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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[ 163131, 3898]*) (*NotebookOutlinePosition[ 204240, 5236]*) (* CellTagsIndexPosition[ 204150, 5230]*) (*WindowFrame->Normal*) Notebook[{ Cell["16.21 Techniques of structural analysis and design", "Title", TextAlignment->Center, FontSize->18], Cell["\<\ Home assignment 4 \ \>", "Subtitle", TextAlignment->Center, FontSize->18], Cell[TextData[{ "Question 1: Note that we require the complete elasticity solution: ", Cell[BoxData[ \(TraditionalForm\`\(u\_\(\(i\)\(,\)\)\) \[Epsilon]\_ij, \ \[Sigma]\_ij\ \)]] }], "Subtitle", FontSize->18], Cell[CellGroupData[{ 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\(\[Sigma]\_12 = 0\)\);\)\)}], "Input",\ FontSize->18], Cell[TextData[{ "From equilibrium:\n", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x\_1\)\[Sigma]\_11 = 0\)]], " \[Implies] ", Cell[BoxData[ \(TraditionalForm\`\(\(\[Sigma]\_11 = \ C\)\(,\)\)\)]], " b.c.: ", Cell[BoxData[ FormBox[ RowBox[{\(\(\[Sigma]\_11\)(\(-w\)\/2, x\_2, x\_3)\), " ", "=", " ", RowBox[{\(0\ \[Implies] C\), " ", "=", " ", RowBox[{"0", Cell[""]}]}]}], TraditionalForm]]], "\n\[DoubleLongRightArrow]" }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(\[Sigma]\_11 = 0;\)\)], "Input", FontSize->18], Cell[" Similarly (from the plane stress condition)", "Subtitle", FontSize->18], Cell[BoxData[ \(\(\[Sigma]\_22 = 0;\)\)], "Input", FontSize->18], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x\_3\)\[Sigma]\_33 = 0\)]], " \n\nConstitutive:\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33 = \ \(1\/E\)[\[Sigma]\_33 - \[Nu]\ \ \((0 + 0)\)]\)]], "\n\nThen:\n", Cell[BoxData[ \(TraditionalForm\`\[PartialD]\_\(x\_3\)\((E\ \[Epsilon]\_33)\)\ = \ \ \(0\ \[DoubleLongRightArrow]\ \[Epsilon]\_33 = \ \(\[PartialD]\_\(x\_3\)u\_3 \ = c\)\)\)]] }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(u\_3 = c\ x\_3 + d;\)\)], "Input", FontSize->18], Cell[TextData[{ "\tThe bondary conditions are:\n\n", Cell[BoxData[ \(TraditionalForm\`u\_3[L\/2]\ = \ \(c\ L\/2 + d\ = \ 0\)\)]], "\n", Cell[BoxData[ \(TraditionalForm\`u\_3[\(-L\)\/2]\ = \ \(\(-c\)\ L\/2 + d\ = \ \[Delta]\)\)]] }], "Subtitle", FontSize->18], Cell[BoxData[{ \(\(rules\ = \ \ Solve[{c\ L\/2 + d\ \[Equal] 0, \ \(-c\)\ L\/2 + d\ \[Equal] \[Delta]}, {c, d}] // Flatten;\)\), "\[IndentingNewLine]", \(\(sol\ = \ u\_3 /. \ rules;\)\ (*\ this\ auxiliary\ step\ avoids\ infinite\ recursion\ *) \), "\ \[IndentingNewLine]", \(\(u\_3\ = \ sol;\)\)}], "Input", FontSize->18], Cell[BoxData[{ \(\(\[Epsilon]\_33 = \ \[PartialD]\_\(x\_3\)u\_3;\)\), "\ \[IndentingNewLine]", \(\(\(\[Sigma]\_33 = \ EE\ \[Epsilon]\_33;\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(\(\[Epsilon]\_11 = \ \(\[Epsilon]\_22 = \ \(-\[Nu]\)\ \[Epsilon]\_33\);\ \)\)}], "Input", FontSize->18], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_11 = \ \(\[PartialD]\_\(x\_1\)u\_1\ = \ \ \(-\[Nu]\)\ \[Epsilon]\_33\)\)]], "\n", Cell[BoxData[ \(u\_1 = \ \(\[Epsilon]\_11\) x\_1 + \ d\)]], "\nThe boundary condition is:\n", Cell[BoxData[ \(TraditionalForm\`u\_1\ = \ \(0\ at\ x\_1 = \ 0\)\)]], " \[Implies] d = 0" }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(u\_1 = \ \(\[Epsilon]\_11\) x\_1;\)\)], "Input", FontSize->18], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_22 = \ \(\[PartialD]\_\(x\_2\)u\_2\ = \ \ \(-\[Nu]\)\ \[Epsilon]\_22\)\)]], "\n", Cell[BoxData[ \(u\_2 = \ \(\[Epsilon]\_22\) x\_2 + \ d\)]], "\nThe boundary condition is:\n", Cell[BoxData[ \(TraditionalForm\`u\_2\ = \ \(0\ at\ x\_2 = \ 0\)\)]], " \[Implies] d = 0" }], "Subtitle", FontSize->18], Cell[BoxData[ \(\(u\_2 = \ \(\[Epsilon]\_22\) x\_2;\)\)], "Input", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{\({u\_1, u\_2, u\_3} // MatrixForm\), "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Epsilon]\_11\), \(\[Epsilon]\_12\), \(\[Epsilon]\_12\)}, {\(\[Epsilon]\_12\), \(\[Epsilon]\_22\), \(\[Epsilon]\_23\)}, {\(\[Epsilon]\_13\), \(\[Epsilon]\_23\), \(\[Epsilon]\_33\)} }], ")"}], "//", "MatrixForm"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Sigma]\_11\), \(\[Sigma]\_12\), \(\[Sigma]\_12\)}, {\(\[Sigma]\_12\), \(\[Sigma]\_22\), \(\[Sigma]\_23\)}, {\(\[Sigma]\_13\), \(\[Sigma]\_23\), \(\[Sigma]\_33\)} }], ")"}], "//", "MatrixForm"}]}]}]], "Input", FontSize->18], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\ x\_1\)\/L\)}, {\(\(\[Delta]\ \[Nu]\ x\_2\)\/L\)}, {\(\[Delta]\/2 - \(\[Delta]\ x\_3\)\/L\)} }], "\[NoBreak]", ")"}], MatrixForm[ { Times[ Power[ L, -1], \[Delta], \[Nu], Subscript[ x, 1]], Times[ Power[ L, -1], \[Delta], \[Nu], Subscript[ x, 2]], Plus[ Times[ Rational[ 1, 2], \[Delta]], Times[ -1, Power[ L, -1], \[Delta], Subscript[ x, 3]]]}]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\)\/L\), "0", "0"}, {"0", \(\(\[Delta]\ \[Nu]\)\/L\), "0"}, {"0", "0", \(-\(\[Delta]\/L\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0", "0"}, {"0", "0", "0"}, {"0", "0", \(-\(\(EE\ \[Delta]\)\/L\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18] }, Open ]], Cell[TextData[{ "b) Plane strain conditions:\nThe only things that change are:\n\n", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_22\)]], "\[NotEqual]0, ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_22 = \ 0\)]], "\n\nUse this in the constitutive equation in compliance form for ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_22\)]], ":\n\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_\(\(22\)\(\ \)\) = \ \(0\ = \ \(1\/EE\) \ \((\[Sigma]\_22 - \ \[Nu]\ \((\[Sigma]\_11 + \ \[Sigma]\_33)\))\)\)\)]], " \[Implies] ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_22 = \ \[Nu]\ \((\ \[Sigma]\_11 + \ \ \[Sigma]\_33)\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`\(\(\[Sigma]\_11 = \ 0\)\(,\)\(\ \)\)\)]], "as before\n\nreplace ", Cell[BoxData[ \(TraditionalForm\`\[Sigma]\_22\)]], "in constitutive equation for ", Cell[BoxData[ \(TraditionalForm\`\(\(\[Epsilon]\_33\)\(:\)\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33 = \ \(\(1\/EE\) \((\[Sigma]\_33 - \ \ \[Nu]\ \[Sigma]\_22)\)\ = \ \(\(1\/EE\) \((\[Sigma]\_33 - \ \(\[Nu]\^2\) \ \[Sigma]\_33)\)\ = \ \(\((1 - \[Nu]\^2)\)\/EE\) \[Sigma]\_33\)\)\)]], "\n\nWe note that this gives a stiffer behavior, since the factor in \ parenthesis is smaller than \"1\". \nNote that from here on the solution is \ the same as in a) but with\n", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(\((1 - \[Nu]\^2)\)\/EE\) \[Sigma]\_33\)]], ", instead of ", Cell[BoxData[ \(TraditionalForm\`\[Epsilon]\_33\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(1\/EE\) \[Sigma]\_33\)]], "\nSo we can infer the solution by replacing E with ", Cell[BoxData[ \(TraditionalForm\`E\/\(1 - \[Vee]\^2\)\)]], "\n" }], "Subtitle", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(u\_1 = \ \[Nu] \( \[Delta]\/L\) x\_1; \ \[Epsilon]\_11 = \ \[Nu]\ \[Delta]\/L; \ \[Sigma]\_11 = \ 0;\[IndentingNewLine] \(\(u\_2 = \ 0\) \); \ \(\(\[Epsilon]\_22 = \ 0\)\(\ \)\);\)\(\ \)\)\)], "Input", FontSize->18], Cell[BoxData[ \(\[Sigma]\_22 = \ \[Nu]\ \[Sigma]\_33\)], "Subtitle", FontSize->18], Cell[BoxData[ \(\(\(\(\[Sigma]\_22 = \ \(-\[Nu]\)\ \(\[Delta]\/L\) EE\/\(1 - \[Nu]\^2\);\)\[IndentingNewLine] \(\(u\_3 = \ \(\[Delta]\/L\) \((L\/2 - x\_3)\)\) \); \ \(\(\[Epsilon]\_33 = \ \(-\[Delta]\)\/L\) \); \ \ \(\(\[Sigma]\_33 = \ \(\(-\[Delta]\)\/L\) EE\/\(1 - \[Nu]\^2\)\) \);\)\(\[IndentingNewLine]\)\)\)], "Input", FontSize->18] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{" ", RowBox[{\({u\_1, u\_2, u\_3} // MatrixForm\), "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Epsilon]\_11\), \(\[Epsilon]\_12\), \(\[Epsilon]\_12\)}, {\(\[Epsilon]\_12\), \(\[Epsilon]\_22\), \(\[Epsilon]\_23\)}, {\(\[Epsilon]\_13\), \(\[Epsilon]\_23\), \(\[Epsilon]\_33\)} }], ")"}], "//", "MatrixForm"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"(", GridBox[{ {\(\[Sigma]\_11\), \(\[Sigma]\_12\), \(\[Sigma]\_12\)}, {\(\[Sigma]\_12\), \(\[Sigma]\_22\), \(\[Sigma]\_23\)}, {\(\[Sigma]\_13\), \(\[Sigma]\_23\), \(\[Sigma]\_33\)} }], ")"}], "//", "MatrixForm"}]}]}]], "Input", FontSize->18], Cell[BoxData[ InterpretationBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\ x\_1\)\/L\)}, {"0"}, {\(\(\[Delta]\ \((L\/2 - x\_3)\)\)\/L\)} }], "\[NoBreak]", ")"}], MatrixForm[ { Times[ Power[ L, -1], \[Delta], \[Nu], Subscript[ x, 1]], 0, Times[ Power[ L, -1], \[Delta], Plus[ Times[ Rational[ 1, 2], L], Times[ -1, Subscript[ x, 3]]]]}]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {\(\(\[Delta]\ \[Nu]\)\/L\), "0", "0"}, {"0", "0", "0"}, {"0", "0", \(-\(\[Delta]\/L\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "0", "0"}, {"0", \(-\(\(EE\ \[Delta]\ \[Nu]\)\/\(L\ \((1 - \[Nu]\^2)\)\)\)\), "0"}, {"0", "0", \(-\(\(EE\ \[Delta]\)\/\(L\ \((1 - \[Nu]\^2)\)\)\)\)} }], "\[NoBreak]", ")"}], Function[ BoxForm`e$, MatrixForm[ BoxForm`e$]]]], "Output", FontSize->18] }, Open ]], Cell[TextData[{ "Question 2: Problem 4.4 from textbook\n\nFor bar:\n", Cell[BoxData[ \(TraditionalForm\`U\_0 = \ \(1\/2\) \[Sigma]\)]], "\[Epsilon] = ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) E\ \[Epsilon]\^2\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) E\ \((du\/dx)\)\^2\)]], "\n", Cell[BoxData[ \(TraditionalForm\`U\_bar\)]], " = ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_V\( U\_0\) dV\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_0\^L E\)]], "A ", Cell[BoxData[ \(TraditionalForm\`1\/2\ \((du\/dx)\)\^2\)]], "dx\n\nFor spring:\n", Cell[BoxData[ \(TraditionalForm\`U\_spring = \ \(1\/2\) k\ \(u(L)\)\^2\)]], "\n\nU = ", Cell[BoxData[ \(TraditionalForm\`U\_bar + \ U\_spring\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_0\^L