cvG8WfLHYPmuxQ1ltK/q9fAHz1TDZtzf2XCWkzPPj9+M8o9LfX2m1OZsLYKmW8swdqu8t WX1+iAvB2qgGLjYMfhdn8UVKhUQJe95hWkKNqlaQfvAsZS96Uo/HAwqrALMkPctqssdXFcdX zYivcmtPX8rykBVG4s5IE1bi0Tj5zqs/j3+qnd7Mifh54hh9aqf1PCTieL57N85/98KE/lQP i63wm6zwpRbnXefBm/pKIpY/BTqPLWFu5shEjKSKQSJdPLwcFJh9lBVwYQHMX16/gJ6HzB++ Q0aBQ0qdpqy2K4vdsvoUaslVebAgJyoVDqXWVbRH7hL2FfXKEXwFBJSKFB3hReveAqY6SfEc nuV3qLZ5Rb38fQdQyv6iY/zXcVndgaXpXwZf80ACDvFqVW2nHFrPYBPOoq1YTNqJ/1oa5t9C nIve1RhD+NUmDBAbMJ6aO75ZZxUXAJ/eyidJO0/H1tm3ge+iCIezDYS5AjB+fsBcQXI235lv BCZ2MA0y9CGOQPy5tyjmZOvNTAF62Jy3amPPw6l0Z/x9qDu7FYz+x1HyDzjBvj5ZvYXpY/nA +57gqLixydA/8TlmqC+AuSxnUYVxwyZfGgK57mYhYbX6C4uD3b1MIBEOy/euIJyhDDiANvOS aLMGz84ZCeHOICwviK9KxZwBXsaFZYaSmDPP/O37JE0UKIJSU6gsu2NwFknMTAWQuyrYeD0W M33xPM3iLSmaKLRdoO1qJMGnnHrtjFDGG6aQqjcSlS8iMYMLGw2LFNJSL0GsWJO5o4lEDipp VHhJA67CYOKhqW/13QyiAhjJpzpJvzqvXhipZAUv6U6HGWZr+Q/5bF3eiCEe9YUJeY5NWbIa mo5fXmLgUS4bl2IN7TByP8MkKnPJTQyZrkqh1WYfl5f/FQlbvhLOk8IFFrJdvsLIFGCV1dk8 HUXQo0Cqpfcccq90aLqyLMcmd7z2odyF2gaaEutZ86s+wsxcMSbkR1o5CCm97zeKuLAIYlti jWgz70YL9SBLCMZtK1/9AKTJCoFHnYHaEALSawq4UpONT1z6mR0fC9L7GSSxykdeO6SPY6SZ 4gRXMn3GTyqD0dzFlCo2r9xTgPbrQWpOfx+awxPazBJN5e69KwmWs/mRhHluN5Z90sL2FwoW ybDwfD04hKGQfISpV/yE6ms39abOnnbmUT4M7kR/pvL+jJKPSO+6hFf0aRnhXn0yk5+GdUWI YnQxMUfx9MV9fUBvHlF8PbMQhAIyUoxhI++u0Z64gWK+m2P5ms//380O4XpYOFq3urpEvr1E 9trlJTa5FsSZApY0olbTrueBB2G01oDY0f43zKLL+EnS0Jduj/z23Yn4Ap58oOijZJAqb3dZ xNMRQJqQWmNkgtp1J1D90m7Cqi9VpcLVQ3EGECo0S5CfM7D8rHfwrVaTAGs0gVX0Nyaqm/ca U+Pw//GuBOGsy1c8SM6zpEYA6VzFV1jjr00h2toRTiLzodg1WCCo1X4DhKmlGDm6DoN5qHV9 qvQigrq2BLcElqZC24jQFtbUBrUfXWeA6iKmCrV/9zASA4C3HyUebeS93aK7mPaw0q02lAAl 9hZizPNQ22B8TYH29u0W48nsNsr9h+cm19o1uzTifl+a/5fKqq5wQ0eAuUVLlLVM72W1xFeW aGs/4eJLyC5XO0rb9eo2RNHrpOMVoXM40uZK72NEdqFXn4n4OmwtKr5BpbLEQOMKwOEMjyMl B6wJqDIOFEZxdqvrSuqF+Bp7fI0tPicJ1FfnUXKVbAaRleTFRHqC4eeE37+T7fEAV7FJA95Q pjRQKU7GJJ1ZJA9l0Gzc9C6s6DPQdBETxHLDAkBq50A+V6JDowOaD8sNMPIGMrdob/EW4DaQ 9wz9JmYfi01vvAaUDnFO84HwOF57Nn6119DnpQZ7XNwtNQDe/RLWqaFgdT+OMdAxRLMUyxAn wafY+v5D8KksmOwloL8XY164VSWy2FvWyTZAaBfTbmG+PkQwDSPGrPtZ1opYXByt1A3iGXfM Q9fiGVDFAcTkI7JPUzEW+mHV9znQMRZh/TB0Pj9gGIEUb168CyUgN6yFPys+rczXx6O7iy7a whVBN33w+8zmNdcSuh1kGfZL9hwOaA3sHsU/+L/vcJkQuiqg3cKfutTVcblEH0P25dW4oyKv Km71DLRUgb6GUo3vsCL2fhlQMCTwYWWxFAfO9QcUDUW7cxtMj69AFogyYqBmNN1kYVDBiSmG gpopsLDPwnjb8YzQ1Po4jb3/L6ih1lKBBX9J7r+8lWabTub/auV+ecy7B3XQOYgLuVKj3WLE WdPPNHIMB7UPBQO3chOp7Lo/R2NYo9/SYFfW2rq3W5ivdVVxeVWJOAHnliUorr2P7QF06qOc 20qgSLyqGHdP6hqnSkOLQrc670bPEWkoHvq6NJQTmqSvJPwcqg1dueEmaWh56MfS0LXiNVLj MkvokWg1c4BgMeASsNTnBbXFf4ae17M8zDw38l8xw2m1H1rvvh43e/r1GYFkp37K8/G6otnk GlHNIsVXk9+FvNaGTj8XUOSaUDaQ/A/fAam5X8zCwA4Y7yGFNpjyP8mJo01j5S5jhyp0Piyz qf17XCF7VCCL0bSogCYjI/4LLvnRuORzooKX1pn+HbmrsFeKlYQ+lQbOC30sDdSGSteOBg51 oTSwKDRNny8NXBnKlgauDuXoJVGBTN1lUQEN3Xopr72It3Y6t1+c9Q5t2K2xRL00gvXWgDb2 HYMfJfMCDtsHq25hdgsrLPq1yyhCy8G1FISJrXc3vB8D1/zN7AI68TeGEbUJA/IhC8ciZ/NW klHI1n0QCAeGdSMzOgqahjEeRV2VWdjJLqmPksh2YGmYZzYTMOEbi9UbVu26YCCl4bsHkD9g jo2dcM3Xl8j9rPGJ0LhewfaLsGo/KVyqp8mf8v12Qn/Mu7mPjGqwSF7B+PdGAsfkRtDw/L25 mwUiPkDaF9l4Mt7GZXK4rwmko/DXyCx5FdCl3HprjbbpTzAYlyF9xRw4TOqaqYRjKZmpu98i QhpjAhyxsNcOUT4Ww0Qeq4kf6P4F9iQ8KId7eWiOFVHPx8iJi8u9JaJb/6bcJR26TF/D7a0e Tf8X5zZX3FvM+MNAHOON9kqXTRaDKxTPxyvicAHXaThbrwb86d9TIe5Sq7qk2Kg1gIMFoV06 CBUaRj5bVtUlg1bN2nkG6ggyCr+ojRGCPfoP5f5IexhEt0HtlgmICLhz3PpHtv8JCwTHlfKI ZvPwyCBJekEECscqxVxyEHNkePrk6mW6m+zytHDlSrsS7lsqr1+WTHDLaZ95PhoiyGcxPhIl uJDah6BTa1yYI94OEHTfxOJJ0jTZYZpY6gkphhw5hhw5nM/oI2d8r70NH5WweMaY9MV4DQtg Cjwtq+tryJDr+iIvhTYwHqR4S4q6yj194XwWprIvWBNA+q797QHal+zGyNZtUJuzcSawPMWH 3zpbrUpYa8muqpbD2iLxCOb5CBR3d1oS+Vqgntoa7d3HMXQt2qGEhuJuzHBs8GO04z96H3kl 3A790tBbpcIue3qQs+VAE+OUKseshQ7hODDWImS26JKhzcJg1BrmqO/L8GjErrWr7mM6IIv1 1GRE+54f0C5lb6CN1Xbg+ok2qAEHa0DuFfbpGYqnd5anZxZgnZ3thwBbDOfL2SytAdzOygYR n6nOUS85xilePxolG/xyDEjI3Q9Rr+xRL/OMY3HByYmkuLy6RByPqWODNLBdKtt5Af6DBeLV xVIMGE3jaDQen60vYPLQGJzgYnEOrDxMxsNs+Z+9yey9JRQpmaVyZvuJVgtHXD2H9B8rlf/N mwn7MOYqCeeXXRzOYDxkDEPzx6EE5x8pOGr2B/7jHUwWXG+X4sxVZ6lgiDCEPmWx8DRKBor6 E8Oef6dNAbd+BecncWfjLHiLOl+4Fz1OAIPEvpasKi8IU3Ffr/gJiiE1xVx/C9biLoj2gx8w /PG5hPXFcgzamQj9KoIJwMy2H7yB8iHXJ2HdsWmp9OM+zyq/3IvT8riFb5alTAvudhE9mITT wuhB2Z1sWsaweGhYCKgPTs34xmycmul6WWJazmfTspD7nQAgwP9wTrLZnGTyCYFJoP0amA8s eNEbxqZgLsu/gx9mwnsc/8Pm8TfHSPzqRoFxLpStkQGcTQwEOVfkJu5FscoOIosIahHanVGs UW4vVqpKimJlvRuyhSF5dbEu1gsBspF+S6m8kYmAjkhcdNfbqdLv/QFGE+2XxH8wwTPTwFFy efte7uYWPhtqKKq0B6mWW+JdaAfAr6/Br99Krn/y76XMQxj5lLMp5520fqrYRFX5ccNysV/e F2lvyAWs+p6JPmA6l5QpIwG+vBJYBU4ZA2tTK5uynDacL58rXpk6X+WJ+Spl8/UQ47P/8ToM +10jzRdOUhu+dcGMYVHp9cT66DnZ/LzQyPRj6OQ8QZxtjBrTV2N8qkL5iRzLzIYHFXd/LZG/ CWSZ1Xbc8SvFeXQltJv5LP6pNORqHMvkWWVxSVGHvA/mYh6fJY4a2oX3GLN0EdRXVEX1CTBD tdqLr0FrvcnxjfSHeHWtFtz8KK5egivQvIj8cbnGL2MeqLsfGXERJaRrom0MhL4WE21jsrV5 QuYmJuQ8NiHVbMhPew2P9o80ITAHul3u5+vnswPJ9YOzg7/1fMoHYWdDBtyXecWQ2JycNkOX N8+btYHPm1k2+yyxtH7E8FBZvaxsqMFWNKQvB3k7ALRroQrUJ+Wrok+NSGpjAvRgXZ+x33hD SsEFo4yt5a8sFX+FnsrcHtSfUmyUAYVYCL/LVi9reJ1Sj5vLbD3K2wztpd/dr+IWX49J7jPH bZ8YRrkvj1R6qDZL9Rz06xeqdQdRgK6kOJX5EsWpJHh+u0GwPAzX6/xiinJcPL82xdZTymDQ z5BiBY3jSain575XGd/JIQOcTab9SWdEwPeeg2W94vmq5y2/OckLffbDQcNwchPDi0yop/u3 Vow3fNDiVBXCvtfJRgPfq+FDqUbCbwwm9o3uR7nJ8zpjSR3v20eLB5k18CqgfMykjvlAum+1 8vWVLZ4eF98KxsWDKVXeezl1Sa60gcTNlN6VXQDUHBSxtJlSbIZz83Qrj/S5vNlIK2P5rkDX fev/+69TaRfL4B6cby9hBCJBFUOCCOU4+o/bYd7heoRfKWPy758aNG0a/f7OK5RpUD+X222W vsJm/zQacDsu/WzFt1cWQITz7TVIG84SUqR6QfG8RdsU6ZzJBZwJ64v/Hgb8NzT3XagmyuH9 9TC5XSB5ZSAaePbDtc+fAuOsj3ALdr/saS9Cx+B22fcWOWQVoIvsFyHFhKABCXA3WKB+pn8A fpyB/sTDEOShy0wIYv6WIcvlv0dXhTY+Mhf9HteoOb682Q6yej13RTWExslMqEJWd1szJ6xG vgMQEa8NzWgM0Ogikc3XFzPJDv1L9/8OJZId6LKqX4T0EX0MRqNR5Syyo02XGvwWcTLVHdD6 sw17yiZT/osR7Qm/X2fkvoiXoH/B5avIv2D571L8C0yd+rd1PF+dO8BcEoLa5x8Z1DI7ENR8 nyQjhaR9e/06puWjw6ub6fqL5T/Pel7avxmw9H1z/iYo+fFaweJexy5yFArWam3QlH6+3A/S R1wsMJ7ejk8nI80aw/0WHt6PqT+UKpssfMGZoVfXJowpwDayEJ5LWADoFrI9JOG5C0reCNd9 /KJBn0msuiagDfQwslmAILi5LWTyfrZqRpM84LVhOgQcomBAm/lxcojSbb+XcJgMgOoIoB4G 0BoDHhuU6lsjWPbyC/XLp34LfV7C8MnwiNn/ibG0TwtoD2AB5h+G5df9lhIAMfnOS8vaLmcz fcNQMkeOr/u9NQnEzkJL8cT4GhtHvfKLYD2DQrvXxcD3EvjPyGnjWQg1LIDLzS/+9WkJcKcF NO1ldFTh+/UA7z78fXoqvGhEs4K8mDDV0Rjbo1kZlvSzW6lr8w2RO60MMjgvJWp5RSsR/DWW Znj9BFwhfhnjueFj03hWv8zo5EyQZwC+GS+zCZ+K6/Mk44l7CAEtF3tSaNb7nUrAQZkiKCX7 GurvWy8hlvSm+Jck+T+DX2qwVbLjKEjAAtr88/nwOxI9W0A9K1ZS8qs+AbL8Xrju41eyhoc+ Mno4NaDd9BLr4QyEZ+FLp9q/8146lf7F9qX0z7z/ETLwi+PFS7oBFNTetY98BdYs4y/7PkuJ A52s5uhtbIwuFcTpxgT+qseoCX5soppofQaWcfBS/MdSx/yHtxlgtfGmSw24RMygXRZY1jAt QeID2l81Q6LrCmhT9hlm0JH3fDyJymHcmtvD44xaitJW1AJaUYN3psSvfn010AO49vKLf/s7 3bSeHoymrqd10VNaTyOeP31gNe1QSetCltA4flAQU5Sv/JZSQXw26ScHY5js5ddXs16CruG1 z4IRRyPMv1pSjDCgRC4hJbLxuwnrC9tJSKgng/5aZFaBDYyJZqO+mKqbTNNnJ3STmYyPngt8 rbkTMRP4R3hwBHuLbkWD9XWdpg3UkWjHQ6sofWlpfEXUM2SYPEM3MPOmYW9H+6bPJZVNFi/H 8FQr4nChffNVkNLJvgns+73L5C5mH2KmzrWjVNtudUNVl/60NFAg5sgx/WxT/C19Mi5TJodc 813D2nkffX8yOvHxSs6uXQG2LdGgGSjrUbwlZd5iNp70VstkteoZ0JFote1a7AlujOSlbozg fsi834yAz5R3PkXjS4xfEqRrVho4MNKkN6A9KkIYMcLcT0rM/VdvZ6CObuP2nfT5n5+Yf77L 8u84/3sB6kdONv8B7UZ8n4P6aUC7ai+nK8PkmO995yRrNVxqrFX+4AothTZRRDraubQqlSXG WVNKKvzyLH+xvLCYTqBy/ztsztTqmd/BYzW3kPtOIf2bj5pxpIT2KpxMUzv2awzhLW9ZQBsW amQ2bjug2T5+IBpBXxxkjNHIdfyOvnkav4lcZbhdP0U/l5PbZj6dx1W34mkmStexCSfMSNeh Utt+hcCp0f7ya2IQKNstKpDVAnhI7vWl/ao6gwDOQ9do1PqUCD5A9jAK2IMz8jDB4i4vdTYj NfCqkWKq2SyZx2LwaGsxHXPAuslTMJ9a/sNrtAODpx9NHkLppc6ZSvZpqtr5sxhzHPIoBFWq 4ur5DEcRafcBZ7OfHEXFYjR3lsrrHQx2ssWU9usFhH9RenYeotPrLF9nHtOL5DeM0ckEdJJ7 1ScdKWcbulLn+LJvwxyTF5afnQzMI92GYieyKeKOQ7szmFOUNjNsGN13lpAVzqWstJPRXVZx 8iMvhc5QqnDDuahDeMXIrxaN3MLh7a6i/SD6GL0KsW3hFXnnMtwYY7tWIIsGtRUd5JmidJBE AHdi4k7id6qvSVb9NNEV1OU/7yIcYijKMWEnIfDOuYgJmDKU8x+CJ4kPPyV8KEB8+CHDh28x SPD0Z16NshObCWp/60eUYD597GgkTV/nqwY6pJZPKTR5MsMG+pq6DzjBBpEww9n8JjlWziXs SGu48FMTglzGEGQWbrGXsqoITehEjq9QFqI0c9hPfYKxn1LIRCZ5y1XcI1G77rsE0GqaPba1 QQOnzJN30kzGQ+fymYyqtotn0cuyCE6UeHb3bZhcjFYtzWo+/Jy1lUpsxRLO5lrmrqGMktUr sNZwgdLokHcupOYLogL8bVR33kizsyBBWIz1u5ymdT7O2vdovpYPn69wQfnFifm6LgWHOUJc 9BnO13XUvItyvdKmxcSuxPJNKZ9S6JuT2HzR1yqbr32yapqvEzhfO+ezmU5tmHxz0+ZrGgAs X8yqkpc6WJcU6juItQ5FpVEQ2HQVKNUOubpYobGTnYq6kH0F1IWjxDs72YmynTTX4gVxOhqT soo/7jdWMTqRJXBAoUfETJ8sjJvP/G3suc+aQh+mf1OgZY/VqepbJ3BSNpzAHuYUMHcDB5qC A9TcAwBRdygD91OQMTsj38f1xjiIzx6N3HfCYBxQeNdOxjieOsEYx4MnTIxj3wmDcew9YTAO +GY1fhN58QR2E35+h362nzAzjmfwwO8ay0i8A5tnZsEfsaFT1f3UoXUnDD/y3y1Dn90mrGNn 2wljXsmHEdp7lLvN5hlcMXQCfSickR7cUKcPKpl0qUbuPGGgo/F19xGTM+4L6Oqe8rrK7Kv7 fVo7hTXM6y5ZKoVpFKPfdSeupUrKfQ4Y3T2O779EI80n+MpEw1dbgi82U49XYtSAzYQK+CC5 rh5M0kGVrauWYR05dAQXVcsJTgQNcDr2mxfVSABPcrMVhZ8a/NDZXEPra+UJ7pKbaKb0Y9MS WsaWUB6RPCJ2zSc4sQOe6GiDO4P/qdLyHw0hiZErXdHKYhoZPB/hSviX3nY9d6qmU7voK/8t rOx2O3OXH292l+fyHpDtE3h+kKqdoXCUUZsSmPPrWvSJHva4p5ZcLRRClTKfXWReiN98kTgY LJ3TUFzYMKzz/tPYod7kK23MNIIavhnHltuMF1L8QZ9EX86UvQqzD2bgJjp0JbXb/NrUW9nZ BptSbadjP5ZgvRWdXB0o7RpeFzBQl4rcO/rHV/Cbp7hzpptEXGfkzxbmqu5SxiqVheQiuapA 21bDNtxqChhfyaic4QfhVLoMPsbs2vJSmyr1wSzJ1XZq6G+isUNH24PLlPV+ci/pS+4akUNo w3eSpwzH1OcEtMdq2dmxLHaALvk2tx6k6zv42+y2TqsfXuMeSL0QDNRbtMd/y06jJqtTfH01 AW0pfKKPamv19dF5RdQ3NDN9nJ1KH+M34HnhwRPce0fMV7LkiG2Ip7Vp7s6k0BXc9WUekHXu +uKUd1rwZMST+K9Lrwa84g7MEXxCTjD0Ti/m5yvtAU3ZQVjDJyhcEGRnRukLZYuNIizgcWk8 NON1lO1psBuwgDhRNEnaiT8szrvOzUQKhVEUmL8iSihY/+4PkZ4OnkgIfTYEX8WC8svlvgJn JBPpktcPeqXzLszvrFCV8s4YYnd0Q/ZCOYK3ylb8Vz7m/Bn1Ut6JdDZ9vz/iGKKjn8Cs2Jb/ 8yLb8r8W91PoE2fjxfBa3tmFnxOxBulyMuVntCpb8Sk5ANDdIgzW45KDxfppaC/aiqUDtVi7 9v2NzAsg7BLWFtMQjWcQBkjS7LuIkQPqBboHNPiLGpYpNHRFMTaErD5BzJP3dL8PnKZpp4vG Ur2NMofbpUY/DMkK3NR57zp069x6iJiIm7r/Ot5vteP9VuShKAjsPAg3HU/iv3ZpoCJ0bn+H HVT0d12yivEr9AoDH/AXwwd6PiOJD9/dZsKH+FaEiGMEltxxCL4qPXBsK/6QI3aGCNQbhhr8 CQUBKdtDk2enrh5iQ+MKapes4uv+eR8yxj6a215jbqkCmhwcvpTpnZ6YXuo8n+EDt7EZ/lqb RJ/h/NJ7hiHyq8oWfIzhlvBY736a4EqYYLxbzCZ4abE+Xe5nsw/zy6rXdjSappgG52tbUbh6 i5j41tdZj0AsolEatRWHXaEpgEVk4DxuHF5gdH9nL3Ep6qRCPRdizF9oxko+KK8QVXQoOw+x VvoS45ZpFOlhRdi6jBMKkGNK04UM59iIh+1F1f6i6mVsEQPjob/OnzFa4MmTdhKFcUZQ6O5e IbB8pc5mFLqVrbQEaYhUvhx78P65F58EArtVo57S8LJ1JLqlzhJ562GG7Jg3eW0Jen7vxCfy WpxI9BaF541uilA6RakuVBa0DZZVz2jIpXDEAe1hOp1O2xjVjrIIVt8AlI8aYM1sRSCKLlUI gAAtc+r5ODRZ8IJYRMgGjGXoYAmdphBc6KyPIrj3uSRBsuNpSoPQ8gERV/AR20IEhsbA+bOt NGpinl6BNFIR81iGQPQ5xkpPfzdZKcy4eAZbE+j0Q0OpEM0SgO4cBRJ+92sDOP/0QswXsnjL QGTphhHOR35hiNPtqTzYxCn+cC0/BFEYSJzxCDIrMR54buzjPp20p7X+9dQ9rVRe3gpVqeE+ NPnEVxdoeYuRJ6P9h3MG3M2/8hdMR6Yf88w/PPyHti8TcZAOMqx21WqREuRsvM6+RaYf5yxm dlnNdDbuvtSzmseWs7Oa5GBgr1V3rhwifXl8qs9sQLvQRqfikFStgbXkKiEY6i3BFN+EGreF PdEmTUAhFcuDgDOUGp/E7IuxZjnJNyhEoEdGvnKBGiyR69C5SA6WKHWDMp4/tRFOy3WxYWjN HKN+08/QGnC6s8GKg5pfdAFMVwAnSwuexwY6X7iA5HR0gRmMr3bQpw89a9gnU/x8zPN24BqO Ani0pVheW4Gg9GF8dhMoOTtQkelGj+LEOZnTA6QI1OXVBlOcg+qPcfNWm3pvAa526C9o3KXU 9VjyaMxiOhqT6H3fCL2nOGufpfe+oOgCxTeIoTygaS14LvXfVyCUJvofw/7TPvbPjP5r5v6b bcMHvvrlZ1+kdwxK7GAnTb7C4gv9g+dfrhp+/iUVtjkMttIDqdApFSXSOr/QOMUEpl/780EC EmW8ULYcRDAXJCA8i0PoSEA4Q+7/u+Az4/f9V5uOJFF2WjZka0q0B981tsOvlMKDXvFyFHOT r0sPG69nK14bhoC2tZV5YmJ+vZAsVPAnOkM7jlmoXW31Gfi086dAKnEWUv2CzOM2dJUR/gpo WTCgPX1L8uyeeIE0JIQKbysieC/WrqliXBFu11VCMUoqmUvzC4++fYnF5DbQlvrfsLW0CdpF pye7cnuhUmtDdIf7cYDcctdiRHHQLJ+xJPzV2DkKd23iLMVrfzGp2z8hHXHQG8rZhbEluskX ty5Wm/JF0XuJL8QNoOWa3737dvLddUiB3bWacAuXAdYtwL5KUQzrC7UqVop4GyMnNH6Y0Bm5 BhXc/tAs/XR+/lCKDsYvpop23MwrenQBkzfq7OW3F649mDzAxnWT+am6yQ1BfhKwQKktkLeg KFR/nRpBI7VfZWxZW1kE+tuNKp2h9qtbUJCRt6DNpVarg1cKSPpIr2cj+5PcdD+XxA1MZ6bS c7/2KR54pPrlLTOG0JJXPGQEUCrhd+pWfBNQt2AeInkLCmS1fi1yI7ZxI9U7g9rYQPfFpNHs pRpLqMZebjuSScSR9s5Am1Ffwmb0ZjRSOGTYjAr4XfJwDB3G6KJuvfAUfl6IuFPAcYdJD/Bz nLwFLU+IQXSDSDSTzo+pkYNkB2GA48kMVtud75jQ6GwyA2FBbyiXYdJ4bo9RqI3aYd+/bkbD 9y1MsAvVsOLxC4DX1CLtJTy47ldmA5KFPJ/S6ksp/5SVH6TUT2sbXlQ7980kzn4HH9N7bfFN