# LaTeX2HTML 96.1-g (June 11, 1996)
# Associate images original text with physical files.

$key = q/{figure}[htb]centerlinepsfigfigure=fig93.epslabelfig93{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=289 HEIGHT=265 ALIGN=BOTTOM  SRC="img700.gif"  > |; 
$key = q/{_inline}$diag;(L)=I${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=95 HEIGHT=27 ALIGN=MIDDLE  SRC="img684.gif"  > |; 
$key = q/{figure}[htb]minipage[t]9cmcenterlinepsfigfigure=fig34.eps,height=4cmminipagehfillminipage[t]6cmvspace*-3cm1:_inline$chris111,;chris112,...,chris133$_inline2:_inline$chris211,;chris212,...,chris233$_inline3:_inline$chris311,;chris312,...,chris333$_inlineminipagelabelfig34{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=556 HEIGHT=182 ALIGN=BOTTOM  SRC="img119.gif"  > |; 
$key = q/{displaymath}mboxrmrowsum(LD^-1U)=mboxrmrowsum(A);;;mboxrmforeveryrow;,{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=442 HEIGHT=20 ALIGN=BOTTOM  SRC="img680.gif"  > |; 
$key = q/{_inline}$phi_i+12^mboxtinyHOS${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=44 HEIGHT=26 ALIGN=MIDDLE  SRC="img235.gif"  > |; 
$key = q/{_inline}$beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=10 HEIGHT=25 ALIGN=MIDDLE  SRC="img271.gif"  > |; 
$key = q/{_inline}$phi_i+12^mboxtinyLOS${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=44 HEIGHT=26 ALIGN=MIDDLE  SRC="img234.gif"  > |; 
$key = q/{_inline}$omega,(equivvarepsilonk)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=71 HEIGHT=27 ALIGN=MIDDLE  SRC="img306.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^3|_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=70 HEIGHT=36 ALIGN=MIDDLE  SRC="img470.gif"  > |; 
$key = q/{_inline}$phi_(i+1,j,k-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=78 HEIGHT=25 ALIGN=MIDDLE  SRC="img252.gif"  > |; 
$key = q/{_inline}$B(bmV^n)(bmV^n+theta-bmV^*)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=152 HEIGHT=33 ALIGN=MIDDLE  SRC="img647.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=figA3.epslabelfigA3{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=804 HEIGHT=396 ALIGN=BOTTOM  SRC="img731.gif"  > |; 
$key = q/{_inline}$times${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=18 ALIGN=MIDDLE  SRC="img688.gif"  > |; 
$key = q/{_inline}$theta=1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=39 HEIGHT=12 ALIGN=BOTTOM  SRC="img621.gif"  > |; 
$key = q/{eqnarray*};SPMamp;;SPMamp;(barsigma^ij(fracsign(bma^(n)cdotbmn)|bma^(n)|bma^(n)cdotbme_i)bme_j)cdotbma_t_l)=S^ntau(alpha_1bma_(t_1)+alpha_2bma_(t_2))cdotbma_(t_l);SPMamp;;SPMamp;sign(bma^(n)cdotbmn)barsigma^ij(bma^(n))_i(bma_(t_l))_j=|bma^(n)|S^ntau(alpha_1bma_(t_1)cdotbma_(t_l)+alpha_2bma_(t_2)cdotbma_t_l));SPMamp;;SPMamp;sign(bma^(n)cdotbmn)barsigma^ij(bma^(n))_ig_pt_l(bma^(p))_j=sqrtg^nnS^ntau(alpha_1g_t_1t_l+alpha_2g_t_2t_l);SPMamp;;SPMamp;sign(bma^(n)cdotbmn)g_pt_lbarsigma^ijfracpartialxi^npartialx^ifracpartialxi^ppartialx^j=sqrtg^nnS^ntau(alpha_1g_t_1t_1+alpha_2g_t_2t_l){eqnarray*}/;
$cached_env_img{$key} = q| <IMG WIDTH=547 HEIGHT=145 ALIGN=BOTTOM  SRC="img749.gif"  > |; 
$key = q/{_inline}$c_mu${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=14 HEIGHT=17 ALIGN=MIDDLE  SRC="img272.gif"  > |; 
$key = q/{_inline}$bmu${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=11 HEIGHT=8 ALIGN=BOTTOM  SRC="img44.gif"  > |; 
$key = q/{_inline}$V^1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=15 ALIGN=BOTTOM  SRC="img144.gif"  > |; 
$key = q/{_inline}$u_t${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=14 HEIGHT=17 ALIGN=MIDDLE  SRC="img519.gif"  > |; 
$key = q/{_inline}$sigma^alpha3|_(0,0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=79 HEIGHT=29 ALIGN=MIDDLE  SRC="img446.gif"  > |; 
$key = q/{_inline}$partialphipartialxi^1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=53 HEIGHT=30 ALIGN=MIDDLE  SRC="img249.gif"  > |; 
$key = q/{_inline}$bfa_(2)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=17 ALIGN=MIDDLE  SRC="img2.gif"  > |; 
$key = q/{_inline}$K^alphabeta=a^(alpha)_gammaa^(beta)_deltak^gammadelta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=137 HEIGHT=38 ALIGN=MIDDLE  SRC="img177.gif"  > |; 
$key = q/{_inline}$n_3=1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=49 HEIGHT=25 ALIGN=MIDDLE  SRC="img658.gif"  > |; 
$key = q/{_inline}$alpha=1,2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=59 HEIGHT=25 ALIGN=MIDDLE  SRC="img473.gif"  > |; 
$key = q/{_inline}$V^1_(2,-2)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=47 HEIGHT=29 ALIGN=MIDDLE  SRC="img516.gif"  > |; 
$key = q/{_inline}$sigma^23${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=14 ALIGN=BOTTOM  SRC="img554.gif"  > |; 
$key = q/{_inline}$alpha_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=17 ALIGN=MIDDLE  SRC="img510.gif"  > |; 
$key = q/{_inline}$1leqMleq4${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=81 HEIGHT=26 ALIGN=MIDDLE  SRC="img222.gif"  > |; 
$key = q/{_inline}$c_varepsilon3=0.05${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=75 HEIGHT=25 ALIGN=MIDDLE  SRC="img300.gif"  > |; 
$key = q/{_inline}$(xi,eta)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=36 HEIGHT=27 ALIGN=MIDDLE  SRC="img153.gif"  > |; 
$key = q/{_inline}$psi=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=25 ALIGN=MIDDLE  SRC="img704.gif"  > |; 
$key = q/{_inline}$c_varepsilon1=1.35${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=75 HEIGHT=25 ALIGN=MIDDLE  SRC="img299.gif"  > |; 
$key = q/{_inline}$chris211,chris212,...,chris233${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=158 HEIGHT=43 ALIGN=MIDDLE  SRC="img117.gif"  > |; 
$key = q/{_inline}$Re_mboxtinyT;SPMlt;1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=61 HEIGHT=25 ALIGN=MIDDLE  SRC="img351.gif"  > |; 
$key = q/{displaymath}left[arraycU^t_1U^t_2arrayright]=left[arrayccg_t_1t_1;SPMamp;g_t_1t_2g_t_2t_1;SPMamp;g_t_2t_2arrayright]^-1left{left[arrayccalpha_11;SPMamp;alpha_12alpha_21;SPMamp;alpha_22arrayright]^-1left[arraycbmucdotbmtau_1bmucdotbmtau_2arrayright]-U^nleft[arraycg_nt_1g_nt_1arrayright]right}footnote[1]Thisformulacanbemodifiedinthefollowingway:displaymathleft[arraycU^t_1U^t_2arrayright]=left[arrayccg_t_2t_2;SPMamp;g_t_1t_2-g_t_2t_1;SPMamp;g_t_1t_1arrayright]left{left[arrayccbeta_11;SPMamp;beta_12beta_21;SPMamp;beta_22arrayright]^-1left[arraycunderlineucdotunderlinetau_1underlineucdotunderlinetau_2arrayright]-fracU^ng_t_1t_1g_t_2t_2-g_t_1t_2g_t_2t_1left[arraycg_nt_1g_nt_2arrayright]right}displaymathwheredisplaymathbeta_i1=left|arrayccunderlinetau_icdotunderlinea_(t_1);SPMamp;g_t_1t_2underlinetau_icdotunderlinea_(t_2);SPMamp;g_t_2t_2arrayright|displaymathanddisplaymathbeta_12=left|arrayccg_t_1t_1;SPMamp;underlinetau_icdotunderlinea_(t_1)g_t_2t_1;SPMamp;underlinetau_icdotunderlinea_(t_2)arrayright|displaymath{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=658 HEIGHT=969 ALIGN=BOTTOM  SRC="img730.gif"  > |; 
