(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 22226, 590]*) (*NotebookOutlinePosition[ 51318, 1635]*) (* CellTagsIndexPosition[ 51274, 1631]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ StyleBox["F", FontWeight->"Bold"], StyleBox[" = m "], StyleBox["A", FontWeight->"Bold"], StyleBox[ " in an inertial frame, in polar coordinates, and in a rotating frame using \ quaternions"] }], "Subtitle", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[StyleBox["doug "]], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[StyleBox[ "Preamble\nNewton's 2nd law for an inertial reference frame in Cartesian \ coordinates\nNewton's 2nd law in polar coordinates for a central force in a \ plane\nNewtons's 2nd law in a nonintertial, rotating frame\nImplications"]], "Text"], Cell[TextData[StyleBox[" Preamble"]], "Subsection"], Cell[TextData[StyleBox[ "The form of Newton's second law for three separate cases will be generated \ using quaternion operators acting on position quaternions. In classical \ mechanics, time and space are decoupled. One way that can be acheived \ algebraically is by having a time operator cat only on space, or by space \ operator only act on a scalar function. I call this the \"2 zero\" rule: if \ there are two zeros in the generator of a law in physics, the law is \ classical."]], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Newton's 2nd law for an inertial reference frame in Cartesian \ coordinates\ \>", "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell["Define a position quaternion as a function of time.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(\(R\ = \ q[t, \ x[t], \ y[t], \ z[t]]; \)\)], "Input", FontSize->16], Cell[BoxData[ \(R\ = \ \((t, \ r\&\[RightVector])\)\)], "Input", FontSize->16], Cell[TextData[StyleBox[ "Operate on this once with the differential operator to get the velocity \ quaternion."]], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(V\ == \ oneoponq[q[D, 0, 0, 0], \ R]\ .\ {1, 0, 0, 0}\n\ \ == {1, \(\ \(d\ x[t]\)\/\(d\ t\)\ \), \(\ \(d\ y[t]\)\/\(d\ t\)\ \), \(\ \(d\ z[t]\)\/\(d\ t\)\ \)}\)], "Input", FontSize->16], Cell[BoxData[ \(V\ = \ \(\((\(d\ \)\/\(d\ t\), 0\&\[RightVector])\)\ R = \((1, \ \(d\ r\&\[RightVector]\)\/\(d\ t\)\ )\)\)\)], "Input", FontSize->16], Cell[TextData[ "Operate on the position quaternion twice to get the classical inertial \ acceleration quaternion."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(A\ == \n\t oneoponq[q[D, 0, 0, 0], \n\toneoponq[q[D, 0, 0, 0], \ R]]\ . \ {1, 0, 0, 0}\n\ \ == {0, \(\ \(\(d\^2\) x[t]\)\/\(d\ t\^2\)\ \), \(\ \(\(d\^2\) y[t]\)\/\(d\ t\^2\)\ \), \(\ \(\(d\^2\) z[t]\)\/\(d\ t\^2\)\ \)}\)], "Input", FontSize->16], Cell[BoxData[ \(A\ = \(\((\(d\ \)\/\(d\ t\), 0\&\[RightVector])\)\^2\ R = \((0, \ \(\(d\^2\) r\&\[RightVector]\)\/\(d\ t\^2\))\)\)\)], "Input", FontSize->16], Cell["\<\ This is the standard form for acceleration in Newton's second law \ in an inertial reference frame. Because the reference frame is inertial, the \ first term is zero.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Newton's 2nd law in polar coordinates for a central force in a \ plane\ \>", "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Repeat this process, but this time start with polar coordinates."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(\(R\_plane\ = \ q[t, \ r[t]\ Cos[\[Theta][t]], \ r[t]\ Sin[\[Theta][t]], \ 0]; \)\)], "Input", FontSize->16], Cell[BoxData[ \(R\_plane\ \ = \((t, \ r\ Cos[\[Theta]], \ r\ Sin[\[Theta]], \ 0)\)\)], "Input", FontSize->16], Cell["The velocity in a plane.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ RowBox[{ "V", "==", " ", \(oneoponq[q[D, 0, 0, 0], \ R\_plane\ ]\ .