HNs6Kk1oy4aIMJduAXndCpnp4iofqchbQwYKy/0G/vJKP7uRV3qwkqNwAaLw20lonD9mB15Y efVGPI2tPrnjRHLvwoTZ8jLm1wPTd4E+ma0XzFwJ1M2OAssa1orcuyTS3njYtB+WSkOqln05 DcFTYTwfOACdGGDt3j+ZJmMgjX58mKAfpi+6zaiyz7BKLUIWekEKMVn3S1PBR9k8mypKKUve 6zTHeamltCV/SE7vtUiSCmq1W2/g0/C3y06BJNkZSZqhT0vOJ9Yyw6jFWfFF9CgxzH+qFSz1 Ni7nPl4IQ2PK8W6m78WmuflRLRGvemb4veTfETuC2k5avC7Vd1D2va74Xk81msXfTlguHLhd VXdQGrjaufl67l5574s/Jd9ExJfQUsHy6f+A6xd+dv297/+Rq3GEepeZnh08hXaxzMnK4fOm xuUW553nkDk7bbbefSsxW+jGHhcPBrUfPGNELIssFiyWkSzJQW0QVIjuQcvJXpcZp9uczVmo Lh9B+bjeG9QWJCv/yMI8gFMAsv8pARAe58UQoIlKn30m8e7nForTCmKweoVdkH0F3XdbmINx uKxWFQ8FUip97oChZ26Ik7eoUeM9Pzde3KDXtPGzkeLFIGY//LTh+71o5B5+J9M4v5dn+Gtw 12locNwTIIefF0dr3Z8G0YNdPx3oV1C7/0lmcm4PgQ4sP4nnD6n80cdR1dxnliMGU3W7qTCX 6tY8ZMOeO3HXThafkbfOpQ1/HiUhH9r9OqcK4Tn8ZuVsNDPaSbLw3SmrtqE0K3cAv9b+0Iue tneqtqaOQ1Zp7+x6Gzp2J3155Z24my6H2xTfnapbJWHCNk/23Cd0ySTMwF/Ps/hjPu0k8Gag a79mNcsR3HCHHsTRPGPekNi0Hfn+gyAOSDtn0C5aUe1Jdy+u/pxv/IVqYVBXqRG2k2mXVXbj kBeSmrXQhhv3qmOI7dmrLFptvqyiLVCVdmwbivtruXksoGUU0HmzgDbleAJ4Lfc4bT25DVdg FlXgydiJVP3XfA5wjQ/pZT6wM59bwaDMZZVzQ5fggYIa7SvPG1NfTH74cy3iUigmlVnFavLK rwwm8PWVvYa7DvofKGNBwxmtVNqowvlinjRgFXPxRaWdHlWImbsQOGRVuCfLI9lMeBzjLyMa aQPLATErXKRW9QQ13fhplz0aYHlQe3s5P6TuktblWULFQS3KnsidQe1F/jLgoo/yklszGZ4e PHaHZ+78Qe2+5fwMnzneyNpKtolSXVJWXSyOxRz11FFtRZBZ5Rpxk/Jq3NBtdMPdUtwvFAuC mnek2opYbVK40BIqwPT1NF67H6PtsUI2em8/it7adJ4Efv3qEdqopOmQK+fSsNnofn5iCOXK Crp30P0CuncpLM413rOY11ekna/b2JNvS1mja78iWOSf9nxOGOncVrlcjgx+jnJz7HMmf4O4 rOITWdU+JycVdSe+CoIQ/Xn6Bt/5u7gtyhk5hsRuCxaJHBDPi2/FKuoTB3PNe3tPkBDII5V1 d7AtW/Te34nfWEHdtGLaB0vqAZBDj1NT6lYL0CpV7SUID+O/W2PUlMLgVVTsW01QoZepjKRp p2E6u4IBqGzBehTqWVGXP05VBVIbvvlx46NJSoSapeLwO8J0YDLnvfW52XfGljrmGYDgKvUu mCJ3P3zAULhv4/CgfehrPzOo+rWst8FbLDbSUUyfnkarDyn7XPZp6jGhNY8ZPGNyapO/M5oM ZQFtcsn9bNQtjQ9x0tH7eYpd0pT/a1Ei9IffrVaZQ3+stMVXgjhdon29nwZmtNybEt99WH4A s13g/YWGH6ASsAPuZEkNoNgUchfAceQCCMT/4JVMhKQyM7GMyJ0U1Go7kMcXr+LM5EL0Sq22 6adxfyIe44DcAwNqtduvbQ2QSb0e/ULVzRjD1a89+f2ky+9wG0LVQnaWPZwHgyjNs4hXJOL3 BrQfXc2iajTYLeIRAkxXPG6p3Y52hPhqW0Ar4LCRIP755ca54UnMd/JqKu2GPjzMACOSgbN4 58O44DzuTIKRHv3g+wlrNPfn/ERYPQnPWxpT3/iSMcOHDSmb9SfZnduqyU1UutQiTlS9dj/M IsxsvES7eTZzXXQhCKoXxurcIB8rdRMbqLbv88Nf5nguKf7f1Xw+0c4TCGq/DphiNEVmocwV F0JzndI0HjoqPkf7lxJu75mjtaCfeBYFQhFHKV5bvKkQ9eouks4AJ6HIt2fh3qJNacM3lMOi UGBTMCA4I5haRFlj2zHKws9K3flLJsyz+drnESxvwvUBXENwOb2C5TS4ZsN1OVxX8Cugffww MUN10wwBO/74EfoZ31aMMui2Z1Hq3IS5JnAnzR7fhiH8tAMzCRAcrgdpuK5/iBZzfNsTI30F KLgtD7/rrKNhDqSWSPNh3diDaZ1MQ/00wB/1tGHYDBC4CNuNXE1URJU2/H4oDtyUJxhSfQ/L vqYaCovoOcz2qJrr+Lr5pJjffIzOiJ4W4mAPA7M7moHz1If4CWVveZ5E8EHU/rqMYIPNJ6wE AjuG2ydvforiIMbkzc/QzaC8mfrlcZFbwV6fEUGThA1n8y72Obq6Ar/HKEzk7EBOkszfQPG1 KBR/V86VG2yqdHAHdMxrj27GqSfKtRkHkvXJXcfi7N6N2163WKwmgDc/IfDl52xeaDXebsen 6vaHMeaZtmliwtQEwjuzM3kOyuIhpgfYa9TtOLey2BzQbn2AZF0kLtHNiCco9Sp8jOtZ8IEz lvGBVWfxmzunwOebFxIkxdR/gfqfScrGg371bqxKZgMQ355HZ+AxEE4z/MLPSBzu/BsxJoXa VW0VIBT7E/3cgxzkgLOZuvEAoqyynZXD/QKLsEd+oERgfyk8PmtLwT5tg3rl3RhiM7r5OnKV wdFske9eTpuINAnb5xPEjyW8eyc/SE5adc8jaj1huGd5Xic7m6eLHLNwA+ztBzC62j6A27jf D0PCXLJ8O1iXnbv3sGZSHbM01fMYCHDjoSWFAU1DyGREhYYsY0Er0BMaIkVsCWjlp+FUYsA9 efNc6lBBokPoQ4I5UipLxKmq5z4/TJn2KN+EjXnFCfqUtrTz+d5QNqw2/BqEw5YarQPpkKet +zUy0dw5yrl5F3XzTiQ7zw3uJLJTVylYboZrLVx3wfUoXD+Fay9cr8F1kF9BreFBRm82M3pz 4UeM3mwnerOd1s/mJL2hTmrfONugN5sZvTmyhdEbwuhhX8GkEDZpgRqiN8FhJWjYHGczP6GV 8RRZYGPPslR9bxbAzeRbV43WWJPwlaosKassFt1qpBdVFyYU5/MtcJ9L6rDJahepL79aRPtE XnQsVX/1rVeG4mUxcboyR96KJsKAdux86p6q9lCoUAwYqi9mjkgBwxHJ9K4mKW5qz/j5Yps0 g99MRDdNsj3KWXIDNAkAakPcl1s75EeD8GH4bbUwTyUMBctCUu4nYO+4l1ivSs7LsoqGcFU9 PGTEilXVQ3T/PN0fpHsKgLr1Rdorxkow38FWLJYIJRvkEUp5mNT4Vo2UQFTeD/yCre8IflDU 6w8o6lsEyNVFDEt3YiOWxp+y58oiUDD3kWMw/VzlkrfuxZsGuxJwK150WKPoXktceKpf2FM0 IG95JlkeFbgpoF7M8juUCNYjdBXFlJ1YoiiqjyvaSXXT71nsXqXqK13llRjqNscAb865zJeK +cNh+HMvkXM2iv57sfesn9orS5D0pE/dkSV8xpafzW+umYBT9zrZ8wul+GWNxbjqmTvWBOmV ChjF16n2F4pZ22Xy8aaXKsgxSz9X3dpH4L5I7QhBTfsREiu1qr2oE4R9/mnGDO6Ax1CzoJrZ S22AnakYxz6Qc1Wp5xViQgT0FUuRdruZ2+hfn0d7glt98rGhlDixabGl9EsES3K9gNr5sJ8i nmmfLGSLhfPL+7yJALEVbKlYfk9LZSKLUKqMkpEevcQ4uL6MM1ByP0+sE+ArpjFWfXxoY4X8 5tj4JNt/ENj+VLQTURW0XFBIZc5pl4AuhS5IExi1lp7Ef13KToqIXQ3lOjRBOsTyF8gdr31A wfjp5Zl4vo7D4GbZDK5KZDNwp1YHL9f4gceqvsdkljtCbJPFJtXXzkL863O5v3oiwgpRcRZh 5WfVFiOm3tjuHwr8FDPIKfcT22qrsKRHlaGPgyxLBQ8ss2Qp80G6CkPKzGOvZBpvmcLSRuKh fLkf/cvwGfMvw7s4nVQQ3+dhZiYFaxVKaRHQ5l+TEmQGei02BXibLAVBQKJhxFB4HjeG4M+i v7P8xuFxPGwntqCVY7GLAVO+OF+cAmxIas9wVICQtr2ILYE8Nj6tnjYbvDCAjFe5UJRKZtqp r6rRmvknGD+m01qF7pHQhsl/siGgXVeU8J9swALmSsZC89B2jVbOC41u9bUZ6y8utjm3edoz +IkN5C8PEs454r5mzNrhvHsu+cw0o0fnKj8mRG1kIkeyhTGYCOGdGakunKkwog6YLMCcOO/0 o5Nxcw22Cuz9rR+kuXKOI+Oi1sy/Y/kn3C2sdhDd1n4F9+nYjPCEB6Mo4QFT+q9L549p+UBG zzOv7/E8knsNHhIb40lZ4b+oMjFCBVc3S8hQtk/MVS4Nah/P4Eu7LY37sSwLpoX9/CK+nqef zm+muZgTr1uimHKwtFEEkC9lJ2rkJXZVbKpjztja73+AlHExzDFcVbX1gtxb1AVv1GahieSL n/6Akc4mJJ1B7fdnMM8g+JYcX3adwbpVncSvnKBWeI4Zv2h00brotzR8NVkSZjCoDZydOoMM aSh3XHyVPwhz6GaWjeR3TpzDoNbOv7QnJjDhEByvXEZD8+NFLLiMQBYBFjyNh2+BVZaMR5Ce jyI1RtWcueZJdaEGSzNafnnKjB6qwFFXqk0z6uuF6XQqFwe06eew6bwC48GlulXHzJP5QTWf w9rp/KYml7tVYwgbZwQzbKOjdK+81M48xQLavNMZIGn+z2elLh4+AVelLaH1Z6Utob7E6OMK uv+RtBXkYiuoin+G/tAnG/6ZC79w+E3xilPiU/nN8Y/mGAlBsqJcjAdue24BpU+E8Vkhrcu3 hBws0Ukr7cdTXk7y3fc9i4GPyHF/Slqce88+3ZnIl/ds0TE5vE8V9wMv2Rsvja+yaffiCTnP 88RSzl/rwBxI4Xb9NBa/7XkMKbI3vioPyBWmyGtHEw6W2AGPkTW/qNQUA7pg8Lvnw9MDSvj5 IEsY+GKQPrRpf13IWM1iPA/zvLOxQBHboZgcfhaYzOhWKzKXuO9Z8TPF9yLylDOwjlqsRNOW cX/WvUo2PM1YV4xl1sO/WEOnzWmpF2qoGTs6NcIcnreFq11uxbejzNeOOQnbg0YX3EwNQF9f W1m2aA9qL0/AM7OIAwK0siJanc+CtNW4lNvdAGJiVN2mUY0Z8UMUz7NFvbM8+9SbnkjaogrN 9r/ZwjCzxdyXUswWnkP+hM0CXf26FvDVUJ7Pb+aNJiWd1sUhWBftFmazoOJ/g+L1BQnVmG+Y N7dyYwXgsicme/GgguzNo4zHdmMVT7mEH4CAebh22CEIpe6gPElea1Ol5V10RCHqdSByky1W u2sB1u+QvbYVUW8+PT1Yq915GrluXClmsxxdUylBl+4OxNfkUXInKtWax1ZCV3LMlpnG7BcX pgmOL3Ita9ulKUTomvlmtjKIQPqeASI0BnnKQ2cwIpSuUHl2mEnQjZcbPsxT+M3vRxn8JLwD hnocYya+Z5CTeJ5PnIzVvtaBePYsyCW0bi5z3n0vjnjQSH83AUSGoGY/nVGO8Xz9tXqeRXmF SSom5lAV1N4pSNAmklFMbxuC2u7k24aUt+ObfM9WKL5ngUl8n5epaPU9m9APLuz0xAs6PUMN at2JTs8J5HoqLD+C3K+9+JBJVwAYpjItAYfm6stpKheJo5lMQPH8mJRA7o2PnTS299HSVF+4 RytNvnAL0BduxupsacgamqGXcpe4hVMTLnE3TTFc4ibL/dwPDx4HJlL03EweWdxsyzbzrzWl I9HQ7imEKbtmM0tqJG6ki+JhDfn5J1+vstiOwVzTF3yGp7doH3QB94p7Z/lism9QvYusWL4+ Vdrw6hBy8QCenNHmZRgG8DOWhqYzA2h8G5rqDKPpFduN4BB7E4QmQWVyU6iMVY4heRlMzeNu HutNJaljfWGFaawX4lgXr87BsS6m+EV8uN+enBju/jxjuKfgefzEeL/vPul4m9vPSmv/uctM 7c/B9qffNpO3ekOy1aZEq+Pg1+2srWw+30ZrI+HW/edzZz7MnwNNAtJWmJu8Ac3v59/2Veao 5IhfoH2Ul9iegF/ZeegQ45CtdHBLnB33OvTz2as+dNL2OjBgX8CB9vaYII6rR5N8FrSQoGBJ s/VI8PWflzoej196KvOxKC8xMismjTwfgfEnmQ9T/G9q21EvjIB18W3L6dF19C+aP7U25uvq iG9Cs6Hci/EX5E1oUk3uahn+tzyza5bsiZUeOCa6MGFSaFQREGmPS/DEFK9tlidWFtvgzAjH gFx6Yub4V6ac33WY8EG2pv/OwOxltpH2pn50LmPHYyMHGjDfnLqgbVD29AFBJf5LkZD7op5B gVk9KRJzn3SZJXQBjz8bi/vQn2uScZ4Z3QlelT0OtgeZGQdQ18Mncaf4GoZ2BcGxzBK6Wamx l70Rug71g46YlaQsm2K7Q86SOgdhmSuVgxizdv0g4shYFhlEJNqCPLQIys9aa+8YsqpeATgC Zp/wBzHHnJ3PH+4VLSNviRiOITrr24uWOihbRmouBpYiQwZyv9amLLUrkxZLA/HQeJgJQeq0 SR02itj/oXDbR8pSmzKJ1X4gZOzfOX8mQJnF4jG52hGtzvvwaacFJBwauZtiZt3OTrZP3P6E Bi+Td8bQiTEO8jwAttbRfZeF+2/SC9W2E6ugQ1MZQZu0Z1AFJRNtAwsHZXUQPWQqaEbiKhYP nS11DCo78bmSDXBHB2X64fyZFX7tGWSlxD+ytpSgPdLfUMDlK6Goc509noN/18eETuiMtMcW 6W98X30Sza/DfSLFWcYGHWLBLKgNJrLQmMjkLMZzxXEB4KtxYzsakw1PTZu2LJy2xJrrG+6R ndr28ZkMWVe5pIYSS2hZfE2h9rX8pIx1uVrt8qvVDr/inQ0tZigeO9yW4IaGDJB5i+VqN1lQ sArFWxg50OgOZ0e9JWSV92tV+UQDKqRGh0V0wIPSfCRZefp5SiAPwM3FMAVkAF1sgydBdjqi DbcJqm0Z1SCs5YM8KMdOFgOtjMO/3iU1zrCExsbXFmqPTOWWwkg/hSx+AofCC93wQjeqk92o ngHdoAhY6I/FwgG64isLNXUqC3vP1mN1McqixPbI79NNmb1tQpVbXmVnOTH0STKdpZBXgZbn kCttshDNIq3Kaye0W50nNdgsDQ6lqkDIilYVEKJ4aZF4bRl4k59MyzHCGYfaIkr+LIXzLGKW 6huUfXl4Tp/ydUaFAlLTur8t8HjINdp00xC4qIydlVkksLi8XnfUm0civjffBGh9BQWFpOkN uPD7A2LuDsqI1s3XU9RK5avc9HWVjf2xsz/zufwiLy4E5CmkhA7TpEabJZQnV82AKZWrijED dVUJBkmomq0vbVOlO4+CGFw1Qwq7LOJYFjhSrpqrOxL5N+XFc1UpRqWKodoxrAbdweKpVJWw tmezPwXsD+tclYv9yWd/mIrr5X8Y6FnsR8Hov+zKiXoLLTROFLIFYB/HCKVtCiGEMzVeS+/J /RN+eA5b0hfLYl/5Wpt4HSxOPOKz1AHkvmxxnjiqfLVrtRPPlwAqZVQ6yjx9t01VxMGyJXli plLlArFNjBm4YdNB/xwsh1fjgOCjqO6KVxXoLhYvW7OigFDtiDO35LPgliVfhVHy2lDsrihU /HnqakFemScfxXegTyFhhvUHWiVuMAivyvtS6XiqjHrgbLbMFrkodRPlDoAJ7OQrjDYiMVRj X/l6W3gME1SrBRa/HnhPjVupTJzPX+8qisoxoavM42jM1meU1TkazsRCi0CaBVrep1RjURfl PYkZpT2OeC4iCHJFlyKw0PvoEYkxZqvt+hyjefeGsdAWuV6xytz6JFq8dmgoPJYeOfAd4CLg 2R7CN4fuwC1LqlQO2jP8tvI6x4aeuIXRBKXGUebHeQHlxEidiGVtONR1jln4hUOepCyF0enV L0dXiHCvUI07FVChMW6D8TUudM9ZA9TDREvdGC80PIiEa8Ikrsv0KqswOEemdKml4ecKni46 PLKuPu8sdKd3UJD7QWWeHO7BAOvKYoccm1XpEHrLPK6GbP20MtHVmAcCmhTusTibN2aSQAmU t/sFK23M497UMSXgpmwJCXsM35fqwkquStpj6rSyOldDtbLUjblvqvP0c5S6Hnw0m7RMdr4U mXwhQeZSllBBqvcPWO8aV1Enxt6Hehv3EyCggTrKViZGmNAe/QUqbUpZWVT0IHywHGoccl0P wFgWyBPt5Q2uEMvP3MOXUFTMV3yaUhcrX5wXWky+PR+4mRMidLGMQwNj4+uBtRSaUb7EIZ4p lQmN0ygPKq4T2aNhgqgKG2bsqbQ5m1kkaADRHsGYd76eWesdAqA/YGUk7ryrwMZeWzE1Zqd4 Za12ro1TXmko7mxGPzGOQ34gABrFNwjUaI+P5Uo2yK9HYERJ8ZV7yQOvrNcZ2Qcq2VL933B9 lw01WOWhANvH+sRB5gQocueTGZgKGRoXrN2rUDCr68FRPOZstvJJrURHTaXGJtRpRaIG66bM pzVkyD4NumIrOobd0LAbDRtMXVhYq9VnJLsQui4dfCeAf9jFwHfj/ulw+MVZS/WnUuC+2IB7 g4vDrG9O5l9WVgH69illclgj9K1B9K1i6BvK1s8E9BWnKZ4+KawB+u4xuueYtc6h2i7u/rmV TUItogfDZgCpvMYmXg4ThhR1NCLLeH02i7few5Yw4AvQHUKFcwhZXhiXQJZFiCQcYaiIM/JM AhOUC2BtEi6sAhgTuOC2puBCsFY73WrGhT5hOC6Mg8F8wMkGcxLjdyPiA4pzS/XvDcOHv+Qk 8GGLkMSHbxM+2EErl+t6cYGsssdHsSWvrLNl3I6hSM7n45/RYCsPu8IFQGsap9K4uspX5gH9 hXGqteOIrobi4luzGmxImBblyb5D5PTaCwJREdDPQ3JN4s1BdJOt6wXZiM0QGuRgwHBaeuWa PC4n4OziMM+qtBuF+RqWq/JlWIhEE0CkklfSze12eZ0NYAd6nCAVdiQVlA/bTC1A/mpwyGWA +oBImbMakmu1YZ1pbr5Sq2HcwASSL0+fFwfMS3wMm5exI2H4zKX602y+UuZj6SgDz0cZeN7M EFwpIwJCSCsMoezQZZIdzOdFV0xnvLaMC9WIizF5H5MMAigZAFussWUAU3rzNpSXYPyd27K7 X7YQvy3z5mF8MQBmXJ9BiUmqEuRoeaUt9ONujOnPWDTF5/LFADeICyp+m1BjV/xQI6KKLMCY IOPDlMD6GGO9Mv5Hca/hG5iT9S79EpiF/xTDg5erCrVCF2N4axPcbjtBijEahfT4/Sn+n9ME cijzDTINOvKS865xhrxBXVVWwUSzNNIJwYXkAIf8BggKZTU4mpUJfl4WvW006xMMpV6OJVbl iTNpHF8+aozjePM46uNI/mI+o6OQLlQ4APByj9vZvMnCzXjTyEXChnEmReh0i1CJ4+KL6dfK UWgJCoeuLRdjDRkg7hWJMWkoo2EaxQgK4ult7d+BTwieQSFa1ElRo6F/MFKTdTv/1tmaTbVW Y7VLxG5BpLPjZbQZdfeRoYS+7nGl+J6aZbt+2j5wOX+GOVoGaVRjpiEDXaMXh/dpQ59GW4JL WZUP6wjoa8y5raySf7EKpjuvRvvqUUNBzWaDM1YBFe54iz2OmhytIByPb8ZBWFrSBqMp9mL/ ezcOxRstlobMXfinSOyVhlwNEwKYRCqo3VN+Ii4cg+6hN+x4GAMnPG8VWrKx7eol4hEASwYl MNwL/b6adrAGZ3l65T3rnSA8+wYrUTLTKZ47SpE5ctf3joVdeibI3x632VYJOJqun/9hqmEg g3bnwDK+oD4//gagw0y5BAhTtMJuATyOVjC1ooKpHBVMP6ogPcScZDPV/sWqhnrPAHWQIrij i20XoExAu2AMej8+j//Sw7R4w2aaccFUfqzSpQQLQdGIO6XLLA1ukmsccXutdutogOIaI99I FTZ1SRzdcvr5muXcIpZcs1XpaxYjBhRqKx3JNSvuUaoLgyAuEcSUucVl1rQMtZBpWlaTglar 1A3Was840EjRM8I50eunkMKriC7Sc3N24FfdE0h7zZOr3dFqpuBVM+21epj2isYQ+IxU1z9T 66eotvaHzqSQ+aehxh6ahGqrl9RWL6mtXlJbF5q0VrdFHJ3UWrPQccasr/aDvur9h/RVIx0g gzmb/WD6ajXXV78ob+nEyQZuMKzI5ShxDfAq/aq2L8aHwS/Ch0HEh+tyRsSH/wwymPVoijKB orjZDoLDi3Y+l7Q+H0PNgGru3LKnpW5Qek8AsQLz29vkbN1F45uVHCYYlkS9CA8NsnQ71JHJ jbrUBrQZraAhT8AAv4XEb1P+50lsLEEs9OaXeV2iGyherXbLR2SXziZ00ydHvfPJuBvAKBKy SwnkA/01RQynNny0I1DpilYQ9sl+V1LTHI0M17B/EH8CxjSSnWHeJBa3HE0nzC7kYhYfV8Iq RHEBvUy5ifm1TNwsBFEa+Zk4ngoy05C+mp9faHBYxCmY9f6eHoOOj2YdKyT6Ee4b/CXMueXT JxkrAAmAxADoaqUbTScuMp1Mwr0lJN4aBtWA+scl7Dk8Uqanz8STWHSRxFxhbVXuEeNpeCey OSD0VOpcFBPGedd2gz/BQ5QSkT99BYbYuW1elVznYLNGs/WCPhJ/GmhxpfAnEQRmF3wZ069D fl2DfIrx6TQ+FUM+NZnHzP5wNuNTDuRTkxAe4lV1jlZrSzbCQbyqblC+3cV4tI9E9VhRHePR PUkebe5z7YQR+4wBIlkXy8MgdWyjn8nuL4p7zP3e82FyPqnfE1i+iRH6nmP0fUUbdj6Q7DwX UqYG2GF27LMVUEqICh4HF1Kgx/n6aILLSkJKavffRyHFNALlI43ACPO+xE22jpQB+Ffqsd2Q 68+s1X7alxC4/gVaabFWIRGDPlzJ5dcvnscJmFQLONMZF8I8ioPCsYS8AZIWVleN9dEc2uV5 rAPfRYM83DXgKZlOq2VYZ5jNHTEcVIF1GHVZcdHpzAq0vam2CzApc9E+udqOVrjYCLlXasfT