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Notebook[{
Cell[TextData[StyleBox["Appendix G\n\nSIMULATOR AND RANDOM NUMBER GENERATOR \
FOR STABLE DISTRIBUTIONS",
  FontSize->12]], "Text",
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  TextAlignment->Center,
  FontSize->16,
  FontWeight->"Bold"],

Cell[TextData[StyleBox[
"Chapter 5 illustrates various \"efficient\" frontiers that may be created \
when \[Alpha] < 2 and \[Beta] > 0.  Those illustrations employed the random \
number generator in the Fortran program, Stable.exe provided by Nolan (1997). \
 This notebook replicates that random number generator, permitting the faster \
creation of a wider variety of possible portfolios.  This notebook is in the \
experimental phase.  Enhancements are expected in the future. Monitoring the \
author's Web site for updates is suggested.\n\nThe procedure is as follows:\n\
\n1. Generate several series of stable quasi-random variables using the \
method of McCulloch (1998) based on Chambers, Mallows and Stuck (1976) using \
any value for \[Alpha] \[Subset] [1,2]; \[Beta] \[Subset] [-1,1].\n3. Form a \
portfolio from three sets, each with \[Alpha] = 2, \[Beta] = 0 (asset201, \
asset 202, asset 203), draw the efficient frontier.\n4. Repeat the process, \
each time with a different \[Alpha]. (numbering sets 141, 142,143 for \
\[Alpha] = 1.4 asset1, \[Alpha] = 1.4 asset2, \[Alpha] = 1.4 asset3, etc.)\n\n\
The goal is to show the change in the \"efficient\" frontier as \[Alpha] \
declines. "]], "Text",
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Cell[TextData[{
  "Stable Random variates are computed using Chambers, Mallows and Stuck \
(1976) using the form and notation of McCulloch (1998) p.373, Adler, et al, \
editors\n\nIt is necessary to use ",
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  "'s Finance Essentials Pack to plot the efficient frontiers"
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    \(<< Finance`Examples`\), "\n", 
    \(<< Statistics`ContinuousDistributions`\), "\n", 
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We require u and v to be two iid uniform (0,1) quasi-random variables. We \
begin with two vectors of 1000 uniform random variables to serve as u and v\
\>", "Text",
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            Log[1/u]; \n\[CapitalPhi] = \[Pi]\ \((v -  .5)\); \n
          z = \(Cos[\((1 - \[Alpha])\)\ \[CapitalPhi]] + \[Beta]\ Tan[\(\[Pi]\
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\[CapitalPhi]]\); \[IndentingNewLine]\(Sin[\[Alpha]\ \[CapitalPhi]] + \[Beta]\
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We now form a portfolio of these three assets, each having returns that are \
normally distributed\
\>", "Text",
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We now have three assets, each with 1000 return observations, forming a \
portfolio for which we can compute a return vector (meanvect) and covariance \
matrix (cov), determine efficient set portfolios and plot.\
\>", "Text",
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We now require a stable NON NORMAL draw where \[Alpha] = 1.4 and \[Beta] = 0 \
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\>", "Text",
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We now form a portfolio of these three assets, each having returns that are \
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We now have three assets, each with 1000 return observations, forming a \
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\>", "Text",
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We now form a portfolio of these three assets, each having returns that are \
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We now have three assets, each with 1000 return observations, forming a \
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We now require a stable NON NORMAL draw where \[Alpha] = 1.5 and \[Beta] = 0 \
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We now form a portfolio of these three assets, each having returns that are \
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We now have three assets, each with 1000 return observations, forming a \
portfolio for which we can compute a return vector (meanvect) and covariance \
matrix (cov), determine efficient set portfolios and plot.\
\>", "Text",
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PrintingPageRange->{Automatic, Automatic},
PageHeaders->{{None, Inherited, Cell[ 
        TextData[ {
          ValueBox[ "Page"]}], "PageNumber"]}, {None, Inherited, None}},
PrintingOptions->{"PrintingMargins"->{{108, 72}, {72, 93.5625}}},
StyleDefinitions -> Notebook[{
  
  Cell[CellGroupData[{
  Cell[TextData[StyleBox["Style Definitions"]], "Subtitle"],
  