$key = q/{displaymath}bma_(alpha),g_alphabeta,sqrtg,chrisalphabetagamma{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=323 HEIGHT=33 ALIGN=BOTTOM  SRC="img79.gif"  > |; 
$key = q/{_inline}$c_tau3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=17 ALIGN=MIDDLE  SRC="img275.gif"  > |; 
$key = q/{_inline}$frac12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=7 HEIGHT=31 ALIGN=MIDDLE  SRC="img225.gif"  > |; 
$key = q/{_inline}$U^alpha_,beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=25 ALIGN=MIDDLE  SRC="img150.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^1|_(0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=59 HEIGHT=36 ALIGN=MIDDLE  SRC="img428.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig32.epslabelfig32{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=270 HEIGHT=246 ALIGN=BOTTOM  SRC="img102.gif"  > |; 
$key = q/{_inline}$frac12fracrhosqrtgV^3V^2|_(0,-1,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=127 HEIGHT=32 ALIGN=MIDDLE  SRC="img540.gif"  > |; 
$key = q/{displaymath}rhosqrtg(a_1^(alpha)f_1+a_2^(alpha)f_2)|_(0,0){displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=345 HEIGHT=25 ALIGN=BOTTOM  SRC="img141.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig52.epslabelfig52{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=748 HEIGHT=437 ALIGN=BOTTOM  SRC="img400.gif"  > |; 
$key = q/{_inline}$fracpartialU^alphapartialxi^beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=33 ALIGN=MIDDLE  SRC="img151.gif"  > |; 
$key = q/{_inline}$3cdotn_1cdotn_2cdotn_3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=98 HEIGHT=25 ALIGN=MIDDLE  SRC="img661.gif"  > |; 
$key = q/{_inline}$n+theta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=39 HEIGHT=25 ALIGN=MIDDLE  SRC="img627.gif"  > |; 
$key = q/{_inline}$p+frac23rhok${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=60 HEIGHT=31 ALIGN=MIDDLE  SRC="img263.gif"  > |; 
$key = q/{_inline}$U^-1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=15 ALIGN=BOTTOM  SRC="img683.gif"  > |; 
$key = q/{_inline}$R^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=16 ALIGN=BOTTOM  SRC="img258.gif"  > |; 
$key = q/{_inline}$alpha_ij${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=17 ALIGN=MIDDLE  SRC="img721.gif"  > |; 
$key = q/{_inline}$bmphi_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=24 ALIGN=MIDDLE  SRC="img609.gif"  > |; 
$key = q/{_inline}$f_mu;SPMgt;1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=48 HEIGHT=26 ALIGN=MIDDLE  SRC="img352.gif"  > |; 
$key = q/{displaymath}sigma^nn=g^nnS^nn;.{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=307 HEIGHT=17 ALIGN=BOTTOM  SRC="img745.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig511.eps,height=5cmlabelfig5.11{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=340 HEIGHT=226 ALIGN=BOTTOM  SRC="img560.gif"  > |; 
$key = q/{_inline}$V^3_(0,-2,-2)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=68 HEIGHT=29 ALIGN=MIDDLE  SRC="img547.gif"  > |; 
$key = q/{_inline}$|r_k|_2=|b-Ax_k|_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=146 HEIGHT=27 ALIGN=MIDDLE  SRC="img672.gif"  > |; 
$key = q/{_inline}$chrisalphabetagamma${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=41 ALIGN=MIDDLE  SRC="img91.gif"  > |; 
$key = q/{_inline}$chrisalphagammabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=41 ALIGN=MIDDLE  SRC="img56.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=figA2.epslabelfigA2{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=439 HEIGHT=295 ALIGN=BOTTOM  SRC="img720.gif"  > |; 
$key = q/{_inline}$phi_(i+1,j+1,k)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=79 HEIGHT=25 ALIGN=MIDDLE  SRC="img248.gif"  > |; 
$key = q/{_inline}$fracpartialU^2partialxi^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=36 ALIGN=MIDDLE  SRC="img463.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^2|_(0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=59 HEIGHT=36 ALIGN=MIDDLE  SRC="img427.gif"  > |; 
$key = q/{_inline}$eta=sqrtP^n_krhoc_muvarepsilon^n${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=122 HEIGHT=39 ALIGN=MIDDLE  SRC="img374.gif"  > |; 
$key = q/{_inline}$phi_(i,j+1,k)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=62 HEIGHT=25 ALIGN=MIDDLE  SRC="img247.gif"  > |; 
$key = q/{_inline}$sqrtg_,beta=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=67 HEIGHT=26 ALIGN=MIDDLE  SRC="img157.gif"  > |; 
$key = q/{_inline}$mboxsmall$Phi$=1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=12 ALIGN=BOTTOM  SRC="img223.gif"  > |; 
$key = q/{_inline}$Omega_ijk${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=30 HEIGHT=25 ALIGN=MIDDLE  SRC="img188.gif"  > |; 
$key = q/{displaymath}left[arraycsigma^nt_1sigma^nt_2arrayright]=sign(bma^(n)cdotbmn)sqrtg^nnS^ntauleft[arraycalpha_1alpha_2arrayright]-sigma^nnleft[arrayccg_t_1t_1;SPMamp;g_t_2t_1g_t_1t_2;SPMamp;g_t_2t_2arrayright]^-1left[arraycg_nt_1g_nt_2arrayright]{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=559 HEIGHT=51 ALIGN=BOTTOM  SRC="img754.gif"  > |; 
$key = q/{_inline}$S^ntau${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=13 ALIGN=BOTTOM  SRC="img430.gif"  > |; 
$key = q/{_inline}$relax_2delimiter;SPMquot;026B30D=1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=47 HEIGHT=27 ALIGN=MIDDLE  SRC="img15.gif"  > |; 
$key = q/{_inline}$psi${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=10 HEIGHT=25 ALIGN=MIDDLE  SRC="img703.gif"  > |; 
$key = q/{_inline}$bma^(n)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=15 ALIGN=BOTTOM  SRC="img714.gif"  > |; 
$key = q/{_inline}$kappa${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=8 HEIGHT=8 ALIGN=BOTTOM  SRC="img230.gif"  > |; 
$key = q/{_inline}$Y^+_mboxtinyP;SPMgt;11.3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=79 HEIGHT=28 ALIGN=MIDDLE  SRC="img572.gif"  > |; 
$key = q/{_inline}$S(bmV^n+1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=66 HEIGHT=32 ALIGN=MIDDLE  SRC="img626.gif"  > |; 
$key = q/{_inline}$sigma^nt${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=14 ALIGN=BOTTOM  SRC="img409.gif"  > |; 
$key = q/{_inline}$K^12_(i+12,j,k);SPMgt;0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=113 HEIGHT=29 ALIGN=MIDDLE  SRC="img245.gif"  > |; 
$key = q/{_inline}$sqrtgU^alpha_,beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=47 HEIGHT=25 ALIGN=MIDDLE  SRC="img155.gif"  > |; 
$key = q/{_inline}$i+frac12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=36 HEIGHT=31 ALIGN=MIDDLE  SRC="img206.gif"  > |; 
