(*********************************************************************** 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[ 187039, 4518]*) (*NotebookOutlinePosition[ 215734, 5437]*) (* CellTagsIndexPosition[ 215690, 5433]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Recoil Polarization Bases", "Title", TextAlignment->Center, TextJustification->0], Cell["James J. Kelly", "Author", TextAlignment->Center, TextJustification->0], Cell["\<\ Department of Physics University of Maryland College Park, MD 20742 jjkelly@physics.umd.edu\ \>", "Address", TextAlignment->Center, TextJustification->0], Cell[TextData[{ "Several bases useful for analysis of recoil polarization in ", Cell[BoxData[ \(TraditionalForm\`\((\(e\& \[RightVector] \), \(e\^\[Prime]\) \(N\& \ \[RightVector] \))\)\)]], " reactions and their interrelationships are developed." }], "Abstract"], Cell[TextData[StyleBox["Last revised: November 15, 1999", FontSlant->"Italic"]], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell["Initialization", "SectionFirst"], Cell[CellGroupData[{ Cell["Defaults and packages", "Subsection"], Cell[BoxData[{ \(\(ClearAll["\"];\)\), "\n", \(Off[General::spell, General::spell1]\)}], "Input", CellLabel->"In[1]:="], Cell[BoxData[ \(Needs["\"]\)], "Input", CellLabel->"In[3]:="], Cell[BoxData[{ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(x\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(y\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(z\&^\), NotationBoxTag, Editable->True], "]"}], ";"}], "\n", RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(t\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(n\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(\[ScriptL]\&^\), NotationBoxTag, Editable->True], "]"}], ";"}], "\n", RowBox[{ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(a\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(b\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(c\&^\), NotationBoxTag, Editable->True], "]"}], ";"}], " "}], "\n", RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(d\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(e\&^\), NotationBoxTag, Editable->True], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(f\&^\), NotationBoxTag, Editable->True], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Theta]\_s\), NotationBoxTag, Editable->True], "]"}], ";"}]}], "Input", CellLabel->"In[4]:="] }, Open ]], Cell[CellGroupData[{ Cell["Rotation matrices", "Subsection"], Cell[TextData[{ "We begin with a primitive basis in which ", Cell[BoxData[ \(TraditionalForm\`z\&^ = q\&^\)]], " is along the virtual photon, ", Cell[BoxData[ \(TraditionalForm\`y\&^ \[Proportional] k\&^\_i\[Cross]k\&^\_f\)]], " is normal to the electron scattering plane, and ", Cell[BoxData[ \(TraditionalForm\`x\&^ = y\&^\[Cross]z\&^\)]], " is transverse within that plane. It is convenient to call this the ", StyleBox["photon", FontSlant->"Italic"], " basis. Other bases can be generated by a sequence of rotations based \ upon the matrices" }], "Text"], Cell[BoxData[{ \(\(rotz[\[Theta]_] := {{Cos[\[Theta]], \(-Sin[\[Theta]]\), 0}, {Sin[\[Theta]], Cos[\[Theta]], 0}, {0, 0, 1}};\)\), "\n", \(\(rotx[\[Theta]_] := {{1, 0, 0}, {0, Cos[\[Theta]], \(-Sin[\[Theta]]\)}, {0, Sin[\[Theta]], Cos[\[Theta]]}};\)\), "\n", \(roty[\[Theta]_] := {{Cos[\[Theta]], 0, Sin[\[Theta]]}, {0, 1, 0}, {\(-Sin[\[Theta]]\), 0, Cos[\[Theta]]}}\)}], "Input", CellLabel->"In[7]:="], Cell[TextData[{ "which generate counterclockwise rotations of a vector about the specified \ coordinate axis. Note that these matrices produce ", StyleBox["active", FontSlant->"Italic"], " rotations of a vector wrt the original coordinate system." }], "Text"], Cell[TextData[{ "Next, we define a general rotation in terms of three Euler angles \ representing rotation about ", Cell[BoxData[ \(TraditionalForm\`z\&^\)]], " through angle \[Alpha], followed by rotation about ", Cell[BoxData[ \(TraditionalForm\`\(y\^\[Prime]\)\&^\)]], " through angle \[Beta], and finally rotation about ", Cell[BoxData[ \(TraditionalForm\`\(z\^\[DoublePrime]\)\&^\)]], " through angle \[Gamma]. One can show that the same transformation is \ achieved by rotation \[Gamma] about the ", Cell[BoxData[ \(TraditionalForm\`\(z\&^\)\)]], ", followed by rotation \[Beta] about the original ", Cell[BoxData[ \(TraditionalForm\`\(y\&^\)\)]], " axis, and finally rotation \[Alpha] about the original ", Cell[BoxData[ \(TraditionalForm\`\(z\&^\)\)]], " axis, whereby" }], "Text"], Cell[BoxData[ \(euler[\[Alpha]_, \[Beta]_, \[Gamma]_] := rotz[\[Alpha]] . roty[\[Beta]] . rotz[\[Gamma]]\)], "Input", CellLabel->"In[10]:="], Cell[CellGroupData[{ Cell[BoxData[ \(euler[\[Alpha], \[Beta], \[Gamma]] // Simplify\)], "Input", CellLabel->"In[79]:="], Cell[BoxData[ \({{Cos[\[Alpha]]\ Cos[\[Beta]]\ Cos[\[Gamma]] - Sin[\[Alpha]]\ Sin[\[Gamma]], \(-Cos[\[Gamma]]\)\ Sin[\[Alpha]] - Cos[\[Alpha]]\ Cos[\[Beta]]\ Sin[\[Gamma]], Cos[\[Alpha]]\ Sin[\[Beta]]}, {Cos[\[Beta]]\ Cos[\[Gamma]]\ Sin[\ \[Alpha]] + Cos[\[Alpha]]\ Sin[\[Gamma]], Cos[\[Alpha]]\ Cos[\[Gamma]] - Cos[\[Beta]]\ Sin[\[Alpha]]\ Sin[\[Gamma]], Sin[\[Alpha]]\ Sin[\[Beta]]}, {\(-Cos[\[Gamma]]\)\ Sin[\[Beta]], Sin[\[Beta]]\ Sin[\[Gamma]], Cos[\[Beta]]}}\)], "Output", CellLabel->"Out[79]="] }, Open ]], Cell["\<\ Several special cases are shown below, where the columns provide the \ transformed basis vectors in terms of the original coordinate system.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(euler[\[Phi], 0, 0] // MatrixForm\)], "Input", CellLabel->"In[12]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(Cos[\[Phi]]\), \(-Sin[\[Phi]]\), "0"}, {\(Sin[\[Phi]]\), \(Cos[\[Phi]]\), "0"}, {"0", "0", "1"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]], "Output", CellLabel->"Out[12]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(euler[0, \[Theta], 0] // MatrixForm\)], "Input", CellLabel->"In[13]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(Cos[\[Theta]]\), "0", \(Sin[\[Theta]]\)}, {"0", "1", "0"}, {\(-Sin[\[Theta]]\), "0", \(Cos[\[Theta]]\)} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]], "Output", CellLabel->"Out[13]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(euler[\[Phi], 0, 0] . {x, y, 0}\)], "Input", CellLabel->"In[14]:="], Cell[BoxData[ \({x\ Cos[\[Phi]] - y\ Sin[\[Phi]], y\ Cos[\[Phi]] + x\ Sin[\[Phi]], 0}\)], "Output", CellLabel->"Out[14]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(euler[0, \[Theta], 0] . {x, 0, z}\)], "Input", CellLabel->"In[15]:="], Cell[BoxData[ \({x\ Cos[\[Theta]] + z\ Sin[\[Theta]], 0, z\ Cos[\[Theta]] - x\ Sin[\[Theta]]}\)], "Output", CellLabel->"Out[15]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Normalized cross product", "Subsection"], Cell["\<\ It will be useful to define a vector cross product with unit normalization.\ \>", "Text"], Cell[BoxData[ \(NormalizedCrossProduct[a_, b_] := Module[{c}, c = Cross[a, b]; Simplify[c/\@\(c . c\)]]\)], "Input", CellLabel->"In[16]:="] }, Open ]], Cell[CellGroupData[{ Cell["Transformation matrices", "Subsection"], Cell[TextData[{ "The following function constructs the transformation matrix from ", StyleBox["basis1", FontSlant->"Italic"], " to ", StyleBox["basis2", FontSlant->"Italic"], ". Note that this is a passive rotation of the coordinate system and \ produces the polarization components with respect to the new basis." }], "Text"], Cell[BoxData[ \(TransformationMatrix[basis2_, basis1_] := Table[Dot[basis1\[LeftDoubleBracket]i\[RightDoubleBracket], basis2\[LeftDoubleBracket]j\[RightDoubleBracket]], {j, 1, 3}, {i, 1, 3}] // Simplify\)], "Input", CellLabel->"In[17]:="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Reaction basis", "Section"], Cell[TextData[{ "The most common basis places the longitudinal direction along the \ momentum, normal perpendicular to the reaction plane, and transverse in the \ reaction plane. We denote the ", StyleBox["reaction basis", FontSlant->"Italic"], StyleBox[" ", FontWeight->"Bold", FontSlant->"Italic"], "vectors", StyleBox[" ", FontWeight->"Bold", FontSlant->"Italic"], Cell[BoxData[ \({\(t\&^\), \(n\&^\), \(\[ScriptL]\&^\)}\)]], StyleBox[". ", FontWeight->"Bold", FontSlant->"Italic"], "Let \[Phi] represent the dihedral angle between the scattering and \ reaction planes and \[Theta] represent the polar angle between the ejectile \ momentum and the virtual photon. The basis vectors then become" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({t\&^, n\&^, \[ScriptL]\&^} = Transpose[euler[\[Phi], \[Theta], 0]] // Simplify\)], "Input", CellLabel->"In[18]:="], Cell[BoxData[ \({{Cos[\[Theta]]\ Cos[\[Phi]], Cos[\[Theta]]\ Sin[\[Phi]], \(-Sin[\[Theta]]\)}, {\(-Sin[\[Phi]]\), Cos[\[Phi]], 0}, {Cos[\[Phi]]\ Sin[\[Theta]], Sin[\[Theta]]\ Sin[\[Phi]], Cos[\[Theta]]}}\)], "Output", CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(euler[\[Phi], \[Theta], 0] . {0, 0, 1}\)], "Input", CellLabel->"In[19]:="], Cell[BoxData[ \({Cos[\[Phi]]\ Sin[\[Theta]], Sin[\[Theta]]\ Sin[\[Phi]], Cos[\[Theta]]}\)], "Output", CellLabel->"Out[19]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(euler[\[Phi], \[Theta], 0] . {1, 0, 0}\)], "Input", CellLabel->"In[20]:="], Cell[BoxData[ \({Cos[\[Theta]]\ Cos[\[Phi]], Cos[\[Theta]]\ Sin[\[Phi]], \(-Sin[\[Theta]]\)}\)], "Output", CellLabel->"Out[20]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(n\&^ /. \[Phi] \[Rule] 0\)], "Input", CellLabel->"In[21]:="], Cell[BoxData[ \({0, 1, 0}\)], "Output", CellLabel->"Out[21]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t\&^ /. \[Phi] \[Rule] 0\)], "Input", CellLabel->"In[22]:="], Cell[BoxData[ \({Cos[\[Theta]], 0, \(-Sin[\[Theta]]\)}\)], "Output", CellLabel->"Out[22]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(t\&^ /. \[Phi] \[Rule] \[Pi]\/2\)], "Input", CellLabel->"In[23]:="], Cell[BoxData[ \({0, Cos[\[Theta]], \(-Sin[\[Theta]]\)}\)], "Output", CellLabel->"Out[23]="] }, Open ]], Cell[TextData[{ "Unfortunately, the reaction basis has the undesirable property that its \ vertical component reverses sign as ", Cell[BoxData[ \(TraditionalForm\`\(p\&^\)\)]], " moves from one side of ", Cell[BoxData[ \(TraditionalForm\`\(q\&^\)\)]], " to the other." }], "Text"], Cell[BoxData[ \(\(ReactionBasis = {t\&^, n\&^, \[ScriptL]\&^};\)\)], "Input", CellLabel->"In[24]:="], Cell[CellGroupData[{ Cell[BoxData[ \(ReactionBasis /. \[Phi] \[Rule] 0 // Simplify\)], "Input", CellLabel->"In[25]:="], Cell[BoxData[ \({{Cos[\[Theta]], 0, \(-Sin[\[Theta]]\)}, {0, 1, 0}, {Sin[\[Theta]], 0, Cos[\[Theta]]}}\)], "Output", CellLabel->"Out[25]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ReactionBasis /. \[Phi] \[Rule] \[Pi] // Simplify\)], "Input", CellLabel->"In[26]:="], Cell[BoxData[ \({{\(-Cos[\[Theta]]\), 0, \(-Sin[\[Theta]]\)}, {0, \(-1\), 0}, {\(-Sin[\[Theta]]\), 0, Cos[\[Theta]]}}\)], "Output", CellLabel->"Out[26]="] }, Open ]], Cell[TextData[{ "Similarly, ", Cell[BoxData[ \(TraditionalForm\`t\&^ . x\&^\)]], " also reverses sign abruptly. These sign reversals are reflected in \ abrupt changes in the polarization components on either side of ", Cell[BoxData[ \(TraditionalForm\`q\&^\)]], ". Smoother behavior is achieved using the ", StyleBox["polarimeter", FontSlant->"Italic"], " basis developed below. First, however, we give the matrix which \ transforms the polarization components from the reaction basis to the photon \ basis." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(ReactionToPhoton = TransformationMatrix[IdentityMatrix[3], ReactionBasis];\)\), "\n", \(MatrixForm[ReactionToPhoton]\)}], "Input", CellLabel->"In[27]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(Cos[\[Theta]]\ Cos[\[Phi]]\), \(-Sin[\[Phi]]\), \(Cos[\[Phi]]\ \ Sin[\[Theta]]\)}, {\(Cos[\[Theta]]\ Sin[\[Phi]]\), \(Cos[\[Phi]]\), \(Sin[\[Theta]]\ \ Sin[\[Phi]]\)}, {\(-Sin[\[Theta]]\), "0", \(Cos[\[Theta]]\)} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]], "Output", CellLabel->"Out[28]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ReactionToPhoton . {P\_t, P\_n, P\_\[ScriptL]} // ColumnForm\)], "Input",\ CellLabel->"In[29]:="], Cell[BoxData[ InterpretationBox[GridBox[{ {\(\(-Sin[\[Phi]]\)\ P\_n + Cos[\[Theta]]\ Cos[\[Phi]]\ P\_t + Cos[\[Phi]]\ Sin[\[Theta]]\ P\_\[ScriptL]\)}, {\(Cos[\[Phi]]\ P\_n + Cos[\[Theta]]\ Sin[\[Phi]]\ P\_t + Sin[\[Theta]]\ Sin[\[Phi]]\ P\_\[ScriptL]\)}, {\(\(-Sin[\[Theta]]\)\ P\_t + Cos[\[Theta]]\ P\_\[ScriptL]\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ { Plus[ Times[ -1, Sin[ \[Phi]], Subscript[ P, n]], Times[ Cos[ \[Theta]], Cos[ \[Phi]], Subscript[ P, t]], Times[ Cos[ \[Phi]], Sin[ \[Theta]], Subscript[ P, \[ScriptL]]]], Plus[ Times[ Cos[ \[Phi]], Subscript[ P, n]], Times[ Cos[ \[Theta]], Sin[ \[Phi]], Subscript[ P, t]], Times[ Sin[ \[Theta]], Sin[ \[Phi]], Subscript[ P, \[ScriptL]]]], Plus[ Times[ -1, Sin[ \[Theta]], Subscript[ P, t]], Times[ Cos[ \[Theta]], Subscript[ P, \[ScriptL]]]]}], Editable->False]], "Output", CellLabel->"Out[29]="] }, Open ]], Cell[TextData[{ "Notice that if the acceptance is symmetric wrt the scattering plane, the \ ", Cell[BoxData[ \(TraditionalForm\`\(x\&^\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(z\&^\)\)]], " components are determined by orthogonal linear combinations of the \ helicity dependent ", Cell[BoxData[ \(TraditionalForm\`\(t\&^\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(\[ScriptL]\&^\)\)]], " components while the ", Cell[BoxData[ \(TraditionalForm\`\(y\&^\)\)]], " component is determined by the helicity-independent ", Cell[BoxData[ \(TraditionalForm\`\(n\&^\)\)]], " component of polarization. " }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Polarimeter basis", "Section"], Cell[CellGroupData[{ Cell["Derivation based upon vector cross product", "Subsection"], Cell[TextData[{ "In this section we derive an alternative {", Cell[BoxData[ \(TraditionalForm\`\(a\&^\)\)]], ",", Cell[BoxData[ \(TraditionalForm\`\(b\&^\)\)]], ",", Cell[BoxData[ \(TraditionalForm\`\(c\&^\)\)]], "} basis that avoids the inconvenient sign reversals exhibited by the \ reaction basis as ", Cell[BoxData[ \(TraditionalForm\`\(p\&^\)\)]], " moves from one side of ", Cell[BoxData[ \(TraditionalForm\`\(q\&^\)\)]], " to the other. We call this the polarimeter basis because a nonmagnetic \ polarimeter with small acceptance would naturally be placed with its central \ ", Cell[BoxData[ \(TraditionalForm\`c\&^\)]], StyleBox[" ", FontSlant->"Italic"], "axis along the ejectile momentum and its sideways ", Cell[BoxData[ \(TraditionalForm\`a\&^\)]], " axis parallel to the scattering plane, which is normally horizontal in \ the lab. Furthermore, since we would not turn the polarimeter upside down, \ we would like to keep the vertical component of ", Cell[BoxData[ \(TraditionalForm\`\(b\&^\)\)]], " positive. It is simplect to construct the polarimeter basis using ", Cell[BoxData[ \(TraditionalForm\`\(c\&^\) = \[ScriptL]\&^\)]], ", ", Cell[BoxData[ \(TraditionalForm\`a\&^ \[Proportional] y\&^\[Cross]\[ScriptL]\&^\)]], ", and ", Cell[BoxData[ \(TraditionalForm\`b\&^ = c\&^\[Cross]a\&^\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(c\&^ = \[ScriptL]\&^\)], "Input", CellLabel->"In[30]:="], Cell[BoxData[ \({Cos[\[Phi]]\ Sin[\[Theta]], Sin[\[Theta]]\ Sin[\[Phi]], Cos[\[Theta]]}\)], "Output", CellLabel->"Out[30]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(a\&^ = NormalizedCrossProduct[{0, 1, 0}, \[ScriptL]\&^]\)], "Input", CellLabel->"In[31]:="], Cell[BoxData[ \({Cos[\[Theta]]\/\@\(Cos[\[Theta]]\^2 + Cos[\[Phi]]\^2\ Sin[\[Theta]]\^2\ \), 0, \(-\(\(Cos[\[Phi]]\ Sin[\[Theta]]\)\/\@\(Cos[\[Theta]]\^2 + \ Cos[\[Phi]]\^2\ Sin[\[Theta]]\^2\)\)\)}\)], "Output", CellLabel->"Out[31]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(b\&^ = Cross[c\&^, a\&^] // Simplify\)], "Input", CellLabel->"In[32]:="], Cell[BoxData[ \({\(-\(\(Cos[\[Phi]]\ Sin[\[Theta]]\^2\ Sin[\[Phi]]\)\/\@\(Cos[\[Theta]]\ \^2 + Cos[\[Phi]]\^2\ Sin[\[Theta]]\^2\)\)\), \@\(Cos[\[Theta]]\^2 + Cos[\ \[Phi]]\^2\ Sin[\[Theta]]\^2\), \(-\(\(Cos[\[Theta]]\ Sin[\[Theta]]\ Sin[\ \[Phi]]\)\/\@\(Cos[\[Theta]]\^2 + Cos[\[Phi]]\^2\ Sin[\[Theta]]\^2\)\)\)}\)], \ "Output", CellLabel->"Out[32]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(a\&^ . b\&^ == b\&^ . c\&^ == a\&^ . c\&^ == 0 // Simplify\)], "Input", CellLabel->"In[33]:="], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[33]="] }, Open ]], Cell[TextData[{ "In contrast with the reaction basis, the polarimeter basis has the \ desirable property that its vertical component is always positive and that ", Cell[BoxData[ \(TraditionalForm\`\(\(a . \)\&^\) \(x\&^\)\)]], " does not reverse sign as ", Cell[BoxData[ \(TraditionalForm\`\(p\&^\)\)]], " moves from one side of ", Cell[BoxData[ \(TraditionalForm\`\(q\&^\)\)]], " to the other." }], "Text"], Cell[BoxData[ \(\(PolarimeterBasis = {a\&^, b\&^, c\&^};\)\)], "Input", CellLabel->"In[34]:="], Cell[CellGroupData[{ Cell[BoxData[ \(PolarimeterBasis /. \[Phi] \[Rule] 0 // Simplify\)], "Input", CellLabel->"In[35]:="], Cell[BoxData[ \({{Cos[\[Theta]], 0, \(-Sin[\[Theta]]\)}, {0, 1, 0}, {Sin[\[Theta]], 0, Cos[\[Theta]]}}\)], "Output", CellLabel->"Out[35]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(PolarimeterBasis /. \[Phi] \[Rule] \[Pi] // Simplify\)], "Input", CellLabel->"In[36]:="], Cell[BoxData[ \({{Cos[\[Theta]], 0, Sin[\[Theta]]}, {0, 1, 0}, {\(-Sin[\[Theta]]\), 0, Cos[\[Theta]]}}\)], "Output", CellLabel->"Out[36]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Derivation using rotation matrix", "Subsection"], Cell[TextData[{ "It is also instructive to express the polarimeter basis in terms of Euler \ angles. This basis can be obtained from the reaction basis using a final \ rotation about the ", Cell[BoxData[ \(TraditionalForm\`\[ScriptL]\&^\)]], " axis through an angle \[Psi] designed to eliminate ", Cell[BoxData[ \(TraditionalForm\`a\&^ . \(y\&^\)\)]], ". Trial solutions are obtained by solving the following equation." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(eq = 0 == Part[Transpose[euler[\[Phi], \[Theta], \[Psi]temp]], 1, 2]\)], "Input", CellLabel->"In[37]:="], Cell[BoxData[ \(0 == Cos[\[Theta]]\ Cos[\[Psi]temp]\ Sin[\[Phi]] + Cos[\[Phi]]\ Sin[\[Psi]temp]\)], "Output", CellLabel->"Out[37]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(sol = Solve[eq, \[Psi]temp]\)], "Input", CellLabel->"In[38]:="], Cell[BoxData[ \(Solve::"ifun" \(\(:\)\(\ \)\) "Inverse functions are being used by \!\(Solve\), so some solutions may \ not be found."\)], "Message", CellLabel->"From In[38]:="], Cell[BoxData[ \({{\[Psi]temp \[Rule] \(-ArcCos[\(-\(Cos[\[Phi]]\/\@\(Cos[\[Phi]]\^2 + \ Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2\)\)\)]\)}, {\[Psi]temp \[Rule] ArcCos[\(-\(Cos[\[Phi]]\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ \ Sin[\[Phi]]\^2\)\)\)]}, {\[Psi]temp \[Rule] \(-ArcCos[ Cos[\[Phi]]\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\[Phi]]\ \^2\)]\)}, {\[Psi]temp \[Rule] ArcCos[Cos[\[Phi]]\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\ \[Phi]]\^2\)]}}\)], "Output", CellLabel->"Out[38]="] }, Open ]], Cell["\<\ To choose between these solutions we must impose a subsidiary condition. \ Since we would not turn the polarimeter upside down, we would like to keep \ the vertical component of the second basis vector positive.