(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 760298, 22443]*) (*NotebookOutlinePosition[ 803681, 23808]*) (* CellTagsIndexPosition[ 803637, 23804]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Relativistic Spin Rotation", "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[{ "\tIt is well known that the spin direction of a particle is affected by a \ boost that is not parallel to its momentum, a relativistic effect described \ as ", StyleBox["Wigner rotation", FontSlant->"Italic"], " or ", StyleBox["Wigner-Thomas precession", FontSlant->"Italic"], ". Thus, we often require a transformation between polarizations expressed \ in either the lab or cm frames. Several versions of this transformation \ appear in the literature, but proving their equivalence can be algebraically \ tedious. Unfortunately, at least one widely cited paper that was intended to \ be pedagogical gets the transformation wrong. Therefore, in this notebook I \ review the standard derivation and then examine several of the published \ variations using ", StyleBox["Mathematica", FontSlant->"Italic"], " to perform as much of the tedious algebra as possible. Numerical results \ are provided for several typical reactions." }], "Abstract"], Cell[TextData[StyleBox["Created: September 13, 1996\nLast revised: October \ 29, 2004", FontSlant->"Italic"]], "Text", TextAlignment->Left, TextJustification->0], Cell[CellGroupData[{ Cell["Initialization", "SectionFirst"], Cell[BoxData[{ \(\(ClearAll["\"];\)\), "\[IndentingNewLine]", \(\(Off[General::spell, General::spell1];\)\)}], "Input", CellLabel->"In[1]:="], Cell[BoxData[{ \(\($DefaultFont = {"\", 12};\)\), "\n", \(\($TextStyle = {FontFamily \[Rule] "\", FontSize \[Rule] 12, FontSlant \[Rule] "\"};\)\)}], "Input", CellLabel->"In[3]:="], Cell[BoxData[{ \(\(Needs["\"];\)\), "\n", \(\(Needs["\"];\)\), "\[IndentingNewLine]", \(\(Needs["\"];\)\), "\n", \(\(Needs["\"];\)\), "\[IndentingNewLine]", \(Off[Convert::temp, Symbolize::boxSymbolExists]\)}], "Input", CellLabel->"In[5]:="], Cell[BoxData[{ RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Beta]\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(\[Gamma]\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(\[Theta]\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";"}], "\n", RowBox[{ RowBox[{"Symbolize", "[", TagBox[\(\[Beta]\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(\[Gamma]\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}], ";", RowBox[{"Symbolize", "[", TagBox[\(\[Theta]\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]}]}], "Input", CellLabel->"In[10]:="], Cell[BoxData[{ \(\(MyAssumptions = {\[Gamma] > 1, \[Gamma]\_1 > 1, \[Gamma]\_2 > 1, \(-1\) < \[Beta] < 1, 0 < \[Beta]\_1 < 1, 0 < \[Beta]\_2 < 1, 0 < \[Theta]\_1 < \[Pi], 0 < \[Theta]\_2 < \[Pi], \[Xi]\_1 > 0, \[Xi]\_2 > 0, \[Xi] \[Element] Reals};\)\), "\[IndentingNewLine]", \(\(MySimplify = Simplify[#, MyAssumptions] &;\)\), "\[IndentingNewLine]", \(\(MyFullSimplify = FullSimplify[#, MyAssumptions] &;\)\)}], "Input", CellLabel->"In[12]:="] }, Open ]], Cell[CellGroupData[{ Cell["Wigner rotation", "Section"], Cell[CellGroupData[{ Cell["Derivation", "Subsection"], Cell[TextData[{ "\tThe intrinsic spin of a massive particle is specified in its rest frame. \ Suppose that ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\&\[RightVector]\)]], " is a unit vector that represents the spin orientation in a rest frame. A \ spacelike spin four-vector is then formed as ", Cell[BoxData[ \(TraditionalForm\`s = \((0, \[Sigma]\&\[RightVector])\)\)]], " such that ", Cell[BoxData[ \(TraditionalForm\`\(s\_\[Mu]\) s\^\[Mu] = \(-1\)\)]], " is invariant. The spin four-vector in an arbitrary frame is obtained by \ applying the boost that represents the momentum in that frame. Nevertheless, \ the orientation of the spin is still represented by the original ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\&\[RightVector]\)]], ". The relationship between spins in frames differing by a boost which is \ not parallel to the particle's momentum can be determined by transforming \ each frame to a rest frame of the particle, using a boost parallel to the \ momentum in that frame, and comparing the orientations of the two rest \ frames. These orientations differ because nonparallel boosts do not \ commute." }], "Text"], Cell[TextData[{ "\tConsider two frames, ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], ", that share a common set of coordinate axes and differ by a boost along \ ", Cell[BoxData[ \(TraditionalForm\`z\&^\)]], ". We assume, without loss of generality, that the velocity of a particle \ lies in the ", StyleBox["xz", FontSlant->"Italic"], "-plane and that the polar angles are in the range ", Cell[BoxData[ \(TraditionalForm\`0 \[LessEqual] \[Theta]\_1, \[Theta]\_2 \[LessEqual] \ \[Pi]\)]], ". If we label the boost direction as ", Cell[BoxData[ \(TraditionalForm\`z\&^\)]], " and the normal to the plane containing the boost and momentum directions \ as ", Cell[BoxData[ \(TraditionalForm\`y\&^\)]], ", the four-vectors take the form ", Cell[BoxData[ \(TraditionalForm\`{E, p\_z, p\_x}\)]], " where the ", Cell[BoxData[ \(TraditionalForm\`y\)]], " component is superfluous. The four-momenta can then be expressed as" }], "Text"], Cell[BoxData[{ \(TextForm\`p\_1 = m\ \(\[Gamma]\_1\) {1, \(\[Beta]\_1\) Cos[\[Theta]\_1], \(\[Beta]\_1\) Sin[\[Theta]\_1]}\), "\[IndentingNewLine]", \(TextForm\`p\_2 = m\ \(\[Gamma]\_2\) {1, \(\[Beta]\_2\) Cos[\[Theta]\_2], \(\[Beta]\_2\) Sin[\[Theta]\_2]}\)}], "DisplayFormula"], Cell[TextData[{ "in ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], ", respectively. The momentum observed in frame ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " moving with velocity ", Cell[BoxData[ \(TraditionalForm\`\(-\[Beta]\&\[RightVector]\) = \(-\[Beta]\) z\&^\)]], " relative to ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " is obtained via the boost ", Cell[BoxData[ \(TraditionalForm\`p\_2 = B\_z[\(-\[Beta]\)] . p\_1\)]], " where" }], "Text"], Cell[BoxData[ FormBox[ RowBox[{\(B\_z[\[Beta]]\), " ", "=", " ", RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {"\[Gamma]", \(\(-\[Gamma]\)\ \[Beta]\), "0"}, {\(\(-\[Gamma]\)\ \[Beta]\), "\[Gamma]", "0"}, {"0", "0", "1"} }], "\[NegativeThinSpace]", ")"}]}], TextForm]], "DisplayFormula"], Cell[TextData[{ "Similarly, the momentum observed in a frame ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " rotated by an angle ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\)]], " relative to ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " is given by ", Cell[BoxData[ \(TraditionalForm\`p\_2 = R\_y[\[Theta]] . p\_1\)]], " where" }], "Text"], Cell[BoxData[ FormBox[ RowBox[{\(R\_y[\[Theta]]\), " ", "=", " ", RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {"1", "0", "0"}, {"0", \(Cos[\[Theta]]\), \(Sin[\[Theta]]\)}, {"0", \(-Sin[\[Theta]]\), \(Cos[\[Theta]]\)} }], "\[NegativeThinSpace]", ")"}]}], TextForm]], "DisplayFormula"], Cell[TextData[{ "Finally, if the relative velocity ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\&\[RightVector] = \(\[Beta]\_x\) x\&^ + \(\[Beta]\_z\) z\&^\)]], " lies at angle ", Cell[BoxData[ \(TraditionalForm\`\[Theta] = ArcTan[\[Beta]\_z, \[Beta]\_x]\)]], " in the ", StyleBox["xz", FontSlant->"Italic"], "-plane, we employ the combined boost " }], "Text"], Cell[BoxData[ \(TextForm\`B[\[Theta], \[Beta]]\ \ = \ R\_y[\(-\[Theta]\)] . B\_z[\[Beta]] . R\_y[\[Theta]]\)], "DisplayFormula"], Cell["\<\ Note that these transformation matrices are expressed in passive form, \ transforming the coordinate systems instead of the particle. \ \>", "Text"], Cell[TextData[{ "\tIf the momentum forms an angle ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_1\)]], " with the ", Cell[BoxData[ \(TraditionalForm\`z\&^\)]], " axis of ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], ", we can reach a rest frame ", Cell[BoxData[ \(TraditionalForm\`R\_1\)]], " using a boost with velocity ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\&\[RightVector]\_1\)]], ", such that" }], "Text"], Cell[BoxData[ \(TextForm\`T\_1\ = \ \(B[\[Theta]\_1, \[Beta]\_1]\ \ = \ R\_y[\(-\[Theta]\_1\)] . B\_z[\[Beta]\_1] . R\_y[\[Theta]\_1]\)\)], "DisplayFormula"], Cell[TextData[{ "represents the complete Lorentz transformation from frame ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " to a rest frame ", Cell[BoxData[ \(TraditionalForm\`R\_1\)]], ". Alternatively, we could first use a boost along the ", Cell[BoxData[ \(TraditionalForm\`z\&^\)]], " axis to transform from ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " to ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " in which the momentum ", Cell[BoxData[ \(TraditionalForm\`p\_2\)]], " appears at angle ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_2\)]], ". We then use a boost with velocity ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\&\[RightVector]\_2\)]], " " }], "Text"], Cell[BoxData[ \(TextForm\`T\_2\ = \ \(B[\[Theta]\_2, \[Beta]\_2]\ . B\_z[\(-\[Beta]\)]\ = \ R\_y[\(-\[Theta]\_2\)] . B\_z[\[Beta]\_2] . R\_y[\[Theta]\_2] . B\_z[\(-\[Beta]\)]\)\)], "DisplayFormula"], Cell[TextData[{ "to reach a rest frame ", Cell[BoxData[ \(TraditionalForm\`R\_2\)]], ". These are both rest frames of the same particle, so can differ at most \ by a rotation about their common ", Cell[BoxData[ \(TraditionalForm\`\(y\&^\)\)]], " axis, such that" }], "Text"], Cell[BoxData[ \(TextForm\`T\_2\ = \ R\_y[\[Chi]] . T\_1\)], "DisplayFormula"], Cell[TextData[{ "Thus, the angles between the spins in ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " can be obtained from the transformation" }], "Text"], Cell[BoxData[ \(TextForm\`R\_y[\[Chi]]\ = \ \(\(T\_2\) T\_1\^\(-1\)\ = \ R\_y[\(-\[Theta]\_2\)] . B\_z[\[Beta]\_2] . R\_y[\[Theta]\_2] . B\_z[\(-\[Beta]\)] . R\_y[\(-\[Theta]\_1\)] . B\_z[\(-\[Beta]\_1\)] . R\_y[\[Theta]\_1]\)\)], "DisplayFormula"], Cell[TextData[{ "Unfortunately, direct multiplication of these seven matrices produces a \ rather complicated result that is difficult to simplify and from which it is \ difficult to determine ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], ". A somewhat simpler method is to use that fact that successive rotations \ about the same axis add, such that" }], "Text"], Cell[BoxData[ \(TextForm\`R\_y[\(-\[CapitalOmega]\)]\ = \ B\_z[\[Beta]\_2] . R\_y[\[Theta]\_2] . B\_z[\(-\[Beta]\)] . R\_y[\(-\[Theta]\_1\)] . B\_z[\(-\[Beta]\_1\)]\)], "DisplayFormula"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`\[CapitalOmega] = \[Theta]\_1 - \[Theta]\_2 - \[Chi]\ \)]], " is easier to evaluate. Once we demonstrate that this matrix represents a \ pure rotation, we can identify ", Cell[BoxData[ \(TraditionalForm\`\[CapitalOmega]\)]], " from its matrix elements and deduce ", Cell[BoxData[ \(TraditionalForm\`\[Chi] = \[Theta]\_1 - \[Theta]\_2 - \[CapitalOmega]\ \)]], ". " }], "Text"], Cell[TextData[{ "\tIt is useful to distinguish between polarizations expressed with respect \ to a common coordinate system, described as ", StyleBox["z", FontSlant->"Italic"], " bases, from those expressed with respect to helicity bases with the \ longitudinal direction along the momentum for either frame. In ", StyleBox["z", FontSlant->"Italic"], " bases we find" }], "Text"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(P\_z\%\((2)\)\)}, {\(P\_x\%\((2)\)\)} }], "\[NegativeThinSpace]", ")"}], " ", "=", " ", RowBox[{ RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(Cos[\[Chi]]\), \(Sin[\[Chi]]\)}, {\(-Sin[\[Chi]]\), \(Cos[\[Chi]]\)} }], "\[NegativeThinSpace]", ")"}], RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(P\_z\%\((1)\)\)}, {\(P\_x\%\((1)\)\)} }], "\[NegativeThinSpace]", ")"}]}]}], TextForm]], "DisplayFormula"], Cell["while for helicity bases we obtain", "Text"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(P\_L\%\((2)\)\)}, {\(P\_S\%\((2)\)\)} }], "\[NegativeThinSpace]", ")"}], " ", "=", " ", RowBox[{ RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(Cos[\[CapitalOmega]]\), \(-Sin[\[CapitalOmega]]\)}, {\(Sin[\[CapitalOmega]]\), \(Cos[\[CapitalOmega]]\)} }], "\[NegativeThinSpace]", ")"}], RowBox[{"(", "\[NegativeThinSpace]", GridBox[{ {\(P\_L\%\((1)\)\)}, {\(P\_S\%\((1)\)\)} }], "\[NegativeThinSpace]", ")"}]}]}], TextForm]], "DisplayFormula"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`\[CapitalOmega] = \[Theta]\_1 - \[Theta]\_2 - \[Chi]\ \)]], ". The signs chosen for ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[CapitalOmega]\)]], " give positive angles when ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " is the cm, ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " is the lab, and ", Cell[BoxData[ \(TraditionalForm\`\[Beta] > 0\)]], ". Notice that ", Cell[BoxData[ \(TraditionalForm\`\[Beta] > 0\ \[DoubleLongRightArrow]\ \[Theta]\_2 < \[Theta]\_1\)]], " corresponds to the typical cm\[Rule]lab transformation while ", Cell[BoxData[ \(TraditionalForm\`\[Beta] < 0\ \[DoubleLongRightArrow]\ \[Theta]\_2 > \[Theta]\_1\)]], " corresponds to the typical lab\[Rule]cm transformation. For small ", Cell[BoxData[ \(TraditionalForm\`\[LeftBracketingBar]\[Beta]\[RightBracketingBar]\)]],\ " we expect ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], " to be small because it represents a relativistic effect that causes \ noncolinear Lorentz transformations not to commute while Galilean \ transformations would commute. Under these circumstances we expect to find \ ", Cell[BoxData[ \(TraditionalForm\`\[CapitalOmega] \[TildeTilde] \[Theta]\_1 - \[Theta]\ \_2\)]], " to be positive for cm\[Rule]lab transformations or negative for \ lab\[Rule]cm transformations." }], "Text"], Cell[TextData[{ "\tWe are now ready to set up a ", StyleBox["Mathematica", FontSlant->"Italic"], " calculation of the spin rotation matrix. First we define the momenta in \ ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " as" }], "Text"], Cell[BoxData[{ \(\(p\_1 = m\ \(\[Gamma]\_1\) {1, \(\[Beta]\_1\) Cos[\[Theta]\_1], \(\[Beta]\_1\) Sin[\[Theta]\_1]};\)\), "\[IndentingNewLine]", \(\(p\_2 = m\ \(\[Gamma]\_2\) {1, \(\[Beta]\_2\) Cos[\[Theta]\_2], \(\[Beta]\_2\) Sin[\[Theta]\_2]};\)\)}], "Input", CellLabel->"In[15]:="], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`0 \[LessEqual] \[Beta]\_1, \[Beta]\_2 \[LessEqual] 1\)]], ". Next, we define the rotation matrix" }], "Text"], Cell[BoxData[ \(\(R\_y[\[Theta]_] = {{1, 0, 0}, {0, Cos[\[Theta]], Sin[\[Theta]]}, {0, \(-Sin[\[Theta]]\), Cos[\[Theta]]}};\)\)], "Input", CellLabel->"In[17]:="], Cell["and boost functions", "Text"], Cell[BoxData[{ \(\(B\_z[\[Beta]_] = {{\[Gamma], \(-\[Gamma]\)\ \[Beta], 0}, {\(-\[Gamma]\)\ \[Beta], \ \[Gamma], 0}, {0, 0, 1}} /. {\[Gamma] \[Rule] 1\/\@\(1 - \[Beta]\^2\)};\)\), "\[IndentingNewLine]", \(\(B\_z[\[Beta]_, \[Gamma]_] = {{\[Gamma], \(-\[Gamma]\)\ \[Beta], 0}, {\(-\[Gamma]\)\ \[Beta], \ \[Gamma], 0}, {0, 0, 1}};\)\)}], "Input", CellLabel->"In[18]:="], Cell[TextData[{ "where, for algebraic reasons, it will prove convenient to define a variant \ in which the relationship between ", Cell[BoxData[ \(TraditionalForm\`\[Gamma]\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\)]], " remains implicit. A boost in an arbitrary direction in the ", StyleBox["xz-", FontSlant->"Italic"], "plane is then" }], "Text"], Cell[BoxData[{ \(\(B[\[Theta]_, \[Beta]_] = R\_y[\(-\[Theta]\)] . B\_z[\[Beta]] . R\_y[\[Theta]];\)\), "\[IndentingNewLine]", \(\(B[\[Theta]_, \[Beta]_, \[Gamma]_] = R\_y[\(-\[Theta]\)] . B\_z[\[Beta], \[Gamma]] . R\_y[\[Theta]];\)\)}], "Input", CellLabel->"In[20]:="], Cell[TextData[{ "Now we verify that a boost with ", Cell[BoxData[ FormBox[ RowBox[{" ", FormBox[\(\(\[Beta]\& \[RightVector] \) = \(\[Beta]\& \ \[RightVector] \)\_1\), "TraditionalForm"]}], TraditionalForm]]], " transforms from ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " to a rest frame ", Cell[BoxData[ \(TraditionalForm\`R\_1\)]], " such that" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(B[\[Theta]\_1, \[Beta]\_1] . p\_1 /. {\[Gamma]\_1 \[Rule] 1\/\@\(1 - \[Beta]\_1\^2\)} // MySimplify\)], "Input", CellLabel->"In[22]:="], Cell[BoxData[ \({m, 0, 0}\)], "Output", CellLabel->"Out[22]="] }, Open ]], Cell[TextData[{ "Although the results are already familiar, we also check our functions by \ evaluating the relationship between ", Cell[BoxData[ \(TraditionalForm\`p\_2\)]], " and ", Cell[BoxData[ \(TraditionalForm\`p\_1\)]], " under a boost ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\)]], " in the ", StyleBox["z", FontSlant->"Italic"], "-direction." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Thread[B\_z[\(-\[Beta]\), \[Gamma]] . p\_1 \[Equal] p\_2] // MySimplify\)], "Input", CellLabel->"In[23]:="], Cell[BoxData[ \({m\ \[Gamma]\ \[Gamma]\_1\ \((1 + \[Beta]\ \[Beta]\_1\ \ Cos[\[Theta]\_1])\) \[Equal] m\ \[Gamma]\_2, m\ \[Gamma]\ \[Gamma]\_1\ \((\[Beta] + \[Beta]\_1\ Cos[\[Theta]\_1])\) \ \[Equal] m\ \[Beta]\_2\ \[Gamma]\_2\ Cos[\[Theta]\_2], m\ \[Beta]\_1\ \[Gamma]\_1\ Sin[\[Theta]\_1] \[Equal] m\ \[Beta]\_2\ \[Gamma]\_2\ Sin[\[Theta]\_2]}\)], "Output", CellLabel->"Out[23]="] }, Open ]], Cell["These results can be represented by substitution rules", "Text"], Cell[BoxData[{ \(\(rule1 = {\[Gamma]\_2 \[Rule] \[Gamma]\_1\ \[Gamma] \((1 + \[Beta]\ \ \[Beta]\_1\ Cos[\[Theta]\_1])\), Sin[\[Theta]\_2] \[Rule] \(\(\(\[Beta]\_1\) \[Gamma]\_1\)\/\(\(\ \[Beta]\_2\) \[Gamma]\_2\)\) Sin[\[Theta]\_1], Cos[\[Theta]\_2] \[Rule] \(\[Gamma]\ \ \[Gamma]\_1\)\/\(\(\[Beta]\_2\) \[Gamma]\_2\)\ \((\[Beta]\_1\ \ Cos[\[Theta]\_1] + \[Beta])\), \[Beta]\_2 \[Rule] \@\(1 - \ 1\/\[Gamma]\_2\^2\)};\)\), "\[IndentingNewLine]", \(\(rule2 = {\[Gamma]\_1 \[Rule] 1\/\@\(1 - \[Beta]\_1\^2\), \[Gamma] \[Rule] 1\/\@\(1 - \[Beta]\^2\)};\)\)}], "Input", CellLabel->"In[24]:="], Cell[TextData[{ "\tWe are now ready to evaluate the angle between ", Cell[BoxData[ \(TraditionalForm\`R\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`R\_2\)]], ". Multiplying five transformations and applying the kinematic \ relationships between ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " gives" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(R\_12 = \((B\_z[\[Beta]\_2, \[Gamma]\_2] . R\_y[\[Theta]\_2] . B\_z[\(-\[Beta]\), \[Gamma]] . R\_y[\(-\[Theta]\_1\)] . B\_z[\(-\[Beta]\_1\), \[Gamma]\_1] //. rule1)\) /. rule2 // MyFullSimplify\)], "Input", CellLabel->"In[26]:="], Cell[BoxData[ \({{1, 0, 0}, {0, \(\[Beta]\_1 + \[Beta]\ Cos[\[Theta]\_1]\)\/\(\((1 + \[Beta]\ \ \[Beta]\_1\ Cos[\[Theta]\_1])\)\ \@\(1 - \(\((\(-1\) + \[Beta]\^2)\)\ \((\(-1\ \) + \[Beta]\_1\%2)\)\)\/\((1 + \[Beta]\ \[Beta]\_1\ Cos[\[Theta]\_1])\)\^2\)\ \), \(\[Beta]\ \((\(-1\) + \[Beta]\_1\%2)\)\ Sin[\[Theta]\_1]\)\/\(\((1 + \ \[Beta]\ \[Beta]\_1\ Cos[\[Theta]\_1])\)\ \@\(\((1 - \[Beta]\_1\%2)\)\ \((1 - \ \(\((\(-1\) + \[Beta]\^2)\)\ \((\(-1\) + \[Beta]\_1\%2)\)\)\/\((1 + \[Beta]\ \ \[Beta]\_1\ Cos[\[Theta]\_1])\)\^2)\)\)\)}, {0, \(-\(\(\[Beta]\ \((\(-1\) + \ \[Beta]\_1\%2)\)\ Sin[\[Theta]\_1]\)\/\(\((1 + \[Beta]\ \[Beta]\_1\ Cos[\ \[Theta]\_1])\)\ \@\(\((1 - \[Beta]\_1\%2)\)\ \((1 - \(\((\(-1\) + \ \[Beta]\^2)\)\ \((\(-1\) + \[Beta]\_1\%2)\)\)\/\((1 + \[Beta]\ \[Beta]\_1\ \ Cos[\[Theta]\_1])\)\^2)\)\)\)\)\), \(\[Beta]\_1 + \[Beta]\ Cos[\[Theta]\_1]\)\ \/\(\((1 + \[Beta]\ \[Beta]\_1\ Cos[\[Theta]\_1])\)\ \@\(1 - \(\((\(-1\) + \ \[Beta]\^2)\)\ \((\(-1\) + \[Beta]\_1\%2)\)\)\/\((1 + \[Beta]\ \[Beta]\_1\ \ Cos[\[Theta]\_1])\)\^2\)\)}}\)], "Output", CellLabel->"Out[26]="] }, Open ]], Cell["where", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(R\_12 . Transpose[R\_12] // MySimplify\)], "Input", CellLabel->"In[27]:="], Cell[BoxData[ \({{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}\)], "Output", CellLabel->"Out[27]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Det[R\_12] // MySimplify\)], "Input", CellLabel->"In[28]:="], Cell[BoxData[ \(1\)], "Output", CellLabel->"Out[28]="] }, Open ]], Cell[TextData[{ "demonstrates that ", Cell[BoxData[ \(TraditionalForm\`R\_12\)]], " is a proper orthogonal matrix or, in other words, a pure rotation. Thus, \ the net effect of three nonparallel coplanar boosts which take a system from \ one rest frame to another in the sequence ", Cell[BoxData[ \(TraditionalForm\`R\_1 \[Rule] \(S\_1 \[Rule] \(S\_2 \[Rule] R\_2\)\)\)]], " is a pure rotation. Thus, by analyzing the components of this matrix" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(-\(R\_12\[LeftDoubleBracket]2, 3\[RightDoubleBracket]\/R\_12\[LeftDoubleBracket]2, 2\[RightDoubleBracket]\)\) /. {\[Beta]\^2 \[Rule] 1 - 1\/\[Gamma]\^2, \[Beta]\_1\^2 \[Rule] 1 - 1\/\[Gamma]\_1\^2, \[Beta]\_2\^2 \[Rule] 1 - 1\/\[Gamma]\_2\^2} // MySimplify\)], "Input", CellLabel->"In[29]:="], Cell[BoxData[ \(\(\[Beta]\ Sin[\[Theta]\_1]\)\/\(\[Beta]\_1\ \[Gamma]\_1 + \[Beta]\ \ \[Gamma]\_1\ Cos[\[Theta]\_1]\)\)], "Output", CellLabel->"Out[29]="] }, Open ]], Cell["we identify", "Text"], Cell[BoxData[ \(\(\[CapitalOmega]\ = \ ArcTan[\(\[Gamma]\_1\) \((\[Beta]\_1 + \[Beta]\ Cos[\[Theta]\_1])\), \ \[Beta]\ Sin[\[Theta]\_1]] /. {\[Gamma] \[Rule] 1\/\@\(1 - \[Beta]\^2\), \[Gamma]\_1 \[Rule] 1\/\@\(1 - \[Beta]\_1\^2\)} // MyFullSimplify;\)\)], "Input", CellLabel->"In[30]:="], Cell["\<\ and use the quadrant-sensitive version of the inverse tangent. The rotation \ angle relative to a fixed set of coordinate axes is then \ \>", "Text"], Cell[BoxData[ \(TextForm\`\[Chi]\ = \ \ \[Theta]\_1 - \[Theta]\_2 - \ \[CapitalOmega]\)], "DisplayFormula"], Cell["or", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Chi] = \(\((\[Theta]\_1 - \[Theta]\_2 - \[CapitalOmega] /. \ \[Theta]\_2 \[Rule] ArcTan[\(\(\[Beta]\_1\) Sin[\[Theta]\_1]\)\/\(\[Gamma]\ \((\ \[Beta]\_1\ Cos[\[Theta]\_1] + \[Beta])\)\)])\) /. {\[Gamma] \[Rule] 1\/\@\(1 - \[Beta]\^2\), \[Gamma]\_1 \[Rule] 1\/\@\(1 - \[Beta]\_1\^2\)}\) /. ArcTan[y_\/x_] \[Rule] ArcTan[x, y] // MyFullSimplify\)], "Input", CellLabel->"In[31]:="], Cell[BoxData[ \(\[Theta]\_1 - ArcTan[\[Beta]\_1 + \[Beta]\ Cos[\[Theta]\_1], \[Beta]\ \@\(1 - \[Beta]\ \_1\%2\)\ Sin[\[Theta]\_1]] - ArcTan[\[Beta] + \[Beta]\_1\ Cos[\[Theta]\_1], \@\(1 - \[Beta]\^2\)\ \ \[Beta]\_1\ Sin[\[Theta]\_1]]\)], "Output", CellLabel->"Out[31]="] }, Open ]], Cell[TextData[{ "Therefore, we can evaluate the spin rotation angle observed in the \ transformation ", Cell[BoxData[ \(TraditionalForm\`S\_1 \[Rule] S\_2\)]], " produced by a boost ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\&\[RightVector] = \[Beta] z\&^\)]], " using" }], "Text"], Cell[BoxData[{ \(TextForm\`\[Chi]\ = \ \ \[Theta]\_1 - \[Theta]\_2 - \[CapitalOmega]\), \ "\[IndentingNewLine]", \(TextForm\`\[CapitalOmega]\ = \ ArcTan[\(\[Gamma]\_1\) \((\[Beta]\_1 + \[Beta]\ Cos[\[Theta]\_1])\), \ \[Beta]\ Sin[\[Theta]\_1]]\), "\[IndentingNewLine]", \(TextForm\`\[Theta]\_2\ = \ ArcTan[\[Gamma]\ \((\[Beta]\_1\ Cos[\[Theta]\_1] + \[Beta])\), \ \(\[Beta]\_1\) Sin[\[Theta]\_1]]\)}], "DisplayFormula"], Cell[TextData[{ "These results are quite general and apply to any spin or to any pair of \ reference frames, although the most common applications are probably to lab\ \[LeftRightArrow]cm transformations for spin one-half. Also note that ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\)]], " may be positive or negative." }], "Text"], Cell["\<\ \tThe following function returns the kinematics and spin rotation angles in \ the form of replacement rules. We will use this below to display some \ specific examples.\ \>", "Text"], Cell[BoxData[ \(transform[\[Beta]1_, \[Theta]1_, \[Beta]_] := Module[{\[Gamma]1, \[Gamma], \[CapitalOmega], \[Theta]2, \[Chi], \ \[Gamma]2}, \[IndentingNewLine]\[Gamma]1 = 1\/\@\(1 - \[Beta]1\^2\); \ \[Gamma] = 1\/\@\(1 - \[Beta]\^2\); \[IndentingNewLine]\[Theta]2 = ArcTan[\[Gamma]\ \((\[Beta]1\ Cos[\[Theta]1] + \[Beta])\), \[Beta]1\ \ Sin[\[Theta]1]]; \[IndentingNewLine]\[CapitalOmega] = ArcTan[\[Gamma]1 \((\[Beta]1 + \[Beta]\ Cos[\[Theta]1])\), \[Beta]\ \ Sin[\[Theta]1]]; \[IndentingNewLine]\[Chi] = \[Theta]1 - \[Theta]2 - \ \[CapitalOmega]; \[IndentingNewLine]\[Gamma]2 = \[Gamma]1\ \[Gamma] \((1 + \ \[Beta]\ \[Beta]1\ Cos[\[Theta]1])\); \[IndentingNewLine]{theta2 \[Rule] \ \[Theta]2/Degree, chi \[Rule] \[Chi]/Degree, omega \[Rule] \[CapitalOmega]/Degree, gamma2 \[Rule] \[Gamma]2}]\)], "Input", CellLabel->"In[32]:="], Cell[TextData[{ "\tSuppose that ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " is the cm frame while ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " is the lab frame reached by a boost with ", Cell[BoxData[ \(TraditionalForm\`\[Beta] > 0\)]], ". The momentum then appears to rotate forward, such that ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_2 \[LessEqual] \[Theta]\_1\)]], ". We also find, at least numerically, that the spin rotates in same \ direction but by a much smaller angle." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[{theta2, chi} /. transform[0.2, \[Theta]\_1\ Degree, 0.5]], {\[Theta]\_1, 0, 180}, \[IndentingNewLine]PlotRange \[Rule] {Automatic, All}, PlotStyle \[Rule] {RGBColor[0, 0, 1], RGBColor[1, 0, 0]}, Frame \[Rule] True, FrameLabel \[Rule] {\*"\"\<\!\(\[Theta]\_1\)\>\"", "\< \>"}, PlotLegend \[Rule] {\*"\"\<\!\(\[Theta]\_2\)\>\"", "\<\[Chi]\>"}, LegendPosition \[Rule] {0. , 0}, LegendSize \[Rule] {0.6, 0.3}, LegendShadow \[Rule] None];\)\)], "Input", CellLabel->"In[33]:="], 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 Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.5 0.47619 0.309017 0.47619 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath % Start of sub-graphic p 0.0238095 0.0147151 0.97619 0.603319 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.00529101 0.0147151 0.0284284 [ [.02381 -0.0125 -5 -15.6875 ] [.02381 -0.0125 5 0 ] [.15608 -0.0125 -8 -15.6875 ] [.15608 -0.0125 8 0 ] [.28836 -0.0125 -8 -15.6875 ] [.28836 -0.0125 8 0 ] [.42063 -0.0125 -8 -15.6875 ] [.42063 -0.0125 8 0 ] [.55291 -0.0125 -11 -15.6875 ] [.55291 -0.0125 11 0 ] [.68519 -0.0125 -11 -15.6875 ] [.68519 -0.0125 11 0 ] [.81746 -0.0125 -11 -15.6875 ] [.81746 -0.0125 11 0 ] [.94974 -0.0125 -11 -15.6875 ] [.94974 -0.0125 11 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -7.03125 -31.375 ] [.5 -0.0125 7.03125 -15.6875 ] [-0.0125 .01472 -10 -7.84375 ] [-0.0125 .01472 0 7.84375 ] [-0.0125 .15686 -10 -7.84375 ] [-0.0125 .15686 0 7.84375 ] [-0.0125 .299 -16 -7.84375 ] [-0.0125 .299 0 7.84375 ] [-0.0125 .44114 -16 -7.84375 ] [-0.0125 .44114 0 7.84375 ] [-0.0125 .58328 -16 -7.84375 ] [-0.0125 .58328 0 7.84375 ] [ 0 0 -0.125 0 ] [-0.01875 .30902 -31.6875 -3.5 ] [-0.01875 .30902 -16 3.5 ] [ 0 .61803 .125 0 ] [ 1 0 .125 0 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 0 m .02381 .00625 L s gsave .02381 -0.0125 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore .15608 0 m .15608 .00625 L s gsave .15608 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (25) show 1.000 setlinewidth grestore .28836 0 m .28836 .00625 L s gsave .28836 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (50) show 1.000 setlinewidth grestore .42063 0 m .42063 .00625 L s gsave .42063 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (75) show 1.000 setlinewidth grestore .55291 0 m .55291 .00625 L s gsave .55291 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (100) show 1.000 setlinewidth grestore .68519 0 m .68519 .00625 L s gsave .68519 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (125) show 1.000 setlinewidth grestore .81746 0 m .81746 .00625 L s gsave .81746 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (150) show 1.000 setlinewidth grestore .94974 0 m .94974 .00625 L s gsave .94974 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (175) show 1.000 setlinewidth grestore .125 Mabswid .05026 0 m .05026 .00375 L s .07672 0 m .07672 .00375 L s .10317 0 m .10317 .00375 L s .12963 0 m .12963 .00375 L s .18254 0 m .18254 .00375 L s .20899 0 m .20899 .00375 L s .23545 0 m .23545 .00375 L s .2619 0 m .2619 .00375 L s .31481 0 m .31481 .00375 L s .34127 0 m .34127 .00375 L s .36772 0 m .36772 .00375 L s .39418 0 m .39418 .00375 L s .44709 0 m .44709 .00375 L s .47354 0 m .47354 .00375 L s .5 0 m .5 .00375 L s .52646 0 m .52646 .00375 L s .57937 0 m .57937 .00375 L s .60582 0 m .60582 .00375 L s .63228 0 m .63228 .00375 L s .65873 0 m .65873 .00375 L s .71164 0 m .71164 .00375 L s .7381 0 m .7381 .00375 L s .76455 0 m .76455 .00375 L s .79101 0 m .79101 .00375 L s .84392 0 m .84392 .00375 L s .87037 0 m .87037 .00375 L s .89683 0 m .89683 .00375 L s .92328 0 m .92328 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave .5 -0.0125 -68.0313 -35.375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (q) show 68.250 17.688 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 73.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 .01472 m .00625 .01472 L s gsave -0.0125 .01472 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore 0 .15686 m .00625 .15686 L s gsave -0.0125 .15686 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (5) show 1.000 setlinewidth grestore 0 .299 m .00625 .299 L s gsave -0.0125 .299 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 1.000 setlinewidth grestore 0 .44114 m .00625 .44114 L s gsave -0.0125 .44114 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (15) show 1.000 setlinewidth grestore 0 .58328 m .00625 .58328 L s gsave -0.0125 .58328 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (20) show 1.000 setlinewidth grestore .125 Mabswid 0 .04314 m .00375 .04314 L s 0 .07157 m .00375 .07157 L s 0 .1 m .00375 .1 L s 0 .12843 m .00375 .12843 L s 0 .18529 m .00375 .18529 L s 0 .21371 m .00375 .21371 L s 0 .24214 m .00375 .24214 L s 0 .27057 m .00375 .27057 L s 0 .32743 m .00375 .32743 L s 0 .35586 m .00375 .35586 L s 0 .38428 m .00375 .38428 L s 0 .41271 m .00375 .41271 L s 0 .46957 m .00375 .46957 L s 0 .498 m .00375 .498 L s 0 .52643 m .00375 .52643 L s 0 .55485 m .00375 .55485 L s 0 .61171 m .00375 .61171 L s .25 Mabswid 0 0 m 0 .61803 L s gsave -0.01875 .30902 -88.3438 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 64.5 11.8438 translate 90 rotate -64.5 -11.8438 translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 66.000 15.813 moveto 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .61178 m .02381 .61803 L s .15608 .61178 m .15608 .61803 L s .28836 .61178 m .28836 .61803 L s .42063 .61178 m .42063 .61803 L s .55291 .61178 m .55291 .61803 L s .68519 .61178 m .68519 .61803 L s .81746 .61178 m .81746 .61803 L s .94974 .61178 m .94974 .61803 L s .125 Mabswid .05026 .61428 m .05026 .61803 L s .07672 .61428 m .07672 .61803 L s .10317 .61428 m .10317 .61803 L s .12963 .61428 m .12963 .61803 L s .18254 .61428 m .18254 .61803 L s .20899 .61428 m .20899 .61803 L s .23545 .61428 m .23545 .61803 L s .2619 .61428 m .2619 .61803 L s .31481 .61428 m .31481 .61803 L s .34127 .61428 m .34127 .61803 L s .36772 .61428 m .36772 .61803 L s .39418 .61428 m .39418 .61803 L s .44709 .61428 m .44709 .61803 L s .47354 .61428 m .47354 .61803 L s .5 .61428 m .5 .61803 L s .52646 .61428 m .52646 .61803 L s .57937 .61428 m .57937 .61803 L s .60582 .61428 m .60582 .61803 L s .63228 .61428 m .63228 .61803 L s .65873 .61428 m .65873 .61803 L s .71164 .61428 m .71164 .61803 L s .7381 .61428 m .7381 .61803 L s .76455 .61428 m .76455 .61803 L s .79101 .61428 m .79101 .61803 L s .84392 .61428 m .84392 .61803 L s .87037 .61428 m .87037 .61803 L s .89683 .61428 m .89683 .61803 L s .92328 .61428 m .92328 .61803 L s .97619 .61428 m .97619 .61803 L s .25 Mabswid 0 .61803 m 1 .61803 L s .99375 .01472 m 1 .01472 L s .99375 .15686 m 1 .15686 L s .99375 .299 m 1 .299 L s .99375 .44114 m 1 .44114 L s .99375 .58328 m 1 .58328 L s .125 Mabswid .99625 .04314 m 1 .04314 L s .99625 .07157 m 1 .07157 L s .99625 .1 m 1 .1 L s .99625 .12843 m 1 .12843 L s .99625 .18529 m 1 .18529 L s .99625 .21371 m 1 .21371 L s .99625 .24214 m 1 .24214 L s .99625 .27057 m 1 .27057 L s .99625 .32743 m 1 .32743 L s .99625 .35586 m 1 .35586 L s .99625 .38428 m 1 .38428 L s .99625 .41271 m 1 .41271 L s .99625 .46957 m 1 .46957 L s .99625 .498 m 1 .498 L s .99625 .52643 m 1 .52643 L s .99625 .55485 m 1 .55485 L s .99625 .61171 m 1 .61171 L s .25 Mabswid 1 0 m 1 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 0 1 r .5 Mabswid .02381 .01472 m .06244 .06604 L .10458 .12176 L .14415 .17357 L .18221 .22268 L .22272 .27388 L .26171 .32179 L .30316 .37082 L .34309 .41573 L .3815 .45626 L .42237 .49584 L .46172 .52974 L .49955 .55759 L .52059 .57071 L .53984 .58105 L .55994 .58997 L .57861 .59637 L .5878 .5988 L .5976 .60084 L .60319 .60175 L .60847 .60241 L .6132 .60286 L .61587 .60305 L .61832 .60318 L .61958 .60323 L .62078 .60326 L .62185 .60329 L .62302 .60331 L .62429 .60332 L .62493 .60332 L .62563 .60332 L .62688 .6033 L .62806 .60328 L .62917 .60325 L .63034 .60321 L .63243 .60311 L .63468 .60297 L .63714 .60277 L .64232 .60221 L .64785 .6014 L .65781 .59932 L .66805 .59636 L .67915 .59216 L .6993 .58176 L .71918 .56778 L .74022 .54867 L .77811 .50225 L .81845 .43478 L .85727 .35198 L .89855 .24629 L Mistroke .93831 .13111 L .97619 .01472 L Mfstroke 1 0 0 r .02381 .01472 m .06244 .02563 L .10458 .03734 L .14415 .04798 L .18221 .05771 L .22272 .06738 L .26171 .07585 L .30316 .08381 L .34309 .09032 L .3815 .09539 L .40095 .09749 L .42237 .09942 L .44268 .10086 L .46172 .10187 L .4721 .10228 L .47721 .10245 L .48196 .10258 L .48661 .10268 L .49082 .10276 L .4955 .10283 L .49807 .10286 L .50049 .10288 L .50165 .10288 L .5029 .10289 L .50397 .1029 L .50514 .1029 L .50586 .1029 L .50652 .1029 L .50782 .10291 L .509 .1029 L .51025 .1029 L .51147 .1029 L .51278 .1029 L .51402 .10289 L .51515 .10288 L .51779 .10286 L .52057 .10283 L .52514 .10277 L .52939 .10269 L .53904 .10245 L .54956 .10208 L .5595 .10164 L .57808 .10056 L .5981 .09902 L .61655 .09728 L .65595 .0925 L .69384 .08662 L .73418 .07907 L .773 .07067 L .81428 .06067 L Mistroke .85404 .05017 L .89229 .03945 L .93298 .02758 L .97217 .01592 L .97619 .01472 L Mfstroke MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.5 0.309017 0.785714 0.451874 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0297619 0.297619 0.0198413 0.198413 [ [ 0 0 0 0 ] [ 1 .5 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .5 L 0 .5 L closepath clip newpath % Start of sub-graphic p 0.0535714 0.0357143 0.35119 0.234127 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 0 r .5 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g gsave .38988 .13492 -61 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 65.250 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (c) show 73.625 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore % Start of sub-graphic p 0.0535714 0.265873 0.35119 0.464286 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 0 1 r .5 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g gsave .38988 .36508 -61 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (q) show 68.250 17.688 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 73.