$key = q/{_inline}$(LU)_ij=a_ij${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=92 HEIGHT=28 ALIGN=MIDDLE  SRC="img686.gif"  > |; 
$key = q/{displaymath}M^n+1u^n+1=f^n+1;;,;;u^n+1=left(arraycu^n+1_1u^n+1_2u^n+1_3arrayright);,{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=409 HEIGHT=67 ALIGN=BOTTOM  SRC="img653.gif"  > |; 
$key = q/{_inline}$kappa=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=41 HEIGHT=13 ALIGN=BOTTOM  SRC="img229.gif"  > |; 
$key = q/{_inline}$p_0,0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=17 ALIGN=MIDDLE  SRC="img426.gif"  > |; 
$key = q/{_inline}$k^alphabeta=kdelta^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=85 HEIGHT=15 ALIGN=BOTTOM  SRC="img201.gif"  > |; 
$key = q/{_inline}$widehatU^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=18 ALIGN=BOTTOM  SRC="img133.gif"  > |; 
$key = q/{_inline}$underlinetau_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=16 ALIGN=MIDDLE  SRC="img398.gif"  > |; 
$key = q/{_inline}$LD^-1U${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=57 HEIGHT=15 ALIGN=BOTTOM  SRC="img677.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig31.epslabelfig31{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=287 HEIGHT=238 ALIGN=BOTTOM  SRC="img80.gif"  > |; 
$key = q/{_inline}$Y^+=11.3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=79 HEIGHT=15 ALIGN=BOTTOM  SRC="img599.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^2|_(0,0,1)=frac12(U^1_(0,2,1)-U^1_(0,-2,1))${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=250 HEIGHT=36 ALIGN=MIDDLE  SRC="img543.gif"  > |; 
$key = q/{_inline}$|r_k|_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=38 HEIGHT=27 ALIGN=MIDDLE  SRC="img673.gif"  > |; 
$key = q/{_inline}$|underlinen|=|underlinetau_1|=|underlinetau_2|=1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=173 HEIGHT=27 ALIGN=MIDDLE  SRC="img399.gif"  > |; 
$key = q/{_inline}$underlineucdotunderlinen,;underlineucdotunderlinetau_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=84 HEIGHT=16 ALIGN=MIDDLE  SRC="img395.gif"  > |; 
$key = q/{_inline}$bmtau_w=rho|bmu_tau|bmu_tau${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=102 HEIGHT=27 ALIGN=MIDDLE  SRC="img590.gif"  > |; 
$key = q/{_inline}$4^2=16${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=57 HEIGHT=15 ALIGN=BOTTOM  SRC="img528.gif"  > |; 
$key = q/{_inline}$Box${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=10 HEIGHT=10 ALIGN=BOTTOM  SRC="img716.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig41.eps,height=5cmlabelfig41{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=646 HEIGHT=227 ALIGN=BOTTOM  SRC="img136.gif"  > |; 
$key = q/{_inline}$bmphi_1,..,bmphi_mboxtinyN${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=65 HEIGHT=24 ALIGN=MIDDLE  SRC="img617.gif"  > |; 
$key = q/{_inline}$wedge${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=10 HEIGHT=12 ALIGN=BOTTOM  SRC="img41.gif"  > |; 
$key = q/{_inline}$bmp^n+theta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=36 HEIGHT=32 ALIGN=MIDDLE  SRC="img649.gif"  > |; 
$key = q/{_inline}$relax_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=5 HEIGHT=11 ALIGN=MIDDLE  SRC="img11.gif"  > |; 
$key = q/{_inline}$sqrtg${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=25 ALIGN=MIDDLE  SRC="img89.gif"  > |; 
$key = q/{_inline}$E_rapprox30${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=60 HEIGHT=25 ALIGN=MIDDLE  SRC="img602.gif"  > |; 
$key = q/{_inline}$bmF^n+theta_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=39 HEIGHT=33 ALIGN=MIDDLE  SRC="img642.gif"  > |; 
$key = q/{_inline}$alpha=2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=12 ALIGN=BOTTOM  SRC="img506.gif"  > |; 
$key = q/{displaymath}arrayccccC^n+1_1;SPMamp;c^n+1_1;SPMamp;=;SPMamp;d^n+1_1;,;SPMamp;vdots;SPMamp;;SPMamp;C^n+1_k;SPMamp;c^n+1_k;SPMamp;=;SPMamp;d^n+1_k;.array{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=340 HEIGHT=74 ALIGN=BOTTOM  SRC="img655.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig92.eps,height=5cmlabelfig92{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=371 HEIGHT=230 ALIGN=BOTTOM  SRC="img698.gif"  > |; 
$key = q/{_inline}$K^12_(i+12,j,k);SPMlt;0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=113 HEIGHT=29 ALIGN=MIDDLE  SRC="img246.gif"  > |; 
$key = q/{_inline}$theta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=7 HEIGHT=12 ALIGN=BOTTOM  SRC="img24.gif"  > |; 
$key = q/{_inline}$p_0,0,0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=37 HEIGHT=17 ALIGN=MIDDLE  SRC="img460.gif"  > |; 
$key = q/{_inline}$U^t_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=15 ALIGN=BOTTOM  SRC="img403.gif"  > |; 
$key = q/{_inline}$bmucdotbmtau_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=17 ALIGN=MIDDLE  SRC="img392.gif"  > |; 
$key = q/{_inline}$bmtau${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=8 ALIGN=BOTTOM  SRC="img431.gif"  > |; 
$key = q/{displaymath}sign(bma^(n)cdotbmn){g_t_1t_1sigma^nt_1+g_t_2t_1sigma^nt_2+g_nt_1sigma^nn}=sqrtg^nnS^ntau(alpha_1g_t_1t_1+alpha_2g_t_2t_1){displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=572 HEIGHT=21 ALIGN=BOTTOM  SRC="img751.gif"  > |; 
$key = q/{_inline}$V^2_(0,i)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=34 HEIGHT=29 ALIGN=MIDDLE  SRC="img526.gif"  > |; 
$key = q/{_inline}$-frac1|a^(n)|bma^(n)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=83 HEIGHT=33 ALIGN=MIDDLE  SRC="img742.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=figA1.epslabelfigA1{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=804 HEIGHT=396 ALIGN=BOTTOM  SRC="img711.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig83.eps,height=10cmvspace*-1,5cmlabelfig83{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=283 HEIGHT=284 ALIGN=BOTTOM  SRC="img670.gif"  > |; 
$key = q/{_inline}$1leqmboxsmall$Phi$leq2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=74 HEIGHT=25 ALIGN=MIDDLE  SRC="img221.gif"  > |; 
$key = q/{_inline}$D^-1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=30 HEIGHT=14 ALIGN=BOTTOM  SRC="img681.gif"  > |; 
$key = q/{_inline}$S^ntaubmtau${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=38 HEIGHT=13 ALIGN=BOTTOM  SRC="img434.gif"  > |; 
$key = q/{_inline}$Gamma${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=12 ALIGN=BOTTOM  SRC="img76.gif"  > |; 
$key = q/{_inline}$U^1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=15 ALIGN=BOTTOM  SRC="img20.gif"  > |; 
$key = q/{_inline}$U^t${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=18 HEIGHT=15 ALIGN=BOTTOM  SRC="img384.gif"  > |; 
$key = q/{_inline}$V^3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=15 ALIGN=BOTTOM  SRC="img542.gif"  > |; 
$key = q/{_inline}$partialcdotpartialxi^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=58 HEIGHT=27 ALIGN=MIDDLE  SRC="img99.gif"  > |; 