\ \>", "Text"], Cell[BoxData[ \(by[\[Psi]_] := Part[Transpose[euler[\[Phi], \[Theta], \[Psi]]], 2, 2] // Simplify\)], "Input", CellLabel->"In[39]:="], Cell[CellGroupData[{ Cell[BoxData[ \(bytemp = by[\[Psi]temp] /. sol\)], "Input", CellLabel->"In[40]:="], Cell[BoxData[ \({\(-\(Cos[\[Phi]]\^2\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ \ Sin[\[Phi]]\^2\)\)\) + Cos[\[Theta]]\ Sin[\[Phi]]\ \@\(1 - Cos[\[Phi]]\^2\/\(Cos[\[Phi]]\^2 \ + Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2\)\), \ \(-\(Cos[\[Phi]]\^2\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ \ Sin[\[Phi]]\^2\)\)\) - Cos[\[Theta]]\ Sin[\[Phi]]\ \@\(1 - Cos[\[Phi]]\^2\/\(Cos[\[Phi]]\^2 \ + Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2\)\), Cos[\[Phi]]\^2\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2\) \ + Cos[\[Theta]]\ Sin[\[Phi]]\ \@\(1 - Cos[\[Phi]]\^2\/\(Cos[\[Phi]]\^2 + Cos[\ \[Theta]]\^2\ Sin[\[Phi]]\^2\)\), Cos[\[Phi]]\^2\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2\) \ - Cos[\[Theta]]\ Sin[\[Phi]]\ \@\(1 - Cos[\[Phi]]\^2\/\(Cos[\[Phi]]\^2 + Cos[\ \[Theta]]\^2\ Sin[\[Phi]]\^2\)\)}\)], "Output", CellLabel->"Out[40]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[ Sign[bytemp] /. {\[Theta] \[Rule] \[Pi]\/4}, {\[Phi], \[Pi]\/4, 7 \[Pi]\/4, \[Pi]\/4}] // MatrixForm\)], "Input", CellLabel->"In[41]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(-1\), \(-1\), "1", "1"}, {"1", \(-1\), "1", \(-1\)}, {\(-1\), \(-1\), "1", "1"}, {\(-1\), \(-1\), "1", "1"}, {\(-1\), \(-1\), "1", "1"}, {\(-1\), "1", \(-1\), "1"}, {\(-1\), \(-1\), "1", "1"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]], "Output", CellLabel->"Out[41]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[ Sign[bytemp] /. {\[Theta] \[Rule] \(3 \[Pi]\)\/4}, {\[Phi], \ \[Pi]\/4, 7 \[Pi]\/4, \[Pi]\/4}] // MatrixForm\)], "Input", CellLabel->"In[42]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(-1\), \(-1\), "1", "1"}, {\(-1\), "1", \(-1\), "1"}, {\(-1\), \(-1\), "1", "1"}, {\(-1\), \(-1\), "1", "1"}, {\(-1\), \(-1\), "1", "1"}, {"1", \(-1\), "1", \(-1\)}, {\(-1\), \(-1\), "1", "1"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]], "Output", CellLabel->"Out[42]//MatrixForm="] }, Open ]], Cell[TextData[{ "Unfortunately, it is not possible to obtain this behavior from a single \ solution; the form of these solutions also presents problems when ", StyleBox["PowerExpand", FontWeight->"Bold"], " is used to simplify subsequent results. Recognizing that for most \ orientations either solution 3 or solution 4 yields the desired behavior, we \ attempt to find a simpler solution using ", StyleBox["PowerExpand", FontWeight->"Bold"] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\[Psi]3 = \[Psi]temp /. sol\[LeftDoubleBracket]3\[RightDoubleBracket];\)\), "\n", \(\({Cos[\[Psi]3], Sin[\[Psi]3], Tan[\[Psi]3]} // Simplify\) // PowerExpand\)}], "Input", CellLabel->"In[43]:="], Cell[BoxData[ \({Cos[\[Phi]]\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2\), \ \(-\(\(Cos[\[Theta]]\ Sin[\[Phi]]\)\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ \ Sin[\[Phi]]\^2\)\)\), \(-Cos[\[Theta]]\)\ Tan[\[Phi]]}\)], "Output", CellLabel->"Out[44]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\[Psi]4 = \[Psi]temp /. sol\[LeftDoubleBracket]4\[RightDoubleBracket];\)\), "\n", \(\({Cos[\[Psi]4], Sin[\[Psi]4], Tan[\[Psi]4]} // Simplify\) // PowerExpand\)}], "Input", CellLabel->"In[45]:="], Cell[BoxData[ \({Cos[\[Phi]]\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2\), \ \(Cos[\[Theta]]\ Sin[\[Phi]]\)\/\@\(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\ \[Phi]]\^2\), Cos[\[Theta]]\ Tan[\[Phi]]}\)], "Output", CellLabel->"Out[46]="] }, Open ]], Cell[TextData[{ "Actually, it is more efficient to identify ", Cell[BoxData[ \(TraditionalForm\`{Cos[\[Psi]], Sin[\[Psi]]}\)]], " with the projections of ", Cell[BoxData[ \(TraditionalForm\`\(a\&^\)\)]], " upon ", Cell[BoxData[ \(TraditionalForm\`\(t\&^\)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(n\&^\)\)]], ", whereby" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({a\&^ . t\&^, a\&^ . n\&^} // Simplify\)], "Input", CellLabel->"In[47]:="], Cell[BoxData[ \({Cos[\[Phi]]\/\@\(Cos[\[Theta]]\^2 + Cos[\[Phi]]\^2\ \ Sin[\[Theta]]\^2\), \(-\(\(Cos[\[Theta]]\ Sin[\[Phi]]\)\/\@\(Cos[\[Theta]]\^2 \ + Cos[\[Phi]]\^2\ Sin[\[Theta]]\^2\)\)\)}\)], "Output", CellLabel->"Out[47]="] }, Open ]], Cell["\<\ Thus, we demonstrate that the following representation does ensure a positive \ vertical component.\ \>", "Text"], Cell[BoxData[ \(\(\[Psi]sol = ArcTan[Cos[\[Phi]], \(-Cos[\[Theta]]\)\ Sin[\[Phi]]];\)\)], "Input", CellLabel->"In[48]:="], Cell[BoxData[ \(\(bytemp2 = by[\[Psi]sol];\)\)], "Input", CellLabel->"In[49]:="], Cell[CellGroupData[{ Cell[BoxData[ \(Table[ Sign[bytemp2] /. {\[Theta] \[Rule] \[Pi]\/4}, {\[Phi], \[Pi]\/4, 7 \[Pi]\/4, \[Pi]\/4}] // MatrixForm\)], "Input", CellLabel->"In[50]:="], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"1"}, {"1"}, {"1"}, {"1"}, {"1"}, {"1"} }], "\[NoBreak]", ")"}], MatrixForm[ {1, 1, 1, 1, 1, 1, 1}]]], "Output", CellLabel->"Out[50]//MatrixForm="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Table[ Sign[bytemp2] /. {\[Theta] \[Rule] \(3 \[Pi]\)\/4}, {\[Phi], \ \[Pi]\/4, 7 \[Pi]\/4, \[Pi]\/4}] // MatrixForm\)], "Input", CellLabel->"In[51]:="], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1"}, {"1"}, {"1"}, {"1"}, {"1"}, {"1"}, {"1"} }], "\[NoBreak]", ")"}], MatrixForm[ {1, 1, 1, 1, 1, 1, 1}]]], "Output", CellLabel->"Out[51]//MatrixForm="] }, Open ]], Cell[TextData[ "Therefore, although it is difficult to obtain simple symbolic results, we \ have found a symbolic expression that appears to give the desired rotation \ for any choice of \[Theta] and \[Phi]."], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[ Table[\[Psi]sol, {\[Theta], 0, \[Pi]\/2, \[Pi]\/16}]], {\[Phi], 0, 2 \[Pi]}];\)\)], "Input", CellLabel->"In[52]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.151576 0.30897 0.0936943 [ [.17539 .29647 -3 -9 ] [.17539 .29647 3 0 ] [.32696 .29647 -3 -9 ] [.32696 .29647 3 0 ] [.47854 .29647 -3 -9 ] [.47854 .29647 3 0 ] [.63011 .29647 -3 -9 ] [.63011 .29647 3 0 ] [.78169 .29647 -3 -9 ] [.78169 .29647 3 0 ] [.93327 .29647 -3 -9 ] [.93327 .29647 3 0 ] [.01131 .02789 -12 -4.5 ] [.01131 .02789 0 4.5 ] [.01131 .12158 -12 -4.5 ] [.01131 .12158 0 4.5 ] [.01131 .21528 -12 -4.5 ] [.01131 .21528 0 4.5 ] [.01131 .40266 -6 -4.5 ] [.01131 .40266 0 4.5 ] [.01131 .49636 -6 -4.5 ] [.01131 .49636 0 4.5 ] [.01131 .59005 -6 -4.5 ] [.01131 .59005 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .30897 m .17539 .31522 L s [(1)] .17539 .29647 0 1 Mshowa .32696 .30897 m .32696 .31522 L s [(2)] .32696 .29647 0 1 Mshowa .47854 .30897 m .47854 .31522 L s [(3)] .47854 .29647 0 1 Mshowa .63011 .30897 m .63011 .31522 L s [(4)] .63011 .29647 0 1 Mshowa .78169 .30897 m .78169 .31522 L s [(5)] .78169 .29647 0 1 Mshowa .93327 .30897 m .93327 .31522 L s [(6)] .93327 .29647 0 1 Mshowa .125 Mabswid .05412 .30897 m .05412 .31272 L s .08444 .30897 m .08444 .31272 L s .11476 .30897 m .11476 .31272 L s .14507 .30897 m .14507 .31272 L s .2057 .30897 m .2057 .31272 L s .23602 .30897 m .23602 .31272 L s .26633 .30897 m .26633 .31272 L s .29665 .30897 m .29665 .31272 L s .35728 .30897 m .35728 .31272 L s .38759 .30897 m .38759 .31272 L s .41791 .30897 m .41791 .31272 L s .44822 .30897 m .44822 .31272 L s .50885 .30897 m .50885 .31272 L s .53917 .30897 m .53917 .31272 L s .56948 .30897 m .56948 .31272 L s .5998 .30897 m .5998 .31272 L s .66043 .30897 m .66043 .31272 L s .69074 .30897 m .69074 .31272 L s .72106 .30897 m .72106 .31272 L s .75138 .30897 m .75138 .31272 L s .81201 .30897 m .81201 .31272 L s .84232 .30897 m .84232 .31272 L s .87264 .30897 m .87264 .31272 L s .90295 .30897 m .90295 .31272 L s .96358 .30897 m .96358 .31272 L s .9939 .30897 m .9939 .31272 L s .25 Mabswid 0 .30897 m 1 .30897 L s .02381 .02789 m .03006 .02789 L s [(-3)] .01131 .02789 1 0 Mshowa .02381 .12158 m .03006 .12158 L s [(-2)] .01131 .12158 1 0 Mshowa .02381 .21528 m .03006 .21528 L s [(-1)] .01131 .21528 1 0 Mshowa .02381 .40266 m .03006 .40266 L s [(1)] .01131 .40266 1 0 Mshowa .02381 .49636 m .03006 .49636 L s [(2)] .01131 .49636 1 0 Mshowa .02381 .59005 m .03006 .59005 L s [(3)] .01131 .59005 1 0 Mshowa .125 Mabswid .02381 .04663 m .02756 .04663 L s .02381 .06536 m .02756 .06536 L s .02381 .0841 m .02756 .0841 L s .02381 .10284 m .02756 .10284 L s .02381 .14032 m .02756 .14032 L s .02381 .15906 m .02756 .15906 L s .02381 .1778 m .02756 .1778 L s .02381 .19654 m .02756 .19654 L s .02381 .23401 m .02756 .23401 L s .02381 .25275 m .02756 .25275 L s .02381 .27149 m .02756 .27149 L s .02381 .29023 m .02756 .29023 L s .02381 .32771 m .02756 .32771 L s .02381 .34645 m .02756 .34645 L s .02381 .36519 m .02756 .36519 L s .02381 .38393 m .02756 .38393 L s .02381 .4214 m .02756 .4214 L s .02381 .44014 m .02756 .44014 L s .02381 .45888 m .02756 .45888 L s .02381 .47762 m .02756 .47762 L s .02381 .5151 m .02756 .5151 L s .02381 .53384 m .02756 .53384 L s .02381 .55257 m .02756 .55257 L s .02381 .57131 m .02756 .57131 L s .02381 .00915 m .02756 .00915 L s .02381 .60879 m .02756 .60879 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30897 m .06244 .28509 L .10458 .25904 L .14415 .23458 L .18221 .21106 L .22272 .18602 L .26171 .16192 L .30316 .1363 L .34309 .11161 L .3815 .08787 L .42237 .06261 L .46172 .03828 L .48147 .02607 L .49012 .02073 L .49468 .01791 L .49719 .01636 L .49842 .0156 L .49955 .0149 L .50085 .60279 L .50154 .60237 L .50226 .60192 L .50471 .60041 L .5095 .59745 L .51896 .5916 L .53984 .57869 L .57781 .55522 L .61824 .53023 L .65714 .50618 L .6985 .48062 L .73835 .45599 L .77668 .43229 L .81746 .40709 L .85673 .38281 L .89448 .35948 L .93468 .33463 L .97337 .31071 L .97619 .30897 L s .02381 .30897 m .06244 .28553 L .10458 .25983 L .14415 .23549 L .18221 .21185 L .22272 .18647 L .26171 .16192 L .30316 .13582 L .34309 .11081 L .3815 .08696 L .42237 .06184 L .46172 .03785 L .48147 .02585 L .49012 .02061 L .49468 .01784 L .49719 .01632 L .49842 .01558 L .49955 .01489 L .50085 .6028 L .50154 .60239 L .50226 .60195 L .50471 .60046 L .5095 .59756 L .51896 .59182 L .53984 .57915 L .57781 .556 L .61824 .53114 L .65714 .50698 L .6985 .48107 L .73835 .45598 L .77668 .43185 L .81746 .40629 L .85673 .3819 L .89448 .35868 L .93468 .33416 L .97337 .31068 L .97619 .30897 L s .02381 .30897 m .06244 .28684 L .10458 .26222 L .14415 .23829 L .18221 .21434 L .22272 .18792 L .26171 .16193 L .30316 .13431 L .34309 .1083 L .3815 .08417 L .42237 .05951 L .46172 .03655 L .48147 .02521 L .49012 .02027 L .49468 .01766 L .49719 .01622 L .49842 .01552 L .49955 .01488 L .50085 .60283 L .50154 .60244 L .50226 .60203 L .50471 .60063 L .5095 .59789 L .51896 .59248 L .53984 .58049 L .57781 .55833 L .61824 .53394 L .65714 .50949 L .6985 .48253 L .73835 .45597 L .77668 .43042 L .81746 .40381 L .85673 .37911 L .89448 .35627 L .93468 .33276 L .97337 .31058 L .97619 .30897 L s .02381 .30897 m .06244 .28898 L .10458 .26625 L .14415 .24319 L .18221 .21888 L .22272 .19065 L .26171 .16194 L .30316 .13146 L .34309 .10372 L .3815 .07928 L .42237 .05559 L .46172 .03443 L .48147 .02416 L .49012 .0197 L .49468 .01735 L .49719 .01606 L .49842 .01543 L .49955 .01485 L .50085 .60288 L .50154 .60253 L .50226 .60216 L .50471 .6009 L .5095 .59843 L .51896 .59356 L .53984 .5827 L .57781 .56225 L .61824 .53882 L .65714 .51407 L .6985 .48529 L .73835 .45595 L .77668 .42773 L .81746 .39928 L .85673 .37421 L .89448 .35221 L .93468 .33047 L .97337 .31042 L .97619 .30897 L s .02381 .30897 m .06244 .2919 L .10458 .27195 L .14415 .25055 L .18221 .22618 L .22272 .19533 L .26171 .16197 L .30316 .12658 L .34309 .09638 L .3815 .07197 L .42237 .05007 L .46172 .03153 L .48147 .02274 L .49012 .01894 L .49468 .01694 L .49719 .01585 L .49842 .01531 L .49955 .01482 L .50085 .60295 L .50154 .60265 L .50226 .60233 L .50471 .60126 L .5095 .59916 L .51896 .59501 L .53984 .5857 L .57781 .56778 L .61824 .54612 L .65714 .5214 L .6985 .49001 L .73835 .45592 L .77668 .42311 L .81746 .39199 L .85673 .36688 L .89448 .34646 L .93468 .32734 L .97337 .3102 L .97619 .30897 L s .02381 .30897 m .06244 .2955 L .10458 .2793 L .14415 .26077 L .18221 .23742 L .22272 .20342 L .26171 .16201 L .30316 .11818 L .34309 .08512 L .3815 .06185 L .42237 .04299 L .46172 .02796 L .48147 .021 L .49012 .01802 L .49468 .01645 L .49719 .01559 L .49842 .01516 L .49955 .01477 L .50085 .60303 L .50154 .60279 L .50226 .60254 L .50471 .6017 L .5095 .60005 L .51896 .59678 L .53984 .58942 L .57781 .57488 L .61824 .55623 L .65714 .53266 L .6985 .49816 L .73835 .45586 L .77668 .41511 L .81746 .38075 L .85673 .3567 L .89448 .33903 L .93468 .32347 L .97337 .30994 L .97619 .30897 L s .02381 .30897 m .06244 .29966 L .10458 .28817 L .12507 .28149 L .14415 .27419 L .16371 .2651 L .18221 .25434 L .20263 .23887 L .2212 .22021 L .25962 .16549 L .27906 .13474 L .30048 .10586 L .3208 .08505 L .33983 .07042 L .36008 .0585 L .3786 .04984 L .41831 .0357 L .45651 .02516 L .47782 .0199 L .48789 .01749 L .4923 .01644 L .49481 .01585 L .49715 .01529 L .49832 .01502 L .49942 .01476 L .5007 .60315 L .50186 .60288 L .50683 .6017 L .5173 .59921 L .53628 .59459 L .57461 .58435 L .594 .57833 L .61539 .57056 L .63588 .56149 L .65466 .55108 L .67401 .53729 L .69486 .5174 L .71379 .49362 L .73449 .46197 L .75574 .42836 L .77505 .40214 L .79513 .38106 L .81409 .36608 L .83411 .35398 L .85256 .34515 L .89196 .33083 L .92985 .32023 L .97019 .31039 L .97619 .30897 L s .02381 .30897 m .06244 .30421 L .10458 .29824 L .12507 .29466 L .14415 .29061 L .16254 .28569 L .18221 .27858 L .19242 .27369 L .20351 .26695 L .21399 .25858 L .22365 .24828 L .23332 .23435 L .24238 .21671 L .25232 .19121 L .263 .15831 L .27311 .1278 L .28414 .10107 L .29456 .08284 L .30423 .0706 L .3148 .06074 L .32475 .05371 L .34336 .04427 L .35312 .04055 L .36344 .03725 L .38191 .03245 L .41988 .02525 L .46031 .01952 L .47894 .01718 L .48877 .01598 L .49416 .01533 L .4968 .01501 L .49795 .01487 L .49921 .01472 L .50044 .60327 L .50174 .60311 L .50446 .60278 L .51025 .60208 L .52045 .60084 L .54057 .59831 L .58114 .59253 L .62018 .585 L .64153 .57917 L .65132 .57578 L .66168 .57147 L .67121 .56662 L .68169 .55989 L .69123 .55195 L .70014 .54226 L .71055 .52692 L .72043 .50678 L Mistroke .73897 .45338 L .74931 .42212 L .75904 .39812 L .76778 .38178 L .77721 .3686 L .78749 .35803 L .79693 .35068 L .80714 .34448 L .81791 .33931 L .83759 .33221 L .85594 .3273 L .8949 .31979 L .93631 .31389 L .97619 .30897 L Mfstroke .02381 .30897 m .06244 .30897 L .10458 .30897 L .14415 .30897 L .18221 .30897 L .22272 .30897 L .24141 .30897 L .25127 .30897 L .25666 .30897 L .2593 .30897 L .26045 .30897 L .26171 .30897 L .26301 .60332 L .26425 .60332 L .26698 .60332 L .27279 .60332 L .28302 .60332 L .30316 .60332 L .3438 .60332 L .38293 .60332 L .42451 .60332 L .46458 .60332 L .50313 .60332 L .54413 .60332 L .58362 .60332 L .62159 .60332 L .66202 .60332 L .70093 .60332 L .7111 .60332 L .72217 .60332 L .72723 .60332 L .73262 .60332 L .73483 .60332 L .73599 .60332 L .73721 .60332 L .73786 .60332 L .73858 .30897 L .73983 .30897 L .74229 .30897 L .78285 .30897 L .82189 .30897 L .86339 .30897 L .90337 .30897 L .94184 .30897 L .97619 .30897 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[52]:=", ImageSize->{288, 177.938}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`030000003oool0oooo08X0oooo000?0?ooo`030000 003oool0oooo0540oooo00<000000?ooo`3oool02@3oool2000000D0oooo0P0000030?ooo`800000 0P3oool400000100oooo00<000000?ooo`3oool0RP3oool000l0oooo00<000000?ooo`3oool0C`3o ool2000000X0oooo0P0000050?ooo`8000000`3oool200000080oooo1000000B0?ooo`030000003o ool0oooo08X0oooo000?0?ooo`030000003oool0oooo04h0oooo00<000000?ooo`3oool0203oool2 000000D0oooo0P0000030?ooo`8000000P3oool4000001@0oooo00<000000?ooo`3oool0RP3oool0 00l0oooo0P00001>0?ooo`030000003oool0oooo00P0oooo00<000000?ooo`3oool00`3oool20000 00<0oooo0P0000020?ooo`D000005@3oool00`000000oooo0?ooo`2:0?ooo`003`3oool00`000000 oooo0?ooo`1<0?ooo`030000003oool0oooo00L0oooo0P0000050?ooo`040000003oool0oooo0?oo o`8000000P3oool5000001L0oooo00<000000?ooo`3oool0RP3oool000l0oooo00<000000?ooo`3o ool0B`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00<0oooo0P0000030?ooo`03 0000003oool0oooo00H00000603oool00`000000oooo0?ooo`2:0?ooo`003`3oool00`000000oooo 0?ooo`1:0?ooo`030000003oool0oooo00L0oooo00<000000?ooo`3oool00`3oool010000000oooo 0?ooo`3oool2000000030?ooo`000000000000@000006P3oool00`000000oooo0?ooo`2:0?ooo`00 3`3oool00`000000oooo0?ooo`190?ooo`030000003oool0oooo00H0oooo0P0000050?ooo`050000 003oool0oooo0?ooo`0000000P3oool6000001/0oooo00<000000?ooo`3oool0RP3oool000l0oooo 0P0000190?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool00`3oool200000080oooo 0P0000000`3oool0000000000004000001d0oooo00<000000?ooo`3oool0RP3oool000l0oooo00<0 00000?ooo`3oool0A`3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo00D0 00000?ooo`3oool0oooo000000020?ooo`H000007P3oool00`000000oooo0?ooo`2:0?ooo`003`3o ool00`000000oooo0?ooo`170?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool00`3o ool01P000000oooo0?ooo`3oool000000?ooo`H00000803oool00`000000oooo0?ooo`2:0?ooo`00 3`3oool00`000000oooo0?ooo`160?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0 0P3oool200000080oooo0P0000000`3oool000000000000400000240oooo00<000000?ooo`3oool0 RP3oool000l0oooo00<000000?ooo`3oool0AP3oool00`000000oooo0?ooo`040?ooo`030000003o ool0oooo0080oooo00D000000?ooo`3oool0oooo000000020?ooo`D000008`3oool00`000000oooo 0?ooo`2:0?ooo`003`3oool00`000000oooo0?ooo`150?ooo`030000003oool0oooo00@0oooo00<0 00000?ooo`3oool00P3oool00`000000oooo0?ooo`02000000030?ooo`000000000000<000009@3o ool00`000000oooo0?ooo`2:0?ooo`003`3oool2000004H0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`020?ooo`040000003oool0oooo00000080oooo1@00000V0?ooo`030000003o ool0oooo08X0oooo000?0?ooo`030000003oool0oooo04@0oooo00<000000?ooo`3oool00`3oool0 0`000000oooo0?ooo`020?ooo`050000003oool0oooo0000003oool01@00000X0?ooo`030000003o ool0oooo08X0oooo000?0?ooo`030000003oool0oooo04@0oooo00<000000?ooo`3oool00P3oool0 10000000oooo0?ooo`3oool2000000040?ooo`00000000000?ooo`@00000:P3oool00`000000oooo 0?ooo`2:0?ooo`001`3oool4000000@0oooo00<000000?ooo`3oool0A03oool00`000000oooo0?oo o`020?ooo`040000003oool0oooo00000080oooo00<000000?ooo`3oool01000000[0?ooo`030000 003oool0oooo08X0oooo00070?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0@`3o ool00`000000oooo0?ooo`020?ooo`040000003oool0oooo00000080oooo00<000000?ooo`000000 0`00000]0?ooo`030000003oool0oooo08X0oooo00080?ooo`030000003oool0oooo00@0oooo0`00 00130?ooo`050000003oool0oooo0?ooo`0000000P3oool01@000000oooo000000000000oooo00@0 0000;P3oool00`000000oooo0?ooo`2:0?ooo`0000<0oooo0000000000000P0000040?ooo`030000 003oool0oooo00<0oooo00<000000?ooo`3oool0@P3oool01@000000oooo0?ooo`3oool000000080 oooo00<000000?ooo`0000000P3oool300000300oooo00<000000?ooo`3oool0RP3oool000L0oooo 00@000000?ooo`3oool00000103oool00`000000oooo0?ooo`120?ooo`0:0000003oool0oooo0?oo o`000000oooo0000003oool000000?ooo`<00000P3oool3000000030?ooo`00 000000000440oooo00<000000?ooo`3oool0RP3oool000l0oooo00<000000?ooo`3oool0>03oool4 000000030?ooo`00000000000480oooo00<000000?ooo`3oool0RP3oool000l0oooo0P00000h0?oo o`@0000000@0oooo0000003oool00000@P3oool00`000000oooo0?ooo`2:0?ooo`003`3oool00`00 0000oooo0?ooo`0e0?ooo`@0000000<0oooo0000000000000P3oool00`000000oooo0?ooo`100?oo o`030000003oool0oooo08X0oooo000?0?ooo`030000003oool0oooo03@0oooo100000001P3oool0 00000?ooo`000000oooo000004<0oooo00<000000?ooo`3oool0RP3oool000l0oooo00<000000?oo o`3oool00?ooo`D0000000<0oooo0000000000000`3o ool2000000D0oooo0`0000020?ooo`D000000`3oool200000200oooo1000000W0?ooo`8000001@3o ool00`000000oooo0?ooo`0R0?ooo`<000009P3oool2000002L0oooo0`00000C0?ooo`003`3oool2 000000d0oooo1@0000000`3oool00000000000030?ooo`800000103oool3000000L0oooo00<00000 0?ooo`3oool00P3oool00`000000oooo0?ooo`0P0?ooo`030000003oool0oooo02L0oooo00@00000 0?ooo`3oool00000103oool00`000000oooo0?ooo`0S0?ooo`030000003oool0oooo02@0oooo00@0 00000?ooo`3oool000009P3oool010000000oooo0?ooo`00000B0?ooo`003`3oool00`000000oooo 0?ooo`0;0?ooo`@0000000<0oooo0000000000000`3oool2000000@0oooo0P00000:0?ooo`030000 003oool0oooo00800000903oool00`000000oooo0?ooo`0X0?ooo`030000003oool0oooo00<0oooo 00<000000?ooo`3oool0803oool5000002P0oooo00<000000?ooo`3oool0903oool010000000oooo 0?ooo`00000B0?ooo`003`3oool00`000000oooo0?ooo`090?ooo`@0000000<0oooo000000000000 0P3oool3000000<0oooo0`00000<0?ooo`<000009`3oool00`000000oooo0?ooo`0X0?ooo`030000 003oool0oooo0080oooo00<000000?ooo`3oool0803oool010000000oooo0?ooo`00000W0?ooo`80 00009`3oool3000001<0oooo000?0?ooo`030000003oool0oooo00P0oooo0`000000103oool00000 0000003oool3000000<0oooo0`00000>0?ooo`8000009`3oool010000000oooo0?ooo`00000V0?oo o`040000003oool0oooo000000@0oooo00<000000?ooo`3oool08@3oool00`000000oooo0000000W 0?ooo`030000003oool0oooo02L0oooo00<000000?ooo`3oool04P3oool000l0oooo00<000000?oo o`3oool01P3oool3000000040?ooo`00000000000?ooo`8000000`3oool3000000`0oooo1`00000X 0?ooo`800000:03oool2000000D0oooo00<000000?ooo`3oool08P3oool2000002L0oooo0`00000W 0?ooo`<000004P3oool000l0oooo0P0000060?ooo`P0000000<0oooo0000000000000P00000:0?oo o`D00000H03oool00`000000oooo0?ooo`2:0?ooo`003`3oool00`000000oooo0?ooo`030?ooo`/0 0000203oool6000006D0oooo00<000000?ooo`3oool0RP3oool000l0oooo00@000000?ooo`3oool0 oooo2@0000070?ooo`D00000J`3oool00`000000oooo0?ooo`2:0?ooo`003`3oool00`000000oooo 0?ooo`07000000@0oooo1P00001`0?ooo`030000003oool0oooo08X0oooo000?0?ooo`h00000MP3o ool00`000000oooo0?ooo`2:0?ooo`00203ooooo000001T00000000?0?ooo`030000003oool0oooo 00D0oooo00<000000?ooo`3oool01P3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo 00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`060?ooo`030000003oool0oooo 00D0oooo00<000000?ooo`3oool0103oool2000000P0oooo00<000000?ooo`3oool01@3oool00`00 0000oooo0?ooo`060?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01P3oool00`00 0000oooo0?ooo`050?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool0103oool00`00 0000oooo000000070?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`00 0000oooo0?ooo`060?ooo`030000003oool0oooo00D0oooo00<000000?ooo`3oool01@3oool00`00 0000oooo0?ooo`060?ooo`030000003oool0oooo0080oooo00@000000?ooo`3oool00000203oool0 0`000000oooo0?ooo`050?ooo`030000003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool0 0`000000oooo0?ooo`060?ooo`030000003oool0oooo00<0oooo3P0000050?ooo`4000000@3oool1 0?ooo`003`3oool00`000000oooo0?ooo`0W0?ooo`030000003oool0oooo01D0oooo00<000000?oo o`3oool03`3oool00`000000oooo0?ooo`0W0?ooo`030000003oool0oooo00@0oooo00<000000?oo o`3oool08@3oool00`000000oooo0?ooo`0K0?ooo`030000003oool0oooo00T0oooo00<000000?oo o`3oool07`3oool600000080oooo2`0000090?ooo`003`3oool00`000000oooo0?ooo`0o0?ooo`03 0000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`0V0?ooo`D0 00001P3oool3000000030?ooo`000000000000D000002`3oool000l0oooo00<000000?ooo`3oool0 ?