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<Text-field style="Text" layout="Normal">Example 7.7 Heat Conduction in a slab with Nonhomogeneous Boundary Conditions</Text-field>
</Input>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(u(x,t),t)=diff(u(x,t),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLUYnNiRGKi1JIiRHRig2JEYtIiIj">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLC1GJDYkLUYkNiRGJ0YrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhRio=">Ly1JInVHNiI2JEkieEdGJSIiIUYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,t)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLy1JInVHRiQ2JEkieEdGJEkidEdGJCIiIQ==">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,t)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLy1JInVHRiQ2JEkieEdGJEkidEdGJCIiIg==">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=eval(subs(u(x,t)=g(x,t)+w(x),eq));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXExRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJnR0YkNiRJInhHRiRJInRHRiRGLiwmLUYnNiRGKi1JIiRHRig2JEYtIiIjIiIiLUYnNiQtSSJ3R0YkNiNGLUYyRjY=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJnRzYiNiRJInhHRilJInRHRilGLCwmLUYkNiQtRiQ2JEYnRitGKyIiIi1GJDYkLUYkNiQtSSJ3R0YpNiNGK0YrRitGMg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqw:=diff(w(x),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXF3RzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIndHRiQ2I0kieEdGJC1JIiRHRic2JEYsIiIj">LUklZGlmZkclKnByb3RlY3RlZEc2JC1GIzYkLUkid0c2IjYjSSJ4R0YqRixGLA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqg:=diff(g(x,t),t)=diff(g(x,t),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFnRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJnR0YkNiRJInhHRiRJInRHRiRGLi1GJzYkRiotSSIkR0YoNiRGLSIiIw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJnRzYiNiRJInhHRilJInRHRilGLC1GJDYkLUYkNiRGJ0YrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1w:=w(x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklYmMxd0c2Ii8tSSJ3R0YkNiNJInhHRiQiIiE=">Ly1JIndHNiI2I0kieEdGJSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2w:=w(x)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklYmMyd0c2Ii8tSSJ3R0YkNiNJInhHRiQiIiI=">Ly1JIndHNiI2I0kieEdGJSIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">w(x):=rhs(dsolve({eqw,w(0)=0,w(1)=1},w(x)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIndHNiI2I0kieEdGJUYn">SSJ4RzYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=subs(g(x,t)=X(x)*T(t),eqg):</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=expand(Eq/X(x)/T(t)):</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_T:=lhs(Eq)=-lambda^2:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T(t):=rhs(dsolve({Eq_T,T(0)=T0},T(t))):</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_X:=rhs(Eq)=-lambda^2:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_X:=expand(Eq_X*X(x)):</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve({Eq_X},X(x)):</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X(x):=c[1]*sin(lambda*x)+c[2]*cos(lambda*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIlhHNiI2I0kieEdGJSwmKiYmSSJjR0YlNiMiIiJGLS1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiZJJ2xhbWJkYUdGJUYtRidGLUYtRi0qJiZGKzYjIiIjRi0tSSRjb3NHRjBGM0YtRi0=">LCYqJiZJImNHNiI2IyIiIkYoLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMqJkknbGFtYmRhR0YmRihJInhHRiZGKEYoRigqJiZGJTYjIiIjRigtSSRjb3NHRitGLkYoRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Bc1:=X(x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkQmMxRzYiLywmKiYmSSJjR0YkNiMiIiJGKy1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjKiZJJ2xhbWJkYUdGJEYrSSJ4R0YkRitGK0YrKiYmRik2IyIiI0YrLUkkY29zR0YuRjFGK0YrIiIh">LywmKiYmSSJjRzYiNiMiIiJGKS1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKiZJJ2xhbWJkYUdGJ0YpSSJ4R0YnRilGKUYpKiYmRiY2IyIiI0YpLUkkY29zR0YsRi9GKUYpIiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Bc2:=X(x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkQmMyRzYiLywmKiYmSSJjR0YkNiMiIiJGKy1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjKiZJJ2xhbWJkYUdGJEYrSSJ4R0YkRitGK0YrKiYmRik2IyIiI0YrLUkkY29zR0YuRjFGK0YrIiIh">LywmKiYmSSJjRzYiNiMiIiJGKS1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKiZJJ2xhbWJkYUdGJ0YpSSJ4R0YnRilGKUYpKiYmRiY2IyIiI0YpLUkkY29zR0YsRi9GKUYpIiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Bc1:=eval(subs(x=0,Bc1)):</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">c[2]:=solve(Eq_Bc1,c[2]):</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Bc2:=eval(subs(x=1,Bc2)):</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Eig:=sin(lambda)=0:</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Eq_Eig,lambda):</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">_EnvAllSolutions := true:</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Eq_Eig,lambda):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">G1:=eval(X(x)*T(t)):</Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Gn:=subs(c[1]=A[n]/T0,lambda=lambda[n],G1):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g(x,t):=Sum(Gn,n=1..infinity):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">g(x,t):=subs(lambda[n]=n*Pi,g(x,t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JImdHNiI2JEkieEdGJUkidEdGJS1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKigmSSJBR0YlNiNJIm5HRiUiIiItSSRzaW5HRis2IyooRjNGNEkjUGlHRixGNEYnRjRGNC1JJGV4cEdGKzYjLCQqKClGMyIiI0Y0KUY5RkBGNEYoRjQhIiJGNC9GMztGNEkpaW5maW5pdHlHRiw=">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqKCZJIkFHRic2I0kibkdGJyIiIi1JJHNpbkdGJDYjKihGLUYuSSNQaUdGJUYuSSJ4R0YnRi5GLi1JJGV4cEdGJDYjLCQqKEYtIiIjRjNGOkkidEdGJ0YuISIiRi4vRi07Ri5JKWluZmluaXR5R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,t):=g(x,t)+w(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JInVHNiI2JEkieEdGJUkidEdGJSwmLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqKCZJIkFHRiU2I0kibkdGJSIiIi1JJHNpbkdGLDYjKihGNEY1SSNQaUdGLUY1RidGNUY1LUkkZXhwR0YsNiMsJCooKUY0IiIjRjUpRjpGQUY1RihGNSEiIkY1L0Y0O0Y1SSlpbmZpbml0eUdGLUY1RidGNQ==">LCYtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCooJkkiQUdGKDYjSSJuR0YoIiIiLUkkc2luR0YlNiMqKEYuRi9JI1BpR0YmRi9JInhHRihGL0YvLUkkZXhwR0YlNiMsJCooRi4iIiNGNEY7SSJ0R0YoRi8hIiJGLy9GLjtGL0kpaW5maW5pdHlHRiZGL0Y1Ri8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_An:=eval(subs(t=0,u(x,t)))=rhs(IC);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZXFfQW5HNiIvLCYtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JComJkkiQUdGJDYjSSJuR0YkIiIiLUkkc2luR0YpNiMqKEYxRjJJI1BpR0YqRjJJInhHRiRGMkYyL0YxO0YySSlpbmZpbml0eUdGKkYyRjhGMiIiIQ==">LywmLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqJiZJIkFHRik2I0kibkdGKSIiIi1JJHNpbkdGJjYjKihGL0YwSSNQaUdGJ0YwSSJ4R0YpRjBGMC9GLztGMEkpaW5maW5pdHlHRidGMEY2RjAiIiE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">phi[n]:=sin(n*Pi*x):</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">r(x):=1:</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=int(phi[n]^2*r(x),x=0..1):</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I2:=int((rhs(IC)-w(x))*phi[n]*r(x),x=0..1):</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:={sin(n*Pi)=0}:</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=subs(vars,I1):</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I2:=subs(vars,I2):</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=I2/I1:</Text-field>
</Input>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(A[n]):</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,t):=eval(u(x,t)):</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,t):=subs(infinity=N,u(x,t)):</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ua:=subs(N=20,u(x,t)):</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">uu:=piecewise(t=0,rhs(IC),t&gt;0,ua);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjdXVHNiItSSpQSUVDRVdJU0VHRiQ2JDckIiIhL0kidEdGJEYpNyQsJi1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkKigtRiY2JDckSSp1bmRlZmluZWRHRjEvSSJuR0YkRik3JCwkKioiIiMiIiJGOiEiIkkjUGlHRjFGQC1JJGNvc0dGMDYjKiZGOkY/RkFGP0Y/Rj9JKm90aGVyd2lzZUdGJEY/LUkkc2luR0YwNiMqKEY6Rj9GQUY/SSJ4R0YkRj9GPy1JJGV4cEdGMDYjLCQqKClGOkY+Rj8pRkFGPkY/RitGP0ZARj8vRjo7Rj8iIz9GP0ZLRj8yRilGKw==">LUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmL0kidEc2IiIiIUYpMkYpRicsJi1JJFN1bUc2JEYkSShfc3lzbGliR0YoNiQqKC1GIzYlL0kibkdGKEYpSSp1bmRlZmluZWRHRiQsJCooRjUhIiJJI1BpR0YkRjktSSRjb3NHRi42IyomRjUiIiJGOkY/Rj8iIiNGPy1JJHNpbkdGLjYjKihGNUY/RjpGP0kieEdGKEY/Rj8tSSRleHBHRi42IywkKihGNUZARjpGQEYnRj9GOUY/L0Y1O0Y/IiM/Rj9GRUY/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(uu,x=1..0,t=0.5..0,axes=boxed,title=&quot;Figure Exp. 7.17.&quot;,labels=[x,t,&quot;u&quot;],orientation=[-135,60]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 13692 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([subs(t=0,uu),subs(t=0.05,uu),subs(t=0.1,uu),subs(t=0.2,uu),subs(t=0.5,uu)],x=0..1,axes=boxed,title=&quot;Figure Exp. 7.18.&quot;,thickness=5,labels=[x,&quot;u&quot;],legend=[&quot;t=0&quot;,&quot;t=0.05&quot;,&quot;t=0.1&quot;,&quot;t=0.2&quot;,&quot;t=0.5&quot;]);</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="true">[encoded data, 14952 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
</Input>
</Group>
</Worksheet>