(************** 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). 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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[ 20689, 731]*) (*NotebookOutlinePosition[ 95331, 3240]*) (* CellTagsIndexPosition[ 95287, 3236]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Problem Set 2", "Title", FontSize->18], StyleBox["\n", FontSize->18], "Klaus Moeltner /APEC 720 / Spring 2005" }], "Text"], Cell[TextData[{ StyleBox["General Instructions:\n", FontVariations->{"Underline"->True}], "* Group work is encouraged, but every student needs to hand in an \ individual version.\n* In the following programming code, replace all \"your \ turn\" entries with appropriate code. \n* Unless otherwise instructed, \ execute all complete commands using Shift+Enter.\n* For ", StyleBox["some", FontWeight->"Bold"], " incomplete commands, the correct output is given for your guidance.\n* \ Use the Palette \"PS2_palette\" to enter symbols- it will make your life \ easier.\n* Some questions require a verbal explanation - please add verbal \ answers as separate cells throughout the program.\n* \ \"DisplayFunction->Identity\" for interim graphics supressed output (to \ conserve on printing resources). If for some reason you would like to see \ interim graphs, just eliminate this element from the command and re-evaluate \ the cell.\n* Save an electronic file of your work to your course folder, \ computer, or a CD-rom for your records, but please hand in a printed \ hard-copy of your work (Note: printing through the library server can be \ slow, and ", StyleBox["Mathematica", FontSlant->"Italic"], " might \"freeze up\" during printing)" }], "Text", CellDingbat->None, Background->RGBColor[0.996078, 0.905882, 0.811765]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Symbolizing ", "Subsection"]], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(<< Utilities`Notation`\)], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(z\_11\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(z\_21\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(z\_12\), 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NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(\[Lambda]\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(\[Lambda]\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"] }, Open ]], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(x\_1\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Symbolize", "[", TagBox[\(x\_2\), NotationBoxTag, TagStyle->"NotationTemplateStyle"], "]"}]], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Part 1: A 2 by 2 Economy", "Subsection", FontSize->14]], "Text"], Cell["Consider a 2x2 economy with the folowing features:", "Text"], Cell[BoxData[ \(f\_1[\(z\_11\) : _, \(z\_21\) : _] = z\_11\^\[Alpha]\_1*z\_21\^\[Alpha]\_2\)], "Input"], Cell[BoxData[ \(f\_2[\(z\_12\) : _, \(z\_22\) : _] = z\_12\^\[Beta]\_1*z\_22\^\[Beta]\_2\)], "Input"], Cell[BoxData[ \(\({\[Alpha]\_1 = 1/4, \[Alpha]\_2 = 3/4, \[Beta]\_1 = 1/3, \[Beta]\_2 = 2/3};\)\)], "Input"], Cell[BoxData[ \(\({\(z\_1\)\&_ = 20, \(z\_2\)\&_ = 4};\)\)], "Input"], Cell[BoxData[ \(\({p\_1 = 8, p\_2 = 7};\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Numerical Solutions", "Subsection", FontSize->14]], "Text"], Cell[TextData[StyleBox["Q.1(2 points) Find the technical coefficients as a \ function of factor prices. 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Explain how this is done.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[BoxData[ \(\(Solve[{your\ turn}, {w\_1, w\_2}]\)[\([1]\)]\)], "Input"], Cell["Use N[] to get numerical solutions:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \({\(w\_1\^*\), \(w\_2\^*\)} = N[{w\_1, w\_2} /. %]\)], "Input"], Cell[BoxData[ \({0.7030780637159332`, 8.501457725947521`}\)], "Output"] }, Open ]], Cell[BoxData[ \({\(a\_11\^*\), \(a\_21\^*\), \(a\_12\^*\), \(a\_22\^*\)} = {your\ turn} \ /. {your\ turn}\)], "Input"], Cell[TextData[StyleBox["Q.3(2 points) Examine factor intensities. Which \ factor is more intensively used in the production of which good? What do \ these results imply with respect to the location of the Pareto Set and the \ equilibrium point relative to the diagonal in the Edgeworth Box?", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[BoxData[ \(your\ turn\)], "Input"], Cell[TextData[StyleBox["Q.4(3 points)) Now solve for equilibrium total \ output and total factor employment for each firm. Explain how this is done. \ Verify your results for outputs using the production functions.