`3oool00`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0 803oool6000000L0oooo100000000`3oool0000000000006000000d0oooo000?0?ooo`800000@03o ool00`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool06`3o ool5000000T0oooo100000020?ooo`T000003`3oool000l0oooo00<000000?ooo`3oool0?`3oool0 0`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool05`3oool4 000000/0oooo0`0000040?ooo`80000000@0oooo000000000000oooo0`00000A0?ooo`003`3oool0 0`000000oooo0?ooo`0o0?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool0 0`000000oooo0?ooo`0E0?ooo`800000303oool3000000@0oooo0`000000103oool000000000003o ool3000001<0oooo000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool0 0`000000oooo0?ooo`0o0?ooo`030000003oool0oooo01<0oooo0P00000<0?ooo`800000103oool3 00000080oooo0P0000000`3oool0000000000002000001@0oooo000?0?ooo`030000003oool0oooo 03l0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo 0140oooo0P00000;0?ooo`<00000103oool2000000<0oooo0P0000000`3oool00000000000020000 01H0oooo000?0?ooo`800000@03oool00`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0 oooo00<000000?ooo`3oool0403oool00`000000oooo0?ooo`090?ooo`8000001@3oool2000000<0 oooo0P0000000`3oool0000000000003000001L0oooo000?0?ooo`030000003oool0oooo03l0oooo 00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo00h0oooo 0P00000:0?ooo`8000001@3oool2000000<0oooo0P0000000`3oool0000000000003000001T0oooo 000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?oo o`0o0?ooo`030000003oool0oooo00d0oooo00<000000?ooo`3oool0203oool2000000D0oooo0P00 00030?ooo`8000000P3oool4000001/0oooo000?0?ooo`030000003oool0oooo03l0oooo00<00000 0?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo00/0oooo0P00000: 0?ooo`030000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`05 000001`0oooo000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool00`00 0000oooo0?ooo`0o0?ooo`030000003oool0oooo00X0oooo00<000000?ooo`3oool0203oool20000 00D0oooo0P0000030?ooo`80000000<0oooo0000000000000`00000N0?ooo`003`3oool00`000000 oooo0?ooo`0o0?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool00`000000 oooo0?ooo`090?ooo`030000003oool0oooo00L0oooo0P0000060?ooo`040000003oool0oooo0?oo o`8000000P3oool00`000000oooo00000002000001l0oooo000?0?ooo`800000@03oool00`000000 oooo0?ooo`100?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool02@3oool00`000000 oooo0?ooo`060?ooo`030000003oool0oooo00@0oooo0P0000030?ooo`030000003oool0oooo00D0 00008@3oool000l0oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`100?ooo`030000 003oool0oooo03l0oooo00<000000?ooo`3oool0203oool00`000000oooo0?ooo`060?ooo`030000 003oool0oooo00<0oooo0P0000030?ooo`80000000@0oooo000000000000oooo0`00000R0?ooo`00 3`3oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0 ?`3oool00`000000oooo0?ooo`070?ooo`030000003oool0oooo00D0oooo0P0000050?ooo`030000 003oool0oooo0080oooo00@000000?ooo`3oool000000P3oool2000002@0oooo000?0?ooo`030000 003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`030000 003oool0oooo00H0oooo00<000000?ooo`3oool01@3oool00`000000oooo0?ooo`030?ooo`800000 0`3oool2000000040?ooo`00000000000?ooo`<000009@3oool000l0oooo00<000000?ooo`3oool0 ?`3oool00`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0 1@3oool00`000000oooo0?ooo`050?ooo`030000003oool0oooo00<0oooo00@000000?ooo`3oool0 oooo0P0000020?ooo`030000003oool0oooo00<000009P3oool000l0oooo0P0000100?ooo`030000 003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`040?ooo`030000 003oool0oooo00D0oooo00<000000?ooo`3oool00`3oool01@000000oooo0?ooo`3oool000000080 oooo0P000000103oool0000000000000000X0?ooo`003`3oool00`000000oooo0?ooo`0o0?ooo`03 0000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`040?ooo`03 0000003oool0oooo00@0oooo00<000000?ooo`3oool00P3oool200000080oooo0P000000103oool0 00000000003oool4000002T0oooo000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3o ool0@03oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3o ool0103oool00`000000oooo0?ooo`020?ooo`050000003oool0oooo0?ooo`0000000P3oool00`00 0000oooo00000003000002/0oooo00070?ooo`D000000`3oool00`000000oooo0?ooo`0o0?ooo`03 0000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`030?ooo`03 0000003oool0oooo00<0oooo00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`0200000003 0?ooo`000000000000@00000;@3oool000T0oooo00<000000?ooo`3oool00`3oool00`000000oooo 0?ooo`0o0?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool00`000000oooo 0?ooo`020?ooo`030000003oool0oooo00<0oooo00<000000?ooo`3oool00P3oool010000000oooo 0?ooo`0000020?ooo`D00000;`3oool000T0oooo00<000000?ooo`3oool00`3oool3000003l0oooo 00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo0080oooo 00<000000?ooo`3oool00P3oool00`000000oooo0?ooo`020?ooo`050000003oool0oooo0000003o ool01@00000a0?ooo`002@3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo03l0oooo 00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`050000003oool0oooo0?ooo`00 0000103oool010000000oooo0?ooo`3oool2000000040?ooo`00000000000?ooo`@00000<`3oool0 00T0oooo00<000000?ooo`3oool00`3oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo 0400oooo00<000000?ooo`3oool0?`3oool01@000000oooo0?ooo`3oool0000000@0oooo00@00000 0?ooo`3oool000000P3oool00`000000oooo00000004000003@0oooo00080?ooo`8000001@3oool0 0`000000oooo0?ooo`0o0?ooo`030000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool0 1@000000oooo0?ooo`3oool0000000<0oooo00@000000?ooo`3oool000000P3oool00`000000oooo 00000003000003H0oooo000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@03o ool00`000000oooo0?ooo`0o0?ooo`040000003oool0oooo000000<0oooo00D000000?ooo`3oool0 00000?ooo`06000003P0oooo000?0?ooo`800000@03oool00`000000oooo0?ooo`100?ooo`030000 003oool0oooo03l0oooo00@000000?ooo`3oool000000P3oool01`000000oooo0?ooo`000000oooo 0000003oool00`00000j0?ooo`003`3oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo 0400oooo00<000000?ooo`3oool0?`3oool010000000oooo0?ooo`0000020?ooo`040000003oool0 00000?ooo`D00000>`3oool000l0oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`10 0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`0000000P3oool010000000oooo0000003o ool4000003d0oooo000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool0 0`000000oooo0?ooo`0o0?ooo`080000003oool000000?ooo`000000oooo0000003oool3000003l0 oooo000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool00`000000oooo 0?ooo`0o0?ooo`040000003oool000000?ooo`80000000@0oooo0000000000000000@03oool000l0 oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0 oooo0P0000000`3oool000000?ooo`0300000480oooo000?0?ooo`800000@03oool00`000000oooo 0?ooo`100?ooo`030000003oool0oooo03l0oooo0P0000000`3oool0000000000002000004<0oooo 000?0?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?oo o`0o0?ooo`D00000A@3oool000l0oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`10 0?ooo`030000003oool0oooo03l0oooo100000160?ooo`003`3oool00`000000oooo0?ooo`0o0?oo o`030000003oool0oooo0400oooo00<000000?ooo`3oool0?`3oool3000004L0oooo000?0?ooo`03 0000003oool0oooo03l0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`03 0000003oool0oooo04L0oooo000?0?ooo`800000@@3oool00`000000oooo0?ooo`0o0?ooo`030000 003oool0oooo03d0oooo0`0000190?ooo`003`3oool00`000000oooo0?ooo`100?ooo`030000003o ool0oooo03l0oooo00<000000?ooo`3oool0?03oool4000004T0oooo000?0?ooo`030000003oool0 oooo0400oooo00<000000?ooo`3oool0?`3oool00`000000oooo0?ooo`0j0?ooo`H00000B@3oool0 00l0oooo00<000000?ooo`3oool0@03oool00`000000oooo0?ooo`0o0?ooo`030000003oool0oooo 03P0oooo10000000103oool000000?ooo`0000190?ooo`003`3oool00`000000oooo0?ooo`100?oo o`030000003oool0oooo03l0oooo00<000000?ooo`3oool0=`3oool4000000050?ooo`0000000000 0?ooo`000000B@3oool000l0oooo0P0000110?ooo`030000003oool0oooo03l0oooo00<000000?oo o`3oool0=@3oool4000000070?ooo`00000000000?ooo`000000oooo000000190?ooo`003`3oool0 0`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool0=03oool4 000000050?ooo`00000000000?ooo`0000000P3oool00`000000oooo0?ooo`170?ooo`003`3oool0 0`000000oooo0?ooo`100?ooo`030000003oool0oooo03l0oooo00<000000?ooo`3oool000000340oooo00<000000?ooo`3oool0A`3oool000P0oooo0P0000050?ooo`030000003oool0 oooo0400oooo00<000000?ooo`3oool0?`3oool8000003X0oooo00<000000?ooo`3oool0A`3oool0 00l0oooo00<000000?ooo`3oool0@03ooon5000004T0oooo000?0?ooo`800000o`3oool@0?ooo`00 3`3oool00`000000oooo0?ooo`3o0?ooo`l0oooo000?0?ooo`030000003oool0oooo0?l0oooo3`3o ool000l0oooo00<000000?ooo`3oool0o`3oool?0?ooo`00o`3ooolQ0?ooo`00o`3ooolQ0?ooo`00 \ \>"], ImageRangeCache->{{{96.0625, 383.063}, {589, 412.063}} -> {-2.64566, \ 12.4175, 0.0237193, 0.0383724}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot3D[\[Psi]sol, {\[Theta], 0, \[Pi]}, {\[Phi], 0, 2 \[Pi]}, PlotPoints \[Rule] 25, ViewPoint -> {\(-2.224\), \ \(-2.259\), \ 1.184}];\)\)], "Input", CellLabel->"In[53]:="], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .62118 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% SurfaceGraphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.00156051 1.00156 -0.135816 1.00156 [ [.4946 -0.01252 -2.99765 -9 ] [.4946 -0.01252 3.00235 0 ] [.67169 .07395 -3.08648 -9 ] [.67169 .07395 2.91352 0 ] [.82571 .14915 -3.16167 -9 ] [.82571 .14915 2.83833 0 ] [.96089 .21516 -3.22614 -9 ] [.96089 .21516 2.77386 0 ] [.4946 -0.01252 -2.99765 -9 ] [.4946 -0.01252 3.00235 0 ] [.32108 .07521 -2.9107 -9 ] [.32108 .07521 3.0893 0 ] [.17048 .15136 -2.83728 -9 ] [.17048 .15136 3.16272 0 ] [.03854 .21808 -2.77445 -9 ] [.03854 .21808 3.22555 0 ] [.99546 .28198 0 -5.95727 ] [.99546 .28198 12 3.04273 ] [1.00163 .36006 0 -5.83573 ] [1.00163 .36006 6 3.16427 ] [1.00795 .44014 0 -5.71162 ] [1.00795 .44014 6 3.28838 ] [ 0 0 0 0 ] [ 1 .62118 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .49459 0 m .97968 .23634 L s .49459 0 m .49458 .00626 L s [(0)] .4946 -0.01252 -0.00078 1 Mshowa .67205 .08646 m .67223 .09272 L s [(1)] .67169 .07395 .02883 1 Mshowa .82638 .16166 m .82672 .16791 L s [(2)] .82571 .14915 .05389 1 Mshowa .96183 .22765 m .9623 .23389 L s [(3)] .96089 .21516 .07538 1 Mshowa .125 Mabswid .53217 .01831 m .5322 .02207 L s .56867 .03609 m .56871 .03985 L s .60412 .05337 m .60418 .05712 L s .63856 .07015 m .63865 .0739 L s .70461 .10233 m .70474 .10608 L s .73629 .11776 m .73644 .12152 L s .76713 .13279 m .76729 .13654 L s .79715 .14741 m .79733 .15116 L s .85486 .17553 m .85508 .17928 L s .88262 .18906 m .88286 .19281 L s .90969 .20224 m .90994 .20599 L s .93608 .2151 m .93635 .21885 L s .25 Mabswid .49459 0 m .0202 .23935 L s .49459 0 m .49458 .00626 L s [(0)] .4946 -0.01252 -0.00078 1 Mshowa .32071 .08773 m .32052 .09398 L s [(2)] .32108 .07521 -0.02977 1 Mshowa .16981 .16386 m .16947 .17011 L s [(4)] .17048 .15136 -0.05424 1 Mshowa .0376 .23056 m .03714 .23681 L s [(6)] .03854 .21808 -0.07518 1 Mshowa .125 Mabswid .44868 .02316 m .44865 .02692 L s .40446 .04547 m .4044 .04923 L s .36183 .06698 m .36174 .07073 L s .28102 .10775 m .28088 .11151 L s .24268 .1271 m .24252 .13085 L s .20563 .14579 m .20545 .14954 L s .13514 .18135 m .13492 .1851 L s .10159 .19828 m .10135 .20203 L s .06909 .21468 m .06883 .21842 L s .25 Mabswid .97968 .23634 m 1 .49629 L s .98355 .28583 m .97759 .28776 L s [(-2)] .99546 .28198 -1 .32384 Mshowa .98963 .36363 m .98363 .36541 L s [(0)] 1.00163 .36006 -1 .29683 Mshowa .99586 .4434 m .98982 .44502 L s [(2)] 1.00795 .44014 -1 .26925 Mshowa .125 Mabswid .98505 .3051 m .98147 .30623 L s .98657 .32449 m .98298 .3256 L s .98809 .34399 m .9845 .34509 L s .99117 .38338 m .98757 .38443 L s .99273 .40326 m .98911 .40428 L s .99429 .42326 m .99067 .42426 L s .98205 .26668 m .97848 .26786 L s .98056 .24766 m .977 .24886 L s .99745 .46366 m .99382 .46461 L s .99904 .48405 m .9954 .48498 L s .25 Mabswid .49459 0 m .49434 .3119 L s .49434 .3119 m 0 .49861 L s 0 .49861 m .0202 .23935 L s .0202 .23935 m .49459 0 L s .97968 .23634 m .50236 .39915 L s .50236 .39915 m .50247 .62118 L s .50247 .62118 m 1 .49629 L s 1 .49629 m .97968 .23634 L s .49459 0 m .49434 .3119 L s .49434 .3119 m 1 .49629 L s 1 .49629 m .97968 .23634 L s .97968 .23634 m .49459 0 L s .0202 .23935 m .50236 .39915 L s .50236 .39915 m .50247 .62118 L s .50247 .62118 m 0 .49861 L s 0 .49861 m .0202 .23935 L s 0 0 m 1 0 L 1 .62118 L 0 .62118 L closepath clip newpath .5 Mabswid .736 .805 .907 r .50219 .48929 .48513 .50326 .50242 .50824 .51946 .49433 Metetra .735 .808 .91 r .48468 .48433 .4676 .4982 .48513 .50326 .50219 .48929 Metetra .731 .811 .914 r .46692 .47944 .44983 .49307 .4676 .4982 .48468 .48433 Metetra .726 .815 .92 r .44892 .47462 .43181 .48788 .44983 .49307 .46692 .47944 Metetra .719 .82 .928 r .43065 .46988 .41354 .48261 .43181 .48788 .44892 .47462 Metetra .709 .824 .936 r .41212 .46519 .39501 .47726 .41354 .48261 .43065 .46988 Metetra .696 .829 .946 r .39332 .46055 .37622 .47184 .39501 .47726 .41212 .46519 Metetra .679 .833 .958 r .37424 .45595 .35716 .46635 .37622 .47184 .39332 .46055 Metetra .656 .836 .969 r .35488 .45137 .33782 .46077 .35716 .46635 .37424 .45595 Metetra .628 .838 .981 r .33522 .44679 .31821 .45511 .33782 .46077 .35488 .45137 Metetra .592 .836 .991 r .31527 .44219 .29831 .44937 .31821 .45511 .33522 .44679 Metetra .547 .829 .998 r .29501 .43754 .27811 .44355 .29831 .44937 .31527 .44219 Metetra .492 .817 1 r .27444 .43282 .25762 .43763 .27811 .44355 .29501 .43754 Metetra .429 .796 .995 r .25355 .42801 .23681 .43163 .25762 .43763 .27444 .43282 Metetra .357 .767 .981 r .23234 .42307 .2157 .42554 .23681 .43163 .25355 .42801 Metetra .279 .73 .958 r .2108 .41798 .19426 .41936 .2157 .42554 .23234 .42307 Metetra .201 .687 .928 r .18892 .41271 .1725 .41308 .19426 .41936 .2108 .41798 Metetra .126 .641 .892 r .1667 .40725 .1504 .40671 .1725 .41308 .18892 .41271 Metetra .059 .596 .855 r .14414 .40157 .12796 .40024 .1504 .40671 .1667 .40725 Metetra .003 .556 .822 r .12122 .39566 .10517 .39366 .12796 .40024 .14414 .40157 Metetra 0 .522 .794 r .09794 .38951 .08201 .38698 .10517 .39366 .12122 .39566 Metetra 0 .498 .774 r .07429 .38309 .05849 .3802 .08201 .38698 .09794 .38951 Metetra 0 .484 .764 r .05026 .37641 .03459 .3733 .05849 .3802 .07429 .38309 Metetra 0 .481 .764 r .02586 .36944 .01031 .3663 .03459 .3733 .05026 .37641 Metetra .736 .806 .907 r .51944 .47515 .50219 .48929 .51946 .49433 .53669 .48026 Metetra .736 .81 .91 r .50195 .47022 .48468 .48433 .50219 .48929 .51944 .47515 Metetra .735 .815 .914 r .48422 .46549 .46692 .47944 .48468 .48433 .50195 .47022 Metetra .732 .821 .92 r .46623 .46095 .44892 .47462 .46692 .47944 .48422 .46549 Metetra .726 .827 .927 r .44797 .45662 .43065 .46988 .44892 .47462 .46623 .46095 Metetra .719 .834 .936 r .42945 .4525 .41212 .46519 .43065 .46988 .44797 .45662 Metetra .707 .842 .947 r .41065 .44859 .39332 .46055 .41212 .46519 .42945 .4525 Metetra .691 .849 .959 r .39156 .44489 .37424 .45595 .39332 .46055 .41065 .44859 Metetra .668 .855 .971 r .37217 .44136 .35488 .45137 .37424 .45595 .39156 .44489 Metetra .635 .859 .984 r .35248 .43799 .33522 .44679 .35488 .45137 .37217 .44136 Metetra .591 .858 .994 r .33248 .4347 .31527 .44219 .33522 .44679 .35248 .43799 Metetra .534 .848 .998 r .31216 .43144 .29501 .43754 .31527 .44219 .33248 .4347 Metetra .463 .828 .994 r .29152 .42813 .27444 .43282 .29501 .43754 .31216 .43144 Metetra .38 .796 .977 r .27055 .42469 .25355 .42801 .27444 .43282 .29152 .42813 Metetra .292 .752 .95 r .24924 .42104 .23234 .42307 .25355 .42801 .27055 .42469 Metetra .204 .702 .915 r .2276 .41712 .2108 .41798 .23234 .42307 .24924 .42104 Metetra .125 .651 .876 r .20561 .41289 .18892 .41271 .2108 .41798 .2276 .41712 Metetra .056 .603 .84 r .18328 .4083 .1667 .40725 .18892 .41271 .20561 .41289 Metetra .001 .561 .808 r .1606 .40334 .14414 .40157 .1667 .40725 .18328 .4083 Metetra 0 .528 .783 r .13756 .398 .12122 .39566 .14414 .40157 .1606 .40334 Metetra 0 .504 .766 r .11416 .39226 .09794 .38951 .12122 .39566 .13756 .398 Metetra 0 .488 .757 r .09039 .38613 .07429 .38309 .09794 .38951 .11416 .39226 Metetra 0 .48 .756 r .06625 .37959 .05026 .37641 .07429 .38309 .09039 .38613 Metetra 0 .481 .762 r .04172 .37265 .02586 .36944 .05026 .37641 .06625 .37959 Metetra .737 .806 .907 r .53689 .46081 .51944 .47515 .53669 .48026 .55411 .46603 Metetra .738 .811 .909 r .51942 .45582 .50195 .47022 .51944 .47515 .53689 .46081 Metetra .738 .816 .912 r .50171 .45108 .48422 .46549 .50195 .47022 .51942 .45582 Metetra .738 .822 .917 r .48374 .44661 .46623 .46095 .48422 .46549 .50171 .45108 Metetra .737 .829 .922 r .46551 .44246 .44797 .45662 .46623 .46095 .48374 .44661 Metetra .733 .838 .929 r .447 .43868 .42945 .4525 .44797 .45662 .46551 .44246 Metetra .727 .848 .939 r .42821 .43533 .41065 .44859 .42945 .4525 .447 .43868 Metetra .715 .861 .951 r .40912 .43244 .39156 .44489 .41065 .44859 .42821 .43533 Metetra .693 .873 .966 r .38973 .43004 .37217 .44136 .39156 .44489 .40912 .43244 Metetra .657 .884 .981 r .37001 .42812 .35248 .43799 .37217 .44136 .38973 .43004 Metetra .597 .885 .991 r .34996 .42658 .33248 .4347 .35248 .43799 .37001 .42812 Metetra .507 .868 .986 r .32958 .42525 .31216 .43144 .33248 .4347 .34996 .42658 Metetra .39 .822 .959 r .30886 .4239 .29152 .42813 .31216 .43144 .32958 .42525 Metetra .262 .754 .91 r .28779 .42229 .27055 .42469 .29152 .42813 .30886 .4239 Metetra .144 .679 .854 r .26638 .42022 .24924 .42104 .27055 .42469 .28779 .42229 Metetra .052 .611 .805 r .24464 .41758 .2276 .41712 .24924 .42104 .26638 .42022 Metetra 0 .559 .77 r .22255 .41432 .20561 .41289 .2276 .41712 .24464 .41758 Metetra 0 .523 .748 r .20011 .41044 .18328 .4083 .20561 .41289 .22255 .41432 Metetra 0 .499 .737 r .17732 .40597 .1606 .40334 .18328 .4083 .20011 .41044 Metetra 0 .485 .734 r .15418 .40095 .13756 .398 .1606 .40334 .17732 .40597 Metetra 0 .478 .737 r .13067 .39541 .11416 .39226 .13756 .398 .15418 .40095 Metetra 0 .476 .743 r .1068 .38938 .09039 .38613 .11416 .39226 .13067 .39541 Metetra 0 .477 .751 r .08255 .38288 .06625 .37959 .09039 .38613 .1068 .38938 Metetra 0 .48 .761 r .05791 .37592 .04172 .37265 .06625 .37959 .08255 .38288 Metetra .737 .805 .906 r .55453 .44627 .53689 .46081 .55411 .46603 .57173 .45164 Metetra .739 .809 .907 r .53709 .44109 .51942 .45582 .53689 .46081 .55453 .44627 Metetra .742 .813 .908 r .5194 .43613 .50171 .45108 .51942 .45582 .53709 .44109 Metetra .745 .818 .91 r .50146 .43144 .48374 .44661 .50171 .45108 .5194 .43613 Metetra .747 .824 .912 r .48325 .42709 .46551 .44246 .48374 .44661 .50146 .43144 Metetra .75 .832 .915 r .46477 .42319 .447 .43868 .46551 .44246 .48325 .42709 Metetra .752 .843 .92 r .44601 .41989 .42821 .43533 .447 .43868 .46477 .42319 Metetra .75 .859 .93 r .42694 .4174 .40912 .43244 .42821 .43533 .44601 .41989 Metetra .74 .881 .945 r .40755 .41597 .38973 .43004 .40912 .43244 .42694 .4174 Metetra .709 .909 .965 r .38782 .41581 .37001 .42812 .38973 .43004 .40755 .41597 Metetra .622 .924 .974 r .36773 .41695 .34996 .42658 .37001 .42812 .38782 .41581 Metetra .431 .866 .918 r .34727 .41897 .32958 .42525 .34996 .42658 .36773 .41695 Metetra .167 .706 .774 r .32644 .42103 .30886 .4239 .32958 .42525 .34727 .41897 Metetra .04 0 0 r .30525 .42224 .28779 .42229 .30886 .4239 .32644 .42103 Metetra .153 0 0 r .28374 .42213 .26638 .42022 .28779 .42229 .30525 .42224 Metetra .199 0 0 r .26189 .42065 .24464 .41758 .26638 .42022 .28374 .42213 Metetra .208 0 0 r .23971 .41797 .22255 .41432 .24464 .41758 .26189 .42065 Metetra .197 0 0 r .21719 .4143 .20011 .41044 .22255 .41432 .23971 .41797 Metetra .178 0 0 r .19432 .40984 .17732 .40597 .20011 .41044 .21719 .4143 Metetra .155 0 0 r .17109 .40472 .15418 .40095 .17732 .40597 .19432 .40984 Metetra 0 .453 .714 r .1475 .39905 .13067 .39541 .15418 .40095 .17109 .40472 Metetra 0 .466 .735 r .12353 .39289 .1068 .38938 .13067 .39541 .1475 .39905 Metetra 0 .475 .75 r .09917 .38629 .08255 .38288 .1068 .38938 .12353 .39289 Metetra 0 .481 .762 r .07443 .37926 .05791 .37592 .08255 .38288 .09917 .38629 Metetra .737 .804 .905 r .57238 .43153 .55453 .44627 .57173 .45164 .58955 .43709 Metetra .74 .806 .905 r .55496 .42606 .53709 .44109 .55453 .44627 .57238 .43153 Metetra .743 .808 .904 r .5373 .42068 .5194 .43613 .53709 .44109 .55496 .42606 Metetra .748 .81 .901 r .51939 .41543 .50146 .43144 .5194 .43613 .5373 .42068 Metetra .755 .812 .898 r .50121 .41039 .48325 .42709 .50146 .43144 .51939 .41543 Metetra .762 .815 .894 r .48276 .40566 .46477 .42319 .48325 .42709 .50121 .41039 Metetra .772 .82 .891 r .46403 .40143 .44601 .41989 .46477 .42319 .48276 .40566 Metetra .782 .829 .889 r .44501 .39803 .42694 .4174 .44601 .41989 .46403 .40143 Metetra .794 .848 .892 r .42566 .39608 .40755 .41597 .42694 .4174 .44501 .39803 Metetra .801 .891 .909 r .40597 .39678 .38782 .41581 .40755 .41597 .42566 .39608 Metetra .741 .972 .929 r .38584 .40204 .36773 .41695 .38782 .41581 .40597 .39678 Metetra .36523 .41258 .34727 .41897 .36773 .41695 .38584 .40204 Metetra .386 0 0 r .34418 .42335 .32644 .42103 .34727 .41897 .36523 .41258 Metetra .502 0 0 r .32284 .42903 .30525 .42224 .32644 .42103 .34418 .42335 Metetra .51 0 0 r .30123 .43006 .28374 .42213 .30525 .42224 .32284 .42903 Metetra .464 0 0 r .27932 .42826 .26189 .42065 .28374 .42213 .30123 .43006 Metetra .394 0 0 r .25709 .4248 .23971 .41797 .26189 .42065 .27932 .42826 Metetra .32 0 0 r .23452 .42029 .21719 .4143 .23971 .41797 .25709 .4248 Metetra .252 0 0 r .2116 .41506 .19432 .40984 .21719 .4143 .23452 .42029 Metetra .195 0 0 r .18831 .40932 .17109 .40472 .19432 .40984 .2116 .41506 Metetra 0 .436 .707 r .16464 .40315 .1475 .39905 .17109 .40472 .18831 .40932 Metetra 0 .46 .736 r .14059 .39664 .12353 .39289 .1475 .39905 .16464 .40315 Metetra 0 .475 .754 r .11614 .3898 .09917 .38629 .12353 .39289 .14059 .39664 Metetra 0 .481 .764 r .09129 .38266 .07443 .37926 .09917 .38629 .11614 .3898 Metetra .737 .803 .905 r .59043 .41661 .57238 .43153 .58955 .43709 .60757 .42237 Metetra .739 .803 .903 r .57304 .41076 .55496 .42606 .57238 .43153 .59043 .41661 Metetra .743 .801 .899 r .5554 .40483 .5373 .42068 .55496 .42606 .57304 .41076 Metetra .748 .8 .894 r .53751 .39881 .51939 .41543 .5373 .42068 .5554 .40483 Metetra .755 .797 .887 r .51936 .39271 .50121 .41039 .51939 .41543 .53751 .39881 Metetra .764 .793 .877 r .50095 .38652 .48276 .40566 .50121 .41039 .51936 .39271 Metetra .776 .788 .863 r .48226 .38024 .46403 .40143 .48276 .40566 .50095 .38652 Metetra .789 .781 .845 r .4633 .37386 .44501 .39803 .46403 .40143 .48226 .38024 Metetra .804 .77 .822 r .44405 .36739 .42566 .39608 .44501 .39803 .4633 .37386 Metetra .82 .755 .792 r .42451 .36082 .40597 .39678 .42566 .39608 .44405 .36739 Metetra .835 .737 .757 r .40468 .35416 .38584 .40204 .40597 .39678 .42451 .36082 Metetra .788 .632 .688 r .38512 .316 .36523 .41258 .38584 .40204 .40468 .35416 Metetra .553 .353 .563 r .36152 .45985 .34418 .42335 .36523 .41258 .38512 .316 Metetra .797 .351 .184 r .34034 .45368 .32284 .42903 .34418 .42335 .36152 .45985 Metetra .717 .201 0 r .31882 .44741 .30123 .43006 .32284 .42903 .34034 .45368 Metetra .605 .039 0 r .29695 .44104 .27932 .42826 .30123 .43006 .31882 .44741 Metetra .483 0 0 r .27473 .43457 .25709 .4248 .27932 .42826 .29695 .44104 Metetra .37 0 0 r .25215 .42799 .23452 .42029 .25709 .4248 .27473 .43457 Metetra .276 0 0 r .22919 .4213 .2116 .41506 .23452 .42029 .25215 .42799 Metetra .203 0 0 r .20585 .4145 .18831 .40932 .2116 .41506 .22919 .4213 Metetra 0 .433 .718 r .18213 .40759 .16464 .40315 .18831 .40932 .20585 .4145 Metetra 0 .461 .746 r .158 .40056 .14059 .39664 .16464 .40315 .18213 .40759 Metetra 0 .477 .762 r .13346 .39341 .11614 .3898 .14059 .39664 .158 .40056 Metetra 0 .482 .767 r .1085 .38614 .09129 .38266 .11614 .3898 .13346 .39341 Metetra .737 .802 .904 r .60868 .40151 .59043 .41661 .60757 .42237 .6258 .40748 Metetra .738 .799 .901 r .59132 .39529 .57304 .41076 .59043 .41661 .60868 .40151 Metetra .741 .796 .897 r .57371 .3888 .5554 .40483 .57304 .41076 .59132 .39529 Metetra .745 .791 .89 r .55584 .38201 .53751 .39881 .5554 .40483 .57371 .3888 Metetra .75 .785 .882 r .53772 .37484 .51936 .39271 .53751 .39881 .55584 .38201 Metetra .756 .777 .87 r .51933 .36718 .50095 .38652 .51936 .39271 .53772 .37484 Metetra .764 .767 .855 r .50068 .35883 .48226 .38024 .50095 .38652 .51933 .36718 Metetra .772 .753 .835 r .48176 .34947 .4633 .37386 .48226 .38024 .50068 .35883 Metetra .78 .734 .81 r .46259 .33847 .44405 .36739 .4633 .37386 .48176 .34947 Metetra .786 .709 .779 r .44317 .32465 .42451 .36082 .44405 .36739 .46259 .33847 Metetra .789 .682 .746 r .42356 .30616 .40468 .35416 .42451 .36082 .44317 .32465 Metetra .737 .656 .77 r .4038 .28239 .38512 .316 .40468 .35416 .42356 .30616 Metetra .526 .341 .573 r .37938 .49745 .36152 .45985 .38512 .316 .4038 .28239 Metetra .781 .283 0 r .35829 .47898 .34034 .45368 .36152 .45985 .37938 .49745 Metetra .661 .113 0 r .33683 .46518 .31882 .44741 .34034 .45368 .35829 .47898 Metetra .535 0 0 r .31498 .45411 .29695 .44104 .31882 .44741 .33683 .46518 Metetra .417 0 0 r .29276 .44455 .27473 .43457 .29695 .44104 .31498 .45411 Metetra .316 0 0 r .27015 .43586 .25215 .42799 .27473 .43457 .29276 .44455 Metetra 0 .352 .668 r .24716 .42767 .22919 .4213 .25215 .42799 .27015 .43586 Metetra 0 .406 .713 r .22377 .4198 .20585 .4145 .22919 .4213 .24716 .42767 Metetra 0 .444 .744 r .19998 .41212 .18213 .40759 .20585 .4145 .22377 .4198 Metetra 0 .468 .762 r .17577 .40457 .158 .40056 .18213 .40759 .19998 .41212 Metetra 0 .481 .77 r .15114 .3971 .13346 .39341 .158 .40056 .17577 .40457 Metetra 0 .483 .769 r .12608 .38969 .1085 .38614 .13346 .39341 .15114 .3971 Metetra .736 .801 .904 r .62715 .38625 .60868 .40151 .6258 .40748 .64423 .39243 Metetra .736 .797 .901 r .60982 .37972 .59132 .39529 .60868 .40151 .62715 .38625 Metetra .737 .792 .897 r .59223 .3728 .57371 .3888 .59132 .39529 .60982 .37972 Metetra .739 .786 .891 r .57439 .36544 .55584 .38201 .57371 .3888 .59223 .3728 Metetra .741 .78 .884 r .55628 .35756 .53772 .37484 .55584 .38201 .57439 .36544 Metetra .743 .772 .877 r .53792 .34904 .51933 .36718 .53772 .37484 .55628 .35756 Metetra .744 .763 .868 r .51929 .33974 .50068 .35883 .51933 .36718 .53792 .34904 Metetra .744 .752 .859 r .5004 .32944 .48176 .34947 .50068 .35883 .51929 .33974 Metetra .74 .74 .852 r .48125 .31789 .46259 .33847 .48176 .34947 .5004 .32944 Metetra .727 .728 .852 r .46184 .30489 .44317 .32465 .46259 .33847 .48125 .31789 Metetra .689 .716 .87 r .44219 .29042 .42356 .30616 .44317 .32465 .46184 .30489 Metetra .579 .691 .918 r .42229 .27491 .4038 .28239 .42356 .30616 .44219 .29042 Metetra .454 .28 .554 r .39834 .5006 .37938 .49745 .4038 .28239 .42229 .27491 Metetra 0 .403 .821 r .37708 .48661 .35829 .47898 .37938 .49745 .39834 .5006 Metetra 0 .329 .736 r .35549 .47385 .33683 .46518 .35829 .47898 .37708 .48661 Metetra 0 .327 .711 r .33356 .46234 .31498 .45411 .33683 .46518 .35549 .47385 Metetra 0 .353 .716 r .31127 .45189 .29276 .44455 .31498 .45411 .33356 .46234 Metetra 0 .386 .731 r .2886 .44227 .27015 .43586 .29276 .44455 .31127 .45189 Metetra 0 .418 .748 r .26554 .43326 .24716 .42767 .27015 .43586 .2886 .44227 Metetra 0 .445 .763 r .24208 .4247 .22377 .4198 .24716 .42767 .26554 .43326 Metetra 0 .465 .773 r .21821 .4165 .19998 .41212 .22377 .4198 .24208 .4247 Metetra 0 .478 .778 r .19392 .40856 .17577 .40457 .19998 .41212 .21821 .4165 Metetra 0 .484 .778 r .1692 .40084 .15114 .3971 .17577 .40457 .19392 .40856 Metetra 0 .484 .771 r .14403 .39332 .12608 .38969 .15114 .3971 .1692 .40084 Metetra .736 .801 .904 r .64583 .37086 .62715 .38625 .64423 .39243 .66288 .3772 Metetra .734 .796 .902 r .62853 .36412 .60982 .37972 .62715 .38625 .64583 .37086 Metetra .733 .792 .899 r .61097 .35696 .59223 .3728 .60982 .37972 .62853 .36412 Metetra .732 .786 .896 r .59316 .34935 .57439 .36544 .59223 .3728 .61097 .35696 Metetra .731 .781 .893 r .57508 .34124 .55628 .35756 .57439 .36544 .59316 .34935 Metetra .728 .775 .89 r .55674 .33257 .53792 .34904 .55628 .35756 .57508 .34124 Metetra .724 .769 .889 r .53813 .32329 .51929 .33974 .53792 .34904 .55674 .33257 Metetra .716 .763 .89 r .51926 .31336 .5004 .32944 .51929 .33974 .53813 .32329 Metetra .703 .758 .894 r .50012 .30273 .48125 .31789 .5004 .32944 .51926 .31336 Metetra .681 .752 .905 r .48071 .29144 .46184 .30489 .48125 .31789 .50012 .30273 Metetra .644 .745 .922 r .46102 .27958 .44219 .29042 .46184 .30489 .48071 .29144 Metetra .585 .733 .946 r .44107 .26731 .42229 .27491 .44219 .29042 .46102 .27958 Metetra .442 .27 .551 r .41774 .49824 .39834 .5006 .42229 .27491 .44107 .26731 Metetra .28 .657 .969 r .39638 .48717 .37708 .48661 .39834 .5006 .41774 .49824 Metetra .151 .596 .931 r .37469 .47639 .35549 .47385 .37708 .48661 .39638 .48717 Metetra .056 .546 .889 r .35265 .46602 .33356 .46234 .35549 .47385 .37469 .47639 Metetra 0 .514 .854 r .33026 .45612 .31127 .45189 .33356 .46234 .35265 .46602 Metetra 0 .497 .83 r .3075 .44666 .2886 .44227 .31127 .45189 .33026 .45612 Metetra 0 .49 .815 r .28436 .4376 .26554 .43326 .2886 .44227 .3075 .44666 Metetra 0 .488 .804 r .26081 .42892 .24208 .4247 .26554 .43326 .28436 .4376 Metetra 0 .488 .797 r .23686 .42055 .21821 .4165 .24208 .4247 .26081 .42892 Metetra 0 .489 .79 r .21247 .41246 .19392 .40856 .21821 .4165 .23686 .42055 Metetra 0 .488 .782 r .18765 .40462 .1692 .40084 .19392 .40856 .21247 .41246 Metetra 0 .485 .772 r .16237 .39703 .14403 .39332 .1692 .40084 .18765 .40462 Metetra .735 .801 .905 r .66474 .35532 .64583 .37086 .66288 .3772 .68175 .36179 Metetra .733 .798 .903 r .64747 .3485 .62853 .36412 .64583 .37086 .66474 .35532 Metetra .731 .794 .903 r .62995 .34131 .61097 .35696 .62853 .36412 .64747 .3485 Metetra .727 .79 .903 r .61216 .33374 .59316 .34935 .61097 .35696 .62995 .34131 Metetra .723 .787 .903 r .59412 .32579 .57508 .34124 .59316 .34935 .61216 .33374 Metetra .716 .784 .905 r .5758 .31744 .55674 .33257 .57508 .34124 .59412 .32579 Metetra .708 .781 .909 r .55722 .30868 .53813 .32329 .55674 .33257 .5758 .31744 Metetra .696 .778 .914 r .53837 .29954 .51926 .31336 .53813 .32329 .55722 .30868 Metetra .68 .775 .923 r .51924 .29001 .50012 .30273 .51926 .31336 .53837 .29954 Metetra .657 .772 .934 r .49983 .28014 .48071 .29144 .50012 .30273 .51924 .29001 Metetra .626 .768 .948 r .48013 .26998 .46102 .27958 .48071 .29144 .49983 .28014 Metetra .586 .761 .962 r .46015 .25959 .44107 .26731 .46102 .27958 .48013 .26998 Metetra .438 .267 .551 r .4375 .49429 .41774 .49824 .44107 .26731 .46015 .25959 Metetra .375 .727 .989 r .41607 .48515 .39638 .48717 .41774 .49824 .4375 .49429 Metetra .284 .689 .972 r .3943 .47603 .37469 .47639 .39638 .48717 .41607 .48515 Metetra .198 .647 .945 r .37218 .46699 .35265 .46602 .37469 .47639 .3943 .47603 Metetra .123 .607 .914 r .34971 .45809 .33026 .45612 .35265 .46602 .37218 .46699 Metetra .063 .573 .882 r .32685 .44935 .3075 .44666 .33026 .45612 .34971 .45809 Metetra .017 .545 .854 r .30361 .44078 .28436 .4376 .3075 .44666 .32685 .44935 Metetra 0 .524 .831 r .27997 .43241 .26081 .42892 .28436 .4376 .30361 .44078 Metetra 0 .508 .811 r .25591 .42423 .23686 .42055 .26081 .42892 .27997 .43241 Metetra 0 .497 .795 r .23143 .41624 .21247 .41246 .23686 .42055 .25591 .42423 Metetra 0 .489 .782 r .2065 .40843 .18765 .40462 .21247 .41246 .23143 .41624 Metetra 0 .484 .771 r .18111 .40081 .16237 .39703 .18765 .40462 .2065 .40843 Metetra .735 .802 .905 r .68387 .33964 .66474 .35532 .68175 .36179 .70084 .3462 Metetra .733 .8 .906 r .66664 .33283 .64747 .3485 .66474 .35532 .68387 .33964 Metetra .729 .799 .907 r .64916 .32577 .62995 .34131 .64747 .3485 .66664 .33283 Metetra .724 .797 .909 r .63141 .31846 .61216 .33374 .62995 .34131 .64916 .32577 Metetra .718 .796 .913 r .6134 .31091 .59412 .32579 .61216 .33374 .63141 .31846 Metetra .709 .795 .918 r .59513 .30311 .5758 .31744 .59412 .32579 .6134 .31091 Metetra .699 .794 .924 r .57657 .29507 .55722 .30868 .5758 .31744 .59513 .30311 Metetra .685 .794 .932 r .55774 .28681 .53837 .29954 .55722 .30868 .57657 .29507 Metetra .667 .793 .941 r .53863 .27832 .51924 .29001 .53837 .29954 .55774 .28681 Metetra .646 .791 .952 r .51923 .26964 .49983 .28014 .51924 .29001 .53863 .27832 Metetra .619 .788 .963 r .49953 .26078 .48013 .26998 .49983 .28014 .51923 .26964 Metetra .586 .783 .974 r .47953 .25175 .46015 .25959 .48013 .26998 .49953 .26078 Metetra .437 .266 .55 r .45761 .48968 .4375 .49429 .46015 .25959 .47953 .25175 Metetra .401 .759 .994 r .43614 .48202 .41607 .48515 .4375 .49429 .45761 .48968 Metetra .328 .729 .981 r .41431 .4743 .3943 .47603 .41607 .48515 .43614 .48202 Metetra .253 .693 .96 r .39212 .46653 .37218 .46699 .3943 .47603 .41431 .4743 Metetra .18 .654 .933 r .36957 .45873 .34971 .45809 .37218 .46699 .39212 .46653 Metetra .113 .615 .901 r .34663 .45092 .32685 .44935 .34971 .45809 .36957 .45873 Metetra .055 .579 .869 r .32329 .44313 .30361 .44078 .32685 .44935 .34663 .45092 Metetra .006 .547 .84 r .29955 .43536 .27997 .43241 .30361 .44078 .32329 .44313 Metetra 0 .521 .814 r .27539 .42762 .25591 .42423 .27997 .43241 .29955 .43536 Metetra 0 .502 .793 r .2508 .41993 .23143 .41624 .25591 .42423 .27539 .42762 Metetra 0 .489 .778 r .22576 .41228 .2065 .40843 .23143 .41624 .2508 .41993 Metetra 0 .483 .769 r .20026 .40468 .18111 .40081 .2065 .40843 .22576 .41228 Metetra .736 .804 .906 r .70322 .32378 .68387 .33964 .70084 .3462 .72015 .33042 Metetra .733 .804 .908 r .68604 .31705 .66664 .33283 .68387 .33964 .70322 .32378 Metetra .73 .805 .911 r .6686 .31021 .64916 .32577 .66664 .33283 .68604 .31705 Metetra .724 .806 .915 r .65091 .30327 .63141 .31846 .64916 .32577 .6686 .31021 Metetra .717 .807 .921 r .63294 .29622 .6134 .31091 .63141 .31846 .65091 .30327 Metetra .708 .808 .927 r .61471 .28907 .59513 .30311 .6134 .31091 .63294 .29622 Metetra .696 .809 .935 r .59619 .28181 .57657 .29507 .59513 .30311 .61471 .28907 Metetra .681 .81 .944 r .5774 .27444 .55774 .28681 .57657 .29507 .59619 .28181 Metetra .663 .81 .954 r .55831 .26695 .53863 .27832 .55774 .28681 .5774 .27444 Metetra .641 .809 .964 r .53892 .25935 .51923 .26964 .53863 .27832 .55831 .26695 Metetra .615 .807 .973 r .51923 .25163 .49953 .26078 .51923 .26964 .53892 .25935 Metetra .584 .802 .983 r .49922 .24378 .47953 .25175 .49953 .26078 .51923 .25163 Metetra .437 .266 .551 r .47807 .48478 .45761 .48968 .47953 .25175 .49922 .24378 Metetra .399 .777 .992 r .45657 .47844 .43614 .48202 .45761 .48968 .47807 .48478 Metetra .332 .747 .978 r .4347 .47199 .41431 .4743 .43614 .48202 .45657 .47844 Metetra .261 .712 .956 r .41246 .46543 .39212 .46653 .41431 .4743 .4347 .47199 Metetra .189 .672 .929 r .38983 .45876 .36957 .45873 .39212 .46653 .41246 .46543 Metetra .121 .631 .897 r .36681 .45197 .34663 .45092 .36957 .45873 .38983 .45876 Metetra .06 .591 .864 r .34339 .44507 .32329 .44313 .34663 .45092 .36681 .45197 Metetra .007 .554 .832 r .31956 .43804 .29955 .43536 .32329 .44313 .34339 .44507 Metetra 0 .524 .805 r .2953 .43089 .27539 .42762 .29955 .43536 .31956 .43804 Metetra 0 .501 .784 r .2706 .4236 .2508 .41993 .27539 .42762 .2953 .43089 Metetra 0 .487 .771 r .24545 .41619 .22576 .41228 .2508 .41993 .2706 .4236 Metetra 0 .482 .767 r .21985 .40864 .20026 .40468 .22576 .41228 .24545 .41619 Metetra .883 .629 .55 r .7311 .53817 .70322 .32378 .72015 .33042 .74854 .5434 Metetra .883 .629 .55 r .71339 .53303 .68604 .31705 .70322 .32378 .7311 .53817 Metetra .883 .629 .551 r .69541 .52797 .6686 .31021 .68604 .31705 .71339 .53303 Metetra .883 .629 .551 r .67715 .52299 .65091 .30327 .6686 .31021 .69541 .52797 Metetra .882 .629 .551 r .65861 .51808 .63294 .29622 .65091 .30327 .67715 .52299 Metetra .882 .629 .551 r .63977 .51324 .61471 .28907 .63294 .29622 .65861 .51808 Metetra .882 .629 .552 r .62063 .50845 .59619 .28181 .61471 .28907 .63977 .51324 Metetra .882 .629 .552 r .60117 .5037 .5774 .27444 .59619 .28181 .62063 .50845 Metetra .882 .629 .552 r .58139 .49897 .55831 .26695 .5774 .27444 .60117 .5037 Metetra .882 .629 .552 r .56129 .49424 .53892 .25935 .55831 .26695 .58139 .49897 Metetra .882 .63 .553 r .54084 .48949 .51923 .25163 .53892 .25935 .56129 .49424 Metetra .882 .63 .553 r .52004 .48468 .49922 .24378 .51923 .25163 .54084 .48949 Metetra .703 .524 .644 r .4989 .22892 .47807 .48478 .49922 .24378 .52004 .48468 Metetra .879 .684 .635 r .47823 .22202 .45657 .47844 .47807 .48478 .4989 .22892 Metetra .879 .684 .635 r .45721 .21496 .4347 .47199 .45657 .47844 .47823 .22202 Metetra .878 .684 .635 r .43584 .20769 .41246 .46543 .4347 .47199 .45721 .21496 Metetra .878 .684 .635 r .4141 .20021 .38983 .45876 .41246 .46543 .43584 .20769 Metetra .878 .684 .636 r .39199 .19247 .36681 .45197 .38983 .45876 .4141 .20021 Metetra .878 .684 .636 r .3695 .18447 .34339 .44507 .36681 .45197 .39199 .19247 Metetra .878 .684 .636 r .34662 .17618 .31956 .43804 .34339 .44507 .3695 .18447 Metetra .878 .683 .636 r .32335 .16759 .2953 .43089 .31956 .43804 .34662 .17618 Metetra .878 .683 .636 r .29967 .15868 .2706 .4236 .2953 .43089 .32335 .16759 Metetra .877 .683 .636 r .27558 .14944 .24545 .41619 .2706 .4236 .29967 .15868 Metetra .877 .683 .636 r .25106 .13986 .21985 .40864 .24545 .41619 .27558 .14944 Metetra .73 .835 .93 r .75171 .52275 .7311 .53817 .74854 .5434 .76911 .52806 Metetra .729 .84 .933 r .73406 .51764 .71339 .53303 .7311 .53817 .75171 .52275 Metetra .727 .846 .937 r .71614 .51274 .69541 .52797 .71339 .53303 .73406 .51764 Metetra .722 .851 .943 r .69794 .50806 .67715 .52299 .69541 .52797 .71614 .51274 Metetra .715 .857 .95 r .67946 .50361 .65861 .51808 .67715 .52299 .69794 .50806 Metetra .704 .864 .958 r .66068 .4994 .63977 .51324 .65861 .51808 .67946 .50361 Metetra .688 .869 .967 r .6416 .49542 .62063 .50845 .63977 .51324 .66068 .4994 Metetra .667 .874 .977 r .6222 .49168 .60117 .5037 .62063 .50845 .6416 .49542 Metetra .637 .876 .986 r .60247 .48813 .58139 .49897 .60117 .5037 .6222 .49168 Metetra .596 .874 .993 r .58241 .48475 .56129 .49424 .58139 .49897 .60247 .48813 Metetra .544 .865 .995 r .562 .48148 .54084 .48949 .56129 .49424 .58241 .48475 Metetra .479 .845 .99 r .54122 .47824 .52004 .48468 .54084 .48949 .562 .48148 Metetra .466 .347 .634 r .51925 .22213 .4989 .22892 .52004 .48468 .54122 .47824 Metetra .469 .813 .998 r .49857 .21662 .47823 .22202 .4989 .22892 .51925 .22213 Metetra .41 .789 .992 r .47754 .21086 .45721 .21496 .47823 .22202 .49857 .21662 Metetra .352 .761 .981 r .45613 .20478 .43584 .20769 .45721 .21496 .47754 .21086 Metetra .298 .732 .968 r .43435 .19834 .4141 .20021 .43584 .20769 .45613 .20478 Metetra .251 .705 .954 r .41218 .19148 .39199 .19247 .4141 .20021 .43435 .19834 Metetra .212 .68 .942 r .38963 .18418 .3695 .18447 .39199 .19247 .41218 .19148 Metetra .182 .659 .931 r .36668 .17644 .34662 .17618 .3695 .18447 .38963 .18418 Metetra .161 .643 .924 r .34332 .16824 .32335 .16759 .34662 .17618 .36668 .17644 Metetra .148 .632 .92 r .31956 .15958 .29967 .15868 .32335 .16759 .34332 .16824 Metetra .142 .626 .919 r .29538 .15045 .27558 .14944 .29967 .15868 .31956 .15958 Metetra .145 .624 .922 r .27077 .14084 .25106 .13986 .27558 .14944 .29538 .15045 Metetra .731 .836 .929 r .77258 .50709 .75171 .52275 .76911 .52806 .78992 .51254 Metetra .731 .841 .932 r .75498 .5019 .73406 .51764 .75171 .52275 .77258 .50709 Metetra .731 .847 .935 r .73712 .49698 .71614 .51274 .73406 .51764 .75498 .5019 Metetra .73 .854 .939 r .71898 .49237 .69794 .50806 .71614 .51274 .73712 .49698 Metetra .727 .861 .945 r .70056 .48812 .67946 .50361 .69794 .50806 .71898 .49237 Metetra .721 .87 .951 r .68185 .48428 .66068 .4994 .67946 .50361 .70056 .48812 Metetra .711 .88 .96 r .66283 .48091 .6416 .49542 .66068 .4994 .68185 .48428 Metetra .693 .89 .97 r .64351 .47807 .6222 .49168 .6416 .49542 .66283 .48091 Metetra .663 .898 .98 r .62385 .47579 .60247 .48813 .6222 .49168 .64351 .47807 Metetra .614 .9 .986 r .60385 .47405 .58241 .48475 .60247 .48813 .62385 .47579 Metetra .54 .888 .983 r .5835 .47275 .562 .48148 .58241 .48475 .60385 .47405 Metetra .437 .852 .96 r .56277 .47168 .54122 .47824 .562 .48148 .5835 .47275 Metetra .465 .347 .634 r .53995 .21577 .51925 .22213 .54122 .47824 .56277 .47168 Metetra .392 .807 .976 r .51928 .21213 .49857 .21662 .51925 .22213 .53995 .21577 Metetra .312 .764 .956 r .49823 .20799 .47754 .21086 .49857 .21662 .51928 .21213 Metetra .247 .723 .938 r .4768 .20321 .45613 .20478 .47754 .21086 .49823 .20799 Metetra .199 .69 .923 r .45498 .19774 .43435 .19834 .45613 .20478 .4768 .20321 Metetra .168 .665 .915 r .43277 .19158 .41218 .19148 .43435 .19834 .45498 .19774 Metetra .149 .648 .91 r .41016 .18475 .38963 .18418 .41218 .19148 .43277 .19158 Metetra .139 .637 .91 r .38714 .1773 .36668 .17644 .38963 .18418 .41016 .18475 Metetra .135 .63 .911 r .36372 .16927 .34332 .16824 .36668 .17644 .38714 .1773 Metetra .135 .626 .914 r .33988 .16067 .31956 .15958 .34332 .16824 .36372 .16927 Metetra .139 .624 .917 r .31562 .15152 .29538 .15045 .31956 .15958 .33988 .16067 Metetra .144 .624 .922 r .29092 .14184 .27077 .14084 .29538 .15045 .31562 .15152 Metetra .731 .835 .929 r .79371 .4912 .77258 .50709 .78992 .51254 .811 .49682 Metetra .733 .84 .93 r .77617 .48578 .75498 .5019 .77258 .50709 .79371 .4912 Metetra .736 .845 .931 r .75835 .48061 .73712 .49698 .75498 .5019 .77617 .48578 Metetra .738 .851 .933 r .74027 .47573 .71898 .49237 .73712 .49698 .75835 .48061 Metetra .741 .858 .935 r .7219 .47124 .70056 .48812 .71898 .49237 .74027 .47573 Metetra .743 .866 .937 r .70325 .46724 .68185 .48428 .70056 .48812 .7219 .47124 Metetra .743 .878 .942 r .6843 .46393 .66283 .48091 .68185 .48428 .70325 .46724 Metetra .737 .894 .95 r .66505 .46153 .64351 .47807 .66283 .48091 .6843 .46393 Metetra .719 .915 .961 r .64548 .46033 .62385 .47579 .64351 .47807 .66505 .46153 Metetra .669 .933 .969 r .62558 .46057 .60385 .47405 .62385 .47579 .64548 .46033 Metetra .55 .918 .947 r .60533 .46229 .5835 .47275 .60385 .47405 .62558 .46057 Metetra .331 .815 .847 r .58469 .46502 .56277 .47168 .5835 .47275 .60533 .46229 Metetra .462 .345 .634 r .56103 .21079 .53995 .21577 .56277 .47168 .58469 .46502 Metetra .163 .699 .833 r .54039 .21007 .51928 .21213 .53995 .21577 .56103 .21079 Metetra .074 .63 .807 r .51933 .20794 .49823 .20799 .51928 .21213 .54039 .21007 Metetra .041 .599 .812 r .49788 .20432 .4768 .20321 .49823 .20799 .51933 .20794 Metetra .039 .59 .83 r .47602 .19942 .45498 .19774 .4768 .20321 .49788 .20432 Metetra .053 .592 .852 r .45376 .19343 .43277 .19158 .45498 .19774 .47602 .19942 Metetra .073 .599 .871 r .4311 .18657 .41016 .18475 .43277 .19158 .45376 .19343 Metetra .093 .607 .888 r .40803 .17897 .38714 .1773 .41016 .18475 .4311 .18657 Metetra .111 .614 .9 r .38455 .17075 .36372 .16927 .38714 .1773 .40803 .17897 Metetra .126 .619 .91 