Re: Integral equations
- To: mathgroup at smc.vnet.net
- Subject: [mg49991] Re: Integral equations
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Mon, 9 Aug 2004 04:29:34 -0400 (EDT)
- Organization: The University of Western Australia
- References: <cen755$bv$1@smc.vnet.net> <cete6p$6as$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <cete6p$6as$1 at smc.vnet.net>, Mike <m.HoneychurcNOSPAMh at uq.edu.au> wrote: > I seem to recall someone, (perhaps Paul Abbott?) writing an article on the > use of Chebyshev polynomials to solve integral equations. See "Tricks of the Trade" in The Mathematica Journal 8(4), appended below. > This was based on an article in The computer journal in the 1960s. I only > have incomplete details of this article: S.E.El-gendi, page 282. The article was S. E. El-gendi, Chebyshev Solution of Differential, Integral and Integro-differential Equations, The Computer Journal, 12, 1969: 282-287 URL: http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_03 > I copied this article at the time I read the mathematica article but > unfortunately the copy doesn't include the year and volume. The full Notebook is appended below. Cheers, Paul Notebook[{ Cell[CellGroupData[{ Cell["Integral Equations", "Section"], Cell["\<\ Inhomogeneous Fredholm integral equations of the second \ kind,\ \>", "Text"], Cell[BoxData[ \(TraditionalForm\`f(x) = g(x) + \[Lambda]\ \(\[Integral]\_a\%b\( \[Kappa](x, t)\)\ \(f( t)\) \[DifferentialD]t\), \ a \[LessEqual] x \[LessEqual] b, \)], "NumberedEquation", CellTags->"inhomogenous Fredholm integral equation"], Cell[TextData[{ "involve solving for ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], ", where ", Cell[BoxData[ \(TraditionalForm\`\[Kappa](x, \ t)\)]], " is the integral kernel, ", Cell[BoxData[ \(TraditionalForm\`\[Lambda]\)]], " is a parameter, and ", Cell[BoxData[ \(TraditionalForm\`g(x)\)]], " is the inhomogeneous term [", StyleBox[ CounterBox["Reference", "Baker (1977)"], "Hyperlink"], ", ", StyleBox[ CounterBox["Reference", "Pearson (1990)"], "Hyperlink"], "]. ", StyleBox["Mathematica", FontSlant->"Italic"], " does not include built-in routines or packages for integral \ equations. However, it is straightforward to implement quite general \ methods for solving such equations." }], "Text"], Cell["\<\ As a specific example, consider Love\[CloseCurlyQuote]s \ equation\ \>", "Text"], Cell[BoxData[ \(TraditionalForm\`\(\(f(x) = 1 + \(1\/\[Pi]\) \(\[Integral]\_\(-1\)\%1\(\( f( t)\)\/\(\((x - t)\)\^2 + 1\)\) \[DifferentialD]t\)\)\(,\)\)\)], \ "NumberedEquation", CellTags->"Love's equation"], Cell[TextData[{ "which arises in electrostatics [", StyleBox[ CounterBox["Reference", "Love (1949)"], "Hyperlink"], ", ", StyleBox[ CounterBox["Reference", "Fox and Goodwin (1953)"], "Hyperlink"], "]. An excellent approximation to the solution ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], " can be found in the form of a ", StyleBox["Chebyshev-series", FontSlant->"Italic"] }], "Text"], Cell[BoxData[ \(TraditionalForm\`f( x) = \[Sum]\+\(i = 0\)\%n\( c\_i\) \(\(\(T\_\(2\ i\)\)( x)\)\(.\)\)\)], "NumberedEquation", CellTags->"Chebyshev-series"], Cell[TextData[{ "The coefficients ", Cell[BoxData[ \(TraditionalForm\`c\_i\)]], " for ", Cell[BoxData[ \(TraditionalForm\`i = 0, 1, \[Ellipsis], n\)]], ", are determined by solving numerically the simultaneous linear \ algebraic equations that result by evaluating the integral equation \ (", CounterBox["NumberedEquation", "Love's equation"], ") at the ", StyleBox["Chebyshev points", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`x\_j = cos(\(j\ \[Pi]\)\/\(2\ n\))\)]], " for ", Cell[BoxData[ \(TraditionalForm\`j = 0, 1, \[Ellipsis], 2 n\)]], ", using the Chebyshev-series (", CounterBox["NumberedEquation", "Chebyshev-series"], ") [", StyleBox[ CounterBox["Reference", "Clenshaw and Curtis (1960)"], "Hyperlink"], ", ", StyleBox[ CounterBox["Reference", "El-gendi (1969)"], "Hyperlink"], "]." }], "Text", CellTags->"Chebyshev points"], Cell[TextData[{ "Here is a direct implementation for ", Cell[BoxData[ \(TraditionalForm\`n = 4\)]], ". The Chebyshev points are calculated using arbitrary-precision \ arithmetic." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(TraditionalForm\`n = 4; xs = N[cos(\(Range[0, 2 n]\ \[Pi]\)\/\(2\ n\)), 20]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{1.`20, 0.92387953251128675612818318939678828768`20, 0.707106781186547524400844362104841`20, 0.382683432365089771728459984030457`20, 0, \(-0.38268343236508977172845998403030093491`20\), \ \(-0.707106781186547524400844362104841`20\), \ \(-0.92387953251128675612818318939673155745`20\), \(-1.`20\)}\)], \ "Output"] }, Open ]], Cell[TextData[{ "Instead of computing the points using ", StyleBox["Table", "InlineInputTraditionalForm"], ", we have used the ", StyleBox["Listable", "InlineInputTraditionalForm"], " attribute of ", StyleBox["Cos", "InlineInputTraditionalForm"], "." }], "Text", CellTags->"Listable attribute"], Cell[TextData[{ "We introduce the undetermined coefficients ", Cell[BoxData[ \(TraditionalForm\`c\_i\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(TraditionalForm\`cs = Thread[c\_\(Range[0, n]\)]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{c\_0, c\_1, c\_2, c\_3, c\_4}\)], "Output"] }, Open ]], Cell[TextData[{ "We evaluate the left-hand side of equation (", CounterBox["NumberedEquation", "Love's equation"], ") at the Chebyshev points." }], "Text"], Cell[BoxData[ \(TraditionalForm\`\(lhs = cs . Table[\(T\_\(2\ i\)\)(xs), {i, 0, n}];\)\)], "InputOnly"], Cell[TextData[{ "Note that we have replaced the sum in the Chebyshev-series (", CounterBox["NumberedEquation", "Chebyshev-series"], ") by a dot product and have used the ", StyleBox["Listable", "InlineInputTraditionalForm"], " attribute of ", StyleBox["ChebyshevT", "InlineInputTraditionalForm"], " to compute the value at ", StyleBox["all", FontSlant->"Italic"], " the Chebyshev points at once." }], "Text", CellTags->"Listable attribute"], Cell[CellGroupData[{ Cell[BoxData[ \(TraditionalForm\`Attributes[ChebyshevT]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{Listable, NumericFunction, Protected, ReadProtected}\)], "Output"] }, Open ]], Cell[TextData[{ "To compute the right-hand side of equation (", CounterBox["NumberedEquation", "Love's equation"], ") we could use a Chebyshev