Oqe8BHfrFPzN65oFgnqXOVdqsvwZRnmKq1hhz/A4/AHtrB6KyzkQD2Wlfc74RuLzv44jdMPP q4zPa7ULBB4AAPtDGDTcHv/jcewkExKRCUhEfBqRxlGMgpxB/j9J+mE30w8X0Y+UmA8p8z+O iWGXyuEY9moJiv9lC1GO96Mcz1SiuthtY+SATQnHUJC/ENsbLFuXJxYENOsHhhzPtgXLvbbQ Nn2MIcBXcgE+Ve8w5b8Zy+P44Grya6EPeGxer6u1zkELyLnN49Azqb4vyA2xaSwNEXAzMnag iXw0zGe1TT+HydcoSpR1boAeOXR3m6GaghJmI3m11g64MyajylbWGT4az6FjWWwgFxawrZC/ Vx3bYh2mjp0kF9AeF81FPfG4xW7mCOAwOQJ01AS0bd1p40A03qGPwXzXdrZPnNNG54vEntL2 YbHzr8VGwnnJfZnfCMldDTuwNlz9bYg3Xhv59VDeEC8MKx50plGrwL0bPUNucLORAekYhibS 3jg5nB2tJkEsUKv9G20g6x6W7wlR1wFPNyO6V+NOVTCxU7WU71QF8wJsp+p9q8WS3MKpdiV3 cYbN+11OQw5Lm59TFrU+s3zx/KS2N83J7AiwuFDtBTlCABSvTVfuU6zaqVp9Jc9H9Heg0uKT g5pGa9bmsmGpwhOSo7jMqGfV5ylWkCIT8UaS+Z9z2TKsc0jrQJOz15K4CXMMAhSWNpedaq47 yw+d5FWmwfDpGF4Oo5flciWBn5eon5EAJCWvye4xSTjcKXC4h8Fxr7n+4XCYJu2bvNYwxcPz I4m4VFk9N/JSKItLTVWFykIH/J5UvtIujpOd8ICrnix/VECxgAKUjVvJNrnXrHmmjmPcwVry OejoRqF0O+A9+tmVV9lDOTUEI9IbebHD6E/CqQK42xIEbTxQLaHSLQd5Bmp9IpSvccgBwjBQ m7IMtYvZ/WrypNtpG7SyQLBGK0n4Jx5k2qU2+29gVEB3a52rpS4uR6HPU1vh9nM9h/7Mq4uH clrrPm+ZWOFdJPYUxVL8NlgdIHj4XC2+IRAX0CXKra6Mt1bEWzzxufswYyoGwsMCuXoOsCWW 1Njeap3nGRI/KTsqult98RZ646xKnC9GfMbnubOwzrQ2zevvkdE8eQlUg4oAcnwoN9ceyqpY LMYoA9JFs4BueQalmHMtuntQWLr8VgFDpy4Wj+ljKf/zYBDj/Aa0u2aeQLOGfh7onKw81A0f TE1+4EJ+5+blv0bl3anrDuauFT70IBNxIL4k4WFTwGIUpJ4rey0HYyXHeEAw/ZaiI+W+PKeK Ycglcq+whGZgeMSllMoU9xVdbF9RteUU9XaPQTv4PrixUXZqF0b0JihdQe0HmeyUmvH7IyxL TbGnzFc44WwWQR5zO9sThBrLPXnOO9eT/GW3iEVA3YS6PApYykdBe+kwC5WLDuok8XQ3Cjzu b57FGWmw0M5lkOKLrrIasChBO26criS/20aXvJMOLMFzJ2Ah7ZkudAgvFx1VPHlFXRkR9taO 2/nUEPA0wZMKR+UwODBAA82vedzGmcYNvi+K6tlFR/DmFXknHm2T6F+L8y482aDutNDhFzy6 pZJ/iryzhw6F0Sm4nb0U6Q2fb4zjmdw1OVE6AWihg7n0OqjQ18HE+H8bl2Rn0dbDVA/WBsvI KMPHKUzjNKN8K9awYRSHqbEFu7KWBm4h6814ozcXFO3Tc/j+Bki66pNvDaXkqU+xf9uZ6aeO 6TpuMhUFtZ5PUU1ww0rufpKkfiOlbnZ5tU0cE9Seo3RFNrlTz3RuK4lnYzZdJ+HFGCo8mRrX ryB9oazKFpoQBDk/g015XZ5sBfT6hf5OkA7tr2BNyFbmH/UQa2V0kORZdNLNRBs15Q8616xm sNhhCO98gLfIExPIk44pCgsNTcdNy/Ikut6KbG4TFHN2IMzd6EkiNeRZxIlKVhnIrN0sYdDN Vh6vTAUKQecUMuJr8FwhHUqSYpOdm9GflOUAwwX1HvGzh6G6ZXD5TuGqP8Vy6ddV2ZgHbzCO ip6jVivrxWDNYqzelgQwnzxDYlOczZfg8o2NBmV8NBKXqfQQY/qASJZr+NMaDk0nGbMLsgQ6 zI6zfSnijJ/2ots/odAmd5fCxzB6BsqA6DhdSOarTnrHjKKj5YMMzVC//MTCtg9K5d5If8My Zb3dpAfDCgUl0IpqIwYZHawJanohU/9xzvW8tqT+P8gV4EFmq7bL6+3dLRby16kbZCaKQYL+ ArYFB1pG+cp8cVywRltLOVftZdFQUB8D/HWgZWK8wlUWDy1kOtU8NUDBjMZGDoSnyqWJVOHV Fu7dh1n/aP8PaKid7PBVduI+2YTh+hjAW4agYw0HPzOCjrT/ssdG/i2l/Uq2stSGbgIyOadm c4OTADSApObrySjVV6OS50sNBi51xw8Y0e1WklvYV9nx2k8HWdg7xPxqw3hUb4EPQApPZmkt xm9C+/VCzo/98bUOmuzXPorHyz2DocxdOCzo3wEzialY7HiQAH5mJ8PcGfqIawQ5/f0M7JuL ZxPTp5UNhUu5by4L6EHrEdf0oEWchMjG8rR+t5fBDxJv429L2+l1TtmQ899YYJ2UvGsp8Y8z DHqXRtAGeg2ClgEEDfeQI3gOj9BkNJnRkDzot5ICkUcYG5rA80BY6YiQGz04XfoYZiJZjBPl G6SEZmWMzDVS2CGXLCANpHaBBdyRaDcL87FQ05SETZpnCd2Dg2iy0Zg68lNrakf4+jK6M/6v X0CfXQn6vCiFPt/BQ9QDM0ihz50Y2xsfptBn4E0/fQ+UeUacT+YzmGlN5nJFjDo3ud5GwXrL 7sVUj3yZcZsYLL5ZbLWdrWShu/VEWGxOOQu03EODZODIjeeijkSWNHuazG2OfykIlD4dY0kz F77zA0GWQP2Gw1hRY1V4jOLLT1hlL6QfjGrpZ9P+Zn6NHHP+rJPlXScttGeATr9mfu9YHE1J 5vjjmJQ8ckA8H2Vpf4ooNTH1zJXu5vwZ7+2kD7pmWRVxcLj/aCot2AbihCr2MU+5HOZSzNLo TcdDLAIdYiFLCT00H9z2OeKr7Jo3J6nWj6VjanmcHv/Cwlw9xiLh8tpJqSCPAK+LmfmpNGlr SgBNakg9azCCDka74MmkQ6cFeEPn5rBdnvV5MJZXm/xPeDwvO1FPpcYGNaArbbzKptTY2A47 vXCxp3hHT12JU3P5Y3qfHsM1mi+Io90aJ9mT/AAHpePCmpWL5KUOvVDJkq2sB2PqLQS/FZeu IxBfa9fWjGJjOgkdT8TXo9XUYXT2czZXklOJg2FItJLtrVSSttV9FvmD4vn6Z+2Go/dF6Iwp 6hSb/G/6OZQf+gua/tye0jR9TIHNQ9epgEd0Ej99ltOP55NX4qSTAAlkGu1f8YU2/UpOL6pd 8YUO3UOfTcRtdR8aK2gLBKe+0q4XnXLb8YuxFxfZLYYPOabdCg8KokOptgfjK9HLEDdWT3ZW 5I8nuM8OekWgeF5fCB+RXzyercmB8eN8gsg9sj9mkx8EDUt+U+4c/CWGPeKmTnui74Q1sLbk VUAuHEqW4uJHf7xuudId9dIMw7KdgWh7djY6rjNn3LHxJeh7GK3OM+ypnGmgAJCGhlXI+2fQ ZsrgcFig9YAxALAcxtJ4j8bg5mGH7IxXOtLPjLjN/H8w6VYxSDqSA62y+MQN7B7rAnkrPAi8 WlgzBkblBpO8ZVcEZa4c7lVXnuIsIi8rxZH4VhZX0Khi5yZMiYgTbMtKUhBnkoJ0/wDbCw8C +p4i/TgnmCAenh4GjpsWwlH0mfT1oJK3NA90CKi0Okk0CImz4hU2uOOeoRgk3sWekjxH2mFi K5fNU3UBg2EwvsgBSM3pEYZ0G5SjydkaVGrsNTBjOFtVMFs43tnoUGVHp4elIN3FMCldttRu V286dFIf3tzPEylSox4MDk4kRCSflkqbtM4mrEH8XcrUYzy84UQHkCzsjZeOFhXKFxMNdDYj ttYDq8CgajBzMFromNH9LKLdurjcgMVZfk6SQ+zaN9At0tPLth3zcTTW2uJeG8djaPYtC+ZC 4P4lRGjHDW+AnYKFUc3AscZAH70wAeRyj8er5UqX/Hus+2KpAUjUWZye4RYXngMmoZydg87D oKuA9Tfh+d4YyGnoF5wtZ6E/KZoG3JbQeQiIIGcxYJwJYBh1VDCJB+vamxl0HDfcJ19KolUu IofBZWxtAEKaf4ligYoSMqjPDiy7g5BFPAbsBhuDJ3sUkHfEGCxiqFugD4blfz9u4c4jKR4L 9W60znZRHgbAokzCopPbAY/FCOf8RAtS7ZJkr7en74F3xjiSOrgLPYb9Mnzq2Y4/o19+7VtW PDiEBfk061PaGKGTs6Jetgi8tAgId2mrILWPV8eIv+E4T7eeTEx4+j8rJswaSUyYaIgJWVaT mFD7XyEf9I20p3LrMR6Saw7S/vbQ2XwYlYnRKhv5E2QpGInPa5OtuMOVBWOmZ7Sl5SE32f9Z fchcgHGcGV9j1w7iyO+BX6OTM8Kzd8M6d0GDAmMcyblIVPdKv4Xl8QYRYHS94Nc+OI7bZm14 24ZqhAlvfKhfvhSaQuuZUDpbGVcB7R4HjlEReUn8cKHpvJjHgYFX7AaqcnOwue0rWdtka4fm HbV+7ZvYOvJfuB9rNG/+Zjr7BlYDIDaaxNG2epbhd2LjHNLwSqlgjLmC2alH2nd45TOqj1KX m1ZK2p7Vjz9jJyGqi9GLHnTTGVrjO/E432uKVhdzIQQPpMNLjGMrjkF6I2ZD5bpN7i9t92tP kAcdhcsJkN41WVxCRbOINFWpa20B7etoobPI1TMC2vOf0202NAt1l1eXiJOxAaYqYX4K0kt1 h5H/uroYHjQWW0SXWl3iV6uLCdC7DlLa4eT+lalfr/YN69e/H/ySfo2mfmViv6zYK+uRRK9q eK8WmXp1CfVKPpHo1Z8H0ns1IdmraxO9ygZtUs+UOwm21B69+Cdzj0bwKRj41ELJj3x5NUZ8 6fiqGdJ6gn59CvTLcNsdeYi7rNfZ/DNEk2OzkNI7qHguFUdRq5tO1YsOqRO688Ig9oG8k6FH jgHjFyncPAoF5tRDCIKKx5WBhgZDrbsWiBc8AFk47mw8RxFdGSAYhGPmEBQxDEHhwBAUUxPy A1YShGXxtXEnMHKZsL4YoBJi6fYcszx39CgxfYygRBvSE+nMlqvehUlmugyrDJ43vBrZJBpX 8GgRUltV2j8eR6ZHlXrpplcWB1VpHd33qdITdBNTPT1+bT4sWiDNTAoYg4IV1ETiJ2mth0bc dw8cJToWX+PQFsD3ASBkZnfIVDwtosKo2PMziFEvoabqxZjQwK8d2vnHWY7H0EXQFSudSaOu gKYBXZO9M5B0L5kd9c4d/aePnVEvuWcBiEb8DG++Wb822z+OWPhB71qNAkimLA6ewpOQPO+4 cZ6+NKB9cCyB8T3HOMajA/xsuXp2tJoBUW0AYWtTqk/W/rms/aBGSiFCMfcLobig1whMWxLQ rk9CseJLocgwAUG4tMB8/rkX89XGRbsabpfDLwa1N4a431GI+1vND2qPkHzwPJBGoZN0sn1I BsKvW0Kwxl+s1d7jYQ/aQ6/tisdZCokLLOzQ3bPXpPOHC3sJ73EDWWof9GsVBOZI9HlUr4X7 8ga0KYQec/FNkBarrzc1d5vp/Nsn7DNvMfnoxtfM0J56E8hfCo4p3hlJnDT8iPkWq3+2YkUt 1kZaLMkS+0awPdZ/YmFJ4BrQhwRpgWgn0L5xxMCYmwPa1s+IjNQBzsJ0bU/8soLkqa4dDGr3 0SNA5bg4qD3AflQPpkGL5uDZsjcN0ZEbl8AUZ9H7/BT/AhOgHR9zXPsD7jEhNpUcM2b5tIA2 /rMENuWx22yMlsDO054Mf79t1LnRqHNDos7JAW13X6LOvX2JOjNOXt9pH1u4PTLBksYRS8Lt T1M8bL82W09wJh/nTB4TZyojYD7pT7S/oC+dM7mSnEkHoPUsxmZT/XJNsG38aBhs6ezyte4E UEs4UF4TUPMIqK8mgfrZp+lAuZNAnRcDoLI5/z/JeH3Uw2inl/N4QPJfv56O5BjLVMyLi24M Jo1pYZ6Cmln0mQYSKLzAfr3F9PUl8HXy6Haaz0VjD5PPKuIr7SifUVSAdhv2fZgsd2VPQv7b M1iLH6TIX8n4pz1JGY0qHUGOy04pk6zHZN9M5r/RMVIxZb9BZbzCLOPW4boGLpLj3CaoV9it i8V+XNLkG8dch1Pz5Ix8/n69ToRFPlbvQtnjVcPOMwpQu4r04RXyBaZEgI4VG+N3WEI58Eey hEbrE9tUqU1HhFOlB9G9DyhMl27HiPnxV9P9wpPx73UaA+aMggYgc16ftLJvfgiqvp2PwjUW i2WEMX3OXOY2C6kv2eivRvLs8HmSzOUvT6kT6GGAR7X3udS6QR7mIB9qQ+lrriXkLFtpC+UI OQr9FI8A7RNjyRxR8LEKYpKIITSWsa/Q3xk+9LZx/2W0njgM/+rmA6HTKypbXfPGhvpaLfOE 0HgQHqBG4VI0w4h9GJT9tzxCh02O8USRZvtugKEmyGeqDy3cpydhnSj3Sx8Kq3OEUgNa/AdR HEFuGwnmr6fAXNX2T4AXeRbORpYR36Qn3d/GwQJp+OwYC/hlMjCV7QtNQ19L3L5Dx4XB8nnh TFCtgeJWuco9feKHcsBd9jLoLWhw0XMVa1lWOFNeDQXk1SB92UllhZomlb3hbH6RIg/F6Lye G/u2zi44Iz9CQWWhG73eu5wRsvbXuKTb4VUz6fR+V9kb4mUg2qNGj8avck8slCGvdGMlVW6o vfxi0SZP0l3woHylQ8yU/Q7mChbuk293yEG33MWVOiihVLjhh8B/+N3KYjTNyVV05pFqhmdV aIHFmidBzU59PDwo97tgiS500X6YvBDEbVf3nyzcXoXgijN5I1ydHNbWSnc35lgh/PM7oFPV 2CkXM1OM1KlR0Cm2f0w9w/b9vH2/gzrn+tLOuRQ8UIn/jtS5bOjcRJwP7J8D++fg/XOhC9di tzF3kcUYHYV1jKNO0kfLQeA6m7ehS0gDJmV5Bu+iNkAcLi8vwRwpZZ3OSJWQmF/xquRIGVAH 0kAe/IL5GBFeaAgjU6ElmvjkBBhbwDOL+C/d5UIin6TxMKCEY/zcEMBCEKSgw/DmM6F5d9vI +JBsv5I0CeoWb864O7UOjuMdzMYOov8d9a/7EoHjG3AIHMDgyAP4xT1I1u/C+l2sfjP86Fxl jN9psOBoqL5jDNAaQors7heoY+xl7Qjj+OW9dPFeZmIvM1Ln0DF8DB3mMfzyPrp4HzOxjxnJ HlJEjt6yzlAO4WrzdSdQvOGY3TuSnPv2X5mzWBQNfGXrHcDWKl1lMXEUoD47DwO0scpRFgu5 5KG25O9e8Zj8Bl+/+HaUvEe3s98BF1/oXjdUlE07N/qYFOpVLjpCY5QstvPlRZ2BkpnkMJ/j hsE0O00S3Jl/JXGivjD+Bqm4xfzwlQpiQYVbroBxc6UefpOt8up8Om1TkDgNkCaj/OE9GoP6 PBC1mTHAFukPTcWPspj3tYr2AKRmgaD2zPFhNhfT/ud7lsQ5hn8RmDEyNAaU87I9IfRB/iJ7 5hL+7ZyAdp3x6Tj26Wj81BSv1PS9qR9jkhVMF9iWGppxp7E6Jim322oD2gnMIrqnVvEWQFdj HJ6R9/J3vpvsDOqzRoWnsQonsgqfSa3wpHb477zL7PBKRYFZHjO153uXMdSLYbgBh89CFT++ xgE6GLynxD+UV/wAe+4KajstFkuqLwATrOwgZ5d1gKY9tuyNkBO4+iKH/omyyKV/iPRsH9vz JxmXiwS0HwFYvQ+wumvEdy7zOzSkM8UVCGLZ0VA+rYhQrnwE60/WpOch/6l0l3WFcssXuoDp dQAXK+sSjxIIw/p/yLDtoB26ncYgiD7oqOC8ilYCHAP8FX8Tnrvo+S/jJp0+Ie+knH/+S2Jf TPkVJkeXw72YQgXzt9TjVlX8TY7zzuZ1JNP0Yvj1sENucHATfWLfgw4YkpNkvYtMTl47eeOR azvbLdHPKz1Q+hKF3qnKK/PmhcfLE9GpVC5l8WtlcVB3y68q4/Q/tTF/7rAj/iYer8XAcTHl V3nWBIjyMBBD6/9R8M5X6mJfDF/sZPDFZJBVf/VUcgg3DYdvzT8Bvr6TwDeFwdenjx0GHx02 PJzuzwZIygPxRT0xooZiHyVAUxsEaWC5eGarV2jJUpdY5YHmdmcz+p22tQot1sqq5naxv3sL /pYGzhTL5d7WifoYaq9p7piQo6LVBXJ6ZtNAjviJvIeMtfLx5vbQLRifvkWoqsTv9a+S/DhQ LI7uzLLo1fz85UAOKMIDY8RzysS+kF31xjHl9xQzJKHTk0DoExIfjIJaYHbioDwMOXdNjBxw RjAzhrmajLhvUMHgnD0j6f8Hjf3EUuVSijg7FhNR8TkAdoXxlmhvEY+nA1+jG3ko0i++cjIa +T2oczfG1WUVX4LxyVh2xvpxRuVIN13SwBmhyTCWISft6wLjA/rggrnajeF4lTnQyG+StoSR 8lydR+Cja5WqXPURMHYJj+US97t34cdAhO997CNM49iG99K+jzDUug2D2PnygMGS86nJR8+s H5kaeelPFn4uHcnBr+EhDLoUdgvOu3D2EOn/A5HeojV9PmhkU3oYnwjarcaT0LigKtW/jQm4 WwfwmV0/u96qLUm8v9V4r0iYAileov0wNkhRpSV0oY+XKB73Qn9AGzw+iGfQLmuamxOaBwPb uSA3bkFcbEauyuTdiibQOAea1sVzRJfcCy+y2JPOirglmS8vxU6wscdeker//0cyDHZGLO0w ovDnEPzBnjE+qu7E5/LOwd3xOKA3lapSVQH+ALLmJDFeVb79Nib5w4JN9JEllFXVNA/ASWI0 1HYIa4vtxtSfAtzrZ7RuwWdNA+udzZhGtGngamdzM93cGmpsGlgSup2OFRS2ShuggRYCUFXC mNv9KIBwkWm9FLVKTaYyG40yY414x4mit1gKLBg+cje5yQ/SHzRPBg6eMDLKYmB6IEbtoQkJ CHHVXy1m/pKybezDRJcu9cme3eb8n4lx/e7bFh76N9+vSitSZvzZ/sF4Yn5GsLlc9jah2WRA gRQDlsHnF9ojLzmbX8fF47dJAxmNo6UBa/isyIENZ+p5GweOw4sNkzcOYALsBvvGAVwo4qg4 qON23Sq41FVxeaVdOg5KOnlxoLrl3DaWlW+cyr4PXwlk+PSNA0g6Q+fo1xL92ziAibdDl7Aq QwW6l8vu+ldY/IMK2szWz+TjDb+xoH62cT7Xb9Oz4aGV3pFCUSnb9Vz+naHsWEhEMNFy5g+H MRD1a4HYOLdleWV+Mj5DrRtcgaFTO61xfdaKS+KWNZNhgkd1WgeqOq0WPa/T+jndYP7PFZcc s6yxdVpjVS3WKsKqTFjt8sS4z+FszhUYjZkIC7CoS4oJjfexdvFonn4Tyfcjt23Hts+n+qH5 KebmJxvNU7zqL2z/LpI/7JxbRT19+Me5Lbta3kMIhy1ldXoG4/pXVuAErDmr+YDohAcDnZ4T ll/imOql8PNz/NlSN/RLzPOlT4ey0OgEeBFrqTvBiuXw+WipGxR8MenbfcJt9ye7DszEeRe5 i2N0up40vsrGZA3OxQocj+1ZUqcVRkTuMI3JS2w+SlZsPA6A5je/JObgiKzo6LazIZH3rejQ 7C1WPQeKJAYl50snxdqomCblvwEAdcRZ2Z4tRa3D5mUhm5cimJccnJcVHR8C9ccpkbuoNc+J xLzkEz7Q3OSmzE2GaVIeSJuUMSmTkrRRknmPBdvtD+UoE439TD4UhJ+LET9pNIpSRuNs82jg COwww3ec4GNDs4PDl1MFrVjliQk7JzvQB3y9VD7amqVnVLVah/bN719zDKn/VO4Y2XSpxbml XY5KHwh4QALPl7UpY+UajCRwCVEe9yVEeDBE/uRLiO5M1+suIYpTfkmc/fZw31LoDtKbyjR6 U5lGbyqR3lQyelNJxKUKFPJc/h1/pAjGKUW+p4dbB4BqoRmNWZH2DSW6i+ALjW08iyAUpwG1 1KeS//zYjvfsuov9dW6rFEbtAZJ+AJWlYbpI/WvMQbIOjzKjoED5E2trtImfx+MU0rhN9vVx RFss1/XiYf6VSriPaEC4z4Ru2YwMtDF8mwX4NiGVDpSw+R9GDfK+EON6hdvaQNJH5L80mRpk JH/DRw6k9mWi0Zc3sC94fo3ZS4b151bsD1s9KT1iC6iadWhGygI6a+QFNJXw+Yt7c8/w3gz3 d7ezGDQeUD7dKONhMEDZNyh7YrT6UBTCVPKto/Q1ndblnVXCrdIeq34t9q9ln+3Q/K+tKZFj SJsyGuqhQMu+di3LUdJSJeBdRmE23lub3s1ueqmkZXGGtMemn950fLk4gX0kNFzEal2OtWaX DYTOggUGcn7cFwtNAUbYmuvc1lHuyRPv4R847xaRDCCFwsjmF8mvYC5IPCByZquzmhUOjeOg ZUp7MvQsbE+oQo+Sd+i7tDjofAxcmD9lkJHXGgFZM555G5T2ZHafyeOvhQc7s5fLvTAXWdgx xRdrEegn7+cJuZfdDEE/cb8BJiJqIwdQoifSUINzk4JzvnEobnFuQks7YNAsPCab6byLflIb UHOnMI+qdqyQYqPW2hwlutV2MTWBqCAdcqY+H6LntmHP43Jv+jOrtCdL8sTgGszSqwCo5eJZ BhRCw9UmCHBSpA4rdcOquwFDysKDoYvlI1CmxQnTFIOVOSh57FZgFqHpgEcrlFKocLpzs4ul 2qFKM5x3d1C8tkEl7JKdRMJ7zXvH3PQxCRWPOTDW3WPJvz+Jb91IeNpWSMenr53PWWGG867R UArKEPXOYgMv0A8D7Vr2sRtEu24kCVADzEAzzQDygud4ZTD4mE+TNTiP6kgbdyvjEcPGN4Oe Dx93m7zPeGaHZ7Q/hc8BI7P08xh9AmiWYz41Jm81XGZaCeTPVl7nDs1EpgwDvCRUAHx4heJ0 bkcMd0Y+GaIB5mviVTqm65InoX0yZsZtjDEFY3sxQ2wMkq02CLiFsSSz24UDmLWcqAvDaJjX bPrJhrDyREsXuxnCYO+09yF12ropF1T/CmkARrOVRnMA8fkdhs9FvTSi75AKuZzwaR5V6hg2 HpUnGGlLH7/KIXo+bFwr43JX+jNB6iBcljqz9Lkr0LhxNgdCaFhuALAc8JjILsBv1ccSfS4X 3aHylomVQG68BhLPwlF2bpu0Ajga/K0WVgh7oE7A6FyG0VgvIPRv+IBfTNjcl7Q5kAsO4DIb