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[33]:=", ImageSize->{288, 177.938}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`05Ool00`00Oomo o`08Ool00`00Oomoo`0>Ool00`00Oomoo`08Ool01000Oomoo`0017oo00<007ooOol03Woo00<007oo Ool01Goo00<007ooOol027oo00<007ooOol05goo0015Ool00`00Oomoo`03Ool00`00Oomoo`0JOol0 0`00Oomoo`07Ool00`00Oomoo`0IOol01000Oomoo`001Goo00<007ooOol05Woo00<007ooOol01goo 00<007ooOol04Woo00<007ooOol00goo00<007ooOol00goo00<007oo00001Goo00<007ooOol03Goo 00<007ooOol01Woo00<007ooOol01goo00<007ooOol03Woo00<007ooOol027oo00@007ooOol000Eo o`03001oogoo00eoo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo01Moo`00AGoo00<007oo Ool00goo00<007ooOol06goo00<007ooOol01Goo00<007ooOol06Goo00D007ooOomoo`0000Eoo`03 001oogoo01Ioo`03001oogoo00Ioo`03001oogoo01Aoo`03001oogoo009oo`03001oogoo00=oo`03 001oo`0000Eoo`03001oogoo00ioo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo011oo`03 001oogoo00Ioo`05001oogooOol00005Ool00`00Oomoo`0>Ool00`00Oomoo`05Ool00`00Oomoo`06 Ool00`00Oomoo`0HOol004Ioo`03001oogoo009oo`03001oogoo01aoo`03001oogoo009oo`8001Yo o`8000Eoo`03001oogoo009oo`03001oogoo01Moo`03001oogoo00=oo`8001Moo`03001oogoo00=o o`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`0>Ool00`00Oomoo`07Ool00`00Oomoo`02 Ool2000COol00`00Oomoo`04Ool20005Ool00`00Oomoo`02Ool00`00Oomoo`0>Ool00`00Oomoo`06 Ool00`00Oomoo`03Ool2000KOol004Ioo`03001oogoo009oo`03001oogoo01aoo`03001oogoo00=o o`03001oogoo01Uoo`03001oogoo00=oo`03001oogoo009oo`03001oogoo01Qoo`03001oogoo00=o o`03001oogoo01Eoo`03001oogoo00=oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`0> Ool00`00Oomoo`07Ool00`00Oomoo`03Ool00`00Oomoo`0AOol00`00Oomoo`05Ool00`00Oomoo`03 Ool00`00Oomoo`02Ool00`00Oomoo`0>Ool00`00Oomoo`07Ool00`00Oomoo`03Ool00`00Oomoo`0I Ool004Moo`05001oogooOol0000JOol01@00Oomoogoo00001Goo00<007ooOol06Goo00<007ooOol0 17oo00D007ooOomoo`0001Eoo`03001oogoo009oo`03001oogoo00=oo`03001oogoo01Ioo`03001o ogoo00=oo`05001oogooOol00003Ool01@00Oomoogoo00004Goo00<007ooOol00Woo00D007ooOomo o`0000Eoo`03001oogoo019oo`03001oogoo00Aoo`03001oogoo00Aoo`05001oogooOol0000AOol0 1@00Oomoogoo000017oo00<007ooOol00goo00<007ooOol06Goo0018Ool3000LOol30006Ool4000H Ool40004Ool3000GOol60004Ool4000DOol20006Ool30005Ool3000AOol20005Ool30006Ool4000@ Ool20006Ool40004Ool3000AOol20004Ool60004Ool4000HOol00?moofUoo`00ogooJGoo003oOomY Ool00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00=Woo0`0027ooo`004P005Woo000eOol0 1@00Oomoogoo00001goo00<007ooOol017oo00<007ooOol017oo00<007ooOol017oo00<007ooOol0 17oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol017oo00<007ooOol017oo00<007ooOol0 17oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol017oo00<007ooOol017oo00<007ooOol0 17oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol017oo00<007ooOol017oo00<007ooOol0 17oo00<007ooOol017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol017oo00<007ooOol0 17oo00<007ooOol017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol017oo00<007ooOol0 17oo00<007ooOol017oo00<007ooOol017oo00<007ooOol01Goo00<007ooOol017oo00<007ooOol0 17oo00<007ooOol017oo00<007ooOol017oo00<007ooOol01Goo00<007ooOol00goo00<007ooOol0 57oo000eOol00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`04Ool00`00Oomoo`0QOol00`00 Oomoo`0QOol00`00Oomoo`0QOol00`00Oomoo`0QOol00`00Oomoo`0QOol00`00Oomoo`0POol00`00 Oomoo`0QOol00`00Oomoo`0;Ool00`00Oomoo`0DOol003Eoo`03001oogoo009oo`03001oogoo00Ao o`03001oogoo0?moo`ioo`03001oogoo01Aoo`00=Goo00<007ooOol00goo00<007ooOol00goo0`00 17oo0W`0oWoo17`00goo0`005Woo000eOol00`00Oomoo`03Ool00`00Oomoo`03Ool00`00Oomoo`05 Ool0100OO01l07`0nGoo0W`00goo00<07gooOol00goo00<007ooOol057oo000fOol00`00Oomoo`02 Ool00`00Oomoo`03Ool00`00Oomoo`05Ool0100OOomoogoo17`0lWoo0g`017oo00<07gooOol017oo 00<007ooOol057oo000fOol00`00Oomoo`02Ool00`00Oomoo`03Ool00`00Oomoo`06Ool00`0OOomo o`04Ool3O03]Ool2O007Ool00`0OOomoo`04Ool00`00Oomoo`0DOol003Moo`05001oogooOol00005 Ool00`00Oomoo`07Ool00`0OOomoo`06Ool4O03VOol3O009Ool00`0OOomoo`04Ool00`00Oomoo`0D Ool003Qoo`<000Ioo`03001oogoo00Qoo`0301moogoo00Uoo`Al0=ioo`Al00]oo`0301moogoo00Eo o`03001oogoo01Aoo`00@Goo00<007ooOol027oo00<07gooOol03Goo17`0eWoo17`03goo00<07goo Ool01Goo00<007ooOol057oo0011Ool00`00Oomoo`09Ool00`0OOomoo`0@Ool4O03?Ool3O00COol0 0`0OOomoo`05Ool00`00Oomoo`0DOol0045oo`8000]oo`0301moogoo01=oo`Al0Woo00<07gooOol02Goo00<007ooOol057oo0011Ool0 0`00Oomoo`0BOol00`0OOomoo`0iOol5O01ZOol6O00mOol00`0OOomoo`0:Ool00`00Oomoo`0DOol0 045oo`03001oogoo01=oo`0301moogoo03eoo`Il05eoo`Ml04=oo`0301moogoo00Yoo`03001oogoo 01Aoo`00@Goo00<007ooOol057oo00<07gooOol0@Woo1g`0Bgoo2g`0BWoo00<07gooOol02Woo00<0 07ooOol057oo0011Ool00`00Oomoo`0DOol00`0OOomoo`19Ool8O00kOol8O01DOol00`0OOomoo`0; Ool00`00Oomoo`0DOol0045oo`8001Ioo`0301moogoo051ooa5l01moo`]l05aoo`0301moogoo00Yo o`8001Ioo`00@Goo00<007ooOol05Woo00<07gooOol0H7oo7g`0Igoo00<07gooOol02goo00<007oo Ool057oo0011Ool00`00Oomoo`0GOol00`0OOomoo`3TOol00`0OOomoo`0=oo`0301moogoo00aoo`03001oogoo01Aoo`00@Goo00<0 07ooOol067oo00<07gooOol0hgoo00<07gooOol037oo00<007ooOol057oo0011Ool00`00Oomoo`0I Ool00`0OOomoo`3QOol00`0OOomoo`0=Ool00`00Oomoo`0DOol0045oo`03001oogoo01Yoo`0301mo ogoo0>1oo`0301moogoo00eoo`03001oogoo01Aoo`00@Goo00<007ooOol06goo00<07gooOol0ggoo 00<07gooOol03Goo00<007ooOol057oo0011Ool2000MOol00`0OOomoo`3MOol00`0OOomoo`0=Ool2 000FOol0045oo`03001oogoo01aoo`0301moogoo0=eoo`0301moogoo00ioo`03001oogoo01Aoo`00 @Goo00<007ooOol07Goo00<07gooOol0g7oo00<07gooOol03Woo00<007ooOol057oo0011Ool00`00 Oomoo`0NOol00`0OOomoo`3JOol00`0OOomoo`0?Ool00`00Oomoo`0DOol003Eoo`@000Qoo`03001o ogoo01moo`0301moogoo0=Uoo`0301moogoo00moo`03001oogoo01Aoo`00=Goo00D007ooOomoo`00 00Moo`03001oogoo021oo`0301moogoo0=Qoo`0301moogoo00moo`03001oogoo01Aoo`00>Woo00<0 07ooOol017oo00<007ooOol087oo00<07gooOol0egoo00<07gooOol047oo00<007ooOol057oo000j Ool00`00Oomoo`04Ool00`00Oomoo`0QOol00`0OOomoo`3FOol00`0OOomoo`0@Ool00`00Oomoo`0D Ool003Yoo`03001oogoo00Aoo`<0029oo`0301moogoo0=Eoo`0301moogoo00ioo`<001Ioo`00>Goo 00<007ooOol01Goo00<007ooOol08goo00<07gooOol0dgoo00<07gooOol04Goo00<007ooOol057oo 000gOol20008Ool00`00Oomoo`0SOol00`0OOomoo`3COol00`0OOomoo`0AOol00`00Oomoo`0DOol0 03Qoo`03001oogoo00Ioo`03001oogoo02Aoo`0301moogoo0=5oo`0301moogoo019oo`03001oogoo 01Aoo`00>7oo00<007ooOol01Woo00<007ooOol09Goo00<07gooOol0d7oo00<07gooOol04Woo00<0 07ooOol057oo000hOol40005Ool00`00Oomoo`0VOol00`0OOomoo`3?Ool00`0OOomoo`0BOol00`00 Oomoo`0DOol0045oo`03001oogoo02Ioo`0301moogoo0goo00<07gooOol0 HGoo0P00CWoo00<07gooOol06goo0P005Woo0011Ool00`00Oomoo`0kOol00`0OOomoo`1QOol00`00 Oomoo`1Ool00`0OOomoo`19Ool01000Oomoo`001Woo00<007ooOol0@7oo 00<07gooOol08goo0P005Woo0011Ool00`00Oomoo`1>Ool00`0OOomoo`18Ool01@00Oomoogoo0000 1Goo00<007ooOol0?goo00<07gooOol09Goo00<007ooOol057oo0011Ool00`00Oomoo`1>Ool00`0O Oomoo`18Ool01@00Oomoogoo00001Woo00<007ooOol0?Woo00<07gooOol09Goo00<007ooOol057oo 0011Ool00`00Oomoo`1?Ool00`0OOomoo`0SOolN01l6Ool60002Ool01000Oomoo`00?goo00<07goo Ool09Woo00<007ooOol057oo0011Ool00`00Oomoo`1@Ool00`0OOomoo`16Ool00`00Oomoo`02Ool0 1000Oomoogoo0P00@7oo00<07gooOol09Woo00<007ooOol057oo0011Ool00`00Oomoo`1AOol00`0O Oomoo`16Ool01@00Oomoogoo0000A7oo00<07gooOol09goo00<007ooOol057oo0011Ool00`00Oomo o`1BOol00`0OOomoo`15Ool01@00Oomoogoo0000A7oo00<07gooOol09goo00<007ooOol057oo0011 Ool2001DOol00`0OOomoo`15Ool01000Oomoo`00@goo00<07gooOol09goo0P005Woo0011Ool00`00 Oomoo`1DOol00`0OOomoo`15Ool20014Ool00`0OOomoo`0XOol00`00Oomoo`0DOol0045oo`03001o ogoo05Eoo`0301moogoo08Uoo`0301moogoo02Uoo`03001oogoo01Aoo`00@Goo00<007ooOol0EWoo 00<07gooOol0R7oo00<07gooOol0:Goo00<007ooOol057oo0011Ool00`00Oomoo`1FOol00`0OOomo o`28Ool00`0OOomoo`0YOol00`00Oomoo`0DOol0045oo`03001oogoo05Moo`0301moogoo08Ioo`03 01moogoo02Yoo`03001oogoo01Aoo`00@Goo00<007ooOol0F7oo00<07gooOol0QGoo00<07gooOol0 :Woo00<007ooOol057oo0011Ool00`00Oomoo`1IOol00`0OOomoo`23Ool00`0OOomoo`0[Ool00`00 Oomoo`0DOol0045oo`8005]oo`0301moogoo089oo`0301moogoo02Yoo`8001Ioo`00@Goo00<007oo Ool0Fgoo00<07gooOol0P7oo00<07gooOol0;7oo00<007ooOol057oo0011Ool00`00Oomoo`1LOol0 0`0OOomoo`1oOol00`0OOomoo`0/Ool00`00Oomoo`0DOol0045oo`03001oogoo05eoo`0301moogoo 07eoo`0301moogoo02eoo`03001oogoo01Aoo`00;Woo100017oo10001goo00<007ooOol0GWoo00<0 7gooOol0O7oo00<07gooOol0;Goo00<007ooOol057oo000_Ool00`00Oomoo`04Ool01@00Oomoogoo 00001Woo00<007ooOol0Ggoo00<07gooOol0NWoo00<07gooOol0;Woo00<007ooOol057oo000`Ool0 0`00Oomoo`08Ool00`00Oomoo`03Ool00`00Oomoo`1POol00`0OOomoo`1iOol00`0OOomoo`0^Ool0 0`00Oomoo`0DOol0031oo`03001oogoo00Qoo`03001oogoo00=oo`03001oogoo061oo`0301moogoo 07Qoo`0301moogoo02moo`03001oogoo01Aoo`00<7oo00<007ooOol027oo00<007ooOol00goo0`00 HGoo00<07gooOol0Mgoo00<07gooOol0;Goo0`005Woo000aOol00`00Oomoo`06Ool00`00Oomoo`04 Ool00`00Oomoo`1ROol00`0OOomoo`1eOol00`0OOomoo`0`Ool00`00Oomoo`0DOol0035oo`03001o ogoo00Aoo`8000Moo`03001oogoo06=oo`0301moogoo07Aoo`0301moogoo031oo`03001oogoo01Ao o`00goo00<007ooOol057oo0011Ool00`00Oomoo`1eOol00`0O Oomoo`1FOol00`0OOomoo`0lOol00`00Oomoo`0DOol0045oo`03001oogoo07Ioo`0301moogoo05Eo o`0301moogoo03aoo`03001oogoo01Aoo`00@Goo00<007ooOol0Mgoo00<07gooOol0Dgoo00<07goo Ool0?Goo00<007ooOol057oo0011Ool00`00Oomoo`1hOol201mBOol00`0OOomoo`0nOol00`00Oomo o`0DOol0045oo`8007]oo`0301moogoo04ioo`0301moogoo03ioo`8001Ioo`00@Goo00<007ooOol0 Ngoo00<07gooOol0C7oo00<07gooOol0@7oo00<007ooOol057oo0011Ool00`00Oomoo`1lOol201m; Ool00`0OOomoo`11Ool00`00Oomoo`0DOol0045oo`03001oogoo07ioo`0301moogoo04Qoo`0301mo ogoo045oo`03001oogoo01Aoo`00@Goo00<007ooOol0Ogoo00<07gooOol0AWoo00<07gooOol0@Woo 00<007ooOol057oo0011Ool00`00Oomoo`20Ool201m5Ool00`0OOomoo`13Ool00`00Oomoo`0DOol0 045oo`03001oogoo089oo`0301moogoo045oo`0301moogoo04Aoo`03001oogoo01Aoo`00@Goo00<0 07ooOol0Pgoo0P0O@7oo00<07gooOol0AGoo00<007ooOol057oo0011Ool20026Ool00`0OOomoo`0l Ool00`0OOomoo`15Ool2000FOol0045oo`03001oogoo08Ioo`807c]oo`0301moogoo04Moo`03001o ogoo01Aoo`00@Goo00<007ooOol0R7oo00<07gooOol0=goo00<07gooOol0B7oo00<007ooOol057oo 0011Ool00`00Oomoo`29Ool201lfOol00`0OOomoo`19Ool00`00Oomoo`0DOol002eoo`D000Eoo`<0 00Moo`03001oogoo08]oo`0301moogoo035oo`807daoo`03001oogoo01Aoo`00;Woo00D007ooOomo o`0000=oo`05001oogooOol00006Ool00`00Oomoo`2"], ImageRangeCache->{{{109, 396}, {367.313, 190.375}} -> {-1.85215, 0.747502, \ 0.00733523, 0.00733523}, {{116.125, 388.813}, {363.063, 194.563}} -> \ {-145.417, 24.1287, 0.870996, 0.162107}, {{252.5, 334.25}, {278.813, \ 237.938}} -> {-10.4781, 6.18077, 0.0411013, 0.0616519}, {{256.875, 281.188}, \ {275.875, 259.625}} -> {-11.1189, 12.6919, 0.0431881, 0.13976}, {{256.875, \ 281.188}, {257.063, 240.813}} -> {-11.1189, 10.0627, 0.0431881, 0.13976}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["example: nucleon-nucleon scattering", "Subsection"], Cell["\<\ \tAn important special case occurs when the projectile scatters from a \ particle of equal mass, such that\ \>", "Text"], Cell[BoxData[ \(m\_1 = \(m\_2\ \ \[DoubleLongRightArrow]\ \ \[Beta] = \(\[Beta]\_c = \(\ \(\[Beta]\_\[ScriptL]\/2\)\ \ \[DoubleLongRightArrow]\ \ \ \[CapitalOmega] = \ \(\[Theta]\_\[ScriptL]\ \ \ \ \ \ \ \[Chi] = \[Theta]\_c - 2 \[Theta]\_\[ScriptL]\)\)\)\)\)], "DisplayFormula", TextAlignment->Left, TextJustification->0, FontFamily->"Times New Roman"], Cell[TextData[{ "where ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\)]], " is the boost from the cm to the lab frame and where ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " and ", Cell[BoxData[ \(TraditionalForm\`\(\(S\_2\)\(\ \)\)\)]], "are now labeled as ", Cell[BoxData[ \(TraditionalForm\`S\_c\)]], " and ", Cell[BoxData[ \(TraditionalForm\`S\_\[ScriptL]\)]], ", respectively. Substituting these kinematics, we find" }], "Text"], Cell[BoxData[ \(TextForm\`\[Theta]\_\[ScriptL]\ = \ \(\[CapitalOmega]\ = \ ArcTan[\(\[Gamma]\_c\) \((1 + Cos[\[Theta]\_c])\), Sin[\[Theta]\_c]]\)\)], "DisplayFormula"], Cell["such that", "Text"], Cell[BoxData[ \(TextForm\`\[Chi]\ = \ \[Theta]\_c\ - \ 2 \[Theta]\_\[ScriptL]\)], "DisplayFormula"], Cell["Finally, in the nonrelativistic limit, we find that", "Text"], Cell[BoxData[ \(\[Gamma] \[Rule] 1\ \ \[DoubleLongRightArrow]\ \ \[Theta]\_c = 2 \[Theta]\_\[ScriptL]\ \ \ \[DoubleLongRightArrow]\ \ \ \[Chi] \ \[Rule] 0\)], "DisplayFormula", TextAlignment->Left, TextJustification->0, FontFamily->"Times New Roman"], Cell[TextData[{ "justifies the identification of ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], " as the \"relativistic\" spin rotation angle. More generally, ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_c > 2 \[Theta]\_\[ScriptL]\)]], " for equal masses so that ", Cell[BoxData[ \(TraditionalForm\`\[Chi] > 0\)]], ". Therefore, we conclude that successive nonparallel boosts rotate the \ spin in the same direction but generally much less than the momentum." }], "Text"], Cell[TextData[{ "\tThe figure below shows ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], " as a function of cm scattering angle for laboratory kinetic energies \ ranging from 0.25 to 2.25 GeV in steps of 0.5 GeV, with the smallest \ (largest) energy producing the smallest (largest) Wigner rotation. The \ maximum Wigner roation angle under these condition is only about 8\[Degree]. \ It is a small effect, but still must be included in the analysis of \ depolarization or polarization transfer data." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[ Table[\(\(chi /. transform[\[Beta]\/2, \[Theta]\_1\ Degree, \[Beta]\/2]\) /. \ {\[Beta] \[Rule] \@\(\[Gamma]\^2 - 1\)\/\[Gamma]}\) /. \[Gamma] \[Rule] \(T + \ 1\)\/0.939, {T, 0.25, 2.25, 0.5}]], {\[Theta]\_1, 0, 180}, PlotPoints \[Rule] 50, Frame \[Rule] True, FrameLabel \[Rule] {\*"\"\<\!\(\[Theta]\_c\) (deg)\>\"", "\<\[Chi] \ (deg)\>"}, PlotLabel \[Rule] "\", Epilog \[Rule] Text[\*"\"\<\!\(T\_lab\)={0.25,2.25,0.5} GeV\>\"", \ {90, 0.5}]];\)\)], "Input", CellLabel->"In[34]:="], 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 Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.00529101 0.0147151 0.0790075 [ [.02381 -0.0125 -5 -15.6875 ] [.02381 -0.0125 5 0 ] [.15608 -0.0125 -8 -15.6875 ] [.15608 -0.0125 8 0 ] [.28836 -0.0125 -8 -15.6875 ] [.28836 -0.0125 8 0 ] [.42063 -0.0125 -8 -15.6875 ] [.42063 -0.0125 8 0 ] [.55291 -0.0125 -11 -15.6875 ] [.55291 -0.0125 11 0 ] [.68519 -0.0125 -11 -15.6875 ] [.68519 -0.0125 11 0 ] [.81746 -0.0125 -11 -15.6875 ] [.81746 -0.0125 11 0 ] [.94974 -0.0125 -11 -15.6875 ] [.94974 -0.0125 11 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -22.3438 -31.375 ] [.5 -0.0125 22.3438 -15.6875 ] [-0.0125 .01472 -10 -7.84375 ] [-0.0125 .01472 0 7.84375 ] [-0.0125 .09372 -10 -7.84375 ] [-0.0125 .09372 0 7.84375 ] [-0.0125 .17273 -10 -7.84375 ] [-0.0125 .17273 0 7.84375 ] [-0.0125 .25174 -10 -7.84375 ] [-0.0125 .25174 0 7.84375 ] [-0.0125 .33074 -10 -7.84375 ] [-0.0125 .33074 0 7.84375 ] [-0.0125 .40975 -10 -7.84375 ] [-0.0125 .40975 0 7.84375 ] [-0.0125 .48876 -10.25 -7.84375 ] [-0.0125 .48876 0 7.84375 ] [-0.0125 .56777 -10.25 -7.84375 ] [-0.0125 .56777 0 7.84375 ] [ 0 0 -0.125 0 ] [-0.01875 .30902 -25.9375 -22.875 ] [-0.01875 .30902 -10.25 22.875 ] [ 0 .61803 .125 0 ] [ 1 0 .125 0 ] [.5 .63053 -87.4688 0 ] [.5 .63053 87.4688 15.6875 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 0 m .02381 .00625 L s gsave .02381 -0.0125 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore .15608 0 m .15608 .00625 L s gsave .15608 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (25) show 1.000 setlinewidth grestore .28836 0 m .28836 .00625 L s gsave .28836 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (50) show 1.000 setlinewidth grestore .42063 0 m .42063 .00625 L s gsave .42063 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (75) show 1.000 setlinewidth grestore .55291 0 m .55291 .00625 L s gsave .55291 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (100) show 1.000 setlinewidth grestore .68519 0 m .68519 .00625 L s gsave .68519 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (125) show 1.000 setlinewidth grestore .81746 0 m .81746 .00625 L s gsave .81746 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (150) show 1.000 setlinewidth grestore .94974 0 m .94974 .00625 L s gsave .94974 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (175) show 1.000 setlinewidth grestore .125 Mabswid .05026 0 m .05026 .00375 L s .07672 0 m .07672 .00375 L s .10317 0 m .10317 .00375 L s .12963 0 m .12963 .00375 L s .18254 0 m .18254 .00375 L s .20899 0 m .20899 .00375 L s .23545 0 m .23545 .00375 L s .2619 0 m .2619 .00375 L s .31481 0 m .31481 .00375 L s .34127 0 m .34127 .00375 L s .36772 0 m .36772 .00375 L s .39418 0 m .39418 .00375 L s .44709 0 m .44709 .00375 L s .47354 0 m .47354 .00375 L s .5 0 m .5 .00375 L s .52646 0 m .52646 .00375 L s .57937 0 m .57937 .00375 L s .60582 0 m .60582 .00375 L s .63228 0 m .63228 .00375 L s .65873 0 m .65873 .00375 L s .71164 0 m .71164 .00375 L s .7381 0 m .7381 .00375 L s .76455 0 m .76455 .00375 L s .79101 0 m .79101 .00375 L s .84392 0 m .84392 .00375 L s .87037 0 m .87037 .00375 L s .89683 0 m .89683 .00375 L s .92328 0 m .92328 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave .5 -0.0125 -83.3438 -35.375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (q) show 68.250 17.688 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (c) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 78.563 15.813 moveto (H) show 82.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (deg) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 99.875 15.813 moveto (L) show 103.688 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 .01472 m .00625 .01472 L s gsave -0.0125 .01472 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore 0 .09372 m .00625 .09372 L s gsave -0.0125 .09372 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 1.000 setlinewidth grestore 0 .17273 m .00625 .17273 L s gsave -0.0125 .17273 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore 0 .25174 m .00625 .25174 L s gsave -0.0125 .25174 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 1.000 setlinewidth grestore 0 .33074 m .00625 .33074 L s gsave -0.0125 .33074 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (4) show 1.000 setlinewidth grestore 0 .40975 m .00625 .40975 L s gsave -0.0125 .40975 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (5) show 1.000 setlinewidth grestore 0 .48876 m .00625 .48876 L s gsave -0.0125 .48876 -71.25 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (6) show 1.000 setlinewidth grestore 0 .56777 m .00625 .56777 L s gsave -0.0125 .56777 -71.25 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (7) show 1.000 setlinewidth grestore .125 Mabswid 0 .03052 m .00375 .03052 L s 0 .04632 m .00375 .04632 L s 0 .06212 m .00375 .06212 L s 0 .07792 m .00375 .07792 L s 0 .10952 m .00375 .10952 L s 0 .12533 m .00375 .12533 L s 0 .14113 m .00375 .14113 L s 0 .15693 m .00375 .15693 L s 0 .18853 m .00375 .18853 L s 0 .20433 m .00375 .20433 L s 0 .22013 m .00375 .22013 L s 0 .23594 m .00375 .23594 L s 0 .26754 m .00375 .26754 L s 0 .28334 m .00375 .28334 L s 0 .29914 m .00375 .29914 L s 0 .31494 m .00375 .31494 L s 0 .34655 m .00375 .34655 L s 0 .36235 m .00375 .36235 L s 0 .37815 m .00375 .37815 L s 0 .39395 m .00375 .39395 L s 0 .42555 m .00375 .42555 L s 0 .44136 m .00375 .44136 L s 0 .45716 m .00375 .45716 L s 0 .47296 m .00375 .47296 L s 0 .50456 m .00375 .50456 L s 0 .52036 m .00375 .52036 L s 0 .53616 m .00375 .53616 L s 0 .55197 m .00375 .55197 L s 0 .58357 m .00375 .58357 L s 0 .59937 m .00375 .59937 L s 0 .61517 m .00375 .61517 L s .25 Mabswid 0 0 m 0 .61803 L s gsave -0.01875 .30902 -101.969 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 83.875 11.8438 translate 90 rotate -83.875 -11.8438 translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 65.250 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (c) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 79.625 15.813 moveto (H) show 83.438 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (deg) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 100.938 15.813 moveto (L) show 104.750 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .61178 m .02381 .61803 L s .15608 .61178 m .15608 .61803 L s .28836 .61178 m .28836 .61803 L s .42063 .61178 m .42063 .61803 L s .55291 .61178 m .55291 .61803 L s .68519 .61178 m .68519 .61803 L s .81746 .61178 m .81746 .61803 L s .94974 .61178 m .94974 .61803 L s .125 Mabswid .05026 .61428 m .05026 .61803 L s .07672 .61428 m .07672 .61803 L s .10317 .61428 m .10317 .61803 L s .12963 .61428 m .12963 .61803 L s .18254 .61428 m .18254 .61803 L s .20899 .61428 m .20899 .61803 L s .23545 .61428 m .23545 .61803 L s .2619 .61428 m .2619 .61803 L s .31481 .61428 m .31481 .61803 L s .34127 .61428 m .34127 .61803 L s .36772 .61428 m .36772 .61803 L s .39418 .61428 m .39418 .61803 L s .44709 .61428 m .44709 .61803 L s .47354 .61428 m .47354 .61803 L s .5 .61428 m .5 .61803 L s .52646 .61428 m .52646 .61803 L s .57937 .61428 m .57937 .61803 L s .60582 .61428 m .60582 .61803 L s .63228 .61428 m .63228 .61803 L s .65873 .61428 m .65873 .61803 L s .71164 .61428 m .71164 .61803 L s .7381 .61428 m .7381 .61803 L s .76455 .61428 m .76455 .61803 L s .79101 .61428 m .79101 .61803 L s .84392 .61428 m .84392 .61803 L s .87037 .61428 m .87037 .61803 L s .89683 .61428 m .89683 .61803 L s .92328 .61428 m .92328 .61803 L s .97619 .61428 m .97619 .61803 L s .25 Mabswid 0 .61803 m 1 .61803 L s .99375 .01472 m 1 .01472 L s .99375 .09372 m 1 .09372 L s .99375 .17273 m 1 .17273 L s .99375 .25174 m 1 .25174 L s .99375 .33074 m 1 .33074 L s .99375 .40975 m 1 .40975 L s .99375 .48876 m 1 .48876 L s .99375 .56777 m 1 .56777 L s .125 Mabswid .99625 .03052 m 1 .03052 L s .99625 .04632 m 1 .04632 L s .99625 .06212 m 1 .06212 L s .99625 .07792 m 1 .07792 L s .99625 .10952 m 1 .10952 L s .99625 .12533 m 1 .12533 L s .99625 .14113 m 1 .14113 L s .99625 .15693 m 1 .15693 L s .99625 .18853 m 1 .18853 L s .99625 .20433 m 1 .20433 L s .99625 .22013 m 1 .22013 L s .99625 .23594 m 1 .23594 L s .99625 .26754 m 1 .26754 L s .99625 .28334 m 1 .28334 L s .99625 .29914 m 1 .29914 L s .99625 .31494 m 1 .31494 L s .99625 .34655 m 1 .34655 L s .99625 .36235 m 1 .36235 L s .99625 .37815 m 1 .37815 L s .99625 .39395 m 1 .39395 L s .99625 .42555 m 1 .42555 L s .99625 .44136 m 1 .44136 L s .99625 .45716 m 1 .45716 L s .99625 .47296 m 1 .47296 L s .99625 .50456 m 1 .50456 L s .99625 .52036 m 1 .52036 L s .99625 .53616 m 1 .53616 L s .99625 .55197 m 1 .55197 L s .99625 .58357 m 1 .58357 L s .99625 .59937 m 1 .59937 L s .99625 .61517 m 1 .61517 L s .25 Mabswid 1 0 m 1 .61803 L s gsave .5 .63053 -148.469 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Wigner) show 101.000 15.813 moveto (Rotation) show 147.250 15.813 moveto (for) show 164.438 15.813 moveto (NN) show 184.563 15.813 moveto (Scattering) show 233.938 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .04273 .03054 L .06337 .04773 L .08275 .06375 L .10139 .07898 L .12123 .09495 L .14033 .11002 L .16063 .12565 L .18019 .14028 L .199 .1539 L .21902 .16784 L .23829 .18067 L .25683 .19242 L .27656 .20424 L .29555 .2149 L .31574 .22543 L .33519 .23472 L .3539 .24285 L .3738 .25058 L .39297 .2571 L .41334 .263 L .43296 .26765 L .45184 .27115 L .46142 .27255 L .47193 .27379 L .47675 .27426 L .48193 .27469 L .48678 .27502 L .49127 .27528 L .49625 .27549 L .49888 .27557 L .50022 .27561 L .50167 .27564 L .50293 .27566 L .50409 .27568 L .50519 .27569 L .5058 .2757 L .50635 .2757 L .50697 .2757 L .50731 .27571 L .50763 .27571 L .50821 .27571 L .50882 .27571 L .50915 .27571 L .50951 .27571 L .50988 .27571 L .51023 .2757 L .51085 .2757 L .51153 .2757 L .51277 .27568 L Mistroke .5141 .27567 L .51649 .27562 L .51933 .27555 L .5219 .27546 L .52697 .27524 L .53174 .27496 L .5416 .27417 L .55065 .27321 L .57002 .27036 L .58864 .26662 L .60847 .26158 L .62755 .25569 L .64783 .24836 L .66737 .24026 L .68617 .23155 L .70617 .22132 L .72543 .21058 L .74395 .19946 L .76366 .18681 L .78264 .1739 L .80281 .15945 L .82225 .14488 L .84094 .13032 L .86083 .1143 L .87998 .09844 L .90033 .08119 L .91994 .06426 L .93881 .04776 L .95887 .03005 L .97619 .01472 L Mfstroke .02381 .01472 m .04273 .04108 L .06337 .06974 L .08275 .09645 L .10139 .12187 L .12123 .14853 L .14033 .17373 L .16063 .19991 L .18019 .22444 L .199 .24732 L .21902 .27079 L .23829 .29245 L .25683 .31234 L .27656 .33241 L .29555 .35059 L .31574 .36859 L .33519 .38458 L .3539 .39863 L .3738 .41209 L .39297 .42353 L .41334 .43399 L .43296 .44237 L .45184 .4488 L .46142 .45144 L .47193 .45385 L .48193 .45566 L .49127 .45692 L .49639 .45744 L .50124 .45781 L .50335 .45794 L .50559 .45805 L .50805 .45815 L .50914 .45818 L .51032 .45821 L .51149 .45823 L .51213 .45824 L .51272 .45825 L .51327 .45825 L .51378 .45826 L .51436 .45826 L .51491 .45826 L .51551 .45826 L .51615 .45826 L .51669 .45825 L .51729 .45825 L .51793 .45824 L .51862 .45823 L .51986 .4582 L .52226 .45813 L .52454 .45803 L Mistroke .52881 .45779 L .53352 .45742 L .53853 .4569 L .54755 .45567 L .55805 .45373 L .56794 .45141 L .58685 .44566 L .60696 .43763 L .62632 .42806 L .64495 .41717 L .66477 .40381 L .68385 .38926 L .70414 .37203 L .72368 .35379 L .74248 .33477 L .76248 .31304 L .78174 .29075 L .80025 .26814 L .81997 .24289 L .83894 .21755 L .85912 .18962 L .87855 .16188 L .89724 .13454 L .91714 .10487 L .93629 .07588 L .95664 .04476 L .97619 .01472 L Mfstroke .02381 .01472 m .04273 .04555 L .06337 .07906 L .08275 .11031 L .10139 .14005 L .12123 .17126 L .14033 .20077 L .16063 .23145 L .18019 .26021 L .199 .28706 L .21902 .31463 L .23829 .3401 L .25683 .36351 L .27656 .38717 L .29555 .40862 L .31574 .42991 L .33519 .44885 L .3539 .46554 L .3738 .48157 L .39297 .49524 L .41334 .5078 L .43296 .51791 L .45184 .52574 L .46142 .52899 L .47193 .53197 L .48204 .53428 L .49127 .53588 L .49617 .53654 L .50082 .53704 L .50573 .53744 L .5085 .5376 L .50984 .53766 L .51107 .53771 L .51215 .53775 L .51334 .53778 L .51453 .53781 L .51518 .53782 L .51578 .53782 L .51636 .53783 L .5169 .53783 L .51739 .53783 L .51792 .53783 L .5185 .53783 L .51911 .53783 L .51963 .53782 L .52021 .53781 L .52152 .53779 L .52272 .53776 L .52411 .53771 L .52542 .53765 L Mistroke .52776 .53753 L .5303 .53737 L .53537 .53692 L .53995 .53639 L .55023 .53477 L .55968 .53273 L .56988 .52996 L .58999 .52273 L .60936 .51356 L .62798 .50272 L .64781 .48903 L .66689 .47378 L .68717 .45541 L .70672 .43566 L .72551 .41482 L .74552 .39077 L .76477 .36586 L .78329 .34039 L .80301 .31174 L .82198 .28279 L .84216 .25068 L .86159 .2186 L .88028 .1868 L .90017 .15213 L .91932 .11808 L .93967 .08136 L .95928 .04564 L .97619 .01472 L Mfstroke .02381 .01472 m .04273 .04784 L .06337 .08385 L .08275 .11742 L .10139 .14938 L .12123 .18293 L .14033 .21466 L .16063 .24765 L .18019 .27859 L .199 .30749 L .21902 .33717 L .23829 .36461 L .25683 .38984 L .27656 .41536 L .29555 .43851 L .31574 .46152 L .33519 .482 L .3539 .50007 L .3738 .51745 L .39297 .5323 L .41334 .54597 L .43296 .55702 L .45184 .5656 L .46142 .56918 L .47193 .57248 L .48204 .57505 L .49127 .57686 L .49584 .57756 L .50082 .57819 L .50356 .57847 L .50608 .57869 L .50848 .57886 L .51107 .579 L .51227 .57905 L .51353 .5791 L .51469 .57914 L .51578 .57916 L .51631 .57917 L .5168 .57918 L .51738 .57918 L .5179 .57919 L .51847 .57919 L .51901 .57919 L .51959 .57919 L .52021 .57918 L .52083 .57918 L .52141 .57917 L .52269 .57915 L .52388 .57911 L .52501 .57907 L Mistroke .52754 .57896 L .5303 .57879 L .53537 .57835 L .53995 .57782 L .55023 .57615 L .55968 .57404 L .56988 .57113 L .58999 .56349 L .60936 .55375 L .62798 .54218 L .64781 .52753 L .66689 .51118 L .68717 .49145 L .70672 .4702 L .72551 .44776 L .74552 .42183 L .76477 .39495 L .78329 .36744 L .80301 .33647 L .82198 .30517 L .84216 .27042 L .86159 .23568 L .88028 .20124 L .90017 .16367 L .91932 .12677 L .93967 .08697 L .95928 .04825 L .97619 .01472 L Mfstroke .02381 .01472 m .04273 .04917 L .06337 .08662 L .08275 .12154 L .10139 .15479 L .12123 .1897 L .14033 .22271 L .16063 .25703 L .18019 .28925 L .199 .31933 L .21902 .35024 L .23829 .37882 L .25683 .40512 L .27656 .43172 L .29555 .45587 L .31574 .47988 L .33519 .50127 L .3539 .52014 L .3738 .53832 L .39297 .55386 L .41334 .56819 L .43296 .57978 L .45184 .58882 L .46142 .59259 L .47193 .59609 L .48204 .59881 L .49127 .60074 L .49584 .6015 L .50082 .60218 L .50356 .60249 L .50608 .60273 L .50848 .60292 L .51107 .60308 L .51227 .60314 L .51353 .6032 L .51469 .60324 L .51578 .60327 L .5168 .60329 L .51738 .6033 L .5179 .60331 L .51847 .60331 L .51909 .60332 L .51967 .60332 L .52021 .60332 L .52079 .60332 L .52141 .60331 L .522 .6033 L .52254 .60329 L .52386 .60326 L .52511 .60323 L Mistroke .52759 .60312 L .5303 .60296 L .53291 .60276 L .53537 .60253 L .53995 .602 L .55023 .60031 L .56009 .59805 L .56914 .59542 L .58851 .58798 L .60713 .57852 L .62696 .56597 L .64604 .55151 L .66632 .53361 L .68586 .51395 L .70466 .49286 L .72466 .46817 L .74392 .44227 L .76244 .41551 L .78215 .38511 L .80113 .35414 L .82131 .31949 L .84074 .2846 L .85943 .24981 L .87932 .2116 L .89847 .17385 L .91882 .13289 L .93843 .09282 L .9573 .05389 L .97619 .01472 L Mfstroke gsave .5 .05422 -124.719 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (T) show 69.688 17.688 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (lab) show 81.188 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 89.688 15.813 moveto (8) show 93.625 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.25) show 114.813 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 117.813 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2.25) show 139.000 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 142.000 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.5) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 157.000 15.813 moveto (<) show 163.938 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (GeV) show 186.438 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[34]:=", ImageSize->{288, 177.938}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`03Ool00`00Ool0002Ool0 0`00Oomoo`2;Ool00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol0 0?moofUoo`00ogooJGoo003oOomYOol004]oo`<001Uoo`D000Aoo`@001Eoo`@000Eoo`<001Eoo`03 001oogoo00Eoo`@0019oo`@000Eoo`<000Eoo`<000ioo`@000=oo`D000Aoo`@000eoo`@000Aoo`@0 00Eoo`<000eoo`@000Aoo`03001oogoo00Eoo`@002Qoo`00BWoo00D007ooOomoo`0001Uoo`05001o ogooOol00003Ool01@00Oomoogoo000057oo00D007ooOomoo`0000=oo`05001oogooOol0000EOol0 0`00Oomoo`04Ool01@00Oomoogoo00004Woo00<007ooOol017oo00D007ooOomoo`0000=oo`05001o ogooOol0000>Ool00`00Oomoo`04Ool01@00Oomoogoo00000goo00D007ooOomoo`0000eoo`03001o ogoo00Aoo`05001oogooOol00003Ool01@00Oomoogoo00003Goo00<007ooOol01Goo00<007ooOol0 17oo00D007ooOomoo`0002Moo`00BWoo00<007ooOol00Woo00<007ooOol05goo00<007ooOol02Goo 00<007ooOol05Woo00@007ooOol000Aoo`03001oogoo01=oo`03001oogoo00Qoo`03001oogoo011o o`03001oogoo00=oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`0goo00<007ooOol00goo00<007ooOol00goo0P0017oo00<007ooOol0kGoo00<007ooOol00Woo0P00 97oo000kOol00`00Oomoo`03Ool00`00Oomoo`03Ool00`00Oomoo`03Ool2003]Ool20005Ool00`00 Oomoo`0ROol003aoo`03001oogoo009oo`03001oogoo00=oo`03001oogoo00Aoo`800>]oo`8000Io o`03001oogoo029oo`00?7oo00<007ooOol00Woo00<007ooOol00goo00<007ooOol017oo0`00Bgoo 00<007ooOol0Cgoo00<007ooOol0BGoo0`001Woo00<007ooOol08Woo000mOol01@00Oomoogoo0000 1Goo0P001Woo00<007oo0000;Woo0P0000=oo`0000000`000Woo0P003goo00<007ooOol06Woo00<0 07ooOol06goo00<007ooOol05Woo00<007ooOol0Agoo0`001goo00<007ooOol08Woo000nOol30006 Ool00`00Oomoo`05Ool200000goo001oo`0/Ool01000Oomoo`000Woo00@007ooOol0009oo`03001o ogoo00aoo`03001oogoo01]oo`03001oogoo01]oo`03001oogoo01Eoo`03001oogoo04Ioo`04001o o`000007Ool00`00Oomoo`0ROol004Moo`03001oogoo00Ioo`04001oogoo000UOol40004Ool00`00 Ool00003Ool00`00Ool00003Ool00`00Oomoo`0;Ool00`00Oomoo`02Ool30003Ool01000Oomoogoo 1@0017oo10000Woo00<007ooOol01@000goo00@007ooOomoo`D000Aoo`@0009oo`03001oogoo00=o o`<000=oo`03001oogoo009oo`@000=oo`03001oogoo00Moo`D000Aoo`<000Eoo`03001oogoo02Yo o`03001oo`00008000Moo`03001oogoo029oo`00Agoo00<007ooOol01Woo0P000Woo0P0097oo00<0 07ooOol017oo00@007ooOol0009oo`04001oogoo0002Ool00`00Oomoo`0;Ool01@00Oomoogoo0000 0goo00<007ooOol01Goo00D007ooOomoo`0000=oo`05001oogooOol00005Ool01@00Oomoogoo0000 1goo00D007ooOomoo`0000=oo`05001oogooOol00006Ool01@00Oomoogoo00001goo00D007ooOomo o`00009oo`03001oogoo00Ioo`03001oogoo00=oo`04001oogoo0003Ool00`00Oomoo`02Ool2000Z Ool00`00Oomoo`020008Ool00`00Oomoo`0ROol004Moo`8000Qoo`8000=oo`03001oogoo029oo`03 001oogoo00=oo`04001oogooOol30002Ool40002Ool80003Ool01@00Oomoogoo000017oo00<007oo Ool01Goo00<007ooOol02Goo00<007ooOol00goo00<007ooOol02Goo00<007ooOol02Goo00<007oo Ool00goo00<007ooOol00Woo00<007ooOol02Goo00<007oo00001goo00<007ooOol017oo00<007oo Ool00`001Woo0P00:Goo00<007ooOol00`0027oo00<007ooOol08Woo0017Ool00`00Oomoo`07Ool3 0003Ool00`00Oomoo`0QOol00`00Oomoo`03Ool00`00Oomoo`06Ool00`00Oomoo`0=Ool00`00Oomo o`02Ool00`00Oomoo`02Ool00`00Oomoo`06Ool00`00Oomoo`08Ool00`00Oomoo`04Ool00`00Oomo o`09Ool00`00Oomoo`08Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`09Ool01000Oomo o`001Woo00<007ooOol017oo00@007ooOol0009oo`8000Aoo`03001oo`0002Moo`03001oogoo00<0 00Uoo`03001oogoo029oo`00Agoo00<007ooOol027oo0`000goo00<007ooOol087oo00<007ooOol0 17oo00<007ooOol01Woo00<007ooOol03Goo00D007ooOomoo`0000Eoo`03001oogoo00Ioo`03001o ogoo00Moo`03001oogoo00Eoo`03001oogoo00Uoo`03001oogoo00Moo`03001oogoo00=oo`03001o ogoo00=oo`03001oogoo00Qoo`03001oo`0000Moo`03001oogoo00=oo`@00003Ool007oo009oo`05 001oogooOol00002Ool00`00Oomoo`0SOol01000Oomoogoo0`002Goo00<007ooOol08Woo0017Ool0 0`00Oomoo`08Ool30004Ool2000QOol00`00Oomoo`02Ool20007Ool20004Ool80003Ool01@00Oomo ogoo00001Goo00<007ooOol01goo00<007ooOol01Goo00<007ooOol01goo00<007ooOol02Goo00<0 07ooOol01Goo00<007ooOol017oo00<007ooOol00goo00<007ooOol01goo00@007ooOol000Moo`03 001oogoo00Qoo`80009oo`03001oogoo009oo`04001oogoo000ROol20003Ool3000:Ool00`00Oomo o`0ROol004Moo`8000Yoo`<000Eoo`03001oogoo01ioo`03001oogoo01aoo`03001oogoo009oo`03 001oogoo009oo`03001oogoo00Qoo`03001oogoo009oo`8000]oo`03001oogoo00Uoo`03001oogoo 009oo`8000Qoo`03001oogoo009oo`03001oogoo00Eoo`8000=oo`03001oogoo00Ioo`03001oogoo 00Aoo`03001oogoo009oo`<000Aoo`04001oogoo000QOol00`00Oomoo`02Ool01000Ool000002Woo 00<007ooOol08Woo0017Ool00`00Oomoo`0:Ool30005Ool00`00Oomoo`0JOol01000Oomoo`000Woo 00<007ooOol06Goo00<007ooOol00Woo00<007ooOol00Woo00<007ooOol027oo00<007ooOol00goo 00<007ooOol02Goo00<007ooOol02Goo00<007ooOol00goo00<007ooOol01Woo00<007ooOol00Woo 00<007ooOol01Woo00D007ooOomoo`0000Qoo`03001oogoo00Aoo`03001oogoo00Uoo`05001oogoo Ool0000OOol00`00Oomoo`03Ool3000;Ool00`00Oomoo`0ROol004Moo`03001oogoo00Yoo`04001o o`000005Ool00`00Oomoo`0JOol01000Oomoo`000Woo00<007ooOol067oo00<007ooOol00goo00D0 07ooOomoo`0000Ioo`05001oogooOol00005Ool00`00Oomoo`05Ool01@00Oomoogoo00001goo00D0 07ooOomoo`0000Eoo`03001oogoo00Moo`05001oogooOol00008Ool01@00Oomoogoo00002Goo0P00 0goo0`002Woo00<007ooOol00Woo00<007ooOol06goo00<007ooOol00goo00@007oo000000]oo`03 001oogoo029oo`00Agoo00<007ooOol02goo0P0000=oo`00Ool017oo0P006Woo1`006Woo00<007oo Ool017oo0`0027oo0`001Woo10001Goo0`002Goo0`001Woo10001goo0`002Goo1@002goo0`000Woo 00<007ooOol01goo0`000Woo10006Goo0P001Woo0`0037oo00<007ooOol08Woo000kOol40008Ool2 000=Ool30007Ool00`00Oomoo`0iOol00`00Oomoo`1?Ool00`00Oomoo`0jOol00`00Oomoo`05Ool0 1000Ool0000037oo00<007ooOol08Woo000lOol00`00Oomoo`08Ool00`00Oomoo`0Ool200000goo001o o`06Ool00`00Oomoo`31Ool20008Ool01000Ool000003Woo00<007ooOol08Woo000mOol00`00Oomo o`07Ool2000?Ool01000Ool0000027oo00<007ooOol0_goo00<007ooOol027oo10003Goo0P0097oo 000nOol00`00Oomoo`06Ool00`00Oomoo`0?Ool200000goo001oo`07Ool00`00Oomoo`2mOol00`00 Oomoo`08Ool01000Ool000003goo00<007ooOol08Woo000nOol00`00Oomoo`06Ool00`00Oomoo`0? Ool300000goo001oo`07Ool2002lOol00`00Oomoo`09Ool4000?Ool00`00Oomoo`0ROol003ioo`03 