quadrature formula [", StyleBox[ CounterBox["Reference", "Clenshaw and Curtis (1960)"], "Hyperlink"], ", ", StyleBox[ CounterBox["Reference", "El-gendi (1969)"], "Hyperlink"], "]. Instead we use ", StyleBox["NIntegrate", "InlineInputTraditionalForm"], " for simplicity, again using arbitrary-precision arithmetic." }], "Text", CellTags->"quadrature formula"], Cell[BoxData[ \(TraditionalForm\`\(rhs = 1 + \(1\/\[Pi]\) cs . Table[ NIntegrate[ Evaluate[\(\(T\_\(2\ i\)\)(t)\)\/\(\((xs - t)\)\^2 \ + 1\)], {t, \(-1\), 1}, WorkingPrecision \[Rule] 20], {i, 0, n}];\)\)], "InputOnly"], Cell[TextData[{ "Solving the resulting simultaneous linear algebraic equations we \ obtain the coefficients ", Cell[BoxData[ \(TraditionalForm\`c\_i\)]], " for ", Cell[BoxData[ \(TraditionalForm\`i = 0, 1, \[Ellipsis], n\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(TraditionalForm\`Solve[lhs \[Equal] rhs, cs]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`{{c\_0 \[Rule] 1.774444805405816089451717`10.0316, c\_1 \[Rule] \(-0.1400430745415970909939`10.0316\), c\_2 \[Rule] 0.004962498177017669262634`10.0316, c\_3 \[Rule] 0.000374672334133862620845`10.0316, c\_4 \[Rule] \ \(-0.0000436865088592062024742579`10.0316\)}}\)], "Output"] }, Open ]], Cell[TextData[{ "The solution ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], " is obtained from the", " Chebyshev-series", " (", CounterBox["NumberedEquation", "Chebyshev-series"], ")." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(TraditionalForm\`f( x_) = \[Sum]\+\(i = 0\)\%n\( c\_i\) \(\(T\_\(2\ i\)\)(x)\) /. First[%]\)], "Input"], Cell[BoxData[ \(TraditionalForm\`\(-0.1400430745415970909939`10.0316\)\ \((2\ x\ \^2 - 1)\) + 0.004962498177017669262634`10.0316\ \((8\ x\^4 - 8\ x\^2 + 1)\) + 0.000374672334133862620845`10.0316\ \((32\ x\^6 - 48\ x\^4 + 18\ x\^2 - 1)\) - 0.0000436865088592062024742579`10.0316\ \((128\ x\^8 - 256\ x\^6 + 160\ x\^4 - 32\ x\^2 + 1)\) + 1.774444805405816089451717`10.0316\)], "Output"] }, Open ]], Cell[TextData[{ "To see how well the Chebyshev-series solution satisfies Love\ \[CloseCurlyQuote]s equation (", CounterBox["NumberedEquation", "Love's equation"], "), we substitute it back into the equation and plot the difference \ of the left- and right-hand sides. The Chebyshev points are also \ displayed and it is apparent that the ", StyleBox["minimum error", FontSlant->"Italic"], " in the Chebyshev-series solution occurs at these points." }], "Text", Evaluatable->False, AspectRatioFixed->True, CellTags->"minimum error"], Cell[BoxData[ \(TraditionalForm\`\(Plot[ 1 + \(1\/\[Pi]\) NIntegrate[\(f(t)\)\/\(\((x - t)\)\^2 + 1\), {t, \(-1\), 1}] - f(x), {x, \(-1\), 1}, Epilog \[Rule] {Hue[0], AbsolutePointSize[3], Point /@ \((xs /. x_?NumberQ \[Rule] {x, 0})\)}, PlotRange \[Rule] All];\)\)], "Input"], Cell[TextData[{ "As an aside, we can get a bound for the ", StyleBox["maximum error", FontSlant->"Italic"], " directly from the ", StyleBox["PlotRange", "InlineInputTraditionalForm"], " of this plot. 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Be careful when modifying, renaming, or removing \ these styles, because the front end associates special meanings with \ these style names.\ \>", "Text"], Cell[TextData[{ "Input cell style to be used for ", StyleBox["Mathematica", FontSlant->"Italic"], " input statements that are followed by either Output or \ GraphicsOnly cell styles. Sets ", "DefaultFormatType->DefaultInputFormatType." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellFrame->{{0.25, 0.25}, {0, 0.25}}, CellMargins->{{67, 24}, {-1, 10}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, CellFrameColor->GrayLevel[0.869993], DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontFamily->"Courier", FontSize->12, FontWeight->"Bold", Background->GrayLevel[0.949996]], Cell[StyleData["Input", "Presentation"], FontSize->14], Cell[StyleData["Input", "Printout"], CellFrame->False, CellMargins->{{96, 72}, {2, 4}}, PrivateEvaluationOptions->{"OutputFormPageWidth"->342}, CellFrameMargins->False, LineSpacing->{1.25, 0}, FontSize->9, Background->None] }, Closed]], Cell[TextData[{ "InputOnly cell style to be used for ", StyleBox["Mathematica", FontSlant->"Italic"], " input statements that produce no output or graphic. See Program \ and ProgramNoLabel cell styles for presenting segments of code that \ do not evaluate." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["InputOnly"], CellFrame->{{0.25, 0.25}, {0, 0.25}}, CellMargins->{{67, 24}, {10, 10}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelAutoDelete->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, CellFrameColor->GrayLevel[0.869993], DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontFamily->"Courier", FontSize->12, FontWeight->"Bold", Background->GrayLevel[0.949996]], Cell[StyleData["InputOnly", "Presentation"], FontSize->14], Cell[StyleData["InputOnly", "Printout"], CellFrame->False, CellMargins->{{96, 72}, {2, 4}}, PrivateEvaluationOptions->{"OutputFormPageWidth"->342}, LineSpacing->{1.25, 0}, FontSize->9, Background->None] }, Closed]], Cell[TextData[{ "Output cell style is usually generated by the ", StyleBox["Mathematica", FontSlant->"Italic"], " kernel. To follow Input cell style. Sets \ DefaultFormatType->DefaultOutputFormatType." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Output"], CellFrame->{{0.25, 0.25}, {0.25, 0}}, CellMargins->{{67, 24}, {10, 0}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelAutoDelete->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, CellFrameColor->GrayLevel[0.869993], DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, CounterIncrements->"Output", StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[0.949996]], Cell[StyleData["Output", "Presentation"], FontSize->14], Cell[StyleData["Output", "Printout"], CellFrame->False, CellMargins->{{96, 72}, {2, 4}}, CellLabelMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1.25, 0}, FontSize->9, Background->None] }, Closed]], Cell[TextData[{ "OutputOnly cell style to be used for output generated by the ", StyleBox["Mathematica", FontSlant->"Italic"], " kernel without the Input. Sets \ DefaultFormatType->DefaultOutputFormatType." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["OutputOnly"], CellFrame->True, CellMargins->{{67, 24}, {15, 10}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelAutoDelete->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, CellFrameColor->GrayLevel[0.869993], DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, CounterIncrements->"Output", StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[0.949996]], Cell[StyleData["OutputOnly", "Presentation"], FontSize->14], Cell[StyleData["OutputOnly", "Printout"], CellFrame->False, CellMargins->{{96, 72}, {2, 4}}, CellLabelMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1.25, 0}, FontSize->9, Background->None] }, Closed]], Cell[TextData[{ "Message cells are sometimes generated by the ", StyleBox["Mathematica", FontSlant->"Italic"], " kernel during evaluation. To follow Input cell style, precede \ Output cell style." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Message"], CellFrame->{{0.25, 0.25}, {0, 0}}, CellDingbat->"\[WarningSign]", CellMargins->{{67, 24}, {0, 0}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, CellFrameColor->GrayLevel[0.869993], CellFrameLabelMargins->-9, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontColor->RGBColor[0, 0, 1], Background->GrayLevel[0.949996]], Cell[StyleData["Message", "Presentation"], FontSize->12], Cell[StyleData["Message", "Printout"], CellFrame->True, CellDingbat->None, CellMargins->{{96, 72}, {2, 4}}, PrivateEvaluationOptions->{"OutputFormPageWidth"->342}, CellFrameMargins->4, CellFrameColor->GrayLevel[0], LineSpacing->{0, 10}, FontSize->8, FontColor->GrayLevel[0], Background->None] }, Closed]], Cell[TextData[{ "Print cells are usually generated by the ", StyleBox["Mathematica", FontSlant->"Italic"], " kernel from such commands as ?Plot." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Print"], CellFrame->True, CellMargins->{{67, 24}, {0, 0}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, CellFrameColor->GrayLevel[0], DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, StyleMenuListing->None, FontSize->10], Cell[StyleData["Print", "Presentation"], FontSize->12], Cell[StyleData["Print", "Printout"], CellFrame->True, CellMargins->{{96, 72}, {2, 4}}, PrivateEvaluationOptions->{"OutputFormPageWidth"->342}, CellFrameMargins->4, CellFrameColor->GrayLevel[0], LineSpacing->{0, 11}, FontSize->9, Background->None] }, Closed]], Cell["\<\ Graphics cell usually output by kernel. To be preceded by \ Input cell, followed by Output cell.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellFrame->{{0.25, 0.25}, {0, 0}}, CellMargins->{{67, 24}, {0, 0}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->True, CellLabelPositioning->Left, CellLabelAutoDelete->True, CellFrameColor->GrayLevel[0.869993], DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, ImageMargins->{{30, 0}, {0, 0}}, StyleMenuListing->None, Background->GrayLevel[0.949996]], Cell[StyleData["Graphics", "Presentation"]], Cell[StyleData["Graphics", "Printout"], CellFrame->False, CellMargins->{{96, 72}, {8, 10}}, LineSpacing->{0, 12}, ImageSize->{144, 144}, Background->None] }, Closed]], Cell["\<\ GraphicsOnly cell to follow Input cell, not followed by \ Output cell. Set Graphics cell to GraphicsOnly cell manually.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["GraphicsOnly"], CellFrame->{{0.25, 0.25}, {0.25, 0}}, CellMargins->{{67, 24}, {10, 0}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->True, CellLabelPositioning->Left, CellLabelAutoDelete->True, CellFrameColor->GrayLevel[0.869993], DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, ImageMargins->{{30, 0}, {0, 0}}, Background->GrayLevel[0.949996]], Cell[StyleData["GraphicsOnly", "Presentation"]], Cell[StyleData["GraphicsOnly", "Printout"], CellFrame->False, CellMargins->{{96, 72}, {8, 10}}, LineSpacing->{0, 12}, ImageSize->{144, 144}, FontSize->10, Background->None] }, Closed]], Cell["\<\ PictureGroup cell style used to group graphic cells that \ comprise an animation.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["PictureGroup"], CellFrame->{{0.25, 0.25}, {0.25, 0}}, CellMargins->{{67, 17}, {0, 0}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, ShowCellLabel->True, CellLabelAutoDelete->True, CellFrameColor->GrayLevel[0.869993], DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, ImageMargins->{{30, 0}, {0, 0}}, StyleMenuListing->None, Background->GrayLevel[0.949996]], Cell[StyleData["PictureGroup", "Presentation"]], Cell[StyleData["PictureGroup", "Printout"], CellFrame->False, CellMargins->{{96, 72}, {8, 10}}, LineSpacing->{0, 12}, ImageSize->{144, 144}, FontSize->10, Background->None] }, Closed]], Cell[TextData[{ "PlacedGraphics cell style to be used when importing a graphic \ from another application or when presenting a graphic not associated \ with ", StyleBox["Mathematica", FontSlant->"Italic"], " input. May be followed by NumberedFigureCaption." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["PlacedGraphics"], CellFrame->False, CellMargins->{{67, 24}, {10, 10}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, ShowCellLabel->False, CellLabelAutoDelete->True, TextAlignment->Center], Cell[StyleData["PlacedGraphics", "Presentation"]], Cell[StyleData["PlacedGraphics", "Printout"], CellMargins->{{72, 72}, {8, 10}}, LineSpacing->{0, 12}, FontSize->10, Background->None] }, Closed]], Cell["\<\ CellLabel style definition controls how labels appear \ when a cell has ShowCellLabels->True.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], CellMargins->{{5, Inherited}, {Inherited, Inherited}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->8, FontSlant->"Oblique", FontColor->RGBColor[0.115343, 0.350561, 0.362966]], Cell[StyleData["CellLabel", "Presentation"], FontSize->10, FontColor->RGBColor[0.115343, 0.350561, 0.362966]], Cell[StyleData["CellLabel", "Printout"], LineSpacing->{1, 0}, FontSize->6, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Automatic Numbering and Lists", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell["\<\ NumberedEquation is for DisplayFormula cells that number \ sequentially throughout a notebook. Sets as \ DefaultFormatType->TraditionalForm.