b9wY6kbXU8pP+SX4POGfic/7/n/H50Uj4fNsxOdOGuoiGN/cFR3v4jh7BaHDwOy/pWB21MBs GmjDf5bHTcMBLANxbJYykQbOPG4jD5s8cQfKY90/h39g8NY04rhZLGtegFq+RbWwEYMBg/5i d0dBd1n+DD5ubNjSR40N2rDxYeOWUhiHDMBA9239XByyydB2rtE2Dhe8JWbuhBdZSlaLPZ5F 4m3SdpxqH8p9mczHkX7xArKiw01h90GoYlH3q/CveoUw2L0PNy87hrrbrYn9Qi8IpeIAfuFE ud/Z/AS8KzvibH7YisaCyvnLnZEWehTa5twmVEpajhS71bkZj2fLf5n1orRhDqyJD+R+9cVz sL7dL1kspVF2me//WVfhKT4zrr0GLF9yGeXv+0/W/19xNX9BP9OffxlsJyuf/vfGKKNPaqVV P4/0H7aeFzIzPGLEL0/E47BMx66Q9nQBOcxee1ulfkittJX1Ojf/CLeBOvTr29T1Q0Bfy47c NpbnAwUUuja0qOzI6s+A9+uLjPehI1gVEHipvQspypqJdL8b7jPX5EATj0ITmWtdlfprzKuS x4+O+1zOyPITLCCFk6KQpZ7jSvF/7iRzJjQYiQNDoEQq4UGQx3HdYYCXpsssoVyUX1DUzAQm oX/EdlGPlIuDzubdMA4A5kQvcpSQm1xBnNv3dDttifVD5R7g5eCd11gg72fwBfJwGS6QNl7+ RQDpX/ewy3z/z7qe2Dv82X0jPDOuZv6uYu8XX0Z56wh17f/1P78fX3TthPbuGKHN2+DZjWnP l30JbAvS3s/mvwv5Xzf/+9Ee7t+COECp9LpHWVF/p99I+rqPkw+D11ruGXRubhaSqFOxdpT8 qvSuk/I54Y3UMQp4ni3xfk0GPJHecwqvUvZgQFBcgKUvoX7X8W6G9F628CpgqLMZayWMO4tX n1hA2UCS4ZlX/73qtREEVlaTjWo6SXOoDx3uPo+diYN+XIb9KOWNSO0o4b3cmuWdf604HVgS O3v2KwfyJWfkHvgXk4jHuy3sg9V/6OYGPKhpOdb0QeInxislHYj9pOOLL1kS44e7+N2/TP7G AHrdP07+HoO/v5f8je6K3XLyN4XW2IDzU/SG6o37a7Xl0KJeL/cz4nE9jGVivYb0lJEbtXY0 jo5eyPT1JBVy0P2jeL8WZRSbMWoUTgkpQYdu9+o/5RHxeob5bX93D/lXqrhRe13qGaK0/Dd7 DLdtjPIRi4dGCb2JfF3KJOGoXDfoR39pbTJWUzdYdFSelOK7TMfgQYCwdlqWx63459a4lQQI 07lfpuNjSF+2vYAqfidXukLfBu0+SPrWKajvZ6I6nbASN5SapDw7SngFTIFfEpoENLXVyTXx lw0xt/F7XE/R5yAMe+Q3APhC7r8I5ZEij6C9LxHfpe9oQ2dEv+NRHQmjDG6jU7wzf7C2RpuM UQ+qcH/+9/Kr0NiFKxS0mcLcTl/rwCamc/yAJw1rRpMVWwO1X8+GB9j2IvF3vOGTnKW+qz3N HqSIeQHDJjTlCDR/NeHXK/Kr0OfIS6HLmf8raAlRKzAONFnMRC0D4OnI0AsS8Aw0rHEwo9AH UgcBBNqNUBn3DYp70JSR+yX573anwpXrx0BIANN7CFMdjkcKPLA0uN4D8vgeGiOAyY4w5SM9 MsGjD4cHdfsvhmdFGjzjMI6UAdOuowBTIAnTgrbh8PCxOpPgykS4JpuB+jgdqJ1pQPGYyOhX Ibua5iW26GS/TbGk5nmrcxBmTgaMHBEdP0hGd0uzYYRu1evauL73T1tPdlpP9i9YTyl6P8Ej H4FhPAe/moTR35zbYPBcoXEtXbw7HdgdGqsl4tup8VlTbTK4y9u9IaFQkgUQ6CsHZa4BSsPa U+uxkZ8DOz410fF5po4zfwPsfaHR+6nUe24MjCT1w2/G0y0fbJ+QYuzJHYBls1coEw1cdkjt J1tf7QnUqVgk7jftwSXHspxMMJPIjmAnXHSdGi4uEX8zfHxpz+AVXH0GPH/v+lsq7k1Un4SZ vPhfClWfZBm5QudQ9aOw+tOYfTJZ/4epS8kh/jLRAp0DGKIYucP8/zf2PJwaX++2XzH2BnMR CaG3bWQlj7UXjazjd2rkRrjzB7RsF/0pdlE4HbibmLgr5HfqzpUU+g3Dw/m1O8bQ+Sl1E+5k +OPbcF8joD21GhSSTXcKlNrxPh6j6MmrUuOymeO8/P4FgwfD6v0qKAcBaRd+bhF90m52s0DZ jKJO2Sb8V5yjbqYWecPakpfwTFMfwLnACXAFA9qNudBXggH/M3kjaCn+WiYgFr1g4bkStcsL QVcfyndu/glq2m/PuvO5Hg/0911YF+b/vCA1LYPLDZcNrn/dYbFcCH+bt5/a9RiUVeG6g9fx HbhuhOsX8O4HcN0A9c2Gyw3X6/D719uRfDMfl6D28jQgCl8DAIPahdPh9kqr+e11IMV2V9Db z/DtRXQ7B29nWo14CA9g/kL4RhHQKTbx7RMFUAp3rZTNT6H+uRmLMbl3hxNJkWbkQ3FD6W+A QN79Bsrf0u7HcCzF+epmvPGrm5Fw+YPa5XaW5fNZPHrHC02Cr3ncUSNsezc6vSj0kXM71i4L 7BdlzcJQUvTLHr8bqyAfKaXaXVbtEvONWsdLu3E+reJ3SS7tvhRhxtN43bMpnI07XornV0rj F2vzptBhEtAYhZBPvwHzy47FgqMT8USg0PemUN5n3JP1ufUMIwL9aY0T9dI2Y8Sg3C9ZZWMw lkVeaXt3J8rHO8Zhfb9K6POEhRRSwIhXkvh+41TcPjc9KMAHBaYHOj5wmh78BLNEA+z/umM8 IjfIj5H+cL5RYOP7gLCNASjXickYzsD5PoZQVYRmpJTZjWU+zGYTVAUPmNRux/GImzwcDXki 35z/YTsdjuzQpkN1wr6OmCDvkfYMSgNCI08pjYZqpD3+ubtRIEbbWt2g1G6XPTH01xqsoUAQ NvT9lcO9HTf12jAFkadXnm1n4RiKq6V4Rmi6PNTxPr6Kzy5loSPIQUzqdOFr8X0WQOtGjP0u 9tEBaTw/NUbx9XUKuJHUt1j8VK0WZE/fC0//5Cc/OfZex4eC6q4tquvruKnPhuE4PA71Crsd W3aUSJ8ITunrZG6OsexPssAD4SIFeStlPMw587K2kbsA1/xksVfubZprSfOXUlcK8rGo5zA+ ac1t8f21+aXQdB6f5LBqk1snNb3ndO46oNqqZM/h6qbLLOL7UE/4rxbDv6pC9vRgvfynuk6Q Y2hNyUo20Nt0qfl31HOQmkPvrTzFdxCaAW2KWjjobc1q2dN8QNToUKjvIOYH6gH8OAxXbw0F yNGmUWoHDaPjYHhFMVuOdV8J2HxLn4VJlJW2hPu2mLObVMwZtODs8hLMeCfnYhwPGJVbEnnr 8AvKVg/18U8wEajsxUDbnZSo2dK56XvEqjY9zOg43D3G7zAsJZL8ehsD8ZxMI9V4zm5CPdSH 42KfugmpF8uhVX6CHSh0ROLi6hXRTTgHgqXfczgnNKlz0yEkHJ2b3oU/l3dueg/+3KBfAC/d xssM9tLPXq7UJ7DHAnu8hD2+NbpJ4yAaB16L+fzj8XIKkMTdHJP3MEI12k1uzF9mZO8y/OXy Uvn5489B17dScNatGm3q2ZX19k4Kvnq9Qn/GWG692XJWHP6R6XcnxWn9ZmfkBPy5tTMyNESe dhhZdkln5DP4c1NnpB+TDndGjmGG4k4KkgsPj8Of1Z2RAfbBR+zPx/CnAGQZulkh0x/nro04 EriLshldK5BnSvmYgOJdMmwy+/Q9v2DXc3C9Dld9hkoA+tkM/jifBT+MWZ13fYoOPhX1VhZj lhdoMQoIzrsOYIHp9Vkq9YMXuNkokOm86+cCekaqBB5/vZC9BkJ31734ub1poDg0vWWit14I shLWRAtiNqzDgQLxIDphQoOR6xGdt1A83K0IU6uKk9CiYhzbeZTmWRyDGk1uFSyoudbQp63W eVmYNtLeufH7iEudGx9CzOq2JuNV8ep6qTpWEd6LPJ/38OpOS1S3klXn737Okjx/xOvrM9XX l1bfpeb6QiXGJx+ZPsF7Ef1jh7f/9UT7t7L2l+hzFMJDtK8NG87nppxkOMWJTZcVh36DwXM2 arQIWR6XxAObwS7VJw+myo1mP5D7n7UYeQ8xOFhv2T7xWjw68EsmAziZDJApJOI/YZSG+CoE LW8KO1XhoFxOFAwX90sjB8I5jE2/YlA2u1zpEvbINW65rhdNNnYpmofe6D77xg4kUqAtl4u9 TqkJ7svDg7d9V6ZMaU2/JAoWmuLcluX31mg3u41Aea8yabSqDbhNUa+/fnlA+4/fDRoBPkXM Vyb3zvLEIu0NOTTeRAOhDYyhBj8pCqoX3rZQeC7bCjlbitq711KEVbu8ykXBzftku1qtzfLY O2IZFM4y6YQyzC6w5Gcs9qezGQVmtFNpghSzOTeH0Q/gz7Oel3r8UPv7afLvKz+1WA7/h8Xy IvolQxX+/0D255YuzXBuupx5zkWzMIGZPoWNP393jvEOnfLhYTQrMd3dY3B1SBK6zu5p+hX+ TfJPbit4tagDA6tMLHu50Sa/qVvlVzAcq8+FmTLvQ5QJxtHXJ78N3VeyWgSvLA5WNreHRmNm eF23kUjQtTjS3viZfrMqtfC2Wt42+QybG7FDI1ncfsQbajifN1KQ1oaLtTGK2R+SDUFd5ZeG s6HXnbaLsc/ypQwLCmhQMMELvMpio5GQFZnGcnJ7zv0/NQ6vo5vQrShdD2Q6m0FdsKwdBwLQ eSCJhRZ11/H9740DuNCczZPh340DQuKeZGOU5/n8nGXMD81IdpJeVbhgoEDw4OeF/y/Ox3ls ENYUKhZ9NL/PUyrcaO3LSsVV8+ww3RtJgGl6jj2NuwBEBqRwAaXRelj2FVBs1vGKryCRSAuz o8D4U5xEtBo0lVnEUapCq8DniHruwzZVWg14ODCfrwfntolldU3igqbwvZbQmrjvvtCqaq9z m1P2Ncu+plZni+/eln22R+dPXjtK8TVLHYfwKUic9/Cnu6ECtepQmacp9KLiaW7y3PsoVDV5 bYbUfqjJcw/8uId+FBR1YZRNgPcMBu/fGL7Ie/TSqKeX5DJPHz/rgrJX1DMYZ76iiC2jm+bO C71GsuhnpQcALb+pSo+gQ3q9TQ0/FlQ9z/rVKsGvde8+QUTQHelv8NbDQGq/WsUZdmiO6uuV fXdKHwurCxUgd7Z6S31OPWj+N76Epxdciu9OUA/R4wvL3HYQhl2wsIwA4nRS4IC3uGFcQzlR j4u0BXsb3LmIyrv6O+yhC6Wb8jOkcH6GYbKAHtewUOMgRsbFXj/Tm0CO/BTXxSHjU5ez+SVq 60GLWIJpIsWZ9RZt9MtA0j0txrEKVfohdlmVnqDDGb4ogY05/aBfLca3fQJ8K2ivQKfkqCI9 KLBP/8P86Tj+qQ3P79OH50vhQatYVG/V7scPOw1H/7QP3+5kHwKDGcS+BaBnwKhbahL9mp6J qT5ops+kmVafDMU59zXoz1yz/vdjJuL7uqRwIeI3niMrVHyFUSFOmRMIn8MO1GHG0eOZOHJP 2/h+nsed4cnL8ORneAqk2KDoVMKF0Wza32uxIc8G8V77tNM47BK5Db/DYE9/ST5bSs8O+7Xf Jp/NoGcH/dr25DMBntWXKL4uSuLo2c/0jlxqkXSP32VgX/ZHK2cITHQ3aVizPI4KvxLuUrLj XVAGBAJ2mOYSTPLuwGMduCxtQHisXjrfQW7cJarnLVBRXvdTdgNfV4129zhUo/YxNWVOsu2q DG5PcdRAK0Htt2OxnIOFWM+lgaNyUxDG8P5oNi2yahv7Y2d/HOyPm/0xcliyPwXsD6V0BEjk pcX1Qv0Y7fKbLRbtnr2AM9VuDJUUizubN1uZKaDHgvIz4NQ0LDQGCvkBqz/7NaxsMab59uLf Hs1DfzXtEvp7ULtoL454wS3I9fmAyZ2lB2C4MJ6thbCi3VYFnAjmY8PHiqcPzTyOTSAKKeE8 eT7cHFZ8+fTkkBIugCekMQa08kxDfvpKAKexkmUGpZGeqMAox0u0c37DjjwVMf5UT/k3VOlZ tgqeY3+20WLI/zUWdcNiq2JIQhWBfL0Pp4Bih8XF1+kvZVNn8qMj8RK+AKqgeWg8erVL6O9h 7SL6e0g7l6p3SeE8S3g0DhRrz4akCB/EtNHGgwJ6cFAb2MMf5NMDTes2HuRZNuQonh7EPEEf lUAArGvDaLJR7EdX8xx8w5ACa90AcuBBemXXnXx/bz/HFmwE32v03mF+T2gEj6Uyy4ZcRAAQ lr++lx0RC+/H4G0bnPR4rU2r5s+h9Hq78XyVXTvfVN6RKO/QJrHn9Vg/lvv8m0g2Cy2hUbQW mM68vxsPPSTy6U452ZS42tLmAypNnZ6D2o862HQ80kGIgTN0bwfDWMV41KM1dbBJXGc86tO+ 3cHw/Cb4i1z+xZPKYOOeIN8vg8EPAoNXJDz4iTFW3IQAuQne2R0SGBliuWSjSEYopVgBX+HL 0HGgegbWjU5paMUZJR/l+aLUe3ehRNCFehnmJ2fEqairwm9UWM0IkzghWePxpH4INTqwxmy5 l/KbqxLV16kEXVR/kn7h2ftsTHlWTWcYl9oVT75c7fhismI3yErPN3g07Ly4+BU2GPJc5bkK ZErPFQJ9qXdq89uB6mQpzy1LPrRq5/CH862Jh1naOHqon4PxxqHM3d8w6MBoP/xsYj/r4xhK +embiWsza7Ic00cHDUvTcDn6CrP+80Paf1Dr2uW652s1e+OJeH2mgrcT4Fb27LilYkwGiDu1 2s8b4JUFsw++gmGbs4DWRdo3jPJr83fTYqUUcPi72PhtZ7/zjd8O9tvBfqvhF/VixZuHc1YP fe4S6OjdHmzWm4drqG5HbXxNvl/b3XiC1o4QjK9xa772QR60bQ/BeRPApXiL8Wg6xZ3yFgfo Rr3pqZPsmX/1B7TdoRfJb+g+bu+evT2gXQ41B7Rv7xqMK7btsm1z1LadKMZeR+mB8jpHOF8e gm7H4qGcsq5QljR/czy0U+q0VcG7De9TQD3MvvA8K9xoFLaVdYkVRrEe/WZ2flp7H+fWMxjQ Tuyk9jAnuO1u3iQJ2bjSzzXiqfWXi47wafKAYe+wsqp7xa3SHpsXXm7owZBEzkgNy/FipHZJ yujm+L+PWXhgyhkkqJxRbzpLPgGPKGtnXgdodCluRQfSEp6lxJxyPmaOeWUzx1hIy//xKNti qkakuakhm6kRN8FCokCEgiq9hMwpqN1lSRhO5qlinK//pnD86tDYeiEQ1NBVmRUIdWMpN9Qh JBQTbu8BgGw0CkNkxx8xR96VjxqwT5LWzQBh3a+9M4jRd6GcX5sy2pLMy5kai3HKo8k182Kt 9vp3YWHYKMDiu3ArR+sdQU2CO0DX/DioUHWuWhY9wqbNuJ6FWy6m4j/B4iPGXtz+iIXFBS7A jR2AThyT0j+Yozgs/BLtX663pMT5MsO5+pEUOIsRzgxquCwB559uHw7nHO3HKWBmpICZGsMx F9ugqG14evtAaAlGsKHgepiWr+GySL9YLh23hqatdUjHhVCufi6L73Q8I+TUT693GvkArbq1 Psuv9e7Es9eGGqK7YA7JfztQ49d2XI8InYilkgBB+TcGAlHbcldoPB+c1XbNB1isu1G+lJoZ X3Ju4RrOSLFAKv8t4RDFKisRJw77kurjTayxax9+3TC+jwZgrzXWJ/8e5DOMFogFtwD4+iWJ 91grBRZkdxU2slSxXyyaNw+fLF2WaPpk8V8eNs1BYhgcgZpazf0NPLAl9yvSPtaeoEglVrrL 4hTCiK1pyn89Yn35NKSBmvhze+FBrTYKq56U6A/WL9tZ7XJJet1mFBkXeSmUqVTlyQJm/VOq 8mWTi3kiDiBm0qMIOnnIkavyefg/Uwz1wtS81oXD53PV99l81jlK452bUKxf3rQLlVdLaJpz F+1ZlO0RxyubcK8XI8TRjX6t3A9vH2Jvz2rdhEbflk0f4bKzqlSNH9bIZzZjk0bQZ0kDNtHB tj9ws0+fgt4LuXwPZzet3Gz+i+/vJMMupMW/eYich4E2Z5EKn70DRQ3dU+9IkGgjJXqp3EBY E7DXBrUpAyDPZDG9aSzGt44fYF+OZvqmHfdjRo7DuvghHsJHOx0qCVD4iETAnxHiO095iPBD eoHs1+KZnXegIWR55x1H4I+t3gqNZfbSKF2gvUKp4NDrCX40UH4hu1Jrw63QvTbaGIUHG/fQ 0b+62C6EmOUbj8VnX0Bpt439zl7pE+G2DyiAqg0QkTZC2a9auqcQfCPGOq7/HkMDmh4pZltb SunbXlwBvOE9Rk8LoUgJv556kF2l7exsKMIDY1N0nOXAbs+UYllrV7EMcKyKNZZfQ/nX4XoH rsNw/QCuX/C/+D2Z2fWqHUX4p1zuZ6hC9rRZ+GiG6QF6meqTTA8IfbIC2geHE6l/h/FXRCrg r+rduOWHhwm5M0AO2wjASEorpN208xoatyK6me4setBYv8yZYKyynflFDILoWOa1ickMMwlX Bf1K6C8QtPicoFaDL7w2JWDPCDgwhp7XJm82ahB4UG6qbW6HNj0D/o0JzJ2h3XoJdq4hKyoM ZbDN5ZScu2YfmZ88wEIUwWSPw5yjYh+gt1DXVy723XaDcd52aPkK5zbPUNP+5Stkz5B8DPTr opi/fnlQu2Jryg5Dn9wLL4KYU1C72kLYKfd6yz19oUmwvD1DfnpzGXsDTax+HBruvONjRPHW O3C7s+WOT4gWIJ7jY/YFOgsnvWzScfD9+8mwHODhOdFODcKbHVjGZMpn1y46GI7kEL6dlDY/ cj+jzTAcVe6yKpc4SnrhMXzX4GBGa6ixVO5na9MqjmEPmafyZFiCDxxDMgEyz5sNmShCdZlb So2FceH9uIvs4hA/cox7EqfKfyllDvSbyozgJ/vuFqJt6r0zPiFl7lf41xKyy/2GPifvSdnP L4qpC1yCn9J7oDkFGMZlrRJ+1ZKlKkXwVw0IFA0lEV9EPi4fRU1vDLOeD4s/crJY/J4tCdNX Ah5m/ErRWENfwyDkFq9q22qxsM11fMvTvaFlbHYAkAtTj7344xNxisJT9kbjOHK9MVQyTHW5 E3VMF2hqTpzvFG2tz2RXvy91D/zR+1K91/COebehb/g6m1rX9EukofKbpe2Dnz7NnNVkcnxj z6P8eRN9+K205wpV5Vd2fotSk9J3/lrQynb8fDCuPnmdeT8yCVTOfYy+GjLTHCa/KBKpvSWg 8v7hSvy5jP20ap30k1TdElBzt19Jaa2Zcrka8SyLFDxUFv/ybKpy+cqzqcrl7mdTlcufGb9H UgiHy45L7yVfeS1/1QmMGzSEutPIOaTPutdQzCkCWsaVXNG3Z4XOaMS/VhBob4a/TvF6QhHd tYtEgVE4v7voZEWciUloHjlvBEkPus/kp3gJKwjy/ZkAGNp7qLRcwkumxF4bIf7xPQl/vhvO S/fne/HbI/jzrflXiwUzCy2AazZcHW0Wyw3w9/m7T+3qgrI74foFr+NRuO6D6z149ypc90J9 N8K1AC4bXJ/ebfbY+3hGwp/vmqIv8uebPDPhz/e1olPx59s78z/jz3dH8f9Of749Z56CP9+o wlPz58Ny/4g/X7gwzZ9vQWGaP9+fCtP8+e4vPDV/vl+M/nJ/vvdG/V3+fN67/58/n9mfb85d /0f9+S4d/T/en2969v92f76fnnYK/nyvKf9r/Pl6Qmn+fHta2fVXuGzKMH++l87+En++p4wC J/Pn22wUGNmf75azv8yf74xEC//Pn++f4M/3WuF/rT9fZ8vf7c83t/C/2Z9PmfYF/nx/fvL/ V3++hs3G1sZ42toYU78uaTcbBeIMHt+V++WGbyE7XLJSu6OKsineVn9TQNtUhdvtj1WhPsTS Fy6hxF2lzPeLO2QV7ZEGblx7Go9Aqy4RQGdvtYIEgAE5YQhBy+yVGh02caxSjUnySrR5HmQG t+jZUe8tRPq9uBlKaZfMOXJT8j9vsrDors7mHyI5aghZnBFkHdqrlUzAwWBOCDT+Dmh6JbK1 PrYxdr2CElw5gzoH8cUM+ZlJyGVfDLTncRg/VwnHWrKrquVwDOGHQZfWO9D+U8m6sHYB68IY tv5SO8KzmH1D7kUpIA5SgKG/95Z5XA0zW32gnjpanNRin1LnqGoKg94/TQn3tWa3WDHGGurm vboDTZ4NGKIdhB3G+dn+gFGdYV4Zbv+KkGIGotKVJidO0XDifOZ2dOLEjV9Gv93NFsu58IkV rgq47ms2/DfXjCf/v7lODNrGHq3FDK7Fhmcg+iimeW66yHPzt9x777cn897Lkd804qmbHQXx RLvhKJjmw+dgPnyZbWZHwZto//oV3torJ2stzSGx4TzexnTmj/pl/ogndRM8m/uzxufQKWOt EqNiwGtmxE+cH0+z56Xkf5aMs7gYTPUHhu/mi/B2bS7M4Dz03Vza3cJ8Na2osJ0L92vHbhyw 0K/x6Ln5TXptpQcYO6D7KiHpg3uFMVsoqjM+BdRvT9N6O/Mf+K/x3/zSOfkv9d+8liPwlYqg 5/L7amUjhT8YwYWTuXsKawpXKBvfYGVW8ELWRKFkPq+0+TTrTjl3WIY5cP7WcODso6AutCjQ U2wqw3/y3zyM/pufWkLfjPv6Qjdy/01N9h1G/81Pk/6bGvlvHkbacjTdf/Mw+m9qTZ5PH4Wq DP/No/DjaMJ/M2cX+Z/cQEYFR6uAQceR4c+fF3LEkb/QM7EXn9+Bsi0oUBiupYdYeT9mCXJJ AwUhu1p1DHcPckGhcO4aC6T+MHDcv0kDs0KnSwPnimfDJ9g3fbzcr1Z1YYiHSaptG2ons6tS vnkXd3fgySLZKfdK4R6LaD32FoY99AyWexziKO5Lque2WgAR7PPnOSNzyXXJZRGnkQ4/lrt0 QlGXjZYd3OC09XtcWeLYXejD2L1KSMhTzMX9SSYISOuRmWCcC6253MxMSLPYWE6FarQHy9km MJ5MDVAu5AsZR7HL/cM4IXwB7A+9KsjeBQwGmAn5AzYQG/EyNlJyKdOkKm9BG2gOpRAmTkJ3 jJm8BPAXWHigLA7/LU8JXIb5VtJ5KGcXqVqt9HlMvvs6rqbdTa5Em28UuO6CnqpWmCPm5CoY u6nk1Bqkrr7jRvM4FbSF8uJiXvLV73kWdJeeSaMKvG48ejyFRpndbSYyA+5KUIHwXSa8k0uT Gjaz5Vak6T8NtMcvRw7T4WQUDslKsRMFZ3nnfvr3LVSM2rqYPIfyywUIT3/kQIOD8Z4z6LdC