(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 18566, 584]*) (*NotebookOutlinePosition[ 49933, 1642]*) (* CellTagsIndexPosition[ 49889, 1638]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Hello Urs: This notebook sets out to be a companion for the three emails that eventually \ end up at the exponential metric. In effect, it serves as a \"mathematical \ grammar checker.\"\ \>", "Text"], Cell["\<\ A function to test for solutions to the vacuum field \ equations:\ \>", "Text"], Cell[BoxData[ \(test[potential_] := Simplify[{D[potential[\([1]\)], {t, 2}] - D[potential[\([1]\)], {x, 2}] - D[potential[\([1]\)], {y, 2}] - D[potential[\([1]\)], {z, 2}], D[potential[\([2]\)], {t, 2}] - D[potential[\([2]\)], {x, 2}] - D[potential[\([2]\)], {y, 2}] - D[potential[\([2]\)], {z, 2}], D[potential[\([3]\)], {t, 2}] - D[potential[\([3]\)], {x, 2}] - D[potential[\([3]\)], {y, 2}] - D[potential[\([3]\)], {z, 2}], D[potential[\([4]\)], {t, 2}] - D[potential[\([4]\)], {x, 2}] - D[potential[\([4]\)], {y, 2}] - D[potential[\([4]\)], {z, 2}]}]\)], "Input", CellLabel->"In[1]:=", InitializationCell->True], Cell[TextData[{ "Test the classical 1/R potential. The units of a potential are ", Cell[BoxData[ \(\@m\/\@L\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(test[{\@\(h\/c\)\/\@\(x\^2 + y\^2 + z\^2\), 0, 0, 0}]\)], "Input", CellLabel->"In[4]:="], Cell[BoxData[ \(TraditionalForm\`{0, 0, 0, 0}\)], "Output", CellLabel->"Out[4]="] }, Open ]], Cell[BoxData[ \(\(units = {\[Gamma] \[Rule] 1, J \[Rule] m\^\(1/2\)\/\(\(L\^\(3/2\)\) t\), V \[Rule] L\^3, q \[Rule] \(m\^\(1/2\)\ L\^\(3/2\)\)\/t, U \[Rule] L\/t, A\^\[Mu] \[Rule] m\^\(1/2\)\/L\^\(1/2\), A\^\[Mu]\[Nu] \[Rule] m\^\(1/2\)\/\(t\ L\^\(1/2\)\), \@G -> L\^\(3/2\)\/\(m\^\(1/2\)\ t\), G \[Rule] L\^3\/\(m\ t\^2\), c \[Rule] L\/t, h \[Rule] \(m\ L\^2\)\/t};\)\)], "Input", CellLabel->"In[7]:="], Cell[CellGroupData[{ Cell[BoxData[ \(\(1\/L\) \@\(h\/c\) /. units\)], "Input", CellLabel->"In[10]:="], Cell[BoxData[ \(TraditionalForm\`\@\(L\ m\)\/L\)], "Output", CellLabel->"Out[10]="] }, Open ]], Cell["Test a potential that is a Lorentz inverse distance squared.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(test[{\(\(\@G\) h/c\^2\)\/\(x\^2 + y\^2 + z\^2 - t\^2\), 0, 0, 0}]\)], "Input", CellLabel->"In[7]:="], Cell[BoxData[ \(TraditionalForm\`{0, 0, 0, 0}\)], "Output", CellLabel->"Out[7]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\@G\) h\)\/\(\(c\^2\) L\^2\) /. units\)], "Input", CellLabel->"In[8]:="], Cell[BoxData[ \(TraditionalForm\`\@m\/\@L\)], "Output", CellLabel->"Out[8]="] }, Open ]], Cell["\<\ The units imply this potential would involve relativistic (c) \ quantum (h) gravity (G).\ \>", "Text"], Cell["Test a potential that is a normalized linear perturbation.", "Text"], Cell[BoxData[ \(\(a = {\(c\/\@G\)\/\(\((1 + \((\(k\ x\)\/\[Sigma]\^2)\))\)\^2 + \((1 + \ \((\(k\ y\)\/\[Sigma]\^2)\))\)\^2 + \((1 + \((\(k\ z\)\/\[Sigma]\^2)\))\)\^2 \ - \((1 + \((\(k\ t\)\/\[Sigma]\^2)\))\)\^2\), 0, 0, 0};\)\)], "Input", CellLabel->"In[9]:="], Cell[CellGroupData[{ Cell[BoxData[ \(test[a]\)], "Input", CellLabel->"In[10]:="], Cell[BoxData[ \(TraditionalForm\`{0, 0, 0, 0}\)], "Output", CellLabel->"Out[10]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(c\/\@G /. units\)], "Input", CellLabel->"In[12]:="], Cell[BoxData[ \(TraditionalForm\`L\/\(\@\(L\^3\/\(m\ t\^2\)\)\ t\)\)], "Output", CellLabel->"Out[12]="] }, Open ]], Cell["\<\ These units imply relativistic (c) gravity (G), but not quantum \ mechanics (no h). Variations on this potential are the focus of the \ following work.\ \>", "Text"], Cell["Look at the derivatives to first order in k.