r .36064 .16197 .33988 .16067 .36372 .16927 .38455 .17075 Metetra .137 .623 .917 r .3363 .15267 .31562 .15152 .33988 .16067 .36064 .16197 Metetra .145 .624 .922 r .31152 .14286 .29092 .14184 .31562 .15152 .3363 .15267 Metetra .731 .834 .928 r .81511 .47506 .79371 .4912 .811 .49682 .83235 .48091 Metetra .734 .837 .928 r .79761 .4693 .77617 .48578 .79371 .4912 .81511 .47506 Metetra .738 .839 .927 r .77985 .46364 .75835 .48061 .77617 .48578 .79761 .4693 Metetra .744 .842 .924 r .7618 .45813 .74027 .47573 .75835 .48061 .77985 .46364 Metetra .752 .845 .921 r .74347 .45285 .7219 .47124 .74027 .47573 .7618 .45813 Metetra .761 .85 .917 r .72486 .44791 .70325 .46724 .7219 .47124 .74347 .45285 Metetra .772 .857 .914 r .70595 .44353 .6843 .46393 .70325 .46724 .72486 .44791 Metetra .784 .868 .911 r .68674 .44009 .66505 .46153 .6843 .46393 .70595 .44353 Metetra .795 .89 .913 r .66725 .43829 .64548 .46033 .66505 .46153 .68674 .44009 Metetra .793 .935 .924 r .64746 .43948 .62558 .46057 .64548 .46033 .66725 .43829 Metetra .67 .974 .888 r .62739 .44585 .60533 .46229 .62558 .46057 .64746 .43948 Metetra .002 0 0 r .60699 .45823 .58469 .46502 .60533 .46229 .62739 .44585 Metetra .451 .338 .634 r .58257 .2112 .56103 .21079 .58469 .46502 .60699 .45823 Metetra .371 0 0 r .56197 .21512 .54039 .21007 .56103 .21079 .58257 .2112 Metetra .331 0 0 r .54091 .21414 .51933 .20794 .54039 .21007 .56197 .21512 Metetra .238 0 0 r .51941 .21016 .49788 .20432 .51933 .20794 .54091 .21414 Metetra 0 .446 .717 r .49751 .20439 .47602 .19942 .49788 .20432 .51941 .21016 Metetra 0 .507 .794 r .4752 .19748 .45376 .19343 .47602 .19942 .49751 .20439 Metetra .012 .55 .844 r .45249 .18978 .4311 .18657 .45376 .19343 .4752 .19748 Metetra .062 .58 .876 r .42937 .18148 .40803 .17897 .4311 .18657 .45249 .18978 Metetra .098 .601 .897 r .40582 .17269 .38455 .17075 .40803 .17897 .42937 .18148 Metetra .123 .614 .911 r .38185 .16348 .36064 .16197 .38455 .17075 .40582 .17269 Metetra .139 .621 .919 r .35744 .15388 .3363 .15267 .36064 .16197 .38185 .16348 Metetra .146 .624 .923 r .33258 .14391 .31152 .14286 .3363 .15267 .35744 .15388 Metetra .731 .833 .928 r .83678 .4587 .81511 .47506 .83235 .48091 .85396 .46479 Metetra .734 .833 .926 r .81933 .45251 .79761 .4693 .81511 .47506 .83678 .4587 Metetra .739 .832 .922 r .8016 .44622 .77985 .46364 .79761 .4693 .81933 .45251 Metetra .746 .831 .917 r .78359 .43983 .7618 .45813 .77985 .46364 .8016 .44622 Metetra .755 .829 .909 r .76528 .43333 .74347 .45285 .7618 .45813 .78359 .43983 Metetra .766 .826 .899 r .74668 .42674 .72486 .44791 .74347 .45285 .76528 .43333 Metetra .78 .821 .884 r .72776 .42003 .70595 .44353 .72486 .44791 .74668 .42674 Metetra .798 .814 .865 r .70853 .41321 .68674 .44009 .70595 .44353 .72776 .42003 Metetra .817 .804 .839 r .68898 .40627 .66725 .43829 .68674 .44009 .70853 .41321 Metetra .838 .788 .804 r .6691 .39922 .64746 .43948 .66725 .43829 .68898 .40627 Metetra .857 .768 .762 r .64888 .39205 .62739 .44585 .64746 .43948 .6691 .39922 Metetra .792 .628 .678 r .62742 .34084 .60699 .45823 .62739 .44585 .64888 .39205 Metetra .165 .195 .646 r .60516 .24734 .58257 .2112 .60699 .45823 .62742 .34084 Metetra .732 .209 0 r .58429 .23883 .56197 .21512 .58257 .2112 .60516 .24734 Metetra .567 0 0 r .56306 .23017 .54091 .21414 .56197 .21512 .58429 .23883 Metetra .379 0 0 r .54147 .22137 .51941 .21016 .54091 .21414 .56306 .23017 Metetra 0 .361 .698 r .51949 .21241 .49751 .20439 .51941 .21016 .54147 .22137 Metetra 0 .461 .791 r .49712 .20329 .4752 .19748 .49751 .20439 .51949 .21241 Metetra 0 .525 .847 r .47436 .194 .45249 .18978 .4752 .19748 .49712 .20329 Metetra .058 .567 .881 r .45118 .18455 .42937 .18148 .45249 .18978 .47436 .194 Metetra .1 .595 .902 r .42758 .17493 .40582 .17269 .42937 .18148 .45118 .18455 Metetra .127 .612 .915 r .40354 .16513 .38185 .16348 .40582 .17269 .42758 .17493 Metetra .142 .621 .922 r .37906 .15514 .35744 .15388 .38185 .16348 .40354 .16513 Metetra .147 .624 .924 r .35412 .14497 .33258 .14391 .35744 .15388 .37906 .15514 Metetra .731 .832 .927 r .85873 .44212 .83678 .4587 .85396 .46479 .87585 .44847 Metetra .733 .829 .924 r .84133 .4355 .81933 .45251 .83678 .4587 .85873 .44212 Metetra .737 .825 .919 r .82364 .42857 .8016 .44622 .81933 .45251 .84133 .4355 Metetra .742 .82 .913 r .80565 .42129 .78359 .43983 .8016 .44622 .82364 .42857 Metetra .749 .815 .904 r .78736 .41358 .76528 .43333 .78359 .43983 .80565 .42129 Metetra .758 .807 .892 r .76876 .40531 .74668 .42674 .76528 .43333 .78736 .41358 Metetra .768 .796 .875 r .74983 .39626 .72776 .42003 .74668 .42674 .76876 .40531 Metetra .779 .781 .854 r .73056 .38604 .70853 .41321 .72776 .42003 .74983 .39626 Metetra .79 .759 .826 r .71092 .37396 .68898 .40627 .70853 .41321 .73056 .38604 Metetra .798 .731 .79 r .69089 .35869 .6691 .39922 .68898 .40627 .71092 .37396 Metetra .802 .699 .751 r .67044 .33811 .64888 .39205 .6691 .39922 .69089 .35869 Metetra .71 .661 .8 r .64957 .31153 .62742 .34084 .64888 .39205 .67044 .33811 Metetra .737 .273 0 r .62848 .28465 .60516 .24734 .62742 .34084 .64957 .31153 Metetra .544 .042 0 r .60724 .26322 .58429 .23883 .60516 .24734 .62848 .28465 Metetra 0 .146 .605 r .5858 .24663 .56306 .23017 .58429 .23883 .60724 .26322 Metetra 0 .296 .714 r .56407 .23286 .54147 .22137 .56306 .23017 .5858 .24663 Metetra 0 .406 .791 r .542 .22062 .51949 .21241 .54147 .22137 .56407 .23286 Metetra 0 .483 .843 r .51955 .20923 .49712 .20329 .51949 .21241 .542 .22062 Metetra .035 .536 .877 r .49672 .19833 .47436 .194 .49712 .20329 .51955 .20923 Metetra .083 .572 .899 r .47349 .1877 .45118 .18455 .47436 .194 .49672 .19833 Metetra .116 .597 .913 r .44983 .17722 .42758 .17493 .45118 .18455 .47349 .1877 Metetra .137 .612 .921 r .42573 .16681 .40354 .16513 .42758 .17493 .44983 .17722 Metetra .148 .621 .925 r .40118 .15644 .37906 .15514 .40354 .16513 .42573 .16681 Metetra .149 .624 .925 r .37616 .14607 .35412 .14497 .37906 .15514 .40118 .15644 Metetra .73 .831 .927 r .88096 .42535 .85873 .44212 .87585 .44847 .89802 .43193 Metetra .731 .826 .924 r .86361 .41837 .84133 .4355 .85873 .44212 .88096 .42535 Metetra .733 .821 .919 r .84597 .41094 .82364 .42857 .84133 .4355 .86361 .41837 Metetra .735 .815 .914 r .82802 .403 .80565 .42129 .82364 .42857 .84597 .41094 Metetra .738 .807 .907 r .80976 .39447 .78736 .41358 .80565 .42129 .82802 .403 Metetra .742 .799 .898 r .79118 .38522 .76876 .40531 .78736 .41358 .80976 .39447 Metetra .744 .789 .889 r .77227 .37506 .74983 .39626 .76876 .40531 .79118 .38522 Metetra .745 .777 .879 r .75302 .36377 .73056 .38604 .74983 .39626 .77227 .37506 Metetra .741 .763 .871 r .73342 .35105 .71092 .37396 .73056 .38604 .75302 .36377 Metetra .726 .748 .87 r .71348 .33667 .69089 .35869 .71092 .37396 .73342 .35105 Metetra .682 .731 .887 r .69318 .32062 .67044 .33811 .69089 .35869 .71348 .33667 Metetra .563 .696 .929 r .67256 .30336 .64957 .31153 .67044 .33811 .69318 .32062 Metetra .341 .61 .949 r .65165 .28585 .62848 .28465 .64957 .31153 .67256 .30336 Metetra .148 .522 .917 r .63045 .26906 .60724 .26322 .62848 .28465 .65165 .28585 Metetra .063 .49 .892 r .60896 .25351 .5858 .24663 .60724 .26322 .63045 .26906 Metetra .046 .497 .887 r .58715 .23923 .56407 .23286 .5858 .24663 .60896 .25351 Metetra .058 .521 .894 r .56501 .22601 .542 .22062 .56407 .23286 .58715 .23923 Metetra .081 .547 .903 r .5425 .2136 .51955 .20923 .542 .22062 .56501 .22601 Metetra .104 .571 .912 r .51961 .20178 .49672 .19833 .51955 .20923 .5425 .2136 Metetra .124 .591 .92 r .49631 .19039 .47349 .1877 .49672 .19833 .51961 .20178 Metetra .14 .605 .925 r .47259 .1793 .44983 .17722 .47349 .1877 .49631 .19039 Metetra .149 .616 .927 r .44843 .16843 .42573 .16681 .44983 .17722 .47259 .1793 Metetra .153 .622 .928 r .42381 .15774 .40118 .15644 .42573 .16681 .44843 .16843 Metetra .15 .624 .926 r .39872 .14719 .37616 .14607 .40118 .15644 .42381 .15774 Metetra .73 .83 .927 r .90349 .40841 .88096 .42535 .89802 .43193 .92048 .41519 Metetra .729 .825 .924 r .8862 .40118 .86361 .41837 .88096 .42535 .90349 .40841 Metetra .728 .82 .921 r .86861 .39346 .84597 .41094 .86361 .41837 .8862 .40118 Metetra .728 .814 .918 r .85072 .38523 .82802 .403 .84597 .41094 .86861 .39346 Metetra .726 .808 .915 r .83252 .37642 .80976 .39447 .82802 .403 .85072 .38523 Metetra .724 .801 .912 r .814 .36698 .79118 .38522 .80976 .39447 .83252 .37642 Metetra .719 .794 .91 r .79515 .35684 .77227 .37506 .79118 .38522 .814 .36698 Metetra .711 .786 .911 r .77598 .34594 .75302 .36377 .77227 .37506 .79515 .35684 Metetra .696 .778 .915 r .75647 .33424 .73342 .35105 .75302 .36377 .77598 .34594 Metetra .671 .769 .924 r .73663 .32178 .71348 .33667 .73342 .35105 .75647 .33424 Metetra .629 .758 .94 r .71646 .30865 .69318 .32062 .71348 .33667 .73663 .32178 Metetra .565 .741 .959 r .69596 .29504 .67256 .30336 .69318 .32062 .71646 .30865 Metetra .48 .715 .973 r .67514 .28122 .65165 .28585 .67256 .30336 .69596 .29504 Metetra .387 .682 .977 r .65399 .26745 .63045 .26906 .65165 .28585 .67514 .28122 Metetra .305 .652 .97 r .63251 .25394 .60896 .25351 .63045 .26906 .65399 .26745 Metetra .245 .629 .959 r .61069 .24081 .58715 .23923 .60896 .25351 .63251 .25394 Metetra .206 .616 .95 r .58851 .2281 .56501 .22601 .58715 .23923 .61069 .24081 Metetra .184 .612 .943 r .56596 .21581 .5425 .2136 .56501 .22601 .58851 .2281 Metetra .172 .612 .939 r .54301 .20389 .51961 .20178 .5425 .2136 .56596 .21581 Metetra .166 .614 .936 r .51966 .1923 .49631 .19039 .51961 .20178 .54301 .20389 Metetra .163 .618 .934 r .49588 .18098 .47259 .1793 .49631 .19039 .51966 .1923 Metetra .16 .621 .932 r .47165 .1699 .44843 .16843 .47259 .1793 .49588 .18098 Metetra .156 .623 .929 r .44697 .15902 .42381 .15774 .44843 .16843 .47165 .1699 Metetra .151 .624 .926 r .4218 .14833 .39872 .14719 .42381 .15774 .44697 .15902 Metetra .73 .831 .927 r .92631 .39129 .90349 .40841 .92048 .41519 .94323 .39822 Metetra .728 .826 .926 r .9091 .38394 .8862 .40118 .90349 .40841 .92631 .39129 Metetra .725 .822 .925 r .89159 .37618 .86861 .39346 .8862 .40118 .9091 .38394 Metetra .721 .818 .925 r .87377 .36798 .85072 .38523 .86861 .39346 .89159 .37618 Metetra .716 .813 .925 r .85565 .35934 .83252 .37642 .85072 .38523 .87377 .36798 Metetra .709 .809 .927 r .83721 .35023 .814 .36698 .83252 .37642 .85565 .35934 Metetra .699 .804 .93 r .81846 .34066 .79515 .35684 .814 .36698 .83721 .35023 Metetra .686 .8 .936 r .79938 .33064 .77598 .34594 .79515 .35684 .81846 .34066 Metetra .667 .795 .943 r .77998 .32017 .75647 .33424 .77598 .34594 .79938 .33064 Metetra .641 .789 .953 r .76025 .3093 .73663 .32178 .75647 .33424 .77998 .32017 Metetra .607 .781 .964 r .74018 .29807 .71646 .30865 .73663 .32178 .76025 .3093 Metetra .563 .77 .975 r .71978 .28658 .69596 .29504 .71646 .30865 .74018 .29807 Metetra .511 .755 .984 r .69904 .27489 .67514 .28122 .69596 .29504 .71978 .28658 Metetra .453 .736 .988 r .67795 .26309 .65399 .26745 .67514 .28122 .69904 .27489 Metetra .394 .715 .987 r .6565 .25127 .63251 .25394 .65399 .26745 .67795 .26309 Metetra .339 .694 .982 r .63469 .23948 .61069 .24081 .63251 .25394 .6565 .25127 Metetra .291 .675 .973 r .6125 .22778 .58851 .2281 .61069 .24081 .63469 .23948 Metetra .252 .659 .964 r .58992 .21619 .56596 .21581 .58851 .2281 .6125 .22778 Metetra .221 .646 .955 r .56694 .20473 .54301 .20389 .56596 .21581 .58992 .21619 Metetra .198 .637 .947 r .54354 .19341 .51966 .1923 .54301 .20389 .56694 .20473 Metetra .18 .631 .94 r .51971 .18224 .49588 .18098 .51966 .1923 .54354 .19341 Metetra .167 .627 .934 r .49543 .17119 .47165 .1699 .49588 .18098 .51971 .18224 Metetra .157 .625 .93 r .47068 .16029 .44697 .15902 .47165 .1699 .49543 .17119 Metetra .15 .624 .925 r .44544 .14951 .4218 .14833 .44697 .15902 .47068 .16029 Metetra .729 .832 .928 r .94944 .37398 .92631 .39129 .94323 .39822 .96628 .38104 Metetra .727 .829 .928 r .93231 .36664 .9091 .38394 .92631 .39129 .94944 .37398 Metetra .723 .827 .93 r .91489 .359 .89159 .37618 .9091 .38394 .93231 .36664 Metetra .717 .825 .932 r .89718 .35108 .87377 .36798 .89159 .37618 .91489 .359 Metetra .709 .823 .935 r .87916 .34287 .85565 .35934 .87377 .36798 .89718 .35108 Metetra .699 .82 .94 r .86083 .33437 .83721 .35023 .85565 .35934 .87916 .34287 Metetra .686 .818 .946 r .84218 .32559 .81846 .34066 .83721 .35023 .86083 .33437 Metetra .67 .815 .953 r .82322 .31655 .79938 .33064 .81846 .34066 .84218 .32559 Metetra .65 .812 .961 r .80393 .30724 .77998 .32017 .79938 .33064 .82322 .31655 Metetra .625 .807 .97 r .7843 .29769 .76025 .3093 .77998 .32017 .80393 .30724 Metetra .595 .801 .978 r .76434 .28793 .74018 .29807 .76025 .3093 .7843 .29769 Metetra .56 .792 .986 r .74403 .27796 .71978 .28658 .74018 .29807 .76434 .28793 Metetra .519 .78 .992 r .72336 .26782 .69904 .27489 .71978 .28658 .74403 .27796 Metetra .473 .766 .995 r .70234 .25753 .67795 .26309 .69904 .27489 .72336 .26782 Metetra .425 .749 .994 r .68093 .24712 .6565 .25127 .67795 .26309 .70234 .25753 Metetra .377 .729 .99 r .65915 .2366 .63469 .23948 .6565 .25127 .68093 .24712 Metetra .33 .709 .982 r .63698 .22601 .6125 .22778 .63469 .23948 .65915 .2366 Metetra .286 .689 .973 r .6144 .21535 .58992 .21619 .6125 .22778 .63698 .22601 Metetra .247 .671 .962 r .5914 .20464 .56694 .20473 .58992 .21619 .6144 .21535 Metetra .215 .654 .952 r .56797 .1939 .54354 .19341 .56694 .20473 .5914 .20464 Metetra .188 .641 .942 r .5441 .18313 .51971 .18224 .54354 .19341 .56797 .1939 Metetra .169 .632 .934 r .51976 .17234 .49543 .17119 .51971 .18224 .5441 .18313 Metetra .156 .626 .928 r .49496 .16153 .47068 .16029 .49543 .17119 .51976 .17234 Metetra .149 .624 .925 r .46966 .15071 .44544 .14951 .47068 .16029 .49496 .16153 Metetra .73 .833 .929 r .97287 .35646 .94944 .37398 .96628 .38104 .98963 .36363 Metetra .727 .833 .931 r .95584 .34918 .93231 .36664 .94944 .37398 .97287 .35646 Metetra .722 .833 .934 r .93853 .34178 .91489 .359 .93231 .36664 .95584 .34918 Metetra .716 .834 .938 r .92093 .33425 .89718 .35108 .91489 .359 .93853 .34178 Metetra .707 .834 .943 r .90303 .3266 .87916 .34287 .89718 .35108 .92093 .33425 Metetra .695 .834 .949 r .88482 .31882 .86083 .33437 .87916 .34287 .90303 .3266 Metetra .681 .833 .956 r .8663 .3109 .84218 .32559 .86083 .33437 .88482 .31882 Metetra .663 .832 .964 r .84746 .30285 .82322 .31655 .84218 .32559 .8663 .3109 Metetra .642 .829 .972 r .82829 .29465 .80393 .30724 .82322 .31655 .84746 .30285 Metetra .617 .825 .98 r .80879 .28631 .7843 .29769 .80393 .30724 .82829 .29465 Metetra .588 .819 .987 r .78893 .27783 .76434 .28793 .7843 .29769 .80879 .28631 Metetra .555 .811 .993 r .76872 .26919 .74403 .27796 .76434 .28793 .78893 .27783 Metetra .517 .8 .997 r .74814 .26039 .72336 .26782 .74403 .27796 .76872 .26919 Metetra .475 .786 .998 r .72719 .25143 .70234 .25753 .72336 .26782 .74814 .26039 Metetra .43 .769 .997 r .70585 .24231 .68093 .24712 .70234 .25753 .72719 .25143 Metetra .384 .749 .992 r .68411 .23302 .65915 .2366 .68093 .24712 .70585 .24231 Metetra .337 .728 .984 r .66197 .22355 .63698 .22601 .65915 .2366 .68411 .23302 Metetra .292 .706 .973 r .6394 .2139 .6144 .21535 .63698 .22601 .66197 .22355 Metetra .251 .684 .962 r .6164 .20407 .5914 .20464 .6144 .21535 .6394 .2139 Metetra .216 .664 .95 r .59296 .19405 .56797 .1939 .5914 .20464 .6164 .20407 Metetra .186 .647 .939 r .56906 .18383 .5441 .18313 .56797 .1939 .59296 .19405 Metetra .165 .634 .931 r .54468 .17341 .51976 .17234 .5441 .18313 .56906 .18383 Metetra .152 .626 .926 r .51983 .16278 .49496 .16153 .51976 .17234 .54468 .17341 Metetra .147 .624 .924 r .49447 .15194 .46966 .15071 .49496 .16153 .51983 .16278 Metetra 0 g .25 Mabswid .49459 0 m .49434 .3119 L s .49434 .3119 m 0 .49861 L s 0 .49861 m .0202 .23935 L s .0202 .23935 m .49459 0 L s .49459 0 m .49434 .3119 L s .49434 .3119 m 1 .49629 L s 1 .49629 m .97968 .23634 L s .97968 .23634 m .49459 0 L s .49459 0 m .97968 .23634 L s .49459 0 m .49458 .00626 L s [(0)] .4946 -0.01252 -0.00078 1 Mshowa .67205 .08646 m .67223 .09272 L s [(1)] .67169 .07395 .02883 1 Mshowa .82638 .16166 m .82672 .16791 L s [(2)] .82571 .14915 .05389 1 Mshowa .96183 .22765 m .9623 .23389 L s [(3)] .96089 .21516 .07538 1 Mshowa .125 Mabswid .53217 .01831 m .5322 .02207 L s .56867 .03609 m .56871 .03985 L s .60412 .05337 m .60418 .05712 L s .63856 .07015 m .63865 .0739 L s .70461 .10233 m .70474 .10608 L s .73629 .11776 m .73644 .12152 L s .76713 .13279 m .76729 .13654 L s .79715 .14741 m .79733 .15116 L s .85486 .17553 m .85508 .17928 L s .88262 .18906 m .88286 .19281 L s .90969 .20224 m .90994 .20599 L s .93608 .2151 m .93635 .21885 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[53]:=", ImageSize->{288, 178.875}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg0?ooo`00OP3oool2000000P0 oooo00<000000?ooo`3oool01`3oool2000008`0oooo001l0?ooo`8000002P3oool00`000000oooo 0?ooo`070?ooo`040000003oool00000000008X0oooo001j0?ooo`<000002`3oool00`000000oooo 0?ooo`0;0?ooo`800000R03oool007P0oooo0P00000>0?ooo`030000003oool0oooo00d0oooo0P00 00260?ooo`00MP3oool200000100oooo00<000000?ooo`3oool03`3oool2000008@0oooo001d0?oo o`8000004P3oool00`000000oooo0?ooo`0A0?ooo`800000PP3oool00780oooo0P00000D0?ooo`03 0000003oool0oooo0140oooo00@000000?ooo`0000000000P03oool005P0oooo1000000D0?ooo`80 00005P3oool00`000000oooo0?ooo`0E0?ooo`8000004`3oool5000006H0oooo001H0?ooo`030000 003oool0oooo01<0oooo0`00000G0?ooo`030000003oool0oooo01L0oooo0P00000C0?ooo`030000 003oool0oooo06H0oooo001I0?ooo`030000003oool0oooo0100oooo0P00000J0?ooo`030000003o ool0oooo01T0oooo0P00000A0?ooo`030000003oool0oooo06H0oooo001J0?ooo`030000003oool0 oooo00d0oooo0P00000L0?ooo`030000003oool0oooo01X0oooo0`00000?0?ooo`030000003oool0 oooo06H0oooo001H0?ooo`040000003oool0oooo000000`0oooo0P00000N0?ooo`030000003oool0 oooo01d0oooo0P00000=0?ooo`030000003oool0oooo06H0oooo001I0?ooo`8000002`3oool20000 0200oooo00<000000?ooo`3oool07`3oool2000000X0oooo0P00001X0?ooo`00I03oool200000280 oooo00<000000?ooo`3oool08@3oool200000780oooo001R0?ooo`80000000<0oooo0000003oool0 8@3oool00`000000oooo0?ooo`0S0?ooo`800000L03oool00600oooo0P00000V0?ooo`030000003o ool0oooo02@0oooo0`00001^0?ooo`00GP3oool2000002P0oooo00<000000?ooo`3oool09`3oool3 000006/0oooo001L0?ooo`800000:P3oool00`000000oooo0?ooo`0Z0?ooo`800000J@3oool005X0 oooo0P00000/0?ooo`030000003oool0oooo02`0oooo0P00001W0?ooo`00F03oool3000002d0oooo 00<000000?ooo`3oool0;03oool010000000oooo00000000001U0?ooo`00EP3oool200000080oooo 00<000000?ooo`3oool0:`3oool00`000000oooo0?ooo`0]0?ooo`030000003oool0oooo00800000 H`3oool005@0oooo0P00000b0?ooo`030000003oool0oooo0380oooo0P00001Q0?ooo`00DP3oool2 000003@0oooo00<000000?ooo`3oool0=03oool2000005l0oooo001@0?ooo`800000=P3oool00`00 0000oooo0?ooo`0e0?ooo`<00000G@3oool004h0oooo0P00000h0?ooo`030000003oool0oooo03P0 oooo0P00001K0?ooo`00C03oool2000000030?ooo`000000oooo03L0oooo00<000000?ooo`3oool0 >P3oool2000005T0oooo001:0?ooo`800000?03oool00`000000oooo0?ooo`0l0?ooo`<00000EP3o ool00380oooo0`00000D0?ooo`030000003oool0oooo03`0oooo00<000000?ooo`3oool0?P3oool2 000001<0oooo1000000n0?ooo`00<`3oool00`000000oooo0?ooo`0A0?ooo`800000?`3oool00`00 0000oooo0?ooo`100?ooo`8000004@3oool00`000000oooo0?ooo`0o0?ooo`00<03oool500000100 oooo0P0000110?ooo`030000003oool0oooo0480oooo0P00000@0?ooo`030000003oool0oooo03h0 oooo000`0?ooo`040000003oool0oooo000000l0oooo0`0000120?ooo`030000003oool0oooo04@0 oooo0`00000>0?ooo`030000003oool0oooo03d0oooo000a0?ooo`030000003oool0000000d0oooo 0P0000150?ooo`030000003oool0oooo04H0oooo0P00000;0?ooo`040000003oool0oooo000003h0 oooo000b0?ooo`8000002`3oool2000000H0oooo2@00000h0?ooo`030000003oool0oooo04P0oooo 0P00000:0?ooo`800000?`3oool003d0oooo0P0000080?ooo`040000003P[Z800000000000@09Io/ 4P00000W0?ooo`030000003oool0oooo04X0oooo0P0000190?ooo`00>`3oool2000000X0oooo00@0 00000>2^XP3P[Z80h:jR0P00000402FOk080000000@099o/00000000000000000P0UWn`2000000@0 9Io/6P00000?0?ooo`030000003oool0oooo04`0oooo0`0000160?ooo`00>@3oool3000000/0oooo 00<000000>2^XP3P[Z800`3P[Z8@000000@09Io/0P00000202FOk0<000000`0VWn`2000000@09Yo] 0P00000402JOkA<00000C`3oool2000004D0oooo000g0?ooo`8000003P3oool00`000000h:jR0>2^ XP040>2^XP030000003P[Z800000008000000P0TX>/40000000302>OjP000000000001<00000100V Wnd2000000@09Yo]0P00000202JOk08000001@0VWn`2000000809Io/00@0000002FOk00000000000 C`3oool2000004<0oooo000e0?ooo`8000003`3oool00`000000h:jR0>2^XP050>2^XP030000003P [Z80h:jR0080h:jR2`00000202>OjP<000000`0SW^/2000000<099k/5P00000502JOk0<000000`0U Wn`2000004l0oooo0`0000100?ooo`00<`3oool200000140oooo00<000000>2^XP3P[Z801@3P[Z80 0`000000h:jR0>2^XP030>2^XP040000003P[Z800000000000@09J7[3P00000302BNk08000000P0U W^`4000000809io]0P00000402NOkA@00000C`3oool2000003h0oooo000a0?ooo`8000004`3oool0 0`000000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00@000000>2^XP3P[Z80h:jR0P00 000402FQj`80000000@08Z3Y00000000000000000P0PW^PE000000@09io]0P00000302ROkP800000 0P0WX>d0100000009j3]00000000000502JPk@800000CP3oool3000003`0oooo000_0?ooo`800000 00<0oooo0000003oool04P3oool00`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR 00<000000>2^XP3P[Z800`3P[Z8F0000008089cZ0P00000402>Lja4000000`0WX>d2000000D09Z3] 0P00001<0?ooo`030000003oool0oooo00800000>P3oool002d0oooo0P00000G0?ooo`030000003P [Z80h:jR00@0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P [Z800000008000000P0YY>`3000000808Z7Y1000000201bMiPT00000100SW>/2000000809Yg]0P00 000402RNkQ@00000CP3oool2000003P0oooo000[0?ooo`8000006@3oool00`000000h:jR0>2^XP04 0>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z801@3P[Z800`000000h:jR0>2^XP02 0>2^XQ4000000P0IVND?000000@0:9k^0`0000000`0ZX>l000000000000502^Qk`8000001@0ZX^h2 000004h0oooo0P00000f0?ooo`00:03oool3000001/0oooo00<000000>2^XP3P[Z80103P[Z800`00 0000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00D0h:jR00<000000>2^XP3P[Z800`3P[Z800`00 0000h:nR0000000200000080;ZS^0`00000302>Sj0h000000P0MV>T@000000D0:j7_0P00000502ZR kP800000C03oool010000000oooo00000000000d0?ooo`009`3oool2000001d0oooo00<000000>2^ XP3P[Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00D0h:jR00<000000>2^ XP3P[Z800`3P[Z800`000000h:nR0>2_XP020>2_XQ0000000`0?U>09000000808i[/0P00000202VN k`030000000YW^l0:Ik_01<00000CP3oool2000001D0oooo0P00000K0?ooo`003@3oool3000001D0 oooo0P00000O0?ooo`030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000 h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j800`3P[j800`000000 h:nR0000000200000080=Zka0`00000302JUj0T000000P0>TN4:000000@0:Ik_0P00000202jQl080 0000100`Y?42000000D0;jG`0P00001>0?ooo`<000004@3oool010000000oooo0?ooo`00000J0?oo o`003@3oool010000000oooo0?ooo`00000B0?ooo`800000803oool00`000000h:jR0>2^XP050>2^ XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^ XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800P3P[j8G000000805I;V40000004032T l@8000001@0_YO02000004h0oooo0P00000B0?ooo`030000003oool0oooo01T0oooo000=0?ooo`04 0000003oool0oooo00000100oooo0P00000R0?ooo`030000003P[Z80h:jR00D0h:jR00<000000>2^ XP3P[Z800`3P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j800000008000000P10]?