\ {1, 0, 0, 0}\), "\n", " ", "==", RowBox[{"{", RowBox[{"1", ",", RowBox[{ RowBox[{\(Cos[\[Theta][t]]\), " ", RowBox[{ SuperscriptBox["r", "\[Prime]", 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For a central force, theta' = L/mr^2, and theta\" = 0. \ Make these substitution and rotate the quaternion to get rid of the theta \ dependence."]], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ RowBox[{ "A", " ", "==", \(Simplify[ Expand[\((\n\t\t\t\t\t\n\t q[Cos[\[Theta][t]], \ 0, \ 0, \ \(-Sin[\[Theta][t]]\)]\ .\ \n\n \toneoponq[q[D, 0, 0, 0], \n\t oneoponq[q[D, 0, 0, 0], \ R\_plane\ ]]\ /. \ \n\n \t{\(\(\[Theta]'\)'\)[t]\ -> \ 0, \ \(\[Theta]'\)[t]\ -> \ L/\ \((m\ r[t]\^2)\)})\).{1, 0, 0, 0}\ ]]\), "\n", " ", "==", RowBox[{"{", RowBox[{"0", ",", RowBox[{\(-\(L\^2\/\(m\^2\ r[t]\^3\)\)\), "+", RowBox[{ SuperscriptBox["r", "\[DoublePrime]", MultilineFunction->None], "[", "t", "]"}]}], ",", FractionBox[ RowBox[{"2", " ", "L", " ", RowBox[{ SuperscriptBox["r", "\[Prime]", MultilineFunction->None], "[", "t", "]"}]}], \(m\ r[t]\^2\)], ",", "0"}], "}"}]}]], "Input", FontSize->16], Cell[BoxData[ RowBox[{"A", " ", "=", RowBox[{ \(\((Cos[\[Theta]], \ 0, \ 0, \ \(-Sin[\[Theta]]\))\) \((\(d\ \)\/\(d\ t\), \(0\& \[RightVector] \))\)\^2\ R\_plane\), " ", "\n", " ", "=", RowBox[{"(", RowBox[{"0", ",", RowBox[{\(-\(L\^2\/\(m\^2\ r\^3\)\)\), "+", SuperscriptBox["r", "\[DoublePrime]", MultilineFunction->None]}], ",", FractionBox[ RowBox[{"2", " ", "L", " ", SuperscriptBox["r", "\[Prime]", MultilineFunction->None]}], \(m\ r\^2\)], ",", "0"}], ")"}]}]}]], "Input", FontSize->16], Cell["\<\ The second term is the acceleration in the radial direction, the \ third is acceleration in the theta direction for a central force in polar \ coordinates.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[" Newton's 2nd law in a noninertial, rotating frame", "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Consider the \"noninertial\" case, with the frame rotating at an angular \ speed omega. The differential time operator is put into the first term of \ the quaternion, and the three directions for the angular speed are put in the \ next terms. This quaternion is then multiplied by the position quaternion to \ get the velocity in a rotating reference frame. Unlike the previous examples \ where t did not interfer with the calcuation, this time it must be set \ explicitly to zero (I wonder what that means?).\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(V\ == \ oneoponq[q[D, \[Omega]\_x[t], \ \[Omega]\_y[t], \ \[Omega]\_z[t]], \ R] \ .\ {1, 0, 0, 0}\n\ \ == {1 - x[t]\ \[Omega]\_x[t] - y[t]\ \[Omega]\_y[t] - z[t]\ \[Omega]\_z[t], \n\t\t\ \ t\ \[Omega]\_x[t] + z[t]\ \[Omega]\_y[t] - y[t]\ \[Omega]\_z[t] + \ \(d\ x[t]\)\/\(d\ t\)\ , \n\t\t \(-z[t]\)\ \[Omega]\_x[t] + t\ \[Omega]\_y[t] + x[t]\ \[Omega]\_z[t] + \ \(d\ y[t]\)\/\(d\ t\)\ , \n\t\t\ \ y[t]\ \[Omega]\_x[t] - x[t]\ \[Omega]\_y[t] + t\ \[Omega]\_z[t] + \(\ \(d\ z[t]\)\/\(d\ t\)\ \)}\)], "Input", FontSize->16], Cell[BoxData[ \(V = \(\((\(d\ \)\/\(d\ t\), \(\[Omega]\& \[RightVector] \))\) \((0, \(r\& \[RightVector] \))\) = \((\(-\(\[Omega]\& \[RightVector] \).\(r\& \[RightVector] \)\), \(d\ \(r\& \[RightVector] \)\)\/\(d\ t\)\ + \ \(\[Omega]\& \[RightVector] \) x \( r\& \[RightVector] \))\)\)\)], "Input", FontSize->16], Cell["Operate on the position quaternion twice.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[ \(A\ == \ Simplify[\n oneoponq[q[D, \[Omega]\_x[t], \ \[Omega]\_y[t], \ \[Omega]\_z[t]], \n oneoponq[ q[D, \[Omega]\_x[t], \ \[Omega]\_y[t], \ \[Omega]\_z[t]], \ \n \t\t\tq[0, \ x[t], \ y[t], \ z[t]]\ ]].