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[D[a, t]] /. k\^2 \[Rule] 0\)], "Input", CellLabel->"In[13]:="], Cell[BoxData[ \(TraditionalForm\`{\(2\ c\ k\)\/\(\@G\ \((\(-\((\(k\ t\)\/\[Sigma]\^2 + \ 1)\)\^2\) + \((\(k\ x\)\/\[Sigma]\^2 + 1)\)\^2 + \((\(k\ y\)\/\[Sigma]\^2 + \ 1)\)\^2 + \((\(k\ z\)\/\[Sigma]\^2 + 1)\)\^2)\)\^2\ \[Sigma]\^2\), 0, 0, 0}\)], "Output", CellLabel->"Out[13]="] }, Open ]], Cell[TextData[{ "For a small oscillation, the denominator will be approximately ", Cell[BoxData[ \(2 \[Sigma]\^2\)]], ". This substitution list will make it so (and for other cases to come)." }], "Text"], Cell[BoxData[ \(\(sublist = {k\^2 \[Rule] 0, \(-\((1 + \(k\ t\)\/\[Sigma]\^2)\)\^2\) + \((1 + \(k\ x\)\/\ \[Sigma]\^2)\)\^2 + \((1 + \(k\ y\)\/\[Sigma]\^2)\)\^2 + \((1 + \(k\ z\)\/\ \[Sigma]\^2)\)\^2 \[Rule] 2, \(-\((1 + \(k\ t\)\/\[Sigma]\^2)\)\^2\) + \((1 - \(k\ x\)\/\ \[Sigma]\^2)\)\^2 + \((1 - \(k\ y\)\/\[Sigma]\^2)\)\^2 + \((1 - \(k\ z\)\/\ \[Sigma]\^2)\)\^2 \[Rule] 2, \(-\((1 - \(k\ t\)\/\[Sigma]\^2)\)\^2\) + \((1 + \(k\ x\)\/\ \[Sigma]\^2)\)\^2 + \((1 - \(k\ y\)\/\[Sigma]\^2)\)\^2 + \((1 - \(k\ z\)\/\ \[Sigma]\^2)\)\^2 \[Rule] 2, \(-\((1 - \(k\ t\)\/\[Sigma]\^2)\)\^2\) + \((1 - \(k\ x\)\/\ \[Sigma]\^2)\)\^2 + \((1 + \(k\ y\)\/\[Sigma]\^2)\)\^2 + \((1 - \(k\ z\)\/\ \[Sigma]\^2)\)\^2 \[Rule] 2, \[IndentingNewLine]\(-\((1 - \(k\ t\)\/\[Sigma]\^2)\)\^2\) + \ \((1 - \(k\ x\)\/\[Sigma]\^2)\)\^2 + \((1 - \(k\ y\)\/\[Sigma]\^2)\)\^2 + \ \((1 + \(k\ z\)\/\[Sigma]\^2)\)\^2 \[Rule] 2};\)\)], "Input", CellLabel->"In[14]:="], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[D[a, t]] /. sublist\)], "Input", CellLabel->"In[15]:="], Cell[BoxData[ \(TraditionalForm\`{\(c\ k\)\/\(2\ \@G\ \[Sigma]\^2\), 0, 0, 0}\)], "Output", CellLabel->"Out[15]="] }, Open ]], Cell["\<\ Write a potential that solves the field equations, but only has \ derivatives along the diagonal.\ \>", "Text"], Cell[BoxData[ \(\(diagonalSHO = {1\/\(\((1 + \((\(k\ x\)\/\[Sigma]\^2)\))\)\^2 + \((1 + \ \((\(k\ y\)\/\[Sigma]\^2)\))\)\^2 + \((1 + \((\(k\ z\)\/\[Sigma]\^2)\))\)\^2 \ - 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Inherited}, {2, 12}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic", FontColor->RGBColor[0, 0, 0.6]], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {2, 8}}, FontSize->12, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellFrame->{{0, 0}, {2, 0}}, CellMargins->{{10, 4}, {2, 50}}, CellElementSpacings->{"ClosedGroupTopMargin"->18}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->18, FontWeight->"Bold"], Cell[StyleData["Section", "Printout"], CellMargins->{{2, 4}, {2, 80}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSquare]", CellMargins->{{24, 4}, {2, 18}}, CellElementSpacings->{"ClosedGroupTopMargin"->12}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CellFrameLabelMargins->6, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->15, FontWeight->"Bold"], Cell[StyleData["Subsection", "Printout"], CellMargins->{{2, 4}, {2, 18}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellMargins->{{10, 4}, {2, 18}}, CellElementSpacings->{"ClosedGroupTopMargin"->12}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, CounterIncrements->"Subsubsection", FontFamily->"Helvetica", FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{2, 4}, {2, 18}}, FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Text", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{10, 4}, {0, 8}}, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, Hyphenation->True, ParagraphSpacing->{0, 8}, CounterIncrements->"Text"], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["MathCaption"], CellFrame->{{4, 0}, {0, 0}}, CellMargins->{{47, 62}, {0, 14}}, CellFrameMargins->5, CellFrameColor->RGBColor[0, 0.2, 1], Hyphenation->True, LineSpacing->{1, 