$key = q/{_inline}$bmucdotbmn,;bmucdotbmtau_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=92 HEIGHT=17 ALIGN=MIDDLE  SRC="img391.gif"  > |; 
$key = q/{_inline}$dtimesd${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=39 HEIGHT=24 ALIGN=MIDDLE  SRC="img174.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig510.eps,height=5cmlabelfig510{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=305 HEIGHT=230 ALIGN=BOTTOM  SRC="img525.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^1|_(0,0,1),;fracpartialU^1partialxi^2|_(0,0,1),;fracpartialU^2partialxi^1|_(0,0,1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=241 HEIGHT=36 ALIGN=MIDDLE  SRC="img468.gif"  > |; 
$key = q/{_inline}$i+group1groupover2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=36 HEIGHT=31 ALIGN=MIDDLE  SRC="img5.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig53.eps,height=6cmlabelfig53{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=319 HEIGHT=272 ALIGN=BOTTOM  SRC="img415.gif"  > |; 
$key = q/{_inline}$gamma=0.012${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=73 HEIGHT=25 ALIGN=MIDDLE  SRC="img292.gif"  > |; 
$key = q/{_inline}$xi^2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=15 HEIGHT=30 ALIGN=MIDDLE  SRC="img256.gif"  > |; 
$key = q/{_inline}$pm1,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=43 HEIGHT=27 ALIGN=MIDDLE  SRC="img84.gif"  > |; 
$key = q/{_inline}$f(h_mboxtinyR^+)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=43 HEIGHT=29 ALIGN=MIDDLE  SRC="img596.gif"  > |; 
$key = q/{_inline}$S^nt${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=24 HEIGHT=15 ALIGN=BOTTOM  SRC="img407.gif"  > |; 
$key = q/{_inline}$eta_0=4.38${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=69 HEIGHT=25 ALIGN=MIDDLE  SRC="img293.gif"  > |; 
$key = q/{_inline}$bma_(3)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=28 HEIGHT=17 ALIGN=MIDDLE  SRC="img108.gif"  > |; 
$key = q/{table}[htb]centertabular|l|c|c|hline;SPMamp;2D;SPMamp;3Dhlinepressurematrix;SPMamp;_inline$9cdotn_1cdotn_2$_inline;SPMamp;_inline$19cdotn_1cdotn_2cdotn_3$_inlinemomentummatrix;SPMamp;_inline$13cdot2cdotn_1cdotn_2$_inline;SPMamp;_inline$51cdot3cdotn_1cdotn_2cdotn_3$_inlinehlinetabularcenterlabeltab81{table}/;
$cached_env_img{$key} = q| <IMG WIDTH=431 HEIGHT=68 ALIGN=BOTTOM  SRC="img665.gif"  > |; 
$key = q/{_inline}$sigma^13|_(0,0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=77 HEIGHT=29 ALIGN=MIDDLE  SRC="img555.gif"  > |; 
$key = q/{figure}[htb]minipage[t]7,3cmhspace*1cm_inline$Omega$_inlinevspace*-1,2cmhspace*1cmcenterlinepsfigfigure=fig21a.eps,height=6cm,angle=-90vspace*-2cm_inline$arrayllly;SPMamp;uparrow;SPMamp;;SPMamp;;;;rightarrow;SPMamp;xarray$_inlineminipagehfillminipage[t]8cm_inline$T$_inline_inline$rightarrow$_inlinevspace*-1cmcenterlinepsfigfigure=fig21b.eps,height=5cmvspace0,5cmminipagelabelfig21{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=633 HEIGHT=263 ALIGN=BOTTOM  SRC="img28.gif"  > |; 
$key = q/{_inline}$bmu^t${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=14 ALIGN=BOTTOM  SRC="img570.gif"  > |; 
$key = q/{_inline}$S^ntbmt${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=32 HEIGHT=15 ALIGN=BOTTOM  SRC="img575.gif"  > |; 
$key = q/{_inline}$c_varepsilon2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=17 ALIGN=MIDDLE  SRC="img286.gif"  > |; 
$key = q/{_inline}$krightarrowvarepsilonmboxoromega${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=82 HEIGHT=13 ALIGN=BOTTOM  SRC="img638.gif"  > |; 
$key = q/{_inline}$phi_i+12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=44 HEIGHT=25 ALIGN=MIDDLE  SRC="img205.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig57.eps,height=5cmlabelfig57{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=628 HEIGHT=229 ALIGN=BOTTOM  SRC="img513.gif"  > |; 
$key = q/{_inline}$bmucdotbmn,;bmucdotbmtau_1,;bmucdotbmtau_2,;bmtau_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=179 HEIGHT=17 ALIGN=MIDDLE  SRC="img401.gif"  > |; 
$key = q/{_inline}$partialphipartialxi^2|_(i+12,j,k)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=125 HEIGHT=29 ALIGN=MIDDLE  SRC="img241.gif"  > |; 
$key = q/{_inline}$h_mboxtinyR^+${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=18 HEIGHT=28 ALIGN=MIDDLE  SRC="img591.gif"  > |; 
$key = q/{_inline}$T_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=15 HEIGHT=25 ALIGN=MIDDLE  SRC="img611.gif"  > |; 
$key = q/{_inline}$underlineS_xi^n=constant=S^nnbmn+S^ntaubmtau${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=214 HEIGHT=25 ALIGN=MIDDLE  SRC="img738.gif"  > |; 
$key = q/{_inline}$diag;(LD^-1U)=diag;(A)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=196 HEIGHT=30 ALIGN=MIDDLE  SRC="img679.gif"  > |; 
$key = q/{_inline}$2cdotn_1cdotn_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=68 HEIGHT=25 ALIGN=MIDDLE  SRC="img660.gif"  > |; 
$key = q/{_inline}$i^mboxscriptsizeth${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=18 HEIGHT=15 ALIGN=BOTTOM  SRC="img610.gif"  > |; 
$key = q/{_inline}$kappa=frac13${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=41 HEIGHT=31 ALIGN=MIDDLE  SRC="img226.gif"  > |; 
$key = q/{_inline}$psi_i+1,j+1:=psi_i,j+1+V^2_i,j+1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=195 HEIGHT=30 ALIGN=MIDDLE  SRC="img706.gif"  > |; 
$key = q/{_inline}$bfa_(1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=17 ALIGN=MIDDLE  SRC="img1.gif"  > |; 
$key = q/{_inline}$K^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=32 HEIGHT=15 ALIGN=BOTTOM  SRC="img239.gif"  > |; 
$key = q/{_inline}$K^12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=28 HEIGHT=14 ALIGN=BOTTOM  SRC="img255.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^2|_(0,0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=80 HEIGHT=36 ALIGN=MIDDLE  SRC="img541.gif"  > |; 
$key = q/{_inline}$sigma^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=15 ALIGN=BOTTOM  SRC="img411.gif"  > |; 
$key = q/{_inline}$n_1cdotn_2cdotn_3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=77 HEIGHT=17 ALIGN=MIDDLE  SRC="img659.gif"  > |; 
$key = q/{_inline}$S^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=28 HEIGHT=16 ALIGN=BOTTOM  SRC="img265.gif"  > |; 
$key = q/{_inline}$xi^n=constant${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=107 HEIGHT=25 ALIGN=MIDDLE  SRC="img16.gif"  > |; 
$key = q/{_inline}$i,j,in{-1,1}${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=100 HEIGHT=27 ALIGN=MIDDLE  SRC="img110.gif"  > |; 
$key = q/{_inline}$V^1_i,-1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=34 HEIGHT=30 ALIGN=MIDDLE  SRC="img387.gif"  > |; 
$key = q/{_inline}$f_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=14 HEIGHT=25 ALIGN=MIDDLE  SRC="img353.gif"  > |; 