{1, 0, 0, 0}\ ]\n\ \ == {\(-2\)\ \[Omega]\_x[t]\ \((\ \(d\ x[t]\)\/\(d\ t\)\ )\) - 2\ \[Omega]\_y[t]\ \((\ \(d\ y[t]\)\/\(d\ t\)\ )\) - 2\ \[Omega]\_z[t]\ \((\ \(d\ z[t]\)\/\(d\ t\)\ )\) - \n\t\t\t x[t]\ \((\ \(d\ \[Omega]\_x[t]\)\/\(d\ t\)\ )\) - y[t]\ \((\ \(d\ \[Omega]\_y[t]\)\/\(d\ t\)\ )\) - z[t]\ \((\ \(d\ \[Omega]\_z[t]\)\/\(d\ t\)\ )\), \n\t\t \(-x[t]\)\ \((\[Omega]\_x[t]\^2 + \[Omega]\_y[t]\^2 + \[Omega]\_z[t]\^2)\)\n \t\t - 2\ \[Omega]\_z[t]\ \((\ \(d\ y[t]\)\/\(d\ t\)\ )\) + 2\ \[Omega]\_y[t]\ \((\ \(d\ z[t]\)\/\(d\ t\)\ )\)\n\t\t\t + z[t]\ \((\ \(d\ \[Omega]\_y[t]\)\/\(d\ t\)\ )\) - y[t]\ \((\ \(d\ \[Omega]\_z[t]\)\/\(d\ t\)\ )\) + \ \(\(d\^2\) x[t]\)\/\(d\ t\^2\)\ , \n\t\t \(-y[t]\)\ \((\[Omega]\_x[t]\^2 + \[Omega]\_y[t]\^2 + \[Omega]\_z[t]\^2)\) + \n\t\t\t2\ \[Omega]\_z[t]\ \((\ \(d\ x[t]\)\/\(d\ t\)\ )\) - 2\ \[Omega]\_x[t]\ \((\ \(d\ z[t]\)\/\(d\ t\)\ )\) - \n\t\t\t z[t]\ \((\ \(d\ \[Omega]\_x[t]\)\/\(d\ t\)\ )\) + x[t]\ \((\ \(d\ \[Omega]\_z[t]\)\/\(d\ t\)\ )\) + \ \(\(d\^2\) y[t]\)\/\(d\ t\^2\)\ , \n\t\t \(-z[t]\)\ \((\[Omega]\_x[t]\^2 + \[Omega]\_y[t]\^2 + \[Omega]\_z[t]\^2)\) - \n\t\t\t2\ \[Omega]\_y[t]\ \((\ \(d\ x[t]\)\/\(d\ t\)\ )\) + 2\ \[Omega]\_x[t]\ \((\ \(d\ y[t]\)\/\(d\ t\)\ )\) + \n\t\t\t y[t]\ \((\ \(d\ \[Omega]\_x[t]\)\/\(d\ t\)\ )\) - x[t]\ \((\ \(d\ \[Omega]\_y[t]\)\/\(d\ t\)\ )\) + \(\ \(\(d\^2\) z[t]\)\/\(d\ t\^2\)\ \)}\)], "Input", FontSize->16], Cell[BoxData[ \(A\ = \(\(\((\(d\ \)\/\(d\ t\), \(\[Omega]\& \[RightVector] \))\)\^2\) \((0, \(r\& \[RightVector] \))\) = \(\((\(d\ \)\/\(d\ t\), \(\[Omega]\& \[RightVector] \))\) \((\(-\(\[Omega]\& \[RightVector] \).\(r\& \[RightVector] \)\), \(d\ \(r\& \[RightVector] \)\)\/\(d\ t\)\ + \ \(\[Omega]\& \[RightVector] \) x \( r\& \[RightVector] \))\)\n \ \ = \(( \(\(d \[Omega]\&\[RightVector]\)\/dt\).\(r\& \[RightVector] \), \ \(-\[Omega]\^2\) r\&\[RightVector]\ - \ 2\ \(d r\&\[RightVector]\)\/dt\ x\ \[Omega]\&\[RightVector]\ + \ \(d \[Omega]\&\[RightVector]\)\/dt\ x\ r\&\[RightVector]\ + \ \(\(d\^2\) r\&\[RightVector]\)\/dt\^2)\)\)\)\)], "Input", CellMargins->{{1, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell["\<\ Looks complex, but it can be simplified with vector notation.\ \>", "Text"], Cell[BoxData[ \(a\&\[RightVector]\_inertial\ = \ \(-\[Omega]\^2\) r\&\[RightVector]\ - \ 2\ \(d r\&\[RightVector]\)\/dt\ x\ \[Omega]\&\[RightVector]\ + \ \(d \[Omega]\&\[RightVector]\)\/dt\ x\ r\&\[RightVector]\ + \ \(\(d\^2\) r\&\[RightVector]\)\/dt\)], "Input", FontSize->16], Cell[BoxData[ \(a\&\[RightVector]\_inertial\ = \ \(-\[Omega]\^2\) r\&\[RightVector]\ - \ 2\ \(d r\&\[RightVector]\)\/dt\ x\ \[Omega]\&\[RightVector]\ + \ \(d \[Omega]\&\[RightVector]\)\/dt\ x\ r\&\[RightVector]\ + \ \(\(d\^2\) r\&\[RightVector]\)\/dt\)], "Input", FontSize->16], Cell["In most applications,", "Text"], Cell[BoxData[ \(\[Omega]\&\[RightVector]\ .\ r\&\[RightVector]\ = \ \(0\ \ \ \ \[Implies] \ \ \ \ \(\[Omega]\^2\) r\&\[RightVector]\ = \ \(-\[Omega]\&\[RightVector]\)\ \ x \((\[Omega]\&\[RightVector]\ \ x\ r\&\[RightVector])\)\)\)], "Input",\ FontSize->16], Cell[BoxData[ \(\[Omega]\&\[RightVector]\ .\ r\&\[RightVector]\ = \ \(0\ \ \ \ \[Implies] \ \ \ \ \(\[Omega]\^2\) r\&\[RightVector]\ = \ \(-\[Omega]\&\[RightVector]\)\ \ x \((\[Omega]\&\[RightVector]\ \ x\ r\&\[RightVector])\)\)\)], "Input",\ FontSize->16], Cell["The usual way the acceleration is written as", "Text"], Cell[BoxData[ \(a\&\[RightVector]\_inertial\ = \ \[Omega]\&\[RightVector]\ \ x \((\[Omega]\&\[RightVector]\ \ x\ r\&\[RightVector])\) + \ 2 \[Omega]\&\[RightVector]\ \ x\ \(d r\&\[RightVector]\)\/dt + \ \(d \[Omega]\&\[RightVector]\)\/dt\ x\ r\&\[RightVector]\ + \ \(\(d\^2\) r\&\[RightVector]\)\/dt\)], "Input", FontSize->16], Cell[BoxData[ \(a\&\[RightVector]\_inertial\ = \ \[Omega]\&\[RightVector]\ \ x \((\[Omega]\&\[RightVector]\ \ x\ r\&\[RightVector])\) + \ 2 \[Omega]\&\[RightVector]\ \ x\ \(d r\&\[RightVector]\)\/dt + \ \(d \[Omega]\&\[RightVector]\)\/dt\ x\ r\&\[RightVector]\ + \ \(\(d\^2\) r\&\[RightVector]\)\/dt\)], "Input", FontSize->16], Cell["\<\ The inertial accelerations are the centrifugal, the coriolis, the \ azimuthal and the translational, respectively. All four of these inertial \ forces are part of the vector component of the same quaternion.\ \>", "Text"], Cell["\<\ The scalar term is not zero. What this implies is not yet clear, \ but it may be related to the fact that the frame is not inertial.\ \>", "Text",\ Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[" Implications", "Subsection"], Cell["\<\ Three forms of Newton's second law were generated by choosing \ appropriate operator quaternions acting on position quaternions. The \ differential time operator was decoupled from any differential space \ operators. This may be viewed as an operational definition of \"classical\" \ physics.\ \>", "Text"] }, Open ]] }, Open ]] }, FrontEndVersion->"Microsoft Windows 3.0", ScreenRectangle->{{0, 640}, {0, 451}}, AutoGeneratedPackage->None, WindowToolbars->{"RulerBar", "EditBar"}, CellGrouping->Manual, WindowSize->{586, 128}, WindowMargins->{{10, Automatic}, {13, Automatic}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], Inherited, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], Inherited, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, PageHeaderLines->{False, Inherited}, PrintingOptions->{"PrintingMargins"->{{72, 57.5625}, {57.5625, 72}}, "PrintCellBrackets"->False, "PrintRegistrationMarks"->False, "PrintMultipleHorizontalPages"->False, "FirstPageHeader"->False}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, 128}}, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, CharacterEncoding->"MacintoshAutomaticEncoding", StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of all cells in \ a given style. Make modifications to any definition using commands in the \ Format menu.\ \>", "Text"], Cell[CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[StyleData[All, "Working"], PageWidth->WindowWidth, ScriptMinSize->9], Cell[StyleData[All, "Presentation"], PageWidth->WindowWidth, ScriptMinSize->12, FontSize->16], Cell[StyleData[All, "Condensed"], PageWidth->WindowWidth, CellBracketOptions->{"Margins"->{1, 1}, "Widths"->{0, 5}}, ScriptMinSize->8, FontSize->11], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, ScriptMinSize->5, FontSize->10, PrivateFontOptions->{"FontType"->"Outline"}] }, Open ]], Cell[CellGroupData[{ Cell["Notebook Options", "Section", FontFamily->"New York"], Cell["\<\ The options defined for the style below will be used at the Notebook level.\ \>", "Text", FontFamily->"New York"], Cell[StyleData["Notebook"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, CellFrameLabelMargins->6, StyleMenuListing->None, FontFamily->"New York"] }, Open ]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section", FontFamily->"Times New Roman"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellMargins->{{7, Inherited}, {8, 40}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 0}, CellHorizontalScrolling->False, PageBreakBelow->False, TextAlignment->Center, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->24, FontWeight->"Bold"], Cell[StyleData["Title", "Presentation"], CellMargins->{{24, 10}, {20, 40}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->44], Cell[StyleData["Title", "Condensed"], CellMargins->{{8, 10}, {4, 8}}, FontFamily->"Times New Roman", FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{2, 10}, {12, 30}}, FontFamily->"Times New