1}, ParagraphSpacing->{0, 8}, FontColor->RGBColor[0, 0, 0.6]], Cell[StyleData["MathCaption", "Printout"], CellMargins->{{34, 62}, {0, 14}}, CellFrameColor->GrayLevel[0.700008], FontSize->10, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Input/Output", "Subsection", FontWeight->"Plain", FontVariations->{"CompatibilityType"->0}], 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", FontVariations->{"CompatibilityType"->0}], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{56, 4}, {3, 9}}, Evaluatable->True, CellGroupingRules->"InputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{21, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->StandardForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], Cell[StyleData["Input", "Printout"], ShowCellBracket->False, CellMargins->{{42, 4}, {3, 8}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{57, 4}, {5, 2}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{21, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->StandardForm, CounterIncrements->"Output", FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], Cell[StyleData["Output", "Printout"], ShowCellBracket->False, CellMargins->{{42, 4}, {4, 2}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{56, 4}, {3, 8}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{21, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0.2, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], Cell[StyleData["Message", "Printout"], ShowCellBracket->False, CellMargins->{{42, 4}, {4, 2}}, FontSize->10, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{56, 4}, {3, 8}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{21, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], Cell[StyleData["Print", "Printout"], ShowCellBracket->False, CellMargins->{{42, 4}, {4, 2}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{56, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], Cell[StyleData["Graphics", "Printout"], CellMargins->{{40, 4}, {4, 2}}, ImageSize->{250, 250}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0.2, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False, "StrikeThrough"->False, "Masked"->False, "CompatibilityType"->0, "RotationAngle"->0}], Cell[StyleData["CellLabel", "Printout"], FontSize->7, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Unique Styles", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["TextTop"], CellFrame->{{0, 0}, {0, 2}}, CellMargins->{{10, 4}, {2, 80}}, CellHorizontalScrolling->True, CellFrameMargins->4, ShowSpecialCharacters->Automatic, ParagraphSpacing->{0, 8}, CounterIncrements->"Text"], Cell[StyleData["TextTop", "Printout"], CellMargins->{{2, 4}, {2, 80}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ItemizedText"], CellMargins->{{20, 4}, {0, 8}}, ShowSpecialCharacters->Automatic, Hyphenation->True, ParagraphSpacing->{0, 8}, ParagraphIndent->-15, CounterIncrements->"Text"], Cell[StyleData["ItemizedText", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["ItemizedTextNote"], CellMargins->{{35, 4}, {0, 4}}, ShowSpecialCharacters->Automatic, Hyphenation->True, ParagraphSpacing->{0, 4}, CounterIncrements->"Text"], Cell[StyleData["ItemizedTextNote", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["IndentedText"], CellMargins->{{20, 4}, {0, 6}}, ShowSpecialCharacters->Automatic, Hyphenation->True, ParagraphSpacing->{0, 8}, CounterIncrements->"Text"], Cell[StyleData["IndentedText", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Note"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ShowSpecialCharacters->Automatic, ParagraphSpacing->{0, 8}, CounterIncrements->"Text", FontFamily->"Helvetica", FontSize->10], Cell[StyleData["Note", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["1ColumnBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnSpacings->1}], Cell[StyleData["1ColumnBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnWidths->{0.39, 0.59}}], Cell[StyleData["2ColumnBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["2ColumnSmallBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.35, ColumnAlignments->{Right, Left}}], Cell[StyleData["2ColumnSmallBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnWidths->0.325}], Cell[StyleData["3ColumnBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnSmallBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnSpacings->1.5, ColumnWidths->0.23, ColumnAlignments->{Right, Center, Left}}], Cell[StyleData["3ColumnSmallBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["4ColumnBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnWidths->{0.145, 0.345, 0.145, 0.345}}], Cell[StyleData["4ColumnBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["5ColumnBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnWidths->0.195}], Cell[StyleData["5ColumnBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["6ColumnBox"], CellFrame->True, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, LineIndent->0, Background->GrayLevel[0.8], FrameBoxOptions->{BoxMargins->{{1, 1}, {1.5, 1.5}}}, GridBoxOptions->{ColumnWidths->{0.13, 0.23, 0.13, 0.13, 0.23, 0.13}}], Cell[StyleData["6ColumnBox", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10, Background->GrayLevel[0.900008]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Picture"], CellMargins->{{10, Inherited}, {0, 8}}, CellHorizontalScrolling->True], Cell[StyleData["Picture", "Printout"], CellMargins->{{2, Inherited}, {0, 8}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Caption"], CellMargins->{{10, 50}, {0, 3}}, PageBreakAbove->False, Hyphenation->True, FontFamily->"Helvetica", FontSize->9], Cell[StyleData["Caption", "Printout"], CellMargins->{{2, 50}, {2, 4}}, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Tables", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["2ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, GridBoxOptions->{ColumnWidths->{0.39, 0.59}, ColumnAlignments->{Left}}], Cell[StyleData["2ColumnTable", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["3ColumnTable"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, StyleMenuListing->None, GridBoxOptions->{ColumnWidths->0.325, ColumnAlignments->{Left}}], Cell[StyleData["3ColumnTable", "Printout"], CellMargins->{{2, 4}, {0, 8}}, FontSize->10] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Subsection"], Cell[CellGroupData[{ Cell[StyleData["ChemicalFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", AutoSpacing->False, ScriptLevel->1, ScriptBaselineShifts->{0.6, Automatic}, SingleLetterItalics->False, ZeroWidthTimes->True], Cell[StyleData["ChemicalFormula", "Printout"], CellMargins->{{34, Inherited}, {Inherited, Inherited}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, SpanMaxSize->Infinity, UnderoverscriptBoxOptions->{LimitsPositioning->True}, GridBoxOptions->{ColumnWidths->Automatic}], Cell[StyleData["DisplayFormula", "Printout"], CellMargins->{{34, Inherited}, {Inherited, Inherited}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", FontFamily->"Courier"], Cell[StyleData["Program", "Printout"], CellMargins->{{2, Inherited}, {Inherited, Inherited}}, FontSize->9.5] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Subsection"], 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", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Subsection"], 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]] }, 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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