$key = q/{displaymath}alpha_2=fracleft|arrayccg_t_1t_1;SPMamp;bmtaucdotbma_(t_1)g_t_2t_1;SPMamp;bmtaucdotbma_(t_2)arrayright|left|arrayccg_t_1t_1;SPMamp;g_t_1t_2g_t_2t_1;SPMamp;g_t_2t_2arrayright|;.{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=343 HEIGHT=102 ALIGN=BOTTOM  SRC="img748.gif"  > |; 
$key = q/{_inline}$S=(2S^alphabetaS_alphabeta)^frac12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=122 HEIGHT=38 ALIGN=MIDDLE  SRC="img288.gif"  > |; 
$key = q/{displaymath}arrayllvspace*0.3cmPsi_kappa(r)=frac12(1+kappa)r+frac12(1-kappa);SPMamp;mboxLinearkappambox-schemevspace*0.3cmPsi_mboxtiny_inline$Phi$_inline(r)=max[,0,,min(mboxsmall_inline$Phi$_inliner,,1),,min(r,,mboxsmall_inline$Phi$_inline),];SPMamp;mboxSwebymboxsmall_inline$Phi$_inline-limitervspace*0.3cmPsi_kappa(r)=left{arrayll(r+|r|),frac-r^2+(3+kappa)r-kappa(1+r)^2,;SPMamp;rleq1,;;-1leqkappa;SPMlt;0frac(2+kappa)r-kappa1+r,;SPMamp;rgeq1,;;-1leqkappa;SPMlt;0(r+|r|),frac(1+kappa)r+1-kappa(1+r)^2,;SPMamp;0leqkappaleq1arrayright.;SPMamp;mboxR-kappamboxlimitervspace*0.3cmPsi_kappa(r)=left{arrayllr+|r|,;SPMamp;rleqfrac13frac(8+9kappa)r^2+(2-12kappa)r+2+3kappa3(1+r)^2,;SPMamp;rgeqfrac13arrayright.;SPMamp;mboxUSR-kappamboxlimitervspace*0.3cmPsi_kappa,mboxtinyM(r)=max[0,,min(M,,frac12(1+kappa)r+frac12(1-kappa),,2r)];SPMamp;mboxPL-kappamboxlimitervspace*0.3cmPsi_kappa,mboxtinyM(r)=max[0,,min(2r,frac23),,min(M,,frac12(1+kappa)r+frac12(1-kappa),,2r)];SPMamp;mboxUSPL-kappamboxlimitervspace*0.3cmPsi_kappa(r)=max[0,,min(2,,frac12(1+kappa)r+frac12(1-kappa),qquadqquad;;frac12(1-kappa)r+frac12(1+kappa),,2r)];SPMamp;mboxSymmetricPL-kappamboxlimiterarray{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=683 HEIGHT=421 ALIGN=BOTTOM  SRC="img219.gif"  > |; 
$key = q/{_inline}$eta=Skvarepsilon${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=69 HEIGHT=27 ALIGN=MIDDLE  SRC="img287.gif"  > |; 
$key = q/{eqnarray*}V^alpha_(i,j,-2);SPMamp;=;SPMamp;2V^alpha_(i,j,-1)-V^alpha_(i,j,0);;;;;mboxfor;;;alpha=1,2;;;;;mboxand;;;jneq-2V^alpha_(i,-2,k);SPMamp;=;SPMamp;2V^alpha_(i,-1,k)-V^alpha_(i,0,k);;;;;mboxfor;;;alpha=1,3;;;;;mboxand;;;kneq-2V^2_(i,-3,0);SPMamp;=;SPMamp;2V^2_(i,-1,0)-V^2_(i,1,0)V^3_(i,0,-3);SPMamp;=;SPMamp;2V^3_(i,0,-1)-V^3_(i,0,1);;.{eqnarray*}/;
$cached_env_img{$key} = q| <IMG WIDTH=500 HEIGHT=108 ALIGN=BOTTOM  SRC="img532.gif"  > |; 
$key = q/{_inline}$U^n,;U^t_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=58 HEIGHT=30 ALIGN=MIDDLE  SRC="img402.gif"  > |; 
$key = q/{displaymath}left[arrayccalpha_11;SPMamp;alpha_12alpha_21;SPMamp;alpha_22arrayright]left[arrayccg_t_1t_1;SPMamp;g_t_1t_2g_t_2t_1;SPMamp;g_t_2t_2arrayright]left[arraycU^t_1U^t_2arrayright]=left[arraycbmucdotbmtau_1bmucdotbmtau_2arrayright]-U^nleft[arrayccalpha_11;SPMamp;alpha_12alpha_21;SPMamp;alpha_22arrayright]left[arraycg_nt_1g_nt_2arrayright]{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=590 HEIGHT=48 ALIGN=BOTTOM  SRC="img729.gif"  > |; 
$key = q/{_inline}$x_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=13 HEIGHT=17 ALIGN=MIDDLE  SRC="img657.gif"  > |; 
$key = q/{_inline}$fracpartialU^2partialxi^2|_(0,0,1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=70 HEIGHT=36 ALIGN=MIDDLE  SRC="img469.gif"  > |; 
$key = q/{_inline}$M_21^T${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=31 ALIGN=MIDDLE  SRC="img664.gif"  > |; 
$key = q/{_inline}$foralljin{1,..,mboxN}${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=103 HEIGHT=27 ALIGN=MIDDLE  SRC="img615.gif"  > |; 
$key = q/{displaymath}left[arrayccalpha_11g_t_1t_1+alpha_12g_t_1t_2;SPMamp;alpha_11g_t_2t_1+alpha_12g_t_2t_2alpha_21g_t_1t_1+alpha_22g_t_1t_2;SPMamp;alpha_21g_t_2t_1+alpha_22g_t_2t_2arrayright]left[arraycU^t_1U^t_2arrayright]=left[arraycbmucdotbmtau_1-(alpha_11g_nt_1+alpha_12g_nt_2)U^nbmucdotbmtau_2-(alpha_21g_nt_1+alpha_22g_nt_2)U^narrayright]{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=667 HEIGHT=48 ALIGN=BOTTOM  SRC="img728.gif"  > |; 
$key = q/{_inline}$sigma^nt_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=28 HEIGHT=14 ALIGN=BOTTOM  SRC="img436.gif"  > |; 
$key = q/{_inline}$bmt${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=6 HEIGHT=11 ALIGN=BOTTOM  SRC="img383.gif"  > |; 
$key = q/{_inline}$theta=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=39 HEIGHT=13 ALIGN=BOTTOM  SRC="img620.gif"  > |; 
$key = q/{_inline}$bmndGamma${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=32 HEIGHT=12 ALIGN=BOTTOM  SRC="img75.gif"  > |; 
$key = q/{_inline}$phi_1rightarrow,..,rightarrowphi_N${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=109 HEIGHT=25 ALIGN=MIDDLE  SRC="img640.gif"  > |; 
$key = q/{_inline}$(g^33S^33)|_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=104 HEIGHT=29 ALIGN=MIDDLE  SRC="img489.gif"  > |; 
$key = q/{_inline}$Delta_gammau^alpha|_(i,j,k)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=81 HEIGHT=27 ALIGN=MIDDLE  SRC="img333.gif"  > |; 
$key = q/{_inline}$g^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=32 ALIGN=MIDDLE  SRC="img48.gif"  > |; 
$key = q/{_inline}$Omega^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=15 ALIGN=BOTTOM  SRC="img267.gif"  > |; 
$key = q/{_inline}$tau^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=15 ALIGN=BOTTOM  SRC="img126.gif"  > |; 
$key = q/{_inline}$c^*${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=13 HEIGHT=12 ALIGN=BOTTOM  SRC="img173.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig33.eps,height=4cmlabelfig33{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=508 HEIGHT=182 ALIGN=BOTTOM  SRC="img106.gif"  > |; 
$key = q/{_inline}$sigma^nn${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=25 HEIGHT=12 ALIGN=BOTTOM  SRC="img408.gif"  > |; 
$key = q/{_inline}$k^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=15 ALIGN=BOTTOM  SRC="img182.gif"  > |; 
$key = q/{_inline}$delimiter;SPMquot;026B30Drelax${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=5 HEIGHT=27 ALIGN=MIDDLE  SRC="img12.gif"  > |; 
$key = q/{_inline}$psi_1,j+1:=psi_1,j+V^1_1,j${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=151 HEIGHT=30 ALIGN=MIDDLE  SRC="img705.gif"  > |; 
$key = q/{_inline}$x^beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=15 ALIGN=BOTTOM  SRC="img328.gif"  > |; 
$key = q/{_inline}$sigma^22${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=14 ALIGN=BOTTOM  SRC="img459.gif"  > |; 
$key = q/{_inline}$sigma^nn,;sigma^nt_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=68 HEIGHT=30 ALIGN=MIDDLE  SRC="img435.gif"  > |; 
$key = q/{displaymath}U^n=sqrtg^nn;bmucdotbmn;.{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=318 HEIGHT=18 ALIGN=BOTTOM  SRC="img713.gif"  > |; 
