# LaTeX2HTML 95.1 (Fri Jan 20 1995)
# Associate image original text (scrambled) with physical files.

$key = q/{_inline}$bfA=M+N${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img125.gif">'; 
$key = q/{_inline}$tilder^(k-1)big|_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img120.gif">'; 
$key = q/{displaymath}underlinex^(k)=(D-L)^-1left(Uunderlinex^(k-1)+underlinebright){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img182.gif">'; 
$key = q/{_inline}$x_i^(k)=x_i^(k-1)+omegaleft(sigma-x_i^(k-1)right)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img239.gif">'; 
$key = q/{displaymath}int_Omeganablaunderlineud^3x=int_partialOmegaunderlineucdotdunderlines{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img18.gif">'; 
$key = q/{displaymath}vertlambdavert^k_maxsim.001{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img210.gif">'; 
$key = q/{_inline}$x_15^(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img187.gif">'; 
$key = q/{_inline}$underlinex^(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img194.gif">'; 
$key = q/{_inline}$x_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img159.gif">'; 
$key = q/{_inline}$l=1ldots11${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img193.gif">'; 
$key = q/{_inline}$Npi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img222.gif">'; 
$key = q/{_inline}$Munderlinex=underliney${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img167.gif">'; 
$key = q/{_inline}$tilder^(k)big|_1=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img130.gif">'; 
$key = q/{_inline}$M^-1A${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img166.gif">'; 
$key = q/{_inline}$left(1-lambda_ilambda_1right)sim1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img121.gif">'; 
$key = q/{_inline}$geq2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img155.gif">'; 
$key = q/{_inline}$FrightarrowF+deltaF${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img15.gif">'; 
$key = q/{_inline}$A_ii${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img156.gif">'; 
$key = q/{displaymath}int_,Omeganablavarphi,nablaetad^3underlinex=-intetanabla^2varphid^3underlinex{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img25.gif">'; 
$key = q/{displaymath}1-epsilonlealambda_Jlea-1+epsilonhspace2emepsilonsimfracpi^22N^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img208.gif">'; 
$key = q/{_inline}$ineqj${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img61.gif">'; 
$key = q/{_inline}$x_i^(k)=left(b_i-sigmaright)a_i,i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img180.gif">'; 
$key = q/{_inline}$eta${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img16.gif">'; 
$key = q/{_inline}$varphi_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img46.gif">'; 
$key = q/{displaymath}rho_GS=1-fracpi^2N^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img218.gif">'; 
$key = q/{}psfigfigure=cps615.fig4.ps,clip=true,width=3.75in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img51.gif">'; 
$key = q/{_inline}$dunderlines${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img19.gif">'; 
$key = q/{displaymath}underbraceSigma_(j,rmnotin,partialOmega)S_ijvarphi_j_rmUnknown+underbraceSigma_(jinpartialOmega)S_ijleft(varphi=f_jright)_rmKnownatBoundary=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img70.gif">'; 
$key = q/{_inline}$nabla^2varphi=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img32.gif">'; 
$key = q/{}psfigfigure=cps615.fig7.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img71.gif">'; 
$key = q/{_inline}$underliner_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img45.gif">'; 
$key = q/{_inline}$bfA${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img127.gif">'; 
$key = q/{displaymath}left(nablavarphiright)^2=left(fracpartialvarphipartialxright)^2+left(fracpartialvarphipartialyright)^2+left(fracpartialvarphipartialzright)^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img29.gif">'; 
$key = q/{_inline}$-nablaF${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img96.gif">'; 
$key = q/{_inline}$sum_jA_ijx_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img158.gif">'; 
$key = q/{_inline}$x_10^(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img189.gif">'; 
$key = q/{displaymath}F=frac14underlinevarphi^TtwelvebxtiSunderlinevarphi{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img52.gif">'; 
$key = q/{displaymath}x_i^(k)=fracleftlbrackb_i-sumlimits_j;SPM_lt;i,a_i,j,x_j^(k)-sumlimits_j;SPM_gt;i,a_i,j,x_j^(k-1)rightrbracka_i,i{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img181.gif">'; 
$key = q/{_inline}$omega=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img228.gif">'; 
$key = q/{_inline}$x_17^(k-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img188.gif">'; 
$key = q/{_inline}$underliner${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img41.gif">'; 
$key = q/{_inline}$underlineu=etanablavarphi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img21.gif">'; 
$key = q/{_inline}$(k-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img123.gif">'; 
$key = q/{displaymath}nablavarphi=left(fracpartialvarphipartialx,fracpartialvarphipartialy,fracpartialvarphipartialzright){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img28.gif">'; 
$key = q/{}psfigfigure=cps615.fig2.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img37.gif">'; 
$key = q/{_inline}$varphirightarrowvarphi+eta${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img8.gif">'; 
$key = q/{}psfigfigure=cps615.fig8b.ps,clip=true,width=3.75in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img75.gif">'; 