001oogoo00Ioo`03001oogoo011oo`800003Ool007oo00Uoo`800;Qoo`8000]oo`04001oo`00000@ Ool00`00Oomoo`0ROol003moo`03001oogoo00Eoo`80015oo`<00003Ool007oo00Yoo`03001oogoo 0;Aoo`03001oogoo00Yoo`03001oo`000080011oo`03001oogoo029oo`00?Woo0P001goo00<007oo Ool04Goo00D007oo001oo`0000]oo`03001oogoo0;9oo`03001oogoo00Yoo`03001oogoo0080015o o`03001oogoo029oo`00Agoo00<007ooOol04Goo0`0000=oo`00Ool02goo0P00/Goo00<007ooOol0 2goo00<007oo00000P004Goo00<007ooOol08Woo0017Ool00`00Oomoo`0BOol300000goo001oo`0< Ool00`00Oomoo`2/Ool2000=Ool01@00Ool007oo00004Woo00<007ooOol08Woo0017Ool2000COol3 0002Ool00`00Oomoo`0;Ool00`00Oomoo`2ZOol00`00Oomoo`0Ool2002POol00`00Oomoo`0>Ool01P00Oomoo`00Ool001Eoo`03001oogoo 029oo`00Agoo00<007ooOol05Goo0`000goo00<007ooOol03goo0P00WGoo00<007ooOol03Woo00@0 07ooOomoo`<001Eoo`03001oogoo029oo`00Agoo00<007ooOol05Woo0`000goo00<007ooOol047oo 00<007ooOol0V7oo0P0047oo00L007ooOomoo`00Ool0000FOol00`00Oomoo`0ROol003Yoo`D000Qo o`8001Moo`800003Ool007oo009oo`03001oogoo011oo`03001oogoo09Ioo`03001oogoo011oo`05 001oogoo001oo`02000FOol00`00Oomoo`0ROol003]oo`05001oogooOol00007Ool00`00Oomoo`0G Ool30004Ool00`00Oomoo`0@Ool2002EOol00`00Oomoo`0@Ool01`00Oomoogoo001oo`0001Moo`03 001oogoo029oo`00?7oo00<007ooOol027oo00<007ooOol05goo0P0000=oo`00Ool00Woo00<007oo Ool04Woo00<007ooOol0T7oo0P004Woo00H007ooOomoo`00Ool2000GOol00`00Oomoo`0ROol003eo o`03001oogoo00Moo`03001oogoo01Qoo`<000Aoo`03001oogoo019oo`03001oogoo08eoo`8001Ao o`04001oogooOol3000HOol00`00Oomoo`0ROol003ioo`03001oogoo00Ioo`8001Yoo`03001oo`00 00Aoo`03001oogoo019oo`8008aoo`03001oogoo01=oo`06001oogooOol007oo0P005goo0P0097oo 000oOol00`00Oomoo`05Ool00`00Oomoo`0IOol200000goo001oo`03Ool00`00Oomoo`0COol20029 Ool00`00Oomoo`0COol00`00Oomoo`02Ool3000IOol00`00Oomoo`0ROol0041oo`03001oogoo00Ao o`03001oogoo01Yoo`03001oo`0000Aoo`03001oogoo01Eoo`03001oogoo08Aoo`8001Eoo`03001o ogoo009oo`04001oo`00000IOol00`00Oomoo`0ROol0041oo`03001oogoo00Aoo`03001oogoo01Yo o`800003Ool007oo00=oo`03001oogoo01Eoo`8008=oo`03001oogoo01Eoo`03001oogoo009oo`<0 01Yoo`03001oogoo029oo`00?7oo00D007ooOomoo`0000Ioo`8001aoo`800003Ool007oo00=oo`03 001oogoo01Ioo`80081oo`03001oogoo01Eoo`03001oogoo009oo`04001oo`00000JOol00`00Oomo o`0ROol003eoo`<000Moo`03001oogoo01aoo`04001oogoo0004Ool00`00Oomoo`0GOol00`00Oomo o`1kOol2000GOol00`00Oomoo`02Ool01000Ool000006goo00<007ooOol08Woo0017Ool00`00Oomo o`0LOol200000goo001oo`03Ool00`00Oomoo`0HOol2001iOol2000IOol00`00Oomoo`02Ool01000 Ool000006goo00<007ooOol08Woo0017Ool00`00Oomoo`0MOol200000goo001oo`03Ool00`00Oomo o`0IOol2001fOol00`00Oomoo`0HOol00`00Oomoo`02Ool01000Ool0000077oo00<007ooOol08Woo 0017Ool2000NOol20002Ool00`00Oomoo`02Ool00`00Oomoo`0JOol00`00Oomoo`1aOol2000JOol0 0`00Oomoo`02Ool01@00Ool007oo000077oo00<007ooOol08Woo0017Ool00`00Oomoo`0NOol20000 0goo001oo`04Ool00`00Oomoo`0JOol00`00Oomoo`1^Ool2000KOol00`00Oomoo`03Ool01000Ool0 00007Goo00<007ooOol08Woo000bOol00`00Oomoo`0BOol00`00Oomoo`0NOol20002Ool00`00Oomo o`03Ool00`00Oomoo`0JOol2001/Ool2000MOol00`00Oomoo`02Ool01@00Ool007oo00007Goo00<0 07ooOol08Woo000aOol00`00Oomoo`0COol00`00Oomoo`0OOol20002Ool00`00Oomoo`02Ool00`00 Oomoo`0LOol2001XOol2000NOol00`00Oomoo`03Ool01000Ool000007Woo00<007ooOol08Woo000` Ool00`00Oomoo`0DOol2000POol01@00Ool007oo00001Goo00<007ooOol07Goo0P00I7oo0P007goo 00<007ooOol00goo00D007oo001oo`0001ioo`03001oogoo029oo`00:Goo00<007ooOol00goo00<0 07ooOol05Goo00<007ooOol087oo0P000Woo00<007ooOol00goo00<007ooOol07Woo0P00H7oo0P00 8Goo00<007ooOol00Woo00<007ooOol00P007goo00<007ooOol08Woo000YOol30002Ool00`00Oomo o`0FOol00`00Oomoo`0QOol200000goo001oo`05Ool00`00Oomoo`0OOol2001LOol2000ROol00`00 Oomoo`03Ool01@00Ool007oo00007goo00<007ooOol08Woo000/Ool7000DOol00`00Oomoo`0QOol0 1@00Ool007oo00001Woo00<007ooOol087oo0P00F7oo0P008goo00<007ooOol00goo00<007ooOol0 0P0087oo00<007ooOol08Woo000/Ool00`00Oomoo`03Ool00`00Oomoo`06Ool30009Ool2000SOol2 0002Ool00`00Oomoo`04Ool00`00Oomoo`0QOol2001DOol2000TOol00`00Oomoo`04Ool01@00Ool0 07oo000087oo00<007ooOol08Woo000[Ool00`00Oomoo`03Ool00`00Oomoo`0:Ool00`00Oomoo`06 Ool00`00Oomoo`0SOol200000goo001oo`05Ool00`00Oomoo`0SOol2001?Ool3000VOol00`00Oomo o`03Ool00`00Oomoo`02000QOol00`00Oomoo`0ROol002Yoo`03001oogoo019oo`03001oogoo00Eo o`03001oogoo02=oo`80009oo`03001oogoo00Aoo`03001oogoo02Aoo`<004Yoo`8002Qoo`03001o ogoo00Aoo`05001oo`00Ool0000QOol00`00Oomoo`0ROol002Uoo`03001oogoo01=oo`03001oogoo 00Eoo`03001oogoo02Aoo`80009oo`03001oogoo00Aoo`03001oogoo02Ioo`8004Eoo`<002Uoo`03 001oogoo00Aoo`03001oogoo0080029oo`03001oogoo029oo`00?goo00<007ooOol01Goo0P009Goo 00<007oo00000Woo00<007ooOol017oo00<007ooOol09goo1000?goo0P00:goo00<007ooOol01Goo 00D007oo001oo`00025oo`8002Aoo`00?Goo0P0027oo00<007ooOol09Goo0P000Woo00<007ooOol0 1Goo00<007ooOol0:Woo1000>7oo0`00;7oo00<007ooOol01Goo00<007ooOol00P008goo00<007oo Ool08Woo000oOol00`00Oomoo`05Ool00`00Oomoo`0VOol20002Ool00`00Oomoo`05Ool00`00Oomo o`0]Ool2000dOol2000_Ool00`00Oomoo`04Ool01P00Oomoo`00Ool002=oo`03001oogoo029oo`00 @7oo00<007ooOol017oo00<007ooOol09Woo00<007oo00000Woo00<007ooOol017oo00<007ooOol0 ;goo1000;7oo1000<7oo00<007ooOol01Goo00<007ooOol00P0097oo00<007ooOol08Woo000mOol0 1000Oomoo`001Woo0P00:7oo0P000Woo00<007ooOol01Goo00<007ooOol07oo00<0 07oo00001Goo00<007ooOol02Goo00<007ooOol0HGoo00<007ooOol02Woo00<007ooOol00Woo00<0 07oo0000=7oo00<007ooOol08Woo000ZOol300000goo00000002Ool00`00Oomoo`0BOol00`00Oomo o`0hOol01000Oomoo`001Goo00<007ooOol02Goo00<007ooOol0Ggoo00<007ooOol02Woo00<007oo Ool00goo00<007oo0000=7oo00<007ooOol08Woo000ZOol01P00Oomoo`00Ool0009oo`03001oogoo 019oo`8003Yoo`04001oogoo0004Ool00`00Oomoo`0:Ool2001NOol00`00Oomoo`0:Ool00`00Oomo o`03Ool00`00Ool0000eOol00`00Oomoo`0ROol002Uoo`07001oogooOol007oo00000Woo00<007oo Ool04Woo00<007ooOol0>Woo00<007oo00001Goo00<007ooOol02goo00<007ooOol0FGoo0P003Goo 00<007ooOol00Woo00@007ooOol003Eoo`03001oogoo029oo`00:Goo00L007ooOomoo`00Ool00002 Ool00`00Oomoo`0BOol00`00Oomoo`0jOol01000Oomoo`001Goo00<007ooOol02goo00<007ooOol0 Egoo00<007ooOol037oo00<007ooOol00Woo00@007ooOol003Ioo`03001oogoo029oo`00:Goo00@0 07ooOol000=oo`03001oo`0001Aoo`03001oogoo03]oo`04001oogoo0005Ool00`00Oomoo`0;Ool2 001FOol00`00Oomoo`0Ool00`00Oomoo`1>Ool2000>Ool00`00Oomoo`03Ool01000Oomoo`00>7oo00<007ooOol0 8Woo000VOol00`00Oomoo`08Ool00`00Oomoo`0Goo00<007ooOol08Woo000WOol20006Ool2000?Ool00`00Oomoo`04Ool00`00Oomo o`0nOol01000Oomoo`0017oo00<007ooOol03goo0P00Bgoo00<007ooOol03Woo00<007ooOol00goo 00@007ooOol003Uoo`03001oogoo029oo`00:Goo1P004Goo00<007ooOol017oo0P00@7oo00@007oo Ool000Aoo`03001oogoo011oo`03001oogoo04Ioo`80011oo`03001oogoo00=oo`04001oogoo000i Ool2000TOol003moo`03001oogoo00Eoo`03001oogoo03moo`05001oogooOol00004Ool00`00Oomo o`0@Ool00`00Oomoo`13Ool2000AOol00`00Oomoo`03Ool01@00Oomoogoo0000>Woo00<007ooOol0 8Woo000mOol20008Ool00`00Oomoo`10Ool01@00Oomoogoo000017oo00<007ooOol047oo0P00@Woo 00<007ooOol047oo00<007ooOol017oo00@007ooOol003]oo`03001oogoo029oo`00?Woo00<007oo Ool01Woo00<007ooOol0@Goo00@007ooOol000Eoo`03001oogoo015oo`8003ioo`80019oo`03001o ogoo00Aoo`04001oogoo000lOol00`00Oomoo`0ROol003ioo`03001oogoo00Ioo`8004=oo`04001o ogoo0005Ool00`00Oomoo`0BOol2000jOol2000COol00`00Oomoo`04Ool01@00Oomoogoo0000?7oo 00<007ooOol08Woo000nOol40005Ool00`00Oomoo`12Ool01@00Oomoogoo00001Goo00<007ooOol0 4goo0P00=Woo0P005Goo00<007ooOol017oo00@007ooOol003eoo`03001oogoo029oo`00Agoo00<0 07ooOol0@goo00@007ooOol000Ioo`03001oogoo01Aoo`<0035oo`8001Ioo`03001oogoo00Aoo`04 001oogoo000nOol00`00Oomoo`0ROol004Moo`03001oogoo04Aoo`04001oogoo0006Ool00`00Oomo o`0FOol2000/Ool3000GOol00`00Oomoo`04Ool01@00Oomoogoo0000?Woo00<007ooOol08Woo0017 Ool20015Ool01@00Oomoogoo00001Woo00<007ooOol05goo0`009goo0P006Goo00<007ooOol017oo 00D007ooOomoo`0003moo`03001oogoo029oo`00Agoo00<007ooOol0AGoo00D007ooOomoo`0000Io o`03001oogoo01Uoo`80029oo`<001Yoo`03001oogoo00Eoo`04001oogoo0010Ool00`00Oomoo`0R Ool004Moo`03001oogoo04Ioo`05001oogooOol00006Ool00`00Oomoo`0JOol2000NOol2000LOol0 0`00Oomoo`05Ool01@00Oomoogoo0000@7oo00<007ooOol08Woo0017Ool00`00Oomoo`16Ool01@00 Oomoogoo00001goo00<007ooOol06goo1@0057oo1@007Goo00<007ooOol01Goo00D007ooOomoo`00 045oo`03001oogoo029oo`00Agoo0P00B7oo00D007ooOomoo`0000Moo`80021ooa@0025oo`03001o ogoo00Eoo`05001oogooOol00012Ool00`00Oomoo`0ROol004Moo`03001oogoo04Qoo`05001oogoo Ool00008Ool00`00Oomoo`1AOol00`00Oomoo`05Ool01@00Oomoogoo0000@goo00<007ooOol08Woo 0017Ool00`00Oomoo`19Ool01@00Oomoogoo000027oo00<007ooOol0CWoo0P001goo00<007ooOol0 0Woo00<007ooOol0@Goo00<007ooOol08Woo0017Ool00`00Oomoo`1:Ool01@00Oomoogoo000027oo 00<007ooOol0C7oo00<007ooOol01Woo00<007ooOol00Woo00<007ooOol0@Woo00<007ooOol08Woo 000kOol30009Ool2001;Ool00`00Oomoo`02Ool00`00Oomoo`06Ool2001;Ool00`00Oomoo`06Ool0 0`00Oomoo`02Ool00`00Oomoo`13Ool00`00Oomoo`0ROol003Yoo`05001oogooOol00008Ool00`00 Oomoo`1;Ool00`00Oomoo`02Ool00`00Oomoo`07Ool00`00Oomoo`17Ool00`00Oomoo`06Ool00`00 Oomoo`02Ool00`00Oomoo`14Ool00`00Oomoo`0ROol003Yoo`03001oogoo009oo`03001oogoo00Eo o`03001oogoo04aoo`03001oogoo009oo`03001oogoo00Moo`03001oogoo04Aoo`8000Qoo`03001o ogoo009oo`03001oogoo04Eoo`03001oogoo029oo`00>Woo00<007ooOol00Woo00<007ooOol01Goo 00<007ooOol0CGoo00<007ooOol00Woo00<007ooOol01goo00<007ooOol0@Woo00<007ooOol027oo 00<007ooOol00Woo00<007ooOol0AGoo00<007ooOol08Woo000jOol00`00Oomoo`02Ool00`00Oomo o`05Ool2001?Ool00`00Oomoo`02Ool00`00Oomoo`07Ool20011Ool00`00Oomoo`08Ool00`00Oomo o`02Ool00`00Oomoo`15Ool2000TOol003]oo`80009oo`03001oogoo00Eoo`03001oogoo04moo`03 001oogoo009oo`03001oogoo00Qoo`03001oogoo03eoo`03001oogoo00Qoo`03001oogoo009oo`03 001oogoo04Moo`03001oogoo029oo`00>goo00@007oo000000Qoo`03001oogoo051oo`03001oogoo 009oo`03001oogoo00Qoo`03001oogoo03Yoo`8000Yoo`03001oogoo009oo`03001oogoo04Qoo`03 001oogoo029oo`00?7oo00<007ooOol027oo00<007ooOol0DGoo00<007ooOol00Woo00<007ooOol0 27oo0P00>Goo00<007ooOol02Goo00<007ooOol00Woo00<007ooOol0BGoo00<007ooOol08Woo000m Ool20008Ool2001COol00`00Oomoo`02Ool00`00Oomoo`09Ool2000fOol00`00Oomoo`09Ool00`00 Oomoo`02Ool00`00Oomoo`1:Ool00`00Oomoo`0ROol003moo`8000Ioo`03001oogoo05=oo`03001o ogoo009oo`8000]oo`80039oo`8000]oo`03001oogoo009oo`03001oogoo04]oo`03001oogoo029o o`00Agoo00<007ooOol0E7oo00<007ooOol00goo00<007ooOol02Woo0P00;Woo0P0037oo00<007oo Ool00Woo00<007ooOol0C7oo00<007ooOol08Woo0017Ool00`00Oomoo`1EOol00`00Oomoo`03Ool0 0`00Oomoo`0;Ool3000YOol2000=Ool00`00Oomoo`02Ool00`00Oomoo`1=Ool00`00Oomoo`0ROol0 04Moo`8005Moo`03001oogoo00=oo`03001oogoo00eoo`8002Eoo`8000eoo`8000Aoo`03001oogoo 04ioo`03001oogoo029oo`00Agoo00<007ooOol0Egoo00<007ooOol00goo0P003goo0P0087oo0`00 3Woo00<007ooOol00goo00<007ooOol0Cgoo00<007ooOol08Woo0017Ool00`00Oomoo`1HOol00`00 Oomoo`04Ool00`00Oomoo`0>Ool3000IOol4000@Ool00`00Oomoo`03Ool00`00Oomoo`1@Ool00`00 Oomoo`0ROol004Moo`03001oogoo05Uoo`03001oogoo00Aoo`03001oogoo011oo`<001Aoo`8001=o o`03001oogoo00=oo`03001oogoo055oo`03001oogoo029oo`00Agoo0P00Fgoo00<007ooOol017oo 00<007ooOol04Woo50004goo0P001Goo00<007ooOol0DWoo00<007ooOol08Woo0017Ool00`00Oomo o`1KOol00`00Oomoo`04Ool2000hOol00`00Oomoo`04Ool00`00Oomoo`1COol00`00Oomoo`0ROol0 04Moo`03001oogoo05aoo`03001oogoo00Eoo`03001oogoo03Aoo`03001oogoo00Aoo`03001oogoo 05Aoo`03001oogoo029oo`00Agoo00<007ooOol0GGoo0P001Woo0P00Woo00<007ooOol00Woo00<007ooOol01Goo0P00KGoo0P009Goo0P00I7oo 00<007ooOol08Woo000kOol60006Ool00`00Oomoo`1^Ool2000QOol2001VOol00`00Oomoo`0ROol0 04Moo`03001oogoo071oo`<001aoo`8006Qoo`03001oogoo029oo`00Agoo00<007ooOol0Lgoo0`00 5Woo0`00JWoo00<007ooOol08Woo0017Ool2001gOol4000=Ool5001]Ool00`00Oomoo`0ROol004Mo o`03001oogoo07Yoo`d0079oo`03001oogoo029oo`00Agoo00<007ooOol0nGoo00<007ooOol08Woo 0017Ool00`00Oomoo`03Ool00`00Oomoo`0NOol00`00Oomoo`0OOol00`00Oomoo`0NOol00`00Oomo o`0NOol00`00Oomoo`0OOol00`00Oomoo`0NOol00`00Oomoo`0OOol00`00Oomoo`09Ool00`00Oomo o`0ROol004Moo`8000Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo 00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo 00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo 00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo 00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo 00Aoo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo 00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo 00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo029oo`00Agooo@00 97oo003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00Jgoo1@00DWoo0P00Igoo 1@00>7oo001ZOol00`00Oomoo`03Ool00`00Oomoo`1?Ool00`00Ool0001UOol00`00Oomoo`03Ool0 0`00Oomoo`0eOol006Yoo`03001oogoo009oo`8005Aoo`03001oogoo069oo`03001oogoo009oo`80 03Moo`00G7oo00D007ooOomoo`0000Eoo`8000=oo`@000=oo`04001oogooOol20003Ool30003Ool0 0`00Oomoo`06Ool30004Ool2000017oo0000000017oo0P000Woo0`0000=oo`0000000Woo0P000Woo 0P000goo0`0017oo00@007ooOomoo`8000Qoo`03001oogoo009oo`<000Aoo`03001oogoo00Aoo`<0 00Aoo`03001oogoo00<000Aoo`03001oogoo00Ioo`03001oogoo00<000=oo`<000=oo`<00003Ool0 0000009oo`80009oo`8000=oo`<000=oo`03001oogoo00=oo`80009oo`04001oogooOol20003Ool4 000iOol005aoo`80009oo`8000Aoo`03001oo`00009oo`03001oogoo00Aoo`09001oogooOol007oo 001oo`0000=oo`04001oogoo0009Ool00`00Oomoo`03Ool00`00Ool00003Ool20002Ool01@00Ool0 07oo00000Woo0P000goo00T007oo001oo`00Ool007oo00000goo0P000Woo00L007ooOomoo`00Ool0 0007Ool01@00Oomoogoo00000goo0P000Woo00<007ooOol01Goo00<007ooOol00goo0P000Woo00<0 07ooOol00goo0P001goo0`000goo00<007oo00000goo00@007ooOol0009oo`8000=oo`09001oo`00 Ool007oo001oo`0000=oo`04001oogoo0005Ool01@00Ool007oo00000goo00<007oo00000Woo00<0 07ooOol0>Woo001LOol20002Ool20005Ool00`00Oomoo`02Ool30004Ool01@00Oomoogoo00000Woo 0`001Goo00<007ooOol01goo00D007ooOomoo`00009oo`03001oogoo009oo`05001oogooOol00002 Ool01000Oomoogoo0P000goo00D007ooOomoo`00009oo`03001oogoo009oo`05001oogooOol00003 Ool00`00Oomoo`07Ool01000Oomoo`0017oo00D007ooOomoo`0000Moo`07001oogooOol007oo0000 0goo00L007ooOomoo`00Ool00008Ool00`00Oomoo`02Ool00`00Ool00006Ool01000Oomoogoo0P00 0goo00D007ooOomoo`00009oo`<000Eoo`03001oogoo00=oo`05001oogooOol00003Ool00`00Oomo o`02Ool3000iOol005aoo`07001oo`00Ool007oo000017oo00D007ooOomoo`0000=oo`04001oogoo Ool20002Ool01000Oomoo`000Woo0P000goo00<007ooOol01goo00D007ooOomoo`00009oo`03001o ogoo00=oo`04001oogoo0002Ool00`00Oomoo`02Ool01@00Oomoogoo00000goo00@007ooOol000Eo o`03001oogoo0080009oo`03001oogoo00Moo`04001oogoo0005Ool01000Oomoo`001goo00L007oo Oomoo`00Ool00003Ool01`00Oomoogoo001oo`0000Qoo`03001oogoo009oo`03001oo`0000Ioo`03 001oogoo009oo`05001oogooOol00003Ool01000Oomoo`000Woo0P000goo00<007ooOol00goo00@0 07ooOomoo`80009oo`05001oogooOol00003Ool00`00Oomoo`0fOol005aoo`800006Ool007oo001o o`000goo00D007ooOomoo`0000Aoo`06001oogoo001oo`000Woo00@007ooOol000=oo`03001oogoo 008000Qoo`04001oogoo0004Ool00`00Oomoo`02Ool01000Oomoo`000goo00D007ooOomoo`0000=o o`05001oogooOol00003Ool00`00Oomoo`02Ool01P00Oomoo`00Ool0009oo`03001oogoo00Ioo`05 001oogooOol00004Ool00`00Oomoo`020006Ool01@00Oomoogoo00000Woo00@007ooOol000=oo`04 001oogoo000;Ool01@00Oomoogoo00001Woo00D007ooOomoo`0000=oo`05001oogooOol00003Ool0 1@00Oomoogoo00000Woo0P0017oo00L007ooOomoo`00Ool00002Ool01000Oomoo`0017oo00<007oo Ool0=Goo001MOol01`00Ool007oo001oo`0000Aoo`03001oogoo008000=oo`09001oogooOol007oo 001oo`00009oo`80009oo`04001oogooOol200000goo001oo`05Ool40003Ool20003Ool01@00Oomo ogoo00000goo00<007ooOol00P000goo00D007ooOomoo`00009oo`8000=oo`09001oogooOol007oo 001oo`0000Uoo`03001oogoo008000=oo`04001oogooOol200000goo001oo`03Ool00`00Ool00003 Ool01`00Oomoogoo001oo`0000=oo`03001oogoo00Moo`8000Aoo`80009oo`05001oogooOol00002 Ool20003Ool01@00Oomoogoo00000Woo0P000Woo00@007ooOomoo`800005Ool007ooOol00003Ool0 1@00Ool007oo00000Woo0P000goo00<007ooOol0=Goo001MOol00`00Oomoo`020002Ool00`00Ool0 00020004Ool5000017oo000007oo0`0017oo0`000Woo0P0000=oo`0000001Woo00@007ooOomoo`80 00=oo`<000=oo`<000=oo`800004Ool007ooOol60004Ool30003Ool2000017oo000000001goo1000 0goo0`000goo0P0000=oo`00000017oo00<007oo00000goo00L007ooOomoo`00Ool00003Ool00`00 Oomoo`06Ool00`00Oomoo`06Ool30004Ool2000017oo001oogoo0`0000Aoo`00000000=oo`<0009o o`800003Ool0000000<0009oo`800004Ool000000004Ool5000fOol005eoo`05001oogooOol00002 Ool00`00Oomoo`0VOol00`00Oomoo`02Ool00`00Oomoo`08Ool00`00Oomoo`09Ool00`00Oomoo`0K Ool00`00Oomoo`0AOol00`00Ool00004Ool01P00Oomoo`00Ool000Aoo`03001oogoo00Eoo`03001o ogoo009oo`03001oogoo00moo`05001oogooOol0001HOol005eoo`05001oogooOol00003Ool01000 Oomoo`009Goo00D007ooOomoo`0000Yoo`03001oogoo00Uoo`05001oogooOol0000JOol00`00Oomo o`0AOol00`00Oomoo`03Ool01@00Oomoogoo00001Goo00<007ooOol01Goo00@007ooOomoo`80015o o`05001oogooOol0000@Ool00`00Oomoo`15Ool005aoo`<00005Ool00000001oo`04000UOol5000f Ool01000Oomoo`003Woo0`0017oo1P0017oo0`001goo0`000Woo00<007ooOol0Jgoo0039Ool3002L Ool00?moofUoo`00ogooJGoo003oOomYOol00001\ \>"], ImageRangeCache->{{{109, 396}, {423, 246.063}} -> {-159.794, 13.1094, \ 0.935775, 0.0626674}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["example: pion electroproduction on the nucleon", "Subsection"], Cell[TextData[{ "\tLet ", Cell[BoxData[ \(TraditionalForm\`S\_1\)]], " represent the cm frame and ", Cell[BoxData[ \(TraditionalForm\`S\_2\)]], " the lab frame for pion electroproduction on the nucleon ", Cell[BoxData[ \(TraditionalForm\`e\ N \[Rule] e\ N\ \[Pi]\)]], ". The following functions evaluate the lab angle and Wigner precession \ angle in terms of the cm angle given ", Cell[BoxData[ \(TraditionalForm\`{W, Q\^2}\)]], ". The example below is relevant to JLab E91-011, but larger precession \ angles would be seen for more extreme kinematics (large ", Cell[BoxData[ \(TraditionalForm\`W\)]], " or large ", Cell[BoxData[ \(TraditionalForm\`Q\^2\)]], ")." }], "Text"], Cell[BoxData[ \(\(eN\[Pi]Rules = {\[Gamma] \[Rule] \(m\_p\^2 + Q\^2 + W\^2\)\/\(2 m\_p\ \ W\), \[Gamma]\_1 \[Rule] \(m\_p\^2 + W\^2 - m\_\[Pi]\^2\)\/\(2 \( m\_p\) \ W\), m\_p \[Rule] 0.939, m\_\[Pi] \[Rule] 0.14};\)\)], "Input", CellLabel->"In[35]:="], Cell[BoxData[ \(eN\[Pi][Win_, Q2_, \[Theta]1_] := \(transform[\@\(\[Gamma]\_1\^2 - \ 1\)\/\[Gamma]\_1, \[Theta]1\ Degree, \@\(\[Gamma]\^2 - 1\)\/\[Gamma]] //. eN\[Pi]Rules\) /. {Q\^2 \[Rule] Q2, W \[Rule] Win}\)], "Input", CellLabel->"In[36]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[{theta2, chi} /. eN\[Pi][1.232, 1.0, \[Theta]\_1]], {\[Theta]\_1, 0, 180}, PlotRange \[Rule] {Automatic, All}, PlotPoints \[Rule] 50, PlotStyle \[Rule] {RGBColor[0, 0, 1], RGBColor[1, 0, 0]}, Frame \[Rule] True, FrameLabel \[Rule] {\*"\"\<\!\(\[Theta]\_c\)\>\"", "\< \>"}, PlotLabel \[Rule] \*"\"\\"", PlotLegend \[Rule] {\*"\"\<\!\(\[Theta]\_\[ScriptL]\)\>\"", "\<\[Chi]\ \>"}, LegendPosition \[Rule] {0. , \(-0.3\)}, LegendSize \[Rule] {0.6, 0.2}, LegendShadow \[Rule] None];\)\)], "Input", CellLabel->"In[37]:="], 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 Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.5 0.47619 0.309017 0.47619 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath % Start of sub-graphic p 0.0238095 0.0147151 0.97619 0.603319 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.00529101 0.0147151 0.0454973 [ [.02381 -0.0125 -5 -15.6875 ] [.02381 -0.0125 5 0 ] [.15608 -0.0125 -8 -15.6875 ] [.15608 -0.0125 8 0 ] [.28836 -0.0125 -8 -15.6875 ] [.28836 -0.0125 8 0 ] [.42063 -0.0125 -8 -15.6875 ] [.42063 -0.0125 8 0 ] [.55291 -0.0125 -11 -15.6875 ] [.55291 -0.0125 11 0 ] [.68519 -0.0125 -11 -15.6875 ] [.68519 -0.0125 11 0 ] [.81746 -0.0125 -11 -15.6875 ] [.81746 -0.0125 11 0 ] [.94974 -0.0125 -11 -15.6875 ] [.94974 -0.0125 11 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -6.78125 -31.375 ] [.5 -0.0125 6.78125 -15.6875 ] [-0.0125 .01472 -10 -7.84375 ] [-0.0125 .01472 0 7.84375 ] [-0.0125 .10571 -10 -7.84375 ] [-0.0125 .10571 0 7.84375 ] [-0.0125 .1967 -10 -7.84375 ] [-0.0125 .1967 0 7.84375 ] [-0.0125 .2877 -10.25 -7.84375 ] [-0.0125 .2877 0 7.84375 ] [-0.0125 .37869 -10 -7.84375 ] [-0.0125 .37869 0 7.84375 ] [-0.0125 .46969 -16 -7.84375 ] [-0.0125 .46969 0 7.84375 ] [-0.0125 .56068 -16 -7.84375 ] [-0.0125 .56068 0 7.84375 ] [ 0 0 -0.125 0 ] [-0.01875 .30902 -31.6875 -3.5 ] [-0.01875 .30902 -16 3.5 ] [ 0 .61803 .125 0 ] [ 1 0 .125 0 ] [.5 .63053 -84.1563 0 ] [.5 .63053 84.1563 15.6875 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 0 m .02381 .00625 L s gsave .02381 -0.0125 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore .15608 0 m .15608 .00625 L s gsave .15608 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (25) show 1.000 setlinewidth grestore .28836 0 m .28836 .00625 L s gsave .28836 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (50) show 1.000 setlinewidth grestore .42063 0 m .42063 .00625 L s gsave .42063 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (75) show 1.000 setlinewidth grestore .55291 0 m .55291 .00625 L s gsave .55291 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (100) show 1.000 setlinewidth grestore .68519 0 m .68519 .00625 L s gsave .68519 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (125) show 1.000 setlinewidth grestore .81746 0 m .81746 .00625 L s gsave .81746 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (150) show 1.000 setlinewidth grestore .94974 0 m .94974 .00625 L s gsave .94974 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (175) show 1.000 setlinewidth grestore .125 Mabswid .05026 0 m .05026 .00375 L s .07672 0 m .07672 .00375 L s .10317 0 m .10317 .00375 L s .12963 0 m .12963 .00375 L s .18254 0 m .18254 .00375 L s .20899 0 m .20899 .00375 L s .23545 0 m .23545 .00375 L s .2619 0 m .2619 .00375 L s .31481 0 m .31481 .00375 L s .34127 0 m .34127 .00375 L s .36772 0 m .36772 .00375 L s .39418 0 m .39418 .00375 L s .44709 0 m .44709 .00375 L s .47354 0 m .47354 .00375 L s .5 0 m .5 .00375 L s .52646 0 m .52646 .00375 L s .57937 0 m .57937 .00375 L s .60582 0 m .60582 .00375 L s .63228 0 m .63228 .00375 L s .65873 0 m .65873 .00375 L s .71164 0 m .71164 .00375 L s .7381 0 m .7381 .00375 L s .76455 0 m .76455 .00375 L s .79101 0 m .79101 .00375 L s .84392 0 m .84392 .00375 L s .87037 0 m .87037 .00375 L s .89683 0 m .89683 .00375 L s .92328 0 m .92328 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave .5 -0.0125 -67.7813 -35.375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (q) show 68.250 17.688 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (c) show 72.563 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 .01472 m .00625 .01472 L s gsave -0.0125 .01472 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore 0 .10571 m .00625 .10571 L s gsave -0.0125 .10571 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore 0 .1967 m .00625 .1967 L s gsave -0.0125 .1967 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (4) show 1.000 setlinewidth grestore 0 .2877 m .00625 .2877 L s gsave -0.0125 .2877 -71.25 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (6) show 1.000 setlinewidth grestore 0 .37869 m .00625 .37869 L s gsave -0.0125 .37869 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (8) show 1.000 setlinewidth grestore 0 .46969 m .00625 .46969 L s gsave -0.0125 .46969 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 1.000 setlinewidth grestore 0 .56068 m .00625 .56068 L s gsave -0.0125 .56068 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (12) show 1.000 setlinewidth grestore .125 Mabswid 0 .03746 m .00375 .03746 L s 0 .06021 m .00375 .06021 L s 0 .08296 m .00375 .08296 L s 0 .12846 m .00375 .12846 L s 0 .15121 m .00375 .15121 L s 0 .17396 m .00375 .17396 L s 0 .21945 m .00375 .21945 L s 0 .2422 m .00375 .2422 L s 0 .26495 m .00375 .26495 L s 0 .31045 m .00375 .31045 L s 0 .3332 m .00375 .3332 L s 0 .35594 m .00375 .35594 L s 0 .40144 m .00375 .40144 L s 0 .42419 m .00375 .42419 L s 0 .44694 m .00375 .44694 L s 0 .49244 m .00375 .49244 L s 0 .51519 m .00375 .51519 L s 0 .53793 m .00375 .53793 L s 0 .58343 m .00375 .58343 L s 0 .60618 m .00375 .60618 L s .25 Mabswid 0 0 m 0 .61803 L s gsave -0.01875 .30902 -88.3438 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 64.5 11.8438 translate 90 rotate -64.5 -11.8438 translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 66.000 15.813 moveto 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .61178 m .02381 .61803 L s .15608 .61178 m .15608 .61803 L s .28836 .61178 m .28836 .61803 L s .42063 .61178 m .42063 .61803 L s .55291 .61178 m .55291 .61803 L s .68519 .61178 m .68519 .61803 L s .81746 .61178 m .81746 .61803 L s .94974 .61178 m .94974 .61803 L s .125 Mabswid .05026 .61428 m .05026 .61803 L s .07672 .61428 m .07672 .61803 L s .10317 .61428 m .10317 .61803 L s .12963 .61428 m .12963 .61803 L s .18254 .61428 m .18254 .61803 L s .20899 .61428 m .20899 .61803 L s .23545 .61428 m .23545 .61803 L s .2619 .61428 m .2619 .61803 L s .31481 .61428 m .31481 .61803 L s .34127 .61428 m .34127 .61803 L s .36772 .61428 m .36772 .61803 L s .39418 .61428 m .39418 .61803 L s .44709 .61428 m .44709 .61803 L s .47354 .61428 m .47354 .61803 L s .5 .61428 m .5 .61803 L s .52646 .61428 m .52646 .61803 L s .57937 .61428 m .57937 .61803 L s .60582 .61428 m .60582 .61803 L s .63228 .61428 m .63228 .61803 L s .65873 .61428 m .65873 .61803 L s .71164 .61428 m .71164 .61803 L s .7381 .61428 m .7381 .61803 L s .76455 .61428 m .76455 .61803 L s .79101 .61428 m .79101 .61803 L s .84392 .61428 m .84392 .61803 L s .87037 .61428 m .87037 .61803 L s .89683 .61428 m .89683 .61803 L s .92328 .61428 m .92328 .61803 L s .97619 .61428 m .97619 .61803 L s .25 Mabswid 0 .61803 m 1 .61803 L s .99375 .01472 m 1 .01472 L s .99375 .10571 m 1 .10571 L s .99375 .1967 m 1 .1967 L s .99375 .2877 m 1 .2877 L s .99375 .37869 m 1 .37869 L s .99375 .46969 m 1 .46969 L s .99375 .56068 m 1 .56068 L s .125 Mabswid .99625 .03746 m 1 .03746 L s .99625 .06021 m 1 .06021 L s .99625 .08296 m 1 .08296 L s .99625 .12846 m 1 .12846 L s .99625 .15121 m 1 .15121 L s .99625 .17396 m 1 .17396 L s .99625 .21945 m 1 .21945 L s .99625 .2422 m 1 .2422 L s .99625 .26495 m 1 .26495 L s .99625 .31045 m 1 .31045 L s .99625 .3332 m 1 .3332 L s .99625 .35594 m 1 .35594 L s .99625 .40144 m 1 .40144 L s .99625 .42419 m 1 .42419 L s .99625 .44694 m 1 .44694 L s .99625 .49244 m 1 .49244 L s .99625 .51519 m 1 .51519 L s .99625 .53793 m 1 .53793 L s .99625 .58343 m 1 .58343 L s .99625 .60618 m 1 .60618 L s .25 Mabswid 1 0 m 1 .61803 L s gsave .5 .63053 -145.156 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (eN) show 77.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\256) show 87.438 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (eN) show %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (p) show 113.688 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (for) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 130.688 15.813 moveto (H) show 134.500 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 145.750 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 148.750 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Q) show 157.375 11.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 162.188 15.813 moveto (L) show 166.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 174.500 15.813 moveto (H) show 178.313 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.232) show 205.500 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 208.500 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.0) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 223.500 15.813 moveto (L) show 227.313 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 0 1 r .5 Mabswid .02381 .01472 m .04273 .04154 L .06337 .07076 L .08275 .09813 L .10139 .12434 L .12123 .15208 L .14033 .1786 L .16063 .20653 L .18019 .23316 L .199 .25846 L .21902 .28499 L .23829 .31011 L .25683 .3338 L .27656 .35849 L .29555 .38166 L .31574 .40559 L .33519 .42787 L .3539 .44851 L .3738 .46954 L .39297 .48879 L .41334 .50805 L .43296 .52535 L .45184 .54071 L .47193 .55553 L .49127 .5682 L .50987 .57878 L .52967 .58815 L .54872 .59519 L .55913 .59816 L .56898 .60038 L .57371 .60123 L .57873 .60198 L .58302 .60249 L .58775 .60291 L .59016 .60307 L .59148 .60314 L .5927 .6032 L .59383 .60324 L .59486 .60327 L .59601 .60329 L .59664 .6033 L .59723 .60331 L .59782 .60332 L .59816 .60332 L .59847 .60332 L .5991 .60332 L .59946 .60332 L .59978 .60331 L .60036 .60331 L .60099 .6033 L Mistroke .60158 .60329 L .60213 .60328 L .60348 .60324 L .60471 .60319 L .60745 .60305 L .60984 .60288 L .61237 .60266 L .61689 .60215 L .62176 .60144 L .6271 .60045 L .63667 .59813 L .64692 .59487 L .66721 .58591 L .68675 .57401 L .70555 .5594 L .72555 .54033 L .7448 .51843 L .76332 .49406 L .78304 .46451 L .80201 .43259 L .82219 .395 L .84162 .35538 L .86031 .31431 L .8802 .2677 L .89935 .22035 L .9197 .16781 L .93931 .11553 L .95818 .0642 L .97619 .01472 L Mfstroke 1 0 0 r .02381 .01472 m .04273 .03073 L .06337 .04814 L .08275 .06436 L .10139 .07981 L .12123 .09601 L .14033 .11132 L .16063 .12723 L .18019 .14215 L .199 .15606 L .21902 .17033 L .23829 .18352 L .25683 .19562 L .27656 .20785 L .29555 .21892 L .31574 .22989 L .33519 .23965 L .3539 .24822 L .3738 .25645 L .39297 .26345 L .41334 .26986 L .43296 .275 L .45184 .27895 L .46142 .28058 L .47193 .28207 L .48193 .2832 L .49127 .28399 L .49639 .28432 L .50124 .28456 L .50559 .28472 L .50805 .28478 L .50924 .28481 L .51032 .28483 L .51141 .28484 L .51259 .28485 L .51321 .28486 L .51379 .28486 L .51439 .28487 L .51473 .28487 L .51504 .28487 L .51561 .28487 L .51613 .28487 L .51671 .28487 L .51732 .28486 L .51785 .28486 L .51834 .28486 L .51947 .28485 L .52077 .28483 L .52201 .28481 L .52433 .28476 L Mistroke .52683 .28469 L .52956 .28459 L .53462 .28434 L .53921 .28405 L .54949 .28318 L .55894 .2821 L .56914 .28064 L .58925 .27685 L .60862 .27207 L .62724 .26643 L .64706 .25932 L .66615 .25143 L .68643 .24192 L .70597 .23172 L .72477 .22097 L .74477 .20857 L .76403 .19575 L .78255 .18264 L .80226 .1679 L .82124 .15302 L .84141 .13653 L .86085 .12005 L .87954 .10373 L .89943 .08593 L .91858 .06845 L .93893 .04961 L .95854 .03129 L .97619 .01472 L Mfstroke MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.5 0.16616 0.785714 0.261398 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0297619 0.297619 0.0132275 0.132275 [ [ 0 0 0 0 ] [ 1 .33333 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .33333 L 0 .33333 L closepath clip newpath % Start of sub-graphic p 0.0535714 0.0238095 0.35119 0.156085 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 1 0 0 r .5 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g gsave .38988 .08995 -61 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 65.250 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (c) show 73.625 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore % Start of sub-graphic p 0.0535714 0.177249 0.35119 0.309524 MathSubStart %% Graphics %%IncludeResource: font Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.309017 0.294302 [ [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath 0 0 1 r .5 Mabswid [ ] 0 setdash .02381 .30902 m .97619 .30902 L s MathSubEnd P % End of sub-graphic 0 g gsave .38988 .24339 -61 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (q) show 68.250 17.688 moveto %%IncludeResource: font Mathematica5 %%IncludeFont: Mathematica5 /Mathematica5 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor ({) show 73.750 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore MathSubEnd P % End of sub-graphic 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[37]:=", ImageSize->{350.875, 216.875}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg]oo`03001oogoo009oo`03001oogoo0<=o o`00k7oo00D007ooOomoo`000Ool00`0OOomoo`0=Ool00`00Oomoo`0XOol004Uo o`D000Uoo`03001oogoo01Eoo`0301moogoo00Uoo`03O01oogoo099oo`04001oogoo001EOol00g`0 Oomoo`0?Ool00`0OOomoo`0=Ool00`00Oomoo`0XOol004Yoo`05001oogooOol00008Ool00`00Oomo o`0FOol00`0OOomoo`09Ool00g`0Oomoo`2BOol00`00Ool0001DOol00g`0Oomoo`0?Ool00`0OOomo o`0>Ool00`00Oomoo`0XOol004]oo`03001oogoo00Uoo`03001oogoo01Moo`0301moogoo00Uoo`9l 09=oo`8005=oo`03O01oogoo011oo`0301moogoo00ioo`03001oogoo02Qoo`00C7oo00<007ooOol0 27oo00<007ooOol067oo00<07gooOol02Woo00=l07ooOol0TGoo00<007ooOol0D7oo00=l07ooOol0 47oo00<07gooOol03goo00<007ooOol0:7oo001=Ool00`00Oomoo`07Ool3000HOol00`0OOomoo`0; Ool2O02AOol2001@Ool00g`0Oomoo`0AOol00`0OOomoo`0=Ool3000ZOol004ioo`03001oogoo00Io o`03001oogoo01Uoo`0301moogoo00aoo`03O01oogoo069ooaYl015oo`04001oogoo001>Ool00g`0 Oomoo`0BOol00`0OOomoo`0?Ool00`00Oomoo`0XOol004moo`03001oogoo00Eoo`03001oogoo01Yo o`0301moogoo00aoo`03O01oogoo08aoo`05001oogooOol0001;Ool2O00DOol00`0OOomoo`0@Ool0 0`00Oomoo`0XOol004moo`03001oogoo00Eoo`03001oogoo01]oo`0301moogoo00aoo`03O01oogoo 08Yoo`8000Aoo`03001oogoo04Moo`03O01oogoo01Aoo`0301moogoo011oo`03001oogoo02Qoo`00 Bgoo00D007ooOomoo`0000Moo`03001oogoo01]oo`0301moogoo00eoo`9l0=Uoo`03O01oogoo01Eo o`0301moogoo011oo`03001oogoo02Qoo`00C7oo0`0027oo00<007ooOol077oo00<07gooOol03Woo 00=l07ooOol0eGoo00=l07ooOol05Goo00<07gooOol04Goo00<007ooOol0:7oo001GOol00`00Oomo o`0MOol00`0OOomoo`0>Ool00g`0Oomoo`3COol00g`0Oomoo`0FOol00`0OOomoo`0AOol00`00Oomo o`0XOol005Moo`8001ioo`0301moogoo00moo`03O01oogoo0=1oo`9l01Qoo`0301moogoo015oo`80 02Yoo`00Egoo00<007ooOol07Woo00<07gooOol03goo00=l07ooOol0cWoo00=l07ooOol067oo00<0 7gooOol04Woo00<007ooOol0:7oo001GOol00`00Oomoo`0OOol00`0OOomoo`0?Ool2O03=Ool00g`0 Oomoo`0IOol00`0OOomoo`0BOol00`00Oomoo`0XOol005Moo`03001oogoo01moo`0301moogoo015o o`03O01oogoo0Goo0W`08Goo00<07gooOol05Goo00<007ooOol0:7oo001GOol0 0`00Oomoo`0UOol00`0OOomoo`0EOol2O01dOol01000Oomoo`0017oo0P00>7oo00=l07ooOol087oo 00<07gooOol05Woo00<007ooOol0:7oo001GOol00`00Oomoo`0VOol00`0OOomoo`0FOol00g`0Oomo o`1aOol01@00Oomoogoo00000goo0`00=Woo00=l07ooOol08Goo00<07gooOol05Woo00<007ooOol0 :7oo001GOol00`00Oomoo`0WOol00`0OOomoo`0FOol00g`0Oomoo`1:OolJ01lOol20007Ool00`00Oomoo`0_Ool00`0OOomoo`0QOol2O02;Ool2O00a Ool00`0OOomoo`0KOol00`00Oomoo`0XOol0051oo`03001oogoo00Aoo`03001oogoo031oo`0301mo ogoo029oo`03O01oogoo08Moo`03O01oogoo035oo`0301moogoo01]oo`03001oogoo02Qoo`00Egoo 00<007ooOol0<7oo00<07gooOol08goo0W`0QGoo0W`0Woo00<07gooOol07Woo00<007ooOol0:7oo001GOol00`00Oomoo`0fOol00`0OOomo o`0ZOol2O01/Ool2O00mOol00`0OOomoo`0NOol00`00Oomoo`0XOol005Moo`8003Moo`0301moogoo 02aoo`9l06Uoo`03O01oogoo03aoo`0301moogoo01ioo`8002Yoo`00Egoo00<007ooOol0=goo00<0 7gooOol0;Goo0W`0IGoo0W`0?goo00<07gooOol07goo00<007ooOol0:7oo001GOol00`00Oomoo`0h Ool00`0OOomoo`0^Ool3O01POol2O010Ool00`0OOomoo`0POol00`00Oomoo`0XOol005Moo`03001o ogoo03Uoo`0301moogoo031oo`=l05Yoo`=l049oo`0301moogoo021oo`03001oogoo02Qoo`00Egoo 00<007ooOol0>Goo00<07gooOol0Ool3O017Ool00`0OOomoo`0QOol00`00Oomo o`0XOol005Moo`03001oogoo03]oo`0301moogoo03Moo`=l04Qoo`=l04Yoo`0301moogoo025oo`03 001oogoo02Qoo`00Egoo0P00?Goo00<07gooOol0>Goo0g`0@Woo0g`0C7oo00<07gooOol08Goo0P00 :Woo001GOol00`00Oomoo`0lOol00`0OOomoo`0lOol3O00lOol3O01?Ool00`0OOomoo`0ROol00`00 Oomoo`0XOol005Moo`03001oogoo03eoo`0301moogoo03ioo`=l03Eoo`Al059oo`0301moogoo029o o`03001oogoo02Qoo`00BWoo0`002Woo00<007ooOol0?Woo00<07gooOol0@7oo17`0;7oo1G`0EGoo 00<07gooOol08goo00<007ooOol0:7oo0019Ool01@00Oomoogoo00002Goo00<007ooOol0?goo00<0 7gooOol0@goo1G`097oo0g`0FWoo00<07gooOol08goo00<007ooOol0:7oo0019Ool00`00Oomoo`02 Ool00`00Oomoo`06Ool00`00Oomoo`0oOol00`0OOomoo`18Ool9O00BOol9O01LOol00`0OOomoo`0T Ool00`00Oomoo`0XOol004Uoo`03001oogoo009oo`03001oogoo00Ioo`03001oogoo041oo`0301mo ogoo051ooa9l06Eoo`0301moogoo02Aoo`03001oogoo02Qoo`00BGoo00<007ooOol00Woo00<007oo Ool01Woo0`00@Goo00<07gooOol0aGoo00<07gooOol08goo0`00:Woo001:Ool20002Ool00`00Oomo o`06Ool00`00Oomoo`12Ool00`0OOomoo`34Ool00`0OOomoo`0UOol00`00Oomoo`0XOol004Yoo`04 001oo`000009Ool00`00Oomoo`12Ool00`0OOomoo`34Ool00`0OOomoo`0UOol00`00Oomoo`0XOol0 04]oo`03001oogoo00Uoo`03001oogoo04=oo`0301moogoo0<9oo`0301moogoo02Ioo`03001oogoo 02Qoo`00C7oo0P002Goo00<007ooOol0A7oo00<07gooOol0`Goo00<07gooOol09Woo00<007ooOol0 :7oo001>Ool20007Ool00`00Oomoo`15Ool00`0OOomoo`2oOol00`0OOomoo`0WOol00`00Oomoo`0X Ool005Moo`03001oogoo04Eoo`0301moogoo0;moo`0301moogoo02Moo`03001oogoo02Qoo`00Egoo 