$key = q/{_inline}$i=0,;j=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=89 HEIGHT=25 ALIGN=MIDDLE  SRC="img123.gif"  > |; 
$key = q/{_inline}$mu_t${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=17 ALIGN=MIDDLE  SRC="img259.gif"  > |; 
$key = q/{_inline}$g_nt_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=17 ALIGN=MIDDLE  SRC="img482.gif"  > |; 
$key = q/{_inline}$c_varepsilon3=0.25${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=75 HEIGHT=25 ALIGN=MIDDLE  SRC="img298.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig59.eps,height=5cmlabelfig59{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=369 HEIGHT=228 ALIGN=BOTTOM  SRC="img518.gif"  > |; 
$key = q/{_inline}$t^n+1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=31 HEIGHT=14 ALIGN=BOTTOM  SRC="img635.gif"  > |; 
$key = q/{_inline}$c^*_varepsilon1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=25 ALIGN=MIDDLE  SRC="img285.gif"  > |; 
$key = q/{_inline}$c_tau2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=17 ALIGN=MIDDLE  SRC="img274.gif"  > |; 
$key = q/{_inline}$frac1|bma^(n)|bma^(n)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=73 HEIGHT=33 ALIGN=MIDDLE  SRC="img741.gif"  > |; 
$key = q/{_inline}$diag;(L)=diag;(U)=D${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=189 HEIGHT=27 ALIGN=MIDDLE  SRC="img678.gif"  > |; 
$key = q/{_inline}$V^alpha_,beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=25 ALIGN=MIDDLE  SRC="img156.gif"  > |; 
$key = q/{_inline}$xi^gamma${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=25 ALIGN=MIDDLE  SRC="img334.gif"  > |; 
$key = q/{_inline}$relax_1delimiter;SPMquot;026B30D=delimiter;SPMquot;026B30Drelax${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=46 HEIGHT=27 ALIGN=MIDDLE  SRC="img14.gif"  > |; 
$key = q/{_inline}$V^alphaV^3|_(0,0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=97 HEIGHT=29 ALIGN=MIDDLE  SRC="img499.gif"  > |; 
$key = q/{_inline}$phi_C${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=25 ALIGN=MIDDLE  SRC="img212.gif"  > |; 
$key = q/{_inline}$bma^(alpha)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=15 ALIGN=BOTTOM  SRC="img37.gif"  > |; 
$key = q/{_inline}$f_mu${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=15 HEIGHT=26 ALIGN=MIDDLE  SRC="img344.gif"  > |; 
$key = q/{_inline}$h_mboxtinyRLll1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=74 HEIGHT=27 ALIGN=MIDDLE  SRC="img588.gif"  > |; 
$key = q/{_inline}$Y_p${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=26 ALIGN=MIDDLE  SRC="img23.gif"  > |; 
$key = q/{displaymath}arraycclbmx;SPMamp;=;SPMamp;(x^1,x^2,x^3)mboxrmistheCartesianco-ordinatesystem,bmxi;SPMamp;=;SPMamp;(xi^1,xi^2,xi^3)mboxrmisthegeneralco-ordinatesystem,;SPMamp;;SPMamp;mboxrmi.e.theco-ordinatesystemcorrespondingtothecomputationalgrid.array{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=583 HEIGHT=62 ALIGN=BOTTOM  SRC="img29.gif"  > |; 
$key = q/{_inline}$sigma^11|_(0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=56 HEIGHT=29 ALIGN=MIDDLE  SRC="img424.gif"  > |; 
$key = q/{_inline}$k=10^-6${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=66 HEIGHT=15 ALIGN=BOTTOM  SRC="img360.gif"  > |; 
$key = q/{_inline}$bmtau_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=17 ALIGN=MIDDLE  SRC="img394.gif"  > |; 
$key = q/{_inline}$dOmega${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=20 HEIGHT=12 ALIGN=BOTTOM  SRC="img70.gif"  > |; 
$key = q/{eqnarray*};SPMamp;;SPMamp;(barsigma^ij(bma^(n)cdotbme_i)bme_j)cdotbma^(n)=S^nnbma^(n)cdotbma^(n);SPMamp;;SPMamp;barsigma^ij(bma^(n))_i(bma^(n))_j=S^nng^nn;SPMamp;;SPMamp;barsigma^ijfracpartialxi^npartialx^ifracpartialxi^npartialx^j=g^nnS^nn{eqnarray*}/;
$cached_env_img{$key} = q| <IMG WIDTH=500 HEIGHT=93 ALIGN=BOTTOM  SRC="img744.gif"  > |; 
$key = q/{_inline}$xi^1=nx${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=59 HEIGHT=30 ALIGN=MIDDLE  SRC="img379.gif"  > |; 
$key = q/{_inline}$relaxdelimiter;SPMquot;026B30D=delimiter;SPMquot;026B30Drelax${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=37 HEIGHT=27 ALIGN=MIDDLE  SRC="img13.gif"  > |; 
$key = q/{_inline}$VsubsetOmega${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=49 HEIGHT=25 ALIGN=MIDDLE  SRC="img72.gif"  > |; 
$key = q/{_inline}$Omega=(2Omega^alphabetaOmega_alphabeta)^frac12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=126 HEIGHT=38 ALIGN=MIDDLE  SRC="img314.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig42.eps,height=15cmlabelfig42{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=561 HEIGHT=682 ALIGN=BOTTOM  SRC="img159.gif"  > |; 
$key = q/{_inline}$fracpartialU^2partialxi^1|_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=70 HEIGHT=36 ALIGN=MIDDLE  SRC="img466.gif"  > |; 
$key = q/{_inline}$phi_(i+1,j,k+1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=78 HEIGHT=25 ALIGN=MIDDLE  SRC="img253.gif"  > |; 
$key = q/{_inline}$5;SPMlt;h_mboxtinyR^+;SPMlt;30${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=93 HEIGHT=28 ALIGN=MIDDLE  SRC="img598.gif"  > |; 
$key = q/{_inline}$U^n${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=20 HEIGHT=13 ALIGN=BOTTOM  SRC="img491.gif"  > |; 
$key = q/{_inline}$Phi${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=11 HEIGHT=12 ALIGN=BOTTOM  SRC="img183.gif"  > |; 
$key = q/{displaymath}U^n=-sqrtg^nn;bmucdotbmn;.{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=324 HEIGHT=18 ALIGN=BOTTOM  SRC="img715.gif"  > |; 
$key = q/{_inline}$Y^+${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=14 ALIGN=BOTTOM  SRC="img568.gif"  > |; 
$key = q/{displaymath}bmucdotbmn=bmucdotfracbma^(n)|bma^(n)|=fracU^nsqrtg^nn{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=351 HEIGHT=45 ALIGN=BOTTOM  SRC="img712.gif"  > |; 
$key = q/{_inline}$h_mboxtinyR^+;SPMlt;11.3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=75 HEIGHT=28 ALIGN=MIDDLE  SRC="img600.gif"  > |; 
$key = q/{_inline}$bma_(alpha)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=17 ALIGN=MIDDLE  SRC="img32.gif"  > |; 
$key = q/{_inline}$U^3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=15 ALIGN=BOTTOM  SRC="img19.gif"  > |; 
$key = q/{_inline}$a_ijneq0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=51 HEIGHT=27 ALIGN=MIDDLE  SRC="img685.gif"  > |; 
$key = q/{_inline}$S(bmV)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=39 HEIGHT=27 ALIGN=MIDDLE  SRC="img629.gif"  > |; 
$key = q/{_inline}$bmS_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=25 ALIGN=MIDDLE  SRC="img613.gif"  > |; 
$key = q/{_inline}$S^nn${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=13 ALIGN=BOTTOM  SRC="img406.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig510a.eps,height=5cmlabelfig510a{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=530 HEIGHT=229 ALIGN=BOTTOM  SRC="img520.gif"  > |; 
