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Psi is a scalar \ function with complex values."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(H\ \[Psi]\ = \ \(\(-i\)\ \[HBar] \[PartialD]\[Psi]\/\[PartialD]t = \ \(-\[HBar]\^2\)\/\(2\ m\)\ \[Del]\^2 \[Psi]\ + \ V \((0, X)\) \[Psi]\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(H\ \[Psi]\ = \ \(\(-i\)\ \[HBar] \[PartialD]\[Psi]\/\[PartialD]t = \ \(-\[HBar]\^2\)\/\(2\ m\)\ \[Del]\^2 \[Psi]\ + \ V \((0, X)\) \[Psi]\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "For the time-independent case, energy is written at the operator -i hbar \ d/dt, and kinetic energy as the square of the momentum operator, i hbar Del, \ over 2m. Given the potential V(0, X) and suitable boundary conditions, \ solving this differential equation generates a wave function psi which \ contains all the properties of the system."]], "Text", FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "In this notebook, I will propose a quaternion form for the total wave \ function. The partial derivatives of the wave function will be analyzed. \ Under the time-independent constraint, the reason for the equivalence of \ energy and momentum to operators will be justified. These will be used to \ formulate the Schr\[ODoubleDot]dinger equation."]], "Text", FontFamily->"Times New Roman"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["The total wave function"]], "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "My hypothesis is that the total wave function Psi is the following \ combination of quaternion operators and fields."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(\(\[CapitalPsi] = \ q[cos, \(V\& \[RightVector] \)\/\@\(V.V\)\ sin] \((\((q[\[Omega], \(K\& \[RightVector] \)].q[t, \(X\& \[RightVector] \)]\n + \ \(\((q[\[Omega], \(K\& \[RightVector] \)].q[t, \ \(X\& \[RightVector] \)])\)\^*\))\)/2)\)\n {cos\[InvisibleComma] \((\[Omega]\ t\ - \ K.X)\), V\/\@\(V.V\)\ sin\[InvisibleComma] \((\[Omega]\ t\ - \ K.X)\))\)} \)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(\[CapitalPsi] = \ \((cos, \(V\& \[RightVector] \)\/\@\(V.V\)\ sin)\) \((\((\[Omega], \(K\& \[RightVector] \))\) \((t, \(X\& \[RightVector] \))\) + \ \(\((\((\[Omega], \(K\& \[RightVector] \))\) \((t, \(X\& \[RightVector] \))\))\)\^*\))\)/2)\)\n = \((cos\[InvisibleComma] \((\[Omega]\ t\ - \ \(K\& \[RightVector] \).\(X\& \[RightVector] \))\), \(V\& \[RightVector] \)\/\@\(V.V\)\ sin\[InvisibleComma] \((\[Omega]\ t\ - \ \(K\& \[RightVector] \).\(X\& \[RightVector] \))\))\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "where w is the scalar angular frequency, K is the wave 3-vector, t is the \ scalar time, X is the position 3-vector, and V is the phase 3-vector."]], "Text", FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "Now to analyze that definition. For any quaternion, (q + q*)/2 gives the \ scalar part of the quaternion."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[{ \(Simplify[ \((\((q[\[Omega], K].q[t, X] + \n Transpose[\((q[\[Omega], K].q[t, \ X])\)])\)/2)\).{1, 0}]\), \({\[Omega]\ t\ - K.X, 0}\)}], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\((\((\[Omega], \(K\& \[RightVector] \))\) \((t, \(X\& \[RightVector] \))\) + \ \(\((\((\[Omega], \(K\& \[RightVector] \))\) \((t, \(X\& \[RightVector] \))\))\)\^*\))\)/2\n = \((\[Omega]\ t\ - K.X, 0)\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox["The trig functions act on this scalar."]], "Text", FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "The phase 3-vector V/(V.V)^.5 is similar to the imaginary number i, except \ that two phases do not necessarily commute."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[{ \(\((q[0, V\/\@\(V\ V\)].q[0, V\/\@\(V\ V\)])\).{1, 0}\), \({\(-1\), 0}\)}], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\((0, V\/\@\(V\ V\))\) \((0, V\/\@\(V\ V\))\) = {\(-1\), 0}\)], "Input",\ CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "The total wave function as defined here is always normalized."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[{ \(\((q[Cos[\[Omega]\ \ t\ - \ K.X], V\/\@\(V\ V\)\ Sin[\[Omega]\ t\ - \ K.X]].\n\t q[Cos[\[Omega]\ t\ - \ K.X], \(-\(V\/\@\(V\ V\)\)\)\ Sin[\[Omega]\ t\ - \ K.X]])\).