lUg7cAgsG8YqO7E2eQd+130WIj69hwn4ziMgnlFbzDv0zm+hM89Oenux9u1LsCi+9WvXX0JS 3sboLchEd74OD+utCv0NarGvnoBq2vHZOL92/1cpdjerRtq9AIEQHS8cuteW4AcHanHDPAHG 8xV8VDFsrnbefNqXE0tZDcoDWAMwgp0KNeGPb19IW87brmEWdbSI3NP9ls2APLqZctbDfyAv 3bXRhjZyVADQxVmlO78a7g0aPbu5LIHYzjuvtCX7H9AqHkYXoF+U4fZOvY28cH8+F0pHDtGI 5Um7r6LOXYWnDtbip+tc8k4EUpmkT5IIXBuDWqGc7snqle1k/75AKy5n8rqtLHCLuJ8VRv+C 5nOgrLQTW7KITvZR52ayduilCkGguGCl0YsWelGlqPhjYwcK/KlR4Z3bPUf92oPzsC32yQr5 AaTz6OP3Y3osP4C8Aab943mk3EQJFGxP3aqjIuRGNehCJYJI2OKqkOmmXgiw+oLaH3Ohmg5U i44L4ujWLfgRxmnfxz7pxDh3oG/2IgJuQXxWlQ+AD7RK+O9cUpidEUzs2wbkhAV7rapsFUBH +0RvVEwr4Esh8Z8aJCu+ABJD52UAoJIoiDlsSHDKm3ZincXOZoxOL9GUA8hIsdSdPQRoF1br 6ZUj+3Cm+FpgCzJPjmVi0Hi/thbNT8b604vYguDvrsF3nWztBgPa899DXDz7YjIG1QsG9spz aF22Sp9RwP1e6kw/3KtbjgxRbgAHyPPJwP+rOSzO7XdjM/JWBL2zKg4DgXdVMv1ZXEbP14zj 8dOsGMiwa3FZ79q+Hb/bv3//sXc7PsxQ598jxIuON3WUtOTKrwKhfpENZhORrITEM4se1iqR /WwziU3R8dFkxZDizM/rw9HmVarQ6MEK3cc+oSHQdl1E2EtjJPtt0t5CfRr3fxLUX2FFQfbS r31/NPMz4CsZXXQfvJQlz37gCkZNptLj+HY/0pL4c3hqI6hdfhntPbFqok1IRwSqv36MNr0M AWOgPHqRiYhielu+qIM2JGIHnHfeOgBd1ornoqSBbg70HfuifG5oVFC79iJKvsseKa6yNkSN UFattuCiBB0j52bQpPxGU0bzTz0wGCdfNv0ipv+nvW+B9+Y+EM/fa+9eDKCQ2erJ5822h409 KN2aeFH1OtRghD8ipYygscuvetxwufy3RIiIrsNnLEGp9i80ZgX18IUNvwCFy69dmpWwQjgj mBkOnkablid58G4mTuljWX6WpDxlR8EIpCIdJakpKElNLo1DMSZCjU2IULzYB/JR4P3WY3+E BlbIbSS6+tytY5sPiKfV35R5kJbSixcQAJlIF+XIShy4s+F3Sxu+rjQ9lvcw/9/EegFFVYqi R5FzewvWLQ91VtgtXjUQLxta40isi1jKurDdI7QXdeC6cNK66JKPtkp/w/VpVZX34a+eaWrB 42htQjhaquKKikCk7mDj2ZPrUs+ebOxZlyo7PLCGzBzyzqdIdnjCoNtcdriP/m1Boh+N/JBe KlRU2k3Y0eBkwkPYxu1J9VZ157P00cOET3lXniDO/mIt5+ymj513zkYOm+C58tDGTuxOQFtR yjkb5utSqlxKrUMV+xTUyi+E/mVVeheLx/QZ0KeANm00zpNjNjdboNuSk3UED1B1P5vBOFX8 QgN0eTNyK+f2zW/QDP8EXqyQPUdfsDNUV8MxeWfbEOXGXWMBgl+xWDy+IuoB5lPvAu4v73yQ KAzVBTxvUym3oIbd2n9ciLQI2/4c256dYbQJ5Q5cSCzySgC0foxK/AKoV3F2CjE7jSz2BerO n9EY3plgWRcrNAstk6rZdAAZp7ccjqD2QHbCrghs62ecbe1ln3VmM4Pt48C2dqFbkLLlPiL3 nxHv+izJuyii1IQloXGcffUi+3JGVqMgHGnhLKy037lrCxrCVRXt4DArE066Ds/GdXgW+5Yk kAlsPTo35yDLS1uTf+2m3RPCO1i5ayyn1PfvZ51C3/9d+LK+j+f23bFLEtybui+u/fu6Xohd P9PU9aQ+NwIx6pUIXFLhVsi02JoIDUBUQIlhhbSTFmDoZk05L4HL1ejOUOfcTuX92jslKcgM TKKNSS2IxPWw/My4C6ztpfO4BIsO57n4JI5P1trwW465+HTLxYwFbiYW2J7CAv0GC6yYy1gg fadUc0eLb9D6sBEjnHiBAThb9eStySnF+0tO8Iw6F/IaslkF3z6PdYV9R5zN+OYX8I1C6019 csNQik3cbFf4xSrDjQE0axfpXqHJrVlALcfLR21d8wEZB6DlqlYrkM1PUo6GdVbbOYUi7rP5 Our/hhw5WxV7uzHGvnaiGEYMYA2Pj3o0tsOb1Jf9Wm4JgY/K8aMCkQA/ThIjKBbtyvMThKs/ lInRjK+ApxPOT51H1RPj/mlsKuNiD7SP29SPFhsbOJTvSpsFX1I6Um4fPBL1HOYME/cvToqs 0xFZp/E92C9imr1S+DAh6VmI1X6t/rxhoA4DcmCWcQj1DK0VpzP2DZwLDQ/pUK4JuKdjjRjW EY8n4kc1Rs/EeqaDuKmlzSh8rogS9Ubu8RafG67hRDcv4KJCdPPCxN0ViTu/IUh4XPJm1MFA SircgY3rp+H5OjaFXN4OZwMcH83C0pqhgnO7ldsc//I7MPD9M3EpoSZ4l8U0v7edS/PLEQ8e zDs3jd8kxiugvXcuxxWxOqAVnYecqwcVzoCGENJW7oZzcXzgyQXGmIpT2fB8VkxCrse+QnbJ vbqLnw85D8pxr4VDw89dPHCr+dzFyhFzst9mlCHj/CRpBwljIbtfu/UTzG3u135o9ukz+X/f yvceQpXMJwt9hwyfrHHSLjbGsMRbZ7Ilbjhn3c5/b0JNN0Bwmf1VzWcT3vh2ytmEtsWJMxT/ ttg4m3DZYjybsA3RIb4N0cN0QuEv55tPKFy/2HxCIe2cx798m52lIGuIRXTzgRBHM7JF8mji PMXUkpOfpzgjFeaDixLnKboXGTAri04O85UlZph/umg4zJhTKJn//VuG9zpmCMExDs8F2RKN Hzy12Bo7bcljPpQ6YK8gkHji6Jq+YiZZ9R7lBxZy5P6aWr+2roQ7jqXh0le+ReNTL8RLYAhW 2rRJ56eOgdl2P+1bxhEJKD8Hj0DYtA/OM/wVEJ6lzH/bFbXSymVHGwn6mSYQv19ELj/i7527 PHE5G/eDEgcsxsj9dGrCr11fknqGKcBDeIouZSPSBtmqbETKYD5BkNK37/wL9Q3PHtS55Bb6 pg2/4NjQMD5eAl2urWHM0K9dWMpN38l1YT67kIdJMZU7cGLp+ALcLxyhfbYTNQ69JqgsUi0q yE8xGPmOmtBGmYylS+XZI1MsxdJ46QF9RtPx80SHHOs4ZFfnW+HBpJZ9yALXZMKQ57Wp7nuc 2zrUZf6u1lxv80viqx0f2FXbPHPcx9R5DNQjlUJ1jrS3plg8ntDeHrOYtDfaqIyCSgT6ENkP /j596AjXhwT1Xq4PJSxV0HH4URmvMucLTL71OLhZMzwKUVSTzzJvRwzz0wx/86RnPvKTZz7G pp/5uOYUTnx8+s868ZF+TuWlW0Y881FtPvMxhjmGXcjlA9PJj9ih5MmPMeaTH9lppz7SfdJr bzHOffzg+Kmc+zjjllM/9xE1n/t45PipnPv4p575WHNz2pmPc+nAxjMP4oENuX82vK7g144V 7Eo77/Hz2PDzHj0P8vMer0H5w3B9BFcfXD+Haw//+0877xH948nPe9y/4v/ueY8XbvqHznss l/4HnPfov/Gfc97jP278x857fNp/yuc9Lr/RfJZjqH+k8x7TU8qcnXreIzUer2lCu29I+KNn TE/3R7/i4RH80d//BqwruJ6H6wm4SuF6Da7C60/tqoAWz4XrjBtYHU74a4OrFt5VwpUBz16H v8/DFYLrhuvNHud3TU74o38++Yv80TH2KfdHH5p8Kv7oN079z/ijn3Ha/05/9Pvdp+CP/qr7 1PzR33b/Y/7olRPS/NEPu9P80XdPSPNHv33Cqfmj59q/3B+9Kufv8kffdt3/80c3+6P/6Ov/ R/3R9/zPjy/b+L/eH/2bY07BH/3ya//X+KNveDzNH/2C5ey6Eq7Q8mH+6N+c9CX+6AuNAifz Rz/HKDCyP7p90pf5o++Z+P/80f+J/ui3Tfiv9Uef89W/2x/9Lfd/sz/6LOcX+KMvWfv/qz/6 x1exvnrI1xXlPBQs5q7OxZXUjHIWeQ8bfqs2gfutItFO8zL+EOesshC9WAv/6/2LM//IfFnx 73+rf3HWiP7DZjvsQ8GEb/wf4ckKxTtlBbqy/Q5+NJzFBgvl3RVR7xTUnl6s1Spmn2D+E90/ sbD8sQ35ltC1hil3LLwG/Q5vp80mU25mUGu/EPe+3fpEGA+M4IKmztkXnWDBp8QfKlnSDoaH 79GH70BxbFHgCvyCgOot9Afiawq0HAcxUFydk1mR+BpXfI0joD2RY+j7E6TYCdHOQNbpb5zC rz07Ml7dHzCcOtcwXwvD5R3TsZHL+8M/Jpd3Rr+m11kss+ETB1x+uB6rS+LcRQbOYcG0eMWT jXcjeL1TRBppKseTqX/8r49X/KU4+V/qXz3u5BGK24btLfUvY7Niio1HwW9zE8Fvu//I9mQz UZLMYgMJ4m0mDguNptypTyA/6R70kz5mCX0b00Xewv2ke2VfD/pJH0v6SfeSn3QPSr796X7S Pegn3dvkOfYoVGX4SffDj/6En7QpVt9lyOEXJGTJ4cH6pgk8wuyXuCNTaLyCFRQ9L1pNcn60 2kUctdIlV9ui1Xb2zG2hBVs9JeGvuwR+5QsYGcFwxUV+THKoM4JOSUp2q9/WEixUV2aqS8+C joMEfqthP84CSRvmuhIf48mSOu7c611BIfxgKtWlhfDyhWlED1LLh8Yy3AAe0cO0nB6GHJ90 Vl9u0UfJ/TvO5BgAaIYbbHJMd6HPrxA0RE9EjkPJtVthPv9QywYv9FXQ8FpdADbpauvQAHxR S92bQG92TafVgbp5q+fNudU25uExaUnIbXZxCGUpl8HEvArrqbkdvthFO7MYOiDqeYt4vGdQ 9nSp0umIT579iu8ttRJ0tbcUsavTM2hZMqLNnvn2/XWJ6v1cBgDp4xbv54pvfyWwO9Jfk95K nVlfR+BXopd4BfbH0uJ5o203wR9g8L8x12vAv3QY/HOAL78KpDyCLk+3kEnC0FtT3byPcrF/ MxKO6OYHuSYQrQ6xP+vYnw30Z3OT8Xpzc+KuJXF3Z+Kujd/BcleX2ggbeDxIQAaDEh1JoUSd 1WfifiH8T60uxNgk8RLtvjls/8QdQS80/vIK/nJt8mUomzqjT6dOOmQy0a9zcDuIxy3PBVlt jNwfNFRx3CF8fqQYflv8Fn7QbRGdvbi83p2M4TcHdxyDWuvsxM5A6DTaMnDIATuqi9h3L61D uRflywC8ih9IbhWk2CBn+o394NPoGMAov3bnbDKOAxvTJp93gu8djGS//HhpglejDRS/F8el QqDXGvz49GgFm8wKNpkVbDKbjMnUZ0SbEtPZlJjOpsR0NhnTyeqbrGRFm+4zZtjg12KRPpX6 cXq06UHTSyooOvzIsfsymOOMtyBA02CKHWKag7FL+WaoS8liLWZL7VfomXK/1F4YjENd2r1z YaBicTELODrom2l7QImaoksI71dI66ZYxDPgT35if3oB8WOLAfyHaPBtU1xUBtrbU0jt7blC sZZX2UR7rZY3H3SGDOc2CwY1Noe7M+wqfnP8zyXMNJu9Qmpk8LP62q+QPS9izjmpMc8ScjGT 0/MWQ79Sw+1y+Pmg9tZM3AMPatpMChZanylHg9rmmSQ4KeEXlYuVRpccfhZvlzqU8LNlS/PE 7PK1rpBD9wBvyah0lHWK5fzFhUp4RxDajK+1o/PSvlmGrDWbVRV0yXXPKtUOuaNscZ7YXr7a BXoOQvENaJBZpaFgUJtUBgMwmt4shDeI1U+MFDev1pewrftcipXvX1/E8tHdDqMxKhOxjY1H CP35Q2NqArhdrN0JsOlZ8kq7vNCRZrvHGq3c6eI0Vk8mfK5nUmXSOntio9u0vwwgGO1XmNpX F4Z0Or+ptuDHqDFlKTWYrlV2RSsZ66yktSRdmgxtmJI/kJLVI4aORXVMqXRADZUuffoKaT20 kKNUheBB1To9V7mDkrNmKXfgwpKzjW4l994TIQER1DHyYoe82qV72pLwTpYXhuSV64av2wKZ 4JefbTnJek3LMW/ec2feKyxmoM2IGWgfMWYgalmsPEaVhW4VYN6GKhtFELSn7b1XuFPjB7qH 78uWfsXYtwCsA0R1KllytUOfJvfDjVWfKO/BoQjlyv1lnaEe+IX7On0o9mu/LQXd33uFX9tT ilur1URD+lJk+QTPny33Rz2DJo4vIMMfhwxzctw3mGCZH5tY/u+RMe44gfbks9A/bDejDpOI Q+I9MRNGQWxy/8lz1/oW/+/bL//eon9kv/z52N+5X37GImO//J3YqeyXH134d+6XvxD7b98v 9y4ccb/84Ha2X26D1y5+tVSzK22/vK53+H55/g6+X/44lH8erp1w7YVrI1z38L//tP3ycz48 +X75iur/u/vlrd5/aL+8+Mb/AfvlnZ5/zn55g+cf2y+/+dT3y8d7zHvhPxxxv/yTBeYyuz77 gv3y0nb23PibqONpqoMqOB2miipIiX9M7+2a23iZ7v+YAsOt3xgcAc7qBRRTGqPM/3SkNs5J qWPeDSPVkZGEc/I3Rqjjr5eb63jj+pHq2J1S5hcjtvP9lDIfj9iftZezMXnsupHHJEjv85gH HK/p9etTyg7LJ3zm5SPFXlxJO0VueaFNDTfJOzF+IkVUZHEWaTuJRVg8hr+3NBnv5TfhN5qE NpxJh4Ax4qL0JP47vUPLZBEYFRWrcz49fyOqeBtOo1TGaQXVb1ERxybkhFAk7JJ3mot8kqlE WBHbC4qK0NbUBhSCM0g7htrBr8P632PKUpw2VrOqDFdBPlD/Ygx56nrISC/36+vN5VC96dhn J/dzUxznkz3r2OfCPwl5bdizJP5XQieqoROKxcC55KTdWkl8TTsHO1mSyqttiVILK9FiMsgt JvU2fz36GsJn7VjttTGTf27iG/ewb6zsmzu/TvlVgIZM1p79GoIF1ItpUKZ4ClRrSj9+XcHS zmAd2tcNrE7Qh1TZ4n4ovItyY6FtMaZVfw3zJukuI99FezhTuswmzmH+t5TEgQ5gU66jE8ip XZH2hrdAP4ixBEhvXGekVbA2ogQ9VfDEijrF3XFxULsdMX0PYp+Lk8OeJC/a2OMYlbJOPr8M 91E3fA7fHCs9IHcN/vJ0+OjTpwl78bGqNsG/Ndpt0Ek1EuvHzNsEw+rl0Ost+EDuUp/U+tPO wBWkrsd7L0OLIW2voiF6eTudULRrt1DOBrvqa5Jpz4+Wm0In41KCovYMpQY/1f8/9q4+Oooq y1d3qqHCNCZqlKgZLVlQxFB8qAgRNAmEjzWBkO8PIul0VycNna5YXQ0JEg0EHLItOwyjZ8az 6CDqjs5xxiPr7LrreIZhOKLn+IfDjnMcdzybw+HMaSfsiK7LwV3W7O/eV9WpTjqBcebPrXNe 3Vvv3Xvffffd91Gv6lVdv+9C3gH66EDqSygyuEzO2/c8sf7Dsk9pZ7lVLR4Ci83gSd71m2wo 2Hd61+yhp3i374tnucn9wWdv8jwwLBred0bykg2FQ+8PDlMiIr7Hy14nDiTf80nSpqTYor5V SrK+m0SzrNh8yfknWP/VqU6hUWJ6eJRLHB58i0Bu3t+upYdTtop5e/+Zu6ZLrCY/f7S///Co X8rbS0+ChMa3C41/8WPefjx45haxkVwUMO/5gv15h36x992EBrVB3TYZ9Tk3tbU0eYCy3HTg LXrI3Ti6XeYpsrNjfxZtPfopJYmnH6m1RWJz4VJa/muhF2Je/HVmH+Sq7Rfp0wT9+bjtIe/s TjW0knnEevxW/iYr+Xdq1X/bvo2b7vvlRGlKc9E10rIYf761q8X29sdohfFqT4X/jlMJeGj+ yLUHxXyD+a3vZ7yok+U96qtW0nddqR/v5w9O9c+kfrh/umjuzalXW/g3HyMzUi+2iBoswYxd vBufrC+ocbYHsFaPfzk6an8VoT8XZIMlcsKzNjw4mgs1L+z62b4Lj/r427JjX46a+P7zCvFk h+6LcmGpfi5P6vYW7h+0sf5hRupaW6N6+utHsr4IShTWNKSqb3TWXY6L3oO/OE89CC14V3M3 Qtp+eNHpRl6jUozyDLQmdWAz/cIh4cuw3IQ562/uE8+v+un99fjBUxX0uovdo/Vfok/yfkbG qLgk/p/V0MiyX2uyq+3RlZ5T6J1SNsNF2pZ8nBkugmHogk2/O00/U9DbP+vD5NeZiI6/t1x5 n7jnr8DtZT/NPx/M3M8gcfd9obox1cWuRmur1/F2hVSjE5H31PG8fzxPN6FdEjqYrXJjahbZ /7z7287u979LnE0VqOUCuyvb+s3UsxA4Usj+OLqr1ImflXqcvvX/FbJK9TTSz8mUhtQ/Ndsl 3VVo59mQer6ZamLXdNfjqmxrjw+WiDX3JPch71p3wN7Ly2RrWjJ337uJ/0LMLF5zQu+f3JTP a09pidm/lfzlcmddFI0LysUk/jzRdzmD09bVQxeWmyT/mn2nIf904vbkIO3J2FrEX/k+Ya/h LE4OEsOQd8iUh5iX12mUoZ1+WtwohyqFQ+UF9H+m8kJ7XMr6f4yttjp2/ix8IzRILEp6hziP 5CBtKauh7EXRKMUzIfbGoV/RMpqVf5D0/x2uPKztZ+lVgIz3X+2Ftypl/eCXo9advOas0Mdy 9oonRjfzBg7SpsDewzj4tjz4iSf+wfi1t/Q6Xn0+/SuOVsP8I55yfgrDHzX/VTna8I30Ztp1 yf45fzN9BHRqcvrbmJFNH2mi9Z/9nmR/ETgvWDNHvAfL+YdX/PzGC3cvTM4auRqMJdMTuYgo Z1Kh0yfAkUq/KStZ67FeKqdf083ipHOOhlzeWnSMz72+W1HepBP9nuj6se+tDY7Ql7hzaCX8 i6bWNtEfKEPn2n4p7k9xnXq9DqN/hdJm+1PqBbrmVydo6cYztEkeKlOGNvnbRP2m9gr6j6U2 tlHKsq9LlTZ7DtghYuwdVG0FyUThUD5m6kNNylCPv/WhNnF/ch+RtfGCoyeJXHKGauVkmQKn H1qlDNX6k0VzxtZ3UjNttZi04uJQ/SVW4rd//O27H33y78MXTlZYvpGb+B1eZTSXNp4to9/h 4GK9PLKG4t3kA2crBi55rJyRGw4SiYfppcTNdFEm87sHiDolttzSN5KowxtwzUdT/bWX6K+j PKCQZNgL4m1dfNBlvp1nKZkS53TGX703cKnUlOl5pj2RTVaI+XNqXq2wXJX/X0gwuD72ZPLl HTox9H66ri7WTEGPAuY9ydRcT++No5U+LlPS+tqEXP9T0FWM0Q2ey0/1gfRjFLHtoj2QoJcC fcVFxwo5I3MOUhz0EpHp4vtGZvD+UWdcEPesNU7fod3D72OnbmqwJ+RS1oM+cubhhc3sh26a himFqrsiEoWKWDA6Mb2kJBEPdOrqSnU2X7cGiruLDTOkm8VWW7Fq6lbCjMVVTpudKZ8ku9jp MoN7HPmEI5N9Ijcp7CKgS6awisMBSn/ERd4/WflbA1sqI3GruFsAJt+yPmbpncS2pUYPRNsm 0U8U6GuzS1fK/ki6UJmlEAXOECBYiNTmrYiFpNV6OBLTK3ot3YwFohIRSnPWBCJRPSRVbA9E EwFLrw4Et+mWVGWEElFdqgXarUtzqgOmHrMqI7Ft0iqju8dIxEIVvT2mHo9HjJhUBQjbO3BD ACwxwwrrUp3hIrvMMfyAA+eNS6mg+lHnz5+vrglYgagagV1M6CucTZPWZ1yrJWq1gRw7oroa imyPhHS1o0/dqZuGNknOl5GvqurClVNpns6fBZVwrlTiy+U7Mf+NPboZsHAxd666QA0Z3YFI TGghoVg0dZqaP62JuiYRC1qkQ/xh05rXe8d4ca6jNBOe/3kmzLCPIzVqdGYRqpqRzi5rpRTV wzhnVgvUL1ywuu5/bs0tFfCG0gWrikbOLL3xgclgQWYxbf2UtJ7qCul+iZxSDZo6fDekGjFk U2kE4d221tKCkB400Jri0oKwYXYHLCCW3mtFQoDGNj2G61iiWzcjwTjiqgJWl/BzFqlGgUPm AjB2ES4toHOMXJyxbsiWomhJekyi2NIuA61qlRGL6UFLtQxHQFDEEFOHGTD7IiH19ltvm3+7 mtZPXSTVxyIPJ/T1q6FFn3rXYnXJokWLi9Uld5UsWlyyaLkUiYWRR0yaq83vnMugkiDUTfQu WOyYyWlH6XrlyNHRT9fa8NT46wQKZOzI4hn2YXXBDgFUfZca5t5C7dCDgURcVymlxzQ6zUC3 GjQS0ZCKdo9UNUxdhJvfobIFkGGEREdUAENI3EiYQV1FtdlWUncE4mp3BK051pnd99P6odLZ M4kjEUPlBbsC1AVAGOkEH7XVQBNTyRPG8du16s7xSniz8hMTW4DK2UGJ5B+TlmECfyAK/UN9 lDFMIwlRMUPt4W6YhAbTDgb+SCyeCIcjwQglxnsCMOGYfV3Gn8x+wUCMNJ7IoAY6qXGHTaOb o+OkYBgVKNm0CeTc02OYaHsStQREBLajhsnyEoRYRtCIZkRmOzL0D5idaI0xK05lgMGF7bnp TVX/TrtV9dj2iGnESES6LiKxiBUJRCM79dBk/AZOphqn0SIYNeLkona2xWqfkVC70SLjViQa VTt1CyUK6dHIdt0EXShAe/SmOgJqT8IiZyJWrt8ONhlcA84E1w+HUZfkcOmiJmJ6bw8iQaSj 7o0w6p4H5mxHVeUGdGhi5FbJc8hxAvAdu10LVrULKZfnR99JDXRHF6qZ9QkmTPY6R4rTvsZK 7lIWhXQaDwkixasqMfeonlx7sk9ID6PzAb/t19SQI3Hb4PA0EZu99iSJ+pSEyU4fCAb1HjQC Q5QlLU0yqAbCarfebZh9Ujd6B0yFVHT8Hah2AzUZjho7YInqhLUaxVI7UbtwPcNQuxNwdC4q p6q2pLiOrjoW1Nl+iCcTzruDq7cnECcHCqgdAeoBMMaAZK0+kTVCJYtz52BxFsxOtpXICzCR QJF1KNdndXF/tA0lQxdq0nRuNTza6LQNW653RmIZMTV6HO3IvqhNxNGSnFrgkdFJ6YtZgV5n 1qfHEja6PgafrbVMZOuOsfG6tL84kz77anUk3hMN9I3VuB2RVoruEsbmhBnRLqEbExYyo4mk