0P00Agoo00<07gooOol0_Goo00<07gooOol09goo0P00:Woo001GOol00`00Oomoo`17Ool00`0OOomo o`2lOol00`0OOomoo`0XOol00`00Oomoo`0XOol005Moo`03001oogoo04Qoo`0301moogoo0;]oo`03 01moogoo02Qoo`03001oogoo02Qoo`00Egoo00<007ooOol0BGoo00<07gooOol0^Goo00<07gooOol0 :Goo00<007ooOol0:7oo001GOol00`00Oomoo`19Ool00`0OOomoo`2iOol00`0OOomoo`0YOol00`00 Oomoo`0XOol005Moo`03001oogoo04Yoo`0301moogoo0;Moo`0301moogoo02Yoo`03001oogoo02Qo o`00Egoo00<007ooOol0Bgoo00<07gooOol0]Woo00<07gooOol0:Woo00<007ooOol0:7oo001GOol2 001=Ool00`0OOomoo`2dOol00`0OOomoo`0ZOol2000ZOol005Moo`03001oogoo04eoo`0301moogoo 0;=oo`0301moogoo02]oo`03001oogoo02Qoo`00Egoo00<007ooOol0CWoo00<07gooOol0/Goo00<0 7gooOol0;7oo00<007ooOol0:7oo001GOol00`00Oomoo`1>Ool00`0OOomoo`2aOol00`0OOomoo`0/ Ool00`00Oomoo`0XOol005Moo`03001oogoo04moo`0301moogoo0:moo`0301moogoo02eoo`03001o ogoo02Qoo`00Egoo00<007ooOol0D7oo00<07gooOol0[Woo00<07gooOol0;Goo00<007ooOol0:7oo 001GOol00`00Oomoo`1AOol00`0OOomoo`2/Ool00`0OOomoo`0^Ool00`00Oomoo`0XOol005Moo`80 059oo`0301moogoo0:aoo`0301moogoo02eoo`8002Yoo`00Egoo00<007ooOol0DWoo00<07gooOol0 ZWoo00<07gooOol0;goo00<007ooOol0:7oo001GOol00`00Oomoo`1COol00`0OOomoo`2YOol00`0O Oomoo`0_Ool00`00Oomoo`0XOol004]oo`<000Uoo`03001oogoo05Aoo`0301moogoo0:Moo`0301mo ogoo031oo`03001oogoo02Qoo`00BWoo00D007ooOomoo`0000Qoo`03001oogoo05Eoo`0301moogoo 0:Ioo`0301moogoo031oo`03001oogoo02Qoo`00BWoo00D007ooOomoo`0000Qoo`03001oogoo05Eo o`0301moogoo0:Eoo`0301moogoo035oo`03001oogoo02Qoo`00BWoo00D007ooOomoo`0000Qoo`03 001oogoo05Ioo`0301moogoo0:Aoo`0301moogoo035oo`03001oogoo02Qoo`00Bgoo00<007oo0000 2Goo0`00Egoo00<07gooOol0XWoo00<07gooOol0<7oo0`00:Woo0017oo0P00:Woo001GOol00`00Oomoo`1TOol00`0OOomoo`2>Ool00`0O Oomoo`0iOol00`00Oomoo`0XOol005Moo`03001oogoo06Eoo`0301moogoo08aoo`0301moogoo03Yo o`03001oogoo02Qoo`00Egoo00<007ooOol0IWoo00<07gooOol0RWoo00<07gooOol0>goo00<007oo Ool0:7oo001GOol00`00Oomoo`1WOol00`0OOomoo`29Ool00`0OOomoo`0kOol00`00Oomoo`0XOol0 05Moo`03001oogoo06Qoo`0301moogoo08Moo`0301moogoo03aoo`03001oogoo02Qoo`00Egoo00<0 07ooOol0JGoo00<07gooOol0QWoo00<07gooOol0?7oo00<007ooOol0:7oo001GOol2001[Ool00`0O Oomoo`24Ool00`0OOomoo`0lOol2000ZOol005Moo`03001oogoo06]oo`0301moogoo089oo`0301mo ogoo03ioo`03001oogoo02Qoo`00Egoo00<007ooOol0K7oo00<07gooOol0PGoo00<07gooOol0?Woo 00<007ooOol0:7oo0012Ool40005Ool30009Ool00`00Oomoo`1]Ool00`0OOomoo`1oOol00`0OOomo o`0oOol00`00Oomoo`0XOol004=oo`03001oogoo00Aoo`05001oogooOol00008Ool00`00Oomoo`1] Ool00`0OOomoo`1oOol00`0OOomoo`0oOol00`00Oomoo`0XOol004Aoo`03001oogoo00=oo`03001o ogoo009oo`03001oogoo00Eoo`03001oogoo06ioo`0301moogoo07eoo`0301moogoo041oo`03001o ogoo02Qoo`00A7oo00<007ooOol00goo00<007ooOol00Woo00<007ooOol01Goo00<007ooOol0Kgoo 00<07gooOol0Ngoo00<07gooOol0@Goo00<007ooOol0:7oo0014Ool00`00Oomoo`03Ool00`00Oomo o`03Ool00`00Oomoo`04Ool3001`Ool00`0OOomoo`1jOol00`0OOomoo`0oOol3000ZOol004Eoo`03 001oogoo009oo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo075oo`0301moogoo07Qoo`03 01moogoo049oo`03001oogoo02Qoo`00AGoo00<007ooOol00goo00<007ooOol00Woo00<007ooOol0 17oo00<007ooOol0LWoo00<07gooOol0MWoo00<07gooOol0@goo00<007ooOol0:7oo0015Ool00`00 Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`1cOol00`0OOomoo`1eOol00`0O Oomoo`13Ool00`00Oomoo`0XOol004Ioo`03001oogoo00=oo`05001oogooOol00006Ool00`00Oomo o`1dOol00`0OOomoo`1cOol00`0OOomoo`14Ool00`00Oomoo`0XOol004Eoo`8000Ioo`<000Moo`03 001oogoo07Eoo`0301moogoo075oo`0301moogoo04Eoo`03001oogoo02Qoo`00Egoo00<007ooOol0 MWoo00<07gooOol0L7oo00<07gooOol0AGoo00<007ooOol0:7oo001GOol2001hOol00`0OOomoo`1^ Ool00`0OOomoo`15Ool2000ZOol005Moo`03001oogoo07Qoo`0301moogoo06aoo`0301moogoo04Mo o`03001oogoo02Qoo`00Egoo00<007ooOol0NGoo00<07gooOol0JWoo00<07gooOol0B7oo00<007oo Ool0:7oo001GOol00`00Oomoo`1jOol00`0OOomoo`1YOol00`0OOomoo`18Ool00`00Oomoo`0XOol0 05Moo`03001oogoo07]oo`0301moogoo06Moo`0301moogoo04Uoo`03001oogoo02Qoo`00Egoo00<0 07ooOol0O7oo00<07gooOol0IGoo00<07gooOol0BWoo00<007ooOol0:7oo001GOol00`00Oomoo`1m Ool00`0OOomoo`1SOol00`0OOomoo`1;Ool00`00Oomoo`0XOol005Moo`8007moo`0301moogoo069o o`0301moogoo04Yoo`8002Yoo`00Egoo00<007ooOol0Ogoo0P0OHGoo00<07gooOol0C7oo00<007oo Ool0:7oo001GOol00`00Oomoo`21Ool00`0OOomoo`1MOol00`0OOomoo`1=Ool00`00Oomoo`0XOol0 05Moo`03001oogoo089oo`0301moogoo05]oo`0301moogoo04ioo`03001oogoo02Qoo`00Egoo00<0 07ooOol0Pgoo00<07gooOol0FGoo00<07gooOol0Cgoo00<007ooOol0:7oo001GOol00`00Oomoo`24 Ool00`0OOomoo`1HOol00`0OOomoo`1?Ool00`00Oomoo`0XOol005Moo`03001oogoo08Eoo`807eMo o`0301moogoo051oo`03001oogoo02Qoo`00Egoo0P00R7oo00<07gooOol0Dgoo00<07gooOol0D7oo 0P00:Woo001GOol00`00Oomoo`28Ool00`0OOomoo`1AOol00`0OOomoo`1BOol00`00Oomoo`0XOol0 05Moo`03001oogoo08Uoo`807e1oo`0301moogoo05=oo`03001oogoo02Qoo`00@Woo10000goo1@00 2Goo00<007ooOol0Rgoo00<07gooOol0C7oo00<07gooOol0E7oo00<007ooOol0:7oo0013Ool00`00 Oomoo`04Ool01@00Oomoogoo000027oo00<007ooOol0S7oo0P0OBgoo00<07gooOol0EGoo00<007oo Ool0:7oo0014Ool00`00Oomoo`04Ool00`00Oomoo`09Ool00`00Oomoo`2>Ool00`0OOomoo`17Ool0 0`0OOomoo`1FOol00`00Oomoo`0XOol004Aoo`03001oogoo00Eoo`03001oogoo00Qoo`03001oogoo 08moo`807dIoo`0301moogoo05Moo`03001oogoo02Qoo`00A7oo00<007ooOol01Woo00<007ooOol0 1goo0`00TGoo00<07gooOol0@Woo00<07gooOol0EWoo0`00:Woo0015Ool00`00Oomoo`06Ool00`00 Oomoo`06Ool00`00Oomoo`2BOol201m0Ool201mKOol00`00Oomoo`0XOol004Eoo`03001oogoo00Mo o`03001oogoo00Eoo`03001oogoo09Aoo`0301moogoo03aoo`0301moogoo05]oo`03001oogoo02Qo o`00AGoo00<007ooOol01goo00<007ooOol01Goo00<007ooOol0UGoo0P0O>Woo0P0OGWoo00<007oo Ool0:7oo0016Ool00`00Oomoo`02Ool01@00Oomoogoo00001goo00<007ooOol0Ugoo00<07gooOol0 =Woo00<07gooOol0GWoo00<007ooOol0:7oo0015Ool20005Ool30008Ool00`00Oomoo`2HOol201ld Ool201mQOol00`00Oomoo`0XOol005Moo`03001oogoo09Yoo`807c5oo`0301moogoo065oo`03001o ogoo02Qoo`00Egoo0P00WGoo0`0O;7oo0P0OHgoo0P00:Woo001GOol00`00Oomoo`2OOol201lYOol0 0`0OOomoo`1TOol00`00Oomoo`0XOol005Moo`03001oogoo0:5oo`807bEoo`807fMoo`03001oogoo 02Qoo`00Egoo00<007ooOol0Xgoo0P0O8Goo0P0OJGoo00<007ooOol0:7oo001GOol00`00Oomoo`2U Ool301lKOol301m[Ool00`00Oomoo`0XOol005Moo`03001oogoo0:Qoo`L07`moo`D07fioo`03001o ogoo02Qoo`00Egoo00<007ooOol0[goo3`0OLgoo00<007ooOol0:7oo001GOol2003oOolbOol2000Z Ool005Moo`03001oogoo0?mooc9oo`03001oogoo02Qoo`00Egoo00<007ooOol017oo00<007ooOol0 1Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Woo00<007ooOol01Goo00<007ooOol0 1Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Woo00<007ooOol0 1Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol0 1Woo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol0 1Goo00<007ooOol01Woo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol0 1Goo00<007ooOol01Goo00<007ooOol01Woo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol0 1Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Woo00<007ooOol0 1Goo00<007ooOol017oo00<007ooOol0:7oo001GOol00`00Oomoo`04Ool00`00Oomoo`05Ool00`00 Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00 Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00`00 Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`06Ool00`00 Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00 Oomoo`06Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00 Oomoo`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00 Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`05Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00`00 Oomoo`04Ool00`00Oomoo`0XOol005Moool003H002Yoo`00ogoo]goo003oOongOol00?mookMoo`00 ogoo]goo003oOongOol00Ool00`00Oomoo`02Ool00`00Oomoo`0>Ool00`00Oomo o`0=Ool00`00Oomoo`0QOol00`00Oomoo`0FOol00`00Oomoo`1NOol008]oo`<0009oo`<000Aoo`03 001oogoo00Uoo`03001oogoo00Aoo`<0009oo`<000Aoo`04001oogooOol20003Ool20009Ool00`00 Oomoo`02Ool30004Ool00`00Oomoo`08Ool00`00Oomoo`02Ool01@00Oomoogoo00001goo00<007oo Ool00Woo1@0037oo00<007ooOol03Goo00<007ooOol010000goo00@007ooOomoo`D000Aoo`<000Ao o`D00003Ool007oo00=oo`@000=oo`03001oogoo00=oo`<000Aoo`03001oogoo05ioo`00RWoo00D0 07ooOomoo`00009oo`03001oogoo00=oo`8000]oo`03001oogoo009oo`05001oogooOol00002Ool0 0`00Oomoo`03Ool20003Ool20002Ool00`00Oomoo`08Ool01@00Oomoogoo00000goo0P000Woo00<0 07ooOol01goo00<007ooOol00goo0P000Woo0P002Woo00<007ooOol00goo00<007ooOol02Woo00<0 07ooOol02goo00<007ooOol00Woo00<007ooOol027oo00D007ooOomoo`0000Ioo`03001oogoo009o o`05001oogooOol00006Ool00`00Oomoo`08Ool01@00Oomoogoo000017oo00<007ooOol0GGoo002: Ool30005Ool01`00Oomoogoo001oo`0000aoo`04001oogooOol30005Ool01`00Oomoogoo001oo`00 00Aoo`04001oogoo000;Ool01000Oomoo`0017oo00D007ooOomoo`0000Qoo`03001oogoo00=oo`80 009oo`8000Yoo`03001oogoo00Aoo`03001oogoo00Uoo`03001oogoo00P000=oo`03001oogoo00=o o`03001oogoo00Qoo`03001oogoo00Qoo`03001oogoo009oo`03001oogoo00Qoo`03001oogoo00Mo o`03001oogoo009oo`05001oogooOol0001OOol008Yoo`03001oogoo008000=oo`07001oogooOol0 07oo000017oo2P000Woo00<007ooOol00P000goo00L007ooOomoo`00Ool00004Ool01000Oomoo`00 2goo00@007ooOol000Eoo`04001oogoo0008Ool00`00Oomoo`03Ool01`00Ool007oo001oo`0000Uo o`03001oogoo00Eoo`03001oogoo00Qoo`03001oogoo00]oo`03001oogoo00=oo`03001oogoo00Uo o`03001oogoo00Moo`03001oogoo00=oo`03001oogoo00Moo`03001oogoo00Moo`03001oogoo009o o`05001oogooOol0001OOol008]oo`05001oogooOol00002Ool01@00Oomoogoo00000Woo00<007oo Ool02Goo00<007ooOol00Woo00D007ooOomoo`00009oo`05001oogooOol00002Ool00`00Oomoo`02 Ool01000Oomoo`002Woo00D007ooOomoo`0000Aoo`03001oogoo008000Moo`03001oogoo00=oo`80 0006Ool007oo001oo`0027oo00<007ooOol01Woo00<007ooOol01goo00<007ooOol02goo00<007oo Ool00goo00<007ooOol02Woo00<007ooOol01Woo00<007ooOol017oo00<007ooOol01Woo00<007oo Ool01goo00<007ooOol00goo00@007ooOol005moo`00Rgoo0P000Woo00L007ooOomoo`00Ool00003 Ool00`00Oomoo`08Ool00`00Oomoo`03Ool20002Ool01`00Oomoogoo001oo`0000=oo`06001oogoo 001oo`000Woo00<007ooOol02Goo00<007ooOol00P000goo00@007ooOomoo`800003Ool007oo00=o o`03001oogoo00Aoo`07001oo`00Ool007oo000027oo00<007ooOol01Woo00<007ooOol01goo00<0 07ooOol020000goo00<007ooOol017oo00<007ooOol02Woo00<007ooOol00goo0P0027oo00<007oo Ool01Woo00<007ooOol01Woo00<007ooOol00goo00@007ooOol005moo`00SGoo0`000goo00<007oo 00000goo00<007ooOol01goo00<007ooOol01Woo0`000goo00<007oo00000goo00@007ooOomoo`L0 00Moo`@000=oo`<000=oo`800003Ool0000000Aoo`03001oogoo00Aoo`03001oogoo0080009oo`03 001oogoo00Ioo`03001oogoo00Eoo`D000Eoo`03001oogoo00]oo`03001oogoo00Aoo`03001oogoo 00]oo`03001oogoo00Aoo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo00Moo`03001oogoo 009oo`04001oogoo001OOol009=oo`03001oo`0000Aoo`03001oogoo01Eoo`03001oo`0000Aoo`03 001oogoo011oo`03001oogoo019oo`03001oogoo00=oo`05001oogooOol00002Ool00`00Oomoo`07 Ool00`00Oomoo`04Ool01@00Ool007oo000017oo00<007ooOol03Goo00<007ooOol00goo00<007oo Ool02goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01Goo00<007ooOol01goo00<007oo Ool00Woo00<007oo0000H7oo002DOol00`00Oomoo`03Ool00`00Oomoo`0FOol00`00Oomoo`03Ool0 0`00Oomoo`0AOol00`00Oomoo`0AOol00`00Oomoo`03Ool01@00Oomoogoo00000goo00<007ooOol0 1goo00<007ooOol00Woo00D007ooOomoo`0000Eoo`03001oogoo00eoo`03001oogoo00Aoo`03001o ogoo00Ioo`05001oogooOol00004Ool01000Oomoo`000goo00D007ooOomoo`0000Qoo`03001oogoo 00Moo`07001oogooOol007oo0000H7oo002BOol30004Ool3000EOol30004Ool3000BOol01000Oomo o`004Goo00@007ooOomoo`<00005Ool00000001oo`040008Ool50004Ool01@00Oomoogoo00004Goo 00<007ooOol00Woo0P002Goo0`001Woo0`0017oo0`0027oo0P002Woo0`0000=oo`00Ool0H7oo003> Ool3000BOol00`00Oomoo`0MOol01000Oomoo`004goo00<007ooOol0=Woo00<007ooOol0H7oo003o Ool5Ool00`00Oomoo`2_Ool00?moo`9oo`04001oogoo002aOol00?moo`=oo`800;9oo`00ogoo]goo 003oOongOol00?mookMoo`00ogoo]goo003oOongOol00?mookMoo`00ogoo]goo0000\ \>"], ImageRangeCache->{{{109, 458.875}, {406.313, 190.438}} -> {-1.70708, 0.496, \ 0.00601217, 0.00601217}, {{117.563, 450.25}, {401.125, 195.563}} -> \ {-141.565, 13.1229, 0.766775, 0.0891704}, {{283.938, 383.688}, {348.25, 315}} -> \ {-9.66432, 9.93272, 0.0336846, 0.0757903}, {{289.25, 318.938}, {345.875, \ 332.625}} -> {-14.3934, 19.5538, 0.0489765, 0.158491}, {{289.25, 318.938}, \ {330.563, 317.375}} -> {-14.464, 17.2131, 0.0492086, 0.159242}}] }, Open ]], Cell[TextData[{ "\tNotice that lab spin is slightly forward of the cm spin while the lab \ momentum is considerably forward. However, recoil polarization is usually \ represented in a helicity basis with the longitudinal component along the \ momentum either in the cm or the lab, as appropriate. Thus, the helicity \ basis for this reaction rotates forward by the angle ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_c - \[Theta]\_\[ScriptL]\)]], " in transforming from the cm to the lab frame. This is usually a large \ angle that produces considerable mixing between the helicity states. The \ apparent spin rotation relative to the helicity bases for the two frames is \ then determined by ", Cell[BoxData[ \(TraditionalForm\`\[CapitalOmega] = \[Theta]\_c - \[Theta]\_\[ScriptL] \ - \[Chi]\)]], ", which the figure below shows is generally large and negative. Thus, a \ spin which appears to be purely longitudinal in the cm frame appears to be \ transverse in the lab when ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_c\)]], " is near about 105\[Degree] for these kinematics." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[{omega} /. eN\[Pi][1.232, 1.0, \[Theta]\_1]], {\[Theta]\_1, 0, 180}, PlotRange \[Rule] {Automatic, All}, PlotPoints \[Rule] 50, Frame \[Rule] True, FrameLabel \[Rule] {\*"\"\<\!\(\[Theta]\_c\)\>\"", "\<\[CapitalOmega]\ \>"}, PlotLabel \[Rule] \*"\"\\""];\)\)], "Input", CellLabel->"In[38]:="], 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 Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.00529101 0.0147151 0.00327002 [ [.02381 -0.0125 -5 -15.6875 ] [.02381 -0.0125 5 0 ] [.15608 -0.0125 -8 -15.6875 ] [.15608 -0.0125 8 0 ] [.28836 -0.0125 -8 -15.6875 ] [.28836 -0.0125 8 0 ] [.42063 -0.0125 -8 -15.6875 ] [.42063 -0.0125 8 0 ] [.55291 -0.0125 -11 -15.6875 ] [.55291 -0.0125 11 0 ] [.68519 -0.0125 -11 -15.6875 ] [.68519 -0.0125 11 0 ] [.81746 -0.0125 -11 -15.6875 ] [.81746 -0.0125 11 0 ] [.94974 -0.0125 -11 -15.6875 ] [.94974 -0.0125 11 0 ] [ 0 0 -0.125 0 ] [.5 -0.0125 -6.78125 -31.375 ] [.5 -0.0125 6.78125 -15.6875 ] [-0.0125 .01472 -10 -7.84375 ] [-0.0125 .01472 0 7.84375 ] [-0.0125 .09647 -16 -7.84375 ] [-0.0125 .09647 0 7.84375 ] [-0.0125 .17822 -16 -7.84375 ] [-0.0125 .17822 0 7.84375 ] [-0.0125 .25997 -16 -7.84375 ] [-0.0125 .25997 0 7.84375 ] [-0.0125 .34172 -22 -7.84375 ] [-0.0125 .34172 0 7.84375 ] [-0.0125 .42347 -22 -7.84375 ] [-0.0125 .42347 0 7.84375 ] [-0.0125 .50522 -22 -7.84375 ] [-0.0125 .50522 0 7.84375 ] [-0.0125 .58697 -22 -7.84375 ] [-0.0125 .58697 0 7.84375 ] [ 0 0 -0.125 0 ] [-0.01875 .30902 -37.6875 -7.03125 ] [-0.01875 .30902 -22 7.03125 ] [ 0 .61803 .125 0 ] [ 1 0 .125 0 ] [.5 .63053 -84.1563 0 ] [.5 .63053 84.1563 15.6875 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .02381 0 m .02381 .00625 L s gsave .02381 -0.0125 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore .15608 0 m .15608 .00625 L s gsave .15608 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (25) show 1.000 setlinewidth grestore .28836 0 m .28836 .00625 L s gsave .28836 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (50) show 1.000 setlinewidth grestore .42063 0 m .42063 .00625 L s gsave .42063 -0.0125 -69 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (75) show 1.000 setlinewidth grestore .55291 0 m .55291 .00625 L s gsave .55291 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (100) show 1.000 setlinewidth grestore .68519 0 m .68519 .00625 L s gsave .68519 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (125) show 1.000 setlinewidth grestore .81746 0 m .81746 .00625 L s gsave .81746 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (150) show 1.000 setlinewidth grestore .94974 0 m .94974 .00625 L s gsave .94974 -0.0125 -72 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (175) show 1.000 setlinewidth grestore .125 Mabswid .05026 0 m .05026 .00375 L s .07672 0 m .07672 .00375 L s .10317 0 m .10317 .00375 L s .12963 0 m .12963 .00375 L s .18254 0 m .18254 .00375 L s .20899 0 m .20899 .00375 L s .23545 0 m .23545 .00375 L s .2619 0 m .2619 .00375 L s .31481 0 m .31481 .00375 L s .34127 0 m .34127 .00375 L s .36772 0 m .36772 .00375 L s .39418 0 m .39418 .00375 L s .44709 0 m .44709 .00375 L s .47354 0 m .47354 .00375 L s .5 0 m .5 .00375 L s .52646 0 m .52646 .00375 L s .57937 0 m .57937 .00375 L s .60582 0 m .60582 .00375 L s .63228 0 m .63228 .00375 L s .65873 0 m .65873 .00375 L s .71164 0 m .71164 .00375 L s .7381 0 m .7381 .00375 L s .76455 0 m .76455 .00375 L s .79101 0 m .79101 .00375 L s .84392 0 m .84392 .00375 L s .87037 0 m .87037 .00375 L s .89683 0 m .89683 .00375 L s .92328 0 m .92328 .00375 L s .97619 0 m .97619 .00375 L s .25 Mabswid 0 0 m 1 0 L s gsave .5 -0.0125 -67.7813 -35.375 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (q) show 68.250 17.688 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (c) show 72.563 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 .01472 m .00625 .01472 L s gsave -0.0125 .01472 -71 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0) show 1.000 setlinewidth grestore 0 .09647 m .00625 .09647 L s gsave -0.0125 .09647 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (25) show 1.000 setlinewidth grestore 0 .17822 m .00625 .17822 L s gsave -0.0125 .17822 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (50) show 1.000 setlinewidth grestore 0 .25997 m .00625 .25997 L s gsave -0.0125 .25997 -77 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (75) show 1.000 setlinewidth grestore 0 .34172 m .00625 .34172 L s gsave -0.0125 .34172 -83 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (100) show 1.000 setlinewidth grestore 0 .42347 m .00625 .42347 L s gsave -0.0125 .42347 -83 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (125) show 1.000 setlinewidth grestore 0 .50522 m .00625 .50522 L s gsave -0.0125 .50522 -83 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (150) show 1.000 setlinewidth grestore 0 .58697 m .00625 .58697 L s gsave -0.0125 .58697 -83 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (175) show 1.000 setlinewidth grestore .125 Mabswid 0 .03107 m .00375 .03107 L s 0 .04742 m .00375 .04742 L s 0 .06377 m .00375 .06377 L s 0 .08012 m .00375 .08012 L s 0 .11282 m .00375 .11282 L s 0 .12917 m .00375 .12917 L s 0 .14552 m .00375 .14552 L s 0 .16187 m .00375 .16187 L s 0 .19457 m .00375 .19457 L s 0 .21092 m .00375 .21092 L s 0 .22727 m .00375 .22727 L s 0 .24362 m .00375 .24362 L s 0 .27632 m .00375 .27632 L s 0 .29267 m .00375 .29267 L s 0 .30902 m .00375 .30902 L s 0 .32537 m .00375 .32537 L s 0 .35807 m .00375 .35807 L s 0 .37442 m .00375 .37442 L s 0 .39077 m .00375 .39077 L s 0 .40712 m .00375 .40712 L s 0 .43982 m .00375 .43982 L s 0 .45617 m .00375 .45617 L s 0 .47252 m .00375 .47252 L s 0 .48887 m .00375 .48887 L s 0 .52157 m .00375 .52157 L s 0 .53792 m .00375 .53792 L s 0 .55427 m .00375 .55427 L s 0 .57062 m .00375 .57062 L s 0 .60332 m .00375 .60332 L s .25 Mabswid 0 0 m 0 .61803 L s gsave -0.01875 .30902 -97.875 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 68.0313 11.8438 translate 90 rotate -68.0313 -11.8438 translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 73.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore .02381 .61178 m .02381 .61803 L s .15608 .61178 m .15608 .61803 L s .28836 .61178 m .28836 .61803 L s .42063 .61178 m .42063 .61803 L s .55291 .61178 m .55291 .61803 L s .68519 .61178 m .68519 .61803 L s .81746 .61178 m .81746 .61803 L s .94974 .61178 m .94974 .61803 L s .125 Mabswid .05026 .61428 m .05026 .61803 L s .07672 .61428 m .07672 .61803 L s .10317 .61428 m .10317 .61803 L s .12963 .61428 m .12963 .61803 L s .18254 .61428 m .18254 .61803 L s .20899 .61428 m .20899 .61803 L s .23545 .61428 m .23545 .61803 L s .2619 .61428 m .2619 .61803 L s .31481 .61428 m .31481 .61803 L s .34127 .61428 m .34127 .61803 L s .36772 .61428 m .36772 .61803 L s .39418 .61428 m .39418 .61803 L s .44709 .61428 m .44709 .61803 L s .47354 .61428 m .47354 .61803 L s .5 .61428 m .5 .61803 L s .52646 .61428 m .52646 .61803 L s .57937 .61428 m .57937 .61803 L s .60582 .61428 m .60582 .61803 L s .63228 .61428 m .63228 .61803 L s .65873 .61428 m .65873 .61803 L s .71164 .61428 m .71164 .61803 L s .7381 .61428 m .7381 .61803 L s .76455 .61428 m .76455 .61803 L s .79101 .61428 m .79101 .61803 L s .84392 .61428 m .84392 .61803 L s .87037 .61428 m .87037 .61803 L s .89683 .61428 m .89683 .61803 L s .92328 .61428 m .92328 .61803 L s .97619 .61428 m .97619 .61803 L s .25 Mabswid 0 .61803 m 1 .61803 L s .99375 .01472 m 1 .01472 L s .99375 .09647 m 1 .09647 L s .99375 .17822 m 1 .17822 L s .99375 .25997 m 1 .25997 L s .99375 .34172 m 1 .34172 L s .99375 .42347 m 1 .42347 L s .99375 .50522 m 1 .50522 L s .99375 .58697 m 1 .58697 L s .125 Mabswid .99625 .03107 m 1 .03107 L s .99625 .04742 m 1 .04742 L s .99625 .06377 m 1 .06377 L s .99625 .08012 m 1 .08012 L s .99625 .11282 m 1 .11282 L s .99625 .12917 m 1 .12917 L s .99625 .14552 m 1 .14552 L s .99625 .16187 m 1 .16187 L s .99625 .19457 m 1 .19457 L s .99625 .21092 m 1 .21092 L s .99625 .22727 m 1 .22727 L s .99625 .24362 m 1 .24362 L s .99625 .27632 m 1 .27632 L s .99625 .29267 m 1 .29267 L s .99625 .30902 m 1 .30902 L s .99625 .32537 m 1 .32537 L s .99625 .35807 m 1 .35807 L s .99625 .37442 m 1 .37442 L s .99625 .39077 m 1 .39077 L s .99625 .40712 m 1 .40712 L s .99625 .43982 m 1 .43982 L s .99625 .45617 m 1 .45617 L s .99625 .47252 m 1 .47252 L s .99625 .48887 m 1 .48887 L s .99625 .52157 m 1 .52157 L s .99625 .53792 m 1 .53792 L s .99625 .55427 m 1 .55427 L s .99625 .57062 m 1 .57062 L s .99625 .60332 m 1 .60332 L s .25 Mabswid 1 0 m 1 .61803 L s gsave .5 .63053 -145.156 -4 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 63.000 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (eN) show 77.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\256) show 87.438 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (eN) show %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (p) show 113.688 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (for) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 130.688 15.813 moveto (H) show 134.500 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (W) show 145.750 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 148.750 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (Q) show 157.375 11.000 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 162.188 15.813 moveto (L) show 166.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (=) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 174.500 15.813 moveto (H) show 178.313 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.232) show 205.500 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (,) show 208.500 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.0) show %%IncludeResource: font Mathematica2 %%IncludeFont: Mathematica2 /Mathematica2 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 223.500 15.813 moveto (L) show 227.313 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor 0.000 0.000 rmoveto 1.000 setlinewidth grestore 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .01472 m .04273 .02333 L .06337 .03273 L .08275 .04158 L .10139 .05011 L .12123 .05921 L .14033 .06801 L .16063 .0774 L .18019 .0865 L .199 .09531 L .21902 .10475 L .23829 .11391 L .25683 .12279 L .27656 .13233 L .29555 .14161 L .31574 .15158 L .33519 .1613 L .3539 .17076 L .3738 .18096 L .39297 .19092 L .41334 .20166 L .43296 .21218 L .45184 .22246 L .47193 .23358 L .49127 .24449 L .50987 .25516 L .52967 .26674 L .54872 .27811 L .56898 .29044 L .5885 .30258 L .60727 .3145 L .62725 .32747 L .64648 .34024 L .66497 .35279 L .68466 .36645 L .70361 .3799 L .72376 .39453 L .74317 .40895 L .76183 .42312 L .7817 .43852 L .80082 .45366 L .82115 .47007 L .84073 .48618 L .85957 .50194 L .87961 .51895 L .89891 .53555 L .91747 .55167 L .93723 .56897 L .95624 .58571 L .97619 .60332 L Mistroke Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[38]:=", ImageSize->{288, 177.938}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol40004Ool00`00Oomoo`05Ool4000POol0055oo`05001o ogooOol0000IOol01@00Oomoogoo00000goo00D007ooOomoo`0001Aoo`05001oogooOol00003Ool0 1@00Oomoogoo00005Woo00<007ooOol017oo00D007ooOomoo`00019oo`03001oogoo00Aoo`05001o ogooOol00003Ool01@00Oomoogoo00003Goo00<007ooOol017oo00D007ooOomoo`0000=oo`05001o ogooOol0000=Ool00`00Oomoo`04Ool01@00Oomoogoo00000goo00D007ooOomoo`0000ioo`03001o ogoo00Eoo`03001oogoo00Aoo`05001oogooOol0000OOol0055oo`03001oogoo009oo`03001oogoo 01Moo`03001oogoo00Uoo`03001oogoo01Ioo`04001oogoo0004Ool00`00Oomoo`0DOol00`00Oomo o`08Ool00`00Oomoo`0@Ool00`00Oomoo`03Ool00`00Oomoo`02Ool01000Oomoo`0017oo00<007oo Ool02goo00<007ooOol017oo00<007ooOol02Goo00<007ooOol02goo00<007ooOol027oo00@007oo Ool000Aoo`03001oogoo00aoo`03001oogoo00Eoo`03001oogoo00Qoo`03001oogoo01aoo`00DGoo 00<007ooOol00Woo00<007ooOol067oo00<007ooOol027oo00<007ooOol05Woo00@007ooOol000Ao o`03001oogoo01Aoo`03001oogoo00Qoo`03001oogoo011oo`03001oogoo00=oo`03001oogoo009o o`04001oogoo0004Ool00`00Oomoo`0;Ool00`00Oomoo`05Ool00`00Oomoo`08Ool00`00Oomoo`0; Ool00`00Oomoo`08Ool01000Oomoo`0017oo00<007ooOol037oo00<007ooOol01Goo00<007ooOol0 27oo00<007ooOol077oo001AOol00`00Oomoo`03Ool00`00Oomoo`0HOol00`00Oomoo`07Ool00`00 Oomoo`0FOol01000Oomoo`001Goo00<007ooOol057oo00<007ooOol01goo00<007ooOol047oo00<0 07ooOol00goo00<007ooOol00goo00<007oo00001Goo00<007ooOol02Woo00<007ooOol01Woo00<0 07ooOol01goo00<007ooOol02goo00<007ooOol027oo00@007ooOol000Eoo`03001oogoo00]oo`03 001oogoo00Ioo`03001oogoo00Moo`03001oogoo01aoo`00DGoo00<007ooOol00goo00<007ooOol0 6Goo00<007ooOol01Goo00<007ooOol05Woo00D007ooOomoo`0000Eoo`03001oogoo01Aoo`03001o ogoo00Ioo`03001oogoo019oo`03001oogoo009oo`03001oogoo00=oo`03001oo`0000Eoo`03001o ogoo00]oo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo00eoo`03001oogoo00Ioo`05001o ogooOol00005Ool00`00Oomoo`0Ool00`00Oomoo`05Ool00`00Oomoo`03Ool00`00Oomoo`02Ool0 0`00Oomoo`0Ool20005Ool30006Ool4000=Ool20006Ool40004Ool3 000?Ool20004Ool60004Ool4000MOol00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00ogoo JGoo003oOomYOol004=oo`<00?moob=oo`00@Woo00D007ooOomoo`0000Moooh001aoo`00@Woo00<0 07ooOol00Woo00<007ooOol017oo00<007ooOol00goo00<007ooOol07Woo00<007ooOol07goo00<0 07ooOol07Woo00<007ooOol07goo00<007ooOol07Woo00<007ooOol07goo00<007ooOol07Woo00<0 07ooOol02Woo00<007ooOol06Woo0012Ool00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`3j Ool00`00Oomoo`0JOol0049oo`03001oogoo00=oo`03001oogoo00=oo`<000=oo`800?=oo`<001ao o`00@Woo00<007ooOol00goo00<007ooOol00goo00<007ooOol01Goo0P00lgoo00<007ooOol06Woo 0013Ool00`00Oomoo`02Ool00`00Oomoo`03Ool00`00Oomoo`07Ool2003aOol00`00Oomoo`0JOol0 04=oo`03001oogoo009oo`03001oogoo00=oo`03001oogoo00Uoo`800>moo`03001oogoo01Yoo`00 A7oo00D007ooOomoo`0000Eoo`8000aoo`800>aoo`8001aoo`00AGoo0`001Woo00<007ooOol03Goo 0P00jgoo00<007ooOol06Woo001>Ool00`00Oomoo`0?Ool2003YOol00`00Oomoo`0JOol004ioo`03 001oogoo015oo`<00>Ioo`03001oogoo01Yoo`00CWoo0P005Goo0P00hgoo0P0077oo001>Ool00`00 Oomoo`0FOol3003QOol00`00Oomoo`0JOol004ioo`03001oogoo01Uoo`800=moo`03001oogoo01Yo o`00CWoo00<007ooOol06goo0P00gGoo00<007ooOol06Woo001>Ool00`00Oomoo`0MOol00`00Oomo o`3JOol00`00Oomoo`0JOol004ioo`8001moo`800=Uoo`8001aoo`00CWoo00<007ooOol087oo0P00 f7oo00<007ooOol06Woo001>Ool00`00Oomoo`0ROol3003EOol00`00Oomoo`0JOol004ioo`03001o ogoo02Eoo`<00=9oo`03001oogoo01Yoo`00>Goo1@0017oo100027oo0P00:Goo0P00cgoo0P0077oo 000jOol01@00Oomoogoo00000goo00D007ooOomoo`0000Moo`03001oogoo02Yoo`800goo00<007ooOol02Goo00<007ooOol017oo00<007ooOol0;7oo00<007ooOol0bgoo 00<007ooOol06Woo000lOol00`00Oomoo`08Ool00`00Oomoo`04Ool00`00Oomoo`0]Ool2003;Ool0 0`00Oomoo`0JOol003eoo`03001oogoo00Moo`03001oogoo00Aoo`<002moo`800goo00D007oo Oomoo`0000Eoo`03001oogoo00Ioo`8003Uoo`800;moo`8001aoo`00?7oo0`001Woo10001Goo00<0 07ooOol0>Woo0P00_Woo00<007ooOol06Woo001>Ool00`00Oomoo`0lOol2002lOol00`00Oomoo`0J Ool004ioo`03001oogoo03ioo`800;Yoo`03001oogoo01Yoo`00CWoo0P00@Goo0P00]goo0P0077oo 001>Ool00`00Oomoo`12Ool3002eOol00`00Oomoo`0JOol004ioo`03001oogoo04Eoo`800;=oo`03 001oogoo01Yoo`00CWoo00<007ooOol0Agoo0P00/Goo00<007ooOol06Woo001>Ool2001:Ool2002^ Ool2000LOol004ioo`03001oogoo04]oo`800:eoo`03001oogoo01Yoo`00CWoo00<007ooOol0CGoo 0P00Zgoo00<007ooOol06Woo001>Ool00`00Oomoo`1?Ool2002YOol00`00Oomoo`0JOol004ioo`80 059oo`800:Ioo`8001aoo`00>Woo10001Goo0`0027oo00<007ooOol0Dgoo00<007ooOol0Y7oo00<0 07ooOol06Woo000jOol01@00Oomoogoo00000goo00D007ooOomoo`0000Moo`03001oogoo05Aoo`80 0:Aoo`03001oogoo01Yoo`00?goo00@007ooOol000Aoo`03001oogoo00Aoo`03001oogoo05Ioo`80 0:9oo`03001oogoo01Yoo`00?goo00@007ooOol000Aoo`03001oogoo00Aoo`03001oogoo05Qoo`<0 09moo`03001oogoo01Yoo`00?goo00@007ooOol000Eoo`03001oogoo00=oo`<005]oo`8009]oo`<0 01aoo`00?Woo00D007ooOomoo`0000Eoo`03001oogoo00=oo`03001oogoo05eoo`03001oogoo09Yo o`03001oogoo01Yoo`00?7oo0P001Goo00<007ooOol00Woo00<007ooOol00goo00<007ooOol0GWoo 0P00VWoo00<007ooOol06Woo000mOol00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`03Ool0 0`00Oomoo`1POol2002HOol00`00Oomoo`0JOol003eoo`03001oogoo00Aoo`05001oogooOol00005 Ool2001SOol2002EOol2000LOol003eoo`@000Aoo`<000Ioo`03001oogoo06Aoo`8009Aoo`03001o ogoo01Yoo`00CWoo00<007ooOol0IWoo0P00TWoo00<007ooOol06Woo001>Ool00`00Oomoo`1XOol2 002@Ool00`00Oomoo`0JOol004ioo`8006]oo`03001oogoo08aoo`8001aoo`00CWoo00<007ooOol0 Jgoo0P00SGoo00<007ooOol06Woo001>Ool00`00Oomoo`1]Ool2002;Ool00`00Oomoo`0JOol004io o`03001oogoo06moo`03001oogoo08Qoo`03001oogoo01Yoo`00CWoo0P00LGoo0P00Qgoo0P0077oo 001>Ool00`00Oomoo`1bOol20026Ool00`00Oomoo`0JOol004ioo`03001oogoo07Aoo`8008Aoo`03 001oogoo01Yoo`00CWoo00<007ooOol0MWoo0P00PWoo00<007ooOol06Woo000jOol00`00Oomoo`05 Ool40008Ool2001iOol2001oOol2000LOol003]oo`03001oogoo00Aoo`05001oogooOol00007Ool0 0`00Oomoo`1jOol2001nOol00`00Oomoo`0JOol003aoo`03001oogoo00Qoo`03001oogoo00Aoo`03 001oogoo07aoo`8007aoo`03001oogoo01Yoo`00?7oo00<007ooOol027oo00<007ooOol017oo00<0 07ooOol0OWoo00<007ooOol0NGoo00<007ooOol06Woo000mOol00`00Oomoo`07Ool00`00Oomoo`04 Ool3001oOol2001gOol3000LOol003eoo`03001oogoo00Ioo`03001oogoo00Eoo`03001oogoo085o o`8007Moo`03001oogoo01Yoo`00?Woo00<007ooOol00goo0P0027oo00<007ooOol0Pgoo00<007oo Ool0M7oo00<007ooOol06Woo000oOol00`00Oomoo`03Ool00`00Oomoo`06Ool00`00Oomoo`24Ool2 001dOol00`00Oomoo`0JOol003Yoo`03001oogoo009oo`03001oogoo00=oo`03001oogoo00Ioo`80 08Moo`80075oo`8001aoo`00>goo1P0017oo10001Goo00<007ooOol0R7oo00<007ooOol0Kgoo00<0 07ooOol06Woo001>Ool00`00Oomoo`29Ool2001_Ool00`00Oomoo`0JOol002Moo`8002Eoo`03001o ogoo08]oo`8006eoo`03001oogoo01Yoo`008Goo1@000Woo00<007ooOol08goo0P00SWoo00<007oo Ool0JGoo0P0077oo000POol00`00Oomoo`03Ool00`00Ool0000UOol00`00Oomoo`2>Ool2001ZOol0 0`00Oomoo`0JOol001moo`03001oogoo00Eoo`8002Eoo`03001oogoo091oo`8006Qoo`03001oogoo 01Yoo`007goo00<007ooOol0;7oo00<007ooOol0TWoo00<007ooOol0IGoo00<007ooOol06Woo000O Ool00`00Oomoo`0/Ool00`00Oomoo`2COol2001UOol00`00Oomoo`0JOol001moo`03001oogoo02ao o`8009Ioo`80069oo`8001aoo`007goo00<007ooOol01Goo0P009Goo00<007ooOol0Ugoo00<007oo Ool0H7oo00<007ooOol06Woo000POol00`00Oomoo`03Ool00`00Ool0000UOol00`00Oomoo`2HOol2 001POol00`00Oomoo`0JOol0025oo`D0009oo`03001oogoo02=oo`03001oogoo09Yoo`8005ioo`03 001oogoo01Yoo`009goo0P002Woo10001Goo0`001Goo0`001goo0P00WGoo00<007ooOol0FWoo0P00 77oo000dOol00`00Oomoo`04Ool01@00Oomoogoo00000goo00D007ooOomoo`0000Ioo`03001oogoo 09eoo`03001oogoo05Yoo`03001oogoo01Yoo`00=Goo00<007ooOol00goo00<007ooOol00Woo00@0 07ooOol000Aoo`03001oogoo00=oo`03001oogoo09ioo`03001oogoo05Uoo`03001oogoo01Yoo`00 =Goo00<007ooOol00goo00<007ooOol00Woo00@007ooOol000Aoo`03001oogoo00=oo`03001oogoo 09moo`03001oogoo05Qoo`03001oogoo01Yoo`00=Goo00<007ooOol00goo00<007ooOol00goo00<0 07oo00001Goo00<007ooOol00Woo0`00X7oo00<007ooOol0EGoo0`0077oo000fOol00`00Oomoo`02 Ool00`00Oomoo`03Ool00`00Ool00005Ool00`00Oomoo`02Ool00`00Oomoo`2QOol2001GOol00`00 Oomoo`0JOol003Ioo`03001oogoo00=oo`03001oogoo009oo`04001oogoo0004Ool00`00Oomoo`02 Ool00`00Oomoo`2SOol2001EOol00`00Oomoo`0JOol003Ioo`03001oogoo00=oo`03001oogoo009o o`04001oogoo0004Ool00`00Oomoo`02Ool00`00Oomoo`2UOol00`00Oomoo`1BOol00`00Oomoo`0J Ool003Moo`03001oogoo00=oo`05001oogooOol00003Ool01@00Oomoogoo000017oo0P00Ygoo0P00 DGoo0P0077oo000fOol20006Ool30005Ool30005Ool00`00Oomoo`2XOol2001@Ool00`00Oomoo`0J Ool004ioo`03001oogoo0:Yoo`03001oogoo04eoo`03001oogoo01Yoo`00CWoo00<007ooOol0Zgoo 00<007ooOol0C7oo00<007ooOol06Woo001>Ool2002]Ool2001;Ool2000LOol004ioo`03001oogoo 0:ioo`03001oogoo04Uoo`03001oogoo01Yoo`00CWoo00<007ooOol0[goo00<007ooOol0B7oo00<0 07ooOol06Woo001>Ool00`00Oomoo`2`Ool20018Ool00`00Oomoo`0JOol004ioo`800;=oo`8004Eo o`8001aoo`00CWoo00<007ooOol0]7oo00<007ooOol0@goo00<007ooOol06Woo001>Ool00`00Oomo o`2eOol00`00Oomoo`12Ool00`00Oomoo`0JOol004ioo`03001oogoo0;Ioo`80049oo`03001oogoo 01Yoo`00CWoo0P00^Goo00<007ooOol0?Woo0P0077oo000cOol40003Ool50004Ool40007Ool00`00 Oomoo`2iOol00`00Oomoo`0nOol00`00Oomoo`0JOol003Aoo`03001oogoo00Aoo`05001oogooOol0 0003Ool01@00Oomoogoo00001Woo00<007ooOol0^Woo0P00?Woo00<007ooOol06Woo000eOol00`00 Oomoo`04Ool00`00Oomoo`09Ool00`00Oomoo`03Ool00`00Oomoo`2lOol2000lOol00`00Oomoo`0J Ool003Eoo`03001oogoo00Eoo`03001oogoo00Qoo`03001oogoo00=oo`03001oogoo0;ioo`03001o ogoo03Uoo`03001oogoo01Yoo`00=Goo00<007ooOol01Woo00<007ooOol01goo00<007ooOol00goo 0`00_goo00<007ooOol0=Woo0`0077oo000fOol00`00Oomoo`06Ool00`00Oomoo`05Ool00`00Oomo o`04Ool00`00Oomoo`30Ool2000hOol00`00Oomoo`0JOol003Ioo`03001oogoo00Moo`03001oogoo 009oo`8000Moo`03001oogoo0<9oo`03001oogoo03Eoo`03001oogoo01Yoo`00=Woo00<007ooOol0 1goo00<007ooOol00goo00<007ooOol01Goo00<007ooOol0`goo00<007ooOol0=7oo00<007ooOol0 6Woo000gOol00`00Oomoo`02Ool01@00Oomoogoo00001Goo00<007ooOol01Goo0P00aGoo00<007oo Ool0Ool20039Ool2000_Ool2000LOol004io o`03001oogoo0Ool00`00Oomoo`3=Ool00`00Oomoo`0ZOol00`00Oomoo`0JOol004ioo`80 0 Ool00`00Oomoo`3AOol00`00Oomoo`0VOol00`00Oomoo`0JOol004ioo`03001oogoo0=9oo`03001o ogoo02Eoo`03001oogoo01Yoo`00Ool00`00Oomoo`3OOol00`00Oomoo`0HOol00`00Oomoo`0JOol004ioo`800>5o o`03001oogoo01Ioo`8001aoo`00CWoo00<007ooOol0hGoo00<007ooOol05Woo00<007ooOol06Woo 001>Ool00`00Oomoo`3ROol2000FOol00`00Oomoo`0JOol004ioo`03001oogoo0>Aoo`03001oogoo 01=oo`03001oogoo01Yoo`00CWoo00<007ooOol0iGoo00<007ooOol04Woo00<007ooOol06Woo001> Ool2003WOol00`00Oomoo`0@Ool2000LOol004ioo`03001oogoo0>Moo`80015oo`03001oogoo01Yo o`00CWoo00<007ooOol0jGoo00<007ooOol03Woo00<007ooOol06Woo001>Ool00`00Oomoo`3ZOol0 0`00Oomoo`0=Ool00`00Oomoo`0JOol003=oo`@000Aoo`03001oogoo00Eoo`@000Moo`800>aoo`03 001oogoo00]oo`8001aoo`00=7oo00<007ooOol01Goo00<007ooOol017oo00D007ooOomoo`0000Io o`03001oogoo0>aoo`03001oogoo00]oo`03001oogoo01Yoo`00=Goo00<007ooOol01Goo00<007oo Ool027oo00<007ooOol00goo00<007ooOol0kGoo00<007ooOol02Woo00<007ooOol06Woo000eOol0 0`00Oomoo`05Ool00`00Oomoo`08Ool00`00Oomoo`03Ool00`00Oomoo`3^Ool00`00Oomoo`09Ool0 0`00Oomoo`0JOol003Eoo`03001oogoo00Ioo`03001oogoo00Moo`03001oogoo00=oo`<00>moo`03 001oogoo00Ioo`<001aoo`00=Woo00<007ooOol01Goo00<007ooOol01Woo00<007ooOol017oo00<0 07ooOol0l7oo00<007ooOol01goo00<007ooOol06Woo000fOol00`00Oomoo`06Ool00`00Oomoo`03 Ool20007Ool00`00Oomoo`3aOol20007Ool00`00Oomoo`0JOol003Ioo`03001oogoo00Moo`03001o ogoo00=oo`03001oogoo00Eoo`03001oogoo0?