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["NumberedEquation"], CellMargins->{{67, 24}, {5, 10}}, PageBreakAbove->False, CellFrameLabels->{{None, Cell[ TextData[ {"(", CounterBox[ "NumberedEquation"], ")"}]]}, {None, None}}, DefaultFormatType->TraditionalForm, TextAlignment->Center, SingleLetterItalics->True, SpanMaxSize->Infinity, CounterIncrements->"NumberedEquation", FormatTypeAutoConvert->False, FontFamily->"Times", FontSize->12, UnderoverscriptBoxOptions->{LimitsPositioning->True}, GridBoxOptions->{AllowScriptLevelChange->False}], Cell[StyleData["NumberedEquation", "Presentation"], FontSize->14], Cell[StyleData["NumberedEquation", "Printout"], CellMargins->{{72, 72}, {2, 4}}, PrivateEvaluationOptions->{"OutputFormPageWidth"->342}, FontSize->10] }, Closed]], Cell["\<\ NumberedFigureCaption to be used directly after a \ PlacedGraphic cell. Use the TMJStyles.nb palette to begin the cell \ and paste in the word \"Figure\" and the NumberedFigure counter \ value. Allows for a descriptive caption.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["NumberedFigureCaption"], CellDingbat->"\[FilledUpTriangle]", CellMargins->{{67, 24}, {8, 10}}, PageBreakAbove->False, CellLabelPositioning->Left, TextAlignment->Left, CounterIncrements->"NumberedFigure", FormatTypeAutoConvert->False, FontFamily->"Helvetica", FontSize->10], Cell[StyleData["NumberedFigureCaption", "Presentation"]], Cell[StyleData["NumberedFigureCaption", "Printout"], CellDingbat->None, CellMargins->{{72, 72}, {18, 4}}, LineSpacing->{0, 11}, FontSize->9] }, Closed]], Cell["\<\ NumberedTableCaption to be used directly after a Table \ cell. Use the TMJStyles.nb palette to begin the cell and paste in the \ word \"Table\" and the NumberedTable counter value. Allows for a \ descriptive caption.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["NumberedTableCaption"], CellDingbat->"\[FilledUpTriangle]", CellMargins->{{67, 24}, {8, 10}}, PageBreakAbove->False, CounterIncrements->"NumberedTable", FontFamily->"Helvetica", FontSize->10], Cell[StyleData["NumberedTableCaption", "Presentation"]], Cell[StyleData["NumberedTableCaption", "Printout"], CellDingbat->None, CellMargins->{{72, 72}, {18, 4}}, LineSpacing->{0, 11}, FontSize->9] }, Closed]], Cell["\<\ NumberedProgramCaption to be used directly after a \ Program cell. Use the TMJStyles.nb palette to begin the cell and \ paste in the word \"Listing\" and the NumberedProgram counter value. \ Allows for a descriptive caption.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["NumberedProgramCaption"], CellDingbat->"\[FilledUpTriangle]", CellMargins->{{67, 24}, {8, 10}}, PageBreakAbove->False, CounterIncrements->"NumberedProgram", FormatTypeAutoConvert->False, FontFamily->"Helvetica", FontSize->10], Cell[StyleData["NumberedProgramCaption", "Presentation"]], Cell[StyleData["NumberedProgramCaption", "Printout"], CellDingbat->None, CellMargins->{{72, 72}, {18, 4}}, LineSpacing->{0, 11}, FontSize->9] }, Closed]], Cell["\<\ BulletedList is an optional style. Adds a CellDingbat of \ FilledSmallCircle. Text indents left a little more.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["BulletedList"], CellDingbat->"\[FilledSmallCircle]", CellMargins->{{86, 24}, {Inherited, Inherited}}, FontFamily->"Times", FontSize->12], Cell[StyleData["BulletedList", "Presentation"]], Cell[StyleData["BulletedList", "Printout"], CellMargins->{{101, 72}, {2, Inherited}}, LineSpacing->{0, 12}, FontSize->10] }, Closed]], Cell["\<\ BeginNumberedList to be used as the first item in a \ numbered list sequence. Use the TMJStyles.nb palette to begin the \ cell and paste in the List counter value.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["BeginNumberedList"], CellMargins->{{87, 24}, {Inherited, Inherited}}, ParagraphIndent->-20, CounterIncrements->"List", CounterAssignments->{{"List", 0}}, FontFamily->"Times", FontSize->12], Cell[StyleData["BeginNumberedList", "Presentation"], ParagraphIndent->-31], Cell[StyleData["BeginNumberedList", "Printout"], CellMargins->{{85, 72}, {2, Inherited}}, LineSpacing->{0, 12}, ParagraphIndent->-17, FontSize->10] }, Closed]], Cell["\<\ NumberedList to be used for subsequent items in a \ numbered list sequence with a single-digit label. Use the \ TMJstyles.nb palette to begin the cell and paste in the List counter \ value.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["NumberedList"], CellMargins->{{87, 10}, {Inherited, Inherited}}, ParagraphIndent->-20, CounterIncrements->"List", FontFamily->"Times", FontSize->12], Cell[StyleData["NumberedList", "Presentation"], ParagraphIndent->-31], Cell[StyleData["NumberedList", "Printout"], CellMargins->{{85, 72}, {2, Inherited}}, LineSpacing->{0, 12}, ParagraphIndent->-17, FontSize->10] }, Closed]], Cell["\<\ NumberedListTwo to be used for subsequent items in a \ numbered list sequence with a two-digit label. Use the TMJStyles.nb \ palette to begin the cell and paste in the List counter value.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["NumberedListTwo"], CellMargins->{{85, 10}, {Inherited, Inherited}}, ParagraphIndent->-20, CounterIncrements->"List", FontFamily->"Times", FontSize->12], Cell[StyleData["NumberedListTwo", "Presentation"], ParagraphIndent->-31], Cell[StyleData["NumberedListTwo", "Printout"], CellMargins->{{85, 72}, {2, Inherited}}, LineSpacing->{0, 12}, ParagraphIndent->-17, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["NolabelList"], CellMargins->{{105, 10}, {Inherited, Inherited}}, FontFamily->"Times", FontSize->12], Cell[StyleData["NolabelList", "Presentation"], FontSize->14], Cell[StyleData["NolabelList", "Printout"], CellMargins->{{102, 72}, {2, Inherited}}, LineSpacing->{0, 12}, ParagraphIndent->0, FontSize->10] }, Closed]], Cell["\<\ BeginSubList to be used as the first item in a lettered \ list sequence used as a subitem to a NumberedList item. Use the \ TMJStyles.nb palette to begin the cell and paste in the SubList \ counter value. Sets SubList counter to 0.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["BeginSubList"], CellMargins->{{107, 10}, {Inherited, Inherited}}, ParagraphIndent->-12, CounterIncrements->"SubList", CounterAssignments->{{"SubList", 0}}, FontFamily->"Times", FontSize->12, CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "a", "z"], #]&)}], Cell[StyleData["BeginSubList", "Presentation"], ParagraphIndent->-19], Cell[StyleData["BeginSubList", "Printout"], CellMargins->{{102, 72}, {2, Inherited}}, LineSpacing->{0, 12}, ParagraphIndent->-12, FontSize->10] }, Closed]], Cell["\<\ SubList to be used as subsequent items in a lettered list \ sequence used as a subitem to a NumberedList item. Use the \ TMJStyles.nb palette to begin the cell and paste in the SubList \ counter value. Increments SubList counter.