ozLNJSbwcayLja+Foi5eId0hyZznroKT2igP5yF9eyRoD+2BBNw/ZkXEwCLiXMM4LniKIHDR IQrc6CGGuLjg+cDYVIExp2d0TybSE4xaTJpQikYzAtk15Av2bIIn7PAlMRlPR4qMKw2jpwMF gaetNmIWz70CSK6qdKHlGCW30TCEFm/EXFfEUm4aOzDYgMpBmDOmWw0Rnk0jhqdW0b6xiA26 tcMwtzkRc+MzECR1hdqnx9VdNGbdr0rAcT8gVUd69GwzmyV3ScVqrmRKC2H9hbFENCrtoP3R 8S5pYUckthDQdf/RLNWtqs4q5h7MeGK6HtrSHe/cQoOS5CArwVVKDTUL11J7vhgVs8apjuO7 FWVqiuyHbMPDz8vKcKWipK9fkJXfu69flJUR9/Xfy8qnuJaqRL6lNhyw4ZGqP02fc5sUhVYB PK64YcR5xsV9mCXu/Sxxp7LEvZUlj2zHo01Cd6tJyGhuEnyrAGm9Qm0SdlAAadfBHxoVhR6T nAakdf+TgCTgCCC9c9MOOIP4AK+jcjUoyvWUDjgLMA5YCFgKSK9qDNcrCr1XcQRQJX7AWwHv BaT1iNsA6TX6awHnEH2doswlekB6SDEASIuH7YB0v6oC0vtBw7WKQh/+OgJILweVAi6gggLS feBwjaLQswfHDv/WLMrzHiC9hPLzZlH+V5tF+V4GvArwaRsOAtJefLNZlDvQLOz014D0wvKK ZlGuOwHp3ctvNgv7XdMs7DutWdj7iyZhp0+ahF1/1yTs974NTwDStvifAtJ29ucBab/5dwHd 92WhFlGP7vpuaZnoF5VZ4spbRFndccuy0N3ZInR3H7dkyffaLHHTssR93jwxj99nict2vGDr 90yLqJ9vtwi777d1HGgR9fFIi/CrBGApYAxwwCXnhlZRdjqU1jE7XLBtQrL+w5ZNx7CNUzht y6bjlI1T+BmV1S7Ajx38cgUad+i9epBkXfqBrDzxnMy2c3TwSJ5dil+W6d8X1JYoWOjTqL2U XaXs85bP9G3S8rPSqzY99YFfuejbtHzvEU1tBRvTrJBEvzgVTbsk+sqpaOiNXuo/J6MhXehd 0cM/lBV6vOPQbEAipZ1EOPeSzG3dSau304YRCl6WlTUuPu9bWj6l0VL35h/JysNZ+GhL9/tI u8/F12yn0Wcq/K/IygEXX7udRvodRtobnokyo4ir+4msHHTxddtpZPezSHvSldaBNLLPC0h7 41XwuWQ2wD7Pasomxz60VWfdazL3gw5NjS2bvv8YRVrYleatFzYg5/010ha40jZP4helti8p x2TukBz6sm/llD0ulw36vGu1/JwRWSuEdq18fsh1buFz0HUOaUp1JuJO3eI6e1dp/natEJrF NL/3Za0IF14Uvit7tNfQCmE970MMQuKi3X1RJ8AaBo/wuVlEPaUVmgDlWlHQHf1k9ui2SXNo YRAWFwJQm0GHQV9Dyz8lK733TmbDmd/4M2x45VZ1n4NXcN6m+R/TCqth6g4GZO12tn2QrvMb p6Jq5sTNWmEr4+nzDj7vnBAvzptdqYKSbNnLtsHZW/sX9ouMWsu4+Et5zN9x9GNXFHuF3pVx 0T4pz590Ab393gpRjxas10m14Deceu6g6hhP0Ozo3pl59m50g4np2aiojmDsfO/DkA8Lexu4 /fTQOIBBe/9XstI+faz9PIRWs85r+9/4c5dWWMv4uDN60EXIu1lTtuMiyrQWXWecpWoaVzEx S/l8yjO+zDzPer5GnvBi2tgSgqz93/Ap/zrD1Q8M5uyE2GTO5GKzxntf0xYltMItWn6fVohB xbuDc7OcMqXP3mc4vY7GBeS/+Xqf8rQ3Sz/URN7o95YRtVLD1Z7Q/Mhiq6bUi5JUcuVHONc2 zU/DHM8JVmCSerHQp+zxZpTLG6C+xu/dqxV3a0W1WiHGJ28pIr6lFW/VitC+Nmr5NN7tAv+u m3zKGdeYVPZ4Ttmg3MM+QPOFI6BpL/IpN+dm0X0rLBiarGJEdxcRRahj5b3osrw7taJG7jV2 cMPze/udCPh0zjHPuJhJ5lpF9tzp5Fyfcq+UUf4QMVH6Mpp7TJJO9y9NNMe4zaf8xuVrOYoH WvxE1grWc95kpwEEf7FPachxjetoMjnnvUzGcwfys4U+pTUzLxS6U1NtOe8gHAdNRyZNhHoE h4a24sxZNDUNfX9i/6IJebVT1+TQ0Nzp7GXk0Msy6xZPoNlKw5BDsws0r4DGJ7vKvlZTcw7l 0CipEs0R0Lx+j0+Z5Z771WqqF5b2bhA0J5H23tLJaUpBQ59SO3uvTxkaZ2d4sooxjrLzPiZA rwBbBGhhIC2CjGK0hZ77fEp9xhyOPN5bzY0LmRHgIdNuR+3geWeFT/mOiwedQ5xJNvO5nc8t fA67YtiPjoB/8/0+5U2XHXu0ggeRWZlW0JD2o3dAV/iATxlx0UExoZ4kfPYcaPaW+pS7M+uk 0fFpP2zzxhTpxUg/N0V6JdLVsuzpPHdG+veRfjhTRy7nfqQ9We5TfuTJ4EUBczaiF2hz2hX9 CqJ09dR0lNeHpGuFT/lg3Fya9KT9vMVrM/WgOQHpQr5SAH98B+nLvOP7LowkmHRjaoTh01/N 2YU1/3atsEVTarlbqrVlNPEiAWyRVUad5n/UJUPnTjlDxhx7jLy70qd0ZdpzM1Wrv05Tqmy6 k6A7fBm6dVT/oJOrfEpu9rHCX8PzIH8ta7CDWKFiUQvPQMc0k7gtLEO/lr/Rp6zPrAdvI08x MLGrosHKRkBP+dPfxTZX+5Q/erLkT8PaWs1vsus3O5bp1vxhHq7c+VPf+wZkVdb4lPh4P+Dm 2MNS2kSjXKf523i+s9G+l/oCvMdrfcpHLnsZSKPxNB9j0uE6n5KaUG+wRoBlBDX/I1Rb/k3c gjdSg/f3OTHtdio5BkcKuV2Qu7fRp8g54+UyD0mJuuS2csw2l9zgRLnky8en0VoIxv/M+8IC DIASrZMNI31Oq0/ZP2Ec3kCTA7meql0VbcaPudgroC130caRSGnzkHYeabeMa0900PoapTk4 QXXv2Fppx7OyYiLsQTiEcBThGMIJhNMIZxA+R/D+QFauQZiNsAShHKEGoQPBRNiDcAjhKMIx hBMIpxHOIHyO4D0CfoTZCEsQyhFqEDoQTIQ9CIcQjiIcQziBcBrhDMLnCN7nwI8wG2EJQjlC DUIHgomwB+EQwlGEYwgnEE4jnEH4HMF7FPwIsxGWIJQj1CB0HJW/1jr2/x/ZD1piu9kn4Lpp 9j+6AGn99W74Ea3rPmGv68/bLfN67Evflnnd9Y19Mq+3LkWN0LotefB1tlxaBzy5W6wr0onW XWlNltaziw/LvD6792mZ12dfQjqtz1LFfjU6atyNeLi+QbznAb/43tevc7GEeFQavEHIp8ew T8KHPC58uSTmF3RQ3zpg46YLf8KFv+nC/9OFL/KM4btd+GkX/r8unOZADt7gwh9z4U+78Ndd +Acu/KqcMXyxC29w4QMu/GXge2z8ly6cjqNZ8FxZ0AQb0P/Z+KetHqlSHuPtcOF98uVluvED Nj39d/JtmfQ8NYHmI45XGf+M8VsZJ4cckMRbmN9k/K8Yv4vxuYw/yDhvz5ACjIsXjnoZX8L4 QcbvYvyHjN/N+HHG72H8Q8aXCh0YXybsM43w5f/H3pVHSVld+a/p7q8+FqERR0VR272Rprr2 pdtEEBDQBpqm4bgQy+pauktqo74qaNRJIOJy1IwcZZQoRicaB42JHZdIDDioqOBKDCfRZDKD Gc5IZszEnKAHlxnn3vvu+96r6sKT/JH5Y073Od3f/d3lvXvvW6v43oPoM4juIvpCosXrd5cS /VWi80SLV502Ej2L6HuInk30j4i+kOi9RM8h+l+Jnkv0x0TPIxrXm/XGRUSfRfR8oruIXkB0 H9ELic4QvZjot4heSvT7RPcS7bKQXkb0qUT3ER0lejnRy4leQXSO6EuJvoHoK4i+n+griX6G aPEuzRtED4p6iRb/iNkwFunVRJ9EtHizK0h0hegeoteIeoleR/TNRF9D9PeIFu+b7iR6PdG/ IPp60Y5EbyT6mHFI30T0OUTfQvSscaJ/vra5wSgzjTfsbB2nxhT+yL76tsY/abzqkyvGK/5l E1QfqxAtZqAXJqi2/nSCatPjj1Ft8QjRl4u8HaNy2zRRlf/uRJXPT4gWb7AsmqRylSd6A9Ef E30j0YEWpOVdIl8+ZidDrN2kfxpNtf1ERxpq9de2qDnhFqb7T1Pl1OpvbanP30vlX/KlvnVP Rp1Tib59ssr//smqzPeZDj4v5rEXND8lfYvmw7c0na2aTm1OJP/IZNUWvzxWm6unqPEYmaJi GSC6m+gtU9T4em2KamvzONXWFxAtXt5aS3Q/0Y8fp+pa+TeKbj5B0Z9pdOlEpH8wIhadvutE NQeOnYp0mOjTp6o5MDpVzYHLiO4cUU5uKn6+nurwk4ZYfw18x82dMDoqdqnDLiU6+iuZbLIj 4AkE/TMz/kio48LlC7vndgxkM/2JmT63zx3oSNiVDmMgkfDFEoVcEd/LdEMx5c5ym6fdO/0r JXp0zfR5A+FAxB8KRLocMtxlJAbjJVL1CVXf9C5Pl9cHkmwhP9AqC/ILqf/oBVXydmYgn0o6 JgFhEoAC9R9A/rDzw9WMMA4K4+CfY1zlaGj6V2bZoUBXieguj9dT76fLE673oxc4wqWwVnJ4 hF/eoxRoDxZKZaeMCJbhDVEZEcil3xcORbrwr6M6ot6oZhPF1gkFg/4gqAs1pwG9HlSMkB7Q XTO9vohoSadIpevVdL1YqC8IRaazhTh3HJ/TcwIgNZKFSn82JUR+RxRBEWVLlwccudeHCtgt s6khJyAvNK4dKaXi2U5Sa4d+5evK5OIDjP0+ZChDza0Qlx3iyqWKXn+YdaCRIG2a0ghPI6wJ TeGjMGMxHHDlTD62Jh7D932FHjTBeTg2IMPiYbjdHZl8IltJpjpoKNrrcv2FrO0e/IuGLqmQ EF8hqwx1JAr5dGYASoHy7XV2MlW0OwbylY7Y/Fg9USWfGUKwpkOY92fKdkd5XTFlCz3pYjoV L1dKtVww7EgkU2lm5zJ2oopHkYC3HTC54AvvHeRoKZUcjJfZX587GlLllZNgCYZ25ppUDFMX wQmI5gDIbCXG3S/AXOh4xKZ+T3wf8aOCLbpLAKceVQQ2IXEDxA0K7upKPBkT2kHih5GvcUPE DSEXio0wNyzc8FAhGj+iuQdsb4j5UeJHpLrD93qU38D3+ySf45QGSuBTMQE/FJB8v/KzUiUI aGHFk8mS5GO4ARoW51GYIE+m1khpmKQiSRmZC+z1lFbgDihuVHEz+QJzqccHhKP44qNke5Vy Hl93lHyf4hfSackVURE3q7EDpEw+Fx0/fEGVM9vpSMAPKX4pm8lJdlg5iGwnY76Iil0VrgWZ th22X0Tp9+K8FIOhDxMTQAgmXkKCJjx6fulqhAtnl5zRYKHA6SSpNZY/oEJI6HzRiP4QzzIo L2dyMnJ/WKWvYqdgHkjaUhRR/ciulUWVmb22PyvbKOBR/AS+Oyr53hq+k56AT/mNfkm/A37F X5VaJ7lalJliQmvaQFANE/BHa9xASNUNkkS+LAXhWoHTwIGI6j5pu9oqqjqFFDl2QY/qGGk7 nckqu6BXtxMiZefTOlS+oPh+xYfOrfiie/uotHLMTsSzcZm5YFCFVYZGrZKF1MwGU0Cx7AjC 2siA9smm8lLidAOYxmliLg/i6+e2s1AUBUMsEAy0deJL1xM7MQhbykGsFalYMV6K5zr72ry0 vbQDDr+UKZQy5XX6og5DgGuLpeN2GbsVWEbbeaTZZViX7E5KhTAAXjGTJ73qvYBTTjJlJ3AV idJqEcXl4Tx4QLaH7GolKL5USZQ7cX5hfrwM6bTJBdyE+EM4XZbjiUH0JKV7zlEVC9lMYl2V L1JCaRBZgNEuJJn8YApyQApsFA1Jo0JR1gA7M8EcqMRLSRwInbRWwkQuKwenVtEcYafK0irq qxF2is0JzLsBTaKV5wuGRPqqElCm9IUofdDPpAxnD5aFSQbdyvb6YDqIiQaJOlMb8tbGM3ja pZNagjPQVVWYVlmUCsSFEjtMspLL1fQTaScnkqhcPQPKwVylnBqSUtH6uGLaPigyF4P9Db5z n6xuxRx4UsmXa1owFyuszadKVb4jd1UmX9tuOT14bDia2atc0uKkhToqtrjoFYq1QmuCLeQT KWmo1jcpLa3l6ZlGTBj7KzRGaW2d1gAmmqRKNlckQwLBWjyCIEOVUbFBTSM6/VKa1cpl9wS5 FpXTMYFdtGGT5zQCd0wVsRMTxRwRyQpPr5HrCRU9BzciOGOgtDafsZpK5ZQhy5QzCpfoc3Zl UqE/XiplUrJGn+hZPupZHlh34nUSDsxSanUlo2qVGQcJnm9JOX1OphwEdbPdVeuHFr1PdCcf d6fqOGs6E1s4y8da3G4T1+ttdxb3tRle7oDp05YNuYknK7EqrE3YuX5b5xxtnaCPN7RYSGXo +v00p4q6/OQAPHyiGfUxyW2IJ3pg2gIdSHwFgoWiOoWXUgU4/aQRUDsz2HT5u2jXxPlQK8b8 WLpYENshUb+oHmc04HeKnWm7mnDLonrRg8T+TRTBazp51ka1w+dxpxBY6GWvqCoEOgQVoiV3 AGbFNfwhDEmH0YrraRidTMVi8+csWbwituSSTk+7BIuX4KPTqzHmXtjp0+CieYs6/Q6et6in 77LYwsU9y/s6Aw73ouXd3bEly/uQG3S4C7u7582f3c3aIcVfPGfJop7ueX3zWBQeYTJ33rI5 vQt7+pb0dkY0u755vYtBOq+3FwTR9i4Znk8Lb+GyWPfsZX1aSAvnL17SO09YLYPYcPtM+Yml E9SJwpR/eARwyYcnjIq03BEJTfz6TKmHhHqY1SMj1FOw4DnaUaGNaxSp4/qT5o/70qBciudt ZUKLED790iYwog5hAiQeV9dMg2wakqbho5iurqRK6zTDCBtG2RCnxrqG1cmgaQ+fPmnnP4pd VVZoBsJnUJqFjpYWPPrIDR3muVPli9Mlh9vIrHBSnCW62hd2xZllqS7e/cgJNg9FCcWI9DWs zbLSWbucKrKbkEI7CCPZHsxm+mOD8Xwym6IS/LIT4GdC2FeyabYAayws2/1Xp8AnZ4tRSOLh P2Hokx/inEBorkuVapYJPI0dE2b00c+JolyoYjtLssyCX1uGnRYWvV0txHra9P1hLpOP4eE6 CAIdkKt0UO514kP1xJHICOtywVlsPSNslTDo02bXdEV+4eeP1GnGgDc0sqG0ToUfw2nHXqiU +ytpkYyASLdXrSNCmsItglBwGiKdjQ/U7o8y+TV85UBNO8nmoFtE8vEsfvSu3b1TVEVRjxge /tpNvFoOsG1okaCOLfup2qGrKSxd4IBDYrHMYyJs3tE7RRMLteT0Br3ZCVXkFaWRqqVypreL U4kZ8GjVyhmWZ8GAMwDwA/b8WMZR8tNXbH6cXCsBWKYTnOiQ+mhQyPVn8rhN8ePca9fXUi4K Z6CXweLtwT4jVl71DZufv5GLTGc+f5Hm52/kvMSv6AbaV3Lz9e/e/NrHitjCJZDHJHRqaNtk 53xRkjF/zpzO1rb5i5dPb8WvN/GcqccT9ntb23pTydYF8XIrXdXRGnZ7SWFmNPx/aBUZtTq6 VWogYc8EidcdCrV6o9Gox+8NdAijNhJ63V63r7WUyqbidmrUeNR41HjUeNR41HjUeNR41HjU eNR41PivZ/xX/TAEHyjl4QB86dTjdXvw7e5R3ihvlDfK+//GM9z2ulw53g/Pckk8ByVF39oW DXe+UE65Z1+4cGY5PmC4B+P2oOFOrsuDoXiWS4Z7IF9xr0mV6HJrHcRABpM46gmimC1jyRn4 SyT+04XhTgMH5AW6W9It/qYGY+kS3gfoTpQLJRvY4jFQKFO98VwmAe7228CjPzbHEe8nlxKF HN58Kvw3/oKfkzlHeF7s8PomCy+qn6LJ5WEEPAXgYj1rQxNdhtWq6TXxE/PczHp45q0N9DY1 KXkT/+Jb8ONZD8/C4TnaD8cK2wbWwTNxeNJH3ouFZ+e2TTKMbu1Em/QPT+zIc2945u3wCYbx 1QZV7xj+xVM4/8N6eFYuMNWgOzmkz1I/Ab9jmYdn7TZOFWft9DjQjaymh2fz2qeJM3tNHJ/U q7CvePYPzwYGThVnXWvzd62m1w163aDX2lSth7/rNb3id5us4hmGMe3RRkdP3idxo6aHZxFv e72RT3dU13ubofrBLtDbBXozJim9Vn5uZj2qKWtZxj83iuTV6N2j660GvfcajeEWpSfrfUjT G95gWcN/bKTzk7V639f0doDeDtCz6ug9oenhGcrdoLdyTLUe/j7DOaE7BzdaVuvhRuMdQ4Ui 220Xl4e/R/As8Ucqx4ah+t/LrE/SG4TeFq1emZfXNBv6Ab2HXKovYL0Y/89kWTJPnzfSOcza en9VU965xzcZOyeO1Ps3Q4xf+XPwrCY6h1+rN7mm3n3Tm4zfGSP1ZF+RP9kOKGy5YZyCPjWo 8Tu2przsxibjfnUE6UuvqcP5yCB7oYXzjsCi5jYHixpwHhFYBIbzhcCiVeVZ2EZqeTH+BRaZ 2ehg0bNwPAs8Vuh/R+JxhLsdPJ5w8bsSix6M403gYwjvcjA3UFZiHmirJRYDZXiDxJMJ73Dw sYR3O1jM2PKse6Mhbmo84mA+WXyDxMdX5bmRThbr+MQaPLUGn1SDT67B02rwKVXt3GT88QvM 0GbnPPoEKkHiMYBn1Oj76tjv0uzxpKiVlXc+TqKToDJfDZCvJailya/Q7LE+OjG5Wspb6FRj 64NKfjs8V94g7hJtgPzhfwbt0eQ4j12l4cfh2aLVt9NQ7dkA7Vk3noWWE89rGsby3oPnds0e 6/tQkz9e5f8kA/+L211a/J/B87ENKr567WFcrOof2zBSXnxQ5fvYBlUfjvQz6uhv0fTbG9Qd kOgv3oUo73tEfHGDutsR8WUN6h5HxIOAZ2XFnZoYXxHPgmfFHa2I1zWo+xdR/+4GdVcj4h80 qLsUEb/VoO5BpPxieTg+xoj2xfg8Wny/rxNf0xMqvk9BXlwizvo3wPhG+wW2sv+ijv36s5sd +wl4Jv0mcdcn1T9G3YGB/p0PeMFScfcolj8LcI+G5wG+VMM9gK/S8BWABzWcxjuENLwa8NBS 5f+1Y9Q9G2O4vbPXqHjuGDMynpaVKp7768hnXankj9aRr79KyZ+uI+9JKvlzIN+dlf5OonuH Nq5vtk5mf98F/ICG8R6VaYDPYXwE8JbBZmsst/8XgOeC/AKWu2BJGVrVbB3fKPAUeG6zm61l Y3h+Anyw0Gy9yPIoPDflm60+Lm8x4D3a+E80joynb4OKJ19Hvl6TD9WRe25W8usbBf41+7+p jv6Hm5T+PY0C38r6/1hH37hH6eN9R/vubbZmcPw7AZe3NTvj7c16/j+i7PEepOSzzVaR9WE7 aOz/STPdIYv4d4Bf395sPc0Y/3/xgz9strZwfVOgoY+Afpbl0wBvBDzFUO23BXAXYy/I90N9 ExmfD/gg4MmML2oa6a/xU+XvUpSbJt2xgfpXAh5+vtmayu27CrDnJNO6mOVrsb5m02pnfCfg bRoeBnwd6D/KeAfg46B8F+NXALedrPTfB9ynYat5pL/rQS79bakjbz1Nyac2C3w35/M8wNtP N63VHM9XALefadI9e9R/AQ+fbVqXsxzvF5xwrmlN5P6+BvC080zreZbfAvjADNN6gu23At7s Nq1HWP5kHf8+7FL+7awj37RAyV+qI+/pqY4PsR7fod7q+Fb2Vcd3YEV1fOdfWh1f9xXV8bV8 rTq+3TEV35uAi3HT6moW+F/ged3XTauB5f8F+LG0ab3PGLegmwdN61XGk/EOwqvBf8Zn4r2H q0zrVsYBwJ4C9DfGs806/eEbKh+XgDywwbSeZP2vAT70TdPKsf85wH13mtY73L+GAD91h2nd x/jGOuV7Nqvyb68nv1vJv11HPmuLkj+I8vtMq4Prexrj1zD+37geDb8LeN9Wk+4WRvwfdcrf dJ8q/yOQt/7ItJpZ/xPAkcdN64eMm2HgHXjGpDuOEU8C3LTdpLvcEU8F7AF8LuMzAV+6XY3H mYA3blf2YcBHnlX2swGf9VMlvwTwIag/xO2xEvACkH/E8n7As3aY1t+yfBDwrp0K51H+TwqX Ub5L4WtQ/oLC61H+IrQ34xvxM+aTprWN69uEcsCnsPzbgD/4nml9wvJtgNsgf88zfhLlgGew /k68h+sfTOtTHi97Mb6HTesz7l9vAz74iGm9x/jXgPc8ZlpFxr/H/L5kWmu4/MOo/2Moj/F/ Y/s8ZdLd6YixZa962rQ2yvYCfBDwNxifCDj5Y4VPB7wN2ucuxjMAz/qJaf094yDgdwB/i/EF gAefVXgh2oN/9zBeAXjuyybd+Y/4KsDZl1X/uBrwZsByf1EGvAOwm/HXAX+g4ZsBT3tF4TsA dwNexngr4AdeUfU9DHjPK6r/DwM+AjjA+FnA7XtMy8N4N+CVGn4T8G2Aexm/A/iAhn8LOLBX xfMB2gM+m/HHgDfuVf0ZPxJv26v6+zjA+wEvZnwc4LNeVeXj3apDgHsYtwHe86qy9wE+/Koq /3zAJ76m5BcBngv4XsZ4h80BwFsYX47lv27Sfeg0nwO23lA4D3jLG6q8IcC731D1fRPwIcA3 Mb4NcPFNJb8L8GbAE7n/PwD4obdMZ//4KODhfQo/BXjHz0zrGMbPAX79beX/HsCDPzet5xi/ PbbOfLpfzWe/Afm+X5jWItY/VEe/9ZdK/0915MPvKPnnIH/ggEn34tL+YtxI/Zb/VPpTQP7B H0zrC47HD/jQn9T46sF7ew6b1iWM03XK23dYlVcAeeuxLmuuzD/glZNd1osy/4C3fWpaf8f1 3Ql4LshPYPm9gPe0uKxrGD9ep75Nx7qc+p4dJ/BBLu8lwOXjXNapTZx/9KfNZd3N5f37OLwT 2GX1sv5HgLeDPMPyY8bDenmKy5ppcn/G+4nOdVnfYflSwAfPcTnzR358nfadrvxbV0fe0qHk 14P8/JDLKrM/dwPe4nNZDzN+GPBw2GXt5fq2A74u4nL6y8/rlL8vosr/TR35A51Kfmi8wGmu zwSFWT0u6w9c/gzAnqUuZ/6dBXgYcI7xCsC7l7isaxkPAf78Ype1n8u7FXBrr8vZf3wf8K5e Vd6rWN8ylxVj/KsJdfxdpvz9bR15S5+SfwCMuStcVoHL+9/2vgXMqrLee2uz91qOmKiImGhL