E\)]], "A ", Cell[BoxData[ \(TraditionalForm\`1\/2\ \((du\/dx)\)\^2\)]], "dx + ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) k\ \(u(L)\)\^2\)]], "\n\nExternal work:\n\n", Cell[BoxData[ \(TraditionalForm\`W\_ext = \ P\ \(u(L)\)\ + \ \[Integral]\_V\( f(x)\)\/A\ \(u(x)\)\ dV\)]], "= P u(L) + ", Cell[BoxData[ \(TraditionalForm\`\(A\/A\) \(\[Integral]\_0\^L\( f(x)\)\ \(u( x)\)\ dx\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`W\_ext\)]], "= P u(L) + ", Cell[BoxData[ \(TraditionalForm\`\(A\/A\) \(\[Integral]\_0\^L\( f(x)\)\ \(u( x)\)\ dx\)\)]], "\n\n" }], "Subtitle", FontSize->18], Cell[TextData[{ "Question 3: Problem 4.5 from textbook\n\nFor linear elastic beam:\n\n", Cell[BoxData[ \(TraditionalForm\`U\_0 = \ \(\[Integral]\_0\^\[Epsilon]\_ij\( \[Sigma]\ \_ij\) d\[Epsilon]\_ij = \ \(\(1\/2\) \(\[Sigma]\_11\) \[Epsilon]\_11 = \ \(1\ \/2\) E\ \[Epsilon]\_11\^2\)\), \ \[Epsilon]\_11 = \ \(-x\_3\)\ \ du\_3\/dx\_1\)]], "\n", Cell[BoxData[ \(TraditionalForm\`U\_0 = \ \(1\/\(\(2\)\(\ \)\)\) E\ \(\(x\_3\^2\)(du\_3\/dx\_1)\)\^2\)]], "\n", Cell[BoxData[ \(TraditionalForm\`U\_beam\)]], " = ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_V\( U\_0\) dV\)]], "= ", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(\[Integral]\_0\^L\(\( 1\/2\) \(E\)\(\ \)\)\), "TraditionalForm"], FormBox[\(\((du\_3\/dx\_1)\)\^2\), "TraditionalForm"], \(\[Integral]\_A\( x\_3\^2\) dA\ dx\_1\)}], TraditionalForm]]], "\n\n", Cell[BoxData[ \(TraditionalForm\`U\_beam = \(1\/2\) \(\[Integral]\_0\^L E\ I\ \((du\_3\/dx\_1)\)\^2\ dx\_1\)\)]], "\n\n", Cell[BoxData[ \(TraditionalForm\`U\_spring = \ \(1\/2\) k\ \(\(u\_3\)(L)\)\^2\)]], "\n\nU = ", Cell[BoxData[ \(TraditionalForm\`\(\(U\_beam + \ U\_spring\)\(=\)\(\ \)\)\)]], Cell[BoxData[ \(TraditionalForm\`\(1\/2\) \(\[Integral]\_0\^L E\ I\ \((du\_3\/dx\_1)\)\^2\ dx\_1\)\)]], " + ", Cell[BoxData[ \(TraditionalForm\`\(1\/2\) k\ \(\(u\_3\)(L)\)\^2\)]], "\n\nExternal work:\n\n", Cell[BoxData[ \(TraditionalForm\`W\_ext\)]], "= ", Cell[BoxData[ \(TraditionalForm\`\[Integral]\_S\( t\_i\) u\_i\ dS\)]], "\nThe only external force in this case is ", Cell[BoxData[ \(TraditionalForm\`q\_0\)]], "which is a force per unit length distributed uniformly over the top \ surface of the beam. Then:\n", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(W\_ext = \ b \[Integral]\_0\^L\), "TraditionalForm"], \(\(q(x)\)\/b\)}], TraditionalForm]]], Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(\(u\_3\)(x\_1)\), "TraditionalForm"], \(dx\_1\)}], TraditionalForm]]], "\n", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(W\_ext = \ \[Integral]\_0\^L\), "TraditionalForm"], \(q(x)\)}], TraditionalForm]]], Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(\(u\_3\)(x\_1)\), "TraditionalForm"], \(dx\_1\)}], TraditionalForm]]], "\n" }], "Subtitle", FontSize->18], Cell[TextData[{ "\nQuestion 4: Problem 4.7 from textbook\n\nonly change is:\n", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ FormBox[\(U\_spring = \ \(\(\[Integral]\_0\^w\_0\( F\_s\) dw\)\(\ \)\(=\)\(\ \)\)\), "TraditionalForm"], \(\[Integral]\_0\^\(\(u\_3\)(L)\)k\ w\_0\^n\ \ dw\_0\)}], "=", " "}], TraditionalForm]]], "k ", Cell[BoxData[ FormBox[ RowBox[{ FormBox[\(\(\(w\_0\^\(n + 1\)\/\(n + 