@30000 00<0:j[Z3`00000201nGj`800000100ZWNlC000004h0oooo0P00000A0?ooo`030000003oool0oooo 01P0oooo000=0?ooo`<000003`3oool2000002@0oooo00<000000>2^XP3P[Z801@3P[Z800`000000 h:jR0>2^XP030>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000 h:nR0>2_XP040>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800P3P[j8M000000@0 :Yg_0P00000203:SlP8000001@0gYo<3000000<0=jWc1000001<0?ooo`800000303oool010000000 oooo0?ooo`00000J0?ooo`003P3oool00`000000oooo0?ooo`0<0?ooo`<000009@3oool00`000000 h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z80103P[Z800`000000 h:jR0>2^XP030>2^XP030000003P[j80h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j800`000000 h:nR0>2_XP030>2_XP030000003P[j800000008000000P1<^oL3000000@0<[3/6P00000403NWl``0 0000B`3oool2000000/0oooo0P00000K0?ooo`003P3oool3000000X0oooo0P00000X0?ooo`030000 003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000 003P[Z80h:jR00<0h:jR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000 003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800P3P[j8:000000D0?kW`2000000201ZBj@800000 100/W?08000000D0?j_f0P000005042_mP800000BP3oool3000002H0oooo000I0?ooo`800000:P3o ool00`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z801@3P [Z800`000000h:jR0>2^XP030>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P [j800`000000h:nR0>2_XP040>2_XP030000003P[j80h:nR00<0h:nR00@000000>2_XP0000000000 101J`_/60000000304o3m0000000Cl?d00<0Cl?d2000000402bLl08000000P0hYO@2000000L0?j_f 0P000005042_mP800000B`3oool2000002@0oooo000G0?ooo`800000;03oool00`000000h:jR0>2^ XP040>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z801@3P[Z800`000000h:jR0>2^ XP030>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_ XP040>2_XP030000003P[j80h:nR00<0h:nR00@000000>2_XP3P[j80h:nR1000000506S9o@<00000 0P1?`o@30000000306C>n@000000000001000000100oZoH<000004/0oooo0`00000Q0?ooo`005@3o ool3000002d0oooo00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P [Z80h:jR00D0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000h:nR0>2_XP030>2_XP030000003P [j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000003P [j80h:nR0080h:nR00<000000>6_XP0000000P00000406S9o@H00000101Tc_T40000008058cW0P00 000302nLl@80000000<0@:Sf0000000000001000000504V`n@8000001@1:]?T2000004/0oooo0P00 000P0?ooo`004`3oool200000300oooo00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP03 0>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:nR0>2_XP03 0>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP04 0>2_XP030000003P[j80h:nR0080h:nR00<000000>6_XP3Q[j800P3Q[j840000000307S@o`000000 N=3o00<0N=3o1000000307MHXPL000000`0_W?400`000000@:Sf042XmP03042XmP8000001P19/?T2 000000D0B[Ci0P00001;0?ooo`8000007P3oool00140oooo0P00000a0?ooo`030000003P[Z80h:jR 00D0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR 00@0h:jR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR 00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR 00<0hJnR00<000000>6_XP0000000P00000207S@o`<0000000<0MeRR0000001gF:800`1gF:800`00 0000MURR07IHXP0:000000D0@:Sf0P00000304V`n@`00000B`3oool2000001`0oooo000>0?ooo`<0 0000<`3oool00`000000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P [Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P [j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P [j800`3P[j800`000000hJnR0>6_XP030>6_XP040000003Q[j80hJnR0>6_XP<00000101gF:800`00 0000MeRR07MHXP0207MHXP030000001fF:80MURR0080MURR0P000000100>QN@000000000000dWO<< 000000D0E;Gk0P00000505Jjn`<00000BP3oool2000001X0oooo000=0?ooo`800000=@3oool00`00 0000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z80103P[Z800`00 0000h:jR0>2^XP040>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`00 0000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`00 0000hJnR0>6_XP030>6_XP040000003Q[j80hJnR0>6_XP8000001@1gF:800`000000MeRR07MHXP02 07MHXP030000001fF:80MURR00@0MURR0P0000000`0>QN@0000003BMl`0303BMl`8000001@1:[?T2 000000H0E;Gk0P00000405Jjn`@00000B@3oool3000001P0oooo000;0?ooo`80000000<0oooo0000 003oool0=03oool00`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2^ XP3P[Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P[j80h:nR00@0h:nR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_ XP3P[j800P3P[j800`000000hJnR0>6_XP040>6_XP040000003Q[j80hJnR0>6_XP8000001@1gF:80 0`000000MeRR07MHXP0307MHXP030000001fF:80MURR00<0MURR1P00000403BMl`8000001@1:[?T2 000000<0E;Gk1`00000406:oo@800000BP3oool2000001H0oooo000:0?ooo`800000>03oool00`00 0000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z80103P[Z800`00 0000h:jR0>2^XP030>2^XP030000003P[j80h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j800`00 0000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800P3P[j800`00 0000hJnR0>6_XP040>6_XP040000003Q[j80hJnR0>6_XP8000001@1gF:800`000000MeRR07MHXP03 07MHXP030000001fF:80MURR00<0MURR00D0000007=FXP000000000000]oh`0A000000D0H;[m0P00 000606:oo@800000A@3oool3000000030?ooo`000000oooo01D0oooo000:0?ooo`030000003oool0 000000800000=@3oool00`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00<0h:jR00<00000 0>2^XP3P[Z801@3P[Z800`000000h:jR0>2^XP030>2^XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j800P3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR0080hJnR0P000006 07MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:800`1fF:801@000000LeJR07=FXP1c EZ80000000802goS0P00000403jQm@8000001@1F/O/2000000L0H;[m0P00000306:oo@D00000@03o ool3000000@0oooo00<000000?ooo`3oool0503oool000X0oooo00<000000?ooo`3oool00P3oool3 00000380oooo00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80 h:jR00D0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000h:nR0>2_XP030>2_XP030000003P[j80 h:nR00<0h:nR00<000000>2_XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80 h:nR0080h:nR00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP020>6_XP8000001P1gF:80 0`000000MeRR07MHXP0207MHXP030000001fF:80MURR00<0MURR00<0000007=FXP1cEZ800P1cEZ82 000000802goS00<0000003jQm@0nXOD00`0nXOD00`000000E[7k05Jan`0405Jan`800000101P^_d6 000000D0K/Co0`00000j0?ooo`<000001`3oool00`000000oooo0?ooo`0D0?ooo`002P3oool00`00 0000oooo0?ooo`050?ooo`<00000;`3oool00`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR 00<0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80h:nR 00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000003P[j80h:nR 00<0h:nR00<000000>2_XP3P[j800P3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR 0080hJnR0`00000507MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:800`1fF:800`00 0000LeJR07=FXP0307=FXPH00000100nXOD2000000<0E[7k1`00000506booP8000001`1^a?l30000 03@0oooo0`00000:0?ooo`030000003oool0oooo01@0oooo000:0?ooo`030000003oool0oooo00P0 oooo0`00000/0?ooo`030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000 h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j800`3P[j800`000000 h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80103P[j800`000000 h:nR0>2_XP020>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j800P3Q[j83000000D0 MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000001cEZ80LeJR00<0 LeJR00<0000002XaY@0000000P0@ON@:000000D0I;Ol0P00000706booP8000000P1^a?l3000000<0 NLWo0`00000^0?ooo`<000003@3oool00`000000oooo0?ooo`0D0?ooo`002P3oool00`000000oooo 0?ooo`0;0?ooo`<00000:03oool00`000000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00<0h:jR 00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80h:nR00<0h:nR 00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00@0h:nR 00<000000>2_XP3P[j800P3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR0080hJnR 0`00000507MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:800`1fF:800`000000LeJR 07=FXP0307=FXP030000000Z2^XP3P[Z801@3P [Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z80103P [Z800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P [j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>6_XP3Q[j800`3Q [j800`000000hJnR0>6_XP020>6_XP<000001@1gF:800`000000MeRR07MHXP0207MHXP030000001f F:80MURR00<0MURR00<0000007=FXP1cEZ800`1cEZ800`000000:S6U02XaY@0202XaY@80000000<0 47gT0000000000001P1>Y_P2000000<0I;Ol1`00000507W4oP8000000`1ibOl400000080Q2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00<00000 0>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR0080hJnR0`000005 07MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:800`1fF:800`000000LeJR07=FXP03 07=FXP030000000Z2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^ XP030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:nR0>2_XP030>2_ XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_ XP030000003P[j80h:nR00<0h:nR00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP020>6_ XP030000002NbOH0000000D0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IH XP030000001cEZ80LeJR00<0LeJR00<0000002XaY@0Z^ nP030000001c_?`0Lkcl00H0Lkcl0P00000207W4oP<000000`24aod2000000L0Q2^XP3P [Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2_XP3P [j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P [j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q [j800P3Q[j800`000000W/Wf0000000507MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1f F:800`1fF:800`000000LeJR07=FXP0407=FXP030000000Z2^XP3P[Z80 0`3P[Z800`000000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2_XP3P[j80 103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80 0`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j80 0P3Q[j83000000D0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0407IHXP030000 001cEZ80LeJR00<0LeJR00<0000002XaY@0Zlo01c_?`01000000208;1n`8000002024aod3000000T0S/on 0`00000?0?ooo`800000803oool00`000000oooo0?ooo`020?ooo`@00000103oool00`000000oooo 0?ooo`060?ooo`002@3oool00`000000oooo0?ooo`0O0?ooo`<000005@3oool00`000000h:jR0>2^ XP040>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z801@3P[Z800`000000h:jR0>2^ XP030>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80103P[j800`000000h:nR0>2_ XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800P3P[j800`000000hJnR0>6_ XP040>6_XP030000003Q[j80hJnR0080hJnR0`00000507MHXP030000001gF:80MeRR00<0MeRR00<0 000007IHXP1fF:800`1fF:800`000000LeJR07=FXP0307=FXP030000000Z2^XP3P[Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00@0h:jR 00<000000>2^XP3P[Z80103P[Z800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR 00<000000>2_XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR0080h:nR 00<000000>6_XP3Q[j80103Q[j800`000000hJnR0>6_XP020>6_XP030000002XaNl0000000D0MeRR 00<0000007MHXP1gF:800`1gF:800`000000MURR07IHXP0307IHXP030000001cEZ80LeJR00<0LeJR 00<0000002XaY@0Z2^XP3P[Z800`3P[Z800`000000h:jR0>2^XP040>2^XP030000 003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000 003P[j80h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP020>2_XP030000 003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j800`3Q[j800`000000Z2^XP3P[Z801@3P[Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00@0h:jR 00<000000>2^XP3P[Z80103P[Z800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR 00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000003P[j80h:nR0080h:nR 00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP030000002XaNl0000000H0MeRR 00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000001cEZ80LeJR00<0LeJR 00<0000002XaY@0Z2^XP3P[Z800`3P[Z800`000000h:jR 0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j800`3P[j800`000000h:nR 0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80103P[j800`000000h:nR 0>2_XP020>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j800`3Q[j8010000000Z2^XP3P[Z80 103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j80 0`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80 0`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j80 0`3Q[j84000000D0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000 001cEZ80LeJR00<0LeJR00<0000002XaY@0Z2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<0 00000>2^XP3P[Z80103P[Z800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<0 00000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<0 00000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP040000002^`>L00000000000D0MeRR 00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000001cEZ80LeJR00<0LeJR 00<0000002XaY@0Zn0800000 00<0WM?j0000000000001`2Te?P3000002<0oooo00<000000?ooo`3oool04P3oool000P0oooo00<0 00000?ooo`3oool0=@3oool3000000H0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000h:jR0>2^ XP050>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_ XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_ XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j800P3Q[j83000000030;?2i000 0000MeRR00@0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000001c EZ80LeJR00<0LeJR00<0000002XaY@0Z n00809o>n0<000001P2Te?P2000000<0ZMCf0P00000P0?ooo`800000503oool000P0oooo00<00000 0?ooo`3oool0=`3oool00`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00<0h:jR00<00000 0>2^XP3P[Z801@3P[Z800`000000h:jR0>2^XP030>2^XP030000003P[j80h:nR00@0h:nR00<00000 0>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR0080hJnR0`000000 0`2c`^@0000007MHXP0407MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:800`1fF:80 0`000000LeJR07=FXP0307=FXP030000000Zn08000000`2VcoH200000080Y=Ch0P0000070:WDmP<000007P3oool00`000000oooo0?ooo`0B 0?ooo`00203oool00`000000oooo0?ooo`0g0?ooo`030000003P[Z80h:jR00@0h:jR00<000000>2^ XP3P[Z800`3P[Z800`000000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2_ XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_ XP3Q[j8010000000102c`^@0000000000000000407MHXP030000001gF:80MeRR0080MeRR00<00000 07IHXP1fF:800`1fF:800`000000LeJR07=FXP0407=FXP030000000Z2^XP040>2^XP030000003P[Z80h:jR00<0h:jR00<00000 0>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP<000000P3Q[j801P000000/l;T0;?2i02c `^@0000007MHXP8000000P1gF:800`000000MeRR07MHXP0207MHXP030000001fF:80MURR00@0MURR 00<0000007=FXP1cEZ800`1cEZ800`000000:S6U02XaY@0502XaY@030000002lA@00_4D00080_4D0 00@000000;FYc02eZL`000002@2@/^d00`000000XL;`0:72l0070:72l080000000<0VlOf00000000 0000202TbO<2000000P0Y/of0P0000000`2[d?<00000000000050:WDmP030000002^eO@0[]Gd00@0 []Gd0`00000I0?ooo`030000003oool0oooo0180oooo00080?ooo`030000003oool0oooo03L0oooo 00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00@0h:jR 00<000000>2^XP3P[Z80103P[Z800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR 00<000000>2_XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR0080h:nR 00@000000>6_XP3Q[j80hJnR100000040>6_XP050000002c`^@0/l;T0;?2i00000000`1gF:830000 00D0MeRR00<0000007IHXP1fF:800`1fF:800`000000LeJR07=FXP0307=FXP030000000Z2^XP050>2^ XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^ XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_ XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800P3P[j8010000000hJnR000000000003 0>6_XP030000003Q[j80hJnR0080hJnR0`0000000`2c`^@0000007MHXP0407MHXP@000000P1gF:80 0`000000MURR07IHXP0307IHXP030000001cEZ80LeJR00<0LeJR00<0000002XaY@0Z2^XP05 0>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP04 0>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP03 0>2_XP030000003P[j80h:nR00@0h:nR00@000000>2_XP3P[j80h:nR0`0000040>6_XP030000003Q [j80hJnR00<0hJnR00<000000;fmfP2m_MX00P00000607MHXP030000001gF:80MeRR00<000001@1f F:800`000000LeJR07=FXP0307=FXP030000000Z2^XP3P[Z80 103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j80 0`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80 103P[j84000000030>2_XP000000hJnR00@0hJnR00<000000>6_XP3Q[j800`3Q[j801@000000_KgJ 0000002n`=/0000000H0MeRR00<0000007MHXP1gF:800P1gF:83000000<0MURR00<0000007=FXP1c EZ800`1cEZ800`000000:S6U02XaY@0602XaY@800000202eZL`00`000000T;;]000000080:jkh`04 0000002Q`_000000000000T0ZlC/00<000000:[;l@2Zbo401P2Zbo42000000030:o2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0 h:jR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0 h:nR00<000000>2_XP3P[j800`3P[j82000000@0h:nR00<000000>6_XP3Q[j800`3Q[j800`000000 hJnR0>6_XP030>6_XP8000000P2n`=/2000000D0MeRR00<0000007MHXP1gF:800P1gF:800`000000 MURR07IHXP04000000D0LeJR00<0000002XaY@0Zl00`2_c>l2000000030:_@l`000000000000L0[m7b0P0000020;;Al08000000P2aeO820000 00H0]=Ga0P0000020;OEl08000003@3oool00`000000oooo0?ooo`0B0?ooo`00203oool00`000000 oooo0?ooo`0f0?ooo`030000003P[Z80h:jR00@0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000 h:jR0>2^XP050>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j800`3P[j800`000000 h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80100000050>2_XP03 0000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j800`3Q[j8010000000_/3K0;k0f`2n`=/20000 00D0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP<000000`1cEZ800`00 0000:S6U02XaY@0602XaY@030000002eZL`0]JW<00P0]JW<0P0000080:jkh`040000002i_mh00000 000000H0ZlC/0P0000040;;7jP80000000<0Z/_a000000000000202_c>l2000000H0[m7b0P000006 0;;Al08000001`2deO400`000000]mG`0;OEl0040;OEl08000002`3oool00`000000oooo0?ooo`0B 0?ooo`00203oool00`000000oooo0?ooo`0f0?ooo`030000003P[Z80h:jR00@0h:jR00<000000>2^ XP3P[Z800`3P[Z800`000000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR0`0000030>2_ XP030000003P[j80h:nR00<0h:nR00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_ XP030000002n`=/0_/3K0080_/3K00<0000007MHXP1gF:800`1gF:800`000000MeRR07MHXP0207MH XP030000001fF:80MURR00<0MURR00<0000007=FXP1cEZ801000000802XaY@030000002eZL`0]JW< 00L0]JW<00@000000`0 ZlC/0080ZlC/00<000000;;7jP2banX01P2banX00`000000[lc_0:o2^XP3P[Z800`3P[Z800`00 0000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2_XP3P[j80103P[j800`00 0000h:nR0>2_XP030>2_XP040000003P[j80h:nR0>2_XP<000001@3P[j800`000000h:nR0>2_XP03 0>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j800`3Q[j800`000000_/3K0;k0f`02 0;k0f`030000001gF:80MeRR00<0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP03 07IHXP030000001cEZ80LeJR00<0LeJR0P00000702XaY@800000202eZL`010000000cK;00`000000;;7jP070;;7jP040000002f bNT00000000000D0[lc_00<000000;;=kP2bcNh0102bcNh2000000P0/]7`00<000000;GBk`2ed^l0 0`2ed^l010000000]=Ga0000000000050;OEl08000001@2heNl3000000L0oooo00D000000?ooo`3o ool0oooo000000020?ooo`030000003oool0oooo00X0oooo00070?ooo`030000003oool0oooo03L0 oooo00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00@0 h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:nR0>2_XP040>2_XP030000003P[j80h:nR00<0 h:nR100000020>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000 hJnR0>6_XP030>6_XP030000003Q[j80hJnR00<0hJnR00<000000;k0f`2n`=/00P2n`=/00`000000 MeRR07MHXP0307MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:800`1fF:800`000000 LeJR07=FXP0307=FXP030000000Z2^XP3P[Z800`3P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00<00000 0>2_XP3P[j800`3P[j800`000000h:nR0>2_XP020>2_XP<000001@3P[j800`000000h:nR0>2_XP03 0>2_XP030000003P[j80h:nR00<0h:nR00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP03 0>6_XP<0000000<0_/3K0000000000001@1gF:800`000000MeRR07MHXP0207MHXP030000001fF:80 MURR00<0MURR00<0000007=FXP1cEZ80101cEZ8010000000:S6U02XaY@0Z2^XP050>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR 0>2^XP040>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800P0000000`3P[j800000 0>2_XP050>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000hJnR 0>6_XP030>6_XP030000003Q[j80hJnR0080hJnR0P00000202^XP050>2^XP03 0000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP03 0000003P[j80h:nR00<0h:nR0`0000030>2_XP030000003P[j80h:nR00@0h:nR00<000000>2_XP3P [j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q [j800P3Q[j820000000502^XP3P [Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR00@000000>2_XP3P [j80h:nR0`0000050>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80103P[j800`00 0000h:nR0>2_XP020>2_XP030000003Q[j80hJnR00@0hJnR00<000000>6_XP3Q[j800P3Q[j800`00 0000aL3E0000000302^XP3P[Z80 103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[Z80h:jR00@0h:jR100000020>2_XP030000 003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000 003P[j80h:nR0080h:nR00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP800000 1033a=X00`000000MeRR07MHXP0407MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:80 0`1fF:800`000000LeJR07=FXP0307=FXP030000000Z`00`000000^=7/0;SAk00200000080 ]m?