=oo`03001oogoo00Aoo`03001oogoo01Yoo`00=goo 00D007ooOomoo`0000Aoo`03001oogoo00=oo`03001oogoo00Eoo`800?Eoo`03001oogoo009oo`80 01aoo`00=Woo0P0017oo1P0017oo100017oo00<007ooOol0nWoo00<007ooOol06Woo001>Ool00`00 Oomoo`03Ool00`00Oomoo`0NOol00`00Oomoo`0OOol00`00Oomoo`0NOol00`00Oomoo`0OOol00`00 Oomoo`0NOol00`00Oomoo`0OOol00`00Oomoo`0NOol00`00Oomoo`0:Ool00`00Oomoo`0JOol004io o`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Ao o`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=o o`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Ao o`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Ao o`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00Ao o`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Ao o`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=o o`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo01Yoo`00CWoooP0077oo 003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00Xgoo0P006Goo00<007ooOol0 57oo10002Goo00<007ooOol047oo00<007ooOol0=Woo00<007ooOol0=goo002SOol00`00Ool0000G Ool00`00Oomoo`0Ool00`00Oomoo`0P Ool00`00Oomoo`0EOol00`00Oomoo`0fOol00:Ioo`03001oogoo01=oo`03001oogoo00ioo`03001o ogoo00=oo`03001oogoo00ioo`03001oogoo00aoo`03001oogoo029oo`03001oogoo01Eoo`03001o ogoo03Eoo`00Igoo0`000Woo0`0017oo00<007ooOol02Goo00<007ooOol00goo0`000Woo0`0017oo 00@007ooOomoo`8000=oo`8000Yoo`03001oogoo009oo`<000Aoo`03001oogoo00Moo`03001oogoo 009oo`05001oogooOol00007Ool00`00Oomoo`03Ool5000"], ImageRangeCache->{{{109, 396}, {327.063, 150.125}} -> {-165.291, 171.478, \ 0.935775, 1.51412}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["derivation using rapidity", "Subsection"], Cell["\<\ Several authors, including both Dmitrasinovic and Giebink, perform their \ analyses using the rapidity representation. In the hope that this is \ algebraically simpler, we now modify our derivation along these lines. \ First, we define the rapidity boost, evaluate the matrix product, and test \ its orthogonality.\ \>", "Text"], Cell[BoxData[ \(\(boost[\[Xi]_] = {{Cosh[\[Xi]], \(-Sinh[\[Xi]]\), 0}, {\(-Sinh[\[Xi]]\), \ Cosh[\[Xi]], 0}, {0, 0, 1}};\)\)], "Input", CellLabel->"In[39]:="], Cell[BoxData[{ \(\(p\_1 = m\ {Cosh[\[Xi]\_1], Sinh[\[Xi]\_1] Cos[\[Theta]\_1], Sinh[\[Xi]\_1] Sin[\[Theta]\_1]};\)\), "\[IndentingNewLine]", \(\(p\_2 = m\ {Cosh[\[Xi]\_2], Sinh[\[Xi]\_2] Cos[\[Theta]\_2], Sinh[\[Xi]\_2] Sin[\[Theta]\_2]};\)\)}], "Input", CellLabel->"In[40]:="], Cell[CellGroupData[{ Cell[BoxData[ \(Thread[boost[\(-\[Xi]\)] . p\_1 \[Equal] p\_2] // MySimplify\)], "Input",\ CellLabel->"In[42]:="], Cell[BoxData[ \({m\ Cosh[\[Xi]]\ Cosh[\[Xi]\_1] + m\ Cos[\[Theta]\_1]\ Sinh[\[Xi]]\ Sinh[\[Xi]\_1] \[Equal] m\ Cosh[\[Xi]\_2], m\ Cosh[\[Xi]\_1]\ Sinh[\[Xi]] + m\ Cos[\[Theta]\_1]\ Cosh[\[Xi]]\ Sinh[\[Xi]\_1] \[Equal] m\ Cos[\[Theta]\_2]\ Sinh[\[Xi]\_2], m\ Sin[\[Theta]\_1]\ Sinh[\[Xi]\_1] \[Equal] m\ Sin[\[Theta]\_2]\ Sinh[\[Xi]\_2]}\)], "Output", CellLabel->"Out[42]="] }, Open ]], Cell[BoxData[ \(\(rule3 = {\[Xi]\_2 \[Rule] ArcCosh[Cosh[\[Xi]\_1]\ Cosh[\[Xi]] + Sinh[\[Xi]]\ Sinh[\[Xi]\_1]\ Cos[\[Theta]\_1]], Sin[\[Theta]\_2] \[Rule] \(Sinh[\[Xi]\_1]\/Sinh[\[Xi]\_2]\) Sin[\[Theta]\_1], Cos[\[Theta]\_2] \[Rule] 1\/Sinh[\[Xi]\_2]\ \((Sinh[\[Xi]\_1] Cosh[\[Xi]]\ Cos[\[Theta]\_1] + Cosh[\[Xi]\_1] Sinh[\[Xi]])\)};\)\)], "Input", CellLabel->"In[43]:="], Cell[CellGroupData[{ Cell[BoxData[ \(test = boost[\[Xi]\_2] . R\_y[\[Theta]\_2] . boost[\(-\[Xi]\)] . R\_y[\(-\[Theta]\_1\)] . boost[\(-\[Xi]\_1\)] //. rule3 // MyFullSimplify\)], "Input", CellLabel->"In[44]:="], Cell[BoxData[ \({{1, 0, 0}, {0, \(Cos[\[Theta]\_1]\ Cosh[\[Xi]\_1]\ Sinh[\[Xi]] + Cosh[\[Xi]]\ \ Sinh[\[Xi]\_1]\)\/\(\((1 + Cosh[\[Xi]]\ Cosh[\[Xi]\_1] + Cos[\[Theta]\_1]\ \ Sinh[\[Xi]]\ Sinh[\[Xi]\_1])\)\ \@\(1 - 2\/\(1 + Cosh[\[Xi]]\ Cosh[\[Xi]\_1] \ + Cos[\[Theta]\_1]\ Sinh[\[Xi]]\ Sinh[\[Xi]\_1]\)\)\), \ \(-\(\(Sin[\[Theta]\_1]\ Sinh[\[Xi]]\)\/\(\((1 + Cosh[\[Xi]]\ Cosh[\[Xi]\_1] + Cos[\[Theta]\_1]\ Sinh[\[Xi]]\ Sinh[\[Xi]\_1])\)\ \@\(1 - \ 2\/\(1 + Cosh[\[Xi]]\ Cosh[\[Xi]\_1] + Cos[\[Theta]\_1]\ Sinh[\[Xi]]\ Sinh[\ \[Xi]\_1]\)\)\)\)\)}, {0, \(Sin[\[Theta]\_1]\ Sinh[\[Xi]]\)\/\(\((1 + Cosh[\ \[Xi]]\ Cosh[\[Xi]\_1] + Cos[\[Theta]\_1]\ Sinh[\[Xi]]\ Sinh[\[Xi]\_1])\)\ \@\ \(1 - 2\/\(1 + Cosh[\[Xi]]\ Cosh[\[Xi]\_1] + Cos[\[Theta]\_1]\ Sinh[\[Xi]]\ \ Sinh[\[Xi]\_1]\)\)\), \(Cos[\[Theta]\_1]\ Cosh[\[Xi]\_1]\ Sinh[\[Xi]] + Cosh[\ \[Xi]]\ Sinh[\[Xi]\_1]\)\/\(\((1 + Cosh[\[Xi]]\ Cosh[\[Xi]\_1] + Cos[\[Theta]\ \_1]\ Sinh[\[Xi]]\ Sinh[\[Xi]\_1])\)\ \@\(1 - 2\/\(1 + Cosh[\[Xi]]\ \ Cosh[\[Xi]\_1] + Cos[\[Theta]\_1]\ Sinh[\[Xi]]\ Sinh[\[Xi]\_1]\)\)\)}}\)], \ "Output", CellLabel->"Out[44]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(test . Transpose[test] // MySimplify\)], "Input", CellLabel->"In[45]:="], Cell[BoxData[ \({{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}\)], "Output", CellLabel->"Out[45]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Det[test] // MySimplify\)], "Input", CellLabel->"In[46]:="], Cell[BoxData[ \(1\)], "Output", CellLabel->"Out[46]="] }, Open ]], Cell["\<\ Unfortunately, this result is not appreciably simpler than the previous \ version. Nevertheless, \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(-\(test\[LeftDoubleBracket]2, 3\[RightDoubleBracket]\/test\[LeftDoubleBracket]2, 2\[RightDoubleBracket]\)\) // MySimplify\)], "Input", CellLabel->"In[47]:="], Cell[BoxData[ \(\(Sin[\[Theta]\_1]\ Sinh[\[Xi]]\)\/\(Cos[\[Theta]\_1]\ Cosh[\[Xi]\_1]\ \ Sinh[\[Xi]] + Cosh[\[Xi]]\ Sinh[\[Xi]\_1]\)\)], "Output", CellLabel->"Out[47]="] }, Open ]], Cell[TextData[{ "agrees with the previous ", Cell[BoxData[ \(TraditionalForm\`Tan[\[CapitalOmega]]\)]], "." }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Alternative representations", "Section"], Cell[TextData[{ "\tMany different versions of these formulas appear in the literature, but \ it is often difficult to demonstrate their equivalence symbolically. Our \ formulation has the advantage that the formulas are relatively simple, much \ simpler than others that appear in the literature, but has the disadvantage \ that ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], " must be evaluated in two steps \[LongDash] we compute ", Cell[BoxData[ \(TraditionalForm\`\[Theta]\_2\)]], " and \[CapitalOmega] separately and then combine them to obtain ", Cell[BoxData[ \(TraditionalForm\`\[Chi] = \[Theta]\_1 - \[Theta]\_2 - \[CapitalOmega]\ \)]], " \[LongDash] and it is not immediately obvious that ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], " is small for most reactions. In the remainder of this section, we \ compare our results with other representations, symbolically when possible or \ numerically when not." }], "Text"], Cell[CellGroupData[{ Cell["Comparison with Dmitrasinovic", "Subsection"], Cell["\<\ \tDmitrasinovic obtained the following formula using a somewhat different \ derivation in Phys. Rev. C 47, 2195 (1993). Here we translate his Eq. (21) \ into the present notation.\ \>", "Text"], Cell[BoxData[ \(\(\[Omega] = 2 ArcTan[\(\[Gamma]\ \[Beta]\ \(\[Gamma]\_1\) \(\[Beta]\_1\) Sin[\ \[Theta]\_1]\)\/\(\((1 + \[Gamma])\) \((1 + \[Gamma]\_1)\) + \[Gamma]\ \ \[Beta]\ \(\[Gamma]\_1\) \(\[Beta]\_1\) Cos[\[Theta]\_1]\)];\)\)], "Input", CellLabel->"In[102]:="], Cell[TextData[{ "It is difficult to prove that these two approaches give identical results, \ but after many attempts I was able to find a successful approach using ", StyleBox["Mathematica", FontSlant->"Italic"], ". Note that because ", StyleBox["Mathematica", FontSlant->"Italic"], " does not simplify expressions involving the two-argument form of ArcTan \ very well, it was necessary to replace those functions with the \ single-argument form. I have not yet checked whether this replacement has \ consequences for some argument pairs." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\((\(Tan[\[Chi] - \[Omega]] /. {\[Gamma] \[Rule] 1\/\@\(1 - \[Beta]\^2\), \[Gamma]\_1 \[Rule] 1\/\@\(1 - \[Beta]\_1\^2\)}\) /. ArcTan[x_, y_] \[Rule] ArcTan[y\/x] // TrigExpand)\) // MyFullSimplify\)], "Input", CellLabel->"In[61]:="], Cell[BoxData[ \(0\)], "Output", CellLabel->"Out[61]="] }, Open ]], Cell[TextData[{ "I have also verified numerically, using many choices of \[Beta] and ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\_1\)]], ", that these formulas agree to machine precision over the entire angular \ range when the two-argument arc tangent is retained. To ensure that possible \ quadrant problems are tested, we include both signs for ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\)]], " and values of ", Cell[BoxData[ \(TraditionalForm\`\[LeftBracketingBar]\[Beta]\[RightBracketingBar]\)]],\ " both larger and smaller than ", Cell[BoxData[ \(TraditionalForm\`\[Beta]\_1\)]], ". Therefore, even though the proof is not completely rigorous, I am \ confident that his ", Cell[BoxData[ \(TraditionalForm\`\[Omega]\)]], " is mathematically identical to our ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\)]], ". " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(diff = \ \[Chi] - \((\[Omega] /. {\[Gamma] \[Rule] 1\/\@\(1 - \[Beta]\^2\), \[Gamma]\_1 \[Rule] 1\/\@\(1 - \[Beta]\_1\^2\)})\)\)], "Input", CellLabel->"In[103]:="], Cell[BoxData[ \(\[Theta]\_1 - 2\ ArcTan[\(\[Beta]\ \[Beta]\_1\ Sin[\[Theta]\_1]\)\/\(\@\(1 - \ \[Beta]\^2\)\ \@\(1 - \[Beta]\_1\%2\)\ \((\((1 + 1\/\@\(1 - \[Beta]\^2\))\)\ \ \((1 + 1\/\@\(1 - \[Beta]\_1\%2\))\) + \(\[Beta]\ \[Beta]\_1\ \ Cos[\[Theta]\_1]\)\/\(\@\(1 - \[Beta]\^2\)\ \@\(1 - \[Beta]\_1\%2\)\))\)\)] - ArcTan[\[Beta]\_1 + \[Beta]\ Cos[\[Theta]\_1], \[Beta]\ \@\(1 - \[Beta]\ \_1\%2\)\ Sin[\[Theta]\_1]] - ArcTan[\[Beta] + \[Beta]\_1\ Cos[\[Theta]\_1], \@\(1 - \[Beta]\^2\)\ \ \[Beta]\_1\ Sin[\[Theta]\_1]]\)], "Output", CellLabel->"Out[103]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[ diff /. {\[Beta]\_1 \[Rule] 0.6, \[Beta] \[Rule] 0.3}], {\[Theta]\_1, 0, \[Pi]}];\)\)], "Input", CellLabel->"In[104]:="], 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 Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.303152 0.281549 1.13102e+015 [ [.17539 .26905 -9.5 -15.6875 ] [.17539 .26905 9.5 0 ] [.32696 .26905 -5 -15.6875 ] [.32696 .26905 5 0 ] [.47854 .26905 -9.5 -15.6875 ] [.47854 .26905 9.5 0 ] [.63011 .26905 -5 -15.6875 ] [.63011 .26905 5 0 ] [.78169 .26905 -9.5 -15.6875 ] [.78169 .26905 9.5 0 ] [.93327 .26905 -5 -15.6875 ] [.93327 .26905 5 0 ] [.01131 .05534 -57.0625 -7.84375 ] [.01131 .05534 0 7.84375 ] [.01131 .16845 -57.0625 -7.84375 ] [.01131 .16845 0 7.84375 ] [.01131 .39465 -48.375 -7.84375 ] [.01131 .39465 0 7.84375 ] [.01131 .50775 -48.375 -7.84375 ] [.01131 .50775 0 7.84375 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .28155 m .17539 .2878 L s gsave .17539 .26905 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.5) show 1.000 setlinewidth grestore .32696 .28155 m .32696 .2878 L s gsave .32696 .26905 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 1.000 setlinewidth grestore .47854 .28155 m .47854 .2878 L s gsave .47854 .26905 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.5) show 1.000 setlinewidth grestore .63011 .28155 m .63011 .2878 L s gsave .63011 .26905 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore .78169 .28155 m .78169 .2878 L s gsave .78169 .26905 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2.5) show 1.000 setlinewidth grestore .93327 .28155 m .93327 .2878 L s gsave .93327 .26905 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 1.000 setlinewidth grestore .125 Mabswid .05412 .28155 m .05412 .2853 L s .08444 .28155 m .08444 .2853 L s .11476 .28155 m .11476 .2853 L s .14507 .28155 m .14507 .2853 L s .2057 .28155 m .2057 .2853 L s .23602 .28155 m .23602 .2853 L s .26633 .28155 m .26633 .2853 L s .29665 .28155 m .29665 .2853 L s .35728 .28155 m .35728 .2853 L s .38759 .28155 m .38759 .2853 L s .41791 .28155 m .41791 .2853 L s .44822 .28155 m .44822 .2853 L s .50885 .28155 m .50885 .2853 L s .53917 .28155 m .53917 .2853 L s .56948 .28155 m .56948 .2853 L s .5998 .28155 m .5998 .2853 L s .66043 .28155 m .66043 .2853 L s .69074 .28155 m .69074 .2853 L s .72106 .28155 m .72106 .2853 L s .75138 .28155 m .75138 .2853 L s .81201 .28155 m .81201 .2853 L s .84232 .28155 m .84232 .2853 L s .87264 .28155 m .87264 .2853 L s .90295 .28155 m .90295 .2853 L s .96358 .28155 m .96358 .2853 L s .9939 .28155 m .9939 .2853 L s .25 Mabswid 0 .28155 m 1 .28155 L s .02381 .05534 m .03006 .05534 L s gsave .01131 .05534 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .16845 m .03006 .16845 L s gsave .01131 .16845 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .39465 m .03006 .39465 L s gsave .01131 .39465 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .50775 m .03006 .50775 L s gsave .01131 .50775 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .125 Mabswid .02381 .07796 m .02756 .07796 L s .02381 .10059 m .02756 .10059 L s .02381 .12321 m .02756 .12321 L s .02381 .14583 m .02756 .14583 L s .02381 .19107 m .02756 .19107 L s .02381 .21369 m .02756 .21369 L s .02381 .23631 m .02756 .23631 L s .02381 .25893 m .02756 .25893 L s .02381 .30417 m .02756 .30417 L s .02381 .32679 m .02756 .32679 L s .02381 .34941 m .02756 .34941 L s .02381 .37203 m .02756 .37203 L s .02381 .41727 m .02756 .41727 L s .02381 .43989 m .02756 .43989 L s .02381 .46251 m .02756 .46251 L s .02381 .48513 m .02756 .48513 L s .02381 .53037 m .02756 .53037 L s .02381 .55299 m .02756 .55299 L s .02381 .57561 m .02756 .57561 L s .02381 .59824 m .02756 .59824 L s .02381 .03272 m .02756 .03272 L s .02381 .0101 m .02756 .0101 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 .28155 m .02499 .28143 L .02605 .28057 L .02729 .28155 L .02846 .28008 L .02954 .28253 L .03053 .27861 L .03163 .28302 L .03279 .28498 L .03395 .27861 L .0352 .28253 L .03638 .27959 L .03746 .27959 L .03873 .28253 L .03939 .29234 L .04011 .28645 L .04141 .28155 L .04262 .28253 L .04377 .28547 L .04501 .2737 L .04618 .28057 L .04725 .29528 L .04845 .28547 L .04958 .2737 L .05081 .27566 L .0515 .2894 L .05214 .2737 L .05338 .26978 L .05409 .27566 L .05474 .26389 L .05543 .26389 L .05617 .26978 L .05682 .28155 L .05751 .29528 L .05873 .28547 L .05987 .27762 L .06111 .27566 L .06181 .2894 L .06244 .30313 L .06315 .27762 L .06391 .27566 L .06455 .28743 L .06525 .28155 L .06601 .27762 L .06683 .26389 L .0676 .28743 L .0683 .31098 L .069 .29332 L .06965 .27174 L .07037 .27959 L Mistroke .07113 .28547 L .07186 .2737 L .07254 .25408 L .07382 .26978 L .07513 .30902 L .07579 .28155 L .07651 .30117 L .07779 .26585 L .07898 .28547 L .0797 .30509 L .08038 .28155 L .08166 .25016 L .08238 .28155 L .08304 .26585 L .08377 .26585 L .08454 .28155 L .08578 .29332 L .08691 .258 L .08816 .29332 L .08946 .29724 L .0906 .24623 L .09167 .28155 L .09283 .26978 L .09407 .29332 L .09478 .29332 L .09544 .28547 L .09615 .26585 L .09691 .28547 L .09818 .30902 L .09891 .2737 L .09958 .27762 L .10082 .2894 L .10199 .29724 L .10264 .28155 L .10335 .31687 L .10458 .24231 L .10579 .29724 L .10691 .30117 L .10813 .2737 L .10942 .31687 L .11054 .258 L .11159 .27762 L .11274 .24231 L .11396 .30509 L .11466 .2737 L .1153 .23054 L .11601 .28155 L .11676 .27762 L .11801 .26585 L .11872 .30902 L Mistroke .11939 .32471 L .12064 .26193 L .12177 .29332 L .12308 .26585 L .12433 .23446 L .12501 .2894 L .12565 .34433 L .12685 .2737 L .12814 .30509 L .12887 .2894 L .12954 .31294 L .13066 .24231 L .13189 .2894 L .13317 .32079 L .13437 .25016 L .13505 .258 L .13579 .32864 L .13649 .22661 L .13714 .258 L .13836 .26585 L .13966 .26585 L .14033 .2894 L .14105 .25016 L .14236 .2894 L .14311 .26585 L .14391 .23446 L .14459 .2737 L .14533 .32079 L .14665 .258 L .14787 .2894 L .14851 .26585 L .14921 .28155 L .14994 .32079 L .15062 .258 L .15188 .32864 L .15303 .2894 L .15366 .21092 L .15436 .26585 L .15561 .258 L .15685 .22661 L .15796 .26585 L .15925 .22661 L .16046 .2894 L .16159 .29724 L .16262 .23446 L .16376 .28155 L .16495 .26585 L .16626 .17168 L .16746 .19522 L .16811 .2894 L Mistroke .16883 .32864 L .17013 .29724 L .17124 .22661 L .17243 .36003 L .17373 .23446 L .17495 .18737 L .17569 .258 L .1764 .30509 L .17772 .24231 L .17845 .30509 L .17912 .2894 L .17986 .2894 L .18065 .22661 L .18133 .31294 L .18207 .31294 L .18277 .23446 L .18341 .2894 L .18463 .28155 L .18591 .26585 L .18713 .32864 L .18782 .33649 L .18845 .15598 L .18962 .31294 L .19086 .28155 L .19197 .35218 L .19301 .32079 L .19415 .21876 L .19538 .33649 L .19661 .34433 L .19731 .35218 L .19796 .23446 L .19928 .26585 L .20001 .24231 L .20068 .18737 L .20188 .12459 L .20318 .28155 L .20441 .2737 L .20554 .36003 L .20659 .32079 L .20773 .35218 L .2088 .258 L .20978 .26585 L .21092 .32079 L .21217 .36003 L .21335 .28155 L .21444 .25016 L .21568 .30509 L .21684 .10104 L .21788 .20307 L .21901 .36003 L Mistroke .22024 .35218 L .22154 .24231 L .22265 .26585 L .22387 .21092 L .22518 .2737 L .22639 .24231 L .22769 .24231 L .22843 .32864 L .22912 .16383 L .23028 .35218 L .23154 .35218 L .23219 .20307 L .23287 .21876 L .2341 .28155 L .23521 .14028 L .2364 .34433 L .23753 .15598 L .23855 .32864 L .23975 .26585 L .24105 .32864 L .24228 .36003 L .24341 .34433 L .24462 .26585 L .24591 .15598 L .24714 .28155 L .24825 .29724 L .24956 .28155 L .2503 .21876 L .25099 .28155 L .25224 .31294 L .25288 .25016 L .25358 .25016 L .25489 .31294 L .25562 .31294 L .25629 .23446 L .25759 .37573 L .25881 .31294 L .26008 .37573 L .26079 .26585 L .26145 .23446 L .26212 .17168 L .26285 .29724 L .26362 .34433 L .26433 .25016 L .26563 .32864 L .26687 .26585 L .26798 .36003 L .26919 .23446 L .2705 .29724 L .27123 .29724 L Mistroke .27189 .28155 L .27319 .17168 L .2744 .28155 L .27553 .37573 L .27672 .25016 L .27773 .25016 L .27885 .29724 L .28004 .23446 L .28133 .26585 L .28254 .25016 L .28365 .28155 L .28494 .31294 L .28559 .25016 L .28631 .20307 L .28758 .25016 L .28878 .31294 L .28946 .18737 L .29018 .23446 L .29146 .25016 L .29218 .28155 L .29284 .21876 L .29357 .29724 L .29435 .20307 L .29567 .25016 L .2964 .25016 L .29709 .36003 L .29834 .28155 L .29897 .28155 L .29967 .29724 L .30087 .31294 L .30216 .21876 L .30338 .26585 L .30449 .21876 L .30579 .10889 L .307 .40712 L .3081 .31294 L .30928 .28155 L .31057 .29724 L .31122 .29724 L .31193 .32864 L .31319 .45421 L .31437 .28155 L .31556 .25016 L .31668 .21876 L .31769 .26585 L .31879 .29724 L .31998 .21876 L .32125 .25016 L .32233 .23446 L .32352 .25016 L Mistroke .32418 .23446 L .3249 .37573 L .32621 .23446 L .32749 .31294 L .32868 .25016 L .3294 .25016 L .33008 .23446 L .33136 .34433 L .33208 .29724 L .33274 .20307 L .33346 .25016 L .33423 .20307 L .33542 .26585 L .3367 .20307 L .33791 .20307 L .33901 .29724 L .3403 .18737 L .34103 .17168 L .34171 .28155 L .34294 .25016 L .34426 .18737 L .3454 .39142 L .34664 .21876 L .34793 .36003 L .34914 .20307 L .35028 .31294 L .35131 .31294 L .3525 .25016 L .35362 .14028 L .35484 .31294 L .35614 .32864 L .35724 .40712 L .35846 .20307 L .35977 .40712 L .3605 .29724 L .36117 .37573 L .36248 .31294 L .36371 .25016 L .36487 .26585 L .36591 .28155 L .36711 .0932 L .36825 .29724 L .3693 .36003 L .37027 .28155 L .37133 .20307 L .37245 .23446 L .37359 .32864 L .37481 .17168 L .37595 .20307 L .377 .18737 L Mistroke .37823 .15598 L .37892 .28155 L .37956 .25016 L .38074 .29724 L .38199 .29724 L .38322 .36003 L .38437 .21876 L .38557 .25016 L .38688 .29724 L .38802 .36003 L .38905 .25016 L .39025 .37573 L .39137 .20307 L .3926 .28155 L .3939 .14028 L .395 .10889 L .39622 .36003 L .39753 .36003 L .39825 .25016 L .39894 .36003 L .39957 .25016 L .40027 .31294 L .40148 .34433 L .40272 .18737 L .40389 .15598 L .40494 .28155 L .40608 .42281 L .40732 .31294 L .40863 .25016 L .40975 .29724 L .41097 .28155 L .41212 .25016 L .41317 .15598 L .41438 .43851 L .41552 .28155 L .41658 .20307 L .41756 .37573 L .41863 .17168 L .41977 .31294 L .42097 .28155 L .42228 .26585 L .42353 .32864 L .42468 .36003 L .42582 .29724 L .42685 .36003 L .42805 .18737 L .42917 .25016 L .43041 .36003 L .43171 .29724 L .43282 .23446 L Mistroke .43404 .29724 L .43535 .15598 L .43609 .29724 L .43676 .37573 L .43806 .29724 L .4393 .18737 L .44035 .29724 L .4415 .26585 L .44271 .29724 L .44385 .29724 L .44491 .26585 L .44588 .25016 L .44694 .18737 L .44806 .18737 L .4492 .36003 L .45042 .37573 L .45157 .31294 L .45261 .29724 L .45384 .26585 L .45454 .28155 L .45518 .32864 L .45635 .20307 L .4576 .15598 L .45881 .42281 L .46012 .28155 L .46137 .26585 L .46253 .39142 L .46367 .21876 L .46471 .23446 L .4659 .32864 L .46703 .20307 L .46827 .29724 L .46957 .42281 L .47068 .23446 L .4719 .39142 L .47322 .29724 L .47394 .31294 L .47463 .15598 L .47526 .21876 L .47596 .45421 L .47717 .17168 L .4783 .23446 L .47936 .40712 L .48053 .26585 L .48178 .25016 L .48303 .20307 L .48434 .04611 L .48546 .21876 L .48668 .26585 L .48784 .18737 L Mistroke .48889 .29724 L .4901 .15598 L .49124 .32864 L .4923 .29724 L .49328 .20307 L .49435 .37573 L .49548 .26585 L .49669 .25016 L .49738 .42281 L .49802 .25016 L .49918 .26585 L .50042 .40712 L .50153 .32864 L .50257 .14028 L .50371 .34433 L .50494 .4856 L .50617 .21876 L .50687 .17168 L .50752 .17168 L .50883 .29724 L .50956 .26585 L .51023 .39142 L .51143 .39142 L .51273 .34433 L .51509 .28155 L .51624 .25016 L .51748 .25016 L .51865 .21876 L .51972 .10889 L .52091 .42281 L .52205 .26585 L .52328 .32864 L .52397 .32864 L .52462 .37573 L .52577 .34433 L .52685 .17168 L .52782 .23446 L .52888 .23446 L .53003 .36003 L .53124 .29724 L .53228 .31294 L .53341 .25016 L .53472 .26585 L .53593 .39142 L .53656 .25016 L .53725 .32864 L .53798 .37573 L .53866 .28155 L .53991 .18737 L .54105 .31294 L Mistroke .5423 .20307 L .54363 .25016 L .54474 .34433 L .54593 .25016 L .54705 .15598 L .54807 .14028 L .54927 .37573 L .55057 .31294 L .5518 .14028 L .55293 .12459 L .55414 .31294 L .55544 .28155 L .55666 .12459 L .55777 .36003 L .55908 .32864 L .55982 .20307 L .56051 .18737 L .56176 .20307 L .56246 .25016 L .5631 .37573 L .56377 .21876 L .56449 .31294 L .56576 .39142 L .56647 .39142 L .56714 .31294 L .56786 .15598 L .56864 .32864 L .56931 .31294 L .57004 .39142 L .57073 .29724 L .57137 .23446 L .57257 .37573 L .57385 .31294 L .57506 .36003 L .57637 .37573 L .57753 .10889 L .57876 .40712 L .57998 .25016 L .58109 .32864 L .58221 .32864 L .58326 .34433 L .58448 .29724 L .58562 .23446 L .58681 .36003 L .58812 .40712 L .58944 .21876 L .59018 .25016 L .59085 .15598 L .59215 .18737 L .59337 .17168 L Mistroke .59442 .15598 L .59558 .31294 L .59679 .26585 L .59792 .26585 L .59898 .25016 L .59995 .23446 L .60101 .25016 L .60214 .23446 L .60328 .29724 L .60449 .36003 L .60564 .34433 L .60669 .32864 L .60792 .32864 L .60861 .17168 L .60925 .15598 L .61043 .25016 L .61167 .37573 L .61288 .32864 L .6142 .28155 L .61544 .40712 L .6166 .39142 L .61771 .40712 L .61892 .31294 L .62005 .28155 L .6211 .34433 L .62235 .29724 L .62367 .21876 L .62479 .31294 L .62601 .32864 L .62731 .18737 L .62804 .39142 L .62871 .34433 L .63001 .31294 L .63123 .36003 L .63228 .23446 L .63344 .25016 L .63465 .21876 L .63579 .12459 L .63685 .29724 L .63782 .20307 L .63889 .40712 L .64001 .21876 L .64115 .29724 L .64237 .37573 L .64352 .36003 L .64456 .32864 L .64571 .31294 L .64693 .36003 L .64764 .42281 L .64828 .21876 L Mistroke .64954 .12459 L .65073 .34433 L .65203 .17168 L .65326 .31294 L .6544 .28155 L .65558 .37573 L .65689 .26585 L .65755 .20307 L .65826 .42281 L .65954 .36003 L .66066 .28155 L .66188 .17168 L .66315 .0618 L .66434 .39142 L .66546 .29724 L .66647 .34433 L .66764 .37573 L .66875 .56408 L .66995 .29724 L .67127 .32864 L .67193 .20307 L .67265 .39142 L .67394 .23446 L .67522 .36003 L .67644 .31294 L .67753 .20307 L .67873 .42281 L .67946 .18737 L .68015 .31294 L .68145 .28155 L .68217 .26585 L .68284 .45421 L .68357 .14028 L .68434 .17168 L .68563 .12459 L .68683 .20307 L .68815 .25016 L .68888 .42281 L .68956 .14028 L .69074 .40712 L .69184 .20307 L .69306 .20307 L .69437 .37573 L .69566 .0932 L .69632 .42281 L .69703 .28155 L .6983 .21876 L .69947 .39142 L .70067 .26585 L .7018 .4699 L Mistroke .70281 .23446 L .70391 .18737 L .7051 .26585 L .70637 .29724 L .70745 .21876 L .70865 .21876 L .70931 .25016 L .71003 .26585 L .71135 .34433 L .71263 .40712 L .71382 .36003 L .71454 .42281 L .71523 .39142 L .71651 .42281 L .71722 .43851 L .71788 .37573 L .71861 .25016 L .71937 .31294 L .72057 .42281 L .72185 .37573 L .72306 .37573 L .72416 .37573 L .72545 .0618 L .72618 .28155 L .72686 .42281 L .72809 .32864 L .72941 .36003 L .73055 .21876 L .7318 .25016 L .7331 .10889 L .73431 .42281 L .73545 .20307 L .73648 .0618 L .73768 .23446 L .7388 .34433 L .74003 .26585 L .74133 .43851 L .74244 .28155 L .74366 .36003 L .74497 .36003 L .74571 .25016 L .74638 .20307 L .74768 .15598 L .74892 .0932 L .74997 .15598 L .75112 .31294 L .75233 .32864 L .75347 .36003 L .75452 .23446 L .75549 .50129 L Mistroke .75656 .25016 L .75768 .36003 L .75882 .14028 L .76003 .29724 L .76118 .28155 L .76223 .25016 L .76346 .29724 L .76415 .12459 L .76479 .14028 L .76597 .18737 L .76721 .4699 L .76842 .36003 L .76974 .4856 L .77098 .0775 L .77213 .50129 L .77328 .18737 L .77431 .10889 L .77551 .4699 L .77663 .43851 L Mfstroke .77663 .43851 m .77725 .61803 L s .77839 .61803 m .77917 .34433 L .78028 .20307 L .7815 .0932 L .78282 .51699 L .78355 .28155 L .78422 .4856 L .78553 .29724 L .78676 .258 L .7879 .35218 L .78897 .17168 L .79009 .17952 L .79132 .38357 L .79238 .21092 L .79335 .34433 L .79441 .29724 L .79553 .46205 L .79668 .05396 L .7979 .16383 L .79905 .03826 L .80009 .17168 L .80132 .56408 L .80201 .46205 L .80265 .45421 L .80383 .45421 L .80507 .14813 L .80628 .4856 L .8076 .47775 L .80885 .54053 L .81001 .26585 L .81116 .47775 L .81219 .35218 L .81339 .35218 L .81452 .24231 L .81576 .26585 L .81706 .24231 L .81817 .16383 L .8194 .258 L .82071 .60332 L .82145 .30509 L .82212 .4856 L .82343 .37573 L .82466 .50129 L .82572 .13244 L .82688 .03041 L .82809 .26585 L .82923 .60332 L .83029 .25016 L .83126 .39927 L .83238 .49345 L Mistroke .83344 .15598 L .83459 .258 L .83581 .35218 L .83696 .40712 L .838 .46205 L .83923 .0932 L .83993 .52484 L .84057 .42281 L Mfstroke .84057 .42281 m .84161 .61803 L s .84182 .61803 m .84298 .26585 L .8442 .60332 L .84489 .17952 L .84552 .4856 L .84669 .12459 L .84793 .43066 L .84904 .35218 L .85008 .38357 L .85122 .01472 L .85245 .19522 L .85369 .58762 L .85438 .36788 L .85503 .39927 L .85635 .36003 L .85708 .08535 L .85775 .20307 L .85895 .17168 L .86025 .15598 L .86148 .41497 L .86261 .32864 L s .86261 .32864 m .86356 .61803 L s .86481 .61803 m .86587 .47775 L .86685 .2737 L .86799 .14028 L .86924 .61117 L .87042 .2894 L .87151 .53269 L .87275 .32864 L .87391 .26585 L .87495 .50129 L .87608 .47775 L .87731 .31294 L .87861 .17168 L .87972 .14028 L .88094 .24231 L .88216 .2737 L .88346 .52484 L .88414 .31294 L .88488 .4699 L .8862 .52484 L .88743 .33649 L .88813 .51307 L .88876 .39142 L .88994 .15206 L .89117 .23446 L .89228 .30509 L .89332 .49737 L .89453 .43851 L .89562 .56015 L .89683 .1756 L .89814 .15206 L .89936 .52876 L .90048 .36788 L .90169 .53661 L .90299 .32864 L .90421 .51699 L .90533 .48952 L .90664 .31687 L .90738 .46205 L .90806 .32471 L .90932 .35611 L .90995 .1913 L .91065 .08535 L .91133 .52876 L .91204 .46205 L .91332 .21484 L .91403 .50522 L .91469 .35611 L .91542 .34041 L .9162 .568 L Mistroke .91687 .25016 L .9176 .21484 L .91829 .22269 L .91893 .33649 L .92013 .08142 L .92141 .03041 L .92262 .39142 L .92393 .26978 L .92517 .01864 L .92633 .42281 L .92747 .12851 L .9285 .43459 L .9297 .21876 L .93083 .4856 L .93206 .4856 L .93336 .4856 L .93447 .26585 L .93569 .35022 L .937 .5425 L .93774 .08927 L .93841 .28351 L .93972 .49345 L .94095 .11085 L .942 .35218 L .94316 .3306 L .94437 .49737 L .94551 .2168 L .94656 .44243 L .94753 .3718 L .94859 .37376 L .94972 .19718 L .95087 .46794 L .95194 .45028 L .95321 .09712 L .95437 .32962 L .95557 .22759 L .95688 .22759 L .95812 .36984 L .95926 .32668 L .96031 .40417 L .96126 .31098 L .96237 .21975 L .96342 .2325 L .96439 .11968 L .96529 .4905 L .96627 .51846 L .96732 .43851 L .96847 .12606 L .96972 .13783 L .9709 .27223 L Mistroke .97198 .23544 L .97295 .20233 L .97403 .2737 L .97515 .42379 L .97619 .31711 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[104]:=", ImageSize->{288, 177.938}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgioo`03001oogoo01=oo`03001oogoo01Aoo`00 BWoo00<007ooOol0kWoo00<007ooOol04goo00<007ooOol057oo001:Ool00`00Oomoo`3^Ool00`00 Oomoo`0COol00`00Oomoo`0DOol004Yoo`03001oogoo0>ioo`03001oogoo01=oo`03001oogoo01Ao o`00BWoo0`00igoo00<007ooOol017oo00<007ooOol04Woo0P005Woo001:Ool00`00Oomoo`3WOol0 0`00Oomoo`04Ool00`00Oomoo`0BOol2000FOol004Yoo`03001oogoo0=moo`03001oogoo00Eoo`03 001oogoo00Aoo`03001oogoo019oo`8001Ioo`003Goo1@001Goo00<007ooOol00goo00<007ooOol0 1Goo10001Goo0`006Goo00<007ooOol0ggoo00<007ooOol01Goo00<007ooOol017oo00<007ooOol0 4Woo0P005Woo000>Ool01@00Oomoogoo00001Goo00D007ooOomoo`0000Uoo`03001oogoo00Aoo`05 001oogooOol0000HOol00`00Oomoo`23Ool00`00Oomoo`1IOol00`00Oomoo`05Ool00`00Oomoo`04 Ool00`00Oomoo`0BOol2000FOol000moo`03001oogoo00Moo`03001oo`0000]oo`03001oogoo00=o o`03001oogoo009oo`03001oogoo01Eoo`03001oogoo08=oo`03001oogoo05Uoo`03001oogoo00Eo o`03001oogoo00Aoo`03001oogoo019oo`8001Ioo`000goo20001Goo00<007ooOol01goo00<007oo Ool02Woo00<007ooOol00goo00<007ooOol00Woo00<007ooOol05Goo00<007ooOol0Pgoo00<007oo Ool0FGoo00<007ooOol01Goo00<007ooOol017oo00<007ooOol04Woo0P005Woo000AOol00`00Oomo o`05Ool00`00Ool0000;Ool00`00Oomoo`03Ool00`00Oomoo`03Ool00`00Oomoo`0DOol30023Ool0 0`00Oomoo`1HOol20007Ool00`00Oomoo`04Ool00`00Oomoo`0BOol2000FOol0019oo`03001oogoo 00=oo`05001oogooOol0000;Ool00`00Oomoo`02Ool00`00Oomoo`03Ool00`00Oomoo`0DOol00`00 Oomoo`23Ool00`00Oomoo`1HOol20007Ool00`00Oomoo`04Ool00`00Oomoo`0AOol3000FOol001=o o`05001oogooOol00005Ool00`00Oomoo`08Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomo o`05Ool30004Ool20006Ool00`00Oomoo`23Ool00`00Oomoo`0aOol00`00Oomoo`0@Ool01000Oomo o`0047oo0P001goo00<007ooOol017oo00<007ooOol04Goo0`005Woo000COol00`00Oomoo`0BOol0 0`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`06Ool00`00Oomoo`02Ool01000Oomoo`001Goo 00<007ooOol0Pgoo00<007ooOol0Ool00`00Oomoo`05Ool00`00 Oomoo`0GOol00`00Oomoo`08Ool00`00Oomoo`0>Ool00`00Oomoo`0EOol00`00Oomoo`07Ool00`00 Oomoo`06Ool01000Ool000000Woo00<007ooOol017oo0P0000=oo`00Ool00Woo0P001goo00D007oo Oomoo`00009oo`<000moo`03001oo`000080009oo`8000=oo`03001oogoo00aoo`00BWoo00<007oo Ool0=Woo00<007ooOol05goo00<007ooOol03Woo00<007ooOol01Goo00<007ooOol05goo00<007oo Ool027oo00<007ooOol03Woo00<007ooOol05Goo00<007ooOol01goo00<007ooOol01Woo00@007oo 0000009oo`03001oogoo00Aoo`800003Ool007oo009oo`8000Moo`05001oogooOol00002Ool3000? Ool00`00Ool000020002Ool20003Ool01000Oomoo`002goo001:Ool3000aOol00`00Oomoo`02Ool0 0`00Oomoo`0GOol00`00Oomoo`0>Ool00`00Oomoo`05Ool00`00Oomoo`0GOol00`00Oomoo`08Ool0 0`00Oomoo`06Ool00`00Ool00005Ool00`00Oomoo`0>Ool01@00Oomoogoo00000Woo00<007ooOol0 17oo00@007ooOol000Qoo`04001oo`000002Ool20003Ool01P00Ool00000Ool000=oo`8000Moo`06 001oogooOol007oo10003goo00<007oo00000P000Woo0P000goo00@007ooOol000]oo`00BWoo00<0 07ooOol0Ool01@00 Oomoogoo00000Woo00<007ooOol00goo0`0000=oo`00Ool01goo00@007oo0000009oo`800005Ool0 07oo001oo`0200000goo001oo`02Ool20007Ool01P00Oomoogoo001oo`@0009oo`05001oogooOol0 0007Ool2000017oo000000000Woo0P000goo00<007ooOol00`002Goo001:Ool00`00Oomoo`0aOol0 0`00Oomoo`02Ool00`00Oomoo`02Ool00`00Oomoo`0BOol00`00Oomoo`0:Ool01@00Oomoogoo0000 1goo00<007ooOol05goo0P0017oo00<007ooOol00Woo00<007ooOol01Goo0P0000=oo`00Ool017oo 00<007ooOol03Woo00D007ooOomoo`00009oo`03001oogoo00=oo`<00003Ool007oo00Moo`04001o o`000002Ool200001Goo001oo`00Ool00P0000=oo`00Ool00Woo0P0000=oo`00Ool017oo00H007oo Oomoo`00Ool40002Ool01@00Oomoogoo00001goo0P0000Aoo`000000009oo`8000=oo`03001oogoo 00<000Uoo`00BWoo00<007ooOol0Ool40005Ool00`00 Oomoo`03Ool00`00Oomoo`05Ool40005Ool3000IOol00`00Oomoo`0]Ool01@00Oomoogoo000017oo 00<007ooOol00Woo0P0000=oo`00Ool047oo00<007ooOol02Woo00D007ooOomoo`0000=oo`05001o ogooOol00002Ool01000Oomoo`001Goo00<007ooOol017oo00<007ooOol00Woo00<007oo00000P00 0goo00<007ooOol00Woo00<007ooOol01Goo0P0000Eoo`00Oomoo`00009oo`03001oogoo008000Ao o`03001oogoo00Eoo`05001oogooOol00002Ool00`00Oomoo`03Ool300000goo001oo`07Ool01000 Ool000000Woo0P0000Eoo`00Ool007oo00800003Ool007oo009oo`800003Ool007oo00Aoo`06001o o`00Ool007oo1@0000=oo`00Ool00Woo00<007oo00000Woo00<007ooOol00P0000Aoo`000000009o o`8000=oo`03001oogoo00<000Uoo`003goo00<007ooOol01Woo00D007ooOomoo`0000Uoo`03001o ogoo00Aoo`05001oogooOol0000HOol00`00Oomoo`0]Ool01@00Oomoogoo000017oo00<007ooOol0 0Woo0P0000=oo`00Ool047oo00<007ooOol02Woo00D007ooOomoo`0000=oo`05001oogooOol00002 Ool01000Oomoo`001Goo00<007ooOol017oo00<007ooOol00Woo00<007oo00000P000goo00<007oo Ool00Woo00<007ooOol01Goo0P0000Eoo`00Oomoo`00009oo`03001oogoo008000Aoo`03001oogoo 00Eoo`05001oogooOol00002Ool00`00Oomoo`03Ool300000goo001oo`07Ool01000Ool000000Woo 0P0000Eoo`00Ool007oo00800003Ool007oo009oo`800003Ool007oo00Aoo`06001oo`00Ool007oo 1@0000Aoo`00Oomoo`800005Ool007ooOol00002Ool2000017oo000000000Woo0P000goo00<007oo Ool00`002Goo000@Ool00`00Oomoo`06Ool00`00Ool0000;Ool00`00Oomoo`03Ool00`00Oomoo`02 Ool00`00Oomoo`0EOol00`00Oomoo`0]Ool01@00Oomoogoo000017oo00<007ooOol00Woo0P0000=o o`00Ool047oo00<007ooOol02Woo00D007ooOomoo`0000=oo`05001oogooOol00002Ool01000Oomo o`001Goo00<007ooOol017oo00<007ooOol00Woo00<007oo00000P000goo00<007ooOol00Woo00<0 07ooOol01Goo0P0000Eoo`00Oomoo`00009oo`03001oogoo008000Aoo`03001oogoo00Eoo`05001o ogooOol00002Ool00`00Oomoo`03Ool300000goo001oo`07Ool01000Ool000000Woo0P0000Eoo`00 Ool007oo00800003Ool007oo009oo`800003Ool007oo00Aoo`06001oo`00Ool007oo1@0000Aoo`00 Oomoo`800005Ool007ooOol00002Ool2000017oo000000000Woo0P000goo00<007ooOol00`002Goo 0003Ool80005Ool00`00Oomoo`07Ool00`00Oomoo`0:Ool00`00Oomoo`03Ool00`00Oomoo`02Ool0 0`00Oomoo`0EOol00`00Oomoo`0]Ool01@00Oomoogoo000017oo00D007ooOol007oo00800003Ool0 07oo00moo`8000aoo`05001oogooOol00003Ool01@00Oomoogoo00000Woo00@007ooOol000Eoo`03 001oogoo00Aoo`03001oogoo009oo`03001oo`00008000=oo`04001oogooOol20007Ool200001Goo 001oogoo00000Woo00<007ooOol00P0017oo00<007ooOol01Goo00D007ooOomoo`00009oo`03001o ogoo00=oo`<00003Ool007oo00Moo`04001oo`000002Ool200001Goo001oo`00Ool00P0000=oo`00 Ool00Woo0P0000=oo`00Ool00Woo00P007oo001oo`00Ool007oo1@0000Aoo`00Oomoo`800003Ool0 07oo0080009oo`800004Ool000000002Ool20003Ool00`00Oomoo`030009Ool0011oo`03001oogoo 00Ioo`03001oo`0000]oo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo01Aoo`<002eoo`05 001oogooOol00004Ool01@00Oomoo`00Ool00P0000=oo`00Ool03goo0P0037oo00D007ooOomoo`00 00=oo`05001oogooOol00002Ool01000Oomoo`001Goo00<007ooOol017oo00<007ooOol00Woo00<0 07oo00000P000goo00@007ooOomoo`8000Moo`800005Ool007ooOol00002Ool00`00Oomoo`020004 Ool00`00Oomoo`05Ool01@00Oomoogoo00000Woo00<007ooOol00goo0`0000=oo`00Ool01goo00@0 07oo0000009oo`800005Ool007oo001oo`0200000goo001oo`02Ool200000goo001oo`02Ool02000 Ool007oo001oo`00Ool5000017oo001oogoo0P0000=oo`00Ool00P000Woo0P0000Aoo`000000009o o`8000=oo`03001oogoo00<000Uoo`004Goo00<007ooOol017oo00D007ooOomoo`0000]oo`03001o ogoo009oo`03001oogoo00=oo`03001oogoo01Aoo`03001oogoo02Moo`03001oogoo00=oo`05001o ogooOol00004Ool01@00Oomoo`00Ool00P0000=oo`00Ool00goo00@007ooOol000Qoo`8000Uoo`04 001oogoo0003Ool00`00Oomoo`020003Ool01000Oomoo`000Woo0P0017oo00<007ooOol017oo00<0 07ooOol00Woo00<007oo00000P000goo0P000Woo0P0000=oo`00Ool017oo0P0000Eoo`00Oomoo`00 009oo`03001oogoo008000Aoo`03001oogoo00Aoo`80009oo`80009oo`03001oogoo00=oo`<00003 Ool007oo00Moo`04001oo`000002Ool200001Goo001oo`00Ool00P0000Eoo`00Ool007oo00800003 Ool007oo009oo`08001oo`00Ool007oo001oo`D00004Ool007ooOol200000goo001oo`020002Ool2 000017oo000000000Woo0P000goo00<007ooOol00`002Goo000AOol00`00Oomoo`03Ool00`00Oomo o`03Ool00`00Oomoo`08Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`05Ool30004Ool2 0006Ool00`00Oomoo`0WOol00`00Oomoo`03Ool01@00Oomoogoo000017oo00D007ooOol007oo0080 0003Ool007oo00=oo`04001oogoo0008Ool20009Ool01000Oomoo`000goo00<007ooOol00P000goo 00@007ooOol0009oo`8000Aoo`03001oogoo00Aoo`03001oogoo009oo`03001oo`00008000=oo`80 