1\)\)\(\( | \_0\)\^\(\(u\_3\) L\)\)\)\(=\)\(\ \)\(k\)\(\ \)\), "TraditionalForm"], \(\(\(u\_3\)(L)\)\^\(n + 1\)\/\(n + 1\)\)}], TraditionalForm]]], "\n" }], "Subtitle", FontSize->18], Cell[TextData[{ "\nQuestion 5: Problem 4.9 from textbook\n\n", Cell[BoxData[ \(TraditionalForm\`U\_c = \ \[CapitalSigma]\ \((U\_c)\)\_i\)]], " sum of the complementary energy of each bar\n", Cell[BoxData[ \(TraditionalForm\`\(\(U\_c\)\(\ \)\)\)]], "for a bar is:\n\n", Cell[BoxData[{ \(TraditionalForm\`U\_c = \ \(\[Integral]\_V\( U\_\(\(c0\)\(\ \)\)\) dV\ = \ A\ L\ U\_c0\), \ \(U\_c0\) : \ complementary\ strain\ energy\ density\), "\[IndentingNewLine]", \(TraditionalForm\`U\_c0 = \ \(\[Integral]\_0\^\[Sigma]\_ij\( \ \[Epsilon]\_ij\) d\[Sigma]\_ij = \ \[Integral]\_0\^\[Sigma] \[Epsilon]\ d\ \[Epsilon]\)\)}]] }], "Subtitle", FontSize->18], Cell[CellGroupData[{ Cell[BoxData[{ \(\(\(\[Sigma]\ = \ If[\[Epsilon] > 0, \ kk\ \@\[Epsilon], \ \(-kk\)\ \@\(-\[Epsilon]\)];\)\(\ \[IndentingNewLine]\) \) (*\ this\ in\ Mathematica\ \(means : \ if\ \[Epsilon] > 0\ the\ first\ option\ applies\), \ otherwise\ the\ second\ option\ applies\ *) \), "\[IndentingNewLine]", \(?? 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DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", FormatType->InputForm, FontSize->12, Background->GrayLevel[0.850004]], Cell[StyleData["Output", "Presentation"], CellMargins->{{60, Inherited}, {10, 0}}], Cell[StyleData["Output", "Printout"], CellMargins->{{55, Inherited}, {10, 0}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["InputOnly"], CellFrame->1, CellMargins->{{55, 10}, {15, 0}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelPositioning->Automatic, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, FontSize->12, FontWeight->"Bold", Background->GrayLevel[0.966674]], Cell[StyleData["InputOnly", "Presentation"], CellMargins->{{60, Inherited}, {10, 10}}], Cell[StyleData["InputOnly", "Printout"], CellMargins->{{55, Inherited}, {10, 10}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellFrame->{{1, 1}, {0, 0}}, CellDingbat->"\[LongDash]", CellMargins->{{55, 10}, {0, 0}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, FormatType->InputForm, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontSlant->"Oblique", FontColor->GrayLevel[0], Background->GrayLevel[1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{60, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Printout"], CellMargins->{{55, Inherited}, {0, 0}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{55, 26}, {1, 6}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, TextAlignment->Left, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, FormatType->InputForm, StyleMenuListing->None, Background->GrayLevel[0.700008]], Cell[StyleData["Print", "Presentation"], CellMargins->{{60, Inherited}, {10, 2}}], Cell[StyleData["Print", "Printout"], CellMargins->{{54, Inherited}, {2, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellFrame->{{1, 1}, {0, 0}}, CellMargins->{{55, 10}, {0, 0}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, ImageMargins->{{35, Inherited}, {Inherited, 0}}, StyleMenuListing->None, Background->GrayLevel[0.850004]], Cell[StyleData["Graphics", "Presentation"], CellMargins->{{60, Inherited}, {0, 