(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 781416, 21168] NotebookOptionsPosition[ 555441, 16510] NotebookOutlinePosition[ 772356, 20917] CellTagsIndexPosition[ 771000, 20877] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["'As presented' revised version of a paper included in the \ electronic proceedings of the International Mathematica Symposium, \ Maastricht, The Netherlands, June 20", FontFamily->"Arial"], "\[Dash]", StyleBox["24th 2008 ", FontFamily->"Arial"], "[", CounterBox["Reference", "RefMcGovern2008"], "]" }], "Text", CellFrame->{{0, 0}, {0.5, 0}}], Cell["\<\ \ \>", "Text"], Cell[CellGroupData[{ Cell["An Exploration of a Discrete Rhombohedral Lattice", "IMS2008Title"], Cell["of Possible Engineering or Physical Relevance", "Subtitle"], Cell["Jim McGovern", "Author"], Cell["\<\ Dublin Institute of Technology School of Mechanical and Transport Engineering Bolton Street, Dublin 1, Ireland jim.mcgovern@dit.ie\ \>", "Address"], Cell["\<\ \ \>", "Text"], Cell["\<\ A particular discrete rhombohedral lattice consisting of four symmetrically \ interlaced cuboctahedral point lattices is described that is interesting \ because of the high degree of symmetry it exhibits. The four constituent \ cuboctahedral lattices are denoted by four colours and the composite lattice \ is referred to as a 4-colour rhombohedral lattice. Each point of the 4-colour \ lattice can be referenced by an integer 4-tuple containing only the positive \ non-zero integers (the counting numbers). The relationship between the \ discrete rhombohedral lattice and a discrete Cartesian lattice is explained. \ Some interesting aspects of the lattice and of the counting-number 4-tuple \ coordinate system are pointed out.\ \>", "Abstract"], Cell[CellGroupData[{ Cell["Introduction", "SectionFirst"], Cell[TextData[{ "Symmetry underlies nature and has a major role to play in science [", CounterBox["Reference", "RefBoardman1973"], "], art, mathematics [", CounterBox["Reference", "RefRonan2006"], "] and engineering. In two dimensions there are only three fully regular or \ symmetric point lattices and in three dimensions there is only one fully \ regular or symmetric point lattice ", "[", CounterBox["Reference", "RefCoxeter1973"], "]", ". These are the triangular tessellation, the square tessellation and the \ hexagonal tessellation in two dimensions and the cubic lattice in three. Here \ the expression ", StyleBox["fully regular or symmetric", FontSlant->"Italic"], " is used in the sense that the fundamental cells (triangles, squares, \ hexagons and cubes respectively) of the point lattices are regular, having \ equal sides or edges and equal angles. The number of distinct lattices (not \ necessarily fully regular or symmetric) that can allow displacements, \ rotations and reflections is small. This paper is an exploration of such a \ lattice: the 4-colour rhombohedral lattice." }], "Text"], Cell[TextData[{ "Details of possible application areas in science and engineering are left \ for treatment elsewhere, but some highly speculative possibilities have \ already been outlined by the author [", CounterBox["Reference", "RefMcGovern2007"], "]." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["The Cuboctahedral or Bell-Fuller Lattice", "Section"], Cell[TextData[{ "In the twentieth century the cuboctahedral lattice attracted the attention \ of Alexander Graham Bell [", CounterBox["Reference", "RefBell1907"], "] and of Richard Buckminster Fuller [", CounterBox["Reference", "RefFuller1979"], "], largely because of its symmetry: each point is surrounded by twelve \ nearest neighbours, Figure ", CounterBox["NumberedFigure", "FigBellGusset"], ", that form a quasi-regular polyhedron, the cuboctahedron, Figure ", CounterBox["NumberedFigure", "FigCuboctahedron"], ". (In the field of crystallography a sphere-packing arrangement of \ cuboctahedral form is described as the cubic close-packed lattice or the \ face-centred cubic lattice.) 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", "SB"], "The central joint with twelve equally distributed spokes is a gusset. \ Alexander Graham Bell used gussets of this type to build structures, \ including many kites. Replication of the gusset and the links between gussets \ gives rise to cuboctahedral trusses, structures and space frames, which in \ engineering terms can be strong, rigid and light." }], "NumberedFigureCaption", CellTags->"FigBellGusset"], Cell[BoxData[ Graphics3DBox[{{ {Hue[1], SphereBox[{{0, -2, -2}}, 0.15]}, {Hue[1], SphereBox[{{-2, -2, 0}}, 0.15]}, {Hue[1], SphereBox[{{-2, 0, -2}}, 0.15]}, {Hue[1], SphereBox[{{2, -2, 0}}, 0.15]}, {Hue[1], SphereBox[{{0, -2, 2}}, 0.15]}, {Hue[1], SphereBox[{{2, 0, -2}}, 0.15]}, {Hue[1], SphereBox[{{-2, 0, 2}}, 0.15]}, {Hue[1], SphereBox[{{0, 2, -2}}, 0.15]}, {Hue[1], SphereBox[{{-2, 2, 0}}, 0.15]}, {Hue[1], SphereBox[{{2, 0, 2}}, 0.15]}, {Hue[1], SphereBox[{{2, 2, 0}}, 0.15]}, {Hue[1], SphereBox[{{0, 2, 2}}, 0.15]}}, {Hue[1], SphereBox[{{0, 0, 0}}, 0.15]}, { {Hue[1], CylinderBox[{{0, 0, 0}, {0, -2, -2}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {-2, -2, 0}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {-2, 0, -2}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {2, -2, 0}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {0, -2, 2}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {2, 0, -2}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {-2, 0, 2}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {0, 2, -2}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {-2, 2, 0}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {2, 0, 2}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {2, 2, 0}}, 0.05]}, {Hue[1], CylinderBox[{{0, 0, 0}, {0, 2, 2}}, 0.05]}}, { {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{-2, 0, -2}, {0, 2, -2}, {2, 0, -2}, {0, -2, -2}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{2, -2, 0}, {0, -2, 2}, {-2, -2, 0}, {0, -2, -2}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{2, 0, 2}, {0, 2, 2}, {-2, 0, 2}, {0, -2, 2}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{2, 2, 0}, {0, 2, -2}, {-2, 2, 0}, {0, 2, 2}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{2, 0, 2}, {2, -2, 0}, {2, 0, -2}, {2, 2, 0}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{-2, 0, 2}, {-2, 2, 0}, {-2, 0, -2}, {-2, -2, 0}}]}}, { {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{0, -2, -2}, {2, 0, -2}, {2, -2, 0}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{0, -2, -2}, {-2, -2, 0}, {-2, 0, -2}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{0, 2, -2}, {2, 0, -2}, {2, 2, 0}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{-2, 0, 2}, {0, 2, 2}, {-2, 2, 0}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{0, 2, 2}, {2, 0, 2}, {2, 2, 0}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{0, 2, -2}, {-2, 2, 0}, {-2, 0, -2}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{0, -2, 2}, {2, -2, 0}, {2, 0, 2}}]}, {GrayLevel[0.5], Opacity[0.5], Polygon3DBox[{{0, -2, 2}, {-2, 0, 2}, {-2, -2, 0}}]}}}, BoxRatios->{1.1, 1.1, 1.1}, Boxed->False, ImageSize->{92.99999999999994, 101.}, Lighting->"Neutral", ViewAngle->0.40496623221626227`, ViewPoint->{-1.7895272650403522`, 1.7294549494948135`, -2.2927227798722374`}, ViewVertical->{0.34275912178123796`, 0.36175421163572785`, -0.8669775514969046}]], "PlacedGraphics"], Cell[TextData[{ StyleBox["Figure ", "SB"], StyleBox[ CounterBox["NumberedFigure"], "SB"], StyleBox[". ", "SB"], "Illustration of how the Bell gusset forms a cuboctahedron" }], "NumberedFigureCaption", CellTags->"FigCuboctahedron"], Cell[TextData[{ "Figure ", CounterBox["NumberedFigure", "FigCuboctahedralSize4"], " illustrates a size-4 Bell-Fuller lattice. The first ", StyleBox["size", FontSlant->"Italic"], " would be the trivial case of the single point at the centre of the \ lattice. The central point is surrounded by three more cuboctahedral ", StyleBox["shells", FontSlant->"Italic"], ". 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", "SB"], "The points of four interlaced Bell-Fuller lattices" }], "NumberedFigureCaption", CellTags->"FigPoints4BF"] }, Open ]], Cell[CellGroupData[{ Cell["The 4-colour Rhombohedral Lattice", "Section"], Cell[CellGroupData[{ Cell["Structure of the 4-colour Rhombohedral Lattice", "Subsection"], Cell[TextData[{ "The points of four Bell-Fuller lattices, when interlaced as shown in Figure \ ", CounterBox["NumberedFigure", "FigFiveGussets"], " and Figure ", CounterBox["NumberedFigure", "FigPoints4BF"], ", comprise what is described here as a 4-colour rhombohedral lattice. All \ pairs of points that are nearest neighbours can be joined by links, as shown \ in Figure ", CounterBox["NumberedFigure", "FigRhombohedralSize2"], ". The thicker gray links are described as primary spokes or axes. The black \ links that are opposite the primary spokes, and collinear with them, are \ described as secondary spokes." }], "Text"], Cell[TextData[{ "The external form of the lattice shown in Figure ", CounterBox["NumberedFigure", "FigRhombohedralSize2"], " is the rhombic dodecahedron. There are twelve rhombic faces, twenty four \ edges and fourteen vertices. 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", "SB"], "Size 2 of the 4-colour rhombohedral lattice" }], "NumberedFigureCaption", CellTags->"FigRhombohedralSize2"], Cell[TextData[{ "Figure ", CounterBox["NumberedFigure", "FigRhombohedralSize3"], " illustrates a 4-colour rhombohedral lattice of size 3. As for Figure ", CounterBox["NumberedFigure", "FigRhombohedralSize2"], ", the external shape is the rhombic dodecahedron." }], "Text"], Cell["\<\ The term 'strut' is used here for a link of unit length between successive \ shells (and therefore not on any one shell) that is parallel to one of the \ spokes, but is not radial with respect to the centre of the overall \ polyhedron. Primary struts are parallel to primary spokes and secondary \ struts are parallel to secondary spokes.\ \>", "Text"], Cell[TextData[{ "The secondary spokes and struts have been omitted from Figure ", CounterBox["NumberedFigure", "FigRhombohedralSize3"], " to emphasise the rhombohedral nature of the cells of the lattice. When \ this is done there are four different orientations of the rhombohedral cells, \ corresponding to the orientations of the four quadrants of the rhombic \ dodecahedron that is shown. Each of the four quadrants of the rhombic \ dodecahedron is itself a rhombohedron. " }], "Text"], Cell[TextData[{ "The first size shell or lattice would be the trivial case of the single red \ point at the centre of the rhombohedral lattice. The central point is \ surrounded by two more dodecahedral shells. 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", "SB"], "Size 3 of the 4-colour rhombohedral lattice. The secondary spokes and \ struts have been omitted to emphasise the rhombohedral cells of the lattice, \ which are oriented in accordance with the primary spokes." }], "NumberedFigureCaption", CellTags->"FigRhombohedralSize3"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ A Natural Coordinate System for the 4-colour Rhombohedral Lattice\ \>", "Subsection"], Cell[TextData[{ "Every point position on the 4-colour rhombohedral lattice can be described \ by an integer 4-tuple, as in Figure ", CounterBox["NumberedFigure", "FigIntegerCoords"], " and Figure ", CounterBox["NumberedFigure", "FigSampleCoords"], ". The full range of the set of integers can be used arbitrarily within the \ 4-tuple to describe the position of any point with respect to a specified \ \[OpenCurlyQuote]origin\[CloseCurlyQuote] and therefore the representation is \ not unique. However, any such 4-tuple can be converted to zero-based form \ without negative integers by the addition of a unique integer to all elements \ that makes at least one of the elements zero and all elements non-negative. A \ \[OpenCurlyQuote]standard form\[CloseCurlyQuote] 4-tuple can also likewise be \ defined in which at least one of the elements is unity and none are zero or \ negative. As negative ordinates are not used, it is considered more natural \ to count from the integer 1, with the origin represented as ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], ")"}], TraditionalForm]]], ", as in Figure ", CounterBox["NumberedFigure", "FigIntegerCoords"], ". Conversions between zero-based and standard form 4-tuples are easily \ implemented, as explained in the following subsections." }], "Text"], Cell[BoxData[ Graphics3DBox[{{ {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{1, -1, -1}, 0.13]}, {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{-1, -1, 1}, 0.13]}, {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{-1, 1, -1}, 0.13]}, {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{1, 1, 1}, 0.13]}}, {Text3DBox[ FormBox[ StyleBox[ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "2"}], "}"}], StripOnInput->False, FontSize->12], StandardForm], {1, -1, -1}, {-1.4, 0}], Text3DBox[ FormBox[ StyleBox[ RowBox[{"{", RowBox[{"1", ",", "1", ",", "2", ",", "1"}], "}"}], StripOnInput->False, FontSize->12], StandardForm], {-1, -1, 1}, {-1.4, 0}], Text3DBox[ FormBox[ StyleBox[ RowBox[{"{", RowBox[{"1", ",", "2", ",", "1", ",", "1"}], "}"}], StripOnInput->False, FontSize->12], StandardForm], {-1, 1, -1}, {-1.4, 0}], Text3DBox[ FormBox[ StyleBox[ RowBox[{"{", RowBox[{"2", ",", "1", ",", "1", ",", "1"}], "}"}], StripOnInput->False, FontSize->12], StandardForm], {1, 1, 1}, {-1.4, 0}]}, {Hue[1], SphereBox[{{0, 0, 0}}, 0.15]}, Text3DBox[ FormBox[ StyleBox[ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}], StripOnInput->False, FontSize->12], StandardForm], {0, 0, 0}, {-1.4, 0}], { {GrayLevel[0.5], CylinderBox[{{0, 0, 0}, {1, -1, -1}}, 0.05]}, {GrayLevel[0.5], CylinderBox[{{0, 0, 0}, {-1, -1, 1}}, 0.05]}, {GrayLevel[0.5], CylinderBox[{{0, 0, 0}, {-1, 1, -1}}, 0.05]}, {GrayLevel[0.5], CylinderBox[{{0, 0, 0}, {1, 1, 1}}, 0.05]}}}, Boxed->False, ImageMargins->0, ImagePadding->None, ImageSize->{184.3333333333288, 184.}, Lighting->"Neutral", SphericalRegion->True, ViewAngle->0.7726554254234638, ViewCenter->{{0.5, 0.5, 0.5}, {0.26225898320116114`, 0.49787606196901524`}}, ViewPoint->{-1.2936213289206195`, 0.43450000340904543`, -3.0964097927114254`}, ViewVertical->{0.5183690031333259, 0.07671592188998384, -0.8517090136420608}]], "PlacedGraphics"], Cell[TextData[{ StyleBox["Figure ", "SB"], StyleBox[ CounterBox["NumberedFigure"], "SB"], StyleBox[". 