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["SubList"], CellMargins->{{107, 10}, {Inherited, Inherited}}, ParagraphIndent->-14, CounterIncrements->"SubList", FontFamily->"Times", FontSize->12, CounterBoxOptions->{CounterFunction:>(Part[ CharacterRange[ "a", "z"], #]&)}], Cell[StyleData["SubList", "Presentation"], ParagraphIndent->-19], Cell[StyleData["SubList", "Printout"], CellMargins->{{102, 72}, {2, Inherited}}, LineSpacing->{0, 12}, ParagraphIndent->-12, FontSize->10] }, Closed]], Cell["\<\ Reference style to be used in the bibliography portion of \ a notebook. One cell for each bibliography entry. Use the \ TMJStyles.nb palette to begin cell and paste in the Reference counter \ value. Use Inline style SB for bold font changes. Use Inline style SO \ for italic font changes.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Reference"], CellMargins->{{67, 25}, {Inherited, Inherited}}, ParagraphIndent->-20, CounterIncrements->"Reference", FontFamily->"Helvetica", FontSize->10], Cell[StyleData["Reference", "Presentation"], ParagraphIndent->-25], Cell[StyleData["Reference", "Printout"], CellMargins->{{85, 72}, {2, 4}}, LineSpacing->{0, 10}, ParagraphIndent->-15, FontSize->8] }, Closed]], Cell["\<\ ReferenceTwo is for two-digit reference entries. See the \ TMJStyles.nb palette. Use Inline style SB for bold font changes. Use \ Inline style SO for italic font changes.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["ReferenceTwo"], CellMargins->{{67, 25}, {Inherited, Inherited}}, ParagraphIndent->-22, CounterIncrements->"Reference", FontFamily->"Helvetica", FontSize->10], Cell[StyleData["ReferenceTwo", "Presentation"], ParagraphIndent->-27, FontFamily->"Helvetica", FontSize->12], Cell[StyleData["ReferenceTwo", "Printout"], CellMargins->{{84, 72}, {2, 4}}, LineSpacing->{0, 10}, ParagraphIndent->-16, FontSize->8] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Journal Element Styles", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell["\<\ OnlineHeader to be used at the beginning of a notebook. \ Precedes the Title cell.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["OnlineHeader"], ShowCellBracket->False, ShowSelection->True, CellMargins->{{0, 25}, {0, 0}}, CellGroupingRules->{"TitleGrouping", 30}, PageBreakBelow->False, CellFrameMargins->{{54, 4}, {2, 8}}, LineSpacing->{1, 1}, StyleMenuListing->None, FontFamily->"Times", FontSize->12, FontWeight->"Plain", FontSlant->"Italic", FontColor->GrayLevel[1], Background->RGBColor[0.725383, 0.0545968, 0.0770581]], Cell[StyleData["OnlineHeader", "Presentation"], FontSize->14], Cell[StyleData["OnlineHeader", "Printout"], PageWidth->PaperWidth, CellFrame->False, CellMargins->{{72, 72}, {0, 0}}, FontSize->10, FontColor->GrayLevel[0], Background->None] }, Closed]], Cell["\<\ Cell Style PreTitle to be used for such things that \ precede a title as in EDITOR'S PICK. Should be entered all caps with \ a space between each letter, two spaces between words. FontTracking \ is set to Wide.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["PreTitle"], ShowCellBracket->False, CellMargins->{{54, 25}, {Inherited, 0}}, CellGroupingRules->{"TitleGrouping", 0}, PageBreakBelow->False, CellFrameMargins->{{55, 4}, {8, 20}}, LineSpacing->{1.125, 0}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold"], Cell[StyleData["PreTitle", "Presentation"]], Cell[StyleData["PreTitle", "Printout"], CellMargins->{{72, 72}, {14, 0}}, CellFrameMargins->False, FontSize->12, FontColor->GrayLevel[0], Background->None] }, Closed]], Cell["\<\ Author to be used after the Title cell with author \ name(s). Author name(s) may be preceded by \"Edited by \" for certain \ columns. Text in author cell to be used as the left page header. \ Usually followed by an Address cell.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Author"], ShowCellBracket->False, ShowSelection->True, CellMargins->{{54, 24}, {4, 0}}, CellGroupingRules->"NormalGrouping", PageBreakBelow->False, FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["Author", "Presentation"], FontSize->16], Cell[StyleData["Author", "Printout"], CellMargins->{{72, 72}, {4, 4}}, LineSpacing->{0, 14}, FontSize->12] }, Closed]], Cell["\<\ Abstract to be used after the Author cell. Contains a \ short summary of the article.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Abstract"], ShowCellBracket->False, ShowSelection->True, CellMargins->{{54, 86}, {4, 25}}, LineSpacing->{1, 3}, FontFamily->"Times", FontSize->14, FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["Abstract", "Presentation"], FontSize->16], Cell[StyleData["Abstract", "Printout"], CellMargins->{{72, 72}, {Inherited, 2}}, LineSpacing->{0, 12}, FontSize->10, FontWeight->"Bold", FontSlant->"Plain"] }, Closed]], Cell["\<\ BeginQuestion is used in the In and Out column directly \ after a section cell. Followed by either Question or Input, \ InputOnly, etc. Last paragraph of the question should be in \ EndQuestion cell style.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["BeginQuestion"], CellFrame->{{0, 0}, {0, 2}}, CellDingbat->"Q:", CellMargins->{{89, 34}, {8, 8}}, CellFrameMargins->{{0, 0}, {2, 4}}, LineSpacing->{1, 2}, FontFamily->"Times", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0.115511, 0.321752, 0.580118]], Cell[StyleData["BeginQuestion", "Presentation"]], Cell[StyleData["BeginQuestion", "Printout"], PageWidth->PaperWidth, CellFrame->{{0, 0}, {0, 2}}, CellMargins->{{72, 72}, {4, 16}}, LineSpacing->{0, 12}, FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }, Closed]], Cell["\<\ Question used for text cells within the Question portion \ of a QuestionAnswer.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Question"], CellMargins->{{89, 34}, {8, 8}}, LineSpacing->{1, 2}, FontFamily->"Times", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0.115511, 0.321752, 0.580118]], Cell[StyleData["Question", "Presentation"]], Cell[StyleData["Question", "Printout"], PageWidth->PaperWidth, CellMargins->{{72, 72}, {2, 4}}, LineSpacing->{0, 12}, FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }, Closed]], Cell["\<\ EndQuestion used in the In and Out column as the last \ paragraph of the question.