0}}, ImageMargins->{{10, 10}, {10, 10}}], Cell[StyleData["Graphics", "Printout"], CellMargins->{{55, Inherited}, {0, 0}}, ImageSize->{0.0625, 0.0625}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontSlant->"Oblique", FontColor->RGBColor[0.6, 0, 0.6]], Cell[StyleData["CellLabel", "Presentation"], CellMargins->{{18, Inherited}, {Inherited, Inherited}}], Cell[StyleData["CellLabel", "Printout"], CellMargins->{{0, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Unique Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["Author"], CellMargins->{{20, 30}, {45, 5}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, CellFrameMargins->{{0, 4}, {8, 4}}, LineSpacing->{1, 0}, CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Author", "Presentation"], CellMargins->{{20, 30}, {45, 10}}], Cell[StyleData["Author", "Printout"], CellMargins->{{18, 30}, {45, 5}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Abstract"], CellFrame->False, CellMargins->{{18, 140}, {4, 30}}, Hyphenation->True, LineSpacing->{0.9, 0}, FontFamily->"Times", FontSize->12], Cell[StyleData["Abstract", "Presentation"], CellFrame->True, CellMargins->{{20, 10}, {Inherited, 30}}], Cell[StyleData["Abstract", "Printout"], LineSpacing->{1, 2}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Caption"], CellMargins->{{55, 10}, {5, 3}}, PageBreakAbove->False, Hyphenation->True, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["Caption", "Presentation"], CellMargins->{{60, 65}, {6, 4}}, FontSize->10], Cell[StyleData["Caption", "Printout"], CellMargins->{{55, 55}, {5, 4}}, LineSpacing->{1, 2}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Reference"], CellMargins->{{24, 40}, {6, 6}}, TextJustification->1, Hyphenation->True, LineSpacing->{1, 0}, FontFamily->"Times"], Cell[StyleData["Reference", "Presentation"], CellMargins->{{20, 40}, {Inherited, 6}}, TextJustification->0, LineSpacing->{1, 4}, FontSize->12], Cell[StyleData["Reference", "Printout"], CellMargins->{{18, 4}, {4, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PictureGroup"], CellFrame->{{1, 1}, {0, 0}}, CellMargins->{{55, Inherited}, {0, 0}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, ShowCellLabel->False, ImageMargins->{{35, Inherited}, {Inherited, 0}}, StyleMenuListing->None, Background->GrayLevel[0.850004]], Cell[StyleData["PictureGroup", "Presentation"], CellMargins->{{60, Inherited}, {0, 0}}, ImageMargins->{{10, 10}, {10, 10}}], Cell[StyleData["PictureGroup", "Printout"], CellMargins->{{55, Inherited}, {0, 0}}, ImageSize->{0.0625, 0.0625}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], 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", "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", "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", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{55, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, StyleMenuListing->None, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], CellMargins->{{60, 10}, {Inherited, 6}}, LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Printout"], CellMargins->{{18, 4}, {4, 4}}] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], CellMargins->{{55, 10}, {Inherited, 