{1, 0}\), \({Cos[\[Omega]\ t - K.X]\^2 + Sin[\[Omega]\ t - K.X]\^2, 0}\)}], "Input",\ CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\((Cos \((\[Omega]\ \ t\ - \ K.X)\), V\/\@\(V\ V\)\ Sin \((\[Omega]\ t\ - \ K.X)\))\)\^2\n = \((Cos \((\[Omega]\ t - K.X)\)\^2 + Sin \((\[Omega]\ t - K.X)\)\^2, 0) \)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "Extend Euler's formula--Exp[i theta] = Cos[theta] + i Sin[theta]--to \ quaternions, with\n i -> V/(V.V)^.5, and theta = w t - K.X."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(\[CapitalPsi]\ = \ Exp[\(V\/\@\(V\ V\)\) \((\[Omega]\ t - K.X)\)]; \)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\[CapitalPsi]\ = \ Exp \((\(V\/\@\(V\ V\)\) \((\[Omega]\ t - K.X)\))\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "According to my hypothesis, the total wave function is the normalized \ quaternion exponential with a phase 3-vector V/(V.V)^.5 and an angle \ determined by the scalar wt - K.X. The angular frequency w is related to the \ energy E by Einstein's photon hypothesis, E = h nu."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\[Omega]\ = \ \(2\ \[Pi]\ \[Nu]\ = \ \(\(2\ \[Pi]\ E\)\/h\ = \ E\/\[HBar]\)\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\[Omega]\ = \ \(2\ \[Pi]\ \[Nu]\ = \ \(\(2\ \[Pi]\ E\)\/h\ = \ E\/\[HBar]\)\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "The wave 3-vector maps to the momentum 3-vector P by de Broglie's wavelength \ equation, P = h/lambda."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(K\ = \ \(\(2\ \[Pi]\)\/\[Lambda]\ = \ \(\(2\ \[Pi]\ P\)\/h\ = \ P\/\[HBar]\)\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(K\ = \ \(\(2\ \[Pi]\)\/\[Lambda]\ = \ \(\(2\ \[Pi]\ P\)\/h\ = \ P\/\[HBar]\)\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "Substitute these into the total wave function"]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(\[CapitalPsi]\ = \ Exp[\(V\/\@\(V\ V\)\) \((E\ t - P.X)\)\/\[HBar]]; \)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\[CapitalPsi]\ = \ Exp \((\(V\/\@\(V\ V\)\) \((E\ t - P.X)\)\/\[HBar])\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "This is starting to look like physics, specifically the plane wave solution \ for a free particle. Examine the partial time derivative."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\[PartialD]\[CapitalPsi]\/\[PartialD]t = \ \(V\/\(\(\@\(V\ V\)\) \[HBar]\)\) \((E\ + \ t\ \[PartialD]E\/\[PartialD]t\ - \ \[PartialD]P.X\/\[PartialD]t)\) \[CapitalPsi]\ \n \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ + \ \(\((E\ t - P.X)\)\/\[HBar]\) \(\[PartialD]\(V\/\@\(V\ V\)\)\/\[PartialD]t\) \[CapitalPsi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\[PartialD]\[CapitalPsi]\/\[PartialD]t = \ \(V\/\(\(\@\(V\ V\)\) \[HBar]\)\) \((E\ + \ t\ \[PartialD]E\/\[PartialD]t\ - \ \[PartialD]P.X\/\[PartialD]t)\) \[CapitalPsi]\ \n \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ + \ \(\((E\ t - P.X)\)\/\[HBar]\) \(\[PartialD]\(V\/\@\(V\ V\)\)\/\[PartialD]t\) \[CapitalPsi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "Multiply both sides by (V/(V.V)^.5)^-1 hbar = -V/(V.V)^.5 hbar. Why does \ the inverse of the phase equal its negative? The inverse of any quaternion \ is the transpose divided by the norm. The transpose of a 3-vector is the \ negative of the 3-vector. The norm is one."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(-\(\(V\ \[HBar]\)\/\@\(V\ V\)\)\) \[PartialD]\[CapitalPsi]\/\[PartialD]t = \((E\ + \ t\ \[PartialD]E\/\[PartialD]t\ - \ \[PartialD]P.X\/\[PartialD]t)\) \[CapitalPsi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(-\(\(V\ \[HBar]\)\/\@\(V\ V\)\)\) \[PartialD]\[CapitalPsi]\/\[PartialD]t = \((E\ + \ t\ \[PartialD]E\/\[PartialD]t\ - \ \[PartialD]P.X\/\[PartialD]t)\) \[CapitalPsi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "In the time-independent case, E, P and X are not functions of time."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(-\(\(V\ \[HBar]\)\/\@\(V\ V\)\)\) \[PartialD]\[Psi]\/\[PartialD]t = \ E\ \[Psi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(-\(\(V\ \[HBar]\)\/\@\(V\ V\)\)\) \[PartialD]\[Psi]\/\[PartialD]t = \ E\ \[Psi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "For the time-independent wave function psi, energy is identical to the \ operator -I hbar d/dt! The equivalence of energy and this operator is know \ as the first quantization."]], "Text", FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "Repeat this process for the spatial derivative of the total wave \ function."