$key = q/{displaymath}beta_k=-fracunderlinep^(k-1)TAunderliner^(k-1)underlinep^(k-1)TAunderlinep^(k-1){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img141.gif">'; 
$key = q/{_inline}$sigma=sigma+a_i,j,x_j^(k-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img237.gif">'; 
$key = q/{_inline}$deltaF${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img68.gif">'; 
$key = q/{_inline}$underlinevarphi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img53.gif">'; 
$key = q/{_inline}$A_ij${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img157.gif">'; 
$key = q/{_inline}$x_22^(k-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img190.gif">'; 
$key = q/{_inline}$partialOmega${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img24.gif">'; 
$key = q/{_inline}$M^-1N${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img204.gif">'; 
$key = q/{_inline}$nabla^2varphi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img27.gif">'; 
$key = q/{_inline}$P^TP=I${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img98.gif">'; 
$key = q/{displaymath}nablaunderlineu=nablaetacdotnablavarphi+etanabla^2varphi{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img22.gif">'; 
$key = q/{displaymath}F=frac12,twentysyint_Omegaleft(nablavarphiright)^2d^3underlinex{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img1.gif">'; 
$key = q/{_inline}$1h${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img169.gif">'; 
$key = q/{displaymath}leftvertlambda_GSrightvert_rmmax=left(leftvertlambda_Jrightvert_maxright)^2sim1-2epsilon{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img209.gif">'; 
$key = q/{_inline}$kproptofrac1left(1-vertlambdavert_rmmaxright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img212.gif">'; 
$key = q/{displaymath}underlinep^(k)TAunderlinep^(k-1)=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img136.gif">'; 
$key = q/{displaymath}rho_J=1-fracpi^22N^2{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img217.gif">'; 
$key = q/{_inline}$Rightarrowlambda_igeq0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img129.gif">'; 
$key = q/{}psfigfigure=cps615.fig5.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img55.gif">'; 
$key = q/{displaymath}sum_iS_ii+sum_ineqjS_ij=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img63.gif">'; 
$key = q/{_inline}$eta=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img23.gif">'; 
$key = q/{_inline}$varphi(underlinex)=1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img64.gif">'; 
$key = q/{_inline}$tilder^(k+2)big|_3=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img132.gif">'; 
$key = q/{_inline}$rightarrow${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img128.gif">'; 
$key = q/{_inline}$underliner_2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img47.gif">'; 
$key = q/{_inline}$varphi${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img54.gif">'; 
$key = q/{_inline}$lambda_J${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img206.gif">'; 
$key = q/{}psfigfigure=918_10.ps,clip=true,width=5.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img192.gif">'; 
$key = q/{}psfigfigure=cps615.fig9.ps,clip=true,width=4.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img153.gif">'; 
$key = q/{_inline}$underlinep^(k-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img138.gif">'; 
$key = q/{_inline}$underliner^(k-1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img139.gif">'; 
$key = q/{displaymath}deltaFapproxint_Omegaleft(nablavarphicdotnablaetaright)d^3underlinex{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img17.gif">'; 
$key = q/{_inline}$lambda_GS=lambda_J^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img207.gif">'; 
$key = q/{_inline}$underliner^(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img85.gif">'; 
$key = q/{_inline}$underlinex^(k+1)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img89.gif">'; 
$key = q/{_inline}$x^(0)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img230.gif">'; 
$key = q/{_inline}$widetilde${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img104.gif">'; 
$key = q/{_inline}$fraclambda_nlambda_1simh^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img134.gif">'; 
$key = q/{}psfigfigure=cps615.fig3.ps,clip=true,width=4.75in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img38.gif">'; 
$key = q/{displaymath}sum_mboxProcessorsPleftlbracksum_jepsilonPy_jx_jrightrbrack{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img164.gif">'; 
$key = q/{_inline}$deltaF=frac12sum_ijeta_j,S_ji,varphi_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img67.gif">'; 
$key = q/{_inline}$ldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img236.gif">'; 
$key = q/{_inline}$tilder^(k+1)big|_2=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img131.gif">'; 
$key = q/{_inline}$ileftrightarrowj${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img60.gif">'; 
$key = q/{_inline}$sigma=left(b_i-sigmaright)a_i,i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img238.gif">'; 
$key = q/{_inline}$-12underlinex^TAunderlinex-underlineb^Tcdotunderlinex${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img144.gif">'; 
$key = q/{tabular}|ccc|hline;SPM_amp;;SPM_amp;_inline$tildexbig|_irmcompt$_inline;SPM_amp;=;SPM_amp;_inline$tildeb_ilambda_i$_inline;SPM_amp;;SPM_amp;hline{tabular}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img105.gif">'; 
$key = q/{}psfigfigure=918_09.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img185.gif">'; 