0}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, TextJustification->1, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", AutoSpacing->False, ScriptLevel->1, ScriptBaselineShifts->{0.6, Automatic}, SingleLetterItalics->False, ZeroWidthTimes->True], Cell[StyleData["ChemicalFormula", "Presentation"], CellMargins->{{60, 10}, {Inherited, 6}}], Cell[StyleData["ChemicalFormula", "Printout"], CellMargins->{{18, 4}, {4, 4}}, LineSpacing->{1, 3}, FontSize->10] }, Open ]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellMargins->{{55, 10}, {Inherited, 0}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{60, 10}, {Inherited, 6}}], Cell[StyleData["Program", "Printout"], CellMargins->{{18, 4}, {4, 4}}, LineSpacing->{1, 3}, FontSize->9.5] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering", "Section"], Cell["\<\ The following styles are useful for numbered equations, figures, \ etc. They automatically give the cell a FrameLabel containing a reference to \ a particular counter, and also increment that counter.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CellMargins->{{55, 85}, {Inherited, Inherited}}, CellFrameLabels->{{None, Cell[ TextData[ {"(", CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}}, DefaultFormatType->DefaultInputFormatType, "TwoByteSyntaxCharacterAutoReplacement"->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, CounterIncrements->"NumberedEquation", FormatTypeAutoConvert->False, FontFamily->"Times"], Cell[StyleData["NumberedEquation", "Presentation"], CellMargins->{{60, 10}, {Inherited, 6}}, LineSpacing->{1, 0}], Cell[StyleData["NumberedEquation", "Printout"], CellMargins->{{18, 4}, {4, 4}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedFigure"], CellMargins->{{55, 95}, {Inherited, Inherited}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Figure ", CounterBox[ "NumberedFigure"]}], FontWeight -> "Bold"], None}}, CounterIncrements->"NumberedFigure", FormatTypeAutoConvert->False, FontFamily->"Times"], Cell[StyleData["NumberedFigure", "Presentation"], CellMargins->{{60, 80}, {Inherited, 6}}, LineSpacing->{1, 0}], Cell[StyleData["NumberedFigure", "Printout"], CellMargins->{{18, 80}, {4, 4}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NumberedTable"], CellMargins->{{55, 95}, {Inherited, Inherited}}, CellFrameLabels->{{None, None}, {Cell[ TextData[ {"Table ", CounterBox[ "NumberedTable"]}], FontWeight -> "Bold"], None}}, TextAlignment->Center, CounterIncrements->"NumberedTable", FormatTypeAutoConvert->False, FontFamily->"Times"], Cell[StyleData["NumberedTable", "Presentation"], CellMargins->{{60, 80}, {Inherited, 6}}, LineSpacing->{1, 0}], Cell[StyleData["NumberedTable", "Printout"], CellMargins->{{18, 80}, {4, 4}}, FontSize->8] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["PageNumber"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontWeight->"Bold"], Cell[StyleData["Footer"], TextAlignment->Center, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell["Slide Show Styles", "Section"], Cell[CellGroupData[{ Cell[StyleData["SlideShowNavigationBar"], Editable->False, CellFrame->True, CellMargins->{{0, 0}, {3, 3}}, CellGroupingRules->{"SectionGrouping", 