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\[Del]\ \[CapitalPsi]\ = \ \(V\/\(\(\@\(V\ V\)\) \[HBar]\)\) \((\(-P\)\ - \ X \[Del]\(.P\)\ + \ \[Del]\ Et)\) \[CapitalPsi]\ \n \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ + \ \(\((E\ t - P.X)\)\/\[HBar]\) \[Del]x \( V\/\@\(V\ V\)\) \[CapitalPsi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\[Del]\ \[CapitalPsi]\ = \ \(V\/\(\(\@\(V\ V\)\) \[HBar]\)\) \((\(-P\)\ - \ X \[Del]\(.P\)\ + \ \[Del]\ Et)\) \[CapitalPsi]\ \n \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ + \ \(\((E\ t - P.X)\)\/\[HBar]\) \[Del]x \( V\/\@\(V\ V\)\) \[CapitalPsi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "If Psi is time-independent, then Del Et = 0. I think X Del.P must also be \ zero, perhaps by a continuity argument, but I am not sure. Multiply through \ by -V/(V.V)^.5 hbar. "]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(-\(\(V\ \[HBar]\)\/\@\(V\ V\)\)\) \[Del]\ \[Psi]\ = \ \(-P\)\ \[Psi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(-\(\(V\ \[HBar]\)\/\@\(V\ V\)\)\) \[Del]\ \[Psi]\ = \ \(-P\)\ \[Psi]\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "Momentum is equivalent to the operator I hbar Del. This operator can be \ squared to yield:"]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(-\ \[HBar]\^2\) \[Del]\^2\ = \ \(-P\^2\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(-\ \[HBar]\^2\) \[Del]\^2\ = \ \(-P\^2\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "Define the kinetic energy in terms of this momentum."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(KE\ = \(\(\ m\ v\^2\)\/2\ = \ \(\((m\ v)\)\^2\/\(2\ m\)\ = \ \(P\^2\/\(2\ m\)\ = \ \(-\(\(\ \(\[HBar]\^2\) \[Del]\^2\)\/\(2\ m\)\)\)\)\)\)\ \)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(KE\ = \(\(\ m\ v\^2\)\/2\ = \ \(\((m\ v)\)\^2\/\(2\ m\)\ = \ \(P\^2\/\(2\ m\)\ = \ \(-\(\(\ \(\[HBar]\^2\) \[Del]\^2\)\/\(2\ m\)\)\)\)\)\)\ \)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "The Hamiltonian of a system is the sum of the kinetic energy and the \ potential energy. Write out the Hamiltonian of the time-independent wave \ function psi."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(H\ \[Psi]\ = \ \(\(-\(V\/\@\(V.V\)\)\)\ \[HBar] \[PartialD]\[Psi]\/\[PartialD]t = \ \(-\[HBar]\^2\)\/\(2\ m\)\ \[Del]\^2 \[Psi]\ + \ V \((0, X)\) \[Psi]\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(H\ \[Psi]\ = \ \(\(-\(V\/\@\(V.V\)\)\)\ \[HBar] \[PartialD]\[Psi]\/\[PartialD]t = \ \(-\[HBar]\^2\)\/\(2\ m\)\ \[Del]\^2 \[Psi]\ + \ V \((0, X)\) \[Psi]\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "This is the Schr\[ODoubleDot]dinger equation written as a quaternion. One \ change involves the replacement of the imaginary number i by the \ non-commuting phase 3-vector. Another important difference is that Psi is \ now a quaternion, not a scalar with complex values. "]], "Text", FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "By choosing different potentials V(0, X), it should be possible to solve the \ standard collection of problems that confront the Schr\[ODoubleDot]dinger \ equation using quaternions (but I haven't done that work yet :-)"]], "Text", FontFamily->"Times New Roman"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Implications"]], "Subsection", CellMargins->{{0, Inherited}, {Inherited, Inherited}}, FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "We ended up very close to the Schr\[ODoubleDot]dinger equation, a difference \ involving the commutativity of i. A subtle difference with subtle \ consequences? That will have to await further work."]], "Text", FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "The lesson of first quantization--that energy and momentum are \ operators--holds only under the assumption of time-independence. When E, P, \ and X are functions of time, other terms in the partial time derivative of \ the total wave function survive, and make the math much more difficult to \ interpret."]], "Text", FontFamily->"Times New Roman"], Cell[TextData[StyleBox[ "What is most interesting about this line of work is where I start, often one \ step back from more typical derivations. At the center of the total wave \ function is the scalar, wt - K.X. This scalar gets packaged into a polar \ form to ease analysis. There are a number of equivalent ways to write this \ scalar."]