  Cell[TextData[StyleBox[
  "Modify the definitions below to change the default appearance of all cells \
in a given style.  Make modifications to any definition using commands in the \
Format menu."]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Style Environment Names"]], "Section"],
  
  Cell[StyleData[All, "Working"],
    PageWidth->WindowWidth,
    CellLabelMargins->{{12, Inherited}, {Inherited, Inherited}},
    ScriptMinSize->9],
  
  Cell[StyleData[All, "Presentation"],
    PageWidth->WindowWidth,
    CellLabelMargins->{{24, Inherited}, {Inherited, Inherited}},
    ScriptMinSize->12],
  
  Cell[StyleData[All, "Condensed"],
    PageWidth->WindowWidth,
    CellLabelMargins->{{8, Inherited}, {Inherited, Inherited}},
    ScriptMinSize->8],
  
  Cell[StyleData[All, "Printout"],
    PageWidth->PaperWidth,
    CellLabelMargins->{{2, Inherited}, {Inherited, Inherited}},
    ScriptMinSize->5,
    PrivateFontOptions->{"FontType"->"Outline"}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Notebook Options"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The options defined for the style below will be used at the Notebook \
level."]], "Text"],
  
  Cell[StyleData["Notebook"],
    PageHeaders->{{Cell[ 
            TextData[ {
              CounterBox[ "Page"]}], "PageNumber"], None, Cell[ 
            TextData[ {
              ValueBox[ "FileName"]}], "Header"]}, {Cell[ 
            TextData[ {
              ValueBox[ "FileName"]}], "Header"], None, Cell[ 
            TextData[ {
              CounterBox[ "Page"]}], "PageNumber"]}},
    CellFrameLabelMargins->6,
    StyleMenuListing->None]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Styles for Headings"]], "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Title"],
    CellMargins->{{12, Inherited}, {20, 40}},
    CellGroupingRules->{"TitleGrouping", 0},
    PageBreakBelow->False,
    CounterIncrements->"Title",
    CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, {
        "Subtitle", 0}, {"Subsubtitle", 0}},
    FontFamily->"Helvetica",
    FontSize->36,
    FontWeight->"Bold"],
  
  Cell[StyleData["Title", "Presentation"],
    CellMargins->{{24, 10}, {20, 40}},
    LineSpacing->{1, 0},
    FontSize->44],
  
  Cell[StyleData["Title", "Condensed"],
    CellMargins->{{8, 10}, {4, 8}},
    FontSize->20],
  
  Cell[StyleData["Title", "Printout"],
    CellMargins->{{2, 10}, {12, 30}},
    FontSize->24]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subtitle"],
    CellMargins->{{12, Inherited}, {20, 15}},
    CellGroupingRules->{"TitleGrouping", 10},
    PageBreakBelow->False,
    CounterIncrements->"Subtitle",
    CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, {
        "Subsubtitle", 0}},
    FontFamily->"Helvetica",
    FontSize->24],
  
  Cell[StyleData["Subtitle", "Presentation"],
    CellMargins->{{24, 10}, {20, 20}},
    LineSpacing->{1, 0},
    FontSize->36],
  
  Cell[StyleData["Subtitle", "Condensed"],
    CellMargins->{{8, 10}, {4, 4}},
    FontSize->14],
  
  Cell[StyleData["Subtitle", "Printout"],
    CellMargins->{{2, 10}, {12, 8}},
    FontSize->18]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsubtitle"],
    CellMargins->{{12, Inherited}, {20, 15}},
    CellGroupingRules->{"TitleGrouping", 20},
    PageBreakBelow->False,
    CounterIncrements->"Subsubtitle",
    CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}},
    FontFamily->"Helvetica",
    FontSize->14,
    FontSlant->"Italic"],
  
  Cell[StyleData["Subsubtitle", "Presentation"],
    CellMargins->{{24, 10}, {20, 20}},
    LineSpacing->{1, 0},
    FontSize->24],
  
  Cell[StyleData["Subsubtitle", "Condensed"],
    CellMargins->{{8, 10}, {8, 8}},
    FontSize->12],
  