009oo`800003Ool007oo00Aoo`800005Ool007ooOol00002Ool00`00Oomoo`020004Ool00`00Oomo o`04Ool20002Ool20002Ool00`00Oomoo`03Ool300000goo001oo`07Ool01000Ool000000Woo0P00 00Eoo`00Ool007oo00800005Ool007oo001oo`0200000goo001oo`02Ool02000Ool007oo001oo`00 Ool5000017oo001oogoo0P0000=oo`00Ool00P000Woo0P0000Aoo`000000009oo`8000=oo`03001o ogoo00<000Uoo`004Goo00<007ooOol057oo00<007ooOol00goo00<007ooOol00Woo00<007ooOol0 1Woo00<007ooOol00Woo00@007ooOol000Eoo`03001oogoo02Moo`03001oogoo00=oo`05001oogoo Ool00004Ool01@00Oomoo`00Ool00P0000=oo`00Ool00goo00@007ooOol000Qoo`8000Uoo`04001o ogoo0003Ool00`00Oomoo`020003Ool01000Oomoo`000Woo0P0017oo00<007ooOol00goo0P0017oo 00<007oo00000P000goo0P000Woo0P0000=oo`00Ool017oo0P0000Eoo`00Oomoo`00009oo`03001o ogoo008000Aoo`03001oogoo00Aoo`80009oo`80009oo`03001oogoo00=oo`<00003Ool007oo00Mo o`04001oo`000002Ool200001Goo001oo`00Ool00P0000Eoo`00Ool007oo00800003Ool007oo009o o`06001oo`00Ool007oo1`0000Aoo`00Oomoo`800003Ool007oo0080009oo`800004Ool000000002 Ool20003Ool00`00Oomoo`030009Ool0019oo`03001oogoo01Aoo`03001oogoo00=oo`04001oogoo Ool60004Ool01@00Oomoogoo00000goo00<007ooOol00Woo00<007ooOol09goo00<007ooOol00goo 00D007ooOomoo`0000Aoo`05001oogoo001oo`0200000goo001oo`03Ool01000Oomoo`0027oo0P00 2Goo00@007ooOol000=oo`03001oogoo008000=oo`04001oogoo0002Ool20004Ool00`00Oomoo`03 Ool20004Ool00`00Ool000020003Ool20002Ool200000goo001oo`04Ool200001Goo001oogoo0000 0Woo00<007ooOol00P0017oo00<007ooOol017oo0P000Woo0P000Woo00<007ooOol00goo0`0000=o o`00Ool01goo10000Woo0P0000Eoo`00Ool007oo00800005Ool007oo001oo`0200000goo001oo`02 Ool01P00Ool007oo001oo`L00004Ool007ooOol200000goo001oo`020002Ool2000017oo00000000 0Woo0P000goo00<007ooOol00`002Goo000AOol2000EOol20006Ool3000:Ool01@00Oomoogoo0000 0goo00<007ooOol00Woo00<007ooOol09goo00<007oo00000goo00D007ooOomoo`0000Aoo`05001o ogoo001oo`0200000goo001oo`03Ool01000Oomoo`0017oo00@007ooOomoo`8000Uoo`800003Ool0 07oo009oo`03001oogoo008000=oo`04001oogoo0002Ool20002Ool01000Ool000000Woo00@007oo 000000Aoo`03001oo`00008000=oo`80009oo`800003Ool007oo009oo`05001oo`00001oo`020000 1Goo001oogoo00000Woo0P0017oo00<007ooOol00Woo00@007oo0000009oo`80009oo`03001oogoo 009oo`@00004Ool007oo0006Ool40002Ool200001Goo001oo`00Ool00P0000Eoo`00Ool007oo0080 0003Ool007oo009oo`06001oo`00Ool007oo1`0000Aoo`00Oomoo`800003Ool007oo0080009oo`80 0004Ool000000002Ool20003Ool00`00Oomoo`030009Ool003eoo`05001oogooOol00003Ool00`00 Oomoo`02Ool3000WOol00`00Ool00003Ool01@00Oomoogoo000017oo00D007ooOol007oo00800003 Ool007oo00=oo`04001oogoo0004Ool01000Oomoogoo0P002Goo0P0000=oo`00Ool00Woo00<007oo Ool00P000goo00@007ooOol0009oo`80009oo`04001oo`000002Ool01000Ool0000017oo00<007oo 00000P000goo0P000Woo0P0000=oo`00Ool00Woo00D007oo000007oo00800005Ool007ooOol00002 Ool20004Ool00`00Oomoo`02Ool01000Ool000000Woo0P000Woo00<007ooOol00Woo100000Aoo`00 Ool000Ioo`@0009oo`800005Ool007oo001oo`0200001Goo001oo`00Ool00P0000=oo`00Ool00Woo 00H007oo001oo`00Ool7000017oo001oogoo0P0000=oo`00Ool00P000Woo0P0000Aoo`000000009o o`8000=oo`03001oogoo00<000Uoo`00?Goo00<007ooOol00Woo0`001Goo00<007ooOol09goo00<0 07oo00000goo00D007ooOomoo`0000Aoo`05001oogoo001oo`0200000goo001oo`03Ool01000Oomo o`0017oo00@007ooOomoo`8000Uoo`800003Ool007oo009oo`03001oogoo008000=oo`04001oogoo 0002Ool20002Ool01000Ool000000Woo00@007oo000000Aoo`03001oo`00008000=oo`80009oo`80 0003Ool007oo009oo`05001oo`00001oo`0200001Goo001oogoo00000Woo0P0017oo00<007ooOol0 0Woo00@007oo0000009oo`80009oo`03001oogoo009oo`@00004Ool007oo0006Ool40002Ool20000 1Goo001oo`00Ool00P0000Eoo`00Ool007oo00800003Ool007oo009oo`06001oo`00Ool007oo1`00 00Aoo`00Oomoo`800003Ool000000080009oo`800004Ool000000002Ool20003Ool00`00Oomoo`03 0009Ool003ioo`03001oogoo009oo`03001oogoo00Aoo`03001oogoo02Moo`03001oo`0000=oo`05 001oogooOol00004Ool01@00Oomoo`00Ool00P0000=oo`00Ool00goo00@007ooOol000Aoo`04001o ogooOol20009Ool200000goo001oo`02Ool200000goo00000003Ool01000Oomoo`000Woo0P000Woo 00@007oo0000009oo`04001oo`000004Ool00`00Ool000020003Ool20002Ool200000goo001oo`02 Ool01@00Ool00000Ool00P0000Eoo`00Oomoo`00009oo`8000Aoo`03001oogoo009oo`04001oo`00 0002Ool20002Ool00`00Oomoo`02Ool4000017oo001oo`001Woo10000Woo0P0000Eoo`00Ool007oo 00800005Ool007oo001oo`0200000goo001oo`02Ool01P00Ool007oo001oo`L00004Ool007ooOol2 00000goo000000020002Ool2000017oo000000000Woo0P000Woo0P000Woo0`002Goo000mOol20005 Ool20004Ool00`00Oomoo`0WOol00`00Ool00003Ool01@00Oomoogoo000017oo00D007ooOol007oo 00800003Ool007oo00=oo`04001oogoo0004Ool01000Oomoogoo0P002Goo0P0000=oo`00Ool00Woo 0P0000=oo`0000000goo00@007ooOol0009oo`80009oo`04001oo`000002Ool01000Ool0000017oo 00<007oo00000P000goo0P000Woo0P0000=oo`00Ool00Woo00D007oo000007oo00800005Ool007oo Ool00002Ool20004Ool00`00Oomoo`02Ool01000Ool000000Woo0P000Woo00<007ooOol00Woo1000 00Aoo`00Ool000Ioo`@0009oo`800005Ool007oo001oo`0200001Goo001oo`00Ool00P0000=oo`00 Ool00Woo00H007oo001oo`00Ool7000017oo001oogoo0P0000=oo`0000000P000Woo0P0000Aoo`00 0000009oo`80009oo`80009oo`<000Uoo`00BWoo00<007ooOol09goo00<007oo00000goo00@007oo Oomoo`80009oo`80009oo`@00003Ool007oo00=oo`04001oogoo0003Ool30002Ool20006Ool70000 0goo001oo`050002Ool20002Ool00`00Ool000020002Ool01000Ool000000Woo00H007oo000007oo 0002Ool60002Ool20002Ool200000goo001oo`02Ool700001Goo001oogoo00000Woo0P0017oo00<0 07ooOol00Woo00@007oo0000009oo`800003Ool00000009oo`03001oo`0000D00003Ool007oo00Eo o`@0009oo`800005Ool007oo001oo`0200001Goo001oo`00Ool00P0000Aoo`00Oomoo`800005Ool0 07oo001oo`07000017oo001oogoo0P0000=oo`0000000P000Woo0P0000Aoo`000000009oo`80009o o`80009oo`@000Qoo`00BWoo00<007ooOol09goo00<007oo00000goo00@007ooOomoo`80009oo`80 009oo`@00003Ool007oo00=oo`04001oogoo0003Ool30002Ool20006Ool700000goo001oo`050002 Ool20002Ool00`00Ool000020002Ool01000Ool000000Woo00H007oo000007oo0002Ool60002Ool2 0002Ool200000goo001oo`02Ool700001Goo001oogoo00000Woo0P0017oo00<007ooOol00Woo00@0 07oo0000009oo`800003Ool00000009oo`03001oo`0000D00003Ool007oo00Eoo`@0009oo`800005 Ool007oo001oo`0200001Goo001oo`00Ool00P0000Aoo`00Oomoo`800005Ool007oo001oo`070000 17oo001oogoo0P0000=oo`0000000P000Woo0P0000Aoo`000000009oo`80009oo`80009oo`@000Qo o`00BWoo00<007ooOol08goo00L007ooOomoo`00Ool00003Ool01000Oomoogoo0P000Woo0P0000=o o`0000000`0000=oo`00Ool00goo00@007ooOol000=oo`<0009oo`8000Ioo`L00003Ool007oo00D0 009oo`80009oo`03001oo`000080009oo`04001oo`000002Ool01P00Ool00000Ool0009oo`H0009o o`80009oo`800003Ool007oo009oo`L00005Ool007ooOol00002Ool20004Ool00`00Oomoo`02Ool0 1000Ool000000Woo0P0000=oo`0000000Woo00<007oo00001@0000=oo`00Ool01Goo10000Woo0P00 00Eoo`00Ool007oo00800003Ool007oo00@00004Ool007ooOol200001Goo001oo`00Ool01`0000Ao o`00Oomoo`800003Ool000000080009oo`800004Ool000000002Ool20002Ool20002Ool40008Ool0 04Yoo`<002=oo`07001oogooOol007oo00000goo00@007ooOomoo`80009oo`800003Ool0000000<0 0003Ool007oo00=oo`04001oogoo0003Ool30002Ool20006Ool700000goo001oo`050002Ool20002 Ool00`00Ool000020002Ool01000Ool000000Woo00H007oo000007oo0002Ool60002Ool20002Ool2 00000goo001oo`02Ool700001Goo001oogoo00000Woo0P0017oo00<007ooOol00Woo00@007oo0000 009oo`800003Ool00000009oo`03001oo`0000D00003Ool007oo00Eoo`@0009oo`800005Ool007oo 001oo`0200000goo001oo`04000017oo001oogoo0P0000Eoo`00Ool007oo00L00004Ool007ooOol2 00000goo000000020002Ool2000017oo000000000Woo0P000Woo0P000Woo100027oo001:Ool00`00 Oomoo`0SOol01`00Oomoogoo001oo`0000=oo`04001oogooOol20002Ool200000goo000000030000 0goo001oo`03Ool01000Oomoo`000goo0`000Woo0P001Woo1`0000=oo`00Ool01@000Woo0P000Woo 00<007oo00000P000Woo00@007oo0000009oo`06001oo`00001oo`000Woo1P000Woo0P000Woo0P00 00=oo`00Ool00Woo1`0000Eoo`00Oomoo`00009oo`8000Aoo`03001oogoo009oo`04001oo`000002 Ool200000goo00000002Ool00`00Ool0000500000goo001oo`05Ool40002Ool200001Goo001oo`00 Ool00P0000=oo`00Ool0100000Aoo`00Oomoo`800005Ool007oo001oo`07000017oo001oogoo0P00 00=oo`0000000P000Woo0P0000Aoo`000000009oo`800004Ool000000002Ool40008Ool004Yoo`03 001oogoo029oo`<0009oo`<000=oo`H0009oo`800003Ool0000000<00003Ool0000000=oo`04001o ogoo0003Ool3000017oo000000000Woo2`0000=oo`00Ool01P0000=oo`0000000Woo00<007oo0000 0P000Woo00D007oo000007oo00L00003Ool0000000T0009oo`800003Ool007oo009oo`T0009oo`03 001oogoo008000Aoo`03001oo`0000L00004Ool00000Ool20002Ool00`00Ool000090003Ool50002 Ool600000goo0000000200000goo000000040002Ool200001Goo001oo`00Ool01`0000Aoo`00Oomo o`800003Ool000000080009oo`800003Ool0000000800004Ool00000Ool30002Ool40008Ool004Yo o`03001oogoo025oo`08001oo`00Ool007oo001oo`80009oo`04001oo`00Ool20002Ool200000goo 0000000300000goo00000003Ool01000Oomoo`000goo0`0000Aoo`000000009oo`80009oo`L00003 Ool007oo00H00003Ool00000009oo`03001oo`000080009oo`05001oo`00001oo`070002Ool60002 Ool20002Ool200000goo001oo`02Ool90002Ool00`00Oomoo`020004Ool00`00Oomoo`0300001Goo 00000000Ool00P0000=oo`0000000Woo00<007oo00002@000goo1@000Woo2@0000=oo`00Ool01000 00Aoo`00001oo`800005Ool007oo001oo`07000017oo001oogoo0P0000=oo`0000000P000Woo0P00 00=oo`0000001@0000Aoo`000000009oo`@000Qoo`00BWoo00<007ooOol07Woo00D007ooOol007oo 00T00005Ool007oo001oo`020002Ool200000goo0000000300000goo00000003Ool01000Oomoo`00 0goo1`000Woo0`0000=oo`0000001`0000=oo`000000100000=oo`0000000Woo00<007oo00000P00 0Woo00D007oo000007oo00800003Ool000000080009oo`H0009oo`80009oo`800003Ool007oo009o o`T0009oo`03001oogoo008000Aoo`04001oogooOol200001Goo00000000Ool00P0000Moo`000000 07oo001oo`0200000goo000000050003Ool50002Ool200001Goo00000000Ool00P0000=oo`00Ool0 100000=oo`00Ool00`0000Eoo`00Ool007oo00L00004Ool007ooOol200000goo000000020002Ool2 00000goo00000002000017oo000007oo100000=oo`0000000P0027oo001:Ool00`00Oomoo`0HOol0 0`00Oomoo`03Ool01@00Oomoo`00Ool02@0000Eoo`00Ool007oo0080009oo`800003Ool0000000<0 0003Ool0000000=oo`04001oogoo0003Ool70002Ool300000goo0000000700000goo000000040000 0goo00000002Ool00`00Ool000020002Ool01@00Ool00000Ool00P0000=oo`0000000P000Woo1P00 0Woo0P000Woo0P0000=oo`00Ool00Woo2@000Woo00<007ooOol00P0017oo00@007ooOomoo`800005 Ool00000001oo`0200001goo00000000Ool007oo00800003Ool0000000D000=oo`D0009oo`800005 Ool00000001oo`0200000goo001oo`0400000goo001oo`0300001Goo001oo`00Ool01`0000Aoo`00 Oomoo`800003Ool000000080009oo`800003Ool0000000800003Ool0000000D00003Ool000000080 00Qoo`00BWoo00<007ooOol067oo00@007ooOol0009oo`05001oo`00001oo`0@0002Ool200000goo 00000003000027oo000007oo001oo`00Ool200000goo001oo`070002Ool300000goo000000070000 0goo0000000400000goo00000002Ool00`00Ool000020002Ool4000017oo000007oo30000Woo0`00 00Eoo`00001oo`00009oo`/00003Ool007oo00800006Ool00000001oo`000goo1P0000Aoo`00001o o`<00003Ool0000000800003Ool0000000D000=oo`D0009oo`H00006Ool00000Ool007oo100000=o o`00Ool00`0000Eoo`00Ool007oo00L00004Ool007ooOol200000goo000000020002Ool700000goo 0000000500000goo000000020008Ool004Yoo`<001Qoo`04001oogoo0002Ool01@00Ool00000Ool0 40000Woo200000Qoo`00001oo`00Ool007oo0P0000=oo`00Ool01`0000=oo`000000300000=oo`00 0000200000=oo`00Ool00`000Woo100000Aoo`00001oo``00003Ool0000000800005Ool00000Ool0 0002Ool;00000goo001oo`0200001Woo00000000Ool000=oo`800005Ool00000001oo`0200001Goo 00000000Ool0100000=oo`0000001@000goo1@000Woo2@0000=oo`00Ool0100000Aoo`00001oo`80 0005Ool007oo001oo`07000017oo001oogoo0P0000=oo`0000000P000Woo3`0000=oo`0000000P00 27oo001:Ool00`00Oomoo`0EOol01000Ool000000Woo00L007oo000007oo001oo`0A0002Ool80000 27oo000007oo001oo`00Ool200000goo001oo`0700000goo0000000<00000goo0000000800000goo 001oo`030002Ool700000goo0000000?00001Goo000007oo00000Woo2`0000=oo`00Ool00P0000Io o`00000007oo0003Ool200001Goo00000000Ool00P0000Eoo`00000007oo00@00003Ool0000000D0 00=oo`D0009oo`H00006Ool00000Ool007oo1P000Woo0P0000Eoo`00Ool007oo00L00004Ool007oo Ool200000goo000000020002Ool700000goo0000000500000goo000000020008Ool004Yoo`03001o ogoo01Eoo`04001oo`000002Ool01`00Ool00000Ool007oo0140009oo`P00008Ool00000Ool007oo 001oo`800003Ool007oo00L00003Ool0000000`00003Ool0000000P00003Ool007oo00@00003Ool0 000000D00003Ool0000000X00003Ool0000000800005Ool00000Ool00002Ool=000017oo000007oo 0`0000=oo`00Ool00Woo0P0000Eoo`00000007oo00H00003Ool0000000800003Ool0000000D000=o o`D0009oo`H00006Ool00000Ool007oo100000Aoo`00Oomoo`800005Ool007oo001oo`07000017oo 001oogoo0P0000=oo`0000000P000Woo1`0000=oo`0000001@0000=oo`0000000P0027oo001:Ool0 0`00Oomoo`0AOol01P00Oomoogoo001oo`80009oo`06001oo`00001oo`000Woo40000Woo200000Qo o`00001oo`00Ool007oo0P0000=oo`00Ool01`0000=oo`000000300000=oo`000000200000=oo`00 Ool0100000=oo`0000001@0000=oo`0000002P0000=oo`0000000P0000Eoo`00001oo`00009oo`d0 0004Ool00000Ool300000goo001oo`02Ool200001Goo00000000Ool01P0000=oo`0000000P0000=o o`0000001@000goo1@000Woo1P0000Ioo`00001oo`00Ool4000017oo001oogoo0P0000Eoo`00Ool0 07oo00L00004Ool007ooOol200000goo000000020002Ool700000goo0000000500000goo00000002 0008Ool004Yoo`03001oogoo00ioo`04001oogoo0003Ool01@00Ool00000Ool00P0000Eoo`00001o o`00009ooa400003Ool0000000H00003Ool0000000@00003Ool0000000X00003Ool0000001000003 Ool0000000/00003Ool0000000D00003Ool0000000l00006Ool00000Ool007oo3P0000Aoo`00001o o`D000=oo`H00003Ool0000000@00003Ool0000000800003Ool0000000D0009oo`H0009oo`T00003 Ool007oo00@00003Ool0000000<00005Ool00000001oo`07000017oo001oogoo0P0000=oo`000000 0P000Woo3`0000=oo`0000000P0027oo001:Ool00`00Oomoo`0000017oo000007oo1@000goo0P0000Eoo`00000007oo00H00003Ool0000000800003 Ool0000000D0009oo`H0009oo`H00006Ool00000Ool007oo100000Aoo`00Oomoo`800005Ool00000 001oo`07000017oo001oogoo0P0000=oo`0000000P000Woo1`0000=oo`0000001@0000=oo`000000 0P0027oo001:Ool3000000017oo 000007oo1@000goo0P0000Eoo`00000007oo00H00003Ool0000000800003Ool0000000D0009oo`H0 009oo`H00004Ool00000Ool6000017oo001oogoo0P0000Eoo`00000007oo00L00004Ool007ooOol2 00000goo000000020002Ool700000goo0000000500000goo000000020008Ool004Yoo`03001oogoo 00aoo`04001oo`00Ool20003Ool01@00Ool00000Ool00P0000=oo`0000001@0000=oo`0000005P00 00=oo`000000100000=oo`0000002P0000Aoo`00001oo`l00003Ool0000000/00003Ool0000000D0 0003Ool0000000H00003Ool0000000H00006Ool00000Ool007oo3P0000Aoo`00001oo`D000=oo`80 0005Ool00000001oo`0600000goo0000000200000goo000000050002Ool60002Ool6000017oo0000 07oo1P0000Aoo`00Oomoo`800005Ool00000001oo`07000017oo001oogoo0P0000=oo`0000000P00 0Woo1`0000=oo`0000001@0000=oo`0000000P0027oo001:Ool00`00Oomoo`06Ool20002Ool80000 1Goo001oo`00Ool01@0000=oo`0000001@0000=oo`0000005P0000=oo`0000004@0000Aoo`00001o o`l00003Ool0000000/00003Ool0000000D00003Ool0000000H00003Ool0000000H00006Ool00000 Ool007oo3P0000Aoo`00001oo`D000=oo`800005Ool00000001oo`0600000goo0000000200000goo 000000050002Ool700000goo00000004000017oo000007oo1P0000Aoo`00001oo`800005Ool00000 001oo`0700000goo001oo`0300000goo000000020002OolD0008Ool004Yoo`03001oogoo00Ioo`80 009oo`X00003Ool007oo00D00003Ool0000000D00003Ool0000000X00003Ool0000000T00003Ool0 000000l00003Ool007oo00800005Ool00000001oo`0;00000goo0000000;00000goo000000050000 0goo000000060002Ool800001Goo001oo`00Ool03P0000Ioo`00001oo`00Ool30003Ool200001Goo 00000000Ool01P0000=oo`0000000P0000=oo`0000001@000Woo1`0000=oo`000000100000Aoo`00 001oo`H00004Ool00000Ool200001Goo00000000Ool01`0000=oo`00Ool00`0000=oo`0000000P00 0Woo500027oo001:Ool00`00Oomoo`06Ool20002Ool:00000goo001oo`0500000goo000000050000 0goo0000000:00000goo0000000900000goo0000000?00000goo001oo`0200001Goo00000000Ool0 2`0000=oo`0000002`0000=oo`0000001@0000=oo`0000001P000Woo200000Eoo`00Ool007oo00h0 0006Ool00000Ool007oo0`000goo0P0000Eoo`00000007oo00H00003Ool0000000800003Ool00000 00D0009oo`L00003Ool0000000@00004Ool00000Ool6000017oo000007oo0P0000Eoo`00000007oo 00L00003Ool007oo00<00003Ool000000080009ooa@000Qoo`00BWoo00<007ooOol017oo400000=o o`0000001@0000=oo`0000001@0000=oo`0000002P0000=oo`0000002@0000=oo`0000003`0000=o o`00Ool00P0000Eoo`00000007oo00/00003Ool0000000/00003Ool0000000D00003Ool0000000H0 009oo`P00005Ool007oo001oo`0>00001Woo000007oo001oo`<000=oo`800005Ool00000001oo`06 00000goo0000000200000goo000000050002Ool700000goo0000000400000goo00000007000017oo 000007oo0P0000Eoo`00000007oo00L00003Ool007oo00<00003Ool000000080009ooa800003Ool0 07oo00Moo`00BWoo00<007oo00000P000Woo800000=oo`0000002P0000=oo`000000100000=oo`00 00000P0000=oo`0000003`0000=oo`00Ool00P0000Eoo`00000007oo00/00003Ool0000000/00003 Ool0000000D00003Ool0000000H0009oo`P00005Ool007oo001oo`0>00001Woo000007oo001oo`<0 00=oo`800005Ool00000001oo`0600000goo0000000200000goo000000050002Ool700000goo0000 000400000goo00000007000017oo000007oo0P0000=oo`0000002@0000=oo`00Ool00`0000=oo`00 00000P000Woo4P0000=oo`00Ool01goo0014Oooo000U000004Yoo`05001oogoo001oo`0R00000goo 0000000:00000goo0000000400000goo0000000200000goo0000000:00000goo0000000200000goo 0000000200001goo00000000Ool007oo00H00004Ool00000Ool400000goo0000000600000goo0000 000>0002Ool800000goo001oo`0@000017oo000007oo1P0000=oo`0000001@0000=oo`0000001000 00=oo`0000000P0000=oo`0000001@000Woo3P0000=oo`0000001`0000=oo`0000000`0000=oo`00 00002@0000=oo`0000000`0000=oo`0000000`0000=oo`000000400000=oo`00Ool017oo0@000Goo 0Goo001:Ool00`00Oomoo`02Ool00`00Ool0000B00000goo0000000:00000goo0000000:00000goo 0000000400000goo0000000200000goo0000000:00000goo0000000200000goo0000000200001goo 00000000Ool007oo00H00004Ool00000Ool400000goo0000000600000goo0000000>0002Ool80000 0goo001oo`0@00001Woo000007oo001oo`@00003Ool0000000D00003Ool0000000@00003Ool00000 00800003Ool0000000D0009oo`h00003Ool0000000L00004Ool00000Ool200000goo000000090000 0goo0000000300000goo000000020002OolB00000goo001oo`07Ool004Yoo`03001oogoo009oo`03 001oo`00009oo`03001oo`0000d00003Ool0000000D0009oo`<0009oo`/00003Ool0000000@00003 Ool0000000800003Ool0000000X00003Ool0000000800003Ool0000000800007Ool00000001oo`00 Ool01P0000Aoo`00001oo`@00003Ool0000000H00003Ool0000000h0009oo`P00003Ool007oo01<0 0003Ool007oo00@00005Ool00000001oo`0300000goo0000000400000goo0000000200000goo0000 00050002Ool>00000goo00000007000017oo000007oo0P0000=oo`0000002@0000=oo`0000000`00 00=oo`0000000P000Woo4P0000=oo`00Ool01goo001:Ool00`00Oomoo`04Ool01@00Oomoo`00Ool0 1P000Woo00<007oo00000`0000Aoo`00001oo`@0009oo`<0009oo`/00003Ool0000000@00003Ool0 000000800003Ool0000000X00003Ool0000000800003Ool0000000800007Ool00000001oo`00Ool0 1P0000Aoo`00001oo`@00003Ool0000001L0009oo`P00003Ool007oo01<00003Ool007oo00@00005 Ool00000001oo`0300000goo0000000900000goo000000050002Ool>00000goo0000000700001goo 00000000Ool007oo00/00003Ool0000000<00003Ool000000080009ooa800003Ool007oo00Moo`00 BWoo00<007ooOol02Goo1P0017oo00D007oo000007oo00800003Ool000000080009oo`<000=oo`X0 0003Ool0000000@00003Ool0000000@00003Ool0000000H00005Ool007oo001oo`02000017oo0000 00000Woo0`000goo1P0000=oo`0000000Woo0`0000=oo`0000000P0000=oo`0000001P000Woo2P00 0Woo200000=oo`0000004`0000=oo`00Ool0100000=oo`0000000P0000Aoo`00001oo`/00003Ool0 000000<00004Ool007ooOol<00000goo001oo`0900001goo00000000Ool007oo00/00003Ool00000 00<00003Ool000000080009ooa800003Ool007oo00Moo`00BWoo0`002Goo0P0000Aoo`00000000Ao o`05001oo`00001oo`0200000goo000000020002Ool30003Ool:00000goo0000000400000goo0000 000400000goo0000000600001Goo001oo`00Ool00P0000Aoo`000000009oo`<000=oo`H00003Ool0 0000009oo`<00003Ool0000000800003Ool0000000H0009oo`X0009oo`P00003Ool0000001<00003 Ool007oo00@00003Ool0000000800004Ool00000Ool;00000goo00000003000017oo001oogoo3000 00=oo`00Ool03@0000=oo`00Ool02`0000=oo`0000000`0000=oo`0000000P000Woo4P0000=oo`00 Ool01goo001:Ool00`00Oomoo`0:Ool01@00Ool007oo000017oo00D007oo000007oo00800003Ool0 00000080009oo`<000=oo`X00003Ool0000000@00003Ool0000000<0009oo`P00005Ool007oo001o o`02000017oo000000000Woo0`000goo1P0000=oo`0000000Woo0`0000=oo`0000000P0000=oo`00 00001P000Woo2P000Woo200000=oo`0000004`0000=oo`00Ool0100000=oo`0000000P0000Aoo`00 001oo`/00003Ool0000000<0009oo`03001oo`0000L00007Ool00000001oo`00Ool03@0000=oo`00 00002`0000=oo`0000000`0000=oo`0000000P000Woo4P0000=oo`00Ool01goo001:Ool00`00Oomo o`0:Ool00`00Ool00006Ool01000Ool000000Woo00<007oo00000`000Woo0`0017oo0P0000=oo`00 0000100000=oo`000000100000=oo`0000000`000Woo200000Eoo`00Ool007oo00800004Ool00000 0002Ool30003Ool600000goo00000002Ool300000goo0000000200000goo000000060002Ool:0002 Ool800000goo0000000C00000goo001oo`0400000goo00000002000017oo000007oo2`0000=oo`00 00000`000Woo00<007oo00001`0000Moo`00000007oo001oo`0=00000goo0000000;00000goo0000 000300000goo000000020002OolB00000goo001oo`07Ool004Yoo`03001oogoo01Eoo`80009oo`03 001oo`0000<0009oo`<000Aoo`800003Ool0000000@00003Ool0000000@00003Ool0000000<0009o o`P00005Ool007oo001oo`02000017oo000000000Woo0`000goo1P0000=oo`0000000Woo0`0000=o o`0000000P0000=oo`0000001P000Woo2P000Woo200000=oo`0000004`0000=oo`00Ool00P0000=o o`00Ool0100000=oo`000000300000=oo`0000000`000Woo1`0000Aoo`00001oo`<00003Ool007oo 00d00003Ool0000000/00003Ool0000000P0009ooa800003Ool007oo00Moo`00BWoo00<007ooOol0 5Goo0P000Woo00@007oo001oo`80009oo`<000Aoo`8000=oo`@00003Ool0000000@00003Ool00000 00<000=oo`L000Eoo`03001oogoo00<0009oo`03001oo`0000=oo`800005Ool00000001oo`020002 Ool300000goo00000002000017oo000007oo1@000Woo2P000Woo200000=oo`000000100000Eoo`00 000007oo00X000=oo`800003Ool007oo00@00003Ool0000000`00003Ool0000000<0009oo`L00004 Ool00000Ool300000goo001oo`0=00000goo0000000;00000goo0000000800000goo0000000A0000 0goo00000007Ool004Yoo`03001oogoo01Uoo`04001oo`00Ool20002Ool30004Ool20003Ool40000 0goo0000000400000goo000000030003Ool70005Ool00`00Oomoo`030002Ool00`00Ool00003Ool2 00001Goo00000000Ool00P000Woo0`0000=oo`0000000P0000Aoo`00001oo`D0009oo`X0009oo`P0 0003Ool0000000@00005Ool00000001oo`0:0003Ool200000goo001oo`0400000goo0000000<0000 0goo000000030002Ool7000017oo000007oo0`0000=oo`00Ool03@0000=oo`0000002`0000=oo`00 0000200000=oo`0000004@0000=oo`0000001goo001:Ool00`00Oomoo`0IOol00`00Ool00002Ool0 0`00Oomoo`02Ool00`00Oomoo`02Ool20003Ool400001Goo00000000Ool00P0000=oo`0000000`00 0goo1`001Goo00<007ooOol00`000Woo00<007oo00000goo0P0000Eoo`00000007oo0080009oo`<0 0003Ool0000000800004Ool00000Ool50002Ool:0002Ool800000goo0000000400001Goo00000000 Ool02P000goo0P0000Eoo`00Ool007oo00800003Ool0000000D00003Ool0000000@00003Ool00000 00<0009oo`L00004Ool00000Ool300000goo001oo`0=00000goo0000000;00000goo000000080000 0goo0000000A00000goo00000007Ool004Yoo`<001]oo`04001oogoo0004Ool00`00Oomoo`02Ool2 0003Ool400001Goo00000000Ool00P0000=oo`0000000`000goo1`001Goo00<007ooOol00`000Woo 00<007oo00000goo0P0000Eoo`00000007oo0080009oo`<00003Ool0000000800004Ool00000Ool5 0002Ool:0002Ool800000goo0000000400001Goo00000000Ool02P000goo0P0000Eoo`00Ool007oo 00800003Ool0000000D00003Ool0000000@00003Ool0000000<0009oo`L00004Ool00000Ool30000 0goo001oo`0=00000goo0000000;00000goo0000000800000goo0000000A00000goo00000007Ool0 04Yoo`03001oogoo01]oo`04001oogoo0004Ool00`00Oomoo`02Ool20003Ool400001Goo00000000 Ool00P0000=oo`0000000`000goo1@0000=oo`00Ool017oo00<007ooOol00`000Woo00<007oo0000 0goo0P0000Eoo`00000007oo0080009oo`<00003Ool0000000800004Ool00000Ool50002Ool:0002 Ool800000goo0000000400001Goo00000000Ool02P000goo0P0000Eoo`00Ool007oo00800003Ool0 000000D00003Ool0000000@00003Ool0000000<0009oo`L00004Ool00000Ool30002Ool>00000goo 0000000Z00000goo00000007Ool004Yoo`03001oogoo01]oo`03001oogoo00]oo`04001oogooOol4 00001Goo00000000Ool00P000Woo0P0000=oo`00Ool00Woo0`0000Aoo`00Ool000Eoo`03001oogoo 00<0009oo`03001oo`0000=oo`800006Ool00000001oo`000goo0`0000=oo`0000000P0000Aoo`00 001oo`D0009oo`800004Ool00000Ool40003Ool700000goo0000000400001Goo00000000Ool02P00 0goo0P0000Eoo`00Ool007oo00800003Ool0000000D00003Ool0000000@00003Ool0000000<0009o o`L00004Ool00000Ool30002Ool>00000goo0000000Z00000goo00000007Ool004Yoo`03001oogoo 01]oo`03001oogoo00]oo`04001oogooOol400001Goo00000000Ool00P000Woo0P0000=oo`00Ool0 0Woo0`0000Aoo`00Ool000Eoo`03001oogoo00<0009oo`03001oo`0000=oo`800006Ool00000001o o`000goo0`0000=oo`0000000P0000Aoo`00001oo`<00004Ool007ooOol2000017oo000007oo1000 0goo1`0000=oo`000000100000Eoo`00000007oo00X000=oo`800005Ool007oo001oo`0200000goo 0000000500000goo0000000400000goo000000030002Ool7000017oo000007oo0`000Woo3P0000=o o`000000:P0000=oo`0000001goo001:Ool00`00Oomoo`0KOol00`00Oomoo`0;Ool00`00Oomoo`02 Ool01000Ool007oo0`0000=oo`0000000Woo0P0000=oo`00Ool00Woo0`0000Aoo`00Ool000Eoo`03 001oogoo00<0009oo`03001oo`0000=oo`800006Ool00000001oo`000goo0`0000=oo`0000000P00 00Aoo`00001oo`<00004Ool007ooOol2000017oo000007oo10000goo1`0000=oo`000000100000Eo o`00000007oo00X000=oo`800005Ool007oo001oo`0200000goo0000000500000goo000000040000 0goo000000030002Ool7000017oo000007oo0`000Woo3P0000=oo`0000006`0000=oo`0000003000 00=oo`0000001goo001:Ool00`00Oomoo`0KOol00`00Oomoo`0;Ool00`00Oomoo`02Ool01000Ool0 07oo0`0000=oo`0000000Woo0P0000=oo`00Ool00Woo0`0000Aoo`00Ool000Eoo`03001oogoo00<0 009oo`03001oo`0000=oo`800006Ool00000001oo`000goo0`0000=oo`0000000P0000Aoo`00001o o`<00004Ool007ooOol2000017oo000007oo10000goo1`0000=oo`000000100000=oo`0000000Woo 2P000goo0P0000Eoo`00000007oo00800003Ool0000000D00003Ool0000000@00003Ool0000000<0 009oo`L00004Ool00000Ool30002Ool>00000goo0000000K00000goo0000000<00000goo00000007 Ool004Yoo`03001oogoo02Uoo`03001oogoo009oo`04001oo`00Ool300000goo00000002Ool01000 Oomoo`000goo0P000Woo00<007oo00001Goo00<007ooOol00`000Woo00<007ooOol00goo0P0000Io o`00000007oo0003Ool300000goo00000002000017oo000007oo0`0000Aoo`00Oomoo`800004Ool0 0000Ool40003Ool700000goo000000040002Ool00`00Oomoo`0700000goo00000003Ool200001Goo 00000000Ool00P0000=oo`0000000P0000Aoo`00001oo`H00003Ool0000000<0009oo`L00003Ool0 0000009oo`80009oo`h00003Ool0000001/00003Ool0000000`00003Ool0000000Moo`00BWoo0`00 :Goo00<007ooOol00Woo00@007oo001oo`<00003Ool00000009oo`04001oogoo0003Ool20002Ool0 0`00Ool00005Ool00`00Oomoo`030002Ool00`00Oomoo`03Ool200001Woo00000000Ool000=oo`<0 0003Ool0000000800004Ool00000Ool3000017oo001oogoo0P0000Aoo`00001oo`@000=oo`L00003 Ool0000000@0009oo`03001oogoo00L00003Ool0000000=oo`800005Ool00000001oo`0200000goo 00000002000017oo000007oo1P0000=oo`0000000`000Woo1`0000=oo`0000000Woo0P000Woo3P00 00=oo`0000006`0000=oo`000000300000=oo`0000001goo001:Ool00`00Oomoo`0YOol00`00Oomo o`06Ool01000Ool007oo0P001Goo00@007ooOomoo`80009oo`03001oo`0000Eoo`03001oogoo00<0 009oo`03001oogoo00=oo`800006Ool00000001oo`000goo0`0000Ioo`00001oo`00Ool200001Woo 00000000Ool0009oo`800004Ool00000Ool40003Ool4000017oo000007oo1P000Woo00<007ooOol0 1`0000=oo`0000000goo00<007ooOol00`0000Aoo`00001oo`@00004Ool00000Ool600000goo0000 00030002Ool700000goo00000002Ool20002Ool600000goo0000000500000goo0000000K00000goo 0000000<00000goo00000007Ool004Yoo`03001oogoo02Uoo`03001oogoo00Ioo`05001oo`00Ool0 0006Ool01000Oomoogoo0P000Woo00<007oo00001Goo00<007ooOol00`000Woo00<007ooOol00goo 0P0000Ioo`00000007oo0003Ool300001Woo000007oo001oo`800006Ool00000001oo`000Woo0P00 00Aoo`00001oo`@000=oo`@00004Ool00000Ool60002Ool00`00Oomoo`0700000goo00000003Ool0 0`00Oomoo`03000017oo000007oo100000Aoo`00001oo`H00003Ool0000000<0009oo`L00003Ool0 0000009oo`80009oo`H00003Ool0000000D00003Ool0000001/00003Ool0000000`00003Ool00000 00Moo`00BWoo00<007ooOol0:Goo00<007ooOol01Woo00D007oo001oo`0000Ioo`04001oogooOol2 0002Ool00`00Ool00005Ool00`00Oomoo`030002Ool00`00Oomoo`03Ool200001Woo00000000Ool0 00=oo`<00006Ool00000Ool007oo0P0000Ioo`00000007oo0002Ool2000017oo000007oo10000goo 100000Aoo`00001oo`800004Ool000000002Ool00`00Oomoo`0700000goo00000003Ool00`00Oomo o`020002Ool200000goo00000002000017oo000007oo1P0000=oo`0000000`000Woo1`0000=oo`00 00000Woo0P000Woo1P0000=oo`0000001@0000=oo`0000006`0000=oo`000000300000=oo`000000 1goo001:Ool00`00Oomoo`11Ool20004Ool00`00Oomoo`06Ool30002Ool00`00Oomoo`03Ool00`00 Oomoo`030007Ool00`00Oomoo`02Ool01000Ool000001Goo00<007ooOol00P0000Aoo`00001oo`@0 00=oo`@00004Ool00000Ool20002Ool20002Ool01000Oomoogoo1P0000=oo`0000001Woo0P000Woo 00<007ooOol0100000Aoo`00001oo`<00004Ool00000Ool50002Ool5000017oo001oo`000goo0P00 0Woo1P0000=oo`0000001@0000=oo`0000006`0000=oo`000000300000=oo`0000001goo001:Ool0 0`00Oomoo`11Ool20004Ool00`00Oomoo`06Ool30002Ool00`00Oomoo`03Ool00`00Oomoo`030007 Ool00`00Oomoo`02Ool01000Ool000001Goo00H007ooOomoo`00Ool200000goo000000020003Ool4 000017oo001oogoo0P000Woo0P000Woo00@007ooOomoo`H00003Ool0000000Ioo`80009oo`03001o ogoo00800003Ool007oo00800005Ool00000001oo`0200000goo000000030002Ool5000017oo001o o`000goo0P000Woo1P0000Aoo`00001oo`@00003Ool0000001/00003Ool0000000`00003Ool00000 00Moo`00BWoo0`00@Goo0P0017oo00<007ooOol01Woo0`000Woo00<007ooOol00goo00<007ooOol0 0`001goo00<007ooOol00Woo00@007oo000000Eoo`06001oogooOol007oo0P0000=oo`0000000P00 0goo100000Aoo`00Oomoo`80009oo`80009oo`04001oogooOol600000goo00000006Ool20002Ool0 0`00Oomoo`0200000goo001oo`0200001Goo00000000Ool00P0000=oo`0000000`000Woo1@0000Ao o`00Ool000=oo`80009oo`H00004Ool00000Ool400000goo0000000K00000goo0000000<00000goo 001oo`07Ool004Yoo`03001oogoo045oo`8000Aoo`03001oogoo00Ioo`<0009oo`03001oogoo00=o o`03001oogoo00<000Moo`03001oogoo009oo`04001oo`000005Ool01P00Oomoogoo001oo`800003 Ool00000008000=oo`@00004Ool007ooOol20002Ool20002Ool01000Oomoogoo1P0000=oo`000000 1Woo0P000Woo00<007ooOol00P0000=oo`00Ool00P0000Eoo`00000007oo00800003Ool0000000<0 009oo`D00004Ool007oo0003Ool20002Ool6000017oo000007oo100000=oo`0000006`0000=oo`00 0000200000Ioo`00000007oo0008Ool004Yoo`03001oogoo051oo`<000Qoo`03001oogoo008000eo o`03001oo`0000aoo`800003Ool00000008000Aoo`<00005Ool007ooOol00003Ool00`00Oomoo`06 Ool20002Ool01000Ool000001goo00@007ooOol0009oo`04001oogoo0002Ool00`00Ool000020000 17oo000007oo1@000Woo1@0000Aoo`00Ool000=oo`04001oogooOol6000017oo000007oo100000=o o`0000006`0000=oo`000000200000Ioo`00000007oo0008Ool000ioo`@000Eoo`03001oogoo00=o o`03001oogoo00Eoo`@000Eoo`<001Uoo`03001oogoo051oo`<000Qoo`03001oogoo008000eoo`03 001oo`0000aoo`800003Ool00000008000Aoo`<00005Ool007ooOol00003Ool00`00Oomoo`06Ool2 0002Ool01000Ool000001goo00@007ooOol0009oo`04001oogoo0002Ool00`00Ool00002000017oo 000007oo1@000Woo1@0000Aoo`00Ool000=oo`04001oogooOol6000017oo000007oo100000=oo`00 00002@0000=oo`0000003`0000=oo`000000200000Ioo`00000007oo0008Ool000moo`03001oogoo 00Ioo`05001oogooOol00009Ool00`00Oomoo`04Ool01@00Oomoogoo000067oo00<007ooOol0D7oo 0`0027oo00<007ooOol00P003Goo00<007oo000037oo0P0000=oo`0000000P0017oo0`0000Eoo`00 Oomoo`0000=oo`03001oogoo00Ioo`80009oo`04001oogoo0007Ool01000Oomoo`000Woo00@007oo Ool0009oo`03001oo`0000800004Ool00000Ool50002Ool5000017oo001oo`000goo00@007ooOomo o`H00004Ool00000Ool400000goo0000000900000goo0000000?00000goo0000000800001Woo0000 0000Ool000Qoo`0047oo00<007ooOol01Woo00<007oo00002goo00<007ooOol00goo00<007ooOol0 0Woo00<007ooOol05Goo00<007ooOol0D7oo0`0027oo00<007ooOol00P003Goo00<007oo000037oo 0P0000=oo`0000000P0017oo0`0000Eoo`00Oomoo`0000=oo`03001oogoo00Ioo`80009oo`04001o ogoo0007Ool01000Oomoo`000Woo00@007ooOol0009oo`03001oo`0000800004Ool00000Ool50002 Ool5000017oo001oo`000goo00@007ooOomoo`H0009oo`03001oo`0000<00003Ool0000000T00003 Ool0000000l00003Ool0000000P00006Ool00000001oo`0027oo000@Ool00`00Oomoo`07Ool00`00 Oomoo`0:Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`0EOol00`00Oomoo`1@Ool00`00 Ool00008Ool00`00Oomoo`02000=Ool00`00Ool0000Ool01000Oomoo`001goo00<007ooOol00goo00@0 07ooOol0009oo`04001oogoo0002Ool200001Woo00000000Ool0009oo`D00004Ool007oo0003Ool0 1000Oomoogoo1P000Woo00<007oo00000`0000=oo`0000001`0000=oo`00Ool01@0000=oo`000000 2@000Woo2@0000Ioo`00000007oo0008Ool0015oo`03001oogoo00Aoo`05001oogooOol0000;Ool0 0`00Oomoo`02Ool00`00Oomoo`03Ool00`00Oomoo`0DOol00`00Oomoo`1@Ool00`00Ool0000;Ool2 000=Ool00`00Ool0000"], ImageRangeCache->{{{109, 396}, {429.75, 252.813}} -> {-2.39665, \ 6.49079*^-16, 0.0141839, 3.80176*^-18}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[ diff /. {\[Beta]\_1 \[Rule] 0.6, \[Beta] \[Rule] 0.8}], {\[Theta]\_1, 0, \[Pi]}];\)\)], "Input", CellLabel->"In[105]:="], 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 Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.303152 0.363517 7.85433e+014 [ [.17539 .35102 -9.5 -15.6875 ] [.17539 .35102 9.5 0 ] [.32696 .35102 -5 -15.6875 ] [.32696 .35102 5 0 ] [.47854 .35102 -9.5 -15.6875 ] [.47854 .35102 9.5 0 ] [.63011 .35102 -5 -15.6875 ] [.63011 .35102 5 0 ] [.78169 .35102 -9.5 -15.6875 ] [.78169 .35102 9.5 0 ] [.93327 .35102 -5 -15.6875 ] [.93327 .35102 5 0 ] [.01131 .04934 -57.0625 -7.84375 ] [.01131 .04934 0 7.84375 ] [.01131 .12789 -57.0625 -7.84375 ] [.01131 .12789 0 7.84375 ] [.01131 .20643 -57.0625 -7.84375 ] [.01131 .20643 0 7.84375 ] [.01131 .28497 -57.0625 -7.84375 ] [.01131 .28497 0 7.84375 ] [.01131 .44206 -48.375 -7.84375 ] [.01131 .44206 0 7.84375 ] [.01131 .5206 -48.375 -7.84375 ] [.01131 .5206 0 7.84375 ] [.01131 .59915 -48.375 -7.84375 ] [.01131 .59915 0 7.84375 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .36352 m .17539 .36977 L s gsave .17539 .35102 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.5) show 1.000 setlinewidth grestore .32696 .36352 m .32696 .36977 L s gsave .32696 .35102 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 1.000 setlinewidth grestore .47854 .36352 m .47854 .36977 L s gsave .47854 .35102 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.5) show 1.000 setlinewidth grestore .63011 .36352 m .63011 .36977 L s gsave .63011 .35102 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore .78169 .36352 m .78169 .36977 L s gsave .78169 .35102 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2.5) show 1.000 setlinewidth grestore .93327 .36352 m .93327 .36977 L s gsave .93327 .35102 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 1.000 setlinewidth grestore .125 Mabswid .05412 .36352 m .05412 .36727 L s .08444 .36352 m .08444 .36727 L s .11476 .36352 m .11476 .36727 L s .14507 .36352 m .14507 .36727 L s .2057 .36352 m .2057 .36727 L s .23602 .36352 m .23602 .36727 L s .26633 .36352 m .26633 .36727 L s .29665 .36352 m .29665 .36727 L s .35728 .36352 m .35728 .36727 L s .38759 .36352 m .38759 .36727 L s .41791 .36352 m .41791 .36727 L s .44822 .36352 m .44822 .36727 L s .50885 .36352 m .50885 .36727 L s .53917 .36352 m .53917 .36727 L s .56948 .36352 m .56948 .36727 L s .5998 .36352 m .5998 .36727 L s .66043 .36352 m .66043 .36727 L s .69074 .36352 m .69074 .36727 L s .72106 .36352 m .72106 .36727 L s .75138 .36352 m .75138 .36727 L s .81201 .36352 m .81201 .36727 L s .84232 .36352 m .84232 .36727 L s .87264 .36352 m .87264 .36727 L s .90295 .36352 m .90295 .36727 L s .96358 .36352 m .96358 .36727 L s .9939 .36352 m .9939 .36727 L s .25 Mabswid 0 .36352 m 1 .36352 L s .02381 .04934 m .03006 .04934 L s gsave .01131 .04934 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (4) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .12789 m .03006 .12789 L s gsave .01131 .12789 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .20643 m .03006 .20643 L s gsave .01131 .20643 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .28497 m .03006 .28497 L s gsave .01131 .28497 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .44206 m .03006 .44206 L s gsave .01131 .44206 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .5206 m .03006 .5206 L s gsave .01131 .5206 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .59915 m .03006 .59915 L s gsave .01131 .59915 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .125 Mabswid .02381 .06505 m .02756 .06505 L s .02381 .08076 m .02756 .08076 L s .02381 .09647 m .02756 .09647 L s .02381 .11218 m .02756 .11218 L s .02381 .1436 m .02756 .1436 L s .02381 .1593 m .02756 .1593 L s .02381 .17501 m .02756 .17501 L s .02381 .19072 m .02756 .19072 L s .02381 .22214 m .02756 .22214 L s .02381 .23785 m .02756 .23785 L s .02381 .25356 m .02756 .25356 L s .02381 .26927 m .02756 .26927 L s .02381 .30068 m .02756 .30068 L s .02381 .31639 m .02756 .31639 L s .02381 .3321 m .02756 .3321 L s .02381 .34781 m .02756 .34781 L s .02381 .37923 m .02756 .37923 L s .02381 .39493 m .02756 .39493 L s .02381 .41064 m .02756 .41064 L s .02381 .42635 m .02756 .42635 L s .02381 .45777 m .02756 .45777 L s .02381 .47348 m .02756 .47348 L s .02381 .48919 m .02756 .48919 L s .02381 .5049 m .02756 .5049 L s .02381 .53631 m .02756 .53631 L s .02381 .55202 m .02756 .55202 L s .02381 .56773 m .02756 .56773 L s .02381 .58344 m .02756 .58344 L s .02381 .03364 m .02756 .03364 L s .02381 .01793 m .02756 .01793 L s .02381 .00222 m .02756 .00222 L s .02381 .61486 m .02756 .61486 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 .36352 m .02499 .36352 L .02605 .36335 L .02729 .36284 L .02846 .36215 L .02954 .36284 L .03053 .36352 L .03162 .36352 L .03279 .36556 L .03396 .36079 L .03506 .36079 L .03636 .36079 L .03756 .35943 L .0388 .36352 L .0395 .35943 L .04015 .36215 L .04135 .36488 L .04262 .36352 L .04519 .36079 L .04589 .35807 L .04654 .36897 L .04722 .36079 L .04797 .35807 L .04924 .36079 L .04995 .36624 L .0506 .36897 L .05184 .37169 L .05302 .36079 L .05415 .35807 L .05536 .36624 L .05639 .35262 L .05753 .36079 L .05875 .36352 L .06007 .36897 L .06131 .36352 L .06244 .37442 L .06373 .36897 L .0649 .37442 L .06555 .35262 L .06625 .36897 L .06752 .35807 L .06872 .35262 L .06998 .36897 L .07106 .37442 L .07225 .36352 L .07296 .36352 L .07364 .35262 L .07492 .34717 L .07564 .35807 L .07641 .35262 L Mistroke .07713 .36897 L .07779 .33082 L .07906 .35807 L .08027 .35262 L .08157 .36352 L .0823 .37987 L .08297 .35807 L .08422 .36352 L .08493 .36352 L .08557 .35807 L .08681 .36352 L .08799 .35262 L .08865 .37442 L .08936 .35807 L .09062 .36897 L .09133 .35807 L .09198 .35262 L .09271 .35262 L .09349 .34717 L .09419 .35262 L .09495 .34717 L .09566 .36897 L .09631 .32537 L .09704 .36897 L .09773 .37442 L .09847 .36352 L .09928 .34172 L .09992 .36352 L .10062 .37442 L .10135 .34172 L .10204 .36352 L .10326 .31992 L .10458 .34172 L .1059 .33082 L .10714 .37442 L .10843 .36352 L .10911 .37442 L .10985 .36352 L .11109 .37442 L .1124 .34172 L .11352 .37442 L .11474 .37442 L .11548 .36352 L .11619 .36352 L .1175 .39622 L .11824 .36352 L .11892 .34172 L .11967 .38532 L .12046 .34172 L .12177 .35262 L Mistroke .123 .36352 L .1237 .31992 L .12435 .36352 L .12509 .38532 L .12579 .35262 L .12706 .35262 L .12821 .34172 L .12885 .35262 L .12954 .37442 L .13078 .37442 L .13196 .39622 L .1332 .35262 L .13425 .35262 L .13541 .39622 L .13612 .35262 L .13679 .35262 L .13803 .36352 L .13873 .34172 L .13938 .35262 L .14009 .35262 L .14084 .35262 L .14209 .36352 L .14325 .34172 L .14453 .36352 L .14525 .36352 L .14591 .33082 L .14719 .30902 L .1484 .35262 L .14948 .36352 L .15065 .37442 L .15194 .36352 L .15329 .35262 L .15446 .36352 L .15572 .33082 L .1569 .35262 L .15797 .34172 L .15905 .34172 L .16007 .38532 L .16126 .35262 L .16236 .33082 L .16356 .29812 L .16485 .31992 L .16553 .33082 L .16625 .33082 L .16754 .30902 L .16826 .34172 L .16893 .34172 L .16966 .38532 L .17045 .36352 L .17113 .40712 L Mistroke .17187 .34172 L .17256 .36352 L .17321 .34172 L .17442 .34172 L .17572 .34172 L .17688 .31992 L .17813 .31992 L .1804 .31992 L .18555 .31992 L .18807 .31992 L .1893 .29812 L .19044 .31992 L .19175 .40712 L .19244 .27632 L .19317 .34172 L .19435 .34172 L .19565 .34172 L .19638 .29812 L .19708 .38532 L .19788 .38532 L .19861 .38532 L .19993 .23272 L .20068 .34172 L .20137 .34172 L .20259 .27632 L .20329 .36352 L .20394 .42892 L .20526 .31992 L .206 .34172 L .20668 .31992 L .20785 .36352 L .2091 .34172 L .21028 .36352 L .21135 .36352 L .21261 .34172 L .21332 .31992 L .21398 .29812 L .21518 .36352 L .21646 .40712 L .21768 .38532 L .219 .34172 L .22023 .36352 L .22137 .34172 L .22205 .34172 L .22269 .34172 L .22345 .31992 L .22414 .34172 L .22541 .31992 L .22611 .29812 L .22676 .38532 L Mistroke .22793 .31992 L .22918 .38532 L .23036 .38532 L .23143 .36352 L .23269 .31992 L .2334 .31992 L .23406 .40712 L .23527 .36352 L .23655 .31992 L .23777 .36352 L .23908 .31992 L .24032 .38532 L .24146 .31992 L .24272 .36352 L .24343 .36352 L .2441 .31992 L .24479 .34172 L .24544 .25452 L .24619 .34172 L .24687 .36352 L .24794 .21092 L .24912 .40712 L .25035 .31992 L .25149 .29812 L .25256 .36352 L .25354 .36352 L .25467 .40712 L .25575 .29812 L .2569 .34172 L .25813 .36352 L .25919 .40712 L .26035 .42892 L .26159 .29812 L .26229 .27632 L .26293 .27632 L .26411 .36352 L .26536 .40712 L .26658 .40712 L .26728 .25452 L .26792 .29812 L .2691 .38532 L .27034 .34172 L .27138 .38532 L .2725 .27632 L .27373 .36352 L .27488 .34172 L .27618 .34172 L .27687 .31992 L .27761 .34172 L .27831 .29812 L Mistroke .27895 .25452 L .2802 .38532 L .2814 .34172 L .2827 .31992 L .28393 .31992 L .28506 .31992 L .28613 .36352 L .28726 .27632 L .28834 .36352 L .28932 .34172 L .29047 .25452 L .29172 .29812 L .2929 .36352 L .29399 .34172 L .29511 .36352 L .29616 .27632 L .29732 .36352 L .29856 .38532 L .2998 .27632 L .3011 .34172 L .30221 .31992 L .30342 .36352 L .30474 .31992 L .30596 .36352 L .30659 .31992 L .30729 .34172 L .30802 .29812 L .30871 .25452 L .30996 .25452 L .31111 .29812 L .31175 .38532 L .31244 .31992 L .3137 .34172 L .31493 .31992 L .31605 .36352 L .31733 .36352 L .31854 .31992 L .31967 .36352 L .3207 .31992 L .32184 .31992 L .32304 .27632 L .32434 .36352 L .32553 .36352 L .32619 .40712 L .32691 .31992 L .32821 .36352 L .32943 .36352 L .33072 .31992 L .33182 .40712 L .33303 .36352 L Mistroke .33376 .40712 L .33445 .27632 L .33576 .36352 L .33648 .31992 L .33716 .18912 L .3379 .36352 L .33869 .40712 L .33937 .36352 L .34012 .40712 L .34082 .40712 L .34147 .36352 L .34269 .31992 L .34399 .31992 L .35345 .31992 L .35476 .40712 L .3555 .31992 L .35618 .36352 L .35743 .27632 L .35806 .36352 L .35876 .31992 L .35996 .27632 L .36126 .36352 L .36248 .27632 L .36361 .23272 L .36467 .27632 L .36581 .40712 L .36689 .27632 L .36787 .31992 L .36902 .31992 L .37027 .36352 L .37145 .40712 L .37253 .31992 L .37365 .40712 L .37471 .31992 L .37586 .31992 L .3771 .31992 L .37839 .40712 L .37962 .40712 L .38073 .36352 L .38193 .36352 L .38258 .40712 L .38327 .31992 L .38449 .23272 L .38581 .36352 L .38656 .31992 L .38726 .36352 L .38852 .23272 L .38968 .36352 L .39031 .31992 L .39101 .36352 L Mistroke .39227 .40712 L .39339 .23272 L .39463 .31992 L .39592 .31992 L .39713 .31992 L .40163 .31992 L .40227 .40712 L .40296 .27632 L .4042 .31992 L .40549 .40712 L .40623 .36352 L .4069 .36352 L .40809 .36352 L .40938 .31992 L .4106 .31992 L .41173 .27632 L .41303 .31992 L .41425 .27632 L .41493 .31992 L .41558 .23272 L .41633 .36352 L .41701 .27632 L .41769 .31992 L .4184 .31992 L .41969 .27632 L .42048 .36352 L .42122 .36352 L .42189 .31992 L .42261 .27632 L .42386 .27632 L .42499 .23272 L .42631 .36352 L .42755 .27632 L .4287 .31992 L .42976 .27632 L .43092 .36352 L .43215 .31992 L .43339 .27632 L .43408 .23272 L .43472 .27632 L .43595 .31992 L .43713 .36352 L .43778 .27632 L .43848 .31992 L .43975 .36352 L .44052 .27632 L .44125 .40712 L .4419 .36352 L .44261 .31992 L .44392 .36352 L Mistroke .44515 .31992 L .44586 .36352 L .4465 .31992 L .44724 .40712 L .44795 .36352 L .44863 .36352 L .44935 .31992 L .45065 .36352 L .45137 .36352 L .45204 .31992 L .45279 .36352 L .45359 .36352 L .45481 .31992 L .45551 .40712 L .45615 .31992 L .45746 .31992 L .45886 .31992 L .45997 .27632 L .46116 .36352 L .46247 .36352 L .46369 .31992 L .46438 .31992 L .46504 .31992 L .46628 .36352 L .46759 .27632 L .46833 .27632 L .46902 .23272 L .47027 .27632 L .4714 .36352 L .4727 .36352 L .47393 .40712 L .47458 .40712 L .47528 .36352 L .47602 .27632 L .47671 .40712 L .47795 .31992 L .47927 .27632 L .48001 .23272 L .48082 .27632 L .48158 .40712 L .48229 .40712 L .48292 .31992 L .48362 .36352 L .48435 .40712 L .48503 .36352 L .48621 .45072 L .4875 .31992 L .48815 .31992 L .48885 .36352 L .4901 .27632 L Mistroke .49135 .31992 L .49253 .36352 L .49359 .31992 L .49474 .18912 L .496 .31992 L .49671 .36352 L .49738 .40712 L .49808 .40712 L .49873 .27632 L .49947 .36352 L .50018 .31992 L .50142 .45072 L .50257 .31992 L .50384 .36352 L .50448 .23272 L .50518 .23272 L .5064 .27632 L .50753 .27632 L .50822 .27632 L .50887 .40712 L .51009 .27632 L .51129 .27632 L .51259 .31992 L .51326 .31992 L .51398 .31992 L .51526 .31992 L .51635 .31992 L .51753 .31992 L .51864 .40712 L .51966 .23272 L .52085 .27632 L .52214 .40712 L .52337 .27632 L .5245 .27632 L .52581 .31992 L .52655 .27632 L .52723 .40712 L .52848 .27632 L .5298 .31992 L .53099 .36352 L .53211 .31992 L .53341 .36352 L .5346 .49432 L .53587 .27632 L .53658 .31992 L .53725 .36352 L .53845 .18912 L .53972 .45072 L .54039 .27632 L .5411 .31992 L Mistroke .5424 .40712 L .54315 .31992 L .54394 .40712 L .54461 .40712 L .54535 .36352 L .54667 .40712 L .54789 .36352 L .54853 .36352 L .54923 .27632 L .54996 .14552 L .55064 .31992 L .5519 .31992 L .55305 .27632 L .55368 .18912 L .55437 .36352 L .55563 .40712 L .55687 .31992 L .55798 .31992 L .55927 .36352 L .56048 .27632 L .56161 .36352 L .56264 .36352 L .56377 .31992 L .56497 .27632 L .56628 .40712 L .56747 .36352 L .56875 .23272 L .56948 .36352 L .57015 .27632 L .57135 .36352 L .57263 .40712 L .57374 .40712 L .57497 .40712 L .57769 .40712 L .57848 .45072 L .57922 .40712 L .5799 .45072 L .58063 .31992 L .58194 .27632 L .58316 .31992 L .58391 .27632 L .58461 .27632 L .58593 .36352 L .58709 .45072 L .58833 .53792 L .5895 .27632 L .59058 .27632 L .59183 .31992 L .59254 .45072 L .5932 .31992 L Mistroke .5944 .27632 L .59568 .36352 L .5969 .23272 L .59821 .36352 L .59945 .27632 L .60058 .45072 L .60184 .27632 L .60255 .36352 L .60322 .27632 L .60392 .36352 L .60456 .27632 L .60529 .23272 L .60599 .27632 L .60706 .27632 L .60823 .31992 L .60945 .27632 L .6106 .45072 L .61167 .23272 L .61265 .23272 L .61378 .36352 L .61485 .31992 L .61601 .40712 L .61724 .36352 L .6183 .18912 L .61945 .27632 L .62015 .36352 L .6208 .36352 L .62208 .36352 L .62324 .36352 L .62446 .36352 L .62568 .23272 L .62637 .27632 L .62701 .36352 L .62818 .36352 L .62943 .36352 L .63054 .40712 L .63158 .31992 L .63272 .31992 L .63395 .23272 L .63519 .40712 L .63589 .27632 L .63654 .27632 L .63786 .31992 L .63859 .40712 L .63926 .53792 L .64046 .18912 L .64176 .45072 L .64299 .49432 L .64412 .27632 L .64518 .45072 L Mistroke .64632 .45072 L .64739 .36352 L .64837 .36352 L .64952 .45072 L .65077 .40712 L .65195 .45072 L .65304 .40712 L .65408 .36352 L .65521 .31992 L .65644 .23272 L .65761 .49432 L .65884 .40712 L .66014 .36352 L .66125 .36352 L .66247 .36352 L .66378 .36352 L .66499 .14552 L .66563 .36352 L .66632 .49432 L .66705 .36352 L .66774 .45072 L .66899 .49432 L .67014 .23272 L .67077 .45072 L .67146 .40712 L .67272 .40712 L .67393 .27632 L .67523 .27632 L .67647 .45072 L .67761 .45072 L .67872 .36352 L .67976 .45072 L .68085 .27632 L .68204 .40712 L .68272 .31992 L .68337 .49432 L .68458 .40712 L .68588 .36352 L .68662 .18912 L .6873 .49432 L .68859 .40712 L .68932 .45072 L .69001 .40712 L .69074 .36352 L .69142 .45072 L .69213 .40712 L .6929 .27632 L .69412 .40712 L .69543 .36352 L .69665 .27632 L Mistroke .69775 .31992 L .69904 .40712 L .69977 .36352 L .70044 .36352 L .70167 .36352 L .70298 .31992 L .70419 .49432 L .70551 .40712 L .70675 .31992 L .70791 .53792 L .70906 .27632 L .71009 .27632 L .71129 .53792 L .71242 .31992 L .71365 .23272 L .71496 .45072 L .71607 .49432 L .71729 .31992 L .71861 .45072 L .71934 .40712 L .72001 .40712 L .72132 .49432 L .72255 .31992 L .72361 .45072 L .72477 .53792 L .72598 .40712 L .72712 .49432 L .72818 .31992 L .72915 .36352 L .73021 .40712 L .73133 .18912 L .73248 .27632 L .7337 .45072 L .73485 .49432 L .73589 .31992 L .73712 .40712 L .73781 .40712 L .73845 .31992 L .73963 .40712 L .74087 .45072 L .74208 .40712 L .74273 .53792 L .74341 .36352 L .74466 .36352 L .74582 .23272 L Mfstroke .74582 .23272 m .7469 .61803 L s .74701 .61803 m .74796 .53792 L .7491 .53792 L .75033 .40712 L .75156 .53792 L .75226 .31992 L .75291 .36352 L .75422 .36352 L .75496 .36352 L .75563 .31992 L .75682 .31992 L .75812 .42892 L .75935 .23272 L .76048 .29812 L .76153 .53792 L .76253 .49432 L .76367 .29812 L .76472 .51612 L .76587 .31992 L .76713 .27632 L .7683 .49432 L .76938 .42892 L .77062 .23272 L .77178 .40712 L .77282 .47252 L .77395 .38532 L .77518 .45072 L .77648 .45072 L .77759 .38532 L .77881 .31992 L .78012 .29812 L .78133 .51612 L .78196 .29812 L .78265 .34172 L .78338 .38532 L .78406 .47252 L .78531 .51612 L .78645 .40712 L .78771 .38532 L .78903 .29812 L .79014 .29812 L .79133 .31992 L .79246 .18912 L .79348 .25452 L .79468 .42892 L .79598 .23272 L .79721 .45072 L .79834 .23272 L .79954 .51612 L .80084 .51612 L Mistroke .80206 .38532 L .80318 .27632 L .80449 .40712 L .80523 .51612 L Mfstroke .80523 .51612 m .80576 .61803 L s .80612 .61803 m .80717 .47252 L .80782 .42892 L .8085 .21092 L .80923 .47252 L .8099 .27632 L .81062 .38532 L .81141 .36352 L .8121 .36352 L s .8121 .36352 m .81275 .61803 L s .81292 .61803 m .81415 .21092 L .81481 .42892 L .81552 .38532 L .81682 .38532 L .81809 .34172 L .81926 .40712 L .8205 .12372 L .82169 .40712 L .82275 .21092 L .82391 .27632 L .82516 .38532 L .82634 .51612 L .82699 .38532 L .82769 .45072 L .82892 .49432 L s .82892 .49432 m .8296 .61803 L s .83053 .61803 m .83137 .42892 L .83244 .60332 L .83362 .25452 L .83471 .55972 L .83587 .40712 L .83697 .47252 L .83798 .40712 L .83925 .25452 L .8399 .51612 L .84061 .47252 L .84187 .42892 L .84305 .25452 L .84372 .36352 L .84443 .18912 L .8457 .29812 L .84642 .29812 L s .84642 .29812 m .84691 .61803 L s .84722 .61803 m .84786 .05832 L .84857 .58152 L s .84857 .58152 m .84956 .61803 L s .84983 .61803 m .85105 .49432 L .85215 .34172 L .85336 .23272 L .85404 .08012 L .85468 .01472 L .85536 .25452 L .85608 .36352 L .8574 .16732 L .8586 .49432 L .85989 .40712 L .86111 .21092 L s .86111 .21092 m .86218 .61803 L s .86223 .61803 m .86338 .34172 L .86467 .51612 L .86532 .53792 L .86603 .47252 L .86729 .34172 L .86847 .31992 L .86965 .47252 L .87078 .27632 L .87179 .25452 L .87288 .12372 L .87408 .53792 L .87534 .34172 L .87642 .53792 L .87762 .27632 L .87893 .31992 L .87959 .12372 L .88031 .43982 L s .88031 .43982 m .88146 .61803 L s .88164 .61803 m .88277 .24362 L s .88277 .24362 m .88322 .61803 L s .88375 .61803 m .88418 .25452 L .88545 .39622 L .88617 .53792 L .88683 .25452 L .88755 .53792 L .88832 .43982 L .88951 .28722 L .89079 .24362 L .892 .49432 L .8931 .18912 L .89439 .38532 L .89512 .22182 L .89579 .40712 L .89703 .27632 L .89835 .41802 L .89948 .54882 L .90072 .14552 L .90202 .42892 L .90323 .47252 L .90436 .30902 L .90539 .35262 L .90658 .48342 L .9077 .17822 L .90892 .51612 L .91022 .40712 L .91132 .23272 L s .91132 .23272 m .9123 .61803 L s .91436 .61803 m .91458 .55972 L .91525 .38532 L .91655 .26542 L .91779 .57062 L .91894 .58152 L .91998 .54882 L .92119 .45072 L .92232 .50522 L .92337 .53792 L .92434 .36352 L .9254 .42892 L .92653 .47252 L .92766 .38532 L .92888 .53792 L .93003 .31992 L .93107 .24907 L .9323 .18912 L .93299 .33627 L .93363 .53247 L .93481 .31992 L s .93481 .31992 m .93603 .61803 L s .9361 .61803 m .9372 .41257 L .93844 .54337 L .93974 .31447 L .94095 .61422 L .94209 .54337 L .94312 .30902 L .94431 .42347 L .94544 .39622 L .94675 .41257 L .94799 .33082 L .94928 .57062 L .94996 .57607 L .95069 .39077 L .95199 .54882 L .95323 .33627 L .95433 .31719 L .95554 .20274 L .9567 .36897 L .95774 .25997 L .95895 .27632 L .96009 .34172 L .96116 .41802 L .96215 .49977 L .96318 .29267 L .96431 .56244 L .96546 .39213 L .9667 .2259 L .96784 .19184 L .96888 .48887 L .9701 .25724 L .97142 .20479 L .97267 .28177 L .97382 .39656 L .97495 .29199 L .97619 .43096 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[105]:=", ImageSize->{288, 177.938}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgmoo`03001oogoo02Uo o`00BWoo0`00kgoo00<007ooOol0:Goo001:Ool00`00Oomoo`3_Ool00`00Oomoo`0YOol004Yoo`03 001oogoo0>moo`03001oogoo02Uoo`00BWoo00<007ooOol0kgoo00<007ooOol0:Goo001:Ool00`00 Oomoo`3_Ool00`00Oomoo`0YOol0011oo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Eo o`@000Eoo`<001Uoo`<00>moo`03001oogoo02Uoo`004Goo00<007ooOol017oo00D007ooOomoo`00 00Uoo`03001oogoo00Aoo`05001oogooOol0000HOol00`00Oomoo`3_Ool00`00Oomoo`0YOol0015o o`03001oogoo00Eoo`03001oo`0000]oo`03001oogoo00=oo`03001oogoo009oo`03001oogoo01Eo o`03001oogoo0>moo`03001oogoo02Uoo`000goo20000goo1P001Woo00<007ooOol02Woo00<007oo Ool00goo00<007ooOol00Woo00<007ooOol05Goo00<007ooOol0kgoo00<007ooOol0:Goo000>Ool0 1@00Oomoogoo00001Woo00<007oo00002goo00<007ooOol00goo00<007ooOol00goo00<007ooOol0 57oo0`00kgoo00<007ooOol0:Goo000?Ool01000Oomoo`001Goo00D007ooOomoo`0000]oo`03001o ogoo009oo`03001oogoo00=oo`03001oogoo01Aoo`03001oogoo0>moo`03001oogoo02Uoo`0047oo 00<007oo000017oo00<007ooOol00goo00<007ooOol027oo00<007ooOol00goo00<007ooOol00Woo 00<007ooOol01Goo0`0017oo0P001Woo00<007ooOol0kgoo00<007ooOol0:Goo000AOol00`00Ool0 000DOol00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`06Ool00`00Oomoo`02Ool01000Oomo o`001Goo00<007ooOol0kGoo00<007oo0000:goo000BOol2000EOol00`00Oomoo`03Ool01000Oomo ogoo1P0017oo00D007ooOomoo`0000=oo`03001oogoo009oo`03001oogoo0>eoo`03001oo`0002]o o`0057oo00<007ooOol04Goo0P001Woo0`002Woo00D007ooOomoo`0000=oo`03001oogoo009oo`<0 0>eoo`03001oo`0002]oo`00?Goo00D007ooOomoo`0000=oo`03001oogoo009oo`03001oogoo0>eo o`03001oo`0002]oo`00?Goo00<007ooOol00Woo0`001Goo00<007ooOol0kGoo00<007oo0000:goo 000nOol00`00Oomoo`02Ool00`00Oomoo`04Ool00`00Oomoo`3]Ool00`00Ool0000[Ool003eoo`80 00Eoo`8000Aoo`<00>eoo`03001oo`0002]oo`00BWoo00<007ooOol0kGoo00<007oo0000:goo001: Ool00`00Oomoo`3]Ool00`00Ool0000[Ool004Yoo`03001oogoo0>eoo`03001oo`0002]oo`00BWoo 00<007ooOol0kGoo00<007oo0000:goo001:Ool3003]Ool00`00Ool0000[Ool004Yoo`03001oogoo 0>eoo`03001oo`0002]oo`00BWoo00<007ooOol0kGoo00<007oo0000:goo001:Ool00`00Oomoo`3] Ool00`00Ool0000[Ool004Yoo`<00>eoo`03001oo`0002]oo`003Woo0`001Woo00<007ooOol00goo 00<007ooOol01Goo10001Goo0`006Goo00<007ooOol0kGoo00<007oo0000:goo000AOol00`00Oomo o`04Ool01@00Oomoogoo00002Goo00<007ooOol017oo00D007ooOomoo`0001Qoo`03001oogoo0>eo o`03001oo`0002]oo`004Woo00<007ooOol017oo00<007oo00002goo00<007ooOol00goo00<007oo Ool00Woo00<007ooOol05Goo00<007ooOol0kGoo00<007oo0000:goo0003Ool80007Ool00`00Oomo o`05Ool00`00Oomoo`0:Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`0EOol00`00Oomo o`3UOol00`00Oomoo`05Ool00`00Ool00005Ool2000TOol0019oo`03001oogoo00Aoo`03001oo`00 00]oo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo01Aoo`<00>Eoo`03001oogoo00Eoo`03 001oo`0000Eoo`8002Aoo`0047oo0P001Woo00D007ooOomoo`0000]oo`03001oogoo009oo`03001o ogoo00=oo`03001oogoo01Aoo`03001oogoo0>Eoo`03001oogoo00Eoo`03001oo`0000Eoo`8002Ao o`004Woo00<007ooOol00Woo00<007ooOol00goo00<007ooOol027oo00<007ooOol00goo00<007oo Ool00Woo00<007ooOol01Goo0`0017oo0P001Woo00<007ooOol0iGoo00<007ooOol01Goo00<007oo 00001Goo0P0097oo000COol00`00Oomoo`0BOol00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomo o`06Ool00`00Oomoo`02Ool01000Oomoo`001Goo00<007ooOol0iGoo00<007ooOol01Goo00<007oo 00001Goo0P0097oo000@Ool01000Oomoo`005Goo00<007ooOol00goo00@007ooOomoo`H000Aoo`05 001oogooOol00003Ool00`00Oomoo`02Ool00`00Oomoo`3UOol00`00Oomoo`05Ool00`00Ool00005 Ool2000TOol0015oo`<001Aoo`8000Ioo`<000Yoo`05001oogooOol00003Ool00`00Oomoo`02Ool3 002GOol00`00Oomoo`0NOol00`00Oomoo`0ZOol00`00Oomoo`05Ool00`00Ool00005Ool20006Ool0 0`00Oomoo`0KOol003eoo`05001oogooOol00003Ool00`00Oomoo`02Ool00`00Oomoo`2GOol00`00 Oomoo`0NOol00`00Oomoo`0ZOol00`00Oomoo`05Ool00`00Ool00005Ool20006Ool00`00Oomoo`0K Ool003eoo`03001oogoo009oo`<000Eoo`03001oogoo09Moo`03001oogoo01ioo`03001oogoo02Yo o`03001oogoo00Eoo`03001oo`0000Eoo`8000Ioo`03001oogoo01]oo`00?Woo00<007ooOol00Woo 00<007ooOol017oo00<007ooOol0Ugoo00<007ooOol07Woo00<007ooOol0:Woo00<007ooOol01Goo 00<007oo00001Goo0P001Woo00<007ooOol06goo000mOol20005Ool20004Ool3002GOol00`00Oomo o`0NOol00`00Oomoo`0ZOol00`00Oomoo`05Ool00`00Ool00005Ool20006Ool00`00Oomoo`0KOol0 04Yoo`03001oogoo09Moo`03001oogoo01ioo`03001oogoo02Yoo`03001oogoo00Eoo`03001oo`00 00Eoo`8000Ioo`03001oogoo01]oo`00BWoo00<007ooOol0Ugoo00<007ooOol07Woo00<007ooOol0 :Woo00<007ooOol01Goo00@007oo000000Aoo`8000Ioo`03001oogoo01]oo`00BWoo00<007ooOol0 Ugoo00<007ooOol07Woo00<007ooOol0:Woo00<007ooOol01Goo00@007oo000000Aoo`8000Ioo`03 001oogoo01]oo`00BWoo00<007ooOol0Ugoo00<007ooOol07Woo00<007ooOol0:Woo00<007ooOol0 1Goo00@007oo000000Aoo`8000Ioo`03001oogoo01]oo`00BWoo0`00Ugoo00<007ooOol07Woo00<0 07ooOol0:Woo00<007ooOol01Goo00@007oo000000Aoo`8000Ioo`03001oogoo01]oo`00BWoo00<0 07ooOol0Ugoo00<007ooOol07Woo00<007ooOol0:Woo00<007ooOol01Goo00@007oo000000Aoo`80 00Ioo`03001oo`0001]oo`00BWoo00<007ooOol0Ugoo00<007ooOol07Woo00<007ooOol0:Woo00<0 07ooOol01Goo00@007oo000000Aoo`8000Ioo`03001oo`0001]oo`00BWoo00<007ooOol0Ugoo00<0 07ooOol07Woo00<007ooOol0:Woo00<007ooOol01Goo00@007oo000000Aoo`8000Ioo`03001oo`00 01]oo`00BWoo0`00FGoo00<007ooOol0:Woo00<007ooOol02Woo00@007ooOomoo`80015oo`03001o ogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Yoo`03001oogoo00moo`03001o ogoo00Eoo`03001oogoo00Aoo`800003Ool0000000=oo`<000=oo`06001oogoo001oo`001Woo00<0 07ooOol04Woo000=Ool50005Ool00`00Oomoo`03Ool00`00Oomoo`05Ool40005Ool3000IOol00`00 Oomoo`1IOol00`00Oomoo`0ZOol00`00Oomoo`0:Ool01000Oomoogoo0P004Goo00<007ooOol017oo 00<007ooOol017oo00<007ooOol00goo00<007ooOol02Woo00<007ooOol03goo00<007ooOol01Goo 00<007ooOol017oo0P0000=oo`0000000goo0`000goo00H007ooOol007oo0006Ool00`00Oomoo`07 Ool00`00Oomoo`08Ool000ioo`05001oogooOol00005Ool01@00Oomoogoo00002Goo00<007ooOol0 17oo00D007ooOomoo`0001Qoo`03001oogoo05Uoo`03001oogoo02Yoo`03001oogoo00Yoo`04001o ogooOol2000AOol00`00Oomoo`04Ool00`00Oomoo`04Ool00`00Oomoo`03Ool00`00Oomoo`0:Ool0 0`00Oomoo`0?Ool00`00Oomoo`05Ool00`00Oomoo`04Ool200000goo00000003Ool30003Ool01P00 Oomoo`00Ool000Ioo`03001oogoo00Moo`03001oogoo00Qoo`003goo00<007ooOol01goo00<007oo 00002goo00<007ooOol00goo00<007ooOol00Woo00<007ooOol05Goo00<007ooOol0FGoo00<007oo Ool0:Woo00<007ooOol02Woo00@007ooOomoo`80015oo`03001oogoo00Aoo`03001oogoo00Aoo`03 001oogoo00=oo`03001oogoo00Yoo`03001oogoo00moo`03001oogoo00Eoo`03001oogoo00Aoo`80 0003Ool0000000=oo`<000=oo`06001oogoo001oo`001Woo00<007ooOol01goo00<007ooOol027oo 0003Ool80005Ool00`00Oomoo`07Ool00`00Oomoo`0:Ool00`00Oomoo`03Ool00`00Oomoo`02Ool0 0`00Oomoo`0EOol00`00Oomoo`1IOol00`00Oomoo`0ZOol00`00Oomoo`0:Ool01000Oomoogoo0P00 4Goo00<007ooOol017oo00<007ooOol017oo00<007ooOol00goo00<007ooOol02Woo00<007ooOol0 3goo00<007ooOol01Goo00<007ooOol017oo0P0000=oo`0000000goo0`000goo00H007ooOol007oo 0006Ool00`00Oomoo`04Ool00`00Oomoo`020009Ool0015oo`03001oogoo00Eoo`03001oo`0000]o o`03001oogoo00=oo`03001oogoo00=oo`03001oogoo01Aoo`<005Uoo`03001oogoo02Yoo`03001o ogoo00Yoo`04001oogooOol2000AOol00`00Oomoo`04Ool00`00Oomoo`04Ool00`00Oomoo`03Ool0 0`00Oomoo`0:Ool00`00Oomoo`0?Ool00`00Oomoo`05Ool00`00Oomoo`04Ool200000goo00000003 Ool30003Ool01P00Oomoo`00Ool000Ioo`03001oogoo00Aoo`03001oogoo008000Uoo`004Woo00<0 07ooOol00goo00D007ooOomoo`0000]oo`03001oogoo009oo`03001oogoo00=oo`03001oogoo01Ao o`03001oogoo03moo`03001oogoo01Moo`03001oogoo02Yoo`03001oogoo00Yoo`03001oogoo00<0 015oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Yoo`03001oogoo 00moo`03001oogoo009oo`800003Ool0000000Eoo`800004Ool000000002Ool30003Ool01P00Oomo o`00Ool000Ioo`03001oogoo00Aoo`03001oogoo008000Uoo`004goo00D007ooOomoo`0000Eoo`03 001oogoo00Qoo`03001oogoo00=oo`03001oogoo009oo`03001oogoo00Eoo`<000Aoo`8000Ioo`03 001oogoo03moo`03001oogoo01Moo`03001oogoo02Yoo`03001oogoo00Yoo`03001oogoo00<0015o o`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Yoo`03001oogoo00mo o`03001oogoo009oo`800003Ool0000000Eoo`800004Ool000000002Ool30003Ool01P00Oomoo`00 Ool000Ioo`03001oogoo00Aoo`03001oogoo008000Uoo`004goo00<007ooOol04Woo00<007ooOol0 0goo00<007ooOol00Woo00<007ooOol01Woo00<007ooOol00Woo00@007ooOol000Eoo`03001oogoo 03moo`03001oogoo01Moo`03001oogoo02Yoo`03001oogoo00Yoo`03001oogoo00<0015oo`03001o ogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Yoo`03001oogoo00moo`03001o ogoo009oo`800003Ool0000000Eoo`800004Ool000000002Ool30003Ool01P00Oomoo`00Ool000Io o`03001oogoo00Aoo`03001oogoo008000Uoo`003goo00D007ooOomoo`0001Eoo`03001oogoo00=o o`04001oogooOol60004Ool01@00Oomoogoo00000goo00<007ooOol00Woo0`00?goo00<007ooOol0 5goo00<007ooOol0:Woo00<007ooOol02Woo00<007ooOol00`004Goo00<007ooOol017oo00<007oo Ool017oo00<007ooOol00goo00<007ooOol02Woo00<007ooOol03goo00<007ooOol00Woo0P0000=o o`0000001Goo0P0000Aoo`000000009oo`<000=oo`800004Ool007oo0005Ool20006Ool00`00Oomo o`020009Ool0011oo`<001Eoo`8000Ioo`<000Yoo`05001oogooOol00003Ool00`00Oomoo`02Ool0 0`00Oomoo`0oOol00`00Oomoo`0GOol00`00Oomoo`0ZOol00`00Oomoo`0:Ool00`00Oomoo`03000A Ool00`00Oomoo`04Ool00`00Oomoo`04Ool00`00Oomoo`03Ool00`00Oomoo`0:Ool00`00Oomoo`0? Ool00`00Oomoo`02Ool200000goo00000005Ool2000017oo000000000Woo0`000goo0P0000Aoo`00 Ool000Eoo`8000Ioo`03001oogoo008000Uoo`00?Goo00D007ooOomoo`0000=oo`03001oogoo009o o`03001oogoo03moo`03001oogoo01Moo`03001oogoo02Yoo`03001oogoo00Yoo`03001oogoo00<0 015oo`03001oogoo00Aoo`03001oogoo00Aoo`03001oogoo00=oo`03001oogoo00Yoo`03001oogoo 00moo`03001oogoo009oo`800003Ool0000000Eoo`800004Ool000000002Ool30003Ool2000017oo 001oo`001Goo0P001Woo00<007ooOol00P002Goo000mOol00`00Oomoo`02Ool30005Ool00`00Oomo o`0aOol00`00Oomoo`0;Ool00`00Oomoo`0GOol00`00Oomoo`04Ool00`00Oomoo`03Ool01000Ool0 00001Goo00@007ooOol0009oo`03001oogoo00Moo`04001oogoo0003Ool00`00Oomoo`020003Ool0 0`00Oomoo`02Ool00`00Oomoo`030003Ool00`00Oomoo`05Ool01@00Oomoo`00Ool00P000Woo00D0 07oo001oo`0000Aoo`05001oo`00Ool00003Ool00`00Oomoo`05Ool00`00Oomoo`02Ool00`00Oomo o`02Ool01000Oomoo`000goo00<007ooOol00goo0`000Woo0P0000=oo`0000001Goo0P0000Aoo`00 0000009oo`<000=oo`800003Ool007oo008000Aoo`8000Ioo`03001oogoo008000Uoo`00?Woo00<0 07ooOol00Woo00<007ooOol017oo00<007ooOol0Ool40005Ool00`00Oomoo`03Ool00`00Oomoo`05Ool40005Ool3000IOol00`00Oomoo`0aOol0 0`00Oomoo`0:Ool20004Ool01@00Oomoogoo00000Woo00<007ooOol00Woo0P001Woo0P001Woo0P00 17oo00@007oo000000Eoo`04001oogoo0002Ool00`00Oomoo`07Ool01000Oomoo`000goo0P0000=o o`0000000goo00<007ooOol00Woo00<007ooOol00`000goo00<007ooOol01Goo00D007oo000007oo 00<00006Ool007oo001oo`0017oo00D007oo001oo`0000=oo`03001oogoo00Eoo`03001oogoo009o o`8000=oo`03001oogoo0080009oo`03001oogoo00=oo`<0009oo`800003Ool00000009oo`03001o o`0000800004Ool000000002Ool800000goo001oo`030003Ool20005Ool3000017oo0000000027oo 000?Ool00`00Oomoo`06Ool01@00Oomoogoo00002Goo00<007ooOol017oo00D007ooOomoo`0001Qo o`03001oogoo02moo`03001oo`0000aoo`8000=oo`800005Ool007oo001oo`02000017oo000007oo 0P000goo00<007ooOol00P001Goo0`0017oo00@007oo0000009oo`03001oo`0000T000Aoo`05001o ogoo001oo`020002Ool70002Ool300001Goo00000000Ool00`0000Aoo`00000000=oo``00003Ool0 07oo00@0009oo`800003Ool007oo00800004Ool00000Ool20003Ool20004Ool20003Ool00`00Oomo o`0200000goo00000005Ool4000017oo000007oo0P000Woo00<007oo00000P0000Aoo`000000009o o`X00004Ool000000003Ool20005Ool3000017oo0000000027oo000@Ool00`00Oomoo`06Ool00`00 Ool0000;Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`0EOol00`00Oomoo`0_Ool00`00 Ool00000003Ool5 0002Ool70008Ool003eoo`8000Eoo`8000Aoo`<0025oo`03001oogoo009oo`8000Eoo`H0009oo`04 001oogoo0005Ool4000027oo000007oo001oo`00Ool2000017oo000007oo0P000Woo0P000Woo0P00 1Goo10000goo10000Woo00<007oo00000`0000=oo`0000000`000goo0P000Woo00@007oo0000009o o`P00003Ool0000000D00005Ool00000001oo`030002Ool800000goo000000090002Ool200000goo 001oo`02000017oo000007oo0`000Woo0P0017oo0P000Woo0P000Woo1@0000Aoo`00001oo`D00004 Ool00000Ool20002Ool00`00Ool0000300000goo00000002Ool>0003Ool50002Ool70008Ool004Yo o`03001oogoo01Eoo`03001oogoo00=oo`03001oogoo00=oo`03001oogoo009oo`80009oo`X00004 Ool007ooOol:000017oo000007oo7`0000=oo`0000001@0000=oo`0000000P0000=oo`0000002P00 00=oo`000000700000=oo`0000001P0000=oo`0000002@000Woo0P0000=oo`00Ool00P0000Aoo`00 001oo`P00003Ool0000000<00003Ool0000000L00004Ool00000Ool500000goo000000030002Ool0 0`00Ool00003000017oo000007oo3`000goo1@000Woo1`0027oo001:Ool00`00Oomoo`0COol00`00 Ool00005Ool00`00Oomoo`03Ool20003Ool20002Ool01000Oomoogoo1P0000Aoo`00Oomoo`X00004 Ool00000OolE0002Ool800000goo0000000200001Woo000007oo001oo`800003Ool0000000X00003 Ool0000000X00003Ool0000000P00003Ool0000000@00003Ool007oo00H00003Ool0000000T0009o o`800003Ool007oo00800004Ool00000Ool800000goo0000000300000goo00000007000017oo0000 07oo2`000Woo00<007oo00000`0000Aoo`00001oo`l000=oo`D0009oo`L000Qoo`00BWoo00<007oo Ool04goo00<007oo00001Goo00<007ooOol00goo0P000goo0P000Woo00@007ooOomoo`H00004Ool0 07ooOol:000017oo000007oo5@000Woo200000=oo`0000000P0000Ioo`00001oo`00Ool200000goo 0000000:00000goo0000000:00000goo0000000800000goo0000000400000goo001oo`0600000goo 000000090002Ool200000goo001oo`02000017oo000007oo200000=oo`0000000`0000=oo`000000 1`0000Aoo`00001oo`/0009oo`03001oo`0000<00004Ool00000Ool?0003Ool50002Ool70008Ool0 04Yoo`<000eoo`03001oogoo00=oo`03001oo`0000Eoo`03001oogoo00=oo`@00003Ool00000009o o`04001oogooOol800000goo00000009000017oo000007oo5@000Woo200000=oo`0000000P0000Io o`00001oo`00Ool200000goo00000007000017oo000007oo300000=oo`000000200000=oo`000000 100000=oo`00Ool01P0000=oo`0000002@000Woo0P0000=oo`00Ool00P0000Aoo`00001oo`P00003 Ool0000000<00003Ool0000000L00004Ool00000Ool<00000goo00000004000017oo000007oo3`00 0goo1P0000=oo`0000001@0027oo001:Ool00`00Oomoo`0=Ool00`00Oomoo`03Ool00`00Ool00005 Ool00`00Oomoo`03Ool200000goo000000020002Ool01000Oomoogoo200000=oo`0000002@0000Ao o`00001ooaD0009oo`P00003Ool0000000800006Ool00000Ool007oo0P0000=oo`0000002P0000=o o`0000002P0000=oo`000000200000=oo`000000100000=oo`00Ool01P0000=oo`0000002@000Woo 0P0000=oo`00Ool00P0000Aoo`00001oo`P00003Ool0000000<00003Ool0000000L00004Ool00000 Ool<00000goo00000004000017oo000007oo3`000goo1P0000=oo`0000001@0027oo001:Ool00`00 Oomoo`0=Ool00`00Oomoo`03Ool00`00Ool00005Ool00`00Oomoo`03Ool200000goo001oo`020002 Ool01000Oomoogoo200000=oo`0000002@0000Aoo`00001ooaD0009oo`P00003Ool0000000800006 Ool00000Ool007oo0P0000=oo`0000001`0000Aoo`00001oo``00003Ool0000000P00003Ool00000 00@00003Ool007oo00H00003Ool0000000T0009oo`800003Ool007oo00800004Ool00000Ool80000 0goo0000000300000goo00000007000017oo000007oo1@0000=oo`000000100000=oo`0000001000 00Aoo`00001oo`l000=oo`H00003Ool0000000D000Qoo`00BWoo00<007ooOol03Goo00<007ooOol0 0goo0`0000=oo`00Ool010000Woo100000Aoo`00001oo`@000=ooa@00003Ool0000001H0009oo`P0 0003Ool0000000800006Ool00000Ool007oo0P0000=oo`0000001`0000Aoo`00001oo`X00003Ool0 07oo00800003Ool0000000D00003Ool0000000@00003Ool007oo00H00003Ool0000000T0009oo`80 0003Ool007oo00800004Ool00000Ool800000goo0000000300000goo00000007000017oo000007oo 300000=oo`000000100000=oo`00000040000goo1P0000=oo`0000001@0027oo001:Ool00`00Oomo o`0=Ool20004Ool300000goo001oo`040002Ool400000goo00000002Ool20004Ool01000Ool007oo 1P0000=oo`0000001`0000=oo`000000100000=oo`0000000P0000=oo`0000002P000Woo200000=o o`0000000P0000Aoo`000000009oo`800004Ool00000Ool6000017oo000007oo2P0000=oo`00Ool0 0P0000=oo`0000001@0000=oo`000000100000=oo`00Ool01P0000=oo`0000002@000Woo0P0000=o o`00Ool00P0000=oo`0000002@0000=oo`0000000`0000=oo`0000001`0000Ioo`00001oo`00Ool: 00000goo0000000400000goo0000000@0003Ool600000goo000000050008Ool004Yoo`<000aoo`<0 00=oo`@00003Ool007oo00@0009oo`L0009oo`8000Aoo`04001oo`00Ool600000goo000000070000 0goo0000000400000goo0000000200000goo0000000:0002Ool800000goo00000002000017oo0000 00000Woo0P0000Aoo`00001oo`H00004Ool00000Ool:00000goo001oo`0200000goo000000050000 0goo0000000400000goo001oo`0600000goo000000090002Ool200000goo001oo`0200000goo0000 000900000goo0000000300000goo0000000700001Woo000007oo001oo`X00003Ool0000000@00003 Ool00000010000=oo`H00003Ool0000000D000Qoo`00BWoo00<007ooOol01goo00<007ooOol01@00 00=oo`000000100000=oo`00Ool03@000Woo0P0017oo00@007oo001oo`H00003Ool0000000L00003 Ool0000000@00003Ool0000000800003Ool0000000X0009oo`P00003Ool0000000800004Ool00000 0002Ool2000017oo000007oo1P0000Aoo`00001oo`X00003Ool007oo00800003Ool0000000D00003 Ool0000000@00003Ool007oo00H00003Ool0000000T0009oo`800003Ool007oo00800003Ool00000 00T00003Ool0000000<00003Ool0000000L00006Ool00000Ool007oo2P0000=oo`000000100000=o o`00000040000goo1P0000=oo`0000001@0027oo001:Ool00`00Oomoo`07Ool00`00Oomoo`050000 0goo00000003000017oo000007oo2`0000Aoo`00Oomoo`8000Aoo`04001oo`00Ool600000goo0000 000<00001Goo001oo`00Ool00P0000=oo`0000002P000Woo200000=oo`0000000P0000Aoo`000000 009oo`800004Ool00000Ool6000017oo000007oo2P0000=oo`00Ool00P0000=oo`0000001@0000=o o`000000100000=oo`00Ool01P0000=oo`0000002@000Woo0P0000=oo`00Ool00P0000=oo`000000 2@0000=oo`0000000`0000=oo`0000001`0000Ioo`00001oo`00Ool:00000goo0000000400000goo 0000000@0003Ool600000goo000000050008Ool004Yoo`04001oogooOol200000goo001oo`020002 Ool;00000goo0000000<000017oo001oogoo0P0017oo00@007oo001oo`H00003Ool0000000`00005 Ool007oo001oo`0200000goo0000000:0002Ool800000goo00000002000017oo000000000Woo0P00 00Aoo`00001oo`H00004Ool00000Ool:00000goo001oo`0200000goo0000000500000goo00000004 00000goo001oo`0600000goo000000090002Ool200000goo001oo`0200000goo0000000900000goo 0000000300000goo0000000700001Woo000007oo001oo`X00003Ool0000000@00003Ool000000100 00=oo`H00003Ool0000000D000Qoo`00BWoo1P0000=oo`0000000P000Woo2`0000=oo`0000003000 00Aoo`00Oomoo`8000Aoo`04001oo`00Ool600000goo0000000<00001Goo001oo`00Ool00P0000=o o`0000002P000Woo200000=oo`0000000P0000Aoo`000000009oo`800004Ool00000Ool6000017oo 000007oo2P0000=oo`00Ool00P0000=oo`0000001@0000=oo`000000100000=oo`00Ool01P0000=o o`0000002@000Woo0P0000=oo`00Ool00P0000=oo`0000002@0000=oo`0000000`0000=oo`000000 1`0000Ioo`00001oo`00Ool:00000goo0000000400000goo0000000@0003Ool600000goo00000006 0007Ool004Aoool002D00000BWoo00<007ooOol017oo0`0000=oo`0000002`0000=oo`0000000P00 00=oo`0000000P000Woo0`0000Aoo`00Oomoo`<000=oo`05001oo`00Ool00002Ool20002Ool40002 Ool800000goo001oo`03Ool01@00Oomoogoo00000goo1P000goo00<007ooOol00`0000=oo`000000 0`000Woo0P000Woo00<007ooOol017oo00D007oo001oo`0000Aoo`D0009oo`<00003Ool007oo0080 0003Ool007oo00D00004Ool007ooOol300000goo001oo`0300001goo001oogoo001oo`0000=oo`H0 0003Ool0000001/00003Ool0000000<00006Ool00000Ool007oo2P0000=oo`000000100000=oo`00 0000400000=oo`00Ool01P0000=oo`0000001P0017oo0@000Goo0Goo001:Ool00`00Oomoo`06Ool0 1P00Oomoo`00Ool0009oo`03001oo`00009oo`800003Ool0000000800003Ool00000008000=oo`04 001oogoo0002Ool20004Ool01@00Ool007oo00000Woo0P000Woo10000Woo200000=oo`00Ool00goo 00D007ooOomoo`0000=oo`03001oo`0000<000=oo`03001oogoo00<00004Ool00000Ool20002Ool2 0009Ool01@00Ool007oo000017oo0P0000=oo`0000000Woo0`0000=oo`00Ool00P0000Eoo`00Ool0 07oo00<00004Ool007ooOol300000goo001oo`0300001goo001oogoo001oo`0000=oo`H00003Ool0 000001400003Ool0000000L00003Ool0000000<00006Ool00000Ool007oo2P0000Eoo`00000007oo 00800003Ool0000001000003Ool007oo00H00003Ool007oo00H000Moo`00BWoo00<007ooOol02Goo 00<007oo00000Woo00<007oo00000Woo0P0000=oo`0000000P0000=oo`0000000P000goo00@007oo Ool0009oo`03001oogoo00=oo`05001oo`00Ool00002Ool20002Ool40002Ool800000goo001oo`03 Ool01@00Oomoogoo00000goo00<007oo00000`000goo00<007ooOol00`0000Aoo`00001oo`80009o o`8000Uoo`05001oo`00Ool00004Ool200000goo00000002Ool300000goo001oo`0200001Goo001o o`00Ool00`0000Aoo`00Oomoo`<00003Ool007oo00<00007Ool007ooOol007oo00000goo1P0000=o o`0000004@0000=oo`0000001`0000=oo`0000000`0000Ioo`00001oo`00Ool:00001Goo00000000 Ool00P0000=oo`000000400000=oo`00Ool01P0000=oo`00Ool00`0000=oo`0000001goo001:Ool3 000>Ool00`00Oomoo`07Ool200000goo001oo`020006Ool01000Oomoo`001Goo00D007oo001oo`00 009oo`80009oo`@0009oo`P00003Ool007oo00=oo`05001oogooOol00003Ool00`00Ool000030003 Ool00`00Oomoo`03000017oo000007oo0P000Woo0P002Goo00D007oo001oo`0000Aoo`800003Ool0 0000009oo`<00003Ool007oo00800005Ool007oo001oo`03000017oo001oogoo0`0000=oo`00Ool0 0`0000Moo`00Oomoo`00Ool00003Ool600000goo0000000A00000goo0000000700000goo00000003 00001Woo000007oo001oo`X00005Ool00000001oo`0200000goo0000000@00000goo001oo`060000 0goo001oo`0300000goo00000007Ool004Yoo`03001oogoo01Uoo`04001oo`00Ool20006Ool01000 Oomoo`001Goo00D007oo001oo`00009oo`80009oo`@0009oo`P00003Ool007oo00=oo`05001oogoo Ool00003Ool00`00Ool000030003Ool00`00Oomoo`03000017oo000007oo0P000Woo0P002Goo00D0 07oo001oo`0000Aoo`800003Ool00000009oo`<00003Ool007oo00800005Ool007oo001oo`030000 17oo001oogoo0`0000=oo`00Ool00`0000Moo`00Oomoo`00Ool00003Ool600000goo0000000A0000 0goo0000000700000goo0000000300001Woo000007oo001oo`X00005Ool00000001oo`0200000goo 0000000@00000goo001oo`0600000goo001oo`0300000goo00000007Ool004Yoo`03001oogoo01Uo o`04001oo`00Ool20006Ool01000Oomoo`001Goo00D007oo001oo`0000=oo`03001oogoo00@0009o