$key = q/{_inline}$|bmxi^n+1-bmxi^n|;SPMlt;0.001${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=154 HEIGHT=32 ALIGN=MIDDLE  SRC="img695.gif"  > |; 
$key = q/{_inline}$V^2_(1,1,-2)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=58 HEIGHT=29 ALIGN=MIDDLE  SRC="img522.gif"  > |; 
$key = q/{_inline}$S(bmV^n+1)simeqA(bmV^n)+B(bmV^n)bmV^n+1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=257 HEIGHT=32 ALIGN=MIDDLE  SRC="img630.gif"  > |; 
$key = q/{_inline}$theta;SPMlt;0.5${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=53 HEIGHT=25 ALIGN=MIDDLE  SRC="img625.gif"  > |; 
$key = q/{_inline}$bma_(1),bma_(2)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=64 HEIGHT=17 ALIGN=MIDDLE  SRC="img107.gif"  > |; 
$key = q/{_inline}$bmu^n${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=12 ALIGN=BOTTOM  SRC="img577.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=nwallcell.eps,height=10cmlabelnearwll{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=296 HEIGHT=442 ALIGN=BOTTOM  SRC="img580.gif"  > |; 
$key = q/{_inline}$sigma^31,sigma^32${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=56 HEIGHT=30 ALIGN=MIDDLE  SRC="img537.gif"  > |; 
$key = q/{_inline}$S_alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=25 ALIGN=MIDDLE  SRC="img266.gif"  > |; 
$key = q/{_inline}$bmF${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=13 HEIGHT=12 ALIGN=BOTTOM  SRC="img612.gif"  > |; 
$key = q/{_inline}$U^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=13 ALIGN=BOTTOM  SRC="img128.gif"  > |; 
$key = q/{displaymath}PDeltap^n+1=g^n+1;;,;;Deltap^n+1=p^n+1-p^n;,{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=401 HEIGHT=19 ALIGN=BOTTOM  SRC="img654.gif"  > |; 
$key = q/{_inline}$eta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=8 HEIGHT=17 ALIGN=MIDDLE  SRC="img289.gif"  > |; 
$key = q/{_inline}$P_k${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE  SRC="img281.gif"  > |; 
$key = q/{_inline}$V^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=13 ALIGN=BOTTOM  SRC="img139.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=36 ALIGN=MIDDLE  SRC="img462.gif"  > |; 
$key = q/{_inline}$xi^3=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=48 HEIGHT=30 ALIGN=MIDDLE  SRC="img22.gif"  > |; 
$key = q/{_inline}$underlinetau_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=16 ALIGN=MIDDLE  SRC="img397.gif"  > |; 
$key = q/{_inline}$phi${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=25 ALIGN=MIDDLE  SRC="img4.gif"  > |; 
$key = q/{_inline}$chris311,...,chris333${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=110 HEIGHT=43 ALIGN=MIDDLE  SRC="img118.gif"  > |; 
$key = q/{_inline}$bmV${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=14 HEIGHT=13 ALIGN=BOTTOM  SRC="img607.gif"  > |; 
$key = q/{_inline}$g_alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=25 HEIGHT=17 ALIGN=MIDDLE  SRC="img47.gif"  > |; 
$key = q/{_inline}$Omega_alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=25 ALIGN=MIDDLE  SRC="img268.gif"  > |; 
$key = q/{_inline}$sigma^11,;sigma^12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=60 HEIGHT=30 ALIGN=MIDDLE  SRC="img458.gif"  > |; 
$key = q/{_inline}$f^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=18 HEIGHT=25 ALIGN=MIDDLE  SRC="img130.gif"  > |; 
$key = q/{_inline}$varepsilon^n+1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=33 HEIGHT=15 ALIGN=BOTTOM  SRC="img375.gif"  > |; 
$key = q/{_inline}$relax_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=5 HEIGHT=11 ALIGN=MIDDLE  SRC="img10.gif"  > |; 
$key = q/{displaymath}arraylllV^alpha;SPMamp;=;SPMamp;sqrtgU^alpha;,bmu;SPMamp;=;SPMamp;U^alphabma_alpha;,array{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=312 HEIGHT=38 ALIGN=BOTTOM  SRC="img701.gif"  > |; 
$key = q/{_inline}$bmx(bmxi^alpha)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=41 HEIGHT=27 ALIGN=MIDDLE  SRC="img33.gif"  > |; 
$key = q/{_inline}$bmV^*${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=22 HEIGHT=14 ALIGN=BOTTOM  SRC="img643.gif"  > |; 
$key = q/{displaymath}alpha_1=fracleft|arrayccbmtaucdotbma_(t_1);SPMamp;g_t_1t_2bmtaucdotbma_(t_2);SPMamp;g_t_2t_1arrayright|left|arrayccg_t_1t_1;SPMamp;g_t_1t_2g_t_2t_1;SPMamp;g_t_2t_2arrayright|{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=337 HEIGHT=102 ALIGN=BOTTOM  SRC="img747.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig56.epslabelfig56{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=624 HEIGHT=274 ALIGN=BOTTOM  SRC="img447.gif"  > |; 
$key = q/{_inline}$Psi(r)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=33 HEIGHT=27 ALIGN=MIDDLE  SRC="img232.gif"  > |; 
$key = q/{_inline}$sigma^21,sigma^22${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=56 HEIGHT=30 ALIGN=MIDDLE  SRC="img553.gif"  > |; 
$key = q/{_inline}$Yrightarrow0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=50 HEIGHT=13 ALIGN=BOTTOM  SRC="img350.gif"  > |; 
$key = q/{_inline}$bma_(2)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=28 HEIGHT=17 ALIGN=MIDDLE  SRC="img83.gif"  > |; 
$key = q/{_inline}$V^alpharightarrowp${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=59 HEIGHT=25 ALIGN=MIDDLE  SRC="img637.gif"  > |; 
$key = q/{_inline}$alpha=1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=12 ALIGN=BOTTOM  SRC="img322.gif"  > |; 
$key = q/{_inline}$bmxi^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=18 HEIGHT=27 ALIGN=MIDDLE  SRC="img38.gif"  > |; 
$key = q/{_inline}$h_mboxtinyR^+rightarrow0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=56 HEIGHT=28 ALIGN=MIDDLE  SRC="img594.gif"  > |; 
$key = q/{_inline}$N_omega${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=25 ALIGN=MIDDLE  SRC="img362.gif"  > |; 
$key = q/{_inline}$bmdGamma${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=22 HEIGHT=12 ALIGN=BOTTOM  SRC="img74.gif"  > |; 
$key = q/{_inline}$U^t_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=22 HEIGHT=15 ALIGN=BOTTOM  SRC="img480.gif"  > |; 
$key = q/{_inline}$chris111,chris112,...,chris133${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=158 HEIGHT=43 ALIGN=MIDDLE  SRC="img116.gif"  > |; 
$key = q/{_inline}$u^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=12 ALIGN=BOTTOM  SRC="img329.gif"  > |; 
$key = q/{figure}[htb]vspace*-1,5cmcenterlinepsfigfigure=fig81.eps,height=10cmlabelfig81{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=283 HEIGHT=284 ALIGN=BOTTOM  SRC="img666.gif"  > |; 
$key = q/{_inline}$V^3=sqrtgU^3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=88 HEIGHT=30 ALIGN=MIDDLE  SRC="img498.gif"  > |; 
$key = q/{_inline}$bma_1,bma_2,bma_3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=70 HEIGHT=17 ALIGN=MIDDLE  SRC="img36.gif"  > |; 