  Cell[StyleData["Subsubtitle", "Printout"],
    CellMargins->{{2, 10}, {12, 8}},
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Section"],
    CellDingbat->"\[FilledSquare]",
    CellMargins->{{25, Inherited}, {8, 24}},
    CellGroupingRules->{"SectionGrouping", 30},
    PageBreakBelow->False,
    CounterIncrements->"Section",
    CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}},
    FontFamily->"Helvetica",
    FontSize->16,
    FontWeight->"Bold"],
  
  Cell[StyleData["Section", "Presentation"],
    CellMargins->{{40, 10}, {11, 32}},
    LineSpacing->{1, 0},
    FontSize->24],
  
  Cell[StyleData["Section", "Condensed"],
    CellMargins->{{18, Inherited}, {6, 12}},
    FontSize->12],
  
  Cell[StyleData["Section", "Printout"],
    CellMargins->{{13, 0}, {7, 22}},
    FontSize->14]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsection"],
    CellDingbat->"\[FilledSmallSquare]",
    CellMargins->{{22, Inherited}, {8, 20}},
    CellGroupingRules->{"SectionGrouping", 40},
    PageBreakBelow->False,
    CounterIncrements->"Subsection",
    CounterAssignments->{{"Subsubsection", 0}},
    FontFamily->"Times",
    FontSize->14,
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsection", "Presentation"],
    CellMargins->{{36, 10}, {11, 32}},
    LineSpacing->{1, 0},
    FontSize->22],
  
  Cell[StyleData["Subsection", "Condensed"],
    CellMargins->{{16, Inherited}, {6, 12}},
    FontSize->12],
  
  Cell[StyleData["Subsection", "Printout"],
    CellMargins->{{9, 0}, {7, 22}},
    FontSize->12]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Subsubsection"],
    CellDingbat->"\[FilledSmallSquare]",
    CellMargins->{{22, Inherited}, {8, 18}},
    CellGroupingRules->{"SectionGrouping", 50},
    PageBreakBelow->False,
    CounterIncrements->"Subsubsection",
    FontFamily->"Times",
    FontWeight->"Bold"],
  
  Cell[StyleData["Subsubsection", "Presentation"],
    CellMargins->{{34, 10}, {11, 26}},
    LineSpacing->{1, 0},
    FontSize->18],
  
  Cell[StyleData["Subsubsection", "Condensed"],
    CellMargins->{{17, Inherited}, {6, 12}},
    FontSize->10],
  
  Cell[StyleData["Subsubsection", "Printout"],
    CellMargins->{{9, 0}, {7, 14}},
    FontSize->11]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Styles for Body Text"]], "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Text"],
    CellMargins->{{12, 10}, {7, 7}},
    LineSpacing->{1, 3},
    CounterIncrements->"Text"],
  
  Cell[StyleData["Text", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["Text", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["Text", "Printout"],
    CellMargins->{{2, 2}, {6, 6}},
    TextJustification->0.5,
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SmallText"],
    CellMargins->{{12, 10}, {6, 6}},
    LineSpacing->{1, 3},
    CounterIncrements->"SmallText",
    FontFamily->"Helvetica",
    FontSize->9],
  
  Cell[StyleData["SmallText", "Presentation"],
    CellMargins->{{24, 10}, {8, 8}},
    LineSpacing->{1, 5},
    FontSize->12],
  
  Cell[StyleData["SmallText", "Condensed"],
    CellMargins->{{8, 10}, {5, 5}},
    LineSpacing->{1, 2},
    FontSize->9],
  
  Cell[StyleData["SmallText", "Printout"],
    CellMargins->{{2, 2}, {5, 5}},
    TextJustification->0.5,
    FontSize->7]
  }, Closed]]
  }, Open  ]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Styles for Input/Output"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The cells in this section define styles used for input and output to the \
kernel.  Be careful when modifying, renaming, or removing these styles, \
because the front end associates special meanings with these style names. \
Some attributes for these styles are actually set in FormatType Styles (in \
the last section of this stylesheet). "]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Input"],
    CellMargins->{{45, 10}, {5, 7}},
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    DefaultFormatType->DefaultInputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    LinebreakAdjustments->{0.85, 2, 10, 0, 1},
    CounterIncrements->"Input",
    FontWeight->"Bold"],
  
  Cell[StyleData["Input", "Presentation"],
    CellMargins->{{72, Inherited}, {8, 10}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Input", "Condensed"],
    CellMargins->{{40, 10}, {2, 3}},
    FontSize->11],
  