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["EndQuestion"], CellFrame->{{0, 0}, {2, 0}}, CellMargins->{{89, 35}, {8, 8}}, LineSpacing->{1, 2}, FontFamily->"Times", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0.115511, 0.321752, 0.580118]], Cell[StyleData["EndQuestion", "Presentation"]], Cell[StyleData["EndQuestion", "Printout"], CellFrame->{{0, 0}, {2, 0}}, CellMargins->{{72, 72}, {18, 4}}, LineSpacing->{0, 12}, FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }, Closed]], Cell["\<\ BeginEndQuestion is used in the In and Out column \ directly after a section cell. Used if the question is a single text \ paragraph.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["BeginEndQuestion"], CellFrame->{{0, 0}, {2, 2}}, CellDingbat->"Q:", CellMargins->{{89, 35}, {8, 8}}, LineSpacing->{1, 2}, FontFamily->"Times", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0.115511, 0.321752, 0.580118]], Cell[StyleData["BeginEndQuestion", "Presentation"]], Cell[StyleData["BeginEndQuestion", "Printout"], CellMargins->{{72, 72}, {18, 14}}, LineSpacing->{0, 12}, FontSize->10, FontWeight->"Plain", FontColor->GrayLevel[0]] }, Closed]], Cell["\<\ BeginAnswer is used in the In and Out column directly \ after an EndQuestion or BeginEndQuestion cell style to begin the \ answer portion. Followed by Text or Input/Output etc.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["BeginAnswer"], CellDingbat->"A:", CellMargins->{{89, 35}, {Inherited, Inherited}}, LineSpacing->{1, 4}, CounterIncrements->"Text", FontFamily->"Times", FontSize->12], Cell[StyleData["BeginAnswer", "Presentation"]], Cell[StyleData["BeginAnswer", "Printout"], CellMargins->{{72, 72}, {2, 4}}, LineSpacing->{0, 12}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Answer"], CellMargins->{{89, 35}, {Inherited, Inherited}}, LineSpacing->{1, 4}, FontFamily->"Times", FontSize->12], Cell[StyleData["Answer", "Presentation"]], Cell[StyleData["Answer", "Printout"], CellMargins->{{72, 72}, {2, 4}}, LineSpacing->{0, 12}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["EditorialComment"], CellFrame->False, CellDingbat->"\[FilledCircle]", CellMargins->{{36, 25}, {Inherited, Inherited}}, LineSpacing->{1, 3}, CounterIncrements->"Text", FontColor->RGBColor[1, 0, 0], Background->GrayLevel[1]], Cell[StyleData["EditorialComment", "Presentation"]], Cell[StyleData["EditorialComment", "Printout"], CellMargins->{{24, 80}, {Inherited, 0}}, LineSpacing->{1, 3}, FontSize->10, FontColor->GrayLevel[0]] }, Closed]], Cell["\<\ SecondAuthor to be used after a Section cell. Author \ name(s) credit a particular portion of a notebook. Used for columns \ Tech Support and Tricks of the Trade. Usually followed by a \ TextAboutAuthor cell with author affiliation/address/hyperlink.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["SecondAuthor"], ShowCellBracket->False, ShowSelection->True, CellMargins->{{67, 24}, {Inherited, Inherited}}, CellGroupingRules->"NormalGrouping", PageBreakBelow->False, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->14, FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SecondAuthor", "Presentation"], FontSize->16], Cell[StyleData["SecondAuthor", "Printout"], CellMargins->{{72, 72}, {2, 4}}, LineSpacing->{0, 14}, FontSize->12] }, Closed]], Cell["\<\ SectionAboutAuthor to be used as the section head for the \ About the Author portion of a notebook.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["SectionAboutAuthor"], CellMargins->{{54, 25}, {10, 60}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CellFrameMargins->4, FontFamily->"Helvetica", FontSize->12, FontWeight->"Bold"], Cell[StyleData["SectionAboutAuthor", "Presentation"]], Cell[StyleData["SectionAboutAuthor", "Printout"], CellFrame->False, CellMargins->{{72, 72}, {0, 30}}, FontSize->12] }, Closed]], Cell["\<\ TextAboutAuthor is to be used for the text in the About \ the Author portion of a notebook. The last paragraph should be \ affiliation and contact information with author name set in \ bold.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["TextAboutAuthor"], CellMargins->{{54, 24}, {2, 5}}, LineSpacing->{1, 3}, CounterIncrements->"Text", FontSize->12], Cell[StyleData["TextAboutAuthor", "Presentation"], FontSize->14], Cell[StyleData["TextAboutAuthor", "Printout"], CellMargins->{{72, 72}, {2, 4}}, LineSpacing->{0, 11}, FontFamily->"Helvetica", FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsubsection"], CellDingbat->None, CellMargins->{{67, 25}, {6, 20}}, CellGroupingRules->{"SectionGrouping", 60}, PageBreakBelow->False, CounterIncrements->"Subsubsubsection", StyleMenuListing->None, FontFamily->"Helvetica", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsubsection", "Presentation"]], Cell[StyleData["Subsubsubsection", "Printout"], CellDingbat->None, CellMargins->{{72, 72}, {-4, 2}}, FontSize->9, FontWeight->"Bold", FontSlant->"Plain"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Display Formulas and Programming", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{67, 24}, {4, 4}}, CellHorizontalScrolling->True, PageBreakAbove->False, DefaultFormatType->TraditionalForm, TextAlignment->Center, ScriptLevel->0, SingleLetterItalics->True, SpanMaxSize->Infinity, FormatTypeAutoConvert->False, FontFamily->"Times", FontSize->12, UnderoverscriptBoxOptions->{LimitsPositioning->True}, GridBoxOptions->{AllowScriptLevelChange->False}], Cell[StyleData["DisplayFormula", "Presentation"]], Cell[StyleData["DisplayFormula", "Printout"], CellMargins->{{72, 72}, {2, 4}}, PrivateEvaluationOptions->{"OutputFormPageWidth"->342}, LineSpacing->{1.25, 0}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], CellMargins->{{67, 24}, {4, 4}}, PageBreakAbove->False, DefaultFormatType->DefaultInputFormatType, AutoSpacing->False, ScriptLevel->1, ScriptBaselineShifts->{0.6, Automatic}, SingleLetterItalics->False, ZeroWidthTimes->False, FontFamily->"Times", FontSize->12], Cell[StyleData["ChemicalFormula", "Presentation"], FontSize->14], Cell[StyleData["ChemicalFormula", "Printout"], CellMargins->{{72, 72}, {2, 4}}, LineSpacing->{0, 12}, FontSize->10] }, Closed]], Cell[TextData[{ "Program cell style to be followed by NumberedProgramCaption. See \ ProgramNoLabel cell style if nonevaluatable source code to be \ displayed (e.g., program listings from a program language other than \ ", StyleBox["Mathematica", FontSlant->"Italic"], ")." }], "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Program"], CellMargins->{{67, 25}, {Inherited, 6}}, FontFamily->"Courier", FontSize->10, FontWeight->"Plain"], Cell[StyleData["Program", "Presentation"]], Cell[StyleData["Program", "Printout"], CellMargins->{{72, 72}, {2, 18}}, LineSpacing->{0, 11}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ProgramNoLabel"], CellMargins->{{67, 25}, {10, 10}}, FontFamily->"Courier", FontSize->10, FontWeight->"Plain"], Cell[StyleData["ProgramNoLabel", "Presentation"]], Cell[StyleData["ProgramNoLabel", "Printout"], CellMargins->{{72, 72}, {2, 4}}, LineSpacing->{0, 11}, FontSize->9] }, Closed]], Cell["\<\ Table cell style to be used for cells containing \ displayed tabular material. May be followed by NumberedTableCaption \ cell.