wBxkgLlxU9CBGW46M0zMkJfIxb6sPXs5e/be7gszk5BUpphYoGSkZKiYWGRqnrKiEyUVlsdD HjMqKvokJcMi8xR1qL7f/72vvTd2jj3V+Z7PeXxw/db7rvf6v//ftdfvq9Tf+Q5d/7iTOJb8 ejJwe8FS8vstwEVgaR+cD3ykaNlRgZvot6YutxS/zQbejfrNAi8E7kb9awReCrwDeLbAK4CP Gu0PAG/KW/aDAq8G3oJyKa/XA9cVNb6PMOpnBN5xUuV8V5T0fL9VpXz/Sl3+TJXy0HsNekL5 5lsspQ9+BXwIWMrT4+CYpYCl/qoFfvUGy35E0MMZwNtutOzbpT385sr+Rq7T/U1B+fqPWMqf nAn82Ed0f+3Asz+i1+/t1D+w1HcrqrS//yO6/f4q5a136PIiynsHbJYXI39/DfDyjG3vDHG8 rsrzezbp5z+K8pq7LPuHwj56ADh9j2UvEeP7UpXnd96jn/8GynfdZ9mWWK/vVKm/9n5d/3so H5u17cNifAeBR+Rse5HAv6P5AA8JHDm5sr3DRnsnVynfsk2XvwXl6x+07JvF+KYAj/20Zd8m cFu19j+rn++qUl73TV1+ZZXyVqM8VqU89y1dTv7Cnl9ayl+4BvWPvmDZBYEHgXMvWuwbT0xf AT/8Hct+l9ivDcDdBy17vyi/G3gz6j8i8KeBG35hsd/6Jfx5mv8vNb8/Aex817IXifX4N+At 37aU/fAj4JFPW/bJwt7+BfD2X2r6pt+gW2vg40fCv8D4HxN4BPCWvZZ9nPBPxwBv/bGl/NtJ wMVDlv0JUX8W8F60t1ngVuDl+y37TaL+ZcCpn1r2b0X51cCHcvybUkQvPvDDL1vs98Kp/P3A I16y7G8IvB74WeBFAn9sZOX+tP46uD87z7YD+3N4jG2XjP1JnWkH9mfNb4P70/4W295n7M9G 1P+MsT/OWXZgf0agP3N/Dh8J7k/uleD+7P/P4P5sPtsO7M+QgWl/ZmP8jwp8H83/vyy7QbT3 BeAVZ9j2D0Q5/XZf+gSMV/YHvP94275F2B+HgROn2vZXRf0/AdeMtO2rxfwp8DX2RNt+Udg7 ZwOPQvuXGvtzFPM392fXWFvtz5RTKvdnz9l2YH8Ozw7ujzMzuD+bZgb3Z+Q4O7A/xVnB/dk1 M7g/3RcG92f27OD+rDnfDuwPnMDA/uQm2IH9eWp2cH+2zQ7uT3qG3p8ZmP+h6ba9WuB24H1T bHuhGH838FqUJ4z1rL8ouJ6vXqTXc3mV9QzN0evZV6XcmavL86dwLO3v64CP5nQ8fB3w+ptk fH906A6qP8+2fyP9FeDuRVy+M/1SbX8X6f6+cYr+zf1TSX9Q/Q/YTJ+egvZ/CLzft9g36qj8 ZeD0/WH2rTnCR4F7V/P4A+ETT4V/tibM3A7C5wGva4nYcYFnAV/RZ9nzj+N4EfDDEe6/EU4B b706zL9xBzwE/Bj6f4vAN5/K7dv7BL6TArmwTy4Q7d0PnL4zwvQr4UdP5etvCfx14LW36f5+ CLzjMv5tv3HAvwY+ekuExbOp/PjT0N6KMFswwiOB164OM/+d8NnAibRlHy/6rwN+dnrEvleU twA7sCfkelwKXPO8ZV8s8OXAB86J2NMFvgZ4p8h/nIL9Xgk8Ksrj8VT+AeCGA5a9QOANwNua OL8T/jjw8o9y+5LwNuDuzoi9QuAvA+//pGVfLcb77dN4fmaDKP8+PX93DVsPWrqDwKl5YbVe v6Xxn27b/QK/aRTW73sWiwcRPgn46MdBHwKPAk6jvU/M5+01Ave+GLHniufpNztHbg3bHQIv Ad6bsUT/sN+AD9yn+78GeCvsWbkeQ8BjQT8bBf4I8K7BsP0ugT8JXDPVUvT0L1Qf/uV2gXeO 0t+FYPQPXDw7wvwbwgeAZ8fCzP8l/J/AqzCfpuP4fGrBCA3Xa344FxfOB8L2FwWedDrPb1Fe gnAz1Tf298LT9bcVqLzjdO4/niPGkwbeOSLC5D/h953O80fjxfp+FHjrsxGWPyF8z+n6ex6E PwW8DuPdLfbzy8C7btb0/SRw6oMRxf8/Pl1/B47wYRofnj9PPP+m0eC/N0fsyWJ8JwAfyVn2 HFF/DHDLi2H7v0T5OcAzP8rzc4SbRlO+McLsJ8IXj9bfjCG8FHgI/rxcT3e0/o4e4Tzwpucj 9rI3CX4Yze3Vl0X5RuB94P8rBL4b+IBn2csFfhB4/xK9Xl8crb/bQvhp4MebI8x/JPyT0WTf he07xHwOACcuthU9/h54K+Rhs8B/Bt611mLfHiUcOQPzO9mymwQ+DXjviRH755I+gFdgfSRu Ba7/kN6fZcDbid7E+vedoc+DnAJ5ngNufSliXyXqrzqD28cPCHzLGfrbPoS3AD/VaLN8IuGH zuD+g1yfHcDpdbr/7wOPWavl3y+A113Gv4FK8vLPNN42Hu9k8nEM9NM5PN7J6AF4x901Yv9D oQuAr4B8l/w9A3jVWi3P5gJ3nxqx/yLwQuBX1+v2Lwcuxi27Q+xHDPjosB4v/Xavc6Kl+GUN 8M6Ftv0hgW8HpnzFT8XznwB+CuMbIfj5YeDefot9c5XK/xV4nyFffjiGx29uFPRyGLgO8zlV lNORmlWPhO23ivLTgF9dZdnfFeVvBU612EoeTwFeZ6zfJcA1XZb9FTG+y4EP/TBiPy34PQW8 D+NtFes5DLx/vs3iUVR+E/AByK+3S34AHrWc5/uZPDxTf8uR8GP0+8PwN6X+eAJ490mWvVju P/Bh6G9X4BdoPtA3Uv6+Cjzzk2Glv46Doj5k6I9RpLi/HLY/E+HlDvDYdq0fpwMPzeD5KcJd wHs+HFH85AFPOI1/w5dwAfjZVRH7PQK/F/jocZb9L2K97gQ+fJ2WZ58Brm/V9LGb6mN8F4rx /QB4/d2WoteDVA77ZZncz7NAj6Nsdl6D8MnA6y+xlTyjfPDuXXq9xp7Fz4Pxc3JvDo0HHvGJ GlEO2Qi8Z7WlxnMx8MY7dH89wPUvaPqLAtf9ImKPkfoAeM3PNb9eD9wCeSb1x43Uf71tjxX0 suEs/S0iwg8AjzX45XEaT4dlt4j2vwM889dh+36Bf36W/lYRk3fAN/wsYo8SeMRYrMeHefyP zX+s/m4Z4ZnAB86z2Hkfwr3Am2+32PdkmH4HHvsJSY+hUAF4xE1h5n8yeh6rvwVG+C7g9gst +3Ipv4Dl95oIfx244ail8H8A16P9PaL9nwPvOBhR9svxZ0P+gt/fLOUzcKJD6/8JwI8b+90I vC+n9fd84E2beT6Gyt8OfPg9YaUPrzybnwcZJXDsbB6Pk/ZPDvipeZr/rwdeXtL28i3AW1tt RZ93A++G/Jgq8KeBZ/8+ouy5r1D/C2zFH88BH+2x2HkKwj8F3rbQsr8n6v8BeOf+sH292M+/ AOcsnl9h+vscni/4sCi/AHjfn8F/4vmLgGdjfe88nq9vF5VD30p9cSXwtnvC9kuivg/cgfon ifrDwJv3hO2fifLrgQ+BH6Q82gRcD/0q7eX7gIvv0fbEZ4G3wD6U67kD+Eg8zPJRhPcAP/5c RPHTT4Gf/arF/G/CvwVejvF0CPoIQ1B23G4p/+Fk4I1zuP/I6Bs4jfq7pD4DXr4tzM4PsvUA TmUt+71Sf71VfwuK7T/wod9gv6S+Ah4Lef0Oqa+A12G85wj8IeDDvpZPdwPXGPrwM8BbpnF/ mTCdV6l5wlLy82sodwx780ngI1u1v/d96s+QBy8B74E9Ifn398B7N2h/aYTD45stgh5GA3cA rxbl5wI3QD7J9W8Bbt1mCXkL/Q687mptT/QAv2rw09XAW1zNLyng/Ub5dVT/Ms2fNztkf+ry O4APzdXz+TTwetg70h96nMazWduHXwd+Fvw+LPAzTkh9Y47w88CrsN+jxH5bMOzWd0WU/3ky 8LOztD47C3jVcsv+j7DgF+Aa6NezRPkM4JnGfsw7V3+jksqXAu+7OKL2813ANyyzWLyZ8DXA u4z9vw54+1+w38LeuAl4HcY7Roz3PuC94B8pL7YD734pbF8h+O0LwJtR/0zBj98EHvUNi+V3 mb4HdibZ9idE/d8Bv1rU+uY4KObZsD+2CnwicE1rmOX3Cb9tnP4+GOE24DrYEwmBrwDejv7v EvbXNcBPfT1s/0LQV3Ecz/9I/boaeMxMbS/cBvzwwoj9Y4G3Uv0RPF5L+HPAmyEvJP98GXjH rfAHxXy+NY7H248T/T1D5RhPnVi/54FHGPT0J5rPaJvlFwifCsFQf4f2L+uAR2yKqPhAM/Ca 07S9Nw84YcQTuoFbv6r9hRjwU+h/jui/CLwPuE+sz63ALXfx8ypU/2PAqQHL/o6Uj8BjT7DY eTnCj1J/V1j2Z8V8vwz8KvTZKaL8SeA9P7PY+QmmL4B3fMmybxD+6gvANXdo+j06nud7r5H+ /gTQszGf84AnrIwoe/tC4Pr36f4vBR67N6LqXw788E7LHhQ4A9xgtHcjsL1L2/MfA960G/ak oPfPAR88Erb7xHieBD5k2NM/mcDPKyYEP/4a+PFvhO0fi/oWHNsdKy3bEfVHAt9gyCcHeK+r 8Yzz9PsCp4ZqQ3PIMT5Dr2c38Hr4h38S2AXOQX83SnkP7JwSYfFgwkNUPiZizxH4PcA7Df3/ IeCRhv+1GbjjVk2PnwceAXu5T8ov4EMG/RwA3jjGsp8U6/V74O6vW/Ztov5pUKSj1uh42wXA h8BvJwncBNzaoP3VVuA9tRE7Isb7DuBnczweSfIsA7z/cNi+VZTfCDwS9jDxA/mLdwHfAHk0 WrT3APBuY32/AnwU488JefTvwIuuD7PzAVT+C+D6ol6f3wGnntH2fxiMecUHIvagwKcDLw9Z 9t0Cnwtsb+Pngdl8gSdsMPyv8/U3MQm/HfhxyJt1AifO5/kvGW94N/COCZb9PoE3AD+2PmxP k/t1vv4mKpO/wK3Pw98X49l1vv6+IuEfAtd9LGx/X+DfAB/KanvxKPCILdp/GYGFHfpsjbKP JgF3fJCfD2D6F3hnAvwr+ru4Tn9PmnBXHa03z+cSXg5cZ+inbB0/zynl8Y3AqWZb2fMbgA+e oOlpM/BI8Nt5Aj9Yp7/zTPibdTw/N1nQ4x7gGwbDwp8dEToAPPOPlv0tgQ8Dr8hHFD+FYIjs MPy70cCbjXjJVOD0dFvZexcDb3/est8vcAcZMpfajL6JHq8AHov1fE7qH+C1rZZ9iRjfDcAH 1kZYfp3wncD1xvrcC7wC8lPGB7cDj7jesj8p+RO446MRpb+foP5D/D0qkhnfAx71ssXOD1H5 fuCZ4JdeMb5XyurXXAD9B/tWxkvOAG6Bfy/l19uA9xvyvQX44BYtv+cCbzfsuXcC12P+pwt+ SwOn/o+2H4eBZ6N8OxtPKLQBuAN4rKC/zwCPWM/PczB7Cngj/GVpnz1NGOPbKOhv/wX0Pojm 918CL5+n969mEuZoxOfPnkT2to4v1gMPXRhh5y8IT5/Ez0fJ9lon6e8UE+4BXgV+HStwFLge /PphgQeBN0LeS3l3I/A2rK+0/+8Cblij/dv7KbBhyONHgJdv0fL2W5P4+QKpz/cB35C07GcF fgGY3peQ8u+3NL8m7Y/W1OtvyDP5Bdz9X2HFLxOA01t0PHAa8HaMb6GUX8BrngnbVwp+uxQ4 t9BW8uBdwK8+bLHzpEzfAu9t0vHOYeD9Z0VU/Pz99fr774TvoOfXWip+uhX4qOG/frme5w/l eL9J89mm5cF3gXe3WfaPRfkrwGOgf++R/D0Z+4X5TRXzOw24/RpL+SPnTebnM0oCTwF27rds T+ALgRMftpR91A58+IWIop9O4LoHwvZPBO4F3n+aptco8KirLPvfBM4BH4C+PFvgG4AbPqL1 973Aawx+egy4Y62l1uOrwFshb24V/Pzvk/X7hFT+HM1vuraXXgBuMeLxfwE+BHku7QcLDScM +/9MXIz5UdheJvZnBrAzHLbbRPkC4I5WHT97J/DhSyNKX6WAWzI6Pj0IvA7r3yrk4VrgNOxr 2d4W4Anwp+T+f3qK/n46my/w7tXa/38auGjIp33ADTnL/qbAv5pC+fYwyxcT/sMU/V13wieB EDYa8x0/VX/jm/As4DHvDqv9XgC8/caw8q+vAl5v2Av9wA936vj/IPAQ9IWM/9wMvOj4CPuO MuH7gFNG/OZzwM6d2r7fCbzv/ZZ9upj/08C7PmQp/+SHwC2Gvvg54c9oe/0o8GZjv09qCIV6 5+r9GwM8akuYnZciPA74se9pfp1M9R+qUfGaduB1J0TsuaJ+F/C+Z8P2D8R8rgHuHrbskCgv AidALzIf827gsaAXGS9aC/zwBs1/dzbw83YniOcfaODnWZU8BLYN+fhV4NYWy/6jjC/S8+CH cwQ/7AXe+TVL5XdeAd4M+vt0hNPfyY1UX8/3TOChA5b9eanvgJ+arunvQuAJz0WUPr6Uyge1 fnlXI52n0PGwFPDMay0V3ykCNxj656ZG8k+1fbQJeI8Rb3gYeI0RX/oq8PIbwuy8K+EnG/V3 xAn/CLiuUdPfy9TfwQh7X4vwH2m8o3W86VQw5uNDYYXHAzfAXpb2SAvwmpP4eRum34H3fM6y s6K/pcCbPmrZeTl/4O0rtX05ALwZ+l7au0MkCDZHlD12A/C+D4SVPLyN8Cs6f7cVeO2fa+wV luAP4Jkv6HjqLuAD92v/+FmqHw3bnxP4Z8A7fhyx7xf4EPDBy7S/cBwMkX3wT6T8fStwTVbn 06cD906z9X4D73k6zN6/Ibwc+DH41zL/MUDYDav9HwRelYvYvxH4A8Abb9HxjS3AKwra3ni0 Wb9/Tfm3f6Xnt4bZeWUq/zaVwx6R7e8F3j6k6e8Q8NHVOn/xJ+DNRn7iNBIEl4ZVfO28Fv4+ mNTHU4GL99Uoed4CvLvOZueZCc8Dzl0EfSDzRy36e/OE3wPcOjai4jO3AG+HPSLjjZuBt7wc sTtE/QeBu2OwZ0R7jwGnf2Upfb4beNFTYfsmUf9ACz9fIvfjt/T8BZa9X8YL4Bit/21E5TvO BV5xs2W/JOcDPPMcHQ9tBR66lJ8vInq4HHjsMq3vPeD0HyL2RWJ8WXK8bM2/G4C3Q558W9gT DwHvMOjp29Tfs9r+2gs8cknYXizaewl4n5EPpU8dt8wLK318InDudJ0fOBN4E/hX2s+NwAfu 1vm1S4BrOsP2CWI9eoF3YHwvifElgPf9ybKfFv0XgHc/oc+L3AbcAHk0S9InsHOLpeb7KeCn tkh/MBT6EvCaP2P/RXvPUn+rwipeeQB4S41l3yfjA8ATIG9kvPbNEPyzDfo9B7g42bKvEe11 E36zZX9WlMeAW94Wtp8T9ut7gMd8Vuu7TcD7jHjZJ4FToYi9X+ZvZlB8Tvf33Az+/tmZAv8E eMIqrS9fBl61wGbnOZn8BD7SYttXCmzPhPycYyv74wzgHWdG7KLA5wPvMuT3TODNS7S9cylw r+Fvvos+7Sre/3Ug/1PAR438wBBwu2GP3AxsQ/7K+OvtNJ47LMW/W2by9zcuFPTwEPCzL+p8 /g7g5Vt1/vabwNvabXVe5xngfYY/cID6v9hW9H1kJp2/0P0dD8I5ZPgrpwJPQP9SXp8NvMvI 380CXnFXhL3/QLhtlv79i1NDJ4UWAx9Fe+3Cf7wKeMQ9NSI/jKUCHnuPtE+wV7P4+5/SProZ uGjszybghjl6/A8Bb35Jr/8XgW3jPNeTwK0rtH78CfCqWkvFo38NvHtzRNX/I3B7JqL8wwgI PfETvf6nAz+2UuvjiYSvt5R8bwY+YOzfHOAV14fV+bdLgevv0esbpfL5EXuLKM8C77kR+kH0 dxNw2tf+2ybgRfBH5Po/cCHZhzqf8iXg1kv57wmQPHyaGPUj2r8+CJzrt9jvPRF+BfjIbTp/ 9KcL+fnr40T90y7C+hjyshl45oNhNb9W4NZ/gX0g6vcCd58WUfbFVcC7FoSVPB4AHgX6lPGg IeBFj9So/fkgsG3Yl5uANx+J2E8LfB9w6huW0nc7gZcb8dznKLD9kKXOi/0CeDbW++MhHp8I z4a99RB/X4bKxwLfMKDjLxOBc+DP88T4Z1B9PL9G7FcX8A6jv6uBu9+t8+Mp4F7DnylRYgn+ sy/w+4Adw/69E3ikQd8Pzab8gKXij1+i9g35sQf48Wk63vg88CboF0mPr1D7hjwiQuveq+Xj GcAjbgY9CntsPPByzO8Lwp+bPYfeP6gR9mwo1AO8E/aAlJcrgHdcouVvAbjOiMd/EHjfkM63 fhT4CshjFR8B3vZ5ne9/HLgD9PcpgXcDH1xn2c/I/aTnT9D2/wHgVUa+5Qhwu63jacdBsd1w no7fjgXe93NLnWdpupjOG1si3w9/gPBl2t5qB16F+YfFevQCz9xo2beL8ihw63mW0o/XAqcy 2p+/HvixN1lKfqwHXgR/cIKU59TeE3o+DwMfGK/5e+fFFL/R8cJnaD7XWex9XsL7gEfCvpX5 yReAdxW0PXoE+Aj4R8aXTsJCjDDk91jgNYa/NBG49T2WsH9gXwHnro2o+HU38KaMjq9dBVz8 cESdF8sDr9oQZu93MHkFvCIeVv7GXZcE7eF7aWMWROwjovxR4FGwN+T+fQ3Yvj1s/176Q9Tf o5Z9pcC/pvFepP2BP1+ifw+J2h/VCv1zT42Qb9BdwJtu0uUTgTcb8ncW8O7r9HmCBcB7DX5b RvUfqLG75fkE4P1TtHxfCWw/WmPTgUTCm4GfMvy/R4APflPHl78IPBL+8pDA3wVeu8FS+cL9 1L6r47evAu/5VI2yX08HY21s1PLkfOBDtrYfpgI3LNb7Owt45tGIfa/QJwvn8ve5sgIvA95j 5FfSwCtW6/MT1wFvv0fbD7cSY4+OqPN1twM/tdFS8bEtwDtQf5ao/wiVG+u9i54PGfFt4Prb dH7teRrfiTqf/Z/A+y7U8Zm/AK9ZDH0r+h89D/yyV8fv3gbcPkvHy6YDj5iu82udwBvv0+fP r5rH3yfbK3AfPf+8pfJl1wIfAb1K//hWau8FHe+7D7jjjIg9XoznQeCdU3V86ivAE4z4zi7g FZCPkn9/ANwwmb8Py+gb+NC2GrX+ZGh2X6r93dFt/P0nOf4G4LWGvL8EeER92H6HsNffCbxo mz5/mAfebtiz1wMvN/T5LWTY3hm2/13M5+PAHaO1v/Yo8A7IM7lfXwPedJ0+P/AU8L57dP7p R8CrrtHre5DaC0fU+bRXgMe+J6z8uT9Q+SsRFX8/vZ2/DyTjxecCr7gjouT3ZOCtfpi9T8rk OfDYxbaKFy8GHvmtGntoBsfvBR4Ff0TG/24FPoTxni7k/d3Ay434zqOEr7XspwTeAbztC5Z9 ijwPDLy2QZ+ffR54V4fc7zeHXgFuMfTvcfPBbzEtH08BPjQ/bH9P4PHAm2DfS/+tGXi5r+Ml rcBH79H+Wzfwgasse5OY/zuB93/csh8W9T3gnaMiIl47ItQPvPsbljqveQvwqzZ/n5vwA8Aj 7tXnWT43n/I5lvL/nwB+aqs+//Fdms+rYfvXov0XgZ2Ltfz8L+AWIz57KgTbxl/p9zPOBc79 OGx3ivW8CHj2Wp1fbgPuuEXnZ5YAb0lZ6vz6CuCx92r5kgPe+v6w/QVRPgTcOhixPyjwOuD6 e/V5wk9Q+S36POxjhKfb6vzxd0gQC39uJPh3L/CeD2r748UF/PdRpD1zFPjwaB0vHgHFPtsY 3znAV5xsqfhfE/DDhry9GLjXyBdcAbzIOG+eAE58VccbS8D1tj5/fDvwHuN9nAcWUvwvYi8R +/MZ4Nakzhd/Hnjdeov9vgbbX+Cnrg6reNb3gQ8a+uw3wN2wP6U9HwYh754dtjeI9s9cRL8P hPoCnw+8vDts/0rg2cBHS2H2eyyELwVuMN4nWkIY9ovc7wTwDZeHVbz9Q8CPz7VV/3cCP7xd 69fPUrmRT98JvNPW/t1e4M2Phe3J4vzKy8Atl9lMHpN8PXEx/f5UjVrPusX892WuFvVnAE+4 Tecv2oD3rg6r879LgXe2a38uDtyB/X9viPsfw9Tey7C/xXpsAD64Qb+PcxdwDvJ5pMAPAjdA /p8sxrcDeIuh35+k8hcjit9+ADzyexEl/w4Bb/+ZtleOAC+/V58PJ8PngLG/Y4Ht2Za9Wsx3 NvCiS7T+uxy47vsRFe/1yHAaCX0g5Qvwzt/BfxL2xfuBx3ZF1HnwD9HzX9PniR6g/j6p9cej wL3G+ydPAK+NaXvo+8CPb9H2zvPAD58ZUfrwILDzrCXOi8F+AN7eGLbDYj61l/HfS3pEnvcw fpOUdFoD8Kqzwux9fSqfB7xoU1idH7sCOIfxPi5wDPjgWn0eOwP8+F6dr1oH7BwKK/v9Y8B1 P4f9IcpD9DPR9MvQU+Khvni8ib6Jl/PTXmJKKB5Np92+gWyGPg+YL7KaqBXPFwvFUjKJy9yU hpDrtvcuWep2LO7pdd0QPZ32ini8ESWJrNuXzsaiaZf9rLQbLQ3h7vxF7oKlczvnu/PmL1zc hYeoe/6l7RD/YOWUphD7VWpxk308kl8ms3n6EHWWfZQPbbUZfZv9xY3+WJ35Xe2sSrsJ+DA4 Goj6mSnxXE7dlqNjBcUBTNct5htQ2j2ts8PP9BNsDMKmIGwOwuhArhDyVkbThWK+EHITHubt 5aJF+myjrtkd7230UZoVNXWJH8p7yVKBTT/muVH68mWmSB/QNLrp7OjEeOkOGmrojoeS0bwb zfetnDKtMZQsZeL0BUk2T/r4eoj9/Dg6YncW0/d4Q/xrkH6cfbPTj6b9d/OvTkYz7Gv17Ev1 hLH13YtDbhP9k872uV4+n82HXG8oJy8LGIi4jGcL8pI+v5nOZrHQCzuWzJvb4U5ZPIV/gNId zOYToXy2lEn4mT42pAEsQSLhrcTqD6Tx/3gxzS6zOQ+zCImR9uVCfV7RzZQG3IRfwJLGU+wG +2RrzOvzM5yGQD0D0WLCjxdDuTymXgiV0rSaBdEiW6gQ/UN32Z1clAgRi1QIdXYs9DJe3o8v QQEoPcPXAhPq93i9EO+AminRz6IXpjS2TEfb6SgWPsUGHk17eeIiVMEjBY8mgZEO+sWUm/KG 6H4hHs3wGm5f3htI+xkaH/WCu50d8+nH19N+IeWGrnWLKayUnvRAGk941D5Nny1ngaZSSoe8 TDyb8Fzxk/FN7OudZTeb+U16FJ16oYRX5RFaZL/gDiXyWP2ES1/RLrBtynsZ2iaU5UpFvqGh eDqb8dwYfZW8AJb21LXLe064RIVuNunOjGF/6FaVssbpujBe4B+TxaKFEiB/dJT3QUvZdOI1 