^0P0000060;WCkP8000000P2je>d2000000030;[EkP000000000000D0^]G]0P0000000`3oool0 00000?ooo`0B0?ooo`001`3oool00`000000oooo0?ooo`060?ooo`L00000:@3oool00`000000h:jR 0>2^XP040>2^XP030000003P[Z80h:jR00<0h:jR00<000000>2^XP3P[Z801@3P[Z800`000000h:jR 0>2^XP020>2^XP<000001@3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR 00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR 00<000000>6_XP3Q[j800`3Q[j800`000000`lCJ0`2000000D0 ^=7/0`0000060;WCkP030000002je>d0^]C]00@0^]C]0P0000050;[Ek@050000003oool0oooo0?oo o`0000004`3oool000L0oooo00<000000?ooo`3oool02@3oool8000002D0oooo00<000000>2^XP3P [Z80103P[Z800`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR00D0h:jR00<000000>2^XP3P [Z800P0000020>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000 h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000 hJnR0>6_XP030>6_XP030000003Q[j80hJnR00<0hJnR00<000000jP0000000000102g d>`00`000000^=7/0;SAk0050;SAk0030000002id^`0^M;/008000000P2idnh2000000D0^]C]0P00 00020;[Dk@8000000P2jeNd00`000000oooo0?ooo`020?ooo`030000003oool0oooo0140oooo0007 0?ooo`030000003oool0oooo00`0oooo2P00000P0?ooo`030000003P[Z80h:jR00@0h:jR00<00000 0>2^XP3P[Z800`3P[Z800`000000h:jR0>2^XP040>2^XP@00000103P[Z800`000000h:nR0>2_XP03 0>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP03 0>2_XP030000003P[j80h:nR00<0h:nR00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP03 0>6_XP<000000P33a=X3000000D0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP03 07IHXP030000001cEZ80LeJR00<0LeJR00<0000002XaY@0Z`000000;SAk0050;SAk08000001@2i d^`3000000D0^]C]00<000000;[Dk@2je>d0102je>d2000000D0oooo00<000000?ooo`3oool04@3o ool000L0oooo00<000000?ooo`3oool03`3oool;000001`0oooo00<000000>2^XP3P[Z80103P[Z80 0`000000h:jR0>2^XP030>2^XP030000003P[Z80h:jR0080h:jR0`0000060>2^XP030000003P[j80 h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80 h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80 hJnR00<0hJnR00<000000jP2ic^X01P2ic^X2000000D0^=7/00<000000;WBk02id^`01@2id^`0 0`000000^]?]0;[Ck@02000000030;[Dk@000000000000H0^]C]0P0000060?ooo`030000003oool0 oooo0140oooo00070?ooo`030000003oool0oooo0180oooo3@00000G0?ooo`030000003P[Z80h:jR 00@0h:jR00<000000>2^XP3P[Z800`3P[Z800`000000h:jR0>2^XP0200000080h:jR00<000000>2^ XP3P[Z80103P[Z800`000000h:nR0>2_XP040>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>6_ XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP0400000036bM`0a/WL00000080`l_P0P000005 07MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:800`1fF:800`000000LeJR07=FXP03 07=FXP030000000ZD0_LcU008000000P2icNT00`000000^LkZ0;W> jP050;W>jP8000000P2jd>/200000080^=7/00<000000;WBk02id^`0102id^`2000000D0^]?]0P00 00060;[Dk@030000003oool0oooo00L0oooo00<000000?ooo`3oool0403oool000H0oooo00<00000 0?ooo`3oool05P3oool?00000140oooo00<000000>2^XP3P[Z801@3P[Z800`000000h:jR0>2^XP03 0>2^XP<00000103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<00000 0>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR00<0hJnR00<00000 0d0^]C]008000000P2je>d2000000X0oooo00<000000?ooo`3oool0403oool0 00H0oooo00<000000?ooo`3oool06@3oool30000008008kB3000000<0?ooo`030000003P[Z80h:jR 00D0h:jR00<000000>2^XP3P[Z80100000060>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00@0h:nR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_ XP3Q[j800`3Q[j82000000D0`l_P00<0000007MHXP1gF:800`1gF:800`000000MeRR07MHXP0207MH XP030000001fF:80MURR00<0MURR00<0000007=FXP1cEZ80101cEZ801@000000:S6U02XaY@0ZD0_LcU00D0_LcU00<00000 0;c>j02lc^P00P0000020;W>jP8000001P2jd>/200000080^]7[0P0000020;WBk0030000002jdnd0 ^]?]00<0^]?]0P0000050;[Dk@800000303oool00`000000oooo0?ooo`0@0?ooo`001P3oool00`00 0000oooo0?ooo`0L0?oooa<000001`3oool00`000000h:jR0>2^XP040>2^XP040000003P[Z800000 000000<0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80 h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000003P[j80 h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80 hJnR00<0hJnR00<000000D0_LcU00@0_LcU0P0000050;c>j0<000001P2jd>/00`000000^]7[0;[Aj`040;[Aj`<00000102j dnd00`000000^]C]0;[Dk@050;[Dk@030000003oool0oooo00/0oooo00<000000?ooo`3oool0403o ool000H0oooo00<000000?ooo`3oool08@3ooolC00000080oooo00<000000>2^XP3P[Z800`3P[Z83 000000D0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP040>2^XP030000003P[j80 h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80 h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80 hJnR00<0hJnR0P0000030<0000000D0MeRR00<0000007MHXP1gF:800P1gF:80 0`000000MURR07IHXP0407IHXP030000001cEZ80LeJR00<0LeJR00D0000002XaY@0Zj02lc^P01@2lc^P00`000000_=3Y0;c@j@0200000080^]3[0P0000060;[Aj`800000 0P2jdn`2000000030;[Ck@000000^]C]00D0^]C]0P00000=0?ooo`8000004P3oool000H0oooo00<0 00000?ooo`3oool09@3oool3000000808:CT3P0000020>2^XP80000000<0h:jR0000003P[Z80103P [Z800`000000h:jR0>2^XP050>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_XP3P[j800`3P [j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j80103P [j800`000000h:nR0>2_XP020>2_XP030000003Q[j80hJnR00@0hJnR00<000000>6_XP3Q[j800P3Q [j82000000030d00`000000oooo0?ooo`0>0?ooo`030000 003oool0oooo0100oooo00060?ooo`030000003oool0oooo02P0oooo500000000`3P[Z8000000>2^ XP040>2^XP030000003P[Z80h:jR00D0h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:nR0>2_ XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_ XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>6_XP3Q[j80103Q[j800`000000hJnR0>6_ XP020>6_XP0500000033d>@0`m3T0i00200000004 0<;>i00000000000000000D0_T01@2ld>T00`000000^m;[0;_Bj`020000 0080^]7[0P0000050;[Ck08000000P2je>d200000080^]C]00<000000?ooo`3oool03`3oool00`00 0000oooo0?ooo`0@0?ooo`001P3oool00`000000oooo0?ooo`0[0?ooo`<00000100c[nd=000000@0 h:jR00<000000>2^XP3P[Z80103P[Z800`000000h:jR0>2^XP050>2^XP030000003P[j80h:nR00<0 h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0 h:nR00<000000>2_XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR00<0 hJnR00@000000@000001031cnD00`000000MeRR07MHXP0407MHXP030000001gF:80MeRR 0080MeRR00<0000007IHXP1fF:800`1fF:800`000000LeJR07=FXP0307=FXP040000000Zi032c^@00`32c^@3000000030;o@i`00000000000080_T0102ld>T2 000000D0^m;[0`0000050;[Ck0030000002je>d0^]C]00@0^]C]0P00000B0?ooo`030000003oool0 oooo0100oooo00060?ooo`030000003oool0oooo02h0oooo1P00000204Njm@`0000000<0h:jR0000 003P[Z801@3P[Z800`000000h:jR0>2^XP050>2^XP030000003P[j80h:nR00<0h:nR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_ XP3P[j800`3P[j800`000000hJnR0>6_XP030>6_XP030000003Q[j80hJnR00<0hJnR00<000000i032c^@00`32c^@200000080_m3W1P000005 0;c@j@030000002kd^/0^m;[00D0^m;[00<000000;_Ck02kdn`00P0000000`2jdn`0000000000006 0;[Dk@8000004`3oool00`000000oooo0?ooo`0@0?ooo`001P3oool00`000000oooo0?ooo`0_0?oo o`<0000000<0oooo000000000000400000050>2^XP030000003P[Z80h:jR00@0h:jR00<000000>2_ XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_ XP3Q[j800`3Q[j82000000D0`LoU0`00000507MHXP030000001gF:80MeRR0080MeRR00<0000007IH XP1fF:800`1fF:800`000000LeJR07=FXP0307=FXP040000000Zi032c^@00`32c^@0 0`000000_m3W0;o@i`050;o@i`D000000P2ld>T00`000000^m;[0;_Bj`040;_Bj`8000001@2kdn`2 000000H0^]C]00<000000?ooo`3oool04P3oool200000180oooo00060?ooo`030000003oool0oooo 02`0oooo0`0000080?ooo`8000000`1Ka?/=000000030>2^XP000000h:jR00D0h:jR00<000000>2_ XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>2_ XP3P[j800`3P[j800`000000h:nR0>2_XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_ XP3Q[j800`3Q[j83000000<0`LoU00@000000;o?iP2ocnH000001@1gF:800`000000MeRR07MHXP02 07MHXP030000001fF:80MURR00<0MURR00<0000007=FXP1cEZ800`1cEZ8010000000:S6U02XaY@00 00050L0102od>L2000000<0_M7Y1@0000050;_Bj`030000002kdn`0^m?/00@0^m?/00<0 00000;[Dk@2je>d00P0000020;[Dk@8000005P3oool00`000000oooo0?ooo`020?ooo`@000002P3o ool000H0oooo00<000000?ooo`3oool0:P3oool2000000d0oooo1000000206g;oPd000001@3P[Z80 0`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j80 0`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<000000>6_XP3Q[j800`3Q[j80 0`000000hJnR0>6_XP030>6_XP030000002od^T0_m;Y00D0000000<0_loV0000001gF:80101gF:80 0`000000MeRR07MHXP0207MHXP030000001fF:80MURR00<0MURR00<0000007=FXP1cEZ800`1cEZ80 0`000000:S6U0000000502_XP040>2_XP030000003P[j80h:nR00<0h:nR00<0 00000>2_XP3P[j80103P[j800`000000h:nR0>2_XP030>2_XP030000003P[j80h:nR00<0h:nR00<0 00000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP050000002od^T0_m;Y0;oBj@000000 0`2ndNP2000000D0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000 001cEZ80LeJR00<0LeJR00<0000002XaY@0000001@3:X:d00`000000flC30=_4``020=_4``030000 003FbLd0e/W=0080e/W=00<000000=7=eP3AcMH00P3AcMH00`000000c=3M0d0^]C]00@0^]C] 0P00000J0?ooo`030000003oool0oooo0080oooo00<000000?ooo`3oool02P3oool000D0oooo00<0 00000?ooo`3oool09@3oool3000001P0oooo1000000207gAo`h00000103P[j800`000000h:nR0>2_ XP030>2_XP030000003P[j80h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_ XP030>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j800`3Q[j8010000000_m;Y0000 000000050;kAj0030000001gF:80MeRR00<0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR 07IHXP0307IHXP030000001cEZ80LeJR00@0LeJR0P0000050P0 0`31e>P3000000D0_M7Y00<000000;cCj`2ldn/01@2ldn/5000000030;_Ck0000000^]C]00D0^]C] 00<000000?ooo`3oool06P3oool00`000000oooo0?ooo`030?ooo`030000003oool0oooo00T0oooo 00050?ooo`030000003oool0oooo02<0oooo0P00000O0?ooo`T000000P04RmX8000000030>2_XP00 0000h:nR00@0h:nR00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000003P [j80h:nR00<0h:nR00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP8000001@2n dNP3000000D0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000001c EZ80LeJR00@0LeJR0P0000040P0`MCX00@0`MCX00<000000;kDjP2ne>X00P0000020;gAj@030000002ldn/0_=?[00@0_=?[ 0P0000040;_Dk0@000000`2je>d2000001`0oooo0P0000030?ooo`040000003oool0oooo000000X0 oooo00050?ooo`030000003oool0oooo0200oooo0`00000U0?ooo`/000000P0>U=h700000080h:nR 00<000000>2_XP3P[j800`3P[j800`000000h:nR0>2_XP040>2_XP030000003P[j80h:nR00<0h:nR 00<000000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP<000000`2ndNP010000000_M3X 0;g@j000000507MHXP030000001gF:80MeRR0080MeRR00<0000007IHXP1fF:80101fF:800`000000 LeJR07=FXP0307=FXP8000000`3:X:d3000000030:_ih`000000bno/00<0bno/00<000000<_Sj@3; hnT00P3;hnT00`000000b=kY0P0`MCX00<0`MCX0P0000050;kDjP<000001@2ldn/00`000000^mC/0;_Dk0030;_Dk080 000000<0^mC]0000000000000`00000M0?ooo`030000003oool0000000@0oooo0P00000;0?ooo`00 1@3oool00`000000oooo0?ooo`0M0?ooo`<00000:`3ooolE000000@0h:nR00<000000>2_XP3P[j80 0`3P[j800`000000h:nR0>2_XP040>2_XP030000003Q[j80hJnR00<0hJnR00<000000>6_XP3Q[j80 0`3Q[j800`000000_=;Z0;cBjP05000000030;g@j0000000MeRR00@0MeRR00<0000007MHXP1gF:80 0P1gF:800`000000MURR07IHXP0407IHXP030000001cEZ80LeJR00<0LeJR00<000000X0_]CZ00D0_]CZ00<000000;gDk02me>`00P0000020;cCj`030000 002ke>`0^mC/00<0^mC/00<000000;_Dk@2ke>d0102ke>d3000001h0oooo00<000000?ooo`3oool0 3`3oool000D0oooo00<000000?ooo`3oool06`3oool200000380oooo1@0000000`0@T^4000000000 00020000008079gV0`00000201jQi@<0000000<0h:nR0000003P[j80103P[j800`000000h:nR0>2_ XP030>2_XP030000003Q[j80hJnR00@0hJnR00<000000>6_XP3Q[j800`3Q[j801@000000_=;Z0;cB jP2ld^X0000000<0_=3Y0P00000507MHXP030000001gF:80MeRR00<0MeRR00<0000007IHXP1fF:80 0`1fF:800`000000LeJR07=FXP0307=FXP@000000`2[nN<00`000000bno/0<__k0020<__k0030000 003;hnT0bn?Y00<0bn?Y00<000000X0102ne>X2000000D0_MC/100000020;_Dk0800000 1@2ke>d2000000<0oooo0`00000K0?ooo`030000003oool0oooo00l0oooo00050?ooo`030000003o ool0oooo01P0oooo0`00000g0?oooa@00000103P[j800`000000h:nR0>2_XP030>2_XP030000003Q [j80hJnR00<0hJnR00<000000>6_XP3Q[j80103Q[j8010000000_=;Z0000000000050;c@j@030000 001gF:80MeRR00@0MeRR00<0000007MHXP1gF:800P1gF:800`000000MURR07IHXP0307IHXP030000 001cEZ80LeJR0080LeJR100000030:_ih`030000003;kn`0bno/0080bno/00<000000<_Sj@3;hnT0 0`3;hnT00`000000b=kY0/4000000D0_]CZ00<000000;gDk02me>`0102me>`2000000<0 ^mG]0`0000050;_Dk@030000003oool0oooo00H0oooo0P00000I0?ooo`030000003oool0oooo00l0 oooo00050?ooo`030000003oool0oooo01H0oooo0P00000l0?ooo`D000000`0OVnT300000080;ZO^ 0`000002032/k@<0000000<0h:nR0000003P[j80103P[j800`000000hJnR0>6_XP030>6_XP030000 003Q[j80hJnR00<0hJnR00<000000;cBjP0000001@2ld>T3000000H0MeRR00<0000007MHXP1gF:80 0P1gF:800`000000MURR07IHXP0307IHXP030000001cEZ80000001H000000`38g^T00`000000aM_Y 0/00`30f>/00`000000_]O/ 0;kGk00200000080_]CZ00<000000;gDk02me>`0102me>`00`000000^mG]0;_Ek@030;_Ek@030000 002keNd0^mG]008000000P2ke>d00`000000oooo0?ooo`090?ooo`<000005P3oool00`000000oooo 0?ooo`0?0?ooo`001@3oool00`000000oooo0?ooo`0C0?ooo`<00000@03ooolF000000@0h:nR00<0 00000>6_XP3Q[j800`3Q[j800`000000hJnR0>6_XP030>6_XP@000000`2ld>T01@000000_Cc2@0000050<;IjP030000 0030f>/0`=S[00<0`=S[00<000000;kGk02nen`00`2nen`4000000<0_MC/0P0000050;_Ek@030000 002keNd0^mG]00<0^mG]0P00000?0?ooo`<000004P3oool200000140oooo00050?ooo`030000003o ool0oooo0100oooo0`0000140?ooo`@0000000<03X_S0000000000000`0bYO42000000@0@;7e0`00 000204:fm0<0000000<0h:nR0000003Q[j80103Q[j800`000000hJnR0>6_XP030>6_XP040000002l d>T0_=3Y0;c@j@@000000`2lcnP00`000000MeRR07MHXP0307MHXP030000001gF:80MeRR0080MeRR 00<0000007IHXP0000000P00000205C@f08000000`2Cc00<0_>Cc0P0000040;kPl@030000002ngNl0_]g_008000000P32fNX00`000000`=S[ 0<3Hj`030<3Hj`030000002nen`0_]O/00<0_]O/0P0000030;cFk@@000001@2keNd00`000000^mG] 0;_Ek@030;_Ek@8000004`3oool300000100oooo00<000000?ooo`3oool03`3oool000D0oooo00<0 00000?ooo`3oool03P3oool2000004T0oooo1`00000303:Ul@8000000`10/OD<00000080hJnR00<0 00000>6_XP3Q[j800`3Q[j800`000000_=3Y0;c@j@020;c@j@030000002lcnP0_Cc00<000000;kPl@2nh?400P2nh?42000000D0_]g_100000030<3Hj`030000002n en`0_]O/00<0_]O/00<000000;cFk@2le^d00`2le^d200000080^mK]0P0000020;_Ek@030000002k eNd0^mG]00<0^mG]00<000000?ooo`3oool05P3oool2000000h0oooo00<000000?ooo`3oool03`3o ool000D0oooo00<000000?ooo`3oool02`3oool3000004`0oooo3P00000505>jn`<00000101D_oX4 000000@0hJnR00D000000;c@j@2ld>T0_=3Y000000050;c?j0800000101gF:84000000@0Km[e0`00 000408[Sn`800000102Mi_`:000000<0_>Cc0P0000040;kPl@030000002ngNl0_]g_00@0_]g_0P00 00030;gKk`D000000P2nen`2000000D0_=K]00<000000;_Fk@2ke^d0102ke^d400000080^mG]0P00 000K0?ooo`<00000303oool00`000000oooo0?ooo`0>0?ooo`00103oool00`000000oooo0?ooo`09 0?ooo`<00000D@3oool3000000<09YS^0P00000304R`n0<00000101C^_/6000000@0I/Km0`000000 1@3Q[j8000000;c@j@2ld>T0000000D0_h2000000<0B;3h1@00000506K2oP800000101V a_d800000080_j0<00000101jf?d3000000D0Rmgn1@00000309gVo08000001@2Y iOX00`000000/N?h0;7Sn0030;7Sn08000000`2fhOD5000000<0_]g_0P0000050;gKk`030000002l fNh0_=W^00<0_=W^00@000000;cHkP2lf>h0_=S^100000060;_Fk@030000002keNd0^mG]0080^mG] 0P00000T0?ooo`<000001@3oool200000100oooo00040?ooo`030000003oool0oooo00@0oooo0`00 001H0?ooo`0300000000Im80000000P00000101O^_d2000000H0I/;n100000040;_?j@040000002l c^P0_j0<000001@2lc^P5000000L0Rmgn0P00000409SOoPD000000`2YiOX2000000D0/N?h 00<000000;KQm@2fhOD00`2fhOD2000000<0^=kc1@0000030;gKk`800000102lfNh2000000D0_=S^ 00<000000;_GkP2kenh00P0000020;_Fk@800000102keNd00`000000oooo0?ooo`0W0?ooo`800000 103oool00`000000oooo0?ooo`0>0?ooo`00103oool010000000oooo0?ooo`3oool3000005`0oooo 00@00000001WdP00Im8006OB0P00000304NXn08000001@1O^_d200000080I/;n0`0000050;_?j@80 0000102lc^P00`000000_j00200000080_j02lc^P00`2lc^P00`000000_j0030;c>j080 00002@3oool4000000<0V=on0P0000060:?Po08000000`2ZgoX5000000<0]^7e0P0000050;SNl`03 0000002jg?40^]ca00<0^]ca0P0000030;[Jl0@000001@2lf>h00`000000^mO^0;_GkP030;_GkP80 00000`2keNd200000300oooo0`00000@0?ooo`00103oool300000680oooo3P0000090?ooo`@00000 0`2lc^P00`000000_j0030;c>j08000003P3oool6000000<0Xn3l0P0000050:[OnP800000 0`2`g_L5000000<0^=kc0P0000050;[Ll@030000002jf_00^][`00@0^][`00<000000;_Hk`2kf>l0 0P0000020;cHkP030000002kenh0^mO^00<0^mO^00<000000;_Ek@2keNd00`2keNd00`000000oooo 0?ooo`0[0?ooo`@000004`3oool000L0oooo1000001i0?ooo`D000000P2lc^P2000001H0oooo1@00 00030:[OnP8000001P2`g_L010000000]=ge0;CMm@2dgOD5000000<0^]ca0P0000050;[Jl0800000 1@2kf>l400000080^mO^0P0000050;_Ek@030000003oool0oooo02P0oooo1000000G0?ooo`002`3o ool4000007X0oooo0P00000M0?ooo`@000001@2`g_L2000000D0]=ge00@000000;OKl`2gfo<0]m_c 100000050;[Jl0030000002kf>l0^mS_00@0^mS_0P0000030;_GkP<000001@2keNd00`000000oooo 0?ooo`0U0?ooo`@000006`3oool000l0oooo1000001g0?ooo`030000003oool0oooo01l0oooo0P00 00020;3Nm`030000002dgOD0]=ge00<0]=ge0P0000050;OKl`030000002hfO40^=Wa008000000P2j f_000`000000^mS_0;_Hk`040;_Hk`030000002kenh0^mO^00<0^mO^00<000000;_Fk@2ke^d00P00 00020;_Ek@030000003oool0oooo0280oooo1000000O0?ooo`004`3oool4000007<0oooo00<00000 0?ooo`3oool08@3oool4000000<0]=ge00<000000;OKl`2gfo<00`2gfo<2000000D0^=Wa10000003 0;_Hk`800000102kenh2000000D0^mK]0P00000Q0?ooo`@000008`3oool001L0oooo1@00001^0?oo o`030000003oool0oooo02D0oooo1@0000030;OKl`030000002hfO40^=Wa00D0^=Wa00@000000;[H k`2jf>l0^]S_1@0000030;_GkP030000002ke^d0^mK]00@0^mK]0P00000N0?ooo`@000009`3oool0 01`0oooo1000001Z0?ooo`030000003oool0oooo02X0oooo100000050;SIl@800000102jf>l20000 00<0^]O^100000050;_Fk@030000003oool0oooo01X0oooo1000000[0?ooo`00803oool4000006H0 oooo00<000000?ooo`3oool0;P3oool200000080^=Wa00<000000;[Hk`2jf>l00`2jf>l00`000000 ^]O^0;[GkP030;[GkP8000000P2jeNh2000000030;_Fk@000000000001T0oooo1000000_0?ooo`00 903oool400000680oooo00<000000?ooo`3oool0<03oool400000080^]S_0P0000050;[GkP030000 002jeNh0^]G^00@0^]G^00<000000?ooo`3oool05@3oool4000003<0oooo000X0?ooo`@00000GP3o ool00`000000oooo0?ooo`0d0?ooo`@000000`2jenh2000000H0^]G^00<000000?ooo`3oool04P3o ool4000003L0oooo000/0?ooo`@00000FP3oool00`000000oooo0?ooo`0h0?ooo`@000001@2jeNh2 00000140oooo1000000k0?ooo`00<03oool5000005D0oooo00<000000?ooo`3oool0?03oool20000 0080^]G^00<000000?ooo`3oool03@3oool4000003l0oooo000e0?ooo`@00000D@3oool00`000000 oooo0?ooo`0n0?ooo`800000303oool4000004<0oooo000i0?ooo`@00000C@3oool00`000000oooo 0?ooo`180?ooo`@00000A`3oool003d0oooo100000190?ooo`030000003oool0oooo04@0oooo1000 001;0?ooo`00@@3oool4000004D0oooo00<000000?ooo`3oool0@03oool4000004l0oooo00150?oo o`D00000@03oool00`000000oooo0?ooo`0l0?ooo`@00000D`3oool004X0oooo1000000l0?ooo`03 0000003oool0oooo03P0oooo1000001G0?ooo`00CP3oool4000003P0oooo00<000000?ooo`3oool0 =03oool4000005/0oooo001B0?ooo`@00000=03oool00`000000oooo0?ooo`0`0?ooo`@00000G`3o ool005H0oooo1000000`0?ooo`030000003oool0oooo02`0oooo1000001S0?ooo`00FP3oool50000 02/0oooo00<000000?ooo`3oool0:03oool4000006L0oooo001O0?ooo`@000009`3oool00`000000 oooo0?ooo`0T0?ooo`@00000J`3oool006<0oooo1000000S0?ooo`030000003oool0oooo0200oooo 1000001_0?ooo`00I`3oool4000001l0oooo00<000000?ooo`3oool0703oool4000007<0oooo001[ 0?ooo`@000006`3oool00`000000oooo0?ooo`0H0?ooo`@00000M`3oool006l0oooo1000000G0?oo o`030000003oool0oooo01@0oooo1000001k0?ooo`00L`3oool500000180oooo00<000000?ooo`3o ool0403oool4000007l0oooo001h0?ooo`@000003P3oool00`000000oooo0?ooo`0<0?ooo`@00000 P`3oool007`0oooo1000000:0?ooo`030000003oool0oooo00P0oooo100000270?ooo`00P03oool4 000000H0oooo00<000000?ooo`3oool0103oool4000008/0oooo00240?ooo`@000000P3oool00`00 0000oooo0?ooo`04000008l0oooo00280?ooo`D00000T`3oool00001\ \>"], ImageRangeCache->{{{96.0625, 383.063}, {288.875, 111}} -> {-0.376569, \ 0.505261, 0.00374667, 0.00374667}}] }, Open ]], Cell[BoxData[""], "Input", CellLabel->"In[54]:="], Cell[TextData[{ "We can transform from the reaction basis to the polarimeter basis by \ rotation about ", Cell[BoxData[ \(TraditionalForm\`\[ScriptL]\&^\)]], " through angle \[Psi]. " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(ReactionToPolarimeter = TransformationMatrix[PolarimeterBasis, ReactionBasis];\)\), "\n", \(MatrixForm[ReactionToPolarimeter]\)}], "Input", CellLabel->"In[55]:="], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(Cos[\[Phi]]\/\@\(Cos[\[Theta]]\^2 + Cos[\[Phi]]\^2\ Sin[\ \[Theta]]\^2\)\), \(-\(\(Cos[\[Theta]]\ Sin[\[Phi]]\)\/\@\(Cos[\[Theta]]\^2 + \ Cos[\[Phi]]\^2\ Sin[\[Theta]]\^2\)\)\), "0"}, {\(\(Cos[\[Theta]]\ Sin[\[Phi]]\)\/\@\(Cos[\[Theta]]\^2 + Cos[\ \[Phi]]\^2\ Sin[\[Theta]]\^2\)\), \(Cos[\[Phi]]\/\@\(Cos[\[Theta]]\^2 + Cos[\ \[Phi]]\^2\ Sin[\[Theta]]\^2\)\), "0"}, {"0", "0", "1"} }], "\[NoBreak]", ")"}], (MatrixForm[ #]&)]], "Output", CellLabel->"Out[56]//MatrixForm="] }, Open ]], Cell[TextData[{ "Although I seem to have lost my earlier notes on this derivation, the \ following verifies that this result agrees with the polarimeter basis coded \ in ", StyleBox["epiprod", FontSlant->"Italic"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Cos[\[Phi]]\^2 + Cos[\[Theta]]\^2\ Sin[\[Phi]]\^2 == 1 - \(Sin[\[Theta]]\^2\) Sin[\[Phi]]\^2 // Simplify\)], "Input", CellLabel->"In[57]:="], Cell[BoxData[ \(True\)], "Output", CellLabel->"Out[57]="] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Spectrometer basis", "Section"], Cell[TextData[{ "The spectrometer basis {", Cell[BoxData[ \(TraditionalForm\`\(d\&^\), \(e\&^\), \(f\&^\)\)]], "} is similar to the photon basis in that ", Cell[BoxData[ \(TraditionalForm\`\(e\&^\) = \(y\&^\)\)]], " is vertical, but now we set ", Cell[BoxData[ \(TraditionalForm\`\(f\&^\)\)]], " at some angle ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_s\)]], " wrt to the nominal ", Cell[BoxData[ \(TraditionalForm\`\(q\&^\)\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[{ \(\({d\&^, e\&^, f\&^} = Transpose[euler[0, \[Theta]\_s, 0]] // Simplify;\)\), "\[IndentingNewLine]", \(SpectrometerBasis = {d\&^, e\&^, f\&^}\)}], "Input", CellLabel->"In[69]:="], Cell[BoxData[ \({{Cos[\[Theta]\_s], 0, \(-Sin[\[Theta]\_s]\)}, {0, 1, 0}, {Sin[\[Theta]\_s], 