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["Table"], CellMargins->{{67, 24}, {5, 10}}, TextAlignment->Center, FontFamily->"Times", FontSize->12, Background->GrayLevel[0.899001]], Cell[StyleData["Table", "Presentation"], FontSize->14], Cell[StyleData["Table", "Printout"], CellMargins->{{72, 72}, {0, 18}}, FontSize->10, Background->None] }, Closed]], Cell["DefinitionBox, 2 left-aligned columns.", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["DefinitionBox"], CellFrame->0.5, CellMargins->{{67, 24}, {8, 10}}, CellHorizontalScrolling->True, AutoIndent->False, AutoSpacing->False, SingleLetterItalics->False, LineIndent->0, FontFamily->"Times", FontSize->12, Background->GrayLevel[0.899001], GridBoxOptions->{RowSpacings->1.5, ColumnSpacings->1, ColumnWidths->{0.4, 0.6}, ColumnAlignments->{Left}}], Cell[StyleData["DefinitionBox", "Presentation"]], Cell[StyleData["DefinitionBox", "Printout"], CellMargins->{{72, 72}, {8, 10}}, FontSize->10, Background->None] }, Closed]], Cell["\<\ PseudoCellExpression cell style to be used when \ displaying unformatted box expressions. \ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["PseudoCellExpression"], CellFrame->{{0, 0}, {0, 0.5}}, CellMargins->{{67, 17}, {Inherited, Inherited}}, CellFrameMargins->2, LineSpacing->{1, 4}, FontFamily->"Courier", FontSize->12], Cell[StyleData["PseudoCellExpression", "Presentation"]], Cell[StyleData["PseudoCellExpression", "Printout"], CellMargins->{{84, 96}, {Inherited, Inherited}}, LineSpacing->{0, 12}, FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontWeight->"Bold"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontSlant->"Oblique"] }, Closed]], Cell[CellGroupData[{ Cell["Frontmatter Styles", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell[CellGroupData[{ Cell[StyleData["tocentry"], CellMargins->{{67, 24}, {Inherited, Inherited}}, AutoIndent->True, TabFilling->".", LineSpacing->{1, 4}, FontFamily->"Times", FontSize->12], Cell[StyleData["tocentry", "Presentation"]], Cell[StyleData["tocentry", "Printout"], CellMargins->{{84, 72}, {0, 0}}, LineSpacing->{0, 12}, ParagraphIndent->0, FontSize->10] }, Closed]], Cell["\<\ LetterWriter to be used after a letter. Use inline \ formatting SCBO for person's name. Use Text cell style for letter \ text.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["LetterWriter"], CellMargins->{{213, Inherited}, {6, 0}}, LineSpacing->{0, 10}, FontFamily->"Helvetica", FontSize->10, FontSlant->"Oblique"], Cell[StyleData["LetterWriter", "Presentation"], LineSpacing->{0, 12}, FontSize->12], Cell[StyleData["LetterWriter", "Printout"], CellMargins->{{250, Inherited}, {6, 0}}, LineSpacing->{0, 8}, FontFamily->"Helvetica", FontSize->8, FontSlant->"Oblique"] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["LetterReply"], CellMargins->{{67, 24}, {Inherited, Inherited}}, LineSpacing->{1, 4}, FontFamily->"Times", FontSize->12, FontSlant->"Italic"], Cell[StyleData["LetterReply", "Presentation"], FontSize->14], Cell[StyleData["LetterReply", "Printout"], CellMargins->{{72, 72}, {8, 4}}, LineSpacing->{0, 12}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["IndexEntry"], CellMargins->{{67, 24}, {Inherited, Inherited}}, LineSpacing->{1, 4}, FontFamily->"Times", FontSize->12], Cell[StyleData["IndexEntry", "Presentation"], FontSize->14], Cell[StyleData["IndexEntry", "Printout"], PageWidth->336, CellMargins->{{72, 72}, {0, 0}}, AutoIndent->True, LineSpacing->{0, 10}, ParagraphIndent->-27, TabSpacings->1, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Classified"], CellFrame->{{0, 0}, {0, 2}}, CellMargins->{{67, 24}, {Inherited, Inherited}}, CellFrameMargins->False, LineSpacing->{1, 4}, FontFamily->"Helvetica", FontSize->12], Cell[StyleData["Classified", "Presentation"], FontSize->14], Cell[StyleData["Classified", "Printout"], CellMargins->{{72, 24}, {Inherited, 0}}, LineSpacing->{1, 3}, FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell["The cells below define styles used for ButtonBoxes.", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0]] }, Closed]], Cell["\<\ The following styles are for linking automatically to the \ locally installed on-line help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Printout"], FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[1, 0, 0], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell["\<\ These cells define styles that are mixed in with other \ cells. If the FormatType of a cell style matches the name of one of \ the styles defined below, then that style is applied along with the \ local cell style definitions. \ \>", "Text", CellMargins->{{24, 0}, {Inherited, Inherited}}], Cell[StyleData["CellExpression"], CellMargins->{{54, 24}, {2, 4}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, Hyphenation->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, Hyphenation->False, LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier", FontProperties->{"FontSerifed"->True, "FontMonospaced"->True}], Cell[StyleData["OutputForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier", FontProperties->{"FontSerifed"->True, "FontMonospaced"->True}], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->False, StyleMenuListing->None, FontFamily->"Courier", FontProperties->{"FontSerifed"->True, "FontMonospaced"->True}], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, ZeroWidthTimes->False, StyleMenuListing->None, FontFamily->"Times", FontProperties->{"FontSerifed"->True, "FontMonospaced"->False}], Cell["\<\ The style defined below is mixed in to any cell that is \ in an inline cell within another.