  Cell[StyleData["Input", "Printout"],
    CellMargins->{{39, 0}, {4, 6}},
    LinebreakAdjustments->{0.85, 2, 10, 1, 1},
    FontSize->9]
  }, Closed]],
  
  Cell[StyleData["InputOnly"],
    Evaluatable->True,
    CellGroupingRules->"InputGrouping",
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    ShowStringCharacters->True,
    NumberMarks->True,
    LinebreakAdjustments->{0.85, 2, 10, 0, 1},
    CounterIncrements->"Input",
    StyleMenuListing->None,
    FontWeight->"Bold"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Output"],
    CellMargins->{{47, 10}, {7, 5}},
    CellEditDuplicate->True,
    CellGroupingRules->"OutputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    DefaultFormatType->DefaultOutputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Output"],
  
  Cell[StyleData["Output", "Presentation"],
    CellMargins->{{72, Inherited}, {10, 8}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Output", "Condensed"],
    CellMargins->{{41, Inherited}, {3, 2}},
    FontSize->11],
  
  Cell[StyleData["Output", "Printout"],
    CellMargins->{{39, 0}, {6, 4}},
    FontSize->9]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Message"],
    CellMargins->{{45, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"OutputGrouping",
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Message",
    StyleMenuListing->None,
    FontSize->11,
    FontColor->RGBColor[0, 0, 1]],
  
  Cell[StyleData["Message", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Message", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}},
    FontSize->11],
  
  Cell[StyleData["Message", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontSize->7,
    FontColor->GrayLevel[0]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Print"],
    CellMargins->{{45, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"OutputGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GroupPageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    AutoItalicWords->{},
    FormatType->InputForm,
    CounterIncrements->"Print",
    StyleMenuListing->None],
  
  Cell[StyleData["Print", "Presentation"],
    CellMargins->{{72, Inherited}, {Inherited, Inherited}},
    LineSpacing->{1, 0},
    FontSize->16],
  
  Cell[StyleData["Print", "Condensed"],
    CellMargins->{{41, Inherited}, {Inherited, Inherited}},
    FontSize->11],
  
  Cell[StyleData["Print", "Printout"],
    CellMargins->{{39, Inherited}, {Inherited, Inherited}},
    FontSize->8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Graphics"],
    CellMargins->{{4, Inherited}, {Inherited, Inherited}},
    CellGroupingRules->"GraphicsGrouping",
    CellHorizontalScrolling->True,
    PageBreakWithin->False,
    GeneratedCell->True,
    CellAutoOverwrite->True,
    ShowCellLabel->False,
    DefaultFormatType->DefaultOutputFormatType,
    FormatType->InputForm,
    CounterIncrements->"Graphics",
    ImageMargins->{{43, Inherited}, {Inherited, 0}},
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontSize->10],
  
  Cell[StyleData["Graphics", "Presentation"],
    ImageMargins->{{62, Inherited}, {Inherited, 0}}],
  
  Cell[StyleData["Graphics", "Condensed"],
    ImageMargins->{{38, Inherited}, {Inherited, 0}},
    Magnification->0.6],
  
  Cell[StyleData["Graphics", "Printout"],
    ImageMargins->{{30, Inherited}, {Inherited, 0}},
    Magnification->0.8]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["CellLabel"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->9,
    FontColor->RGBColor[0, 0, 1]],
  
  Cell[StyleData["CellLabel", "Presentation"],
    FontSize->12],
  
  Cell[StyleData["CellLabel", "Condensed"],
    FontSize->9],
  
  Cell[StyleData["CellLabel", "Printout"],
    FontFamily->"Courier",
    FontSize->8,
    FontSlant->"Italic",
    FontColor->GrayLevel[0]]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Inline Formatting"]], "Section"],
  
  Cell[TextData[StyleBox[
  "These styles are for modifying individual words or letters in a cell \
exclusive of the cell tag."]], "Text"],
  
  Cell[StyleData["RM"],
    StyleMenuListing->None,
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["BF"],
    StyleMenuListing->None,
    FontWeight->"Bold"],
  