Roman", FontSize->24] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{7, Inherited}, {6, 15}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 10}, CellHorizontalScrolling->False, PageBreakBelow->False, TextAlignment->Center, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->18], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->36], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontFamily->"Times New Roman", FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontFamily->"Times New Roman", FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellMargins->{{7, Inherited}, {6, 15}}, Evaluatable->False, CellGroupingRules->{"TitleGrouping", 20}, CellHorizontalScrolling->False, PageBreakBelow->False, TextAlignment->Center, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 8}}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontFamily->"Times New Roman", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellDingbat->"\[GraySquare]", CellMargins->{{22, Inherited}, {8, 20}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 30}, CellHorizontalScrolling->False, PageBreakBelow->False, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->18, FontWeight->"Bold", FontVariations->{"Underline"->True}], Cell[StyleData["Section", "Presentation"], CellMargins->{{40, 10}, {11, 32}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontFamily->"Times New Roman", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{19, Inherited}, {8, 15}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 40}, CellHorizontalScrolling->False, PageBreakBelow->False, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontFamily->"Times New Roman", FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[EmptySquare]", CellMargins->{{18, Inherited}, {8, 12}}, Evaluatable->False, CellGroupingRules->{"SectionGrouping", 50}, CellHorizontalScrolling->False, PageBreakBelow->False, CounterIncrements->"Subsubsection", AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontFamily->"Times New Roman", FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontFamily->"Times New Roman", FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontFamily->"Times New Roman", FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section", FontFamily->"Times New Roman"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{7, 10}, {7, 7}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 3}, CounterIncrements->"Text", AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontFamily->"Times New Roman"], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontFamily->"Times New Roman"], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}, FontFamily->"Times New Roman"] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{7, 10}, {6, 6}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 3}, CounterIncrements->"SmallText", AspectRatioFixed->True, FontFamily->"Times New Roman", FontSize->10], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontFamily->"Times New Roman", FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontFamily->"Times New Roman", FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, FontFamily->"Times New Roman", FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section", FontSize->14, FontWeight->"Plain"], Cell["\<\ The cells in this section define styles used for input and output to the \ kernel. Be careful when modifying, renaming, or removing these styles, \ because the front end associates special meanings with these style names.