$key = q/{_inline}$lambda_illlambda_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img122.gif">'; 
$key = q/{displaymath}sum_jneqileft|S_ijright|leqleft|S_iiright|{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img72.gif">'; 
$key = q/{_inline}$underlinermif${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img170.gif">'; 
$key = q/{_inline}$1;SPM_lt;omega;SPM_lt;2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img227.gif">'; 
$key = q/{_inline}$odot${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img201.gif">'; 
$key = q/{_inline}$varphi_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img42.gif">'; 
$key = q/{displaymath}Fleft(underlinex^(k+1)right)leqFleft(underlinex^(k)right)mboxrigorously{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img94.gif">'; 
$key = q/{_inline}$left(vertlambdavert_maxright)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img216.gif">'; 
$key = q/{_inline}$Aunderlinex=underlineb${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img103.gif">'; 
$key = q/{_inline}$omegasim2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img215.gif">'; 
$key = q/{displaymath}F(underlinex)=frac12left(nabla-A^-1underlinebright)^TunderlineAleft(underlinex-A^-1underlinebright)-frac12underlineb^TA^-1underlineb{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img79.gif">'; 
$key = q/{_inline}$(l-1),${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img195.gif">'; 
$key = q/{_inline}$6times6${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img191.gif">'; 
$key = q/{_inline}$tilder_kbig|_i=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img113.gif">'; 
$key = q/{_inline}$S_ij=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img59.gif">'; 
$key = q/{_inline}$,widetilde,${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img106.gif">'; 
$key = q/{_inline}$expleftlbrack-kleft(1-leftvertlambdarightvert_rmmaxright)rightrbrack=.001${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img211.gif">'; 
$key = q/{displaymath}sum_j=1^ny_jx_j{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img162.gif">'; 
$key = q/{_inline}$x_16^(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img186.gif">'; 
$key = q/{_inline}$tilder^(k-1)big|_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img116.gif">'; 
$key = q/{_inline}$(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img124.gif">'; 
$key = q/{_inline}$underlinex${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img100.gif">'; 
$key = q/{_inline}$sigma=0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img233.gif">'; 
$key = q/{_inline}$x_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img160.gif">'; 
$key = q/{_inline}$Lambda${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img102.gif">'; 
$key = q/{displaymath}rho_SORsim1-fracpiN{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img220.gif">'; 
$key = q/{}psfigfigure=cps615.fig8a.ps,clip=true,width=3.75in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img74.gif">'; 
$key = q/{}psfigfigure=cps615.fig6.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img58.gif">'; 
$key = q/{displaymath}-fracpartialFpartialx=-nablaF=underlineb-Aunderlinex^(k)=underliner^(k){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img84.gif">'; 
$key = q/{_inline}$bullet${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img224.gif">'; 
$key = q/{_inline}$Omega${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img50.gif">'; 
$key = q/{_inline}$eta(underlinex)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img31.gif">'; 
$key = q/{displaymath}omega_optsim2left(1-fracpiNright){displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img219.gif">'; 
$key = q/{}psfigfigure=918_11.ps,clip=true,width=3.5in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img196.gif">'; 
$key = q/{displaymath}1(1-vertlambdavert_rmmax),{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img213.gif">'; 
$key = q/{_inline}$sigma=sigma+a_i,j,x_j^(k)${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img235.gif">'; 
$key = q/{_inline}$lambda_1geqlambda_2geldots${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img115.gif">'; 
$key = q/{_inline}$left|lambda_1=lambda_maxright|ggleft|lambda_n=lambda_minright|${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img133.gif">'; 
$key = q/{_inline}$kpropto1h^2${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img171.gif">'; 
$key = q/{_inline}$varphi_1${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img44.gif">'; 
$key = q/{_inline}$lambda_GS${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img205.gif">'; 
$key = q/{}psfigfigure=cps615.fig1.ps,clip=true,width=4.0in{}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img7.gif">'; 
$key = q/{_inline}$sum_jx_jy_j${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img150.gif">'; 
$key = q/{_inline}$tilder_kbig|_i${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img118.gif">'; 
$key = q/{_inline}$underliner_0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img43.gif">'; 
$key = q/{_inline}$A_ijneq0${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=MIDDLE ALT="" SRC="img161.gif">'; 
$key = q/{displaymath}fracpartialFpartialleft(eta(underlinex)right)=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img30.gif">'; 
$key = q/{displaymath}sum_iS_ji,varphi_i=0{displaymath}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img69.gif">'; 
$key = q/{_inline}$omega${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img226.gif">'; 
$key = q/{_inline}$i=1ldotsn${_inline}/;
$cached_env_img{$key} ='<IMG  ALIGN=BOTTOM ALT="" SRC="img112.gif">'; 

1;