  Cell[StyleData["IT"],
    StyleMenuListing->None,
    FontSlant->"Italic"],
  
  Cell[StyleData["TR"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["TI"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["TB"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["TBI"],
    StyleMenuListing->None,
    FontFamily->"Times",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[StyleData["MR"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["MO"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["MB"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["MBO"],
    StyleMenuListing->None,
    FontFamily->"Courier",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[StyleData["SR"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Plain",
    FontSlant->"Plain"],
  
  Cell[StyleData["SO"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SB"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Bold",
    FontSlant->"Plain"],
  
  Cell[StyleData["SBO"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontWeight->"Bold",
    FontSlant->"Italic"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["SO10"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->10,
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SO10", "Printout"],
    StyleMenuListing->None,
    FontFamily->"Helvetica",
    FontSize->7,
    FontWeight->"Plain",
    FontSlant->"Italic"],
  
  Cell[StyleData["SO10", "EnhancedPrintout"],
    StyleMenuListing->None,
    FontFamily->"Futura",
    FontSize->7,
    FontWeight->"Plain",
    FontSlant->"Italic"]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Formulas and Programming"]], "Section"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["InlineFormula"],
    CellMargins->{{10, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    ScriptLevel->1,
    SingleLetterItalics->True],
  
  Cell[StyleData["InlineFormula", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["InlineFormula", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["InlineFormula", "Printout"],
    CellMargins->{{2, 0}, {6, 6}},
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["DisplayFormula"],
    CellMargins->{{42, Inherited}, {Inherited, Inherited}},
    CellHorizontalScrolling->True,
    DefaultFormatType->DefaultInputFormatType,
    ScriptLevel->0,
    SingleLetterItalics->True,
    UnderoverscriptBoxOptions->{LimitsPositioning->True}],
  
  Cell[StyleData["DisplayFormula", "Presentation"],
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["DisplayFormula", "Condensed"],
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["DisplayFormula", "Printout"],
    FontSize->10]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Program"],
    CellFrame->{{0, 0}, {0.5, 0.5}},
    CellMargins->{{10, 4}, {0, 8}},
    CellHorizontalScrolling->True,
    ScriptLevel->1,
    FontFamily->"Courier"],
  
  Cell[StyleData["Program", "Presentation"],
    CellMargins->{{24, 10}, {10, 10}},
    LineSpacing->{1, 5},
    FontSize->16],
  
  Cell[StyleData["Program", "Condensed"],
    CellMargins->{{8, 10}, {6, 6}},
    LineSpacing->{1, 1},
    FontSize->11],
  
  Cell[StyleData["Program", "Printout"],
    CellMargins->{{2, 0}, {6, 6}},
    FontSize->9]
  }, Closed]]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[TextData[StyleBox["Hyperlink Styles"]], "Section"],
  
  Cell[TextData[StyleBox[
  "The cells below define styles useful for making hypertext ButtonBoxes.  \
The \"Hyperlink\" style is for links within the same Notebook, or between \
Notebooks."]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["Hyperlink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`NotebookLocate[ #2]}]&),
    Active->True,
    ButtonNote->ButtonData}],
  
  Cell[StyleData["Hyperlink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["Hyperlink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["Hyperlink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[TextData[StyleBox[
  "The following styles are for linking automatically to the on-line help \
system."]], "Text"],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["MainBookLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["MainBookLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["MainBookLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["MainBookLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["AddOnsLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["AddOnsLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["AddOnsLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["AddOnsLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["RefGuideLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontFamily->"Courier",
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["RefGuideLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["RefGuideLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["RefGuideLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
    FontVariations->{"Underline"->False}]
  }, Closed]],
  
  Cell[CellGroupData[{
  
  Cell[StyleData["GettingStartedLink"],
    StyleMenuListing->None,
    ButtonStyleMenuListing->Automatic,
    FontColor->RGBColor[0, 0, 1],
    FontVariations->{"Underline"->True},
    ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ {
        FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&),
    Active->True,
    ButtonFrame->"None"}],
  
  Cell[StyleData["GettingStartedLink", "Presentation"],
    FontSize->16],
  
  Cell[StyleData["GettingStartedLink", "Condensed"],
    FontSize->11],
  
  Cell[StyleData["GettingStartedLink", "Printout"],
    FontSize->10,
    FontColor->GrayLevel[0],
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