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[BoxData[ \(\(Solve[{your\ turn}, {q\_1, q\_2}]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \({\(q\_1\^*\), \(q\_2\^*\)} = {q\_1, q\_2} /. %\)], "Input"], Cell[BoxData[ \({\(z\_11\^*\), \(z\_21\^*\), \(z\_12\^*\), \(z\_22\^*\)} = {your\ turn}\ \)], "Input"], Cell[BoxData[ \(\(f\_1\^*\) = your\ turn /. {your\ turn}\)], "Input"], Cell[BoxData[ \(\(f\_2\^*\) = your\ turn\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Graphs", "Subsection"]], "Text", FontSize->14], Cell[TextData[StyleBox["Q.5(2 points) Generate an Edgeworth Box that shows \ isoquants at equilibrium inputs, equilibrium point, Pareto Set, and \ factor-ratio lines.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell["First,graph the isoquants at equilibrium production levels.", "Text"], Cell[BoxData[ \(Clear[x, y]\)], "Input"], Cell[BoxData[ \(\(IQ\_1 = ContourPlot[f\_1[x, y], {x, 0, \(z\_1\)\&_}, {y, 0, \(z\_2\)\&_}, ContourShading \[Rule] False, Contours -> {\(f\_1\^*\)}, PlotPoints \[Rule] 100];\)\)], "Input"], Cell[BoxData[ \(\(IQ\_2 = ContourPlot[ f\_2[\(z\_1\)\&_ - x, \(z\_2\)\&_ - y], {x, 0, \(z\_1\)\&_}, {y, 0, \(z\_2\)\&_}, ContourShading \[Rule] False, Contours -> {\(f\_2\^*\)}, PlotPoints \[Rule] 100];\)\)], "Input"], Cell["Add the equilibrium factor employment point.", "Text"], Cell[BoxData[ \(<< Graphics`Graphics`\)], "Input"], Cell[BoxData[ \(\(A = LabeledListPlot[{{\(z\_11\^*\), \(z\_21\^*\), "\"}}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell["\<\ Note: The following command is just to increase the point size for C, which \ is not possible using \"LabeledListPlot\".\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(AA = ListPlot[{{\(z\_11\^*\), \(z\_21\^*\)}}, PlotStyle \[Rule] {AbsolutePointSize[8]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell["Add the Pareto Set (all points of touching isoquants)", "Text"], Cell[BoxData[ \(Clear[x, y]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(PS = your\ turn\)], "Input"], Cell[BoxData[ \(y\/\(3\ x\) \[Equal] \(4 - y\)\/\(2\ \((20 - x)\)\)\)], "Output"] }, Open ]], Cell[BoxData[ \(<< Graphics`ImplicitPlot`\)], "Input"], Cell[BoxData[ \(\(B = ImplicitPlot[PS, {x, 0, \(z\_1\)\&_}, PlotStyle \[Rule] Dashing[{0.01}], DisplayFunction \[Rule] Identity];\)\)], "Input"] }, Open ]], Cell["Add factor ratio - lines", "Text"], Cell[BoxData[ \(\(P\_1 = Plot[y = \((\(a\_21\^*\)/\(a\_11\^*\))\)*x, {x, 0, \(z\_1\)\&_}, PlotStyle -> {RGBColor[0, 1, 0]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(P\_2 = Plot[y = \((\(z\_2\)\&_ - \ \((\(a\_22\^*\)/\(a\_12\^*\))\)*\(z\_1\)\&_)\) + \ \((\(a\_22\^*\)/\(a\_12\^*\))\)*x, {x, 0, \(z\_1\)\&_}, PlotStyle -> {RGBColor[0, 0, 1]}, DisplayFunction \[Rule] Identity];\)\)], "Input"], Cell[BoxData[ \(\(Show[your\ turn, PlotRange \[Rule] {{0, \(z\_1\)\&_}, {0, \(z\_2\)\&_}}, DisplayFunction \[Rule] $DisplayFunction];\)\)], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Comparative Statics", "Subsection"]], "Text", FontSize->14], Cell["Assume world prices change as follows:", "Text"], Cell[BoxData[ \(\({p\_1 = 10, p\_2 = 7};\)\)], "Input"], Cell[TextData[StyleBox["Q.6(2 points) Show that the Samuelson-Stolper theorem \ (SST) holds. Explain.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[BoxData[ \(N[\(Solve[{your\ turn}, {your\ turn}]\)[\([1]\)]]\)], "Input"], Cell["\<\ Go back to the original world prices (i.e. use the original a*'s), and now \ assume that endowments change as follows:\ \>", "Text"], Cell[BoxData[ \(\({\(z\_1\)\&_ = 22, \(z\_2\)\&_ = 5};\)\)], "Input"], Cell[TextData[StyleBox["Q.7(2 points) Show that the Rybcszynski theorem (RT) \ holds. Explain.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Text"], Cell[BoxData[ \(\(Solve[your\ turn]\)[\([1]\)]\)], "Input"] }, Open ]], Cell[TextData[StyleBox["Part 2: A Robinson Crusoe Economy", "Subsection", FontSize->14]], "Text"], Cell[TextData[{ "Consider a 1 consumer, 1 firm -type \"Robinson Crusoe\" economy. The \ single consumer (also owner of the firm) derives utility from leisure ", Cell[BoxData[ \(TraditionalForm\`x\_1\)]], ", and consumption of manufactured good ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], ". The individual is endowed with 1 unit of time, which he has to allocate \ to either leisure or work (z). His original endowment of ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], " is zero. \n\nThe firm generates profit Pr by producing ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], " according to the production function q=f(z), with labor as the only \ input. Market price for ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], " is p=1. The wage paid to labor is w. Utility and production functions \ are given as:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(U[\(x\_1\) : _, \(x\_2\) : _] = x\_1\^3*x\_2\^2\)], "Input"], Cell[BoxData[ \(x\_1\%3\ x\_2\%2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[z_] = 2*z\^\(1/2\)\)], "Input"], Cell[BoxData[ \(2\ \@z\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Q.8(2 points) Solve for the equilibrium values of w, ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`x\_1\)], FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[",", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(TraditionalForm\`x\_2\)], FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[",z, and q.", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }], "Text"], Cell["Start with the firm's problem:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Pr = f[z] - w\ z\)], "Input"], Cell[BoxData[ \(2\ \@z - w\ z\)], "Output"] }, Open ]], Cell[BoxData[ \(FOC = D[your\ turn]\)], "Input"], Cell[BoxData[ \(solf = \(Solve[your\ turn, z]\)[\([1]\)]\)], "Input"], Cell["\<\ This is a key step: Explicitly assign the previous result to z. This makes \ profit Pr a function of \"w\" as well, which is precisely what you need for \ the second step. You can check by simply typing \"Pr\" as shown below.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(z = z /. %\)], "Input"], Cell[BoxData[ \(1\/w\^2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Pr\)], "Input"], Cell[BoxData[ \(2\ \@\(1\/w\^2\) - 1\/w\)], "Output"] }, Open ]], Cell["\<\ Curiously, Mathematica doesn't seem to realize that the above expression is \ simply 1/w. Simplify[] doesn't help (you can check), but the following \ command does the trick:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Pr = PowerExpand[Pr]\)], "Input"], Cell[BoxData[ \(1\/w\)], "Output"] }, Open ]], Cell[TextData[{ "Next: the consumer's problem. Solve for ", Cell[BoxData[ \(TraditionalForm\`x\_1\)]], "and ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], " as a function of w." }], "Text"], Cell[BoxData[ \(\[ScriptCapitalL] = U[x\_1, x\_2] + your\ turn\)], "Input"], Cell[BoxData[ \(Simplify[{FOC\_1 = D[\[ScriptCapitalL], x\_1], FOC\_2 = D[\[ScriptCapitalL], x\_2], FOC\_3 = D[\[ScriptCapitalL], \[Lambda]]}]\)], "Input"], Cell[BoxData[ \(solc = Solve[your\ turn]\)], "Input"], Cell[TextData[{ "You want an \"interior\" solution, i.e. a solution with positive values \ for both ", Cell[BoxData[ \(TraditionalForm\`x\_1\)]], "and ", Cell[BoxData[ \(TraditionalForm\`x\_2\)]], ". Therefore:" }], "Text"], Cell[BoxData[ \({x\_1, x\_2, \[Lambda]} = {your\ turn}\)], "Input"], Cell["\<\ Finally, use the market clearing conditions to solve for the equilibrium wage \ rate and all other equilibrium values.\ \>", "Text"], Cell[BoxData[ \(\(Solve[your\ turn]\)[\([1]\)]\)], "Input"], Cell[BoxData[ \(\(w\^*\) = w /. %\)], "Input"], Cell[BoxData[ \({\(x\_1\^*\), \(x\_2\^*\), \(z\^*\), \(q\^*\)} = your\ turn\)], "Input"], Cell[TextData[StyleBox["Q.9(1 point) Show that Walras' Law holds. 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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[CellGroupData[{ Cell[StyleData["InputOnly"], CellMargins->{{66, 10}, {7, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Mathematica", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InputOnly", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["InputOnly", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->11], Cell[StyleData["InputOnly", "Printout"], CellMargins->{{39, 0}, {4, 6}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{66, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, 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->{{66, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, AutoStyleOptions->{"UnmatchedBracketStyle"->None}, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0.6, 0.100008, 0.100008]], 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}}, 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Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LanguageCategory->None, 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"], LanguageCategory->None, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0.269993, 0.308507, 0.6]], 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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"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, 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, 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CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", 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->{{60, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", 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["Outline Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Outline1"], CellMargins->{{60, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 50}, ParagraphIndent->-38, CounterIncrements->"Outline1", FontSize->18, FontWeight->"Bold", CounterBoxOptions->{ CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}], Cell[StyleData["Outline1", "Printout"], CounterBoxOptions->{ CounterFunction:>Utilities`Notation`Private`CapitalRomanNumeral}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline2"], CellMargins->{{90, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 60}, ParagraphIndent->-27, CounterIncrements->"Outline2", FontSize->15, FontWeight->"Bold", CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}], Cell[StyleData["Outline2", "Printout"], CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "A", "Z"], #]&)}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline3"], CellMargins->{{120, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 70}, ParagraphIndent->-21, CounterIncrements->"Outline3", FontSize->12, CounterBoxOptions->{CounterFunction:>Identity}], Cell[StyleData["Outline3", "Printout"], CounterBoxOptions->{CounterFunction:>Identity}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Outline4"], CellMargins->{{150, 10}, {7, 7}}, CellGroupingRules->{"SectionGrouping", 80}, ParagraphIndent->-18, CounterIncrements->"Outline4", FontSize->10, CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "a", "z"], #]&)}], Cell[StyleData["Outline4", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext ButtonBoxes. The \ \"Hyperlink\" style is for links within the same Notebook, or between \ Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonFrame->"None", 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["\<\ 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[0.269993, 0.308507, 0.6], 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[0.269993, 0.308507, 0.6], 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[0.269993, 0.308507, 0.6], 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["RefGuideLinkText"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLinkText", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLinkText", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLinkText", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], 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], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DemosLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Demos", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["DemosLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["TourLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "Tour", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["TourLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Condensed"], FontSize->11], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MasterIndexLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0.269993, 0.308507, 0.6], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MasterIndex", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MasterIndexLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use \ in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, Placeholder]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder objects in \ palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "Condensed"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles of most \ cells. If a cell's FormatType matches the name of one of the styles defined \ below, then that style is applied between the cell's style and its own \ options. This is particularly true of Input and Output.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, Hyphenation->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], InputAutoReplacements->{}, AllowInlineCells->False, Hyphenation->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], InputAutoReplacements->{ "->"->"\[Rule]", ":>"->"\[RuleDelayed]", "<="->"\[LessEqual]", ">="->"\[GreaterEqual]", "!="->"\[NotEqual]", "=="->"\[Equal]", Inherited}, "TwoByteSyntaxCharacterAutoReplacement"->True, LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an inline cell \ within another.