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", "SB"], "Sample integer coordinates for the 4-colour rhombohedral lattice" }], "NumberedFigureCaption", CellTags->"FigSampleCoords"], Cell[CellGroupData[{ Cell["Converting 4-tuple Coordinates to Zero-based Form", "Subsubsection"], Cell[TextData[{ "Listing ", CounterBox["NumberedProgram", "PrgQZeroForm"], " presents a function, ", StyleBox["QZeroForm", "MR"], StyleBox[", ", "TR"], "written in ", StyleBox["Mathematica", FontSlant->"Italic"], ", that converts a 4-tuple coordinate list, or vector, to zero-based form. \ Another version takes four separate arguments for the ordinates of the \ 4-tuple. Variants have also been written to deal with lists of 4-tuples or, \ for instance, lists of 4-tuple pairs." }], "Text"], Cell["\<\ QZeroForm[{q1_, q2_, q3_, q4_}] := Module[{qzf}, qmin = Min[q1, q2, q3, q4]; qzf = {q1, q2, q3, q4} - {qmin, qmin, qmin, qmin}]\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}, PageBreakWithin->False], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "A function, written in ", StyleBox["Mathematica", FontSlant->"Italic"], ", to convert a 4-tuple to zero-based form" }], "NumberedProgramCaption", CellTags->"PrgQZeroForm"], Cell[TextData[{ "An example of a conversion from standard form to zero-based form in a ", StyleBox["Mathematica", FontSlant->"Italic"], " session is as follows:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QZeroForm", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"QZeroForm", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.4252838423430653`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Converting 4-tuple Coordinates to Standard Form", "Subsubsection"], Cell[TextData[{ "Function ", StyleBox["QStdForm", "MR"], StyleBox[", as presented in ", "TR"], "Listing ", CounterBox["NumberedProgram", "PrgQStdForm"], StyleBox[",", "TR"], " converts a 4-tuple coordinate list, or vector, to standard form:" }], "Text"], Cell["\<\ QStdForm[{q1_, q2_, q3_, q4_}] := Module[{qsf}, qsf = QZeroForm[{q1, q2, q3, \ q4}] + {1, 1, 1, 1}]\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "A function to convert a 4-tuple to standard form" }], "NumberedProgramCaption", CellTags->"PrgQStdForm"], Cell["\<\ An example of a conversion from zero-based form to standard form is as \ follows\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QStdForm", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", "2", ",", " ", "3"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"QStdForm", "[", RowBox[{"{", RowBox[{"0", ",", "1", ",", "2", ",", "3"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.4252838424932947`*^9}] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["The Colour of a Lattice Point", "Subsection"], Cell[TextData[{ "Given the colour number of the origin, ", StyleBox["nco", FontSlant->"Italic"], " (an integer from 1 to 4 corresponding to the colours red, yellow, blue and \ violet) and a 4-tuple coordinate list ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["q", "1"], ",", " ", SubscriptBox["q", "2"], ",", " ", SubscriptBox["q", "3"], ",", SubscriptBox["q", "4"]}], ")"}], TraditionalForm]]], " of a point, the function ", StyleBox["CoQ", "MR"], " determines the colour number of the point. This is shown in Listing ", CounterBox["NumberedProgram", "PrgCoQ"], ". This determination amounts to summing the four ordinates and the colour \ number of the origin using clock arithmetic, base 4." }], "Text"], Cell["\<\ CoQ[nco_, {q1_, q2_, q3_, q4_}] := Module[{c}, c = Mod[(q1 + q2 + q3 + q4 + \ nco - 1), 4] + 1]\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "Function to give the colour number of a point on the rhombohedral lattice" }], "NumberedProgramCaption", CellTags->"PrgCoQ"], Cell[TextData[{ "For example, if the origin is red, the point ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{"1", ",", "2", ",", "12", ",", "8"}], ")"}], TraditionalForm]]], " is violet:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"CoQ", "[", RowBox[{"1", ",", RowBox[{"{", RowBox[{"1", ",", " ", "2", ",", " ", "12", ",", " ", "8"}], "}"}]}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"CoQ", "[", RowBox[{"1", ",", RowBox[{"{", RowBox[{"1", ",", "2", ",", "12", ",", "8"}], "}"}]}], "]"}]], "Output", CellChangeTimes->{3.4252838425033097`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Sum, Point Inversion and Difference", "Subsection"], Cell[CellGroupData[{ Cell["4-tuple Vector Addition", "Subsubsection"], Cell["\<\ The sum of a pair of 4-tuples of the 4-colour rhombohedral lattice is \ obtained by adding the corresponding ordinates. The result would normally be \ converted to standard form.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Point Inversion and Vector Difference", "Subsubsection"], Cell[TextData[{ "Listing ", CounterBox["NumberedProgram", "PrgQInvert"], " illustrates the implementation of a function, ", StyleBox["QInvert,", "MR"], " that inverts a 4-tuple and returns the result in standard form. This is \ the point inversion of the 4-tuple through the origin. Each ordinate is \ inverted by adding one to the sum of the other three ordinates. The resulting \ 4-tuple is then converted to standard form." }], "Text"], Cell["\<\ QInvert[{q1_, q2_, q3_, q4_}] := Module[ {p1, p2, p3, p4, qinv}, p1 = 1 + q2 \ + q3 + q4; p2 = q1 + 1 + q3 + q4; p3 = q1 + q2 + 1 + q4; p4 = q1 + q2 + q3 + \ 1; qinv = QStdForm[{p1, p2, p3, p4}]]\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "A function to obtain the additive inverse, or point inversion through the \ origin, of a 4-tuple" }], "NumberedProgramCaption", CellTags->"PrgQInvert"], Cell[TextData[{ "The following is an example of 4-tuple inversion as part of a ", StyleBox["Mathematica", FontSlant->"Italic"], " session:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QInvert", "[", RowBox[{"{", RowBox[{"2", ",", "1", ",", "11", ",", "6"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"QInvert", "[", RowBox[{"{", RowBox[{"2", ",", "1", ",", "11", ",", "6"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.42528384252334*^9}] }, Open ]], Cell[TextData[{ "The vector difference of two 4-tuples, ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["q", "1"], "-", SubscriptBox["q", "2"]}], TraditionalForm]]], ", can be implemented by summing the first 4-tuple and the additive inverse \ of the second, as represented in equation (", CounterBox["NumberedEquation", "EqVectorDiff"], "), where I is the function ", StyleBox["QInvert", "MR"], ". The result would be brought to standard form." }], "Text"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["q", "1"], "-", SubscriptBox["q", "2"]}], "=", RowBox[{ SubscriptBox["q", "1"], "+", RowBox[{ StyleBox["I", "TR", FontSlant->"Plain"], "(", SubscriptBox["q", "2"], ")"}]}]}], TraditionalForm]], "NumberedEquation",\ CellTags->"EqVectorDiff"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Length or Distance Calculations", "Subsection"], Cell[TextData[{ "Any planes of the lattice of Figure ", CounterBox["NumberedFigure", "FigRhombohedralSize2"], " that are made up of rhombs of unit edge length provide an invariant metric \ ground form ", "[", CounterBox["Reference", "RefWeyl1979"], "]", " that allows the length of a vector in the plane to be defined. This \ concept can be extended to the four-tuple discrete space of the lattice. The \ application and implementation of this type of approach (including \ conversions between 4-tuple and Cartesian coordinates) has been described by \ Hasslberger [", CounterBox["Reference", "RefHasslberger1996"], "] and Urner, [", CounterBox["Reference", "RefUrner1997"], "] and [", CounterBox["Reference", "RefUrner2000"], "], in the latter two cases using the term \[OpenCurlyQuote]quadrays\ \[CloseCurlyQuote] for the four basis vectors. " }], "Text"], Cell[TextData[{ "The ", StyleBox["length", FontSlant->"Italic"], " or ", StyleBox["distance", FontSlant->"Italic"], " formula for a vector ", Cell[BoxData[ FormBox[ RowBox[{"(", RowBox[{ SubscriptBox["q", "1"], ",", SubscriptBox["q", "2"], ",", SubscriptBox["q", "3"], ",", SubscriptBox["q", "4"]}], ")"}], TraditionalForm]]], ", which can be derived using the cosine rule, is given by equation ", "(", CounterBox["NumberedEquation", "EqLength"], ")", "." }], "Text"], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"|", "r", StyleBox["|", FontWeight->"Plain"]}], StyleBox["=", FontWeight->"Bold"], RowBox[{ FormBox[ RowBox[{"\[Sqrt]", RowBox[{"[", RowBox[{ RowBox[{"(", RowBox[{ SubsuperscriptBox["q", "1", "2"], "+", SubsuperscriptBox["q", "2", "2"], "+", SubsuperscriptBox["q", "3", "2"], "+", SubsuperscriptBox["q", "4", "2"]}], ")"}], "-", RowBox[{ RowBox[{"(", RowBox[{"2", "/", "3"}], ")"}], RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["q", "1"], SubscriptBox["q", "2"]}], "+", RowBox[{ SubscriptBox["q", "2"], SubscriptBox["q", "3"]}], "+", RowBox[{ SubscriptBox["q", "3"], SubscriptBox["q", "4"]}], "+", RowBox[{ SubscriptBox["q", "4"], SubscriptBox["q", "1"]}], "+", RowBox[{ SubscriptBox["q", "3"], SubscriptBox["q", "1"]}], "+", RowBox[{ SubscriptBox["q", "2"], SubscriptBox["q", "4"]}]}], ")"}]}]}], "]"}]}], TraditionalForm], "."}]}], TraditionalForm]], "NumberedEquation", CellTags->"EqLength"], Cell[TextData[{ "Listing ", CounterBox["NumberedProgram", "PrgDistance4"], " presents the function", StyleBox[" ", "TR"], StyleBox["Dist4Axis", "MR"], " that calculates distance, which is equivalent to calculating the length of \ a vector. The input is a single 4-tuple. To find the distance between two \ points, the input would be the vector difference of the 4-tuples of the \ points." }], "Text"], Cell["\<\ Dist4Axis[{q1_, q2_, q3_, q4_}] := \[Sqrt]((q1^2 + q2^2 + q3^2 + q4^2) - (q1 \ q2 + q2 q3 + q3 q4 + q4 q1 + q3 q1 + q2 q4) 2/3 )\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "Function to calculate distance on the 4-colour rhombohedral lattice" }], "NumberedProgramCaption", CellTags->"PrgDistance4"], Cell["\<\ As can be seen below, this can yield a value that is the square root of a \ fraction that has a three in the denominator. \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Dist4Axis", "[", RowBox[{"{", RowBox[{"3", ",", " ", "1", ",", " ", "12", ",", " ", "7"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"Dist4Axis", "[", RowBox[{"{", RowBox[{"3", ",", "1", ",", "12", ",", "7"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.4252838425333557`*^9}] }, Open ]], Cell[TextData[{ "An integer-only distance measure, which is equal to three-times the square \ of the distance between any two points on the entire lattice, is readily \ defined, as in equation ", "(", CounterBox["NumberedEquation", "EqIntegerDistMeasure"], ")", "." }], "Text"], Cell[BoxData[ FormBox[ RowBox[{"s", "=", RowBox[{ FormBox[ RowBox[{ RowBox[{"3", SuperscriptBox["r", "2"]}], "=", RowBox[{ RowBox[{"3", RowBox[{"(", RowBox[{ SubsuperscriptBox["q", "1", "2"], "+", SubsuperscriptBox["q", "2", "2"], "+", SubsuperscriptBox["q", "3", "2"], "+", SubsuperscriptBox["q", "4", "2"]}], ")"}]}], "-", RowBox[{"2", RowBox[{"(", RowBox[{ RowBox[{ SubscriptBox["q", "1"], SubscriptBox["q", "2"]}], "+", RowBox[{ SubscriptBox["q", "2"], SubscriptBox["q", "3"]}], "+", RowBox[{ SubscriptBox["q", "3"], SubscriptBox["q", "4"]}], "+", RowBox[{ SubscriptBox["q", "4"], SubscriptBox["q", "1"]}], "+", RowBox[{ SubscriptBox["q", "3"], SubscriptBox["q", "1"]}], "+", RowBox[{ SubscriptBox["q", "2"], SubscriptBox["q", "4"]}]}], ")"}]}]}]}], TraditionalForm], "."}]}], TraditionalForm]], "NumberedEquation", CellTags->"EqIntegerDistMeasure"] }, Open ]], Cell[CellGroupData[{ Cell["Scaling and Scalar Division", "Subsection"], Cell[CellGroupData[{ Cell["Scaling", "Subsubsection"], Cell["\<\ A 4-tuple of the 4-colour rhombohedral lattice can be scaled by multiplying \ the ordinates of the zero-based form by an integer. By this means the scaling \ is applied to the ordinate intervals. The result would be brought to standard \ form.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Scalar Division", "Subsubsection"], Cell[TextData[{ "Given two arbitrary points on the 4-colour rhombohedral lattice, the vector \ difference is a vector from the first to the second point. Some vectors \ cannot be divided by any integer other than 1: their scalar divisibility is \ unity. Function ", StyleBox["QSDiv", "MR"], ", as presented in ", "Listing ", CounterBox["NumberedProgram", "PrgQSDiv"], ", can be used to calculate the maximum number of equal (symmetric) \ intervals into which the vector can be divided by an integer. This is a \ matter of finding the greatest common divisor of the intervals of the \ ordinates." }], "Text"], Cell["\<\ QSDiv[{q1_, q2_, q3_, q4_}] := Module[{qsd, v}, v = QZeroForm[{q1, q2, q3, \ q4}]; qsd = GCD[v[[1]], v[[2]], v[[3]], v[[4]] ]]\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "A function to find the scalar divisibility of a vector" }], "NumberedProgramCaption", CellTags->"PrgQSDiv"], Cell["As an example,", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QSDiv", "[", RowBox[{"{", RowBox[{"3", ",", "1", ",", "5", ",", "9"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"QSDiv", "[", RowBox[{"{", RowBox[{"3", ",", "1", ",", "5", ",", "9"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.4252838425533867`*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Relationship Between the Discrete Rhombohedral Lattice and a Discrete \ Cartesian Lattice\ \>", "Section"], Cell[CellGroupData[{ Cell["\<\ Nucleated Cubic (or Cartesian) Lattices Within the 4-colour Rhombohedral \ Lattice\ \>", "Subsection"], Cell[BoxData[ Graphics3DBox[{{ {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{{1, -1, -1}}, 0.15]}, {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{{-1, -1, 1}}, 0.15]}, {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{{-1, 1, -1}}, 0.15]}, {Hue[ NCache[ Rational[1, 8], 0.125]], SphereBox[{{1, 1, 1}}, 0.15]}, {Hue[ NCache[ Rational[3, 4], 0.75]], SphereBox[{{-1, 1, 1}}, 0.15]}, {Hue[ NCache[ Rational[3, 4], 0.75]], SphereBox[{{1, 1, -1}}, 0.15]}, {Hue[ NCache[ Rational[3, 4], 0.75]], SphereBox[{{1, -1, 1}}, 0.15]}, {Hue[ NCache[ Rational[3, 4], 0.75]], SphereBox[{{-1, -1, -1}}, 0.15]}}, {Hue[1], SphereBox[{{0, 0, 0}}, 0.15]}, StyleBox[{}, BoxRatios -> {1.1, 1.1, 1.1}]}, Boxed->False, ImageSize->{35.999999999996334`, 50.}, Lighting->"Neutral", ViewAngle->0.4934199870977538, ViewPoint->{2.969464511444091, -0.48216056794729933`, -1.5491293367536623`}, ViewVertical->{ 0.14884202027788002`, -0.0600983362552989, -0.9870330506011156}]], \ "PlacedGraphics", ImageCache->GraphicsData["CompressedBitmap", "\<\ eJy9U01IFWEUPaKRlJUR0d/mIfgDFkLg29RCMgrSWrgQnob08If3iOcLlUpI 0UWKVBiJP/kHGiqUq9BAN7oRlMCQRAIrisqgIMWIzCce78zcmXJoIUQOnPnm O2fO/e69c+eivyJQHPJXBAv9nvNl/muBYGG551y4TKjoKABeQZYHxjPlUW9e yiXidi1J5hLNE8jnWTQwCy3YY0mJ5hLD4/AxGw95E0u8A6q6W41NpeDLbnCq FTikjlO4zgBm+ADkgOPYpWplPvjtqUjvBJ9wWANdxRzbLANcjrpicH1StBXB GlI2Z/CiQ9jX4McnsKV/bEqyRq4qAOd6wA+PgThL2q9SHoZYgwhDmMcB5SZb JJG3gu/O6/FawWlUshar7BO1FbQdRuP4FebOdUA5FthuKkTCpuyOaEyfjEub YFbw3KYdtU7YRQEtuNT238of6l+bEasJpeEKM1Bj7o5pmLxMsL4EfNYAjjXa JexU9SSKmItBo0cM481Rk95B3xnwdhE40yVnG191Fm7nJXTyFn6yyWqXfdxg LRgZF+6L4JfbdBkjbBSh3xoi2zQqM8tpwQ/Bsm2yq5KI7NA2p255QOLVHc6x rMbuoHJehJiJenNnjSj2qXQvKFV3gq96oa/HMB1BGaZh3sAiSzCtjr2qGhNo /ivvBZ8d0wU0sxorNDp4H3QdwwmhI4J5OFnl4BHv6t8Vt+U6//+CqA0o4/Gp \ \>"]], Cell[TextData[{ StyleBox["Figure ", "SB"], StyleBox[ CounterBox["NumberedFigure"], "SB"], StyleBox[". ", "SB"], "The eight vertices of the smallest cube on the 4-colour rhombohedral \ lattice, shown surrounding the origin of the rhombohedral lattice" }], "NumberedFigureCaption", CellTags->"FigSmallestCube"], Cell[TextData[{ "The smallest cube on the 4-colour rhombohedral lattice (not counting the \ case of a single point) is formed by the pair of smallest regular tetrahedra \ on the lattice, Figure ", CounterBox["NumberedFigure", "FigSmallestCube"], ". This cube consists of eight points (four yellow and four violet) with an \ edge length of 2/", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]]], " rhombohedral lattice units. It is on shell 2 of the rhombohedral lattice. \ The third and fourth shells of the rhombohedral lattice also contain \ corresponding sets of eight points in a cubic arrangement. However, the first \ rhombohedral lattice size that contains a full nucleated cubic lattice is the \ fifth, as shown in Figure ", CounterBox["NumberedFigure", "FigNucleatedCubeSize2"], ". (A lattice is nucleated if it has one of its points at its centre). What \ is remarkable is that all points of the nucleated cubic lattice have the same \ colour, red in this case." }], "Text"], Cell[TextData[{ "The nucleated cubic lattice represented in Figure ", CounterBox["NumberedFigure", "FigNucleatedCubeSize2"], " is a size-2 nucleated cubic lattice. The vertices of its bounding cube are \ contained in the fifth (rhombic dodecahedral) shell of the 4-colour \ rhombohedral lattice. The spokes of the size-2 nucleated cubic lattice each \ contain two red points. The length of each unit link or spoke of the cubic \ lattice is equivalent to 4/", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]]], " rhombohedral lattice units. 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", "SB"], "The size-2 nucleated cubic lattice (the vertices of the smallest possible \ cube on the 4-colour rhombohedral lattice are also shown)" }], "NumberedFigureCaption", CellTags->"FigNucleatedCubeSize2"], Cell[TextData[{ "A red nucleated cubic lattice of any arbitrary size can be constructed \ about any red point of the 4-colour rhombohedral lattice. Yellow, blue and \ violet cubic lattices can be constructed about any point of the respective \ colour, or can be produced by displacing the (originally) red cubic lattice \ within the 4-colour rhombohedral lattice, as was done in generating Figure ", CounterBox["NumberedFigure", "FigFourCubicLattices"], ". Whereas links of four nucleated cubic lattices are shown in Figure ", CounterBox["NumberedFigure", "FigFourCubicLattices"], ", sixteen nucleated cubic lattices (4 of each colour) are required in order \ to include all points of the 4-colour rhombohedral lattice. 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", "SB"], "The points of the 4-colour rhombohedral lattice, with the links of four \ interlaced cubic lattices. Only complete lattice links are shown in this \ diagram. (Pastel colours are used for the links of nucleated cubic \ lattices.)" }], "NumberedFigureCaption", CellTags->"FigFourCubicLattices"], Cell[TextData[{ "If all nucleated cubic lattices were shown in a diagram such as Figure ", CounterBox["NumberedFigure", "FigFourCubicLattices"], ", red links would overlap with blue links and yellow links would overlap \ with violet links. In combination the sixteen nucleated cubic lattices form a \ composite lattice where the spacing between parallel lines of links is 2/", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]]], " rhombohedral lattice units. 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CounterBox["NumberedFigure"], "SB"], StyleBox[". ", "SB"], StyleBox[" ", "SB"], "A Cartesian lattice with a diagonal length of eight rhombohedral lattice \ units and a spacing of 2/", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]]], " rhombohedral lattice units. The points of the 4-colour rhombohedral \ lattice are also shown, but without the rhombohedral lattice links." }], "NumberedFigureCaption", CellTags->"FigCartesianLatticeDiagonal8"], Cell["\<\ The methodology used for conversions between discrete 4-tuple and discrete \ Cartesian coordinates is explained in the following subsections. The \ relationships used have been derived from the trigonometry of the lattices.\ \>", "Text"], Cell[CellGroupData[{ Cell["\<\ Converting 4-tuple Coordinates to Discrete Cartesian Coordinates\ \>", "Subsubsection"], Cell[TextData[{ "Function ", StyleBox["QtoU", "MR"], StyleBox[", as presented in ", "TR"], "Listing ", CounterBox["NumberedProgram", "PrgQtoU"], StyleBox[", c", "TR"], "onverts 4-tuple coordinates to Cartesian coordinates:" }], "Text"], Cell["\<\ QtoU[{q1_, q2_, q3_, q4_}] := Module[{u}, u = {(q1 - q2 - q3 + q4), (q2 - q4 \ - q3 + q1), (q3 - q2 - q4 + q1)}]\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "Function to convert 4-tuple coordinates to Cartesian coordinates" }], "NumberedProgramCaption", CellTags->"PrgQtoU"], Cell[TextData[{ "The following is an example of applying ", StyleBox["QtoU", "MR"], ":" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"QtoU", "[", RowBox[{"{", RowBox[{"3", ",", "1", ",", "12", ",", "7"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"QtoU", "[", RowBox[{"{", RowBox[{"3", ",", "1", ",", "12", ",", "7"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.4252838425634017`*^9}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Converting Discrete Cartesian Coordinates to 4-tuple Coordinates\ \>", "Subsubsection"], Cell[TextData[{ "Function ", StyleBox["UtoQ", "MR"], StyleBox[", which is described in ", "TR"], "Listing ", CounterBox["NumberedProgram", "PrgUtoQ"], StyleBox[", conv", "TR"], "erts the Cartesian coordinate list ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["(", FontColor->GrayLevel[0]], RowBox[{ SubscriptBox["u", "1"], ",", " ", SubscriptBox["u", "2"], ",", " ", SubscriptBox["u", "3"]}], ")"}], TraditionalForm]]], " to a 4-tuple coordinate list ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["(", FontColor->GrayLevel[0]], RowBox[{ SubscriptBox["q", "1"], ",", " ", SubscriptBox["q", "2"], ",", " ", SubscriptBox["q", "3"], ",", " ", SubscriptBox["q", "4"]}], ")"}], TraditionalForm]]], ". In each coordinate system the unit metric for that coordinate system is \ used. This allows the ordinates to be integers in both systems. In the \ Cartesian coordinate list the integers can be positive, negative or zero. The \ 4-tuple coordinate list that is output by the function is automatically \ provided in standard form, where all ordinates are positive." }], "Text"], Cell["\<\ UtoQ[{u1_, u2_, u3_}] := Module[{q}, q = {(u1 + u2 + u3)/4, (u2 - u1 - u3)/4, \ (u3 - u2 - u1)/4, (u1 - u2 - u3)/4}; q = q - Min[q] + {1, 1, 1, 1}]\ \>", "Program", CellFrame->{{0, 0}, {0.5, 0.5}}], Cell[TextData[{ StyleBox["Listing ", "SB"], StyleBox[ CounterBox["NumberedProgram"], "SB"], StyleBox[". ", "SB"], "Function to convert Cartesian coordinates to 4-tuple coordinates" }], "NumberedProgramCaption", CellTags->"PrgUtoQ"], Cell[TextData[{ "An example of applying the function ", StyleBox["UtoQ", "MR"], " is as follows:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"UtoQ", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "15"}], ",", "7"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"UtoQ", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "15"}], ",", "7"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.4252838425734167`*^9}] }, Open ]], Cell["\<\ However, another example below appears, at first, to give an incorrect output \ because a discrete point on the Cartesian lattice is mapped to a non-existent \ point on the 4-colour rhombohedral lattice.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"UtoQ", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "15"}], ",", "8"}], "}"}], "]"}]], "Input"], Cell[BoxData[ RowBox[{"UtoQ", "[", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "15"}], ",", "8"}], "}"}], "]"}]], "Output", CellChangeTimes->{3.4252838425934477`*^9}] }, Open ]], Cell[TextData[{ "Every point on the discrete rhombohedral (or 4-tuple) lattice can be mapped \ (as above) to a point on a conventional Cartesian 3-tuple lattice with \ integer ordinates (positive and negative) where the base distance is 2/", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]]], " rhombohedral units. However, going from discrete Cartesian to 4-tuple \ coordinates, non-integer rational ordinates with a denominator of 2 would be \ produced wherever the Cartesian coordinate list contains a mixture of odd and \ even integers. " }], "Text"], Cell[TextData[{ "If the 4-colour rhombohedral lattice is the fundamental lattice that has to \ be mapped to a single discrete Cartesian coordinate system then each \ Cartesian coordinate list can contain only odd or only even integers: the \ 4-tuple lattice thus maps to Cartesian integer coordinates where the integers \ in each coordinate list (3-tuple) are either even or odd, but not a mixture \ of both. A unit of this single Cartesian lattice corresponds to 2/", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]]], " rhombohedral lattice units. This is equivalent to having sixteen \ interlaced Cartesian lattices, as shown in Figure ", CounterBox["NumberedFigure", "FigFourCubicLattices"], " (where only links of four of the lattices are shown), where the length of \ the unit Cartesian lattice links in each lattice (red, yellow, blue or \ violet; four of each) is 4/", Cell[BoxData[ FormBox[ SqrtBox["3"], TraditionalForm]]], " rhombohedral lattice units." }], "Text"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Conclusion", "Section"], Cell["\<\ The arithmetic associated with the 4-colour rhombohedral lattice is \ remarkably simple and possesses beautiful symmetry. Having undertaken the \ exploration thus far there are many enticements for the present author to \ delve even further.\ \>", "Text"], Cell["\<\ The most important conclusion from this paper is that one 4-colour \ rhombohedral 4-tuple lattice maps onto sixteen distinct, discrete Cartesian \ lattices that each have a cell edge length that is twice the length of the \ smallest possible cube on the 4-colour rhombohedral lattice. The sixteen \ Cartesian lattices can be assimilated into a single Cartesian lattice with \ half the cell edge length (i.e. the edge length would be equal to the edge \ length of the smallest possible cube on the 4-colour rhombohedral lattice). A \ consequence of doing this is that some Cartesian coordinates on the single \ Cartesian lattice will not exist on the underlying 4-colour rhombohedral \ lattice.\ \>", "Text"] }, Open ]], Cell[CellGroupData[{ Cell["References", "Section"], Cell["\<\ A. D. Boardman, D. E. O'Connor and P. A. Young, Symmetry and its Applications \ in Science, McGraw-Hill Book Company, Maidenhead, UK, 1973.\ \>", "Reference", CellTags->"RefBoardman1973"], Cell[TextData[{ "Mark Ronan, Symmetry and the Monster: One of the Greatest Quests of \ Mathematics, ", StyleBox["Oxford University Press, Oxford, 2006.", "SO", FontSlant->"Plain"] }], "Reference", CellTags->"RefRonan2006"], Cell[TextData[{ "H. M. S. Coxeter, Regular Polytopes, Dover Publications, New York, ", Cell[BoxData[ FormBox[ SuperscriptBox["3", "rd"], TraditionalForm]]], " edition,1973." }], "Reference", CellTags->"RefCoxeter1973"], Cell[TextData[{ "Jim McGovern, \[OpenCurlyDoubleQuote]What have spacetime, shape and \ symmetry to so with thermodynamics", StyleBox["?", FontSlant->"Italic"], "\[CloseCurlyDoubleQuote] ECOS 2007, Proceedings of the 20th International \ Conference on Efficiency, Cost, Optimization, Simulation and Environmental \ Impact of Energy Systems, ed. Alberto Mirandola, Ozer Arnas, Andrea \ Lazzaretto, Padova, Italy, 25-28 June 2007 pp. 349\[Dash]356. Also at:\ \[NonBreakingSpace]", ButtonBox["www.arxiv.org/abs/0710.1242", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.arxiv.org/abs/0710.1242"], None}] }], "Reference", CellTags->"RefMcGovern2007"], Cell[TextData[{ "A. G. Bell, \[OpenCurlyDoubleQuote]Aerial \ locomotion\[CloseCurlyDoubleQuote] ", StyleBox["National Geographic", FontSlant->"Italic"], ", ", StyleBox["XVIII", FontWeight->"Bold"], "(I), 1907 pp. 1\[Dash]34." }], "Reference", CellTags->"RefBell1907"], Cell[TextData[{ "R. B. Fuller and E. J. Applewhite, Synergetics: Explorations in the \ Geometry of Thinking, 1979. ", ButtonBox["www.rwgrayprojects.com/synergetics/synergetics.html", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.rwgrayprojects.com/synergetics/synergetics.html"], None}] }], "Reference", CellTags->"RefFuller1979"], Cell["\<\ H. Weyl, Symmetry, Princeton University Press, Princeton, 1952.\ \>", "Reference", PageBreakAbove->False, CellTags->"RefWeyl1979"], Cell[TextData[{ "J. Hasslberger, \[OpenCurlyDoubleQuote]Tetra space coordinates: a \ tetrahedron-based system of space co-ordinates\[CloseCurlyDoubleQuote] 1996", StyleBox[".", FontSlant->"Italic"], " ", ButtonBox["www.hasslberger.com/phy/phy_6.htm", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.hasslberger.com/phy/phy_6.htm"], None}] }], "Reference", CellTags->"RefHasslberger1996"], Cell[TextData[{ "K. Urner, \[OpenCurlyDoubleQuote]An introduction to quadrays\ \[CloseCurlyDoubleQuote] 1997 ", ButtonBox["www.grunch.net/synergetics/quadintro.html", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.grunch.net/synergetics/quadintro.html"], None}] }], "Reference", CellTags->"RefUrner1997"], Cell[TextData[{ "K. Urner, \[OpenCurlyDoubleQuote]Quadray coordinates: a Python \ implementation\[CloseCurlyDoubleQuote] 2000 ", ButtonBox["www.4dsolutions.net/ocn/pyqvectors.html", BaseStyle->"Hyperlink", ButtonData->{ URL["http://www.4dsolutions.net/ocn/pyqvectors.html"], None}] }], "Reference", CellTags->"RefUrner2000"], Cell[TextData[{ "Jim McGovern, \[OpenCurlyDoubleQuote]An Exploration of a Discrete \ Rhombohedral Lattice; of Possible Engineering or Physical Relevance\ \[CloseCurlyDoubleQuote] 2008. e-Proceedings of ", StyleBox["the 9th International Mathematica Symposium, Maastricht, The \ Netherlands, June 20", FontFamily->"Arial"], "\[Dash]", StyleBox["24th.", FontFamily->"Arial"], " " }], "Reference", CellTags->"RefMcGovern2008"] }, Open ]], Cell[CellGroupData[{ Cell["About the Author", "SectionAboutAuthor"], Cell["\<\ Professor Jim McGovern is the Head of the School of Mechanical and Transport \ Engineering at the Dublin Institute of Technology. His research interests \ include mechanical engineering; applied thermodynamics; zero-emissions \ solutions for power, combustion and transport; transport engineering; \ engineering simulation and modelling; and fundamental concepts underlying all \ of these areas: particularly symmetry.\ \>", "TextAboutAuthor"] }, Open ]] }, Open ]] }, Editable->True, WindowToolbars->"RulerBar", WindowSize->{784, 734}, WindowMargins->{{0, Automatic}, {Automatic, -5}}, DockedCells->FEPrivate`If[ FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], { Cell[ BoxData[ Cell[ GraphicsData[ "CompressedBitmap", "eJy9XGdcVUfevkuzu0mMXcOq9GYHUaqxgImiia6xxI3JakzUmDVl35Rd3Y3G\n\ tWGMigKKgtJFKdIEBCnSpPeuYP0l77vv5/fDPu/MOTPnzrn3XMCy+wHuvXPm\n\ zL/MzPP8/zNzzsqtX+7Ytnvrl598tPV3y/du/XzHJx998btle/aSIvPf6HRm\n\ FjqdzvF3Ovod5Cv79zq6urp0FqjJL8CVgLdREBmFjrY2S6l4GBrrG3DXLxB9\n\ U1xR7uSGFl8v9P4hCPc/24Dqzetx9/JlnblUdwi6OjtRc/0aCnbvQuH8hSgZ\n\ Z4/E2R6ovHJFB1qnSaqoG8tEZv1wAFcn2yF2205Ul5RYSMVj0EmaaXhnI3rt\n\ 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FontFamily -> "Helvetica", FontSize -> 10, FontWeight -> "Plain"], Cell[ StyleData["ManipulateLabel", "Printout"], ShowStringCharacters -> False, NumberMarks -> False, FontFamily -> "Helvetica", FontSize -> 8, FontWeight -> "Plain"]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Style Environment Names", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "Corrected style environment names to use the MenuPosition values \ from Core.nb. ", "EditorialComment", CellChangeTimes -> {{3.393589178043051*^9, 3.393589200951569*^9}}], Cell[ StyleData[All, "Working"], CellBracketOptions -> { "Color" -> RGBColor[0.115343, 0.350561, 0.362966]}, ShowCellLabel -> True, CellFrameLabelMargins -> 6, ScriptMinSize -> 9, MenuPosition -> 1100], Cell[ StyleData[All, "Presentation"], ScreenStyleEnvironment -> "Presentation", MenuPosition -> 1200, Magnification -> 1.25], Cell[ StyleData[All, "Printout"], PageWidth -> PaperWidth, PrintingOptions -> { "PageSize" -> {490, 720}, "PrintingMargins" -> {{0, 0}, {82, 56}}}, CellLabelAutoDelete -> False, ScriptMinSize -> 5, MenuPosition -> 1500, PrivateFontOptions -> {"FontType" -> "Outline"}, Magnification -> 1], Cell[ "Disabled Menu appearance for SlideShow and Condensed", "EditorialComment", CellChangeTimes -> {{3.3939379369487267`*^9, 3.39393795032102*^9}, 3.393938092859522*^9}], Cell[ StyleData[All, "SlideShow"], PageWidth -> WindowWidth, DockedCells -> FEPrivate`FrontEndResource["FEExpressions", "SlideshowToolbar"], ScrollingOptions -> { "PagewiseDisplay" -> True, "VerticalScrollRange" -> Fit}, ShowCellBracket -> False, ShowAutoStyles -> False, ScriptMinSize -> 9, MenuPosition -> 1300, StyleMenuListing -> None], Cell[ StyleData[All, "Condensed"], PageWidth -> WindowWidth, CellLabelMargins -> {{8, Inherited}, {Inherited, Inherited}}, ShowAutoStyles -> False, ScriptMinSize -> 8, MenuPosition -> 1400, StyleMenuListing -> None]}, Closed]], Cell[ CellGroupData[{ Cell[ "Notebook Options", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "The options defined for the style below will be used at the \ Notebook level.", "Text"], Cell[ StyleData["Notebook"], PageHeaders -> {{ Cell[ TextData[{ CounterBox["Page"]}], "PageNumber"], Inherited, Cell["Author(s)", "Header"]}, { Cell["Article Title", "Header"], Inherited, Cell[ TextData[{ CounterBox["Page"]}], "PageNumber"]}}, PageFooters -> {{ Cell[ TextData[{"The Mathematica Journal ", StyleBox["volume", FontWeight -> "Bold"], ":issue \[Copyright] year Wolfram Media, Inc."}], "Footer"], Inherited, Cell[ TextData[{ ValueBox["FileName"], " ", ValueBox["Date"]}], "Footer"]}, { Cell[ TextData[{ ValueBox["FileName"], " ", ValueBox["Date"]}], "Footer"], Inherited, Cell[ TextData[{"The Mathematica Journal ", StyleBox["volume", FontWeight -> "Bold"], ":issue \[Copyright] year Wolfram Media, Inc."}], "Footer"]}}, PrintingOptions -> { "FacingPages" -> True, "FirstPageHeader" -> False, "PrintRegistrationMarks" -> False}, CellFrameLabelMargins -> 6, HyphenationOptions -> {"HyphenationCharacter" -> "-"}, StyleMenuListing -> None]}, Closed]], Cell[ CellGroupData[{ Cell[ "Styles for Headings", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "Each notebook should contain a Title cell. Title resets all cell \ CounterBox values to zero (except Title).", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Title"], ShowCellBracket -> False, ShowSelection -> True, CellMargins -> {{54, 24}, {0, 15}}, CellGroupingRules -> {"TitleGrouping", 0}, PageBreakBelow -> False, LineSpacing -> {1, 3}, CounterIncrements -> "Title", CounterAssignments -> {{"Subtitle", 0}, {"Section", 0}, { "Subsection", 0}, {"Subsubsection", 0}, {"List", 0}, { "NumberedFigure", 0}, {"NumberedTable", 0}, { "NumberedProgram", 0}, {"Equation", 0}, {"Text", 0}, { "SmallText", 0}, {"Reference", 0}}, MenuPosition -> 1100, FontFamily -> "Times", FontSize -> 36, FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["Title", "Presentation"]]}, Closed]], Cell[ "Set a fixed line spacing, nonproportional, due to inconsistencies \ in the calculation of spacing of Janson Text Lt Std font family between \ operating systems.", "EditorialComment", CellChangeTimes -> {{3.406498889695311*^9, 3.406499050255167*^9}}], Cell[ StyleData["Title", "Printout"], CellMargins -> {{72, 72}, {14, 0}}, CellFrameMargins -> False, LineSpacing -> {1, -6}, FontFamily -> "Janson Text LT Std", FontColor -> GrayLevel[0], Background -> None], Cell[ "Sub(sub)titles are optional, follows Title, precedes Author.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Subtitle"], ShowCellBracket -> False, ShowSelection -> True, CellMargins -> {{54, 24}, {5, 2}}, CellGroupingRules -> {"TitleGrouping", 10}, PageBreakBelow -> False, LineSpacing -> {1, 3}, CounterIncrements -> "Subtitle", FontFamily -> "Times", FontSize -> 24, FontSlant -> "Italic"], Cell[ StyleData["Subtitle", "Presentation"]]}, Closed]], Cell[ "Set a fixed line spacing, nonproportional, due to inconsistencies \ in the calculation of spacing of Janson Text Lt Std font family between \ operating systems.", "EditorialComment", CellChangeTimes -> {{3.406498889695311*^9, 3.406499050255167*^9}}], Cell[ StyleData["Subtitle", "Printout"], CellMargins -> {{72, 72}, {12, 2}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 12], Cell[ CellGroupData[{ Cell[ StyleData["Subsubtitle"], ShowCellBracket -> False, ShowSelection -> True, CellMargins -> {{54, 24}, {5, 2}}, CellGroupingRules -> {"TitleGrouping", 10}, PageBreakBelow -> False, CounterIncrements -> "Subtitle", StyleMenuListing -> None, FontFamily -> "Times", FontSize -> 18, FontSlant -> "Italic"], Cell[ StyleData["Subsubtitle", "Presentation"]]}, Closed]], Cell[ "Set a fixed line spacing, nonproportional, due to inconsistencies \ in the calculation of spacing of Janson Text Lt Std font family between \ operating systems.", "EditorialComment", CellChangeTimes -> {{3.406498889695311*^9, 3.406499050255167*^9}}], Cell[ StyleData["Subsubtitle", "Printout"], CellMargins -> {{72, 72}, {6, 2}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10], Cell[ "Added MenuPosition->1245 to preced section in menu\nSectionFirst \ should be used for the first section level heading in a notebook. \ SectionFirst sets the Subsection and Subsubsection counters to zero. Sets \ Section counter value to 1. ", "EditorialComment", CellChangeTimes -> {{3.3939315312114477`*^9, 3.39393154849014*^9}}], Cell[ CellGroupData[{ Cell[ StyleData["SectionFirst"], CellFrame -> False, CellDingbat -> "\[FilledSquare]", CellMargins -> {{67, 25}, {10, 30}}, Evaluatable -> False, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, AspectRatioFixed -> True, MenuPosition -> 1245, FontFamily -> "Helvetica", FontSize -> 16, FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["SectionFirst", "Presentation"]], Cell[ StyleData["SectionFirst", "Printout"], CellFrame -> False, CellMargins -> {{72, 72}, {2, 30}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 12]}, Closed]], Cell[ "Section should be used for subsequent Section level headings. Sets \ counter values Subsection and Subsubsection to zero.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Section"], CellFrame -> False, CellDingbat -> "\[FilledSquare]", CellMargins -> {{67, 25}, {10, 30}}, Evaluatable -> False, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, AspectRatioFixed -> True, FontFamily -> "Helvetica", FontSize -> 16, FontWeight -> "Bold"], Cell[ StyleData["Section", "Presentation"], FontSize -> 18], Cell[ StyleData["Section", "Printout"], CellFrame -> False, CellMargins -> {{72, 72}, {2, 30}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 12]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SectionTOP"], CellFrame -> False, CellDingbat -> "\[FilledSquare]", CellMargins -> {{67, 25}, {10, 30}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, Evaluatable -> False, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, AspectRatioFixed -> True, FontFamily -> "Helvetica", FontSize -> 16, FontWeight -> "Bold", CellTags -> "ProductionOnly"], Cell[ StyleData["SectionTOP", "Presentation"], FontSize -> 18, CellTags -> "ProductionOnly"], Cell[ StyleData["SectionTOP", "Printout"], CellFrame -> False, CellMargins -> {{72, 72}, {2, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 12, CellTags -> "ProductionOnly"]}, Closed]], Cell[ "Subsection is an optional style. Sets counter Subsubsection to \ zero.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Subsection"], CellDingbat -> "\[EmptySquare]", CellMargins -> {{67, 25}, {10, 26}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 4}, CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["Subsection", "Presentation"]], Cell[ StyleData["Subsection", "Printout"], CellMargins -> {{72, 72}, {2, 16}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 11]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsectionTOP"], CellDingbat -> "\[EmptySquare]", CellMargins -> {{67, 25}, {10, 26}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold", CellTags -> "ProductionOnly"], Cell[ StyleData["SubsectionTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["SubsectionTOP", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 11, CellTags -> "ProductionOnly"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsectionNoSpace"], CellDingbat -> "\[EmptySquare]", CellMargins -> {{67, 25}, {10, 2}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["SubsectionNoSpace", "Presentation"]], Cell[ StyleData["SubsectionNoSpace", "Printout"], CellMargins -> {{72, 72}, {2, 2}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 11]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubsection"], CellDingbat -> "\[FilledSmallSquare]", CellMargins -> {{67, 25}, {6, 20}}, CellGroupingRules -> {"SectionGrouping", 60}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsubsection", FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold", FontSlant -> "Oblique"], Cell[ StyleData["Subsubsection", "Presentation"]], Cell[ StyleData["Subsubsection", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {-4, 10}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsubsectionTOP"], CellDingbat -> "\[FilledSmallSquare]", CellMargins -> {{67, 25}, {6, 20}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> {"SectionGrouping", 60}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsubsection", FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold", FontSlant -> "Oblique", CellTags -> "ProductionOnly"], Cell[ StyleData["SubsubsectionTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["SubsubsectionTOP", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {-4, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 10, CellTags -> "ProductionOnly"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsubsectionNoSpace"], CellDingbat -> "\[FilledSmallSquare]", CellMargins -> {{67, 25}, {6, 2}}, CellGroupingRules -> {"SectionGrouping", 60}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsubsection", StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold", FontSlant -> "Oblique"], Cell[ StyleData["SubsubsectionNoSpace", "Presentation"]], Cell[ StyleData["SubsubsectionNoSpace", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {-4, 2}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Subsubsubsection"], CellDingbat -> None, CellMargins -> {{67, 25}, {6, 20}}, CellGroupingRules -> {"SectionGrouping", 70}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsubsubsection", StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold"], Cell[ StyleData["Subsubsubsection", "Presentation"]], Cell[ StyleData["Subsubsubsection", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {-4, 10}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsubsubsectionTOP"], CellDingbat -> None, CellMargins -> {{67, 25}, {6, 20}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> {"SectionGrouping", 70}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsubsubsection", StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold", CellTags -> "ProductionOnly"], Cell[ StyleData["SubsubsubsectionTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["SubsubsubsectionTOP", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {-4, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 9, CellTags -> "ProductionOnly"]}, Closed]], Cell[ "NoDingbat heading variants used, for example, in the frontmatter.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SectionNoDingbat"], CellFrame -> False, CellDingbat -> None, CellMargins -> {{67, 25}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 16, FontWeight -> "Bold"], Cell[ StyleData["SectionNoDingbat", "Presentation"]], Cell[ StyleData["SectionNoDingbat", "Printout"], CellMargins -> {{72, 72}, {2, 30}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 12]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SectionNoDingbatTOP"], CellFrame -> False, CellDingbat -> None, CellMargins -> {{67, 25}, {10, 30}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Section", CounterAssignments -> {{"Subsection", 0}, {"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 16, FontWeight -> "Bold", CellTags -> "ProductionOnly"], Cell[ StyleData["SectionNoDingbatTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["SectionNoDingbatTOP", "Printout"], CellFrame -> False, CellMargins -> {{72, 72}, {2, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 12, CellTags -> "ProductionOnly"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsectionNoDingbat"], CellDingbat -> None, CellMargins -> {{67, 25}, {10, 26}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["SubsectionNoDingbat", "Presentation"]], Cell[ StyleData["SubsectionNoDingbat", "Printout"], CellMargins -> {{72, 72}, {2, 16}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 11]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsectionNoDingbatTOP"], CellDingbat -> None, CellMargins -> {{67, 25}, {10, 26}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold", CellTags -> "ProductionOnly"], Cell[ StyleData["SubsectionNoDingbatTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["SubsectionNoDingbatTOP", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 11, CellTags -> "ProductionOnly"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsectionNoSpaceNoDingbat"], CellMargins -> {{67, 25}, {10, 2}}, CellGroupingRules -> {"SectionGrouping", 50}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsection", CounterAssignments -> {{"Subsubsection", 0}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["SubsectionNoSpaceNoDingbat", "Presentation"]], Cell[ StyleData["SubsectionNoSpaceNoDingbat", "Printout"], CellMargins -> {{72, 72}, {2, 2}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 11]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsubsectionNoDingbat"], CellMargins -> {{67, 25}, {6, 20}}, CellGroupingRules -> {"SectionGrouping", 60}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsubsection", StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold", FontSlant -> "Oblique"], Cell[ StyleData["SubsubsectionNoDingbat", "Presentation"]], Cell[ StyleData["SubsubsectionNoDingbat", "Printout"], CellMargins -> {{72, 72}, {-4, 10}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SubsubsectionNoDingbatTOP"], CellMargins -> {{67, 25}, {6, 20}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> {"SectionGrouping", 60}, PageBreakBelow -> False, LineSpacing -> {1, 2}, CounterIncrements -> "Subsubsection", StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold", FontSlant -> "Oblique", CellTags -> "ProductionOnly"], Cell[ StyleData["SubsubsectionNoDingbatTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["SubsubsectionNoDingbatTOP", "Printout"], CellMargins -> {{72, 72}, {-4, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 10, CellTags -> "ProductionOnly"]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Styles for Body Text", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ CellGroupData[{ Cell[ StyleData["Text"], CellMargins -> {{67, 24}, {4, 4}}, CounterIncrements -> "Text", MenuPosition -> 1500, MenuCommandKey -> "7", FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["Text", "Presentation"]], Cell[ StyleData["Text", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, HyphenationOptions -> { "HyphenationFreeZone" -> 12, "HyphenationMinLengths" -> {4, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SmallText"], CellMargins -> {{67, 24}, {4, 4}}, CounterIncrements -> "SmallText", MenuPosition -> 1510, FontFamily -> "Times", FontSize -> 10], Cell[ StyleData["SmallText", "Presentation"]], Cell[ StyleData["SmallText", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Quote"], CellMargins -> {{83, 40}, {Inherited, Inherited}}, MenuPosition -> 1520, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["Quote", "Presentation"]], Cell[ StyleData["Quote", "Printout"], CellMargins -> {{96, 96}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontSlant -> "Plain"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Epigraph"], CellMargins -> {{92, 24}, {4, 4}}, TextAlignment -> Left, MenuPosition -> 1520, FontFamily -> "Times", FontSize -> 12, FontSlant -> "Italic"], Cell[ StyleData["Epigraph", "Presentation"]], Cell[ StyleData["Epigraph", "Printout"], CellMargins -> {{96, 72}, {2, 4}}, TextAlignment -> Left, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontSlant -> "Italic"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["EpigraphCredit"], CellMargins -> {{92, 24}, {4, 4}}, TextAlignment -> Left, MenuPosition -> 1520, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["EpigraphCredit", "Presentation"]], Cell[ StyleData["EpigraphCredit", "Printout"], CellMargins -> {{96, 72}, {2, 4}}, TextAlignment -> Left, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell[ "Styles for Input, Output, and Graphics", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "The cells in this section define styles used for active kernel \ sessions. Be careful when modifying, renaming, or removing these styles, \ because the front end associates special meanings with these style names.", "Text"], Cell[ TextData[{"Input cell style to be used for ", StyleBox["Mathematica", FontSlant -> "Italic"], " input statements that are followed by either Output or \ GraphicsOnly cell styles. Sets ", "DefaultFormatType->DefaultInputFormatType."}], "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Input"], CellFrame -> {{0.25, 0.25}, {0, 0.25}}, CellMargins -> {{103, 24}, {-1, 10}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, ShowStringCharacters -> True, NumberMarks -> True, CounterIncrements -> "Input", MenuPosition -> 1400, FontSize -> 12, FontWeight -> "Bold", Background -> GrayLevel[0.949996]], Cell[ StyleData["Input", "Presentation"]], Cell[ StyleData["Input", "Printout"], CellFrame -> False, CellMargins -> {{101, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, CellFrameMargins -> False, FontSize -> 9, Background -> None]}, Closed]], Cell[ TextData[{"InputOnly cell style to be used for ", StyleBox["Mathematica", FontSlant -> "Italic"], " input statements that produce no output or graphic. See Program \ and ProgramNoLabel cell styles for presenting segments of code that do not \ evaluate."}], "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["InputOnly"], CellFrame -> {{0.25, 0.25}, {0, 0.25}}, CellMargins -> {{103, 24}, {10, 10}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, ShowStringCharacters -> True, NumberMarks -> True, CounterIncrements -> "Input", MenuPosition -> 1410, FontSize -> 12, FontWeight -> "Bold", Background -> GrayLevel[0.949996]], Cell[ StyleData["InputOnly", "Presentation"]], Cell[ StyleData["InputOnly", "Printout"], CellFrame -> False, CellMargins -> {{101, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, FontSize -> 9, Background -> None]}, Closed]], Cell[ TextData[{"Output cell style is usually generated by the ", StyleBox["Mathematica", FontSlant -> "Italic"], " kernel. To follow Input cell style. Sets \ DefaultFormatType->DefaultOutputFormatType."}], "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Output"], CellFrame -> {{0.25, 0.25}, {0.25, 0}}, CellMargins -> {{103, 24}, {13, 0}}, CellEditDuplicate -> True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultOutputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, CounterIncrements -> "Output", StyleMenuListing -> None, FontSize -> 12, Background -> GrayLevel[0.949996], GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}], Cell[ StyleData["Output", "Presentation"]], Cell[ StyleData["Output", "Printout"], CellFrame -> False, CellMargins -> {{101, 72}, {4, 4}}, CellLabelMargins -> {{72, Inherited}, {Inherited, Inherited}}, FontSize -> 9, Background -> None, PanelBoxOptions -> { BaseStyle -> { ButtonBoxOptions -> {ImageSize -> {Automatic, 15}}}}, GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OutputScaled"], CellFrame -> {{0.25, 0.25}, {0.25, 0}}, CellMargins -> {{103, 24}, {13, 0}}, CellEditDuplicate -> True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultOutputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, ShowStringCharacters -> False, CounterIncrements -> "Output", MenuPosition -> 1415, FontSize -> 12, Background -> GrayLevel[0.949996], GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}], Cell[ StyleData["OutputScaled", "Presentation"]], Cell[ StyleData["OutputScaled", "Printout"], CellFrame -> False, CellMargins -> {{101, 72}, {2, 4}}, CellLabelMargins -> {{72, Inherited}, {Inherited, Inherited}}, FontSize -> 9, Magnification -> 0.65, Background -> None, GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}]}, Closed]], Cell[ "OutputPreserved cell style to be used to retain original output for \ Timing results and such. ", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["OutputPreserved"], CellFrame -> {{0.25, 0.25}, {0.25, 0}}, CellMargins -> {{103, 24}, {10, 0}}, CellBracketOptions -> { "Color" -> RGBColor[0.88864, 0.320928, 0.140932]}, CellEditDuplicate -> False, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultOutputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, CounterIncrements -> "Output", FontSize -> 12, Background -> GrayLevel[0.949996], GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}], Cell[ StyleData["OutputPreserved", "Presentation"]], Cell[ StyleData["OutputPreserved", "Printout"], CellFrame -> False, CellMargins -> {{101, 72}, {2, 4}}, CellLabelMargins -> {{72, Inherited}, {Inherited, Inherited}}, FontSize -> 9, Background -> None, GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}]}, Closed]], Cell[ TextData[{ "OutputOnly cell style to be used for output generated by the ", StyleBox["Mathematica", FontSlant -> "Italic"], " kernel without the Input. Sets \ DefaultFormatType->DefaultOutputFormatType."}], "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["OutputOnly"], CellFrame -> True, CellMargins -> {{103, 24}, {15, 10}}, CellEditDuplicate -> True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultOutputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, CounterIncrements -> "Output", StyleMenuListing -> None, FontSize -> 12, Background -> GrayLevel[0.949996], GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}], Cell[ StyleData["OutputOnly", "Presentation"]], Cell[ StyleData["OutputOnly", "Printout"], CellFrame -> False, CellMargins -> {{101, 72}, {2, 4}}, CellLabelMargins -> {{72, Inherited}, {Inherited, Inherited}}, FontSize -> 9, Background -> None, GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}]}, Closed]], Cell[ "Variants for use embedded in NumberedList.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["InputInList"], CellFrame -> {{0.25, 0.25}, {0, 0.25}}, CellMargins -> {{138, 24}, {-1, 10}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, ShowStringCharacters -> True, NumberMarks -> True, CounterIncrements -> "Input", StyleMenuListing -> None, FontSize -> 12, FontWeight -> "Bold", Background -> GrayLevel[0.949996]], Cell[ StyleData["InputInList", "Presentation"]], Cell[ StyleData["InputInList", "Printout"], CellFrame -> False, CellMargins -> {{138, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 329}, CellFrameMargins -> False, FontSize -> 9, Background -> None]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InputOnlyInList"], CellFrame -> {{0.25, 0.25}, {0, 0.25}}, CellMargins -> {{138, 24}, {10, 10}}, Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, ShowStringCharacters -> True, NumberMarks -> True, CounterIncrements -> "Input", StyleMenuListing -> None, FontSize -> 12, FontWeight -> "Bold", Background -> GrayLevel[0.949996]], Cell[ StyleData["InputOnlyInList", "Presentation"]], Cell[ StyleData["InputOnlyInList", "Printout"], CellFrame -> False, CellMargins -> {{138, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 329}, FontSize -> 9, Background -> None]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OutputInList"], CellFrame -> {{0.25, 0.25}, {0.25, 0}}, CellMargins -> {{138, 24}, {10, 0}}, CellEditDuplicate -> True, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultOutputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, CounterIncrements -> "Output", StyleMenuListing -> None, FontSize -> 12, Background -> GrayLevel[0.949996], GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}], Cell[ StyleData["OutputInList", "Presentation"]], Cell[ StyleData["OutputInList", "Printout"], CellFrame -> False, CellMargins -> {{138, 72}, {2, 4}}, CellLabelMargins -> {{72, Inherited}, {Inherited, Inherited}}, FontSize -> 9, Background -> None, GraphicsBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}, Graphics3DBoxOptions -> { BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}]}, Closed]], Cell[ "HiddenInput used for hiding input that evaluates in both Working \ and Printout environments", "EditorialComment", CellChangeTimes -> {{3.4010214861134043`*^9, 3.401021494430964*^9}, {3.401021536048787*^9, 3.4010215375848503`*^9}}], Cell[ CellGroupData[{ Cell[ StyleData["HiddenInput"], CellFrame -> {{0.25, 0.25}, {0, 0.25}}, CellMargins -> {{67, 24}, {-1, 10}}, Evaluatable -> True, CellOpen -> False, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[1], DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, ShowStringCharacters -> True, NumberMarks -> True, CounterIncrements -> "Input", FontSize -> 12, FontWeight -> "Bold", Background -> GrayLevel[1]], Cell[ StyleData["HiddenInput", "Presentation"]], Cell[ StyleData["HiddenInput", "Printout"], CellFrame -> False, ShowCellBracket -> False, ShowSelection -> False, CellMargins -> {{96, 72}, {0, 0}}, CellElementSpacings -> { "ClosedCellHeight" -> 1, "ClosedGroupTopMargin" -> 2}, CellOpen -> False, PrivateEvaluationOptions -> { "OutputFormPageWidth" -> 342}, CellFrameMargins -> False, LineSpacing -> {0, 0}, FontSize -> 1, Background -> None]}, Closed]], Cell[ "HiddenInputPO for hiding input cells that only evaluate in the \ Printout environment", "EditorialComment", CellChangeTimes -> {{3.4010204006968517`*^9, 3.401020410099378*^9}, {3.401020463196204*^9, 3.4010204728063097`*^9}, {3.401021504034895*^9, 3.4010215312965527`*^9}}], Cell[ CellGroupData[{ Cell[ StyleData["HiddenInputPO"], CellFrame -> {{0.25, 0.25}, {0, 0.25}}, CellMargins -> {{67, 24}, {-1, 10}}, Evaluatable -> False, CellOpen -> False, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[1], DefaultFormatType -> DefaultInputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, ShowStringCharacters -> True, NumberMarks -> True, CounterIncrements -> "Input", FontSize -> 12, FontWeight -> "Bold", Background -> GrayLevel[1]], Cell[ StyleData["HiddenInputPO", "Presentation"]], Cell[ StyleData["HiddenInputPO", "Printout"], CellFrame -> False, ShowCellBracket -> False, ShowSelection -> False, CellMargins -> {{96, 72}, {0, 0}}, CellElementSpacings -> { "ClosedCellHeight" -> 1, "ClosedGroupTopMargin" -> 2}, Evaluatable -> True, CellOpen -> False, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, CellFrameMargins -> False, LineSpacing -> {0, 0}, FontSize -> 1, Background -> None]}, Closed]], Cell[ TextData[{"Message cells are sometimes generated by the ", StyleBox["Mathematica", FontSlant -> "Italic"], " kernel during evaluation. To follow Input cell style, precede \ Output cell style."}], "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Message"], CellFrame -> {{0.25, 0.25}, {0, 0}}, CellDingbat -> "\[WarningSign]", CellMargins -> {{103, 24}, {0, 0}}, CellGroupingRules -> "OutputGrouping", PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0.869993], CellFrameLabelMargins -> 0, DefaultFormatType -> DefaultOutputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10, FontColor -> RGBColor[0, 0, 1], Background -> GrayLevel[0.949996]], Cell[ StyleData["Message", "Presentation"]], Cell[ StyleData["Message", "Printout"], CellFrame -> True, CellDingbat -> None, CellMargins -> {{96, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, CellFrameMargins -> 4, CellFrameColor -> GrayLevel[0], FontFamily -> "WriCMTT-Base", FontSize -> 8, FontProperties -> { "FontMonospaced" -> True, "FontSerifed" -> True}, FontColor -> GrayLevel[0], Background -> None]}, Closed]], Cell[ TextData[{"Print cells are usually generated by the ", StyleBox["Mathematica", FontSlant -> "Italic"], " kernel from such commands as ?Plot."}], "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Print"], CellFrame -> True, CellMargins -> {{103, 24}, {0, 0}}, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, CellLabelMargins -> {{23, Inherited}, { Inherited, Inherited}}, CellFrameColor -> GrayLevel[0], DefaultFormatType -> DefaultOutputFormatType, LineSpacing -> {1, 2}, AutoItalicWords -> {}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 10], Cell[ StyleData["Print", "Presentation"]], Cell[ StyleData["Print", "Printout"], CellFrame -> True, CellMargins -> {{101, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, CellFrameMargins -> 4, CellFrameColor -> GrayLevel[0], FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 9, Background -> None]}, Closed]], Cell[ TextData[{"FilePrintPrint is for output returned from the ", StyleBox["Mathematica", FontSlant -> "Italic"], " FilePrint command. "}], "EditorialComment", CellChangeTimes -> {{3.394960987402294*^9, 3.394961026823163*^9}, 3.40335894643512*^9}], Cell[ CellGroupData[{ Cell[ StyleData["FilePrintPrint"], PageWidth -> WindowWidth, CellFrame -> True, CellMargins -> {{67, 24}, {0, 0}}, CellGroupingRules -> "OutputGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GroupPageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, CellLabelMargins -> {{23, Inherited}, {Inherited, Inherited}}, CellFrameColor -> GrayLevel[0], LineSpacing -> {1, 2}, AutoItalicWords -> {}, StyleMenuListing -> None, FontSize -> 10], Cell[ StyleData["FilePrintPrint", "Presentation"]], Cell[ StyleData["FilePrintPrint", "Printout"], PageWidth -> PaperWidth, CellFrame -> True, CellMargins -> {{96, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, CellFrameMargins -> 4, CellFrameColor -> GrayLevel[0], FontSize -> 9, Background -> None]}, Closed]], Cell[ TextData[{ "PlacedGraphics cell style to be used when importing a graphic \ from another application or when presenting a graphic not associated with ", StyleBox["Mathematica", FontSlant -> "Italic"], " input. May be followed by NumberedFigureCaption."}], "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["PlacedGraphics"], CellFrame -> False, CellMargins -> {{67, 24}, {10, 10}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, ShowCellLabel -> False, TextAlignment -> Left, LineSpacing -> {1, 2}, GraphicsBoxOptions -> { BaseStyle -> { Background -> GrayLevel[1], FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { Background -> GrayLevel[1], BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}], Cell[ StyleData["PlacedGraphics", "Presentation"]], Cell[ StyleData["PlacedGraphics", "Printout"], CellFrame -> False, CellMargins -> {{72, 72}, {8, 10}}, TextAlignment -> Center, FontSize -> 10, Background -> None, GraphicsBoxOptions -> { BaseStyle -> { Background -> GrayLevel[1], FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}, Graphics3DBoxOptions -> { Background -> GrayLevel[1], BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["PlacedGraphicsTOP"], CellFrame -> False, CellMargins -> {{67, 24}, {10, 10}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, ShowCellLabel -> False, TextAlignment -> Left, LineSpacing -> {1, 2}, GraphicsBoxOptions -> { BaseStyle -> { Background -> GrayLevel[1], FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, Graphics3DBoxOptions -> { Background -> GrayLevel[1], BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 8, FormatType -> TraditionalForm}, ImageSize -> {288, Automatic}}, CellTags -> "ProductionOnly"], Cell[ StyleData["PlacedGraphicsTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["PlacedGraphicsTOP", "Printout"], CellMargins -> {{72, 72}, {8, 4}}, TextAlignment -> Center, FontSize -> 10, Background -> None, GraphicsBoxOptions -> { BaseStyle -> { Background -> GrayLevel[1], FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}, Graphics3DBoxOptions -> { Background -> GrayLevel[1], BaseStyle -> { FontFamily -> "Helvetica", FontSize -> 6, FormatType -> TraditionalForm}, ImageSize -> {200, Automatic}}, CellTags -> "ProductionOnly"]}, Closed]], Cell[ "CellLabel style definition controls how labels appear when a cell \ has ShowCellLabels->True.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["CellLabel"], CellMargins -> {{5, Inherited}, {Inherited, Inherited}}, LineSpacing -> {1, 2}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 8, FontSlant -> "Oblique", FontColor -> RGBColor[0.115343, 0.350561, 0.362966]], Cell[ StyleData["CellLabel", "Presentation"]], Cell[ StyleData["CellLabel", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 6, FontColor -> GrayLevel[0]]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell[ "Styles for Automatic Numbering and Lists", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "NumberedEquation is for DisplayFormula cells that number \ sequentially throughout a notebook. Sets as \ DefaultFormatType->TraditionalForm.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["NumberedEquation"], CellMargins -> {{67, 24}, {5, 10}}, PageBreakAbove -> False, CellFrameLabels -> {{None, Cell[ TextData[{"(", CounterBox["NumberedEquation"], ")"}], CellSize -> {30, Inherited}, TextAlignment -> Right]}, { None, None}}, DefaultFormatType -> TraditionalForm, TextAlignment -> Center, LineSpacing -> {1, 3}, SingleLetterItalics -> True, SpanMaxSize -> Infinity, CounterIncrements -> "NumberedEquation", MenuPosition -> 1710, FormatTypeAutoConvert -> False, FontFamily -> "Times", FontSize -> 12, UnderoverscriptBoxOptions -> {LimitsPositioning -> True}, GridBoxOptions -> {AllowScriptLevelChange -> False}], Cell[ StyleData["NumberedEquation", "Presentation"]], Cell[ StyleData["NumberedEquation", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, LineSpacing -> {1, 2}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ "Brought in for compatibility, set StyleMenuListing->\"None\"", "EditorialComment", CellChangeTimes -> {{3.3942937542668333`*^9, 3.3942937585633583`*^9}, {3.394294004298411*^9, 3.394294019331209*^9}}], Cell[ CellGroupData[{ Cell[ StyleData["DisplayFormulaNumbered"], CellMargins -> {{67, 24}, {5, 10}}, StripStyleOnPaste -> True, CellFrameLabels -> {{None, Cell[ TextData[{"(", CounterBox["DisplayFormulaNumbered"], ")"}], CellSize -> {30, Inherited}, TextAlignment -> Right]}, { None, None}}, DefaultFormatType -> DefaultInputFormatType, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LineSpacing -> {1, 3}, LanguageCategory -> "Formula", ScriptLevel -> 0, SingleLetterItalics -> True, CounterIncrements -> "DisplayFormulaNumbered", MenuPosition -> 1715, UnderoverscriptBoxOptions -> {LimitsPositioning -> True}], Cell[ StyleData["DisplayFormulaNumbered", "Presentation"]], Cell[ StyleData["DisplayFormulaNumbered", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, PrivateEvaluationOptions -> {"OutputFormPageWidth" -> 342}, LineSpacing -> {1, 2}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineFormula"], CellMargins -> {{10, 4}, {0, 8}}, StripStyleOnPaste -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, LanguageCategory -> "Formula", ScriptLevel -> 1, SingleLetterItalics -> True, MenuPosition -> 1650], Cell[ StyleData["InlineFormula", "Presentation"]], Cell[ StyleData["InlineFormula", "Printout"], CellMargins -> {{2, 0}, {6, 6}}]}, Closed]], Cell[ "NumberedFigureCaption to be used directly after a PlacedGraphics \ cell. Use the TMJpalette.nb palette to begin the cell and paste in the word \ \"Figure\" and the NumberedFigure counter value. Allows for a descriptive \ caption.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["NumberedFigureCaption"], CellDingbat -> "\[FilledUpTriangle]", CellMargins -> {{67, 24}, {8, 10}}, PageBreakAbove -> False, TextAlignment -> Left, LineSpacing -> {1, 3}, CounterIncrements -> "NumberedFigure", MenuPosition -> 1711, FormatTypeAutoConvert -> False, FontFamily -> "Helvetica", FontSize -> 10], Cell[ StyleData["NumberedFigureCaption", "Presentation"]], Cell[ StyleData["NumberedFigureCaption", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {18, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 8]}, Closed]], Cell[ "NumberedTableCaption to be used directly after a Table cell. Use \ the TMJStyles.nb palette to begin the cell and paste in the word \"Table\" \ and the NumberedTable counter value. Allows for a descriptive caption.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["NumberedTableCaption"], CellDingbat -> "\[FilledUpTriangle]", CellMargins -> {{67, 24}, {8, 10}}, PageBreakAbove -> False, LineSpacing -> {1, 3}, CounterIncrements -> "NumberedTable", MenuPosition -> 1712, FontFamily -> "Helvetica", FontSize -> 10], Cell[ StyleData["NumberedTableCaption", "Presentation"]], Cell[ StyleData["NumberedTableCaption", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {18, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 8]}, Closed]], Cell[ "NumberedProgramCaption to be used directly after a Program cell. \ Use the TMJpalette.nb palette to begin the cell and paste in the word \ \"Listing\" and the NumberedProgram counter value. Allows for a descriptive \ caption.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["NumberedProgramCaption"], CellDingbat -> "\[FilledUpTriangle]", CellMargins -> {{67, 24}, {8, 10}}, PageBreakAbove -> False, LineSpacing -> {1, 3}, CounterIncrements -> "NumberedProgram", MenuPosition -> 1713, FormatTypeAutoConvert -> False, FontFamily -> "Helvetica", FontSize -> 10], Cell[ StyleData["NumberedProgramCaption", "Presentation"]], Cell[ StyleData["NumberedProgramCaption", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {18, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 8]}, Closed]], Cell[ "Use of Caption style by itself should be discouraged. See cell \ styles for NumberedFigureCaption, NumberedTableCaption, \ NumberedProgramCaption and the TMJpalette.nb palette.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Caption"], CellDingbat -> "\[FilledUpTriangle]", CellMargins -> {{67, 24}, {Inherited, 5}}, PageBreakAbove -> False, LineSpacing -> {1, 3}, FontFamily -> "Helvetica", FontSize -> 10], Cell[ StyleData["Caption", "Presentation"]], Cell[ StyleData["Caption", "Printout"], CellDingbat -> None, CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 8]}, Closed]], Cell[ "BulletedList is an optional style. Adds a CellDingbat of \ FilledSmallCircle. Text indents left a little more.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["BulletedList"], CellDingbat -> "\[FilledSmallCircle]", CellMargins -> {{104, 24}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, CounterAssignments -> {{"SubList", 0}}, MenuPosition -> 1800, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["BulletedList", "Presentation"]], Cell[ StyleData["BulletedList", "Printout"], CellMargins -> {{110, 72}, {2, Inherited}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ "Brought in for compatibility, disabled menu appearance (Item \ matches BulletedList, Subitem matches SubListBulleted)", "EditorialComment", CellChangeTimes -> {{3.394378613468091*^9, 3.394378650134136*^9}, { 3.394379042604026*^9, 3.39437905673245*^9}}], Cell[ CellGroupData[{ Cell[ StyleData["Item", StyleDefinitions -> StyleData["BulletedList"]], MenuPosition -> None], Cell[ StyleData[ "Item", "Presentation", StyleDefinitions -> StyleData["BulletedList", "Presentation"]]], Cell[ StyleData[ "Item", "Printout", StyleDefinitions -> StyleData["BulletedList", "Printout"]]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "Subitem", StyleDefinitions -> StyleData["SubListBulleted"]], MenuPosition -> None], Cell[ StyleData[ "Subitem", "Presentation", StyleDefinitions -> StyleData["SubListBulleted", "Presentation"]]], Cell[ StyleData[ "Subitem", "Printout", StyleDefinitions -> StyleData["SubListBulleted", "Printout"]]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "ItemNumbered", StyleDefinitions -> StyleData["NumberedList"]], MenuPosition -> None], Cell[ StyleData[ "ItemNumbered", "Presentation", StyleDefinitions -> StyleData["NumberedList", "Presentation"]]], Cell[ StyleData[ "ItemNumbered", "Printout", StyleDefinitions -> StyleData["NumberedList", "Printout"]]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData[ "SubitemNumbered", StyleDefinitions -> StyleData["SubList"]], MenuPosition -> None], Cell[ StyleData[ "SubitemNumbered", "Presentation", StyleDefinitions -> StyleData["SubList", "Presentation"]]], Cell[ StyleData[ "SubitemNumbered", "Printout", StyleDefinitions -> StyleData["SubList", "Printout"]]]}, Closed]], Cell[ "BeginNumberedList to be used as the first item in a numbered list \ sequence. Use the TMJpalette.nb palette to begin the cell and paste in the \ List counter value.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["BeginNumberedList"], CellMargins -> {{79, 24}, {Inherited, Inherited}}, CellFrameLabels -> {{ Cell[ TextData[{ CounterBox["List"], "."}], "TB", CellSize -> {20, Inherited}, TextAlignment -> Right, CellBaseline -> Baseline], Inherited}, { Inherited, Inherited}}, CellBaseline -> Baseline, LineSpacing -> {1., 3.}, CounterIncrements -> "List", CounterAssignments -> {{"List", 0}, {"SubList", 0}}, MenuPosition -> 1750, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["BeginNumberedList", "Presentation"]], Cell[ StyleData["BeginNumberedList", "Printout"], CellMargins -> {{84, 72}, {2, Inherited}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ "NumberedList to be used for subsequent items in a numbered list \ sequence. Use the TMJpalette.nb palette to begin the cell and paste in the \ List counter value.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["NumberedList"], CellMargins -> {{79, 24}, {Inherited, Inherited}}, CellFrameLabels -> {{ Cell[ TextData[{ CounterBox["List"], "."}], "TB", CellSize -> {20, Inherited}, TextAlignment -> Right, CellBaseline -> Baseline], Inherited}, { Inherited, Inherited}}, CellBaseline -> Baseline, LineSpacing -> {1, 3}, TabSpacings -> {4.}, CounterIncrements -> "List", CounterAssignments -> {{"SubList", 0}}, MenuPosition -> 1775, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["NumberedList", "Presentation"]], Cell[ StyleData["NumberedList", "Printout"], CellMargins -> {{84, 72}, {2, Inherited}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["NolabelList"], CellMargins -> {{95, 10}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, ParagraphIndent -> 0, MenuPosition -> 1810, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["NolabelList", "Presentation"]], Cell[ StyleData["NolabelList", "Printout"], CellMargins -> {{99, 72}, {2, Inherited}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ "SubList to be used for a lettered sublist within a NumberedList \ item. Use the TMJpalette.nb palette to begin the cell and paste in the \ SubList counter value.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SubList"], CellMargins -> {{105, 10}, {Inherited, Inherited}}, CellFrameLabels -> {{ Cell[ TextData[{ CounterBox["SubList"], "."}], "TB", CellBaseline -> Baseline], Inherited}, {Inherited, Inherited}}, CellBaseline -> Baseline, LineSpacing -> {1, 3}, CounterIncrements -> "SubList", MenuPosition -> 1776, FontFamily -> "Times", FontSize -> 12, CounterBoxOptions -> {CounterFunction :> (Part[ CharacterRange["a", "z"], #]& )}], Cell[ StyleData["SubList", "Presentation"]], Cell[ StyleData["SubList", "Printout"], CellMargins -> {{110, 72}, {2, Inherited}}, CellFrameLabels -> {{ Cell[ TextData[{ CounterBox["SubList"], "."}], "TB", CellBaseline -> Baseline], Inherited}, {Inherited, Inherited}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, CounterBoxOptions -> {CounterFunction :> (Part[ CharacterRange["a", "z"], #]& )}]}, Closed]], Cell[ "SubListBulleted to be used as subsequent items in a bulleted list \ sequence used as a subitem to a NumberedList item.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SubListBulleted"], CellDingbat -> "\[FilledSmallCircle]", CellMargins -> {{120, 10}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["SubListBulleted", "Presentation"]], Cell[ StyleData["SubListBulleted", "Printout"], CellMargins -> {{124, 72}, {2, Inherited}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ "Reference style to be used in the bibliography portion of a \ notebook. One cell for each bibliography entry. Use the TMJpalette.nb palette \ to begin cell and paste in the Reference counter value. ", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Reference"], CellDingbat -> Cell[ TextData[{"[", CounterBox["Reference"], "]"}], "SR", CellSize -> {25, Inherited}, TextAlignment -> Right], CellMargins -> {{79, 25}, {Inherited, Inherited}}, CellFrameLabels -> {{None, None}, {None, None}}, LineSpacing -> {1, 3}, CounterIncrements -> "Reference", MenuPosition -> 1870, FontFamily -> "Helvetica", FontSize -> 10], Cell[ StyleData["Reference", "Presentation"]], Cell[ StyleData["Reference", "Printout"], CellMargins -> {{85, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 8]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Journal Element Styles", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "OnlineHeader to be used at the beginning of a notebook. Precedes \ the Title cell.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["OnlineHeader"], ShowCellBracket -> False, ShowSelection -> True, CellMargins -> {{0, 25}, {0, 0}}, CellGroupingRules -> {"TitleGrouping", 30}, PageBreakBelow -> False, CellFrameMargins -> {{54, 4}, {2, 8}}, LineSpacing -> {1, 1}, StyleMenuListing -> None, FontFamily -> "Times", FontSize -> 12, FontWeight -> "Plain", FontSlant -> "Italic", FontColor -> GrayLevel[1], Background -> RGBColor[0.725383, 0.0545968, 0.0770581]], Cell[ StyleData["OnlineHeader", "Presentation"]], Cell[ StyleData["OnlineHeader", "Printout"], PageWidth -> PaperWidth, CellFrame -> False, CellMargins -> {{72, 72}, {0, 0}}, CellElementSpacings -> {"CellMinHeight" -> 2}, FontFamily -> "Janson Text LT Std", FontSize -> 10, Background -> None]}, Closed]], Cell[ "Cell Style PreTitle to be used for such things that precede a title \ as in EDITOR'S PICK. Should be entered all caps with a space between each \ letter, two spaces between words. ", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["PreTitle"], ShowCellBracket -> False, CellMargins -> {{54, 25}, {14, 4}}, CellGroupingRules -> {"TitleGrouping", 0}, PageBreakBelow -> False, CellFrameMargins -> {{55, 4}, {8, 20}}, LineSpacing -> {1, 2}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["PreTitle", "Presentation"]], Cell[ StyleData["PreTitle", "Printout"], CellMargins -> {{72, 72}, {14, 0}}, CellFrameMargins -> False, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 11, FontColor -> GrayLevel[0], Background -> None]}, Closed]], Cell[ "Author to be used after the Title cell with author name(s). Author \ name(s) may be preceded by \"Edited by \" for certain columns. Text in author \ cell to be used as the left page header.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Author"], ShowCellBracket -> False, ShowSelection -> True, CellMargins -> {{54, 24}, {4, 6}}, CellGroupingRules -> "NormalGrouping", PageBreakBelow -> False, LineSpacing -> {1, 2}, ParagraphSpacing -> {0, 0}, MenuPosition -> 1155, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["Author", "Presentation"], FontSize -> 16], Cell[ StyleData["Author", "Printout"], CellMargins -> {{72, 72}, {4, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 12]}, Closed]], Cell[ "Abstract is a required element to be used after the Author cell. \ Should contain a short summary of the article as a single paragraph.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Abstract"], ShowCellBracket -> False, ShowSelection -> True, CellMargins -> {{54, 86}, {4, 25}}, LineSpacing -> {1, 3}, MenuPosition -> 1156, FontFamily -> "Times", FontSize -> 14, FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["Abstract", "Presentation"]], Cell[ StyleData["Abstract", "Printout"], CellMargins -> {{72, 72}, {Inherited, 2}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ "BeginQuestion is used, for example, in the In and Out column \ directly after a section cell. Followed by either Question or Input, \ InputOnly, etc. Last paragraph of the question should be in EndQuestion cell \ style.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["BeginQuestion"], CellFrame -> {{0, 0}, {0, 2}}, CellDingbat -> "Q:", CellMargins -> {{89, 34}, {8, 8}}, CellFrameMargins -> {{0, 0}, {2, 4}}, LineSpacing -> {1, 3}, MenuPosition -> 1820, FontFamily -> "Times", FontSize -> 14, FontWeight -> "Bold", FontColor -> RGBColor[0.115511, 0.321752, 0.580118]], Cell[ StyleData["BeginQuestion", "Presentation"]], Cell[ StyleData["BeginQuestion", "Printout"], PageWidth -> PaperWidth, CellFrame -> {{0, 0}, {0, 2}}, CellDingbat -> None, CellMargins -> {{54, 72}, {2, 16}}, CellFrameLabels -> {{ Cell[ BoxData[ AdjustmentBox[ StyleBox["Q:", "TB"], BoxBaselineShift -> 1.15]], CellBaseline -> "Baseline", CellSize -> {18, 24}, TextAlignment -> "Left"], Inherited}, { Inherited, Inherited}}, CellFrameLabelMargins -> False, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["BeginQuestionTOP"], CellFrame -> {{0, 0}, {0, 2}}, CellDingbat -> "Q:", CellMargins -> {{89, 34}, {8, 8}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellFrameMargins -> {{0, 0}, {2, 4}}, LineSpacing -> {1, 3}, FontFamily -> "Times", FontSize -> 14, FontWeight -> "Bold", FontColor -> RGBColor[0.115511, 0.321752, 0.580118], CellTags -> "ProductionOnly"], Cell[ StyleData["BeginQuestionTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["BeginQuestionTOP", "Printout"], PageWidth -> PaperWidth, CellFrame -> {{0, 0}, {0, 2}}, CellDingbat -> None, CellMargins -> {{54, 72}, {2, 16}}, CellFrameLabels -> {{ Cell[ BoxData[ AdjustmentBox[ StyleBox["Q:", "TB"], BoxBaselineShift -> 1.15]], CellBaseline -> "Baseline", CellSize -> {18, 24}, TextAlignment -> "Left"], Inherited}, { Inherited, Inherited}}, CellFrameLabelMargins -> False, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontColor -> GrayLevel[0], CellTags -> "ProductionOnly"]}, Closed]], Cell[ "Question used for text cells within the Question portion of a \ QuestionAnswer.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Question"], CellMargins -> {{89, 34}, {8, 8}}, LineSpacing -> {1, 3}, MenuPosition -> 1830, FontFamily -> "Times", FontSize -> 14, FontWeight -> "Bold", FontColor -> RGBColor[0.115511, 0.321752, 0.580118]], Cell[ StyleData["Question", "Presentation"]], Cell[ StyleData["Question", "Printout"], PageWidth -> PaperWidth, CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]], Cell[ "EndQuestion used in the In and Out column as the last paragraph of \ the question.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["EndQuestion"], CellFrame -> {{0, 0}, {2, 0}}, CellMargins -> {{89, 35}, {8, 8}}, LineSpacing -> {1, 3}, MenuPosition -> 1840, FontFamily -> "Times", FontSize -> 14, FontWeight -> "Bold", FontColor -> RGBColor[0.115511, 0.321752, 0.580118]], Cell[ StyleData["EndQuestion", "Presentation"]], Cell[ StyleData["EndQuestion", "Printout"], CellFrame -> {{0, 0}, {2, 0}}, CellMargins -> {{72, 72}, {4, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]], Cell[ "BeginEndQuestion is used in the In and Out column directly after a \ section cell. Used if the question is a single text paragraph.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["BeginEndQuestion"], CellFrame -> {{0, 0}, {2, 2}}, CellDingbat -> "Q:", CellMargins -> {{89, 35}, {8, 8}}, LineSpacing -> {1, 3}, MenuPosition -> 1850, FontFamily -> "Times", FontSize -> 14, FontWeight -> "Bold", FontColor -> RGBColor[0.115511, 0.321752, 0.580118]], Cell[ StyleData["BeginEndQuestion", "Presentation"]], Cell[ StyleData["BeginEndQuestion", "Printout"], CellDingbat -> None, CellMargins -> {{54, 72}, {4, 16}}, CellFrameLabels -> {{ Cell[ BoxData[ AdjustmentBox[ StyleBox["Q:", "TB"], BoxBaselineShift -> 2.25]], CellBaseline -> "Baseline", CellSize -> {18, 24}, TextAlignment -> "Left"], Inherited}, { Inherited, Inherited}}, CellFrameLabelMargins -> False, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["BeginEndQuestionTOP"], CellFrame -> {{0, 0}, {2, 2}}, CellDingbat -> "Q:", CellMargins -> {{89, 35}, {8, 8}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, LineSpacing -> {1, 3}, FontFamily -> "Times", FontSize -> 14, FontWeight -> "Bold", FontColor -> RGBColor[0.115511, 0.321752, 0.580118], CellTags -> "ProductionOnly"], Cell[ StyleData["BeginEndQuestionTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["BeginEndQuestionTOP", "Printout"], CellDingbat -> None, CellMargins -> {{54, 72}, {4, 4}}, CellFrameLabels -> {{ Cell[ BoxData[ AdjustmentBox[ StyleBox["Q:", "TB"], BoxBaselineShift -> 2.25]], CellBaseline -> "Baseline", CellSize -> {18, 24}, TextAlignment -> "Left"], Inherited}, { Inherited, Inherited}}, CellFrameLabelMargins -> False, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontColor -> GrayLevel[0], CellTags -> "ProductionOnly"]}, Closed]], Cell[ "BeginAnswer is used in the In and Out column directly after an \ EndQuestion or BeginEndQuestion cell style to begin the answer portion. \ Followed by Text or Input/Output etc.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["BeginAnswer"], CellMargins -> {{89, 35}, {Inherited, Inherited}}, CellFrameLabels -> {{ Cell[ "A:", CellBaseline -> "Baseline", CellSize -> {18, 24}, TextAlignment -> "Left", FontWeight -> "Bold"], Inherited}, { Inherited, Inherited}}, LineSpacing -> {1, 3}, CounterIncrements -> "Text", MenuPosition -> 1860, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["BeginAnswer", "Presentation"]], Cell[ StyleData["BeginAnswer", "Printout"], CellMargins -> {{54, 72}, {4, 16}}, CellFrameLabelMargins -> False, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Answer"], CellMargins -> {{89, 35}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, MenuPosition -> 1870, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["Answer", "Presentation"]], Cell[ StyleData["Answer", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["EditorialComment"], CellFrame -> False, CellDingbat -> "\[FilledCircle]", CellMargins -> {{36, 25}, {Inherited, Inherited}}, LineSpacing -> {1, 2}, MenuPosition -> 1900, FontColor -> RGBColor[1, 0, 0], Background -> GrayLevel[1]], Cell[ StyleData["EditorialComment", "Presentation"]], Cell[ StyleData["EditorialComment", "Printout"], CellMargins -> {{24, 80}, {Inherited, 0}}, FontFamily -> "Janson Text LT Std", FontSize -> 10, FontColor -> GrayLevel[0]]}, Closed]], Cell[ "SecondAuthor to be used after a Section cell. Author name(s) credit \ a particular portion of a notebook. Used for columns Tech Support and Tricks \ of the Trade. Usually followed by a Text cell with author affiliation/email, \ etc.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SecondAuthor"], ShowCellBracket -> False, ShowSelection -> True, CellMargins -> {{67, 24}, {Inherited, Inherited}}, CellGroupingRules -> "NormalGrouping", PageBreakBelow -> False, LineSpacing -> {1, 2}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 14, FontWeight -> "Bold"], Cell[ StyleData["SecondAuthor", "Presentation"]], Cell[ StyleData["SecondAuthor", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, LineSpacing -> {1., 0., 2.}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 12]}, Closed]], Cell[ "SectionAboutAuthor to be used as the section head for the About the \ Author portion of a notebook.", "EditorialComment"], Cell[ "TextAboutAuthor is to be used for the text in the About the Author \ portion of a notebook. The last paragraph should be author name (in style \ AboutAuthorB), affiliation and contact information (in style AboutAuthorI).\n\ \nUse \"AboutAuthorI\", \"AboutAuthorB\", and \"AboutAuthorBI\" for inline \ styles. Sets serif in Working, sans serif in Printout and Production.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["TextAboutAuthor"], CellMargins -> {{54, 24}, {2, 5}}, LineSpacing -> {1, 3}, CounterIncrements -> "Text", MenuPosition -> 1880, FontSize -> 12], Cell[ StyleData["TextAboutAuthor", "Presentation"]], Cell[ StyleData["TextAboutAuthor", "Printout"], CellMargins -> {{72, 72}, {2, -2}}, CellFrameMargins -> 4, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 1}, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 8, Background -> GrayLevel[0.899001]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SectionAboutAuthor"], CellMargins -> {{54, 25}, {10, 30}}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, CellFrameMargins -> 4, LineSpacing -> {1, 2}, MenuPosition -> 1875, FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold"], Cell[ StyleData["SectionAboutAuthor", "Presentation"]], Cell[ StyleData["SectionAboutAuthor", "Printout"], CellFrame -> False, CellMargins -> {{72, 72}, {2, 30}}, CellFrameMargins -> 4, LineSpacing -> {1., 0., 2.}, FontFamily -> "Frutiger LT Std 55 Roman", Background -> GrayLevel[0.899001]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["SectionAboutAuthorTOP"], CellMargins -> {{54, 25}, {10, 30}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> {"SectionGrouping", 40}, PageBreakBelow -> False, CellFrameMargins -> 4, LineSpacing -> {1, 2}, FontFamily -> "Helvetica", FontSize -> 12, FontWeight -> "Bold", CellTags -> "ProductionOnly"], Cell[ StyleData["SectionAboutAuthorTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["SectionAboutAuthorTOP", "Printout"], CellFrame -> False, CellMargins -> {{72, 72}, {2, 4}}, CellFrameMargins -> 4, LineSpacing -> {1., 0., 2.}, FontFamily -> "Frutiger LT Std 55 Roman", Background -> GrayLevel[0.899001], CellTags -> "ProductionOnly"]}, Closed]], Cell[ "Styles for algorithm listings, based on BulletedList, indent an \ additonal 12 points for each level, dingbat also changes", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Algorithm1"], CellDingbat -> "\[FilledSmallCircle]", CellMargins -> {{104, 24}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["Algorithm1", "Presentation"]], Cell[ StyleData["Algorithm1", "Printout"], CellMargins -> {{108, 72}, {2, Inherited}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Algorithm2"], CellDingbat -> "\[Dash]", CellMargins -> {{120, 24}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["Algorithm2", "Presentation"]], Cell[ StyleData["Algorithm2", "Printout"], CellMargins -> {{120, 72}, {2, Inherited}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Algorithm3"], CellDingbat -> "\[Star]", CellMargins -> {{132, 24}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["Algorithm3", "Presentation"]], Cell[ StyleData["Algorithm3", "Printout"], CellMargins -> {{132, 72}, {2, Inherited}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Algorithm4"], CellDingbat -> "\[CenterDot]", CellMargins -> {{144, 24}, {Inherited, Inherited}}, LineSpacing -> {1, 3}, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["Algorithm4", "Presentation"]], Cell[ StyleData["Algorithm4", "Printout"], CellMargins -> {{144, 72}, {2, Inherited}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]]}, Open]], Cell[ CellGroupData[{ Cell[ "Enunciations", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ CellGroupData[{ Cell["Theorem", "Subsubsection", MenuPosition -> 1871], Cell[ CellGroupData[{ Cell[ StyleData["Theorem"], CellMargins -> {{67, 24}, {4, 4}}, CellGroupingRules -> "GraphicsGrouping", TextJustification -> 0, LineSpacing -> {1, 3}, ParagraphIndent -> 24, CounterIncrements -> "Theorem", CounterAssignments -> {{"EnunciationItem1Numbered", 0}, { "Item1Numbered", 0}}, MenuPosition -> 1871, FontSlant -> "Italic"], Cell[ StyleData["Theorem", "Presentation"]], Cell[ StyleData["Theorem", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TheoremLabel"], StyleMenuListing -> None, FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["TheoremLabel", "Presentation"]], Cell[ StyleData["TheoremLabel", "Printout"], FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["TheoremContinuation"], CellMargins -> {{67, 24}, {4, 4}}, CellGroupingRules -> "GraphicsGrouping", TextJustification -> 0, LineSpacing -> {1, 3}, CounterIncrements -> "TheoremContinuation", MenuPosition -> 1872, FontSlant -> "Italic"], Cell[ StyleData["TheoremContinuation", "Presentation"]], Cell[ StyleData["TheoremContinuation", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell["Example", "Subsubsection", StyleMenuListing -> None], Cell[ CellGroupData[{ Cell[ StyleData["Example"], CellMargins -> {{67, 24}, {4, 4}}, CellGroupingRules -> "GraphicsGrouping", TextJustification -> 0, LineSpacing -> {1, 3}, ParagraphIndent -> 24, CounterIncrements -> "Example", CounterAssignments -> {{"EnunciationItem1Numbered", 0}, { 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"ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}, CellTags -> "ProductionOnly"], Cell[ StyleData["DefinitionBoxTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["DefinitionBoxTOP", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, Background -> None, CellTags -> "ProductionOnly"]}, Closed]], Cell[ "DefinitionBoxInList, 2 left-aligned columns, additional Left margin \ to allow for use within NumberedList.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["DefinitionBoxInList"], CellFrame -> 0.5, CellMargins -> {{103, 24}, {8, 10}}, CellHorizontalScrolling -> True, AutoIndent -> False, LineSpacing -> {1, 3}, AutoSpacing -> False, SingleLetterItalics -> False, LineIndent -> 0, FontFamily -> "Times", FontSize -> 12, Background -> GrayLevel[0.899001], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.4], { Scaled[0.6]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DefinitionBoxInList", "Presentation"]], Cell[ StyleData["DefinitionBox", "Printout"], CellMargins -> {{109, 72}, {2, 18}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, Background -> None]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["DefinitionBoxInListTOP"], CellFrame -> 0.5, CellMargins -> {{103, 24}, {8, 10}}, CellHorizontalScrolling -> True, AutoIndent -> False, LineSpacing -> {1, 3}, AutoSpacing -> False, SingleLetterItalics -> False, LineIndent -> 0, FontFamily -> "Times", FontSize -> 12, Background -> GrayLevel[0.899001], GridBoxOptions -> { GridBoxAlignment -> { "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxItemSize -> {"Columns" -> { Scaled[0.4], { Scaled[0.6]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, "RowsIndexed" -> {}}, GridBoxSpacings -> {"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.6]}, Offset[0.2]}, "RowsIndexed" -> {}}}], Cell[ StyleData["DefinitionBoxInListTOP", "Presentation"]], Cell[ StyleData["DefinitionBoxInListTOP", "Printout"], CellMargins -> {{109, 72}, {2, 4}}, LineSpacing -> {1, 0}, FontFamily -> "Janson Text LT Std", FontSize -> 10, Background -> None]}, Closed]], Cell[ "PseudoCellExpression cell style to be used when displaying \ unformatted box expressions. ", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["PseudoCellExpression"], CellFrame -> {{0, 0}, {0, 0.5}}, CellMargins -> {{67, 17}, {Inherited, Inherited}}, CellFrameMargins -> 2, LineSpacing -> {1, 3}, FontFamily -> "Courier", FontSize -> 12], Cell[ StyleData["PseudoCellExpression", "Presentation"]], Cell[ StyleData["PseudoCellExpression", "Printout"], CellMargins -> {{84, 96}, {Inherited, Inherited}}, LineSpacing -> {1, 2}, FontFamily -> "WriCMTT-Base", FontSize -> 10]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Styles for Headers and Footers", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ CellGroupData[{ Cell[ StyleData["Header"], CellMargins -> {{0, 0}, {4, 1}}, StyleMenuListing -> None, FontFamily -> "Times", FontSize -> 9, FontSlant -> "Italic"], Cell[ StyleData["Header", "Printout"], PageWidth -> PaperWidth, CellMargins -> {{72, 72}, {2, 2}}, StyleMenuListing -> None, FontFamily -> "Janson Text LT Std", FontSize -> 9]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["PageNumber"], CellMargins -> {{0, 0}, {4, 1}}, StyleMenuListing -> None, FontFamily -> "Times", FontSize -> 9, FontWeight -> "Bold"], Cell[ StyleData["PageNumber", "Printout"], PageWidth -> PaperWidth, CellMargins -> {{72, 72}, {2, 2}}, FontFamily -> "Janson Text LT Std"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Footer"], CellMargins -> {{0, 0}, {0, 4}}, StyleMenuListing -> None, FontFamily -> "Helvetica", FontSize -> 7, FontSlant -> "Oblique"], Cell[ StyleData["Footer", "Printout"], PageWidth -> PaperWidth, CellMargins -> {{72, 72}, {2, 2}}, StyleMenuListing -> None, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 6]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Frontmatter Styles", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ CellGroupData[{ Cell[ StyleData["tocentry"], CellMargins -> {{67, 24}, {Inherited, Inherited}}, AutoIndent -> True, TabFilling -> ".", LineSpacing -> {1, 2}, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["tocentry", "Presentation"]], Cell[ StyleData["tocentry", "Printout"], CellMargins -> {{84, 72}, {0, 0}}, TextJustification -> 0, Hyphenation -> False, TabFilling -> " . ", LineSpacing -> {1., 0., 2.}, ParagraphIndent -> 0, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ "LetterWriter to be used after a letter. Use inline formatting SBO \ for person's name. Use Text cell style for letter text.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["LetterWriter"], CellMargins -> {{67, 24}, {4, 4}}, LineSpacing -> {1, 2}, FontFamily -> "Times", FontSize -> 12, FontSlant -> "Italic"], Cell[ StyleData["LetterWriter", "Presentation"]], Cell[ StyleData["LetterWriter", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1., 0., 2.}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["LetterReply"], CellMargins -> {{67, 24}, {Inherited, Inherited}}, LineSpacing -> {1, 2}, FontFamily -> "Times", FontSize -> 12, FontSlant -> "Italic"], Cell[ StyleData["LetterReply", "Presentation"]], Cell[ StyleData["LetterReply", "Printout"], CellMargins -> {{72, 72}, {8, 4}}, TextJustification -> 1, Hyphenation -> True, LineSpacing -> {1., 0., 2.