0, Cos[\[Theta]\_s]}}\)], "Output", CellLabel->"Out[70]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ReactionToSpectrometer = TransformationMatrix[SpectrometerBasis, ReactionBasis]\)], "Input", CellLabel->"In[80]:="], Cell[BoxData[ \({{Cos[\[Theta]]\ Cos[\[Theta]\_s]\ Cos[\[Phi]] + Sin[\[Theta]]\ Sin[\[Theta]\_s], \(-Cos[\[Theta]\_s]\)\ \ Sin[\[Phi]], Cos[\[Theta]\_s]\ Cos[\[Phi]]\ Sin[\[Theta]] - Cos[\[Theta]]\ Sin[\[Theta]\_s]}, {Cos[\[Theta]]\ Sin[\[Phi]], Cos[\[Phi]], Sin[\[Theta]]\ Sin[\[Phi]]}, {\(-Cos[\[Theta]\_s]\)\ Sin[\[Theta]] + Cos[\[Theta]]\ Cos[\[Phi]]\ Sin[\[Theta]\_s], \(-Sin[\[Theta]\_s]\)\ \ Sin[\[Phi]], Cos[\[Theta]]\ Cos[\[Theta]\_s] + Cos[\[Phi]]\ Sin[\[Theta]]\ Sin[\[Theta]\_s]}}\)], "Output", CellLabel->"Out[80]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ReactionToSpectrometer . {P\_t, P\_n, P\_\[ScriptL]} // Simplify\)], "Input", CellLabel->"In[75]:="], Cell[BoxData[ \({\(-Cos[\[Theta]\_s]\)\ Sin[\[Phi]]\ P\_n + \((Cos[\[Theta]]\ Cos[\ \[Theta]\_s]\ Cos[\[Phi]] + Sin[\[Theta]]\ Sin[\[Theta]\_s])\)\ P\_t + \((Cos[\[Theta]\_s]\ \ Cos[\[Phi]]\ Sin[\[Theta]] - Cos[\[Theta]]\ Sin[\[Theta]\_s])\)\ P\_\[ScriptL], Cos[\[Phi]]\ P\_n + Sin[\[Phi]]\ \((Cos[\[Theta]]\ P\_t + Sin[\[Theta]]\ P\_\[ScriptL])\), \(-Sin[\[Theta]\_s]\)\ Sin[\ \[Phi]]\ P\_n + \((\(-Cos[\[Theta]\_s]\)\ Sin[\[Theta]] + Cos[\[Theta]]\ Cos[\[Phi]]\ Sin[\[Theta]\_s])\)\ P\_t + \((Cos[\ \[Theta]]\ Cos[\[Theta]\_s] + Cos[\[Phi]]\ Sin[\[Theta]]\ Sin[\[Theta]\_s])\)\ P\_\[ScriptL]}\ \)], "Output", CellLabel->"Out[75]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SpectrometerToReaction = TransformationMatrix[ReactionBasis, SpectrometerBasis]\)], "Input", CellLabel->"In[81]:="], Cell[BoxData[ \({{Cos[\[Theta]]\ Cos[\[Theta]\_s]\ Cos[\[Phi]] + Sin[\[Theta]]\ Sin[\[Theta]\_s], Cos[\[Theta]]\ Sin[\[Phi]], \(-Cos[\[Theta]\_s]\)\ Sin[\[Theta]] + Cos[\[Theta]]\ Cos[\[Phi]]\ Sin[\[Theta]\_s]}, {\(-Cos[\[Theta]\_s]\ \)\ Sin[\[Phi]], Cos[\[Phi]], \(-Sin[\[Theta]\_s]\)\ Sin[\[Phi]]}, {Cos[\[Theta]\_s]\ \ Cos[\[Phi]]\ Sin[\[Theta]] - Cos[\[Theta]]\ Sin[\[Theta]\_s], Sin[\[Theta]]\ Sin[\[Phi]], Cos[\[Theta]]\ Cos[\[Theta]\_s] + Cos[\[Phi]]\ Sin[\[Theta]]\ Sin[\[Theta]\_s]}}\)], "Output", CellLabel->"Out[81]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(SpectrometerToReaction . {P\_d, P\_e, P\_f} // Simplify\)], "Input", CellLabel->"In[78]:="], Cell[BoxData[ \({\((Cos[\[Theta]]\ Cos[\[Theta]\_s]\ Cos[\[Phi]] + Sin[\[Theta]]\ Sin[\[Theta]\_s])\)\ P\_d + Cos[\[Theta]]\ Sin[\[Phi]]\ P\_e + \((\(-Cos[\[Theta]\_s]\)\ Sin[\ \[Theta]] + Cos[\[Theta]]\ Cos[\[Phi]]\ Sin[\[Theta]\_s])\)\ P\_f, \(-Cos[\ \[Theta]\_s]\)\ Sin[\[Phi]]\ P\_d + Cos[\[Phi]]\ P\_e - Sin[\[Theta]\_s]\ Sin[\[Phi]]\ P\_f, \((Cos[\[Theta]\_s]\ Cos[\[Phi]]\ \ Sin[\[Theta]] - Cos[\[Theta]]\ Sin[\[Theta]\_s])\)\ P\_d + Sin[\[Theta]]\ Sin[\[Phi]]\ P\_e + \((Cos[\[Theta]]\ Cos[\[Theta]\_s] \ + Cos[\[Phi]]\ Sin[\[Theta]]\ Sin[\[Theta]\_s])\)\ P\_f}\)], "Output", CellLabel->"Out[78]="] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowToolbars->"EditBar", WindowSize->{666, 574}, WindowMargins->{{149, Automatic}, {Automatic, 8}}, Visible->True, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, ShowCellLabel->False, InputAliases->{"notation"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongLeftRightArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "notation>"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongRightArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "notation<"->RowBox[ {"Notation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], " ", "\[DoubleLongLeftArrow]", " ", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"]}], "]"}], "symb"->RowBox[ {"Symbolize", "[", TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], "]"}], "infixnotation"->RowBox[ {"InfixNotation", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], ",", "\[Placeholder]"}], "]"}], "addia"->RowBox[ {"AddInputAlias", "[", RowBox[ { TagBox[ "\[Placeholder]", NotationBoxTag, TagStyle -> "NotationTemplateStyle"], ",", "\[Placeholder]"}], "]"}], "pattwraper"->TagBox[ "\[Placeholder]", NotationPatternTag, TagStyle -> "NotationPatternWrapperStyle"], "madeboxeswraper"->TagBox[ "\[Placeholder]", NotationMadeBoxesTag, TagStyle -> "NotationMadeBoxesWrapperStyle"]}, Magnification->1, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of all cells in \ a given style. Make modifications to any definition using commands in the Format menu.\ \>", "Text"], Cell[CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[StyleData[All, "Working"], ScriptMinSize->9], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, ShowCellLabel->False, ImageSize->{200, 200}, PrivateFontOptions->{"FontType"->"Outline"}] }, Closed]], Cell[CellGroupData[{ Cell["Notebook Options", "Section"], Cell["\<\ The options defined for the style below will be used at the Notebook level.\ \>", "Text"], Cell[StyleData["Notebook"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, PageHeaderLines->{True, True}, PrintingOptions->{"FirstPageHeader"->False, "FacingPages"->True}, CellLabelAutoDelete->False, CellFrameLabelMargins->6, StyleMenuListing->None] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellFrame->{{0, 0}, {0, 0.25}}, CellMargins->{{18, 30}, {4, 20}}, CellGroupingRules->{"TitleGrouping", 0}, PageBreakBelow->False, CellFrameMargins->9, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LineSpacing->{0.95, 0}, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontSize->36], Cell[StyleData["Title", "Printout"], CellMargins->{{18, 30}, {4, 0}}, CellFrameMargins->4, FontSize->30] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{18, 30}, {0, 10}}, CellGroupingRules->{"TitleGrouping", 10}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LineSpacing->{1, 0}, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontSize->24, FontSlant->"Italic"], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{18, 30}, {0, 10}}, FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SectionFirst"], CellFrame->{{0, 0}, {0, 3}}, CellMargins->{{18, 30}, {4, 30}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CellFrameMargins->3, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontSize->18, FontWeight->"Bold"], Cell[StyleData["SectionFirst", "Printout"], FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellMargins->{{18, 30}, {4, 30}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontSize->18, FontWeight->"Bold"], Cell[StyleData["Section", "Printout"], FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{18, 30}, {4, 20}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Printout"], FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{18, 30}, {4, 12}}, CellGroupingRules->{"SectionGrouping", 60}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Subsubsection", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Printout"], FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{18, 10}, {Inherited, 6}}, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-.35999999999999999, \ -.10000000000000001}, {0, 0}}, BoxBaselineShift -> -.20000000000000001], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-.074999999999999997, \ -.085000000000000006}, {0, 0}}, BoxBaselineShift -> .5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, TextJustification->1, Hyphenation->True, LineSpacing->{1, 2}, CounterIncrements->"Text"], Cell[StyleData["Text", "Printout"], CellMargins->{{18, 30}, {Inherited, 4}}, LineSpacing->{1, 3}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Caption"], CellMargins->{{55, 50}, {5, 5}}, PageBreakAbove->False, Hyphenation->True, FontSize->10], Cell[StyleData["Caption", "Printout"], CellMargins->{{55, 55}, {5, 2}}, FontSize->8] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output to the \ kernel. Be careful when modifying, renaming, or removing these styles, \ because the front end associates special meanings with these style names.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{55, 10}, {5, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{26, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Input", "Printout"], CellMargins->{{55, 55}, {0, 10}}, ShowCellLabel->False, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9.5] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{55, 10}, {8, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelPositioning->Left, CellLabelMargins->{{26, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Printout"], CellMargins->{{55, 55}, {10, 10}}, ShowCellLabel->False, FontSize->9.5] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellDingbat->"\[LongDash]", CellMargins->{{55, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{26, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Message", "Printout"], CellMargins->{{55, 55}, {0, 3}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{55, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{26, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, TextAlignment->Left, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Printout"], CellMargins->{{54, 72}, {2, 10}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{55, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", StyleMenuListing->None], Cell[StyleData["Graphics", "Printout"], CellMargins->{{55, 55}, {0, 15}}, ImageSize->{0.0625, 0.0625}, ImageMargins->{{35, Inherited}, {Inherited, 0}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], CellMargins->{{9, Inherited}, {Inherited, Inherited}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontSlant->"Oblique"], Cell[StyleData["CellLabel", "Printout"], CellMargins->{{0, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Unique Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Author"], CellMargins->{{45, Inherited}, {2, 20}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontSize->14, FontWeight->"Bold"], Cell[StyleData["Author", "Printout"], CellMargins->{{36, Inherited}, {2, 30}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Address"], CellMargins->{{45, Inherited}, {2, 2}}, CellGroupingRules->{"TitleGrouping", 30}, PageBreakBelow->False, LineSpacing->{1, 1}, CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontSize->12, FontSlant->"Italic"], Cell[StyleData["Address", "Printout"], CellMargins->{{36, Inherited}, {2, 2}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Abstract"], CellMargins->{{45, 75}, {Inherited, 30}}, Hyphenation->True, LineSpacing->{1, 0}], Cell[StyleData["Abstract", "Printout"], CellMargins->{{36, 67}, {Inherited, 50}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Reference"], CellMargins->{{18, 40}, {2, 2}}, TextJustification->1, Hyphenation->True, LineSpacing->{1, 0}], Cell[StyleData["Reference", "Printout"], CellMargins->{{18, 40}, {Inherited, 0}}, FontSize->8] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \ \"Hyperlink\" style is for links within the same Notebook, or between \ Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line help \ system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use \ in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering", "Section"], Cell["\<\ The following styles are useful for numbered equations, figures, etc. They \ automatically give the cell a FrameLabel containing a reference to a \ particular counter, and also increment that counter.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CellMargins->{{55, 10}, {0, 10}}, CellFrameLabels->{{None, Cell[ TextData[ {"(", CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}}, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, CounterIncrements->"NumberedEquation", FormatTypeAutoConvert->False], Cell[StyleData["NumberedEquation", "Printout"], CellMargins->{{55, 55}, {0, 10}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedFigure"], CellMargins->{{55, 145}, {2, 10}}, CellHorizontalScrolling->True, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Figure ", CounterBox[ "NumberedFigure"]}], FontWeight -> "Bold"], None}}, CounterIncrements->"NumberedFigure", FormatTypeAutoConvert->False], Cell[StyleData["NumberedFigure", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedTable"], CellMargins->{{55, 145}, {2, 10}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Table ", CounterBox[ "NumberedTable"]}], FontWeight -> "Bold"], None}}, TextAlignment->Center, CounterIncrements->"NumberedTable", FormatTypeAutoConvert->False], Cell[StyleData["NumberedTable", "Printout"], CellMargins->{{18, Inherited}, {Inherited, Inherited}}, FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{55, 10}, {2, 10}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], CellMargins->{{55, 10}, {2, 10}}, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", AutoSpacing->False, ScriptLevel->1, ScriptBaselineShifts->{0.6, Automatic}, SingleLetterItalics->False, ZeroWidthTimes->True], Cell[StyleData["ChemicalFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellMargins->{{18, 10}, {Inherited, 6}}, Hyphenation->False, LanguageCategory->"Formula", FontFamily->"Courier"], Cell[StyleData["Program", "Printout"], CellMargins->{{18, 30}, {Inherited, 4}}, FontSize->9.5] }, Closed]] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Notation Package Styles", "Section", GeneratedCell->True, CellTags->"NotationPackage"], Cell["\<\ The cells below define certain styles needed by the Notation package. These \ styles serve to make visible otherwise invisible tagboxes.\ \>", "Text", GeneratedCell->True, CellTags->"NotationPackage"], Cell[StyleData["NotationTemplateStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[1, 1, 0.850004], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"], Cell[StyleData["NotationPatternWrapperStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[1, 0.900008, 0.979995], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"], Cell[StyleData["NotationMadeBoxesWrapperStyle"], GeneratedCell->True, StyleMenuListing->None, Background->RGBColor[0.900008, 0.889998, 1], TagBoxOptions->{SyntaxForm->"symbol"}, CellTags->"NotationPackage"] }, Closed]] }] ] (*********************************************************************** 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[CellGroupData[{ Cell[1739, 51, 91, 2, 72, "Title"], Cell[1833, 55, 81, 2, 41, "Author"], Cell[1917, 59, 167, 7, 72, "Address"], Cell[2087, 68, 275, 6, 67, "Abstract"], Cell[2365, 76, 137, 3, 27, "Text"], Cell[CellGroupData[{ Cell[2527, 83, 38, 0, 62, "SectionFirst"], Cell[CellGroupData[{ Cell[2590, 87, 43, 0, 43, "Subsection"], Cell[2636, 89, 141, 3, 51, "Input"], Cell[2780, 94, 89, 2, 31, "Input"], Cell[2872, 98, 1838, 59, 111, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[4747, 162, 39, 0, 43, "Subsection"], Cell[4789, 164, 600, 15, 63, "Text"], Cell[5392, 181, 468, 8, 71, "Input"], Cell[5863, 191, 270, 6, 44, "Text"], Cell[6136, 199, 852, 22, 79, "Text"], Cell[6991, 223, 153, 3, 31, "Input"], Cell[CellGroupData[{ Cell[7169, 230, 104, 2, 31, "Input"], Cell[7276, 234, 576, 10, 87, "Output"] }, Open ]], Cell[7867, 247, 164, 3, 44, "Text"], Cell[CellGroupData[{ Cell[8056, 254, 91, 2, 31, "Input"], Cell[8150, 258, 314, 8, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8501, 271, 93, 2, 31, "Input"], Cell[8597, 275, 322, 8, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8956, 288, 89, 2, 31, "Input"], Cell[9048, 292, 135, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9220, 300, 91, 2, 31, "Input"], Cell[9314, 304, 143, 3, 30, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[9506, 313, 46, 0, 43, "Subsection"], Cell[9555, 315, 99, 2, 27, "Text"], Cell[9657, 319, 152, 3, 56, "Input"] }, Open ]], Cell[CellGroupData[{ Cell[9846, 327, 45, 0, 43, "Subsection"], Cell[9894, 329, 344, 9, 44, "Text"], Cell[10241, 340, 277, 5, 51, "Input"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[10567, 351, 33, 0, 56, "Section"], Cell[10603, 353, 761, 21, 79, "Text"], Cell[CellGroupData[{ Cell[11389, 378, 144, 3, 32, "Input"], Cell[11536, 383, 273, 5, 49, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11846, 393, 96, 2, 31, "Input"], Cell[11945, 397, 137, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12119, 405, 96, 2, 31, "Input"], Cell[12218, 409, 142, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12397, 417, 82, 2, 31, "Input"], Cell[12482, 421, 68, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12587, 428, 82, 2, 31, "Input"], Cell[12672, 432, 97, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12806, 439, 89, 2, 41, "Input"], Cell[12898, 443, 97, 2, 30, "Output"] }, Open ]], Cell[13010, 448, 302, 9, 44, "Text"], Cell[13315, 459, 106, 2, 32, "Input"], Cell[CellGroupData[{ Cell[13446, 465, 103, 2, 31, "Input"], Cell[13552, 469, 154, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13743, 477, 107, 2, 31, "Input"], Cell[13853, 481, 169, 3, 30, "Output"] }, Open ]], Cell[14037, 487, 554, 14, 61, "Text"], Cell[CellGroupData[{ Cell[14616, 505, 192, 4, 51, "Input"], Cell[14811, 511, 431, 10, 58, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15279, 526, 120, 3, 31, "Input"], Cell[15402, 531, 1370, 43, 61, "Output"] }, Open ]], Cell[16787, 577, 684, 22, 61, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[17508, 604, 36, 0, 56, "Section"], Cell[CellGroupData[{ Cell[17569, 608, 64, 0, 43, "Subsection"], Cell[17636, 610, 1444, 42, 115, "Text"], Cell[CellGroupData[{ Cell[19105, 656, 78, 2, 31, "Input"], Cell[19186, 660, 137, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19360, 668, 113, 2, 32, "Input"], Cell[19476, 672, 240, 4, 48, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19753, 681, 94, 2, 31, "Input"], Cell[19850, 685, 357, 6, 93, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20244, 696, 116, 2, 31, "Input"], Cell[20363, 700, 63, 2, 30, "Output"] }, Open ]], Cell[20441, 705, 439, 12, 44, "Text"], Cell[20883, 719, 100, 2, 32, "Input"], Cell[CellGroupData[{ Cell[21008, 725, 106, 2, 31, "Input"], Cell[21117, 729, 154, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[21308, 737, 110, 2, 31, "Input"], Cell[21421, 741, 154, 3, 30, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[21624, 750, 54, 0, 43, "Subsection"], Cell[21681, 752, 455, 10, 61, "Text"], Cell[CellGroupData[{ Cell[22161, 766, 144, 4, 31, "Input"], Cell[22308, 772, 147, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[22492, 780, 85, 2, 31, "Input"], Cell[22580, 784, 190, 4, 37, "Message"], Cell[22773, 790, 528, 9, 171, "Output"] }, Open ]], Cell[23316, 802, 236, 4, 44, "Text"], Cell[23555, 808, 155, 4, 31, "Input"], Cell[CellGroupData[{ Cell[23735, 816, 88, 2, 31, "Input"], Cell[23826, 820, 859, 15, 201, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24722, 840, 185, 4, 41, "Input"], Cell[24910, 846, 458, 12, 122, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[25405, 863, 183, 4, 43, "Input"], Cell[25591, 869, 458, 12, 122, "Output"] }, Open ]], Cell[26064, 884, 470, 10, 61, "Text"], Cell[CellGroupData[{ Cell[26559, 898, 242, 5, 51, "Input"], Cell[26804, 905, 264, 4, 48, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27105, 914, 242, 5, 51, "Input"], Cell[27350, 921, 250, 4, 48, "Output"] }, Open ]], Cell[27615, 928, 382, 14, 27, "Text"], Cell[CellGroupData[{ Cell[28022, 946, 96, 2, 32, "Input"], Cell[28121, 950, 235, 4, 48, "Output"] }, Open ]], Cell[28371, 957, 123, 3, 27, "Text"], Cell[28497, 962, 136, 3, 31, "Input"], Cell[28636, 967, 86, 2, 31, "Input"], Cell[CellGroupData[{ Cell[28747, 973, 186, 4, 41, "Input"], Cell[28936, 979, 339, 12, 122, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[29312, 996, 184, 4, 43, "Input"], Cell[29499, 1002, 339, 12, 122, "Output"] }, Open ]], Cell[29853, 1017, 218, 3, 44, "Text"], Cell[CellGroupData[{ Cell[30096, 1024, 185, 5, 41, "Input"], Cell[30284, 1031, 38592, 1028, 186, 9879, 668, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[68913, 2064, 216, 4, 51, "Input"], Cell[69132, 2070, 111916, 2261, 187, 50257, 1495, "GraphicsData", \ "PostScript", "Graphics"] }, Open ]], Cell[181063, 4334, 51, 1, 31, "Input"], Cell[181117, 4337, 207, 6, 27, "Text"], Cell[CellGroupData[{ Cell[181349, 4347, 201, 4, 71, "Input"], Cell[181553, 4353, 600, 12, 92, "Output"] }, Open ]], Cell[182168, 4368, 240, 7, 44, "Text"], Cell[CellGroupData[{ Cell[182433, 4379, 171, 3, 31, "Input"], Cell[182607, 4384, 63, 2, 30, "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[182731, 4393, 37, 0, 56, "Section"], Cell[182771, 4395, 501, 17, 45, "Text"], Cell[CellGroupData[{ Cell[183297, 4416, 225, 5, 53, "Input"], Cell[183525, 4423, 166, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[183728, 4431, 144, 3, 31, "Input"], Cell[183875, 4436, 615, 12, 87, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[184527, 4453, 129, 3, 31, "Input"], Cell[184659, 4458, 730, 14, 106, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[185426, 4477, 144, 3, 31, "Input"], Cell[185573, 4482, 604, 11, 106, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[186214, 4498, 113, 2, 31, "Input"], Cell[186330, 4502, 669, 11, 106, "Output"] }, Open ]] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)