30}, CellFrameMargins->False, CellFrameColor->GrayLevel[1], CellFrameLabelMargins->False, TextAlignment->Center, CounterIncrements->"SlideShowNavigationBar", StyleMenuListing->None, FontSize->10, Background->GrayLevel[0.8], GridBoxOptions->{RowSpacings->0, ColumnSpacings->0, ColumnWidths->{3.5, 3.5, 3.5, 3.5, 13, 5, 4}, ColumnAlignments->{ Center, Center, Center, Center, Center, Center, Right, Center}}], Cell[StyleData["SlideShowNavigationBar", "SlideShow"], Deletable->False, ShowCellBracket->False, CellMargins->{{0, 0}, {-1, 0}}, PageBreakAbove->True], Cell[StyleData["SlideShowNavigationBar", "Printout"], CellMargins->{{18, 4}, {4, 4}}, LineSpacing->{1, 3}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SlideShowSection"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{0, 0}, {10, 0}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CellFrameMargins->{{12, 4}, {6, 12}}, CellFrameColor->RGBColor[0.4, 0, 0.239994], InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica", "webMathematica"->FormBox[ RowBox[ {"web", AdjustmentBox[ StyleBox[ "Mathematica", FontSlant -> "Italic"], BoxMargins -> {{-0.175, 0}, {0, 0}}]}], TextForm], Inherited}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->18, FontWeight->"Bold", FontColor->GrayLevel[0], Background->RGBColor[0.6, 0.749996, 0.899992]], Cell[StyleData["SlideShowSection", "SlideShow"], ShowCellBracket->False, PageBreakAbove->True], Cell[StyleData["SlideShowSection", "Printout"], CellMargins->{{18, 30}, {0, 30}}, CellFrameMargins->5, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SlideHyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontSize->16, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonMargins->1.5, ButtonNote->ButtonData}], Cell[StyleData["SlideHyperlink", "SlideShow"], FontSize->16], Cell[StyleData["SlideHyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SlideTOCLink"], CellMargins->{{24, Inherited}, {Inherited, Inherited}}, StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Helvetica", ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonMargins->1.5, ButtonNote->ButtonData}], Cell[StyleData["SlideTOCLink", "SlideShow"]], Cell[StyleData["SlideTOCLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SlideTOC"], CellDingbat->"\[Bullet]", CellMargins->{{18, Inherited}, {Inherited, Inherited}}, StyleMenuListing->None, FontFamily->"Helvetica"], Cell[StyleData["SlideTOC", "SlideShow"], FontSize->14], Cell[StyleData["SlideTOC", "Printout"], FontSize->10, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["1ColumnBox"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, StyleMenuListing->None, Background->RGBColor[1, 0.6, 0.6], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["1ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]], Cell[StyleData["1ColumnBox", "SlideShow"], CellMargins->{{36, 36}, {3, 6}}, Background->RGBColor[0.700008, 0.849989, 0.949996]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnBox"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, StyleMenuListing->None, Background->RGBColor[1, 0.6, 0.6], FrameBoxOptions->{BoxFrame->0.5, BoxMargins->True}, GridBoxOptions->{ColumnWidths->{0.31, 0.67}}], Cell[StyleData["2ColumnBox", "Printout"], CellMargins->{{2, 0}, {0, 8}}, 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