\ \>", "Text", FontSize->14], Cell[CellGroupData[{ Cell[StyleData["Input"], PageWidth->Infinity, CellMargins->{{42, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", AspectRatioFixed->True, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->14, FontWeight->"Plain"], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->14, FontWeight->"Plain"], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, FontSize->14, FontWeight->"Plain"] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", StyleMenuListing->None, FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[CellGroupData[{ Cell[StyleData["Output"], PageWidth->Infinity, CellMargins->{{42, 10}, {7, 5}}, CellEditDuplicate->True, Evaluatable->False, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output", AspectRatioFixed->True, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}, FontSize->14], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0.500008, 0, 0], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->14], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->14, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], PageWidth->Infinity, CellMargins->{{42, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{23, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, LineSpacing->{1, 0}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->14], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->14], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], PageWidth->Infinity, CellMargins->{{7, Inherited}, {Inherited, Inherited}}, Evaluatable->False, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", AspectRatioFixed->True, ImageSize->{387, 393}, ImageMargins->{{34, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}, FontSize->14], Cell[StyleData["Graphics", "Condensed"], ImageSize->{175, 175}, ImageMargins->{{38, Inherited}, {Inherited, 0}}, FontSize->14], Cell[StyleData["Graphics", "Printout"], ImageSize->{250, 250}, ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["CellLabel", "Presentation"], FontSize->14], Cell[StyleData["CellLabel", "Condensed"], FontSize->14], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->14, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{7, 0}, {4, 1}}, Evaluatable->False, PageBreakWithin->Automatic, AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Times", FontSize->12, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{7, 0}, {0, 4}}, Evaluatable->False, PageBreakWithin->Automatic, TextAlignment->Center, AspectRatioFixed->True, StyleMenuListing->None, FontFamily->"Times", FontSize->12, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard ButtonFunctions, for use \ in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, 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["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"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], 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"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], 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"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], 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[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], 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"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], 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"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder objects in \ palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles of most \ cells. If a cell's FormatType matches the name of one of the styles defined \ below, then that style is applied between the cell's style and its own \ options.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{1, -5}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an inline cell \ within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]] }, Open ]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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