o`05001oo`00001oo`0300000goo001oo`03Ool01@00Oomoogoo00000goo00<007oo00000`000goo 00L007ooOol007oo001oo`020002Ool00`00Oomoo`020009Ool01@00Ool007oo000017oo0P0000=o o`0000000Woo0P000Woo00T007oo000007oo001oo`00Ool00`0000Yoo`00Oomoo`00Ool007oo001o o`<00007Ool007ooOol007oo00000goo1P0000Aoo`00001ooaX00003Ool0000000H00003Ool007oo 00X00005Ool00000001oo`0200000goo0000000@00000goo0000000600000goo001oo`0300000goo 00000007Ool004Yoo`03001oogoo01Uoo`04001oogooOol20009Ool00`00Oomoo`03Ool01@00Oomo ogoo00000goo00<007ooOol00Woo00H007ooOomoo`00Ool200000goo001oo`0?Ool00`00Ool00003 0003Ool01`00Oomoo`00Ool007oo0080009oo`03001oogoo008000Uoo`05001oo`00Ool00004Ool2 00000goo00000002Ool20002Ool02@00Ool00000Ool007oo001oo`0300002Woo001oogoo001oo`00 Ool007oo0`0000Moo`00Oomoo`00Ool00003Ool6000017oo000007oo6P0000=oo`0000001P0000=o o`00Ool02P0000Eoo`00000007oo00800003Ool0000001000003Ool0000000P00005Ool00000001o o`020007Ool004Yoo`03001oogoo01Uoo`04001oogooOol20009Ool00`00Oomoo`03Ool01@00Oomo ogoo00000goo00<007ooOol00Woo00H007ooOomoo`00Ool200000goo001oo`0?Ool00`00Ool00003 0003Ool01`00Oomoo`00Ool007oo0080009oo`03001oogoo008000Uoo`05001oo`00Ool00004Ool2 00000goo00000002Ool20002Ool02@00Ool00000Ool007oo001oo`0300002Woo001oogoo001oo`00 Ool007oo0`0000Moo`00Oomoo`00Ool00003Ool6000017oo000007oo6P0000=oo`0000001P0000=o o`00Ool02P0000Eoo`00000007oo00800003Ool0000001000003Ool0000000P00005Ool00000001o o`020007Ool004Yoo`<001Uoo`04001oogooOol20009Ool00`00Oomoo`03Ool01@00Oomoogoo0000 0goo00<007ooOol00Woo00H007ooOomoo`00Ool200000goo001oo`0?Ool00`00Ool000030003Ool0 1`00Oomoo`00Ool007oo0080009oo`03001oogoo008000Uoo`05001oo`00Ool00004Ool200000goo 00000002Ool20002Ool02@00Ool00000Ool007oo001oo`0300002Woo001oogoo001oo`00Ool007oo 0`0000Moo`00Oomoo`00Ool00003Ool6000017oo000007oo6P0000=oo`0000001`000Woo2P0000Eo o`00000007oo00800003Ool0000001000003Ool0000000P00005Ool00000001oo`020007Ool004Yo o`03001oogoo02Qoo`03001oogoo00=oo`05001oogooOol00003Ool00`00Oomoo`02Ool01P00Oomo ogoo001oo`800003Ool007oo00moo`03001oo`0000<000=oo`07001oogoo001oo`00Ool00P000Woo 00<007ooOol00P002Goo00D007oo001oo`0000Aoo`800003Ool00000009oo`80009oo`09001oo`00 001oo`00Ool007oo00<0000:Ool007ooOol007oo001oo`00Ool300001goo001oogoo001oo`0000=o o`H00004Ool00000OolJ00000goo000000070002Ool:00001Goo00000000Ool00P0000=oo`000000 400000=oo`000000200000Aoo`000000009oo`03001oogoo00Eoo`00BWoo00<007ooOol0:7oo00<0 07ooOol00goo00D007ooOomoo`0000=oo`03001oogoo009oo`06001oogooOol007oo0P0000=oo`00 Ool03goo00<007oo00000`000goo00L007ooOol007oo001oo`020002Ool00`00Oomoo`020009Ool0 1@00Ool007oo000017oo0P0000=oo`0000000Woo0P000Woo00T007oo000007oo001oo`00Ool00`00 00Yoo`00Oomoo`00Ool007oo001oo`<00007Ool007ooOol007oo00000goo1P0000Aoo`00001ooaX0 0003Ool0000000L0009oo`X00005Ool00000001oo`0200000goo0000000@00000goo000000080000 17oo000000000Woo00<007ooOol01Goo001:Ool00`00Oomoo`0XOol00`00Oomoo`03Ool01@00Oomo ogoo00000goo00<007ooOol00Woo00H007ooOomoo`00Ool200000goo001oo`0?Ool00`00Ool00003 0003Ool01`00Oomoo`00Ool007oo0080009oo`03001oogoo008000Uoo`05001oo`00Ool00004Ool2 00000goo00000002Ool20002Ool02@00Ool00000Ool007oo001oo`0300001Woo001oogoo001oo`<0 0006Ool00000001oo`000Woo00<007oo00000goo2@0000=oo`000000600000=oo`0000001`000Woo 2P0000Eoo`00000007oo00800003Ool0000001000003Ool0000000P00004Ool000000002Ool00`00 Oomoo`05Ool004Yoo`<0039oo`03001oogoo00eoo`03001oogoo03moo`05001oogooOol00009Ool0 0`00Ool0000:Ool00`00Ool0000200001Goo001oogoo00001goo1`0000=oo`0000001`000Woo2000 00=oo`00Ool0100000=oo`0000001`000Woo1`000Woo00<007oo00000P0000Aoo`00001oo`/00003 Ool0000000@00003Ool0000000P00004Ool000000002Ool00`00Oomoo`05Ool004Yoo`03001oogoo 039oo`03001oogoo00eoo`03001oogoo03moo`05001oogooOol00009Ool00`00Ool0000:Ool00`00 Ool0000200001Goo001oogoo00001goo1`0000=oo`0000001`000Woo200000=oo`00Ool0100000=o o`0000001`000Woo1`000Woo00<007oo00000P0000Aoo`00001oo`/00003Ool0000000@00003Ool0 000000P00004Ool000000002Ool00`00Oomoo`05Ool004Yoo`03001oogoo039oo`03001oogoo00eo o`03001oogoo03moo`05001oogooOol00009Ool00`00Ool0000:Ool00`00Ool0000200001Goo001o ogoo00001goo1`0000=oo`0000001`000Woo200000=oo`00Ool0100000=oo`0000001`000Woo1`00 0Woo00<007oo00000P0000Aoo`00001oo`/00003Ool0000000@00003Ool0000000P00004Ool00000 0002Ool00`00Oomoo`05Ool004Yoo`03001oogoo039oo`03001oogoo00eoo`03001oogoo03moo`05 001oogooOol00009Ool00`00Ool0000:Ool00`00Ool0000200001Goo001oogoo00001goo1`0000=o o`0000001`000Woo200000=oo`00Ool0100000=oo`000000100000=oo`0000000Woo1`000Woo00<0 07oo00000P0000Aoo`00001oo`/00003Ool0000000l00004Ool000000002Ool00`00Oomoo`05Ool0 04Yoo`03001oogoo039oo`03001oogoo00eoo`03001oogoo03moo`05001oogooOol00009Ool00`00 Ool0000:Ool00`00Ool0000200001Goo001oogoo00001goo1`0000=oo`0000001`000Woo200000=o o`00Ool0100000=oo`000000100000=oo`0000000Woo1`000Woo00<007oo00000P0000Aoo`00001o o`/00003Ool0000000l00004Ool000000002Ool00`00Oomoo`05Ool000ioo`@000Eoo`03001oogoo 00=oo`03001oogoo00Eoo`@000Eoo`<001Uoo`<0039oo`03001oogoo00eoo`03001oogoo03moo`05 001oogooOol00009Ool00`00Ool0000:Ool00`00Ool0000200001Goo001oogoo00001goo1`0000=o o`0000001`000Woo200000=oo`00Ool0100000=oo`000000100000=oo`0000000Woo1`000Woo00<0 07oo00000P0000Aoo`00001oo`/00003Ool0000000l00004Ool000000002Ool00`00Oomoo`05Ool0 00moo`03001oogoo00Ioo`05001oogooOol00009Ool00`00Oomoo`04Ool01@00Oomoogoo000067oo 00<007ooOol0Ool2 0003Ool01000Ool000000goo00<007oo00000goo00@007oo001oo`@00004Ool007ooOol30002Ool3 0003Ool20003Ool300000goo001oo`02Ool5000017oo000007oo100000=oo`000000100000=oo`00 Ool01P0000=oo`0000000`0000Aoo`00001oo`<000Yoo`00BWoo00<007ooOol0TWoo00<007ooOol0 37oo0P003Woo0P000goo00@007oo000000=oo`03001oo`0000=oo`04001oo`00Ool4000017oo001o ogoo0`000Woo0`000goo0P000goo0`0000=oo`00Ool00Woo1@0000Aoo`00001oo`@00003Ool00000 00@00003Ool007oo00H00003Ool0000000<00004Ool00000Ool3000:Ool004Yoo`03001oogoo099o o`03001oogoo00aoo`8000ioo`8000=oo`04001oo`000003Ool00`00Ool00003Ool01000Ool007oo 100000Aoo`00Oomoo`<0009oo`<000=oo`8000=oo`<00003Ool007oo009oo`D00004Ool00000Ool4 00000goo0000000400000goo001oo`0600000goo00000003000017oo000007oo0`002Woo001:Ool0 0`00Oomoo`2BOol00`00Oomoo`0Ool20003Ool01000Ool000000goo00<007oo00000goo 00@007oo001oo`@00004Ool007ooOol30002Ool30003Ool20003Ool300000goo001oo`02Ool30000 0goo001oo`0200000goo0000000200000goo00000004000017oo001oogoo1@0000=oo`0000000`00 00Aoo`00001oo`<000Yoo`00BWoo0`00TWoo00<007ooOol037oo0P003Woo0P000goo00@007oo0000 00=oo`03001oo`0000=oo`04001oo`00Ool4000017oo001oogoo0`000Woo0`000goo0P000goo0`00 00=oo`00Ool00Woo0`0000=oo`00Ool00P0000=oo`0000000P0000=oo`000000100000Aoo`00Oomo o`D00003Ool0000000<00004Ool00000Ool3000:Ool004Yoo`03001oogoo099oo`03001oogoo00ao o`8000ioo`8000=oo`04001oo`000003Ool00`00Ool00003Ool01000Ool007oo100000Aoo`00Oomo o`<0009oo`<000=oo`8000=oo`<00003Ool007oo009oo`<00003Ool007oo00800003Ool000000080 0003Ool0000000@00004Ool007ooOol500000goo00000003000017oo000007oo0P002goo001:Ool0 0`00Oomoo`2BOol00`00Oomoo`0=Ool00`00Oomoo`0Ool00`00Ool00004Ool20003Ool20002Ool00`00Oomoo`03Ool20007 Ool30004Ool300000goo001oo`02Ool00`00Oomoo`09Ool004Yoo`03001oogoo0=1oo`03001oogoo 00ioo`03001oo`0000Aoo`8000=oo`80009oo`03001oogoo00=oo`8000Moo`<000Aoo`<00003Ool0 07oo009oo`03001oogoo00Uoo`00BWoo00<007ooOol0d7oo00<007ooOol03Woo00<007oo000017oo 0P000goo0P000Woo00<007ooOol00goo0P001goo0`0017oo0`0000=oo`00Ool00Woo00<007ooOol0 2Goo001:Ool00`00Oomoo`3@Ool00`00Oomoo`0>Ool00`00Ool00004Ool20003Ool20002Ool00`00 Oomoo`03Ool20007Ool30004Ool300000goo001oo`0>Ool004Yoo`<00=1oo`03001oogoo00ioo`03 001oo`0000Aoo`8000=oo`80009oo`03001oogoo00=oo`8000Moo`<000Aoo`<00003Ool007oo00io o`00BWoo00<007ooOol0d7oo00<007ooOol03Woo00<007oo000017oo0P000goo0P000Woo00<007oo Ool00goo0P001goo0`0017oo0`0000=oo`00Ool03Woo001:Ool00`00Oomoo`3@Ool00`00Oomoo`0> Ool00`00Ool00004Ool20003Ool20002Ool00`00Oomoo`03Ool20007Ool30004Ool300000goo001o o`0>Ool004Yoo`03001oogoo0=1oo`03001oogoo00ioo`03001oo`0000Aoo`8000=oo`80009oo`03 001oogoo00=oo`8000Moo`<000Aoo`80019oo`00BWoo00<007ooOol0d7oo00<007ooOol03Woo00<0 07oo000017oo0P000goo0P000Woo00<007ooOol00goo0P001goo0`0017oo0P004Woo000>Ool30006 Ool00`00Oomoo`03Ool00`00Oomoo`05Ool40005Ool3000IOol3003@Ool00`00Oomoo`0>Ool00`00 Ool00004Ool20003Ool20002Ool00`00Oomoo`03Ool20007Ool20005Ool2000BOol0015oo`03001o ogoo00Aoo`05001oogooOol00009Ool00`00Oomoo`04Ool01@00Oomoogoo000067oo00<007ooOol0 d7oo00<007ooOol03Woo00<007oo000017oo0P000goo0P000Woo00<007ooOol00goo0P001goo0P00 1Goo0P004Woo000BOol00`00Oomoo`04Ool00`00Ool0000;Ool00`00Oomoo`03Ool00`00Oomoo`02 Ool00`00Oomoo`0EOol00`00Oomoo`3@Ool00`00Oomoo`0>Ool00`00Ool00004Ool20003Ool20002 Ool00`00Oomoo`03Ool20007Ool20005Ool2000BOol0019oo`03001oogoo00Eoo`03001oogoo00Yo o`03001oogoo00=oo`03001oogoo009oo`03001oogoo01Eoo`03001oogoo0=1oo`03001oogoo00io o`03001oo`0000Aoo`8000=oo`80009oo`03001oogoo00=oo`8000Moo`8000Eoo`80019oo`004Woo 00<007ooOol017oo00<007oo00002goo00<007ooOol00goo00<007ooOol00goo00<007ooOol057oo 0`00d7oo00<007ooOol03Woo00<007oo000017oo0P000goo0P000Woo00<007ooOol00goo0P001goo 0P001Goo0P004Woo000@Ool20006Ool01@00Oomoogoo00002goo00<007ooOol00Woo00<007ooOol0 0goo00<007ooOol057oo00<007ooOol0d7oo00<007ooOol03Woo00<007oo000017oo0P000goo0P00 0Woo00<007ooOol00goo0P001goo0P001Goo0P004Woo000BOol00`00Oomoo`02Ool00`00Oomoo`03 Ool00`00Oomoo`08Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`05Ool30004Ool20006 Ool00`00Oomoo`3@Ool00`00Oomoo`0>Ool00`00Ool00004Ool00`00Oomoo`02Ool20002Ool00`00 Oomoo`03Ool20007Ool20005Ool2000BOol001=oo`03001oogoo019oo`03001oogoo00=oo`03001o ogoo009oo`03001oogoo00Ioo`03001oogoo009oo`04001oogoo0005Ool00`00Oomoo`3@Ool00`00 Oomoo`0>Ool00`00Ool00004Ool00`00Oomoo`02Ool20002Ool00`00Oomoo`03Ool20007Ool20005 Ool2000BOol0011oo`04001oogoo000EOol00`00Oomoo`03Ool01000Oomoogoo1P0017oo00D007oo Oomoo`0000=oo`03001oogoo009oo`03001oogoo0=1oo`03001oogoo00ioo`03001oo`0000Aoo`03 001oogoo009oo`80009oo`03001oogoo00=oo`8000Moo`8000Eoo`80019oo`004Goo0`0057oo0P00 1Woo0`002Woo00D007ooOomoo`0000=oo`03001oogoo009oo`<00=1oo`03001oogoo00ioo`03001o o`0000Aoo`03001oogoo009oo`80009oo`03001oogoo00=oo`8000Moo`8000Eoo`03001oogoo015o o`00?Goo00D007ooOomoo`0000=oo`03001oogoo009oo`03001oogoo0=1oo`03001oogoo00ioo`03 001oo`0000Aoo`03001oogoo009oo`80009oo`03001oogoo00=oo`8000Moo`8000Eoo`03001oogoo 015oo`00?Goo00<007ooOol00Woo0`00ogoo97oo000nOol00`00Oomoo`02Ool00`00Oomoo`3oOolS Ool003eoo`8000Eoo`800?moob=oo`00ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003oOomY Ool00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00 ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo003oOomYOol00?moofUoo`00ogooJGoo0000\ \>"], ImageRangeCache->{{{109, 396}, {645.438, 468.5}} -> {-2.39665, \ 2.02055*^-15, 0.0141839, 5.47451*^-18}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Evaluate[ diff /. {\[Beta]\_1 \[Rule] 0.6, \[Beta] \[Rule] \(-0.3\)}], {\[Theta]\_1, 0, \[Pi]}];\)\)], "Input", CellLabel->"In[106]:="], 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 Times %%IncludeFont: Times /Times findfont 12 scalefont setfont % Scaling calculations 0.0238095 0.303152 0.272229 8.83612e+014 [ [.17539 .25973 -9.5 -15.6875 ] [.17539 .25973 9.5 0 ] [.32696 .25973 -5 -15.6875 ] [.32696 .25973 5 0 ] [.47854 .25973 -9.5 -15.6875 ] [.47854 .25973 9.5 0 ] [.63011 .25973 -5 -15.6875 ] [.63011 .25973 5 0 ] [.78169 .25973 -9.5 -15.6875 ] [.78169 .25973 9.5 0 ] [.93327 .25973 -5 -15.6875 ] [.93327 .25973 5 0 ] [.01131 .00715 -57.0625 -7.84375 ] [.01131 .00715 0 7.84375 ] [.01131 .09551 -57.0625 -7.84375 ] [.01131 .09551 0 7.84375 ] [.01131 .18387 -57.0625 -7.84375 ] [.01131 .18387 0 7.84375 ] [.01131 .36059 -48.375 -7.84375 ] [.01131 .36059 0 7.84375 ] [.01131 .44895 -48.375 -7.84375 ] [.01131 .44895 0 7.84375 ] [.01131 .53731 -48.375 -7.84375 ] [.01131 .53731 0 7.84375 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .27223 m .17539 .27848 L s gsave .17539 .25973 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (0.5) show 1.000 setlinewidth grestore .32696 .27223 m .32696 .27848 L s gsave .32696 .25973 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 1.000 setlinewidth grestore .47854 .27223 m .47854 .27848 L s gsave .47854 .25973 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1.5) show 1.000 setlinewidth grestore .63011 .27223 m .63011 .27848 L s gsave .63011 .25973 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 1.000 setlinewidth grestore .78169 .27223 m .78169 .27848 L s gsave .78169 .25973 -70.5 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2.5) show 1.000 setlinewidth grestore .93327 .27223 m .93327 .27848 L s gsave .93327 .25973 -66 -19.6875 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic /Times-Italic findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 1.000 setlinewidth grestore .125 Mabswid .05412 .27223 m .05412 .27598 L s .08444 .27223 m .08444 .27598 L s .11476 .27223 m .11476 .27598 L s .14507 .27223 m .14507 .27598 L s .2057 .27223 m .2057 .27598 L s .23602 .27223 m .23602 .27598 L s .26633 .27223 m .26633 .27598 L s .29665 .27223 m .29665 .27598 L s .35728 .27223 m .35728 .27598 L s .38759 .27223 m .38759 .27598 L s .41791 .27223 m .41791 .27598 L s .44822 .27223 m .44822 .27598 L s .50885 .27223 m .50885 .27598 L s .53917 .27223 m .53917 .27598 L s .56948 .27223 m .56948 .27598 L s .5998 .27223 m .5998 .27598 L s .66043 .27223 m .66043 .27598 L s .69074 .27223 m .69074 .27598 L s .72106 .27223 m .72106 .27598 L s .75138 .27223 m .75138 .27598 L s .81201 .27223 m .81201 .27598 L s .84232 .27223 m .84232 .27598 L s .87264 .27223 m .87264 .27598 L s .90295 .27223 m .90295 .27598 L s .96358 .27223 m .96358 .27598 L s .9939 .27223 m .9939 .27598 L s .25 Mabswid 0 .27223 m 1 .27223 L s .02381 .00715 m .03006 .00715 L s gsave .01131 .00715 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .09551 m .03006 .09551 L s gsave .01131 .09551 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .18387 m .03006 .18387 L s gsave .01131 .18387 -118.063 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 71.688 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 79.375 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 90.063 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 102.063 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 107.813 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .36059 m .03006 .36059 L s gsave .01131 .36059 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (1) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .44895 m .03006 .44895 L s gsave .01131 .44895 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (2) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .02381 .53731 m .03006 .53731 L s gsave .01131 .53731 -109.375 -11.8438 Mabsadd m 1 1 Mabs scale currentpoint translate 0 23.6875 translate 1 -1 scale /g { setgray} bind def /k { setcmykcolor} bind def /p { gsave} bind def /r { setrgbcolor} bind def /w { setlinewidth} bind def /C { curveto} bind def /F { fill} bind def /L { lineto} bind def /rL { rlineto} bind def /P { grestore} bind def /s { stroke} bind def /S { show} bind def /N {currentpoint 3 -1 roll show moveto} bind def /Msf { findfont exch scalefont [1 0 0 -1 0 0 ] makefont setfont} bind def /m { moveto} bind def /Mr { rmoveto} bind def /Mx {currentpoint exch pop moveto} bind def /My {currentpoint pop exch moveto} bind def /X {0 rmoveto} bind def /Y {0 exch rmoveto} bind def /MISOfy { /newfontname exch def /oldfontname exch def oldfontname findfont dup length dict begin {1 index /FID ne {def} {pop pop} ifelse} forall /Encoding WindowsANSIEncoding def currentdict end newfontname exch definefont pop } def 63.000 15.813 moveto %%IncludeResource: font Times-Italic %%IncludeFont: Times-Italic %%BeginResource: font Times-Italic-MISO %%BeginFont: Times-Italic-MISO /Times-Italic /Times-Italic-MISO MISOfy %%EndFont %%EndResource %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (3) show 70.688 15.813 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (\\264) show 81.375 15.813 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 12.000 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (10) show 93.375 10.938 moveto %%IncludeResource: font Mathematica1 %%IncludeFont: Mathematica1 /Mathematica1 findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (-) show 99.125 10.938 moveto %%IncludeResource: font Times-Italic-MISO %%IncludeFont: Times-Italic-MISO /Times-Italic-MISO findfont 8.500 scalefont [1 0 0 -1 0 0 ] makefont setfont 0.000 0.000 0.000 setrgbcolor (16) show 1.000 setlinewidth grestore .125 Mabswid .02381 .02482 m .02756 .02482 L s .02381 .04249 m .02756 .04249 L s .02381 .06016 m .02756 .06016 L s .02381 .07783 m .02756 .07783 L s .02381 .11318 m .02756 .11318 L s .02381 .13085 m .02756 .13085 L s .02381 .14852 m .02756 .14852 L s .02381 .1662 m .02756 .1662 L s .02381 .20154 m .02756 .20154 L s .02381 .21921 m .02756 .21921 L s .02381 .23688 m .02756 .23688 L s .02381 .25456 m .02756 .25456 L s .02381 .2899 m .02756 .2899 L s .02381 .30757 m .02756 .30757 L s .02381 .32525 m .02756 .32525 L s .02381 .34292 m .02756 .34292 L s .02381 .37826 m .02756 .37826 L s .02381 .39593 m .02756 .39593 L s .02381 .41361 m .02756 .41361 L s .02381 .43128 m .02756 .43128 L s .02381 .46662 m .02756 .46662 L s .02381 .4843 m .02756 .4843 L s .02381 .50197 m .02756 .50197 L s .02381 .51964 m .02756 .51964 L s .02381 .55499 m .02756 .55499 L s .02381 .57266 m .02756 .57266 L s .02381 .59033 m .02756 .59033 L s .02381 .608 m .02756 .608 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 .27223 m .02499 .27084 L .02605 .26677 L .02729 .26801 L .02846 .27395 L .02954 .27185 L .03053 .26725 L .03163 .28258 L .03279 .27491 L .03395 .26342 L .0352 .27836 L .03638 .25613 L .03746 .27223 L .03873 .26227 L .03944 .26993 L .04011 .26993 L .04132 .26533 L .04262 .26457 L .04327 .23927 L .04396 .24234 L .04519 .273 L .04588 .2707 L .04652 .24157 L .04722 .27529 L .04797 .25384 L .04862 .28602 L .04933 .27376 L .05061 .27529 L .05186 .23391 L .05302 .23391 L .05414 .25384 L .05519 .27683 L .05634 .28143 L .05759 .27376 L .05882 .2661 L .06012 .23544 L .06123 .28296 L .06244 .28756 L .06315 .25537 L .06381 .27989 L .06453 .22011 L .06529 .27223 L .06657 .21858 L .06729 .23544 L .06797 .25384 L .06924 .23851 L .0704 .20785 L .07103 .22318 L .07173 .25997 L .073 .25997 L Mistroke .07376 .21092 L .07448 .24464 L .07513 .21092 L .07583 .28756 L .0766 .22624 L .0774 .32435 L .07809 .29982 L .07885 .26303 L .07956 .27223 L .0802 .28756 L .08095 .31515 L .08166 .28449 L .08291 .22318 L .08362 .21705 L .08427 .34274 L .08544 .33661 L .08669 .15573 L .08787 .24157 L .08896 .20172 L .09016 .23544 L .09148 .3642 L .09214 .13121 L .09285 .31208 L .09413 .18946 L .09483 .20479 L .09548 .29062 L .09619 .22011 L .09695 .2569 L .09821 .20172 L .09893 .34274 L .09961 .31208 L .10086 .33048 L .10201 .2477 L .10333 .20785 L .10458 .17719 L .10572 .24464 L .10694 .28449 L .1081 .33661 L .10916 .17106 L .11033 .33048 L .11162 .27223 L .11232 .13121 L .11298 .23851 L .11422 .18639 L .11545 .18639 L .11614 .2661 L .11678 .2661 L .11742 .1496 L .11811 .14347 L .11884 .10055 L Mistroke .11952 .13734 L .12077 .22931 L .1219 .37033 L .12322 .16187 L .12446 .21092 L .1256 .21705 L .12668 .11282 L .12791 .32741 L .12903 .35807 L .13009 .25997 L .13107 .25997 L .13214 .21705 L .13327 .30902 L .13441 .25384 L .13564 .22931 L .1368 .23544 L .13785 .29062 L .13909 .30902 L .13979 .23544 L .14043 .18639 L .14162 .21092 L .14288 .19252 L .14402 .08829 L .14526 .28449 L .14656 .25384 L .14777 .20479 L .14891 .2477 L .14994 .25997 L .15113 .33354 L .15226 .2661 L .15348 .21092 L .15478 .24157 L .15589 .19252 L .15711 .1496 L .15842 .30902 L .15915 .1496 L .15982 .19865 L .16105 .2477 L .16236 .41938 L .16359 .28449 L .16469 .27223 L .16581 .25997 L .16685 .14347 L .16808 .29675 L .16921 .30289 L .17044 .2661 L .17175 .23544 L .17281 .15573 L .17394 .27836 L .17493 .25384 L Mistroke .17599 .43777 L .17725 .21705 L .17843 .35194 L .17958 .22931 L .18065 .19865 L .18189 .18639 L .18308 .19252 L .18414 .08216 L .1853 .1496 L .18656 .1496 L .18726 .21705 L .1879 .19865 L .18914 .38259 L .19031 .07603 L .19141 .12508 L .19257 .33967 L .19357 .15573 L .19466 .19252 L .19583 .22318 L .19709 .2477 L .19819 .32128 L .19936 .28449 L .20002 .20479 L .20074 .33967 L .20202 .21705 L .20273 .22318 L .2035 .16187 L .20423 .32128 L .2049 .13734 L .20612 .30902 L .20681 .12508 L .20746 .29675 L .20876 .23544 L .20949 .18026 L .21015 .30902 L .21141 .21092 L .21258 .27836 L .21385 .13734 L .2145 .13734 L .21521 .17413 L .2164 .3458 L .21768 .17413 L .21888 .25997 L .21999 .17413 L .22128 .06377 L .22249 .19865 L .22358 .23544 L .22476 .17413 L .22605 .3458 L .2267 .23544 L Mistroke .22741 .23544 L .22868 .21092 L .22985 .33354 L .23104 .38259 L .23216 .12508 L .23317 .10055 L .23427 .16187 L .23546 .16187 L .23673 .2477 L .23781 .19865 L .239 .30902 L .24031 .16187 L .24097 .22318 L .24169 .10055 L .24297 .19865 L .24415 .32128 L .24488 .17413 L .24556 .33354 L .24684 .32128 L .24755 .1496 L .24821 .35807 L .24893 .40712 L .2497 .3458 L .25089 .19865 L .25217 .12508 L .25338 .12508 L .25448 .32128 L .25577 .10055 L .2565 .08829 L .25718 .18639 L .25842 .48069 L .25973 .17413 L .26087 .2477 L .26211 .07603 L .2634 .29675 L .26461 .12508 L .26574 .27223 L .26677 .29675 L .26796 .21092 L .26908 .27223 L .2703 .28449 L .2716 .13734 L .2727 .38259 L .27392 .12508 L .27523 .22318 L .27596 .25997 L .27663 .18639 L .27793 .35807 L .27917 .33354 L .28032 .27223 L Mistroke .28137 .25997 L .28257 .35807 L .2837 .37033 L .28475 .22318 L .28572 .16187 L .28679 .08829 L .28791 .28449 L .28904 .16187 L .29026 .17413 L .29141 .2477 L .29245 .2477 L .29368 .32128 L .29437 .27223 L .29501 .3458 L .29619 .38259 L .29744 .1496 L .29858 .16187 L .29982 .22318 L .30112 .16187 L .30233 .17413 L .30347 .18639 L .3045 .1496 L .30569 .23544 L .30681 .32128 L .30804 .21092 L .30934 .43164 L .31044 .30902 L .31166 .28449 L .31297 .29675 L .31371 .2477 L .31438 .1496 L .31568 .2477 L .31692 .25997 L .31807 .35807 L .31912 .29675 L .32032 .40712 L .32146 .45617 L .32251 .25997 L .32348 .16187 L .32454 .27223 L .32567 .11282 L .3268 .19865 L .32802 .32128 L .32917 .29675 L .33021 .44391 L .33144 .19865 L .33214 .22318 L .33278 .07603 L .33395 .33354 L .3352 .32128 L Mistroke .3364 .32128 L .33771 .33354 L .33895 .23544 L .34011 .23544 L .34125 .1496 L .34228 .18639 L .34341 .21092 L .3446 .29675 L .3459 .22318 L .3471 .17413 L .34839 .19865 L .34912 .22318 L .34981 .17413 L .35104 .13734 L .35217 .11282 L .35348 .27223 L .35472 .29675 L .35576 .2477 L .35692 .37033 L .35813 .2477 L .35926 .27223 L .36131 .32128 L .36243 .27223 L .36347 .35807 L .36462 .35807 L .36587 .25997 L .36693 .18639 L .36806 .30902 L .3687 .13734 L .36939 .22318 L .37065 .19865 L .37188 .18639 L .37301 .27223 L .37426 .22318 L .37545 .2477 L .37651 .30902 L .37768 .19865 L .37894 .37033 L .37964 .33354 L .38028 .29675 L .38152 .33354 L .38269 .22318 L .3838 .12508 L .38496 .25997 L .38596 .25997 L .38705 .28449 L .38822 .33354 L .38948 .38259 L .39067 .22318 L .39175 .30902 L Mistroke .39303 .43164 L .39368 .39486 L .39439 .22318 L .39565 .30902 L .39683 .25997 L .39751 .28449 L .39822 .37033 L .39949 .23544 L .4002 .27223 L .40086 .28449 L .40158 .28449 L .40235 .22318 L .40365 .17413 L .40439 .16187 L .40506 .21092 L .4063 .21092 L .40761 .29675 L .40879 .16187 L .40989 .25997 L .41109 .28449 L .41239 .23544 L .4137 .25997 L .41494 .12508 L .41562 .40712 L .41636 .18639 L .41765 .35807 L .41889 .41938 L .4202 .3458 L .42131 .23544 L .42253 .33354 L .42328 .21092 L .42398 .07603 L .4253 .32128 L .42603 .29675 L .42671 .22318 L .42746 .32128 L .42825 .23544 L .42956 .3458 L .43079 .2477 L .43149 .23544 L .43214 .29675 L .43288 .1496 L .43358 .2477 L .43485 .23544 L .436 .1496 L .43663 .25997 L .43732 .18639 L .43857 .25997 L .43974 .33354 L .44098 .21092 L Mistroke .44204 .22318 L .4432 .40712 L .4439 .35807 L .44457 .28449 L .44582 .17413 L .44651 .2477 L .44716 .22318 L .44787 .23544 L .44862 .43164 L .44987 .28449 L .45103 .22318 L .45232 .2477 L .45304 .27223 L .45369 .10055 L .45494 .19865 L .45612 .3458 L .45721 .19865 L .45839 .39486 L .45968 .32128 L .46034 .35807 L .46106 .18639 L .46233 .19865 L .46352 .16187 L .46416 .25997 L .46486 .27223 L .46613 .30902 L .46736 .25997 L .46851 .32128 L .46921 .2477 L .46987 .38259 L .47111 .22318 L .4718 .29675 L .47244 .32128 L .47313 .13734 L .47387 .19865 L .475 .35807 L .47608 .33354 L .47731 .37033 L .47844 .35807 L .4795 .33354 L .48048 .30902 L .48156 .33354 L .4827 .3458 L .48397 .0515 L .48516 .30902 L .4864 .38259 L .48705 .33354 L .48775 .3458 L .48883 .43164 L .48997 .45617 L Mistroke .49122 .10055 L .49237 .43164 L .49358 .23544 L .49427 .11282 L .49491 .45617 L .49606 .23544 L .4973 .13734 L .4985 .27223 L .49964 .39486 L .50066 .22318 L .50177 .1496 L .50298 .43164 L .50367 .03924 L .50431 .33354 L .50561 .2477 L .50635 .37033 L .50702 .18639 L .50815 .32128 L .50939 .17413 L .51068 .30902 L .51188 .28449 L .51302 .29675 L .51426 .43164 L .51543 .40712 L .51651 .33354 L .51748 .33354 L .51855 .3458 L .51967 .43164 L .52072 .3458 L .52194 .23544 L .5231 .29675 L .52414 .40712 L .52528 .23544 L .5265 .29675 L .52782 .23544 L .52905 .22318 L .53017 .3458 L .53138 .13734 L .5325 .43164 L .53373 .16187 L .53505 .2477 L .53572 .27223 L .53644 .35807 L .53775 .19865 L .53902 .16187 L .5402 .35807 L .5413 .27223 L .54233 .10055 L .54346 .2477 L .54468 .2477 L Mistroke .54587 .25997 L .54714 .19865 L .54834 .30902 L .54943 .2477 L .55073 .0515 L .55196 .19865 L .55265 .3458 L .55329 .11282 L .55399 .55427 L .55472 .07603 L .55539 .38259 L .5561 .0515 L .55738 .25997 L .55816 .1496 L .5589 .33354 L .55957 .37033 L .5603 .22318 L .56161 .12508 L .5628 .22318 L .56408 .29675 L .5648 .39486 L .56546 .41938 L .56667 .08829 L .56793 .07603 L .56904 .38259 L .57025 .30902 L .57157 .30902 L .57278 .51748 L .57341 .38259 L .57411 .1496 L .57483 .28449 L .57552 .39486 L .57677 .22318 L .57791 .25997 L .57924 .29675 L .58049 .29675 L .58161 .43164 L .5828 .18639 L .58393 .33354 L .58495 .2477 L .58615 .45617 L .58745 .29675 L .58868 .11282 L .58981 .27223 L .59102 .12508 L .59232 .21092 L .59355 .38259 L .59466 .44391 L .59597 .37033 L .59671 .13734 L Mistroke .5974 .33354 L .59866 .07603 L .59929 .32128 L .59999 .40712 L .60067 .18639 L .60138 .23544 L .60266 .08829 L .60337 .13734 L .60403 .29675 L .60476 .21092 L .60554 .2477 L .60621 .45617 L .60694 .28449 L .60763 .25997 L .60827 .17413 L .60947 .2477 L .61075 .30902 L .61195 .45617 L .61327 .32128 L .61452 .17413 L .61567 .17413 L .61679 .10055 L .61785 .17413 L .61907 .33354 L .62017 .39486 L .62141 .12508 L .62271 .23544 L .62382 .29675 L .62504 .30902 L .63031 .37033 L .63143 .35807 L .63266 .37033 L .63381 .23544 L .63488 .33354 L .63613 .43164 L .63745 .19865 L .63856 .12508 L .63978 .45617 L .64093 .22318 L .64198 .23544 L .64313 .32128 L .64434 .37033 L .6454 .10055 L .64638 .29675 L .64746 .25997 L .64862 .37033 L .64985 .54201 L .65056 .39486 L .65121 .01472 L .6519 .38259 L Mistroke .65254 .60332 L .65327 .41938 L .65396 .32128 L .65518 .13734 L .65631 .45617 L .65755 .38259 L .65888 .22318 L .66019 .16187 L .66092 .21092 L .6616 .30902 L .66284 .27223 L .66416 .38259 L .66485 .33354 L .6656 .40712 L .6663 .3458 L .66694 .23544 L .66769 .50522 L .66851 .2477 L .66928 .19865 L .66999 .51748 L .67115 .30902 L .67239 .52974 L .67357 .11282 L .67465 .11282 L .6759 .33354 L .67662 .33354 L .67728 .41938 L .67849 .32128 L .67978 .43164 L .68048 .33354 L .68112 .41938 L .68183 .28449 L .68258 .19865 L .68384 .41938 L .68455 .39486 L .68522 .22318 L .68646 .46843 L .6876 .39486 L .68891 .25997 L .69015 .39486 L .69129 .27223 L .69252 .45617 L .69368 .19865 L .69474 .35807 L .69592 .23544 L .69721 .07603 L .69786 .22318 L .69855 .25997 L .6998 .37033 L .70049 .11282 L Mistroke .70113 .40712 L .70183 .35807 L .70257 .39486 L .70381 .23544 L .70452 .25997 L .70518 .18639 L .70641 .32128 L .70753 .50522 L .70883 .16187 L .71006 .38259 L .71122 .13734 L .71228 .1496 L .71349 .17413 L .71463 .11282 L .7157 .17413 L .71667 .25997 L .71774 .3458 L .71887 .44391 L .72003 .28449 L .7211 .32128 L .72228 .44391 L .72355 .43164 L .72424 .46843 L .72488 .23544 L .72613 .1496 L .72727 .2477 L .72848 .25997 L .72962 .41938 L .73087 .30902 L .73209 .08829 L .73339 .08829 L .73461 .22318 L .73572 .1496 L .73683 .37033 L .73788 .17413 L .73911 .40712 L .74041 .1496 L .74152 .22318 L .74274 .51748 L .74405 .38259 L .74478 .17413 L .74545 .48069 L .74676 .44391 L .74799 .16187 L .74904 .43164 L .7502 .30902 L .75141 .52974 L .75254 .29675 L .7536 .16187 L .75457 .13734 L Mistroke .75563 .2477 L .75675 .33354 L .75789 .21092 L .75911 .08829 L .76026 .39486 L .7613 .39486 L .76253 .10055 L .76323 .46843 L .76387 .18639 L .76504 .32128 L .76629 .27223 L .76749 .3458 L .76881 .20479 L .77006 .42551 L .77121 .08216 L .77235 .3458 L .77339 .3642 L .77458 .30289 L .77571 .38259 L .77694 .12508 L .77825 .37646 L .77936 .45617 L .78058 .25384 L .78189 .40099 L .78263 .40099 L .7833 .38872 L .7846 .11895 L .78584 .15573 L .78698 .21705 L .78805 .09442 L .78917 .10055 L .7904 .33967 L .79146 .38259 L .79242 .29675 L .79349 .49296 L .79461 .2477 L .79575 .18026 L .79697 .38872 L .79812 .22318 L .79917 .1496 L .8004 .19252 L .80109 .47456 L .80173 .13121 L .8029 .49296 L .80415 .49909 L .80536 .1496 L .80668 .25384 L .80793 .42551 L .80908 .3458 L .81023 .43777 L Mistroke .81127 .43164 L .81247 .15573 L .81359 .25997 L .81483 .2661 L .81614 .43164 L .81725 .29062 L .81847 .18639 L .81979 .16187 L .82053 .42551 L .8212 .06377 L .8225 .18639 L .82374 .45004 L .82479 .3458 L .82595 .33354 L .82717 .40099 L .8283 .10055 L .82936 .23544 L .83033 .18639 L .83145 .3642 L .83252 .168 L .83366 .37033 L .83488 .28449 L .83594 .45617 L .83708 .10055 L .83778 .14347 L .83842 .21092 L .83969 .35807 L .84084 .21092 L .84206 .03311 L .84327 .31515 L .84396 .09442 L .8446 .38872 L .84577 .40712 L .84701 .22931 L .84812 .51748 L .84916 .11282 L .8503 .10668 L .85153 .27223 L .85276 .37646 L .85346 .48682 L .85411 .28449 L .85542 .47456 L .85616 .3458 L .85683 .17413 L .85803 .41938 L .85933 .23544 L .86055 .23544 L .86169 .2477 L .86282 .23544 L .8639 .43777 L Mistroke .86515 .32741 L .86629 .15573 L .86735 .22931 L .86834 .4623 L .86943 .17413 L .87059 .37033 L .8718 .19252 L .87295 .12508 L .87397 .168 L .87508 .33967 L .87633 .22318 L .87765 .13121 L .87878 .15573 L .88002 .22931 L .88133 .24464 L .88254 .08216 L .88317 .08522 L .88386 .2477 L .88459 .40099 L .88527 .27836 L .88652 .20479 L .88767 .20785 L .88892 .45004 L .89024 .20172 L .89136 .14041 L .89255 .08216 L .89368 .19252 L .8947 .3458 L .8959 .31821 L .8972 .33048 L .89843 .2661 L .89956 .23851 L .90077 .47456 L .90206 .44084 L .90329 .18639 L .9044 .26916 L .90571 .31515 L .90645 .36726 L .90714 .17719 L .90839 .15267 L .90903 .18946 L .90973 .08216 L .91041 .19865 L .91112 .33354 L .9124 .36113 L .91311 .30902 L .91377 .31208 L .9145 .41631 L .91527 .28756 L .91595 .07296 L Mistroke .91668 .17719 L .91732 .23238 L .918 .37033 L .91929 .24157 L .92049 .35194 L .92169 .29675 L .92301 .32741 L .92425 .21705 L .9254 .21398 L .92655 .44391 L .92758 .23084 L .92878 .09442 L .9299 .12508 L .93113 .41785 L .93244 .44084 L .93355 .23851 L .93477 .38719 L .93608 .28449 L .9368 .11128 L .93749 .20172 L .93812 .20325 L .93882 .34121 L .94003 .25077 L .94116 .17566 L .94222 .18333 L .94338 .31055 L .94464 .45923 L .94588 .23851 L .94719 .24311 L .94831 .43471 L .94954 .33354 L .95069 .15727 L .95174 .33354 L .95295 .28373 L .95409 .3665 L .95515 .12968 L .95613 .10898 L .9572 .13428 L .95833 .27989 L .95952 .32894 L .96066 .24081 L .96167 .27913 L .96278 .46613 L .96398 .10055 L .96526 .27491 L .96647 .32128 L .96756 .35309 L .96867 .2546 L .9697 .31477 L .97082 .16704 L Mistroke .97201 .21187 L .97619 .35347 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", CellLabel->"From In[106]:=", ImageSize->{288, 177.875}, ImageMargins->{{0, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`03Ool00`00Oomoo`0;Ool20002Ool20008Ool00`00Oomo o`0Ool01@00Oomoogoo00001Goo00D007ooOomo o`0000Uoo`03001oogoo00Aoo`05001oogooOol0000HOol00`00Oomoo`0POol00`00Oomoo`09Ool0 0`00Ool00008Ool00`00Oomoo`07Ool00`00Ool00006Ool00`00Oomoo`0:Ool00`00Oomoo`0HOol0 0`00Oomoo`0>Ool00`00Oomoo`03Ool00`00Oomoo`0;Ool20002Ool20008Ool2000=Ool00`00Oomo o`0:Ool00`00Oomoo`08Ool00`00Oomoo`04Ool01@00Oomoogoo00003Goo00<007ooOol017oo00<0 07ooOol027oo0P0000=oo`00Ool00goo00<007oo00006Goo000?Ool00`00Oomoo`07Ool00`00Ool0 000;Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`0EOol00`00Oomoo`0POol00`00Oomo o`09Ool00`00Ool00008Ool00`00Oomoo`07Ool00`00Ool00006Ool00`00Oomoo`0:Ool00`00Oomo o`0HOol00`00Oomoo`0>Ool00`00Oomoo`03Ool00`00Oomoo`0;Ool20002Ool20008Ool2000=Ool0 0`00Oomoo`0:Ool00`00Oomoo`08Ool00`00Oomoo`04Ool01@00Oomoogoo00003Goo00<007ooOol0 17oo00<007ooOol027oo0P0000=oo`00Ool00goo00<007oo00006Goo0003Ool80005Ool00`00Oomo o`07Ool00`00Oomoo`0:Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomoo`0EOol00`00Oomo o`0POol00`00Oomoo`09Ool00`00Ool00008Ool00`00Oomoo`07Ool00`00Ool00006Ool00`00Oomo o`0:Ool00`00Oomoo`0HOol00`00Oomoo`0>Ool00`00Oomoo`03Ool00`00Oomoo`0;Ool20002Ool2 0008Ool2000=Ool00`00Oomoo`0:Ool00`00Oomoo`08Ool00`00Oomoo`04Ool01@00Oomoogoo0000 17oo00<007ooOol01Woo00<007ooOol017oo00<007ooOol027oo0P0000=oo`00Ool00goo00<007oo 00000goo00<007ooOol04goo000AOol00`00Oomoo`05Ool00`00Ool0000;Ool00`00Oomoo`03Ool0 0`00Oomoo`03Ool00`00Oomoo`0DOol3000POol00`00Oomoo`09Ool00`00Ool00008Ool00`00Oomo o`07Ool00`00Ool00006Ool00`00Oomoo`0:Ool00`00Oomoo`0HOol00`00Oomoo`0>Ool00`00Oomo o`03Ool00`00Oomoo`0;Ool20002Ool20008Ool2000=Ool00`00Oomoo`0:Ool00`00Oomoo`08Ool0 0`00Oomoo`04Ool01@00Oomoogoo000017oo00<007ooOol01Woo00<007ooOol017oo00<007ooOol0 27oo0P0000=oo`00Ool00goo00<007oo00000goo00<007ooOol04goo000BOol00`00Oomoo`03Ool0 1@00Oomoogoo00002goo00<007ooOol00Woo00<007ooOol00goo00<007ooOol057oo00<007ooOol0 6Goo00<007ooOol017oo00<007ooOol02Goo00<007oo000027oo00@007ooOol0009oo`07001oogoo Ool007oo00001Woo00<007ooOol02Woo00<007ooOol067oo00<007ooOol01Woo00<007ooOol01Goo 00<007oo00000goo00<007ooOol027oo00<007ooOol00P000Woo0P0027oo0P000goo00<007ooOol0 1Goo00<007oo000037oo00<007ooOol027oo00<007ooOol017oo0P000Woo00<007ooOol00Woo00<0 07ooOol01Woo00P007ooOol007oo001oo`002Woo0P0000=oo`00Ool00goo00<007oo00000goo00<0 07ooOol01goo00<007ooOol02Goo000COol01@00Oomoogoo00001Goo00<007ooOol027oo00<007oo Ool00goo00<007ooOol00Woo00<007ooOol01Goo0`0017oo0P001Woo00<007ooOol06Goo00<007oo Ool017oo00<007ooOol02Goo00<007oo000027oo00@007ooOol0009oo`07001oogooOol007oo0000 1Woo00<007ooOol02Woo00<007ooOol067oo00<007ooOol01Woo00<007ooOol01Goo00<007oo0000 0goo00<007ooOol027oo00<007ooOol00P000Woo0P0027oo0P000goo00<007ooOol01Goo00<007oo 000037oo00<007ooOol027oo00<007ooOol017oo0P000Woo00<007ooOol00Woo00<007ooOol01Woo 00P007ooOol007oo001oo`002Woo0P0000=oo`00Ool00goo00<007oo00000goo00<007ooOol01goo 00<007ooOol02Goo000COol00`00Oomoo`0BOol00`00Oomoo`03Ool00`00Oomoo`02Ool00`00Oomo o`06Ool00`00Oomoo`02Ool01000Oomoo`001Goo00<007ooOol06Goo00<007ooOol017oo00<007oo Ool02Goo00<007oo000027oo00@007ooOol0009oo`07001oogooOol007oo00001Woo00<007ooOol0 2Woo00<007ooOol067oo00<007ooOol01Woo00<007ooOol01Goo00<007oo00000goo00<007ooOol0 27oo00<007ooOol00P000Woo0P0027oo0P000goo00<007ooOol01Goo00<007oo000037oo00<007oo Ool027oo00<007ooOol017oo0P000Woo00<007ooOol00Woo00<007ooOol01Woo00X007ooOol007oo 001oo`00Ool000Qoo`800003Ool007oo00=oo`03001oo`0000=oo`03001oog