{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Map le Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 14 "limitsixzw.mws" }}} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 143 "The special case v(theta)=1 , diff(Q[infinify](the ta),theta)=0 for consistency and diff(v(theta),theta) = 0 diff(Q[infin ity](theta),theta$2)=0" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 64 "No tation diff(v(thtea),theta$n)=v[n] diff(Q(thtea),theta$n)=Q[n]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 67 "The following substitutions for P(t,theta) and Q(t,theta) are made:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 465 "P(t,theta) = P[infinity] (theta)-v(theta)*ln(t)+1/4*exp(P[infinity](theta))^2*diff(Q[infinity]( theta),`$`(theta,2))^2*t^2*ln(t)^2+V[1](theta)*t^2+(exp(2*P[infinity]( theta))*psi[Q](theta)*diff(Q[infinity](theta),`$`(theta,2))-1/4*diff(Q [infinity](theta),`$`(theta,2))^2-1/4*diff(v(theta),`$`(theta,2)))*t^2 *ln(t)+t^4*Z(t,theta),Q(t,theta) = Q[infinity](theta)+psi[Q](theta)*t^ (2*v(theta))+1/2*diff(Q[infinity](theta),`$`(theta,2))*t^(2*v(theta))* ln(t)+t^4*W(t,theta);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6$/-%\"PG6$%\"t G%&thetaG,.-&F%6#%)infinityG6#F(\"\"\"*&-%\"vGF.F/-%#lnG6#F'F/!\"\"*&# F/\"\"%F/**)-%$expG6#F*\"\"#F/)-%%diffG6$-&%\"QGF,F.-%\"$G6$F(F?F?F/)F 'F?F/)F3F?F/F/F/*&-&%\"VG6#F/F.F/FJF/F/*(,(*(-F=6#,$*&F?F/F*F/F/F/-&%$ psiG6#FFF.F/FAF/F/*&#F/F9F/*$F@F/F/F6*&#F/F9F/-FB6$F1FGF/F6F/FJF/F3F/F /*&)F'F9F/-%\"ZGF&F/F//-FFF&,*FDF/*&FXF/)F',$*&F?F/F1F/F/F/F/*&#F/F?F/ *(FAF/FeoF/F3F/F/F/*&F^oF/-%\"WGF&F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 387 "V[1](theta):=(exp(P[infinity](theta))^2*diff(Q[infin ity](theta),`$`(theta,2))^2/4)*(3/2)-exp(2*P[infinity](theta))*psi[Q]( theta)*diff(Q[infinity](theta),`$`(theta,2))-1/4*diff(Q[infinity](thet a),`$`(theta,2))^2-1/4*diff(v(theta),`$`(theta,2))+exp(P[infinity](the ta))^2*(psi[Q](theta)+diff(Q[infinity](theta),`$`(theta,2))/4)^2+(diff (P[infinity](theta),theta$2)+diff(v(theta),theta$2))/4;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>-&%\"VG6#\"\"\"6#%&thetaG,,*&#\"\"$\"\")F(*&)-% $expG6#-&%\"PG6#%)infinityGF)\"\"#F()-%%diffG6$-&%\"QGF8F)-%\"$G6$F*F: F:F(F(F(*(-F36#,$*&F:F(F5F(F(F(-&%$psiG6#FAF)F(F " 0 "" {MPLTEXT 1 0 9 "latex(%);" }}{PARA 6 "" 1 "" {TEXT -1 68 "3/8\\, \\left( \{e^\{P_\{\{\\infty \}\} \\left( \\theta \+ \\right) \}\} \\right) ^\{2\}" }}{PARA 6 "" 1 "" {TEXT -1 65 " \\left( \{\\frac \{d^\{2\}\}\{d\{\\theta\}^\{2\}\}\}Q_\{\{\\infty \}\} \\left ( \\theta" }}{PARA 6 "" 1 "" {TEXT -1 68 " \\right) \\right) ^\{2\}- \{e^\{2\\,P_\{\{\\infty \}\} \\left( \\theta \\right) \}\}" }}{PARA 6 "" 1 "" {TEXT -1 67 "\\psi_\{\{Q\}\} \\left( \\theta \\right) \{\\frac \{d^\{2\}\}\{d\{\\theta\}^\{2\}\}\}Q_\{\{" }}{PARA 6 "" 1 "" {TEXT -1 70 "\\infty \}\} \\left( \\theta \\right) -1/4\\, \\left( \{\\frac \+ \{d^\{2\}\}\{d\{\\theta\}" }}{PARA 6 "" 1 "" {TEXT -1 70 "^\{2\}\}\}Q_ \{\{\\infty \}\} \\left( \\theta \\right) \\right) ^\{2\}+ \\left( \{ e^\{P_" }}{PARA 6 "" 1 "" {TEXT -1 67 "\{\{\\infty \}\} \\left( \\thet a \\right) \}\} \\right) ^\{2\} \\left( \\psi_\{\{Q\}\}" }}{PARA 6 "" 1 "" {TEXT -1 70 " \\left( \\theta \\right) +1/4\\,\{\\frac \{d^\{2\} \}\{d\{\\theta\}^\{2\}\}\}Q_\{\{\\infty " }}{PARA 6 "" 1 "" {TEXT -1 70 "\}\} \\left( \\theta \\right) \\right) ^\{2\}+1/4\\,\{\\frac \{d^ \{2\}\}\{d\{\\theta\}^\{" }}{PARA 6 "" 1 "" {TEXT -1 40 "2\}\}\}P_\{\{ \\infty \}\} \\left( \\theta \\right) " }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "grtw();" }}{PARA 6 "" 1 "" {TEXT -1 25 "Scalar invariant library." }}{PARA 6 "" 1 "" {TEXT -1 28 "Last modified 25 March 1997." }}{PARA 6 "" 1 "" {TEXT -1 25 "`D ifferential Invariants`" }}{PARA 6 "" 1 "" {TEXT -1 29 "`Last modified Jan. 20, 1995`" }}{PARA 6 "" 1 "" {TEXT -1 41 "`Basis/tetrad related \+ object definitions`" }}{PARA 6 "" 1 "" {TEXT -1 31 "`Last modified 23 \+ January 2001`" }}{PARA 6 "" 1 "" {TEXT -1 25 "`Last built 27 May, 1999 `" }}{PARA 6 "" 1 "" {TEXT -1 25 "`Last built 27 May, 1999`" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%=GRTensorII~Version~1.79~(R4)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%06~February~2001G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%ZDeveloped~by~Peter~Musgrave,~Denis~Pollney~and~Kayll~ LakeG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%DCopyright~1994-2001~by~the~ authors.G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%inLatest~version~availab le~from:~http://grtensor.phy.queensu.ca/G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%4c:/Grtii(6)/MetricsG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "qload(gowdy);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2D efault~spacetimeG%&gowdyG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%9For~the ~gowdy~spacetime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%,CoordinatesG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"xG6#%#upG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/)%#x~G%\"aG-%'vectorG6#7&%\"tG%&thetaG%#x1G%#x2G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%-Line~elementG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",,**-%$expG6#,$*&#F(F'F(-%&gammaG6 $%\"tG%&thetaGF(!\"\"F(F4#F6F'%#~dGF()F4%#2~GF(F6**F+F(F4F7F8F()F5F:F( F(**F4F(-F,6#-%\"PGF3F(F8F()%#x1GF:F(F(*2F'F(F4F(F>F(-%\"QGF3F(F8F()FC %\"~GF(%#d~GF()%#x2GFHF(F(*(,&*(F4F(F>F()FEF'F(F(*&F4F(F>F6F(F(F8F()FK F:F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%,ConstraintsG7&/-%%diffG6$ -%&gammaG6$%\"tG%&thetaGF-,**(F-\"\"\")-%$expG6#-%\"PGF,\"\"#F1)-F(6$- %\"QGF,F-F8F1!\"\"*&F-F1)-F(6$F6F-F8F1F>*(F-F1F2F1)-F(6$F*&F- F1)-F(6$F6F.F8F1F>/-F(6$F*F.,&**F8F1F-F1FIF1FAF1F>*,F8F1F-F1F2F1F:F1FE F1F>/-F(6$F6-%\"$G6$F-F8,(-F(6$F6-FU6$F.F8F1*&FAF1F-F>F>*&-F46#,$*&F8F 1F6F1F1F1,&*$F9F1F1*$FDF1F>F1F1/-F(6$FF>*(F8 F1FAF1F:F1F>*(F8F1FIF1FEF1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grcalc(WeylSq);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G $\"#%*!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "gralter(_,13, 6,7);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simplification of a GR TensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 64 "Applying routine `Apply constraints repeatedly` to object WeylSq" }}{PARA 6 "" 1 "" {TEXT -1 40 "Applying routine expand to obj ect WeylSq" }}{PARA 6 "" 1 "" {TEXT -1 40 "Applying routine factor to \+ object WeylSq" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#Z!