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[ \(\(Et\ - \ P.X\)\/\[HBar]\ = \ \ \(\[Omega]\ t\ - \ K.X\ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \(2\ \[Pi] \((\[Nu]t\ - \ \(1\/\[Lambda]\).X)\) = \ 2\ \[Pi] \((t\/t\_\[Nu]\ - \ \(1\/X\_\[Lambda]\).X)\)\)\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[ \(\(Et\ - \ P.X\)\/\[HBar]\ = \ \ \(\[Omega]\ t\ - \ K.X\ \n\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ \(2\ \[Pi] \((\[Nu]t\ - \ \(1\/\[Lambda]\).X)\) = \ 2\ \[Pi] \((t\/t\_\[Nu]\ - \ \(1\/X\_\[Lambda]\).X)\)\)\)\)], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "There is no difference among these four ways of writing this scalar, which \ is at the heart of the wave function so is the focus of the \ Schr\[ODoubleDot]dinger equation. I find the last way most suggestive:"]], "Text", FontFamily->"Times New Roman"], Cell[BoxData[{ \(if\ \((t\/t\_\[Nu]\ - \ \(1\/X\_\[Lambda]\).X)\)\ is\ an\ integer\ "\", \ then\), \(\[CapitalPsi]\ = \ \(q[Cos[2\ \[Pi]\ n], \ \(V\/\@\(V\ V\)\) Sin[2\ \[Pi]\ n]]\ \n = \ q[1, 0]\)\n\), \(if\ \((t\/t\_\[Nu]\ - \ \(1\/X\_\[Lambda]\).X)\)\ is\ a\ half\ integer \ "\", \ then\), \(\[CapitalPsi] = \(q[Cos[\[Pi]\ n], \(V\/\@\(V\ V\)\) Sin[\[Pi]\ n]]\n = q[1, 0]\ or\ q[0, \(\[PlusMinus]\(V\/\@\(V\ V\)\)\)]\)\)}], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[BoxData[{ \(if\ \((t\/t\_\[Nu]\ - \ \(1\/X\_\[Lambda]\).X)\)\ is\ an\ integer\ "\", \ then\), \(\[CapitalPsi]\ = \ \(q[Cos[2\ \[Pi]\ n], \ \(V\/\@\(V\ V\)\) Sin[2\ \[Pi]\ n]]\ \n = \ q[1, 0]\)\n\), \(if\ \((t\/t\_\[Nu]\ - \ \(1\/X\_\[Lambda]\).X)\)\ is\ a\ half\ integer \ "\", \ then\), \(\[CapitalPsi] = \(q[Cos[\[Pi]\ n], \(V\/\@\(V\ V\)\) Sin[\[Pi]\ n]]\n = q[1, 0]\ or\ q[0, \(\[PlusMinus]\(V\/\@\(V\ V\)\)\)]\)\)}], "Input", CellMargins->{{36, Inherited}, {Inherited, Inherited}}, FontSize->16], Cell[TextData[StyleBox[ "This may be related to the great boson/fermion dichotomy, then again, maybe \ not :-)"]], "Text", FontFamily->"Times New Roman"] }, Open ]] }, Open ]] }, FrontEndVersion->"Microsoft Windows 3.0", ScreenRectangle->{{0, 640}, {0, 451}}, AutoGeneratedPackage->None, WindowToolbars->{"RulerBar", "EditBar"}, CellGrouping->Automatic, WindowSize->{591, 289}, WindowMargins->{{0, Automatic}, {Automatic, 5}}, 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[TextData[StyleBox["Style Definitions"]], "Subtitle"], Cell[TextData[StyleBox[ "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[TextData[StyleBox["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"}] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Notebook Options"]], "Section", FontFamily->"New York"], Cell[TextData[StyleBox[ "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[ 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FontFamily->"Arial", FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{2, 10}, {12, 30}}, FontFamily->"Arial", 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->"Arial", FontSize->18], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontFamily->"Arial", FontSize->36], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontFamily->"Arial", FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontFamily->"Arial", 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->"Arial", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {20, 20}}, LineSpacing->{1, 0}, FontFamily->"Arial", FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 8}}, FontFamily->"Arial", FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {12, 8}}, FontFamily->"Arial", 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->"Arial", FontSize->18, FontWeight->"Bold", FontVariations->{"Underline"->True}], Cell[StyleData["Section", "Presentation"], CellMargins->{{40, 10}, {11, 32}}, LineSpacing->{1, 0}, FontFamily->"Arial", FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontFamily->"Arial", FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontFamily->"Arial", 