26xWbrY7kMao2Q7F5QUtnJ+hydAkQ+ASP+HiNm0yv8VLUQ13jTr8tq5mNlVIZSFKg23xe2Zj Zi2jNX4bQ4zKMfZ5YtD8gki0OGOeX5xbzA64jWW4iePG6bjRg2UD5fA7M8tv8CrDA7Fs2qyi brSlvHh/O0Swy0bDO0/60Bdg+WLKAylHE5xjinPz+ehw73DOawqV2AdiXdAEitr9QnYww0rR yFDSy7OZMCkhWAW0gqul/Ps0PeAXrzOaB/WYd0jsBe/QXLHj4rM27oA3kMtm02gwQ0xJNNq1 pDsEulSERNexXFMsx65SuaYUv/JzTT6/Suea0vwqmWtK8qtErinBr4ZyTUPiCag/X5BYCE1m cqEU+9dn/6bZv0n2b4L9O8T+JZbHgKNpfgXRBAEFoUJCit+vuKQ6rHJXNLM4k2S9F+SACjSe aDxeGiilSbAW2OaGhLDjNZKyakxepOSFLy/SaqYxdZVSV766Qj0mtqG2SrG0JxdUVI2pqjG1 jDG1jDG1jDG1jClzM3x1lVZXSXWVUFdDatNi6kpvZFpdJdVVQl0NqW2OqauUutJEkFRXCXU1 pAgjpq5S6spXV5qAEupqSC2hJqohRVQxdZVSV766SqurpLpKkMrMM+FLBgtsINAMkfhAelDe ZaLOxQXZUIxTvbwUKi4TIt2l4jw/E80Pd5UGYl6e8SjjdlI3xyjv9OgShb301ehk8C4TVNQ2 7JN5w0Wv0JuFZEDNHExGkiUJkgmok4ZmBZEnYtEE00OwbnLReD/p8mw/yoS0oabAIPQfGD4k /s+HR8WxLKTIINkiaT/ug5lKUJeFUgyamcQNrthFufpk8sqcWY93bQlaw3Mri4zpuaVM0U+z cSZesyIJNdYv2wUSeXRVFAvGlEU0zmwNdY8PWMF8dJCbvnqd5w9h+gX2HZg+/90DWWYr5Pt5 H6UMDYs6SdGyQjJVnbhqHyJzpVdgth5/wpDm0ULc98uf5ORTfpfLGz9JojDDVqG8Bn2lG5YQ 08v0IXlvUDzkipLKR6iqbIwMu2PNIUqzSIYg991+tgjMfiOLasAVlIGb2NgScUO0hO6jiQRf 1rmkc9pSJZjS7V5UA9hD/dgfusRQxRWr/HZqh92MwSnCHue9YgkGvUCiFV4Lqv1aF3MdKvIG TK3F+gkqMvYQmSZ4iBlPpQw8AC/Buy9gUP1MvbFJkgEWpctEKQdOZ5vOunYZcv2iNwCLrvJW v+vmsrkGecGKJGA10H+wwdSAbomu+dW14kkvANnA0j63UsjyJgEDcgUXt5Md3s24u8CuIbli mAXtSj4GX4McSTfpD5Vg3/kZGLO087QOg9E0dbSSqVvmklJXMJhFB7Rb0p7nhji7NUDWrAcS EhWYG9PvDRcYo/hD3LNIJzBiElVEbyQSy81Iuhc0HbH7/BmY+tlsfynHd2Q4Q+aLm/NzNKU+ mON4mrsjAkC8yUuy7zGlUB/NCzyQgR/MAXO6ssMcDOaxJ/wyFS0wmmWAeJVWzVV+ScgNNOUm 1eOuAIy/uaPEhCsN1OW+Cr8mIswUZQuZbCHlpdPxgQT2JCT+R+Ik04dlHTAfl0Pm0mFKU0NT lQZlJT4mLGcGjCkBvMcsUQb5R1muAFJ+AYTFnFF5rwDn1cvT0sk7cZhfmaJ5h9eRkwAfkSpg RYxrsRB+vOxxWTmRLaI8zj2oLAwolwZAFJeh6IRaGALwyIpMeQ1kV3ou3WJt5rJ5OQdBB3zZ 4ZGh5wL5fSlI2zQJfVB8dHhKY0NDiKgRNmRfJpp2RbFsGU4/HAHyfryVJaidAjXpDkC0zZTO fCgOI5qLDS8DX9GTUq+zo8crLsOCzCMvjKuqBSImQIEOEifDZDBkS/k41MBKv+CTOcc0PnkA bVpDseY1sZF8gldFIaMYKXiyT7MuZyYyPTs7FqDGlb6XTpAlwR8XohIdFsmpkI2Rke8yERQt 0CKEmN8dTTN5S4yFwbs8KAXRID2JDmxQOzM/uU8B26xIsZw2tS69DUI7Y4DKpsGtRXyF26Js GD0wqrkzxAcJds8Io0jcZrEEra0wEJIwjMAlT3IyZroljrVnDGjEODo7hAxcCloYVo8OFGCj E4UJNmcCponREvx+pee59cRXLOnDLyRy4SMUzcILh7Pe2rqwY/G8NrdpSkMolx30KJbk+5LU WRfUI+udcQwFj/A/Wtt8MUuuJ8WmommzIdbN0uhgDznRtK1eFJvomSsGlRyP5hNkhdAgQe9F r0Fpq3g8N9wk6aWQBesYBMNsDDzEtrpbxl7wbBGmoSt0iwxMkLEo52Vss8/H2JaF31egZVSr LTY6BKKKMqIPTqzdS0ZL6SIjUskWepVxNY/J7gIkV2YlLJgy8uIO8EDCh8Zh28TMKBKB7gBz W+PQDZWTTfBewQUwSQpFHoPShjv0DK4XJELekBcv2wlQAQgo3eEzwuVssBij6fPy4h4FA+dS PEsEBCnYlOvL58x23Gsb3STfuYLn9RezpJXcIr8ZRecUiSLHUXIyuuWhAFBKLk2DM1eB9IkM A9NOZgp8h2SIssJ9ICpaKibPKJltPqvLBsU1ZmdHlzeoeYCivSursDfa1oIAs2hisxASA4YG LqD4qTXiKpIxNFtscjpb8N7hQyFUbBPGROSmF2Nl+WoYYoeJFCxBzk8E1rj9yq65nYvbZMQN pMuYJ5sfBKcsZTstFjM4Iy4OpKpkkkfYOSK80kMxIbHpplATK0qbzwQbxKFXfb3Mh2lMaThL oYE4/PlikNygPHrSnpe7spstHN8XNzoDS8xVSTobLcqADjYOy5CJa5EraMb0AF2h6bwiBJFU dEs5l1MYB8uVYGsyI8vtW95wCSqMiVkhRY6hcap4SCIOnCvR/9wFK0MstsZFmNxSkAvsbVoF 15TGJCrZeplKxnRjDN9ESCClLV2uEMzlZBM3GhaLgsdEKCXjRUkxslGqqL4PLg4xG7hQikNF F7L5KqrB5f1T4K+NtlFMQyon0sXZAWKwxe0hJurTAWKlGGsySimU4UpuFYKFlAD2aRnnDS79 pXotd36lxkl47JukInyoyKErC9qANqFYYTrdm/J4YFEKtADpkBKuSvBx4l9zEsyZIGdrkMX7 WZSBoqiUlegDK1xbQrcFOTS5NFJUQGOvhJWcc1ODoZV4qj/YdIGLSiEShClAEp1kN9OnikQ1 w/OCIK1jK6A0xP4wHez35NKMNrsVo3YnDCYSK20SnqBbJreEsApKrgKjHVNIE9nToywERGbw IGfa/oAD4UYHfMOuNBuovtN851zeENg/HkqyaGWyQpC0+9F0tk9pWViwfnCICaaQ40GbENK6 QtlLc4a8KJah4HZzgKBTzEfhETDap94ll83vcnt65/bOl4qvqHaM69XoIEQn5x6tP6Aq2IL7 feh9QJnmwsnvFAYPkSL+38E9KdPuERJXGaCm+lDdgPgwlmgikdd8y2UE6nZBumBsFE8XwlN6 YJgWqV7UhHHez4PbIRVSktIJLkQ+mYYv4CZnQW6bZliAdKQhhtGykYoImMmgeJac7CBnkFMA dcPYt0TRN6w4z0y6xDVSjsPAyGkDI8hAWGey6slPEbqMEm6LM/MzJAh7IRO7sxhjCyMQct4W Z3jejQiJDCeatEhAMeuNGEXzDkygNOzxsmHzeIfag5if4QFId4YvNA+zXjAGP5/NsG8e82hO DnKAPDDqGHpK1F5qcopcQynXGBa0RY9RpEpGS7jD4Q6if+awme6KIIdyCTI3Rlkh5du1KxqW wpkLT5bI0nZZwFrkzedj2Hu0gKmRz9HEZAcTWn3lXVIWU7odgvqj0BfM0uBUyQx1DEoYDIJt KHOhm2HZIbEQ7Clp4JfrWTYnaQoxwp5rMBz4QZsU5c6wX0Z53dqYcLVZQfYSeWJcw/AFY5uh oopc6w5Eh/yB0gD5AHIa8zNxMlG6EzCo0omEsd8s4FjIsa3MVFiKUnANcJcLLnsm68oAR1Be cglrGKbk9gTMy9dIbbpdHdKMUSJSm2t83Vn0qMAVjxb3moblBYwbZpHoom6xWSxjaIYHIPBS +YAHyrPClMAkZiMjU5kRpmbT69fBgtENQUJxhTzoMdRMJkQBXDa9AlzfTDRT4bGSU1BhNIgd CFI3i7RWePeMveazEwzKmuE2eWcHcxh1/IA9qpaC0nBeLiBu0F8KhBcbJhlvFghO0q4Pm5uS +1zoixjyoJJVENcpEX6QESlylob0doSYZsiVTYo3bBqpxMtsUmX+ss4JGztMLkBCK+jQIFmN 3JIuaLkbMBBVNCDYPug3GGclkq007aU1w9iAJyPKVVV5DEha9uxUBA2gslXOT5QkIIKVoQcl zNSSBKMCXLuqCKM2HrStQEpG6/R+iEEIo5Vg9QIpPndwunSbDH9VBRtE36K0int3LOuL4iwU iKwMFJBBIzLxrt4f3rHmP6w8eR1ZLJqMA5I+haM3IFQkW2i1EOXOMl9OboJ5CRFdhYbjYalK E5VvHii9WqzODFVywgnuwgBjl0rbsnocB4sgFpIzS5k4VKtDrVAkQLkh0m0J7BUnMPBRmWXN lieoeSGw0gmxvGDL7mwBozI6bVcRowY3xE4FcUcC650zw7oyxlpO+ko6s7MTpIvi0EPVwhUN rrRaSrDNaRWqRsAEX+qgzbL0sjTPCbHYgGhhZSjRnfKV7vMT0uniqRvajJwXh6GvBVH13LHQ T0wLsWXhRErHNpRJkAy4RAvVVVdzoy9DmCxM1MOsVDN6KNjUdD4NsuCGUPmOVe61YYMobud0 JJ14c6/KjI62uBBbdA5HblwghlThY8PEoDQV74ONnfmdzKsiJ8OL5oU+KiaypaA968fz2QJZ XiHm+QXicxS+zOcrmCbILfI0x2CGxR+kGEsVQaTCEsKQyBKSC1jhloeiZJcGLACaiVSbRCV5 r4+EVd7lpz0ZL1ZYa81+tuCyf5WDmhs2vFSxuzwBJs4OSjtlpRAiQpxWagghTXUGITADQc56 qmQc0ske0nXczSlcmy8PA6ManENf2ceVbO4yBT2osyFsB8qVIttuxmbC4Gaz0EHMgAFICr5c v6vEMW+fmU8wxcvtoZASG5KNGanqSBpFnldWBkBoIcisFydImCEZNKUqUqVcdzC7k10Sn4fe ga4Nfp7W4DNRo3e4ethHBU38DJcUXE4M+IUCFE+MsZPyenOUh6Og33DAH28ODUb98litcsKU t0SLy6JILEUmMoacGHn0eAGPFnZ2LDbMAp7D4eEFGLLsUIayDxf4+YLWBDJS2Zudn0ksSXZk s7kY/EERL9dxMD5xFnzNFik+StlJfuaK7V9IWNgqyqDsLtFGuZBJKKWutaMwnUxlA4+ilOnP kDhgcWGlFdn5YM+weorQOkV+0leaHTrfV2DG0rWZbCiJJS0EZZA4+SCN/54izxqxTWbiz6WT kWUxIhGKK4rDxVxsxUtFIbWCySjXMB1lxClREdSqkAKLU6V0ZWDeiEQ0hlS4vTdLj5Kyq2iM 8zw/76A9eaVKgjxXZtmytHmbMO5ZCFueapRKWcUPVGAecn6YOyamARKkO04VKodU8NMZP0ph Zm33sgiFyMN2dszH5EsURDPOq4e47CG6E0RTNQgptRdrJpMIuC9pMXLTnyDnmTLebHXyBR1X EkstZHqvctAN9Zs4toErs5vpY2Q3hfXBlRUpFa7ZByryXDQkc7yBkAvvih3C5pEcbnb5mVJB B18C+RLDcKKzcOUWtDoFgF6JxVzJY2I1QnQEv4olanI8X3hOga7hvDAySWqLiJkV2nwSDq55 QxGyy2V8E5n98owMix0xcSkqqhP02lySri5L8gSSVRX+vxsqMzJlGF2xDg8JleXFZCZc6Rki kL7KFJikAiiSYood80roeBYXIbCuSKEyw4Jncjn7lsUNSEpwcSk0oqJBrEKHn+HundTBxtGL 13DnKoswi1ihoOS8ehuA2SRaElZSY0O57StCkZWplGyhGiWR68JehlGBuJXCYBtIVKxqIZte CeWRpFdcQPVx6Efq0YwcdTUFDxMwMigIQ1TMXVKC8luY9SvsSOaqSBFX/fwJF6AD6RIV0PHv vE/vW4i0PE/QC3FKhE2kXH50NFFpcRpsFDpGeoSEl2Gi9vu5YraY7TeHGRCS2tgCe/uxON9f ZtyY4qmSWDWpMhGpuqTXcMo3sUzFszWW5ycSvpEKI5GnY2NB8SAklQgU+6Dvip6CJryvA2aC YI79ngYFfkQHBfg38ZSIMuWKKTrX2BRI6lRRmDz60NkhDSgKFFbJSrrcIF4qAhymZAuk2fSZ Uk4udMCDCYFjn/GoPN9MWbT0MbNoUMxVI2Xq9QWevawyV6lXy1LvgnPmCykgnDPu1qpYrz5o JJHUxuIYm7Ca3Fw0QWKPEVfg9Sp2iC1wvimQr+WTYNlFEfMV7RsRSrYVmDysjHRDSGccAjOX EkIGY3SaXASxWGviFAELuVUmHFXflJiTR/+UkqJUj1l7kB29ScYzLAGaO9bWzVXqy6X3F0P0 QMCUIBcjN2zeIV8xaGwYaQtlQvPxSahixewUmJEa0pPyohl2DK4NsqAicBvIjbjyfLMnT/8p /8DISRlv/ATO+xVE2Mg8lMbiWVwS9nHHlAoqz4vpU0rVNJ3wuYTopWSkOo8pT2IKM9fNYWvS fl+qGMrTv27MdY1NKU8n5lQ+UR3lk8k+nn+oyA7qyHNUqfMyCd3HTyPyJsrNH5JgbnImpVaj sXI9qs98hPiJDvHSFUXsAjEWdpaMHYGHzqiQl6a1VTW5YRr8tIVk7INShqJEqsxj0zvUOKU5 IIYCXqOiENrHBWxIZKOpFEbVzQ6YtZQUoBMO3DMr5URQRtsd1XwnZtqXcQAjOGxFwhvifFvB ISxjHgi/inyvDhDxNHow4scrDXJrXnG+EYYNsGCAn/0+eGHFYRgt1U5Iahum/MBptSSICB4I h1qekVFpE745OpCqqZh7fq7IhvF0tHS9ZbA/sCvqgFg0MczUU+EYIk6mfsv9gx70IYQEa8sb 8oPBqIqhGOnvQDwkVHaqzw2Vv7VXfgI/GKqn81zl7wVIQZUR8a9sXso6I4KkEzNMKcDjGvLi jAgCzpVeRdGsmFLAjr7cL6aMsyLiGKWOaMgBi4hGlTOVwh4JhGApqZsIWsEyOWFaN8c8QeFW RN9INAWSN656BXvJggU983vd3rnzOuazgx1eWXY5wazmIJWzLKw6MsdWk+c6GSmDLFnURB77 FEd4eZAOBkOJ+Mtd4Aci+d0GmBaCHBx2yxzhEMVCKRbBaazSNROBBP1KF6nFsuQdRECWbgsf VscyWojKRS4xQC78nJYg+i5+wk9Ht1xOHdJaDFXNVrE4O1uu3ixzdP1CtFgMGAjuYAulBs3E tlvOXEIjBuRQMeGXH8PpdxULlZ9nEgKBsW5ZmFQeDhqsiG3IeCI3JJX/Wy4aVEys2ZxGXEdT KqMSRupSevbBVt3BaWxVyk/HshNi/F1ilvQj8jBNecF+Bu+xbF7VnQ8EjxKMx2ALoKnerJK5 bdzaFha19NaidAz5GMY9HQ3J0nlD89iQOqFEh8iVLcFisMqZD2qu4IEf8TJEuzoqQ3zICAoe UkUcO+MNMglIZzrlQWomN17jLU99MsU3g9OBmGcT86q5lmSqWbB002vzdPfcZndu8yzXXKXe aL/XwWJ7/BSVOkOVUKttply5VCebguSw2JslySQ/Ql1+jLAXXLV4ictYhPJ2CUbbfkZpehHd UsKh0moLvk3gqjdf2EHffgykYtELTEGqd9hCbl8zUfBr2HHGiYeqNmfKG6JRiSwYc5CpOjOE xItB4vhL+ekIeb5BGUvSSK9UiuJYUvC1o8pRSceTbPIi6DZhyBoecjckR74sdSRSWSH1ywSG i1Godla0Mnumg+dlcsI1/M2gnRCqdhhckrmKI3Jc5eAof6Hazae9JJOFNEwRq6zMq0gLXJ1g C5WdxmmoGibXey3TFuabW25WvaPhsdj5tf1GVF7aDkbKu/wARqGPCMMX8dCyha8M4SXEIsdV zmFltQAzizL0yOPHpYBRrhNBxw4GtpnRwKV+aJB0Nh87d0rEKfrerJK3gSMRfhXy5AQf/O0S 8csmhVKMIqSGx1g2HZHd0G6ZynHQS56u+UMrLBMtMhJsGQIBZ/MtHAonVOa5K4/CSE69VvBV PhDQJdor83bNA8Eh9caB0PE8HBiIW4q4KUumkS42KV2cz4zG8vqApkil8hfbxYvjZib12CqE J8j1QfI8UW+5ZNIBLKkBQtWPjTG7tTcrXlgw45giplCRPBevSPAQYgw8LOeuQtbVEnpVTmGw pIH6CSzX5ecpus3nqp2zEQa9esdIaotjhX95nNokCegMenXpjb//D/+Wzp/b3jn/79tHQ2ND w/SWllAD/mZMnxb4P/1Nb24M4UZDQ9P0GdOaG1C/sWlaU8hp+PsOi/+ViNscJ9TnRzMZ/9j1 /lr5/6N/vSnPaZs0ycnls31QGI5fcKJpEtjDjvx1PgdGvTM0c7oDoVgacgrDBTqCVu8Usk4R T5PnXAsb2XOGsyUnA0ORGqESdnNcvjk2bkrt4iQrHoTD4RSzsm1djfqIOgmffsgCnovT1r3M wa0lPfUOLM8iVeSdjKNzMXQ1zoH8dQayeGaYtUO/I1aorYWameNMTWUHvKl8z6ZSAmtq2o91 dkyJOpPTA7W19GRtbVubM8fpw+Qn5/qcyXFn8uKKx2prefIJcpb1IRIQjjw772STag4FZ5zo hA9tnEycTUmNqx1M+fGUE817tNIrfZjmDr2P73Sijkfvk8SjU2qXljJ8fliwf9D+B34B7+/0 91f4f0ZjSzP4v2n6tIYZ02bMIP5vmtHyBv//Q/7GMxs5QXwqKQHUWjue/2Kks3TJsq52t3Nu z2UO/rqW9DoNbQ0NqbLyrvlzl87vQVnZ/fYll3fRc41Oz6IOp7G8eFm3w/6aqhe3Letlxc3l xYs73Z75vAx/oKDGlFnW1oHh8DI2YFZeO95POrxOoq5jcdeyKybWTp3qsCuHjCAUkjMAvowN O51+fzYdvca5Cn7NYKHfr3Wc4NgWLOtqq8vUO8n0RGdl1k84POfgjB/vZOifOro50VleewIN 4zp54TjsZ/WcwkX6TrQwgCbSEAGQbnX6vuOMSxaK8UHnvIblmeXFcYESyJdBZ0LDULI5max3 zmusrJHNDzrjnPHJtDOueoVkOkGNNwbuXjhuzsA4p64wMXizoezeRDX+1bVYG3NN+JvE9TQ4 Yu6JwWI65VtPz1FxC4ovCpaXcvW8ByqfWVkeLxXrVXmbKB+PpfeSRrXa8V7a2O7F8zon1tYa 21TK8f25Dg+XMmLb+c4kcyXKHMUHqeFqf7RdgT++Sa/jQdIRjvFgvcFt/+1GoCOrNrKs+78/ AUYI5gRWB1aL9uw114sd3X59K/Y/fdRYM/Ho37pqZc2QyHo9K6cmElw7wQ6vuXzy5fvXt4Kv 42ljEfXTf+s6VrYktMLrWU1zUsEFhQB4zcWk87ivbyH/h08ai8if/FsXMNgKlN/rWTg5Cblo BfYuStFLu/7A/451qzJjrs//tumy2dL5lPz/svlWoRNpo/xtMx7vwVxL1pKHUnQCL6PoifPj +k60PlZPvwQYrc/lvZVRdh2r93IFGgF73CuU0sU5kxsvInXOqs6JzmmcMu0i1sh1bKDs2TlR PuroHFaLA/5AXXRy45SGiVObJuF/VLAaTk/aq4uey+tOVI3H0FOw7RirEtPNxebUxSbx5iYH m4vx5mK8OUxiTl1d0wV1bHSTGydOnNo8qZGZBX6yLurMmQPr821vc2J0NZld4hF2eyLvWsyd sd3iroVu55L2+ZL9VnvpgserUWsXNzrUgOpravPFDaKVY7Qj1bDREGsqNntyo3ryGM+aqijw /DHql8nb1bXyX2aj8d8/E09i6aSEMH6kRtMNjOU6YT05ZD05MJXpN/FgKZfSCSeahu8f8xz6 SUSPEo0iSMCtaaL4nu65S9ucWKlIUYIkHKzBaMHJZIssPuAl2NDQ5gI8REewMKxoAd705X5m 1kyHBlqAZ53kZcLFZqFph8WLyRvH3cVdvfM7yJ/mP05TqHdku+h0kJzyfKHIWnPQdjSddsSx 3Gi6vLXqnFjJiBlarotkN0SH1JHoYioNeRwWIuYnEl5G9uZkc16eRQvGlXdLi1Y+C9a4uQF1 rIYrpcbEiWKwZdJuIh/WeKIUUSMg/VU5ExvqopZmwo5qpYeNuSiJ4pBJDmM649H4ovlhTh5k cC/rdiUFck6SxjW3ynn7q/9RkYw3/l7Pn/b6/359/LX477RpM8rjPy2NjW/Ef/4Rf2Bl5jwr TnYXqViKcc+lAIqMFEGsFKsGispVUXlAKKDaSGI0HqNcRYaOUa5CQyyuQ+O/bOncy2rHkzUj Btmfj7LAqzKTzABQz7Iud0nPxMADhVw0H+dPkAQ1i5gMNRs7hsl10TFUKtStePKfvd0Vf2ov /459/BX+b5zW1FDO/03NDW/w/z/ib+rUXrLrWGolzt+P4MmbAvsRE9Cyw1MXdI94isy7qTBb ZFbaoTDqMf8onx/t8wrCBvJqqfb4qn9ODydFMjIHBmCBkHEUyxZTupEqT1GDV2ZLzgD2EX4e PUrpI1jocb/gwaTJZpQFmcym09lBmhWXA4UL8TD+kzKmfUmPIyw7yIrBbL5frAAVULYmC3v2 cvZKRMF47PLFXc2N1R4TVZ3mKY3B6rOmvVb1WdOM2lxSVR/WFeoRSkTxeaI+q8K+VpTNFJQA 5bZ5eStkFzvdbQ5FUIX9ztfEcXqY7Y11yztZ2PzxVNaHBUgprAudzrlt9bQqbtuiejZE+f93 MJsfDw07A9FhJx4tFTxOISu9/LAT8/vI0oVPOlCo/W/RAhEB7Z0iN0EMx6IFmpxKNKqHonns 3gAoOs6zbkn2A7iMToTZ7dDPY8fpV/6pEUlGWT4Zg3LkctIqyWvTDv5n8/P/9E9ovb9rH3/N /psxYzqT/9OnN05rmNZM+f/pM97I//1D/pRVN9v3PC+Zm5K6mMwbyqU7rxXHTuagIFhZ3QKQ f9dECklVPmdmWsoe6T7GI8F0Q9lDncd4KBAWLnvmqopn9C9Z1IkI2QVJ9iS87guSzsWOjOpA mNQ5dRfU1dEv8jsXTExOapw4cfJkCh81THQmTzaLJk6sjBihsdmODhGx5iZNKm9QNBcsmDix SuQo+KCDx4akEXVRZZWJgFRlpqgjGmTDxJLAKv1nU98bf2/8vfH3z/z7vwl9R54AQAYA ---------------0312120425797--