\" $" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 483 "grmap(_,subs,P(t,thet a) = P[infinity](theta)-v(theta)*ln(t)+1/4*exp(P[infinity](theta))^2*d iff(Q[infinity](theta),`$`(theta,2))^2*t^2*ln(t)^2+V[1](theta)*t^2+(ex p(2*P[infinity](theta))*psi[Q](theta)*diff(Q[infinity](theta),`$`(thet a,2))-1/4*diff(Q[infinity](theta),`$`(theta,2))^2-1/4*diff(v(theta),`$ `(theta,2)))*t^2*ln(t)+t^4*Z(t,theta),Q(t,theta) = Q[infinity](theta)+ psi[Q](theta)*t^(2*v(theta))+1/2*diff(Q[infinity](theta),`$`(theta,2)) *t^(2*v(theta))*ln(t)+t^4*W(t,theta),`x`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "Applying routine subs to WeylSq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 57 "Apply co nsistency relation but keep all other derivatives" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 56 "grmap(_,subs,diff(Q[infinity](theta),theta$4 )=Q[4],`x`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "Applying routine subs to \+ WeylSq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "grmap(_,subs,diff (Q[infinity](theta),theta$3)=0,`x`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "A pplying routine subs to WeylSq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "grmap(_,subs,diff(Q[infinity](theta),theta$2)=0,`x`);" } {MPLTEXT 0 21 0 "" }}{PARA 6 "" 1 "" {TEXT -1 31 "Applying routine sub s to WeylSq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "grmap(_,subs ,diff(Q[infinity](theta),theta)=0,`x`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "Applying routine subs to WeylSq" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 46 "Make sure you keep all derivatives of v(theta)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "grmap(_,subs,diff(v(theta),t heta$4)=v[4],`x`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "Applying routine su bs to WeylSq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "grmap(_,sub s,diff(v(theta),theta$3)=v[3],`x`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "Ap plying routine subs to WeylSq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "grmap(_,subs,diff(v(theta),theta$2)=0,`x`);" }}{PARA 6 "" 1 "" {TEXT -1 31 "Applying routine subs to WeylSq" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "grmap(_,subs,diff(v(theta),theta$1)=0,`x`);" }} {PARA 6 "" 1 "" {TEXT -1 31 "Applying routine subs to WeylSq" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "grmap(_,subs,v(theta)=1,`x`) ;" }}{PARA 6 "" 1 "" {TEXT -1 31 "Applying routine subs to WeylSq" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gralter(_,6,7);" }}{PARA 6 " " 1 "" {TEXT -1 48 "Component simplification of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 40 "Applyin g routine expand to object WeylSq" }}{PARA 6 "" 1 "" {TEXT -1 40 "Appl ying routine factor to object WeylSq" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#/%*CPU~Time~G$\"%D;!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "core1:=factor(simplify(subs(t=0,factor(grcomponent(WeylSq,[])/(t*e xp(gamma(t,theta)))))));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&core1G, 8*&\"#;\"\"\")-&%\"VG6#F(6#%&thetaG\"\"#F(F(*&\"\"$F()-%%diffG6$-&%\"P G6#%)infinityGF.F/\"\"%F(F(*&F " 0 "" {MPLTEXT 1 0 487 "core2:=fac tor(expand(subs(V[1](theta)=(exp(P[infinity](theta))^2*diff(Q[infinity ](theta),`$`(theta,2))^2/4)*(3/2)-exp(2*P[infinity](theta))*psi[Q](the ta)*diff(Q[infinity](theta),`$`(theta,2))-1/4*diff(Q[infinity](theta), `$`(theta,2))^2-1/4*diff(v(theta),`$`(theta,2))+exp(P[infinity](theta) )^2*(psi[Q](theta)+diff(Q[infinity](theta),`$`(theta,2))/4)^2+(diff(P[ infinity](theta),theta$2)+diff(v(theta),theta$2))/4,diff(Q[infinity](t heta),theta$2)=0,diff(Q[infinity](theta),theta$3)=0,%)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&core2G,$*(\"\"$\"\"\",*-%%diffG6$-&%\"PG6#%) infinityG6#%&thetaG-%\"$G6$F3\"\"#F(*(F7F(-%$expG6#F-F(-F+6$-&%$psiG6# %\"QGF2F3F(F(**\"\"%F(F9F(F>F(-F+6$F-F3F(F(*$)FEF7F(F(F(,*F*!