\ \>", "Text", CellMargins->{{24, 0}, {Inherited, Inherited}}], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]], Cell[CellGroupData[{ Cell["Inline Formatting", "Section", CellFrame->False, CellDingbat->None, ShowCellBracket->True, CellMargins->{{0, 0}, {10, 40}}, CellFrameMargins->{{20, 4}, {8, 8}}, FontColor->GrayLevel[1], Background->RGBColor[0.269902, 0.558434, 0.715618]], Cell["\<\ InlineInput is for code segments embedded within another \ cell. Sets as FormatType->DefaultInputFormatType.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["InlineInput"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->DefaultInputFormatType, ShowStringCharacters->True, NumberMarks->True, FontFamily->"Courier", FontWeight->"Bold"], Cell[StyleData["InlineInput", "Presentation"]], Cell[StyleData["InlineInput", "Printout"]] }, Closed]], Cell["\<\ InlineInputTraditionalForm is for code segments embedded \ within another cell for articles that set Default Input/Output \ FormatType to TraditionalForm. Sets FormatType->TraditionalForm.\ \>", "EditorialComment"], Cell[CellGroupData[{ Cell[StyleData["InlineInputTraditionalForm"], CellHorizontalScrolling->True, FormatType->TraditionalForm, ShowStringCharacters->True, NumberMarks->True, SingleLetterItalics->True, ZeroWidthTimes->False, FontFamily->"Times", FontWeight->"Bold"], Cell[StyleData["InlineInputTraditionalForm", "Presentation"]], Cell[StyleData["InlineInputTraditionalForm", "Printout"]] }, Closed]], Cell["\<\ The following styles are for modifying individual words \ or letters in a cell exclusive of the cell style.\ \>", "EditorialComment"], Cell["\<\ RM used to change selection to FontWeight->Plain, \ FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["RM"], FontWeight->"Plain", FontSlant->"Plain"], Cell["\<\ BF used to change selection to FontWeight->Bold, \ FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["BF"], FontWeight->"Bold", FontSlant->"Plain"], Cell["\<\ IT used to change selection to FontWeight->Plain, \ FontSlant->Italic\ \>", "EditorialComment"], Cell[StyleData["IT"], FontWeight->"Plain", FontSlant->"Italic"], Cell["\<\ BFI used to change selection to FontWeight->Bold, \ FontSlant->Italic\ \>", "EditorialComment"], Cell[StyleData["BFI"], FontWeight->"Bold", FontSlant->"Italic"], Cell["\<\ TR used to change selection to normal text font, \ FontWeight->Plain, FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["TR"], FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell["\<\ TI used to change selection to normal text font, \ FontWeight->Plain, FontSlant->Italic\ \>", "EditorialComment"], Cell[StyleData["TI"], FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell["\<\ TB used to change selection to normal text font, \ FontWeight->Bold, FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["TB"], FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell["\<\ TBI used to change selection to normal text font, \ FontWeight->Bold, FontSlant->Italic\ \>", "EditorialComment"], Cell[StyleData["TBI"], FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell["\<\ MR used to change selection to monospace font with \ FontWeight->Plain, FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["MR"], HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell["\<\ MO used to change selection to monospace font with \ FontWeight->Plain, FontSlant->Oblique\ \>", "EditorialComment"], Cell[StyleData["MO"], HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Oblique"], Cell["\<\ MB used to change selection to monospace font with \ FontWeight->Bold, FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["MB"], HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell["\<\ MBO used to change selection to monospace font with \ FontWeight->Bold, FontSlant->Oblique\ \>", "EditorialComment"], Cell[StyleData["MBO"], HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Oblique"], Cell["\<\ SR used to change selection to sans serif font with \ FontWeight->Plain, FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["SR"], FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell["\<\ SO used to change selection to sans serif font with \ FontWeight->Plain, FontSlant->Oblique\ \>", "EditorialComment"], Cell[StyleData["SO"], FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Oblique"], Cell["\<\ SB used to change selection to sans serif font with \ FontWeight->Bold, FontSlant->Plain\ \>", "EditorialComment"], Cell[StyleData["SB"], FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell["\<\ SBO used to change selection to sans serif font with \ FontWeight->Bold, FontSlant->Oblique\ \>", "EditorialComment"], Cell[StyleData["SBO"], FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Oblique"], Cell["\<\ SCL used to change selection to sans serif font \ (FontTracking->\"Condensed\", FontWeight->\"Light\")\ \>", "EditorialComment"], Cell[StyleData["SCL"], FontFamily->"Helvetica", FontWeight->"Light", FontTracking->"Condensed"], Cell["\<\ SCLO used to change selection to sans serif font \ (FontSlant->\"Oblique\", FontTracking->\"Condensed\", \ FontWeight->\"Light\")\ \>", "EditorialComment"], Cell[StyleData["SCLO"], FontFamily->"Helvetica", FontWeight->"Light", FontSlant->"Oblique", FontTracking->"Condensed"], Cell["\<\ SCB used to change selection to sans serif font \ (FontWeight->\"Bold\", FontTracking->\"Condensed\")\ \>", "EditorialComment"], Cell[StyleData["SCB"], FontFamily->"Helvetica", FontWeight->"Bold", FontTracking->"Condensed"], Cell["\<\ SCBO used to change selection to sans serif font \ (FontWeight->\"Bold\", FontSlant->\"Oblique\", \ FontTracking->\"Condensed\")\ \>", "EditorialComment"], Cell[StyleData["SCBO"], FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Oblique", FontTracking->"Condensed"], Cell["\<\ SXR used to change selection to sans serif font \ (FontWeight->\"ExtraBold\", FontTracking->\"Condensed\")\ \>", "EditorialComment"], Cell[StyleData["SXR"], FontFamily->"Helvetica", FontWeight->"ExtraBold", FontTracking->"Condensed"], Cell["\<\ SXO used to change selection to sans serif font \ (FontWeight->\"ExtraBold\", FontSlant->\"Oblique\", \ FontTracking->\"Condensed\")\ \>", "EditorialComment"], Cell[StyleData["SXO"], FontFamily->"Helvetica", FontWeight->"ExtraBold", FontSlant->"Oblique", FontTracking->"Condensed"] }, Closed]] }, Open ]] }] ] -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul