<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="11" minor="0"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false"></View-Properties>
<MapleNet-Properties warnlevel="3" longdelim="true" plotoptions="" echo="1" errorcursor="false" elisiontermsthreshold="10000" elisiontermsbefore="100" errorbreak="1" prettyprint="3" prompt="&gt; " latexwidth="6.0" useclientjvm="true" ansi="false" screenheight="25" labelwidth="20" plotdevice="inline" typesetting="standard" displayprecision="-1" indentamount="4" elisiondigitsthreshold="10000" quiet="false" plotoutput="terminal" rtablesize="10" preplot="" showassumed="1" plotdriver="openviz" elisiontermsafter="100" labelling="true" postplot="" screenwidth="79" elisiondigitsbefore="100" elisiondigitsafter="100" verboseproc="1" imaginaryunit="I" ShowLabels="true"/>
<Styles><Font name="Maple Output12" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 4" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Left Justified Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="9" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Variable" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Diagnostic" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[64,128,64]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Page Number" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Italic Small" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 3" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Nonterminal" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Default" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Comment" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Small" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Inert Output" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[144,144,144]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Fixed" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 3" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Popup" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Plot Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Input" background="[255,255,255]" bold="false" executable="true" family="Times New Roman" foreground="[255,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Copyright" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Input Placeholder" background="[255,255,255]" bold="true" executable="true" family="Monospaced" foreground="[200,0,200]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="true"/>
<Font name="2D Math Bold Small" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="1" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Fixed Width" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Error" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 1" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Notes" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Help Underlined Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,128,128]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="2D Math Symbol 2" background="[255,255,255]" bold="false" executable="false" family="SymbolPi" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 5" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Text Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Bullet Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Equation Label" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Author" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Heading 2" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Plot Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="8" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Plot" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Output Labels" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="8" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Heading" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="14" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Normal" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Comment" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Maple Name" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[104,64,92]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dictionary Hyperlink" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[147,0,15]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Help Emphasized" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Italic Bold" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Menus" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="LaTeX" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Dash Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 4" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Prompt" background="[255,255,255]" bold="true" executable="false" family="Monospaced" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Underlined" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="List Item" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Help Underlined Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="true" placeholder="false"/>
<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Monospaced" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="10" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Bold" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="2D Math Italic" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/>
<Layout name="Maple Output12" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 4" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 5" alignment="left" bullet="ROMAN" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="numeric" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Text Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Bullet Item" alignment="left" bullet="dot" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Left Justified Maple Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Help" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Diagnostic" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 3" alignment="left" bullet="roman" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Maple Plot" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Normal" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Annotation Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 3" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 4" alignment="left" bullet="ALPHABETIC" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.5" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="List Item" alignment="left" bullet="indent" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Line Printed Output" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Fixed Width" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Warning" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Heading 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="4" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 2" alignment="left" bullet="alphabetic" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="-1" bulletsuffix=""/>
<Pencil-style name="Pencil 3" pen-color="[0,0,0]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 5" pen-color="[255,0,0]" pen-height="5.0" pen-width="5.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 2" pen-color="[0,0,255]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/>
<Pencil-style name="Pencil 4" pen-color="[0,0,255]" pen-height="3.0" pen-width="3.0" pen-opacity="1.0"/>
<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/>
<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/>
</Styles>
<Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/>
<Task-table>
    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
</Annotation-table>
<Task>
</Task>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font encoding="UTF-8" italic="false">Example 3.2.13  Multiple Steady States in a Catalyst Pellet - \316\267 vs. \316\246</Font></Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The non-isothermal reaction in a rectangular pellet (example 3.2.2) is again considered.  The dimensionless concentration is governed by:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">	 	                                     <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>                                                 (3.2.43)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">with the boundary conditions:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">	 	<Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> (3.2.44)</Text-field>
<Text-field style="Text" layout="Normal">and </Text-field>
<Text-field style="Text" layout="Normal">	</Text-field>
<Text-field style="Text" layout="Normal">	 	                                                            y(1)=1                                                                      (3.2.45)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">The effectiveness factor of the pellet is given by</Text-field>
<Text-field style="Text" layout="Normal">	 	<Font encoding="UTF-8">                                                      \316\267=</Font><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUYjNiUtSSNtaUdGJDYlUScmIzkzNDtGJy8lJ2l0YWxpY0dRJmZhbHNlRidGMi1JI21uR0YkNiZRIjJGJy8lJXNpemVHUSI4RicvJSxzdXBlcnNjcmlwdEdRJXRydWVGJ0YyRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRltvLyUpYmV2ZWxsZWRHRlEtRkw2I1EhRidGMg==</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2JS1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EmZmFsc2VGJ0YyRjItRiw2JS1GSjYlUSNkeEYnRk1GMi1GSjYjUSFGJ0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Znbi8lKWJldmVsbGVkR0ZP">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</Equation> (1)                                                              (3.2.46)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">For a given value of \316\246, equation (3.2.33) can be solved for the boundary conditions ((3.2.35) and (3.2.36)).  Once the numerical solution is obtained the effectiveness factor can be calculated using equation (3.2.37).  It is of interest to plot the effectiveness factor as a function of \316\246.  For this purpose, one can solve the boundary value problem for different values of \316\246 and predict the effectiveness factor.  However, since multiple steady states occur different initial guesses have to be used to capture all of the steady states.  This boundary value problem is difficult to solve because for every value of \316\246, there can be three different \316\267s and, hence, 3 different values for the derivative (</Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation>) at x = 1.  On the contrary, for every value of  <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8">(1), there is a unique value for \316\246.  Hence,   </Font><Equation executable="false" style="2D Math" input-equation="" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2JS1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EmZmFsc2VGJ0YyRjItRiw2JUYuLUZKNiVRInhGJ0ZNRjJGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGWi8lKWJldmVsbGVkR0ZP">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</Equation><Font encoding="UTF-8">(1) can be specified and \316\246 can be treated as an unknown, which can be solved as we know 3 boundary conditions (</Font><Equation executable="false" style="2D Math" input-equation="" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2JS1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EmZmFsc2VGJ0YyRjItRiw2JUYuLUZKNiVRInhGJ0ZNRjJGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGWi8lKWJldmVsbGVkR0ZP">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</Equation>(0) = 0, y(1) = 1,   <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>(1) is known).  The difficulty with this approach is that  <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8">(1) can take any value between 0 and \342\210\236.  </Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Based on the previous argument, for every value of \316\246, there corresponds to 3 different values  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8">(1) and, hence, 3 different values for y(0).  On the contrary, for every value of y(0), there is a unique value for \316\246. The advantage of setting y(0) is that y(0) can practically vary only between 0 and 1.  Now both y(0) and  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8">(0) are known and equation (3.2.43) can be solved as an initial value problem and the unknown \316\246 can be found by using the boundary condition y(1) = 1.  Since the problem is well defined with known initial conditions for y(0) and  </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Font encoding="UTF-8"> (0), stiff solvers can be used to solve equation 3.2.43.  By defining X =\316\246x, this boundary value problem can be transformed as:</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">	 	                                    <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>                                               (3.2.47)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">with the boundary conditions:</Text-field>
<Text-field style="Text" layout="Normal">	 	                                                <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>(3.2.48)</Text-field>
<Text-field style="Text" layout="Normal">and </Text-field>
<Text-field style="Text" layout="Normal">	 	                                                   <Font encoding="UTF-8">y(\316\246)=1                                                                     </Font>(3.2.49)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">The effectiveness factor of the pellet is given by</Text-field>
<Text-field style="Text" layout="Normal">	 	                                              <Font encoding="UTF-8">\316\267=</Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>(3.2.50)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">We know that for low values of \316\246, the concentration at the center y(0) is close to 1.  For high values of \316\246, y(0) approaches zero.  We take the concentration at the center as 	</Font></Text-field>
<Text-field style="Text" layout="Normal">	 	                                                y(0)=y0                                                                          (3.2.51)</Text-field>
<Text-field style="Text" layout="Normal">where y0 varies between 0 and 1.  This system of equations is similar to example 3.2.12.  The program used for example 3.2.12 is modified below to solve this example.</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The values of the parameters are substituted here:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=diff(y(X),X$2)=y(X)*exp(gamma*beta*(1-y(X))/(1+beta*(1-y(X))));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjRXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kiWEdGJC1JIiRHRig2JEYtIiIjKiZGKiIiIi1JJGV4cEc2JEYoSShfc3lzbGliR0YkNiMqKkkmZ2FtbWFHRihGM0klYmV0YUdGJEYzLCZGM0YzRiohIiJGMywmRjNGMyomRjtGM0Y8RjNGM0Y9RjM=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInlHNiI2I0kiWEdGK0YtRi0qJkYpIiIiLUkkZXhwRzYkRiVJKF9zeXNsaWJHRis2IyoqSSZnYW1tYUdGJUYvSSViZXRhR0YrRi8sJkYvRi9GKSEiIkYvLCZGL0YvKiZGN0YvRjhGL0YvRjlGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=subs(beta=0.8,gamma=20,Eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kiWEdGJC1JIiRHRig2JEYtIiIjKiZGKiIiIi1JJGV4cEc2JEYoSShfc3lzbGliR0YkNiMsJCooJCIkZyIhIiJGMywmRjNGM0YqRj1GMywmJCIjPUY9RjMqJiQiIilGPUYzRipGM0Y9Rj1GM0Yz">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInlHNiI2I0kiWEdGK0YtRi0qJkYpIiIiLUkkZXhwRzYkRiVJKF9zeXNsaWJHRis2IywkKigkIiRnIiEiIkYvLCZGL0YvRilGOUYvLCYkIiM9RjlGLyomJCIiKUY5Ri9GKUYvRjlGOUYvRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=D(y)(0)=0,y(0)=1e-6;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiI2JC8tLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJ5R0YkNiMiIiFGMC8tRi5GLyQiIiIhIic=">NiQvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieUdGKjYjIiIhRi4vLUYsRi0kIiIiISIn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,IC},{y(X)},type=numeric,abserr=1e-10,stiff=true,stop_cond=[y(X)-1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g1:=sol(1000);</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of .20038679, stop condition #1 violated</Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZzFHNiI3JS9JIlhHRiQkIjNEc1RranonUSsjISM9Ly1JInlHRiQ2I0YnJCIiIiIiIS8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkRixGJyQiM2lJKlxmPysmZT4hIzs=">NyUvSSJYRzYiJCIzRHNUa2p6J1ErIyEjPS8tSSJ5R0YlNiNGJCQiIiIiIiEvLUklZGlmZkclKnByb3RlY3RlZEc2JEYqRiQkIjNpSSpcZj8rJmU+ISM7</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Phi1:=rhs(g1[1]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklUGhpMUc2IiQiM0RzVGtqeidRKyMhIz0=">JCIzRHNUa2p6J1ErIyEjPQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dydX1:=rhs(g1[3]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZHlkWDFHNiIkIjNpSSpcZj8rJmU+ISM7">JCIzaUkqXGY/KyZlPiEjOw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eta1:=dydX1/Phi1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklZXRhMUc2IiQiK2whKmZ0KCohIik=">JCIrbCEqZnQoKiEiKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[X,y(X)],0..2,thickness=4,title=&quot;Figure Exp. 3.2.25.&quot;,axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of .20038680, stop condition #1 violated</Text-field>
</Output>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">_Env_dsolve_nowarnstop := true;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkk3X0Vudl9kc29sdmVfbm93YXJuc3RvcEc2IkkldHJ1ZUclKnByb3RlY3RlZEc=">SSV0cnVlRyUqcHJvdGVjdGVkRw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Initial guesses ranging from 1e - 10 to 0.9996 are provided for y(0):</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=[1e-10,1e-9,1e-8,1e-7,1e-6,1e-5,1e-4,1e-3,1e-2,5e-2,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,0.7,0.75,0.8,0.825,0.85,0.875,0.9,0.91,0.92,0.93,0.94,0.95,0.955,0.96,0.965,0.968,0.97,0.975,0.98,0.99,0.995,0.996,0.997,0.998,0.999,0.9995,0.9996];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiI3UyQiIiIhIzUkRichIiokRichIikkRichIigkRichIickRichIiYkRichIiUkRichIiQkRichIiMkIiImRjgkRichIiIkIiM6RjgkIiIjRjwkIiNERjgkIiIkRjwkIiNORjgkIiIlRjwkIiNYRjgkRjpGPCQiI2JGOCQiIidGPCQiI2xGOCQiIihGPCQiI3ZGOCQiIilGPCQiJEQpRjYkIiMmKUY4JCIkdilGNiQiIipGPCQiIyIqRjgkIiMjKkY4JCIjJCpGOCQiIyUqRjgkIiMmKkY4JCIkYipGNiQiIycqRjgkIiRsKkY2JCIkbypGNiQiIygqRjgkIiR2KkY2JCIjKSpGOCQiIyoqRjgkIiQmKipGNiQiJCcqKkY2JCIkKCoqRjYkIiQpKipGNiQiJCoqKkY2JCIlJioqKkY0JCIlJyoqKkY0">N1MkIiIiISM1JEYkISIqJEYkISIpJEYkISIoJEYkISInJEYkISImJEYkISIlJEYkISIkJEYkISIjJCIiJkY1JEYkISIiJCIjOkY1JCIiI0Y5JCIjREY1JCIiJEY5JCIjTkY1JCIiJUY5JCIjWEY1JEY3RjkkIiNiRjUkIiInRjkkIiNsRjUkIiIoRjkkIiN2RjUkIiIpRjkkIiREKUYzJCIjJilGNSQiJHYpRjMkIiIqRjkkIiMiKkY1JCIjIypGNSQiIyQqRjUkIiMlKkY1JCIjJipGNSQiJGIqRjMkIiMnKkY1JCIkbCpGMyQiJG8qRjMkIiMoKkY1JCIkdipGMyQiIykqRjUkIiMqKkY1JCIkJioqRjMkIiQnKipGMyQiJCgqKkYzJCIkKSoqRjMkIiQqKipGMyQiJSYqKipGMSQiJScqKipGMQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">M:=nops(Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTUc2IiIjXA==">IiNc</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to M do Sol[i]:=dsolve({eq,D(y)(0)=0,y(0)=Y0[i]},{y(X)},type=numeric,stiff=true,abserr=1e-12,stop_cond=[y(X)-1]);;od:</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to M do g[i]:=Sol[i](100000):od:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to M do Phi[i]:=rhs(g[i][1]);od:</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to M do dydX[i]:=rhs(g[i][3]);od:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to M do eta[i]:=dydX[i]/Phi[i];od:</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">loglogplot([seq([Phi[i],eta[i]],i=1..M)],axes=boxed,title=&quot;Figure Exp. 3.2.26.&quot;,thickness=4,labels=[phi,eta],color=green);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">NiwtJSdDVVJWRVNHNiM3UzckJCIyJiopKnkvVChcJjMkISM8JCIrL29WWmohIik3JCQiMkReKFwjNCozOkchIzwkIitLOzpkcCEiKTckJCIxPTVtej1vV0QhIzskIiskelZrcCghIik3JCQiMicpWztQI1tGdUEhIzwkIisiKmZgNicpISIpNyQkIjJqM087JXonUSsjISM8JCIrKkgpZnQoKiEiKTckJCIyWWZtc2lpTXQiISM8JCIrInA+KUg2ISIoNyQkIjEpXDouMXRJWSIhIzskIitWMWlROCEiKDckJCIyPU0rMyhwJUc+IiEjPCQiKi1iPWsiISInNyQkIjEieWJeIkckcEMqISM8JCIrMj8xO0AhIig3JCQiMU4jWyZwIlwxXyghIzwkIisya1teRCEiKDckJCIxJFsuMWtjcisoISM8JCIrZjN0KWYjISIoNyQkIjEmPktHMV4sInAhIzwkIisxUS1VQyEiKDckJCIxak8nUiVbJUgtKCEjPCQiKzBOJFI9IyEiKDckJCIxLHZcNEBjJkcoISM8JCIrUV1VIik9ISIoNyQkIjFFZU8kXFAjeXchIzwkIit3Oic0ZCIhIig3JCQiMTxQdyF5LyUpPikhIzwkIitGRSFlRiIhIig3JCQiMXIpSC0iM09gKSkhIzwkIitvXnc0NSEiKDckJCIxKj1YMll0dWwqISM8JCIxLCsrYWokenooISM5NyQkIjI6cVIjcEw0ajUhIzwkIiojUkp6ZSEiKDckJCIyZG9SOkwiKSl6NiEjPCQiK1JXKClHViEiKTckJCIyb21UXSZmJSo9OCEjPCQiKzFsejdKISIpNyQkIjFlVHJGLzMkWyIhIzskIipZJilmPSMhIig3JCQiMlUiWztDOj11OyEjPCQiK3lRRypcIiEiKTckJCIyTXEhPSIpXEkiKj0hIzwkIitsJFxYKyIhIik3JCQiMGxZdCRmP0VAISM6JCIrRihvJXpsISIqNyQkIjJVLGMmKjN0TEMjISM8JCIrMmRbIkcmISIqNyQkIjAmKXluLzVFTiMhIzokIit1dnU8VSEiKjckJCIyTW00SXhfS1cjISM8JCIrWUklPU4kISIqNyQkIjFQKSk0MzJLKFwjISM7JCIqKWZmXkUhIik3JCQiMVBST2QoPUJdIyEjOyQiKyYpKVw5VCMhIio3JCQiMkV6THUqM3AkXCMhIzwkIitIK2siPiMhIio3JCQiMVhsdExGXW5DISM7JCIqPk4xKj4hIik3JCQiMCRSSyRSViU9QyEjOiQiK1ZoKnAhPSEiKjckJCIya0E2KHlWMlJCISM8JCIrQ0FQUjshIio3JCQiMiZbRXJzR3olRyMhIzwkIitGIW82YyIhIio3JCQiMm0yNj5pMyU9QSEjPCQiKyl5KVwnWyIhIio3JCQiMi8rXic9TF1QQCEjPCQiK2wtQTo5ISIqNyQkIjF3QU9pUnAhMyMhIzskIitVQy11OCEiKjckJCIxSEsyInlfKVE/ISM7JCIrRz4+WjghIio3JCQiMmMmKj5WJD0neiI+ISM8JCIrKSl5RiNHIiEiKjckJCIydy8lcF9jO288ISM8JCIrL3RNPzchIio3JCQiMS8oKVtAQDhIOCEjOyQiK1FlJFw1IiEiKjckJCIxPCU9XyVRViRwKiEjPCQiK2JjQF41ISIqNyQkIjE7MyM+P3NTcykhIzwkIitfYnhTNSEiKjckJCIxeS0/KGYnUi13ISM8JCIrR1pWSTUhIio3JCQiMWQ5XXV1NVlpISM8JCIqYyM+PzUhIik3JCQiMiZ6Xl9OeEhXVyEjPSQiK2B4LzU1ISIqNyQkIjImKT51KSkqXFRfSiEjPSQiK1I/LDA1ISIqNyQkIjFHYGciPXc4I0chIzwkIittdSsvNSEiKi0mJSZfQVhJU0c2IyIiIjYjLSUmX01PREVHNiMiIiItJiUmX0FYSVNHNiMiIiM2Iy0lJl9NT0RFRzYjIiIiLSUrQVhFU0xBQkVMU0c2Jy1JI21pRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNjVRKSZ2YXJwaGk7NiIvJSdmYW1pbHlHUSE2Ii8lJXNpemVHUSMxMDYiLyUlYm9sZEdRJmZhbHNlNiIvJSdpdGFsaWNHUSZmYWxzZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ25vcm1hbDYiLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEkZXRhNiIvJSdmYW1pbHlHUSE2Ii8lJXNpemVHUSMxMDYiLyUlYm9sZEdRJmZhbHNlNiIvJSdpdGFsaWNHUSZmYWxzZTYiLyUqdW5kZXJsaW5lR1EmZmFsc2U2Ii8lKnN1YnNjcmlwdEdRJmZhbHNlNiIvJSxzdXBlcnNjcmlwdEdRJmZhbHNlNiIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXTYiLyUrYmFja2dyb3VuZEdRLlsyNTUsMjU1LDI1NV02Ii8lJ29wYXF1ZUdRJmZhbHNlNiIvJStleGVjdXRhYmxlR1EmZmFsc2U2Ii8lKXJlYWRvbmx5R1EmZmFsc2U2Ii8lKWNvbXBvc2VkR1EmZmFsc2U2Ii8lKmNvbnZlcnRlZEdRJmZhbHNlNiIvJStpbXNlbGVjdGVkR1EmZmFsc2U2Ii8lLHBsYWNlaG9sZGVyR1EmZmFsc2U2Ii8lNnNlbGVjdGlvbi1wbGFjZWhvbGRlckdRJmZhbHNlNiIvJSxtYXRodmFyaWFudEdRJ25vcm1hbDYiLSUlRk9OVEc2JSUhRyUhRyIjNSUrSE9SSVpPTlRBTEclK0hPUklaT05UQUxHLSUmVElUTEVHNiQtJSlfVFlQRVNFVEc2I1E0RmlndXJlfkV4cC5+My4yLjI2LjYiLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIzUhIiIkIiIhISIiLSUqVEhJQ0tORVNTRzYjIiIlLSUqQVhFU1NUWUxFRzYjJSRCT1hHLSUoU0NBTElOR0c2IyUuVU5DT05TVFJBSU5FREctJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiQ/JyEiIi0lKUJPVU5EU19ZRzYjJCIkSSMhIiItJS1CT1VORFNfV0lEVEhHNiMkIiUhSCQhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlNUIhIiItJSlDSElMRFJFTkc2Ig==</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">This plot captures the multiple steady state part.  However, to predict the effectiveness factor at higher values of \316\246, we choose initial values ranging from 1e - 40 to 1e - 10.  For these low values, one has to perform highly accurate simulations.  For this purpose, absolute error (abserr) is set to 1e - 41 and the relative error (relerr) is set to 1e - 12.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=loglogplot([seq([Phi[i],eta[i]],i=1..M)],axes=boxed,thickness=4,labels=[phi,eta],color=red):</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y00:=[1e-40,1e-35,1e-30,1e-25,1e-20,1e-15,1e-10];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkWTAwRzYiNykkIiIiISNTJEYnISNOJEYnISNJJEYnISNEJEYnISM/JEYnISM6JEYnISM1">NykkIiIiISNTJEYkISNOJEYkISNJJEYkISNEJEYkISM/JEYkISM6JEYkISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">MM:=nops(Y00);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjTU1HNiIiIig=">IiIo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to MM do Sol0[i]:=dsolve({eq,D(y)(0)=0,y(0)=Y00[i]},{y(X)},type=numeric,stiff=true,maxfun=1000000,abserr=1e-41,relerr=1e-12,stop_cond=[y(X)-1]);od:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to MM do g[i]:=Sol0[i](100000):od:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to MM do Phi1[i]:=rhs(g[i][1]);od:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to MM do dydX1[i]:=rhs(g[i][3]);od:</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to MM do eta1[i]:=dydX1[i]/Phi1[i];od:</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=loglogplot([seq([Phi1[i],eta1[i]],i=1..MM)],axes=boxed,title=&quot;Figure Exp. 3.2.27.&quot;,thickness=4,labels=[phi,eta]):</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2});</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">[encoded data, 4112 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The total time to predict this curve is 25 seconds in a 1.5 GHz processor.  Simulating this curve by solving the problem as a boundary value problem will be time consuming.  Next, \316\267 vs. \316\246 curve for a second order reaction is obtained by just changing the governing equation as:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>