}, FontFamily -> "Janson Text LT Std", FontSize -> 10]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["IndexEntry"], CellMargins -> {{67, 24}, {Inherited, Inherited}}, LineSpacing -> {1, 2}, FontFamily -> "Times", FontSize -> 12], Cell[ StyleData["IndexEntry", "Presentation"]], Cell[ StyleData["IndexEntry", "Printout"], CellMargins -> {{72, 72}, {0, 0}}, AutoIndent -> True, TextJustification -> 0, Hyphenation -> False, ParagraphIndent -> -27, TabSpacings -> 1, FontFamily -> "Janson Text LT Std", FontSize -> 8]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["Classified"], CellFrame -> {{0, 0}, {0, 2}}, CellMargins -> {{67, 24}, {Inherited, Inherited}}, CellFrameMargins -> {{0, 0}, {0, 4}}, LineSpacing -> {1, 2}, FontFamily -> "Helvetica", FontSize -> 12], Cell[ StyleData["Classified", "Presentation"]], Cell[ StyleData["Classified", "Printout"], CellMargins -> {{72, 72}, {6, 12}}, TextJustification -> 0.25, Hyphenation -> True, FontFamily -> "Frutiger LT Std 55 Roman", FontSize -> 8]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Hyperlink Styles", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell["The cells below define styles used for ButtonBoxes.", "Text"], Cell[ CellGroupData[{ Cell[ StyleData["Hyperlink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[1, 0, 0], ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["Hyperlink", "Presentation"]], Cell[ StyleData["Hyperlink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ "The following styles are for linking automatically to the locally \ installed on-line help system.", "Text"], Cell[ CellGroupData[{ Cell[ StyleData["MainBookLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[1, 0, 0], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["MainBook", #]}]& )}], Cell[ StyleData["MainBookLink", "Presentation"]], Cell[ StyleData["MainBookLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AddOnsLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[1, 0, 0], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["AddOns", #]}]& )}], Cell[ StyleData["AddOnsLink", "Presentation"]], Cell[ StyleData["AddOnsLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["RefGuideLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[1, 0, 0], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["RefGuide", #]}]& )}], Cell[ StyleData["RefGuideLink", "Presentation"]], Cell[ StyleData["RefGuideLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GettingStartedLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[1, 0, 0], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["GettingStarted", #]}]& )}], Cell[ StyleData["GettingStartedLink", "Presentation"]], Cell[ StyleData["GettingStartedLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OtherInformationLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[1, 0, 0], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["OtherInformation", #]}]& )}], Cell[ StyleData["OtherInformationLink", "Presentation"]], Cell[ StyleData["OtherInformationLink", "Printout"], FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "FormatType Styles", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "These cells define styles that are mixed in with other cells. If \ the FormatType of a cell style matches the name of one of the styles defined \ below, then that style is applied along with the local cell style \ definitions. ", "Text", CellMargins -> {{24, 0}, {Inherited, Inherited}}], Cell[ CellGroupData[{ Cell[ StyleData["CellExpression"], CellMargins -> {{54, 24}, {2, 4}}, ShowCellLabel -> False, ShowSpecialCharacters -> False, AllowInlineCells -> False, Hyphenation -> False, LineSpacing -> {1, 2}, AutoItalicWords -> {}, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 12, Background -> GrayLevel[1]], Cell[ StyleData["CellExpression", "Printout"], CellMargins -> {{72, 72}, {2, 4}}, ShowCellLabel -> False, ShowSpecialCharacters -> False, AllowInlineCells -> False, Hyphenation -> False, AutoItalicWords -> {}, StyleMenuListing -> None, FontFamily -> "WriCMTT-Base", Background -> GrayLevel[1]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InputForm"], PageWidth -> WindowWidth, InputAutoReplacements -> {}, AllowInlineCells -> False, Hyphenation -> False, AutoSpacing -> False, NumberMarks -> True, AutoNumberFormatting -> False, StyleMenuListing -> None, FontFamily -> "Courier", FontProperties -> { "FontMonospaced" -> True, "FontSerifed" -> True}], Cell[ StyleData["InputForm", "Printout"], PageWidth -> PaperWidth, FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OutputForm"], StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["OutputForm", "Printout"], FontFamily -> "WriCMTT-Base", FontProperties -> { "FontMonospaced" -> True, "FontSerifed" -> True}]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["StandardForm"], InputAutoReplacements -> { "->" -> "\[Rule]", ":>" -> "\[RuleDelayed]", "<=" -> "\[LessEqual]", ">=" -> "\[GreaterEqual]", "!=" -> "\[NotEqual]", "==" -> "\[Equal]", ParentList}, "TwoByteSyntaxCharacterAutoReplacement" -> True, SingleLetterItalics -> False, StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["StandardForm", "Printout"], FontFamily -> "WriCMTT-Base", FontProperties -> { "FontMonospaced" -> True, "FontSerifed" -> True}]}, Closed]], Cell[ StyleData["TraditionalForm"], TextClipboardType -> "PlainText", InputAutoReplacements -> { "->" -> "\[Rule]", ":>" -> "\[RuleDelayed]", "<=" -> "\[LessEqual]", ">=" -> "\[GreaterEqual]", "!=" -> "\[NotEqual]", "==" -> "\[Equal]", ParentList}, ShowSyntaxStyles -> False, "TwoByteSyntaxCharacterAutoReplacement" -> True, SingleLetterItalics -> True, TraditionalFunctionNotation -> True, DelimiterMatching -> None, ZeroWidthTimes -> False, StyleMenuListing -> None], Cell[ "The style defined below is mixed in to any cell that is in an \ inline cell within another.", "Text", CellMargins -> {{24, 0}, {Inherited, Inherited}}], Cell[ StyleData["InlineCell"], TextAlignment -> Left, ScriptLevel -> 1, StyleMenuListing -> None], Cell[ StyleData["InlineCellEditing"], StyleMenuListing -> None, Background -> RGBColor[1, 0.749996, 0.8]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Inline Formatting", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "InlineInput is for code segments embedded within another cell. Sets \ as FormatType->DefaultInputFormatType.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["InlineInput"], Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, FormatType -> DefaultInputFormatType, ShowStringCharacters -> True, NumberMarks -> True, FontFamily -> "Courier"], Cell[ StyleData["InlineInput", "Presentation"]], Cell[ StyleData["InlineInput", "Printout"], FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineInputBold"], Evaluatable -> True, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, FormatType -> DefaultInputFormatType, ShowStringCharacters -> True, NumberMarks -> True, FontFamily -> "Courier", FontWeight -> "Bold"], Cell[ StyleData["InlineInputBold", "Presentation"]], Cell[ StyleData["InlineInputBold", "Printout"], FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineOutput"], Evaluatable -> False, CellGroupingRules -> "InputGrouping", CellHorizontalScrolling -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, AutoItalicWords -> {}, FormatType -> DefaultInputFormatType, ShowStringCharacters -> True, NumberMarks -> True, FontFamily -> "Courier", FontWeight -> "Plain"], Cell[ StyleData["InlineOutput", "Presentation"]], Cell[ StyleData["InlineOutput", "Printout"], FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineInputTraditionalForm"], CellHorizontalScrolling -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, FormatType -> TraditionalForm, ShowStringCharacters -> True, NumberMarks -> True, SingleLetterItalics -> True, ZeroWidthTimes -> False], Cell[ StyleData["InlineInputTraditionalForm", "Presentation"]], Cell[ StyleData["InlineInputTraditionalForm", "Printout"]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["InlineInputTraditionalFormBold"], CellHorizontalScrolling -> True, HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, FormatType -> TraditionalForm, ShowStringCharacters -> True, NumberMarks -> True, SingleLetterItalics -> True, ZeroWidthTimes -> False, FontWeight -> "Bold"], Cell[ StyleData["InlineInputTraditionalFormBold", "Presentation"]], Cell[ StyleData["InlineInputTraditionalFormBold", "Printout"]]}, Closed]], Cell[ "The following styles are for modifying individual words or letters \ in a cell exclusive of the cell style.", "EditorialComment"], Cell[ "RM used to change selection to FontWeight->Plain, FontSlant->Plain", "EditorialComment"], Cell[ StyleData["RM"], FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ "BF used to change selection to FontWeight->Bold, FontSlant->Plain", "EditorialComment"], Cell[ StyleData["BF"], FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ "IT used to change selection to FontWeight->Plain, \ FontSlant->Italic", "EditorialComment"], Cell[ StyleData["IT"], FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ "BFI used to change selection to FontWeight->Bold, \ FontSlant->Italic", "EditorialComment"], Cell[ StyleData["BFI"], FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ "TR used to change selection to normal text font (Times for \ \"Working\"; Janson Text LT Std for \"Printout\"), FontWeight->Plain, \ FontSlant->Plain", "EditorialComment", CellChangeTimes -> {3.390651499491132*^9}], Cell[ CellGroupData[{ Cell[ StyleData["TR"], FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["TR", "Printout"], FontFamily -> "Janson Text LT Std"]}, Closed]], Cell[ "TI used to change selection to normal text font, FontWeight->Plain, \ FontSlant->Italic", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["TI"], FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["TI", "Printout"], FontFamily -> "Janson Text LT Std"]}, Closed]], Cell[ "TB used to change selection to normal text font, FontWeight->Bold, \ \nFontSlant->Plain", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["TB"], FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["TB", "Printout"], FontFamily -> "Janson Text LT Std"]}, Closed]], Cell[ "TBI used to change selection to normal text font, FontWeight->Bold, \ \nFontSlant->Italic", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["TBI"], FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ StyleData["TBI", "Printout"], FontFamily -> "Janson Text LT Std"]}, Closed]], Cell[ "MR used to change selection to monospace font with \ FontWeight->Plain, \nFontSlant->Plain (Courier for \"Working\"; WriCMTT-Base \ for \"Production\").", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["MR"], HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["MR", "Printout"], FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ "MO used to change selection to monospace font with \ FontWeight->Plain, \nFontSlant->Oblique", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["MO"], HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Plain", FontSlant -> "Oblique"], Cell[ StyleData["MO", "Printout"], FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ "MB used to change selection to monospace font with \ FontWeight->Bold, \nFontSlant->Plain", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["MB"], HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["MB", "Printout"], FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ "MBO used to change selection to monospace font with \ FontWeight->Bold, \nFontSlant->Oblique", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["MBO"], HyphenationOptions -> { "HyphenationCharacter" -> "\[Continuation]"}, StyleMenuListing -> None, FontFamily -> "Courier", FontWeight -> "Bold", FontSlant -> "Oblique"], Cell[ StyleData["MBO", "Printout"], FontFamily -> "WriCMTT-Base"]}, Closed]], Cell[ "SR used to change selection to sans serif font (Helvetica for \ \"Working\"; Frutiger LT Std 55 Roman for \"Production\")", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SR"], FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["SR", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SO used to change selection to oblique sans serif font ", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SO"], FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Oblique"], Cell[ StyleData["SO", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SB used to change selection to sans serif font bold", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SB"], FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["SB", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SBO used to change selection to bold oblique sans serif font \ (Helvetica for \"Working\"; Frutiger LT Std 55 Roman for \"Production\")", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SBO"], FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Oblique"], Cell[ StyleData["SBO", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AboutAuthorR"], FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Plain"], Cell[ StyleData["AboutAuthorR", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AboutAuthorI"], FontFamily -> "Times", FontWeight -> "Plain", FontSlant -> "Italic"], Cell[ StyleData["AboutAuthorI", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AboutAuthorB"], FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Plain"], Cell[ StyleData["AboutAuthorB", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AboutAuthorBI"], FontFamily -> "Times", FontWeight -> "Bold", FontSlant -> "Italic"], Cell[ StyleData["AboutAuthorBI", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]]}, Closed]], Cell[ CellGroupData[{ Cell[ "Compatibility Styles", "Section", CellFrame -> False, CellDingbat -> None, ShowCellBracket -> True, CellMargins -> {{0, 0}, {10, 40}}, CellFrameMargins -> {{20, 4}, {8, 8}}, FontColor -> GrayLevel[1], Background -> RGBColor[0.269902, 0.558434, 0.715618]], Cell[ "Obsolete inline styles from legacy font set.", "EditorialComment"], Cell[ "SCL used to change selection to sans serif font light", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SCL"], FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Plain", FontTracking -> "Plain"], Cell[ StyleData["SCL", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SCLO used to change selection to sans serif font light oblique", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SCLO"], FontFamily -> "Helvetica", FontWeight -> "Plain", FontSlant -> "Oblique", FontTracking -> "Plain"], Cell[ StyleData["SCLO", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SCB used to change selection to sans serif font cond bold", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SCB"], FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Plain", FontTracking -> "Plain"], Cell[ StyleData["SCB", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SCBO used to change selection to sans serif font cond bold oblique", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SCBO"], FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Oblique", FontTracking -> "Plain"], Cell[ StyleData["SCBO", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SXR used to change selection to sans serif font cond extra bold", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SXR"], FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Plain", FontTracking -> "Plain"], Cell[ StyleData["SXR", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "SXO used to change selection to sans serif font cond extra bold \ oblique", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["SXO"], FontFamily -> "Helvetica", FontWeight -> "Bold", FontSlant -> "Oblique", FontTracking -> "Plain"], Cell[ StyleData["SXO", "Printout"], FontFamily -> "Frutiger LT Std 55 Roman"]}, Closed]], Cell[ "Graphics cell usually output by kernel. To be preceded by Input \ cell, followed by Output cell.", "EditorialComment"], Cell[ CellGroupData[{ Cell[ StyleData["Graphics"], CellFrame -> {{0.25, 0.25}, {0, 0}}, CellMargins -> {{67, 24}, {0, 0}}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultOutputFormatType, ImageMargins -> {{30, 0}, {0, 0}}, StyleMenuListing -> None, Background -> GrayLevel[0.949996]], Cell[ StyleData["Graphics", "Presentation"]], Cell[ StyleData["Graphics", "Printout"], CellFrame -> False, CellMargins -> {{96, 72}, {8, 10}}, CellFrameMargins -> False, ImageSize -> {200, 200}, FontSize -> 10, Background -> None]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GraphicsTOP"], CellFrame -> {{0.25, 0.25}, {0, 0}}, CellMargins -> {{67, 24}, {0, 0}}, CellBracketOptions -> {"Color" -> RGBColor[1, 0, 1]}, CellGroupingRules -> "GraphicsGrouping", CellHorizontalScrolling -> True, PageBreakWithin -> False, GeneratedCell -> True, CellAutoOverwrite -> True, ShowCellLabel -> False, CellFrameColor -> GrayLevel[0.869993], DefaultFormatType -> DefaultOutputFormatType, ImageMargins -> {{30, 0}, {0, 0}}, StyleMenuListing -> None, Background -> GrayLevel[0.949996], CellTags -> "ProductionOnly"], Cell[ StyleData["GraphicsTOP", "Presentation"], CellTags -> "ProductionOnly"], Cell[ StyleData["GraphicsTOP", "Printout"], CellFrame -> False, CellMargins -> {{96, 72}, {8, 4}}, CellFrameMargins -> False, ImageSize -> {200, 200}, FontSize -> 10, Background -> None, CellTags -> "ProductionOnly"]}, Closed]], Cell[ "GraphicsOnly cell to follow Input cell, not followed by Output \ cell. 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