\"\"*(F7F (F9F(FF(FEF(F(FGFJF(FJ" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 9 "latex(%);" }}{PARA 6 "" 1 "" {TEXT -1 68 "3\\, \\left ( \{\\frac \{d^\{2\}\}\{d\{\\theta\}^\{2\}\}\}P_\{\{\\infty \}\} \\lef t( \\theta" }}{PARA 6 "" 1 "" {TEXT -1 67 " \\right) \\right) ^\{2\}+ 3\\, \\left( \{\\frac \{d\}\{d\\theta\}\}P_\{\{\\infty \}\}" }}{PARA 6 "" 1 "" {TEXT -1 65 " \\left( \\theta \\right) \\right) ^\{4\}+6\\, \\left( \{\\frac \{d^\{2\}\}\{d\{" }}{PARA 6 "" 1 "" {TEXT -1 67 "\\t heta\}^\{2\}\}\}P_\{\{\\infty \}\} \\left( \\theta \\right) \\right) \+ \\left( \{" }}{PARA 6 "" 1 "" {TEXT -1 69 "\\frac \{d\}\{d\\theta\}\} P_\{\{\\infty \}\} \\left( \\theta \\right) \\right) ^\{2\}+" }} {PARA 6 "" 1 "" {TEXT -1 70 "16\\, \\left( Z \\left( 0,\\theta \\right ) \\right) ^\{2\}-48\\, \\left( \{e^\{P_" }}{PARA 6 "" 1 "" {TEXT -1 69 "\{\{\\infty \}\} \\left( \\theta \\right) \}\} \\right) ^\{2\} \\l eft( \{\\frac \{d\}\{d" }}{PARA 6 "" 1 "" {TEXT -1 70 "\\theta\}\}P_\{ \{\\infty \}\} \\left( \\theta \\right) \\right) ^\{2\} \\left( \\psi _" }}{PARA 6 "" 1 "" {TEXT -1 70 "\{\{Q\}\} \\left( \\theta \\right) \+ \\right) ^\{2\}-12\\, \\left( \{e^\{P_\{\{\\infty \}" }}{PARA 6 "" 1 " " {TEXT -1 67 "\} \\left( \\theta \\right) \}\} \\right) ^\{2\} \\left ( \{\\frac \{d\}\{d\\theta\}\}" }}{PARA 6 "" 1 "" {TEXT -1 67 "\\psi_ \{\{Q\}\} \\left( \\theta \\right) \\right) ^\{2\}-48\\, \\left( \{e^ \{P_\{\{" }}{PARA 6 "" 1 "" {TEXT -1 67 "\\infty \}\} \\left( \\theta \+ \\right) \}\} \\right) ^\{2\} \\left( \{\\frac \{d\}\{d" }}{PARA 6 "" 1 "" {TEXT -1 63 "\\theta\}\}P_\{\{\\infty \}\} \\left( \\theta \\righ t) \\right) \\psi_\{\{Q\}\}" }}{PARA 6 "" 1 "" {TEXT -1 67 " \\left( \+ \\theta \\right) \{\\frac \{d\}\{d\\theta\}\}\\psi_\{\{Q\}\} \\left( \+ \\theta" }}{PARA 6 "" 1 "" {TEXT -1 9 " \\right) " }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 "kernelopts(cputime);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"%RH!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 462 "subs(diff(Q[infinity](theta),theta$2)=0,diff(Q[infinity](theta),t heta$3)=0,V[1](theta)=(exp(P[infinity](theta))^2*diff(Q[infinity](thet a),`$`(theta,2))^2/4)*(3/2)-exp(2*P[infinity](theta))*psi[Q](theta)*di ff(Q[infinity](theta),`$`(theta,2))-1/4*diff(Q[infinity](theta),`$`(th eta,2))^2-1/4*diff(v(theta),`$`(theta,2))+exp(P[infinity](theta))^2*(p si[Q](theta)+diff(Q[infinity](theta),`$`(theta,2))/4)^2+(diff(P[infini ty](theta),theta$2)+diff(v(theta),theta$2))/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-&%\"VG6#\"\"\"6#%&thetaG,&*&)-%$expG6#-&%\"PG6#%)infi nityGF)\"\"#F()-&%$psiG6#%\"QGF)F6F(F(*&#F(\"\"%F(-%%diffG6$F1-%\"$G6$ F*F6F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "latex(%);" }} {PARA 6 "" 1 "" {TEXT -1 70 "V_\{\{1\}\} \\left( \\theta \\right) = \\ left( \{e^\{P_\{\{\\infty \}\} \\left( \\theta" }}{PARA 6 "" 1 "" {TEXT -1 65 " \\right) \}\} \\right) ^\{2\} \\left( \\psi_\{\{Q\}\} \\ left( \\theta \\right) " }}{PARA 6 "" 1 "" {TEXT -1 70 " \\right) ^\{2 \}+1/4\\,\{\\frac \{d^\{2\}\}\{d\{\\theta\}^\{2\}\}\}P_\{\{\\infty \} \} \\left( " }}{PARA 6 "" 1 "" {TEXT -1 15 "\\theta \\right) " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 10 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }