<?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="false"/>
<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="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 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="2D Math Italic Small201" 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="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="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="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 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="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="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="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="2D Math Italic Small201206" 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="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="0.0" 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="none" firstindent="0" leftmargin="144" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Ordered List 1" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" 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="none" 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="0.0" 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="none" firstindent="0" leftmargin="72" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" 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="none" 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="none" firstindent="0" leftmargin="108" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Output" 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="List Item" alignment="left" bullet="none" 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="none" firstindent="0" leftmargin="36" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" 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="L22" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 3.2.12 Diffusion with a Second Order Reaction</Font></Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Diffusion with a second order reaction (example 3.2.1) is considered here again.  The dimensionless concentration is governed by:</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><Font encoding="UTF-8">=\316\246</Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2I1EhRictRiM2JC1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2I1EhRictRiM2JC1JI21uR0YkNiRRIjJGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOA==</Equation><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjJGJ0Y1RjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjJGJ0Y1RjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjU=</Equation>                                                            (3.2.34)</Text-field>
<Text-field style="Text" layout="Normal">with the boundary condition </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>(0)=0<Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZeby1JI21vR0YkNi1RIn5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGQ0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRi8=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZeby1JI21vR0YkNi1RIn5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGQ0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRi8=</Equation>(3.2.35)</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">and </Text-field>
<Text-field style="Text" layout="Normal">	 	                                                     y(1)=1                                                                     (3.2.36)</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="Text" 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> (1)                                                             (3.2.37)</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">For a given value of \316\246, equation (3.2.34) 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.  Alternatively, this problem can be solved as an initial value problem.  For convenience, the transformation X = \316\246x is introduced.  The boundary value problem changes as:	</Font></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>= y<Font superscript="true">2</Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZeby1JI21vR0YkNi1RIn5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGQ0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRi8=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZeby1JI21vR0YkNi1RIn5GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGQ0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRitGK0YrRi8=</Equation>(3.2.38)</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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">LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JJW1yb3dHRiQ2JS1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EmZmFsc2VGJ0YyRjItRiw2JUYuLUklbXN1cEdGJDYlLUYsNiQtRlM2JS1GSjYlUSJYRidGTUYyLUYsNiQtRko2I1EhRidGMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMkZmbkZbb0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zjby8lKWJldmVsbGVkR0ZP</Equation> (0)=0                                                            (3.2.39)</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>(3.2.40)</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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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21vR0YkNi1RMCZEaWZmZXJlbnRpYWxEO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGLUYjNiQtSSNtaUdGJDYlUScmIzkzNDtGJy8lJ2l0YWxpY0dRJmZhbHNlRidGMkYyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZXLyUpYmV2ZWxsZWRHRlEtRkw2I1EhRidGMg==</Equation><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>                                                                (3.2.41)</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                                                                   (3.2.42)</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">where y0 varies between 0 and 1. Next equation (3.2.38) is solved with two initial conditions given by equations (3.2.39) and (3.2.42).  This is solved as an initial value problem.  The stop condition illustrated in chapter 2.2.5 is used to find the value of X for which equation (3.2.40) is satisfied.  That is, equation (3.2.38) is integrated with the initial conditions given by equation (3.2.39) and (3.2.40) until y(X) becomes 1.  The corresponding value of X gives the value for \316\246.  Once \316\246 is found, the effectiveness factor is found using equation (3.2.41).  This procedure is illustrated in the following Maple program.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L24" 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="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(y(X),X$2)=y(X)^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInlHRiQ2I0kiWEdGJC1JIiRHRig2JEYtIiIjKiQpRipGMSIiIg==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInlHNiI2I0kiWEdGK0YtRi0qJClGKSIiIyIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial conditions for y and its derivative are provided:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=D(y)(0)=0,y(0)=0.1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiI2JC8tLUkiREc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJ5R0YkNiMiIiFGMC8tRi5GLyQiIiIhIiI=">NiQvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieUdGKjYjIiIhRi4vLUYsRi0kIiIiISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,D(y)(0)=0,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="L26" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution is evaluated for large values of X.  The solution stops at 6.95.</Text-field>
</Input>
</Group>
<Group labelreference="L7" 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 6.9564589, stop condition #1 violated</Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZzFHNiI3JS9JIlhHRiQkIjNzeUZlKSoqZWsmcCEjPC8tSSJ5R0YkNiNGJyQiMikpKioqKioqKioqKioqKioqRiovLUklZGlmZkclKnByb3RlY3RlZEc2JEYsRickIjMtJz0nKltcejM7KSEjPQ==">NyUvSSJYRzYiJCIzc3lGZSkqKmVrJnAhIzwvLUkieUdGJTYjRiQkIjIpKSoqKioqKioqKioqKioqKkYoLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiRGKkYkJCIzLSc9JypbXHozOykhIz0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The value for \316\246 is obtained as:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L8" 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="PkklUGhpMUc2IiQiM3N5RmUpKiplayZwISM8">JCIzc3lGZSkqKmVrJnAhIzw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The derivative at X = \316\246 is given by:</Font></Text-field>
</Input>
</Group>
<Group labelreference="L9" 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="PkkmZHlkWDFHNiIkIjMtJz0nKltcejM7KSEjPQ==">JCIzLSc9JypbXHozOykhIz0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The effectiveness factor is calculated as:</Text-field>
</Input>
</Group>
<Group labelreference="L10" 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="PkklZXRhMUc2IiQiKzNxOHQ2ISM1">JCIrM3E4dDYhIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained is plotted as:</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[X,y(X)],0..10000,thickness=4,axes=boxed,title=&quot;Figure Exp. 2.2.23.&quot;);</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, cannot evaluate the solution further right of 6.9564590, stop condition #1 violated</Text-field>
</Output>
<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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We can ask Maple to not print the warning about the violation of stop conditions using the following command:</Text-field>
</Input>
</Group>
<Group labelreference="L12" 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="L32" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Different initial guesses for y0 ranging from 1e - 4 to 0.999 are chosen.</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=[1e-4,1e-3,1e-2,seq(i/40.,i=1..39),0.999];</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="L14" 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="PkkiTUc2IiIjVg==">IiNW</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">A 'for loop' is written to find the corresponding values of \316\246 and effectiveness factors.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L15" 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="L16" 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="L17" 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="L18" 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="L19" 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="L34" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">A loglogplot is made:</Text-field>
</Input>
</Group>
<Group labelreference="L20" 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. 3.2.24.&quot;,thickness=4,labels=[Phi,eta],color=red);</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, 4172 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">We observe that the effectiveness factor remains close to 1 until \316\246=1 and then decreases with \316\246.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>