\ \>", "Text"], Cell[StyleData["InlineCell"], LanguageCategory->"Formula", ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216]] }, Closed]], Cell[CellGroupData[{ Cell["Automatic Styles", "Section"], Cell["\<\ The cells below define styles that are used to affect the display of certain \ types of objects in typeset expressions. For example, \"UnmatchedBracket\" \ style defines how unmatched bracket, curly bracket, and parenthesis \ characters are displayed (typically by coloring them to make them stand out).\ \ \>", "Text"], Cell[StyleData["UnmatchedBracket"], StyleMenuListing->None, FontColor->RGBColor[0.760006, 0.330007, 0.8]], Cell[StyleData["Completions"], StyleMenuListing->None, FontFamily->"Courier"] }, Closed]], Cell[CellGroupData[{ Cell["Styles from HelpBrowser", "Section"], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{66, 12}, {2, 24}}, PageBreakBelow->False, CellFrameMargins->{{8, 8}, {8, 2}}, CellFrameColor->GrayLevel[0.700008], CellFrameLabelMargins->4, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, StyleMenuListing->None, FontColor->GrayLevel[0.2]], Cell[StyleData["MathCaption", "Presentation"], FontSize->18], Cell[StyleData["MathCaption", "Printout"], CellMargins->{{39, 0}, {0, 14}}, Hyphenation->True, FontSize->9, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ObjectName"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["ObjectName", "Presentation"], FontSize->18], Cell[StyleData["ObjectName", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Usage"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Usage", "Presentation"], FontSize->18], Cell[StyleData["Usage", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Notes"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["Notes", "Presentation"], FontSize->18], Cell[StyleData["Notes", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["InlineOutput"], ShowCellBracket->True, CellMargins->{{66, 4}, {8, 8}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->False, CellLabelMargins->{{14, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, ShowSpecialCharacters->Automatic, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Mathematica", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["InlineOutput", "Presentation"], FontSize->18], Cell[StyleData["InlineOutput", "Printout"], ShowCellBracket->False, CellMargins->{{39, 0}, {6, 6}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell["Emphasis Boxes and Pictures", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["Box"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["Box", "Presentation"], FontSize->18], Cell[StyleData["Box", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DoubleBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->2, RowAlignments->Top}], Cell[StyleData["DoubleBox", "Presentation"], FontSize->18], Cell[StyleData["DoubleBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["1ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["1ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["1ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics->False, LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.31, 0.67}}], Cell[StyleData["2ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->9, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnEvenBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->0.46}], Cell[StyleData["2ColumnEvenBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnEvenBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnSmallBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.35, ColumnAlignments->{Right, Left}}], Cell[StyleData["2ColumnSmallBox", "Presentation"], FontSize->18], Cell[StyleData["2ColumnSmallBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->0.32}], Cell[StyleData["3ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["3ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnSmallBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.24, ColumnAlignments->{Right, Center, Left}}], Cell[StyleData["3ColumnSmallBox", "Presentation"], FontSize->18], Cell[StyleData["3ColumnSmallBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["4ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], SingleLetterItalics->False, LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.13, 0.35, 0.13, 0.35}}], Cell[StyleData["4ColumnBox", "Presentation"], FontSize->18], Cell[StyleData["4ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["5ColumnBox"], CellFrame->0.5, CellMargins->{{27, 12}, {0, 8}}, CellHorizontalScrolling->True, CellFrameColor->RGBColor[0.74902, 0.694118, 0.552941], LineIndent->0, StyleMenuListing->None, Background->RGBColor[0.964706, 0.929412, 0.839216], 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