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->"Arial", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontFamily->"Arial", FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontFamily->"Arial", FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontFamily->"Arial", 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->"Arial", FontSize->12, FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontFamily->"Arial", FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontFamily->"Arial", FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontFamily->"Arial", FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Styles for Body Text"]], "Section", FontFamily->"Arial"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{7, 10}, {7, 7}}, Evaluatable->False, CellHorizontalScrolling->False, PageBreakWithin->Automatic, LineSpacing->{1, 3}, CounterIncrements->"Text", AspectRatioFixed->True, FontFamily->"Arial", FontSize->12], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontFamily->"Arial"], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontFamily->"Arial"], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}, FontFamily->"Arial"] }, 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->"Arial", FontSize->10], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontFamily->"Arial", FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontFamily->"Arial", FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, FontFamily->"Arial", FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Styles for Input/Output"]], "Section", FontFamily->"Courier", FontSize->14, FontWeight->"Plain"], Cell[TextData[StyleBox[ "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", FontFamily->"Courier", 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}, FontFamily->"Courier", FontSize->14, FontWeight->"Plain"], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontFamily->"Courier", FontSize->14, FontWeight->"Plain"], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, FontFamily->"Courier", 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, FontFamily->"Courier", 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}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontFamily->"Courier", 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}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontFamily->"Courier", 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}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontFamily->"Courier", 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}}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Graphics", "Condensed"], ImageSize->{175, 175}, ImageMargins->{{38, Inherited}, {Inherited, 0}}, FontFamily->"Courier", FontSize->14], Cell[StyleData["Graphics", "Printout"], ImageSize->{250, 250}, ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontFamily->"Courier", FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Courier", FontSize->14, FontWeight->"Plain", FontSlant->"Plain", FontTracking->"Plain", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->False, "Outline"->False, "Shadow"->False}], Cell[StyleData["CellLabel", "Presentation"], FontFamily->"Courier", FontSize->14], Cell[StyleData["CellLabel", "Condensed"], FontFamily->"Courier", FontSize->14], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->14, FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["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[TextData[StyleBox["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[TextData[StyleBox["Palette Styles"]], "Section"], Cell[TextData[StyleBox[ "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[TextData[StyleBox["Hyperlink Styles"]], "Section"], Cell[TextData[StyleBox[ "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[TextData[StyleBox[ "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[TextData[StyleBox["Placeholder Styles"]], "Section"], Cell[TextData[StyleBox[ "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[TextData[StyleBox["FormatType Styles"]], "Section"], Cell[TextData[StyleBox[ "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[TextData[StyleBox[ "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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