$key = q/{_inline}$V^1_(0,-2,-2)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=68 HEIGHT=29 ALIGN=MIDDLE  SRC="img533.gif"  > |; 
$key = q/{_inline}$bmn${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=12 HEIGHT=8 ALIGN=BOTTOM  SRC="img355.gif"  > |; 
$key = q/{_inline}$0.5leqthetaleq1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=85 HEIGHT=26 ALIGN=MIDDLE  SRC="img623.gif"  > |; 
$key = q/{_inline}$sigmaphi+(knablaphi)cdotbmn${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=114 HEIGHT=27 ALIGN=MIDDLE  SRC="img378.gif"  > |; 
$key = q/{_inline}$-1leqkappaleq1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=86 HEIGHT=25 ALIGN=MIDDLE  SRC="img220.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig35.eps,height=15cmlabelfig35{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=663 HEIGHT=679 ALIGN=BOTTOM  SRC="img120.gif"  > |; 
$key = q/{_inline}$V^alpha=sqrtgU^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=92 HEIGHT=26 ALIGN=MIDDLE  SRC="img135.gif"  > |; 
$key = q/{_inline}$g^alphabeta_,gamma=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=58 HEIGHT=31 ALIGN=MIDDLE  SRC="img162.gif"  > |; 
$key = q/{displaymath}(xi,eta)^1=(12,12){displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=320 HEIGHT=20 ALIGN=BOTTOM  SRC="img693.gif"  > |; 
$key = q/{_inline}$lambda_1(xi)=1-xi,;;lambda_2(xi)=xi${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=189 HEIGHT=27 ALIGN=MIDDLE  SRC="img690.gif"  > |; 
$key = q/{_inline}$bmv${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=8 ALIGN=BOTTOM  SRC="img68.gif"  > |; 
$key = q/{_inline}$V^2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=15 ALIGN=BOTTOM  SRC="img146.gif"  > |; 
$key = q/{_inline}$S^nnbmn${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=40 HEIGHT=13 ALIGN=BOTTOM  SRC="img433.gif"  > |; 
$key = q/{_inline}$sigma^22|_(0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=56 HEIGHT=29 ALIGN=MIDDLE  SRC="img477.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=onedimfv.eps,height=35mmlabelonedfv{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=508 HEIGHT=151 ALIGN=BOTTOM  SRC="img207.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig513a.epslabelfig513a{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=639 HEIGHT=594 ALIGN=BOTTOM  SRC="img531.gif"  > |; 
$key = q/{_inline}$f^*${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=26 ALIGN=MIDDLE  SRC="img175.gif"  > |; 
$key = q/{_inline}$barV^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=16 ALIGN=BOTTOM  SRC="img143.gif"  > |; 
$key = q/{_inline}$xi^1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=15 HEIGHT=30 ALIGN=MIDDLE  SRC="img204.gif"  > |; 
$key = q/{_inline}$bmucdotbmt${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=32 HEIGHT=11 ALIGN=BOTTOM  SRC="img381.gif"  > |; 
$key = q/{displaymath}left[arrayccg_t_1t_1;SPMamp;g_t_2t_1g_t_1t_2;SPMamp;g_t_2t_2arrayright]left[arraycsigma^nt_1sigma^nt_2arrayright]+sigma^nnleft[arraycg_nt_1g_nt_2arrayright]=sign(bma^(n)cdotbmn)sqrtg^nnS^ntauleft[arrayccg_t_1t_1;SPMamp;g_t_2t_1g_t_1t_2;SPMamp;g_t_2t_2arrayright]left[arraycalpha_1alpha_2arrayright]{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=659 HEIGHT=48 ALIGN=BOTTOM  SRC="img753.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig91.eps,height=5cmlabelfig91{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=459 HEIGHT=228 ALIGN=BOTTOM  SRC="img687.gif"  > |; 
$key = q/{_inline}$U^1,U^2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=48 HEIGHT=30 ALIGN=MIDDLE  SRC="img539.gif"  > |; 
$key = q/{_inline}$c_varepsilon1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=17 ALIGN=MIDDLE  SRC="img295.gif"  > |; 
$key = q/{_inline}$alpha_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=17 ALIGN=MIDDLE  SRC="img511.gif"  > |; 
$key = q/{_inline}$underlinetau_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=14 HEIGHT=16 ALIGN=MIDDLE  SRC="img719.gif"  > |; 
$key = q/{_inline}$c_varepsilon1=1.15${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=75 HEIGHT=25 ALIGN=MIDDLE  SRC="img297.gif"  > |; 
$key = q/{_inline}$frac23rhokg^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=54 HEIGHT=31 ALIGN=MIDDLE  SRC="img262.gif"  > |; 
$key = q/{_inline}$0leqs(Pe)leq1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=106 HEIGHT=27 ALIGN=MIDDLE  SRC="img214.gif"  > |; 
$key = q/{_inline}$frac13${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=7 HEIGHT=31 ALIGN=MIDDLE  SRC="img227.gif"  > |; 
$key = q/{_inline}$fracpartialU^2partialxi^2|_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=70 HEIGHT=36 ALIGN=MIDDLE  SRC="img467.gif"  > |; 
$key = q/{_inline}$Y^+=rhou_tauYmu${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=106 HEIGHT=29 ALIGN=MIDDLE  SRC="img363.gif"  > |; 
$key = q/{_inline}$0leqtheta;SPMlt;0.5${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=85 HEIGHT=26 ALIGN=MIDDLE  SRC="img624.gif"  > |; 
$key = q/{_inline}$mu${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=17 ALIGN=MIDDLE  SRC="img131.gif"  > |; 
$key = q/{_inline}$varepsilon${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=7 HEIGHT=9 ALIGN=BOTTOM  SRC="img6.gif"  > |; 
$key = q/{_inline}$bme^T_2=[0;;1]${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=79 HEIGHT=31 ALIGN=MIDDLE  SRC="img508.gif"  > |; 
$key = q/{_inline}$relax_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=4 HEIGHT=13 ALIGN=MIDDLE  SRC="img27.gif"  > |; 
$key = q/{_inline}$sigma^alphabeta=-g^alphabetap+tau^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=147 HEIGHT=32 ALIGN=MIDDLE  SRC="img442.gif"  > |; 
$key = q/{_inline}$kappa=frac12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=41 HEIGHT=31 ALIGN=MIDDLE  SRC="img228.gif"  > |; 
$key = q/{_inline}$R^alphabetaequiv-rhooverlinewidehatU^alphawidehatU^beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=123 HEIGHT=41 ALIGN=MIDDLE  SRC="img132.gif"  > |; 
$key = q/{_inline}$K^11${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=28 HEIGHT=14 ALIGN=BOTTOM  SRC="img254.gif"  > |; 
$key = q/{_inline}$bfa_(3)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=17 ALIGN=MIDDLE  SRC="img3.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig55.epslabelfig55{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=566 HEIGHT=382 ALIGN=BOTTOM  SRC="img443.gif"  > |; 
$key = q/{_inline}$bmtau_w${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=20 HEIGHT=17 ALIGN=MIDDLE  SRC="img566.gif"  > |; 
$key = q/{_inline}$partialV^alphapartialxi^beta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=69 HEIGHT=32 ALIGN=MIDDLE  SRC="img325.gif"  > |; 
$key = q/{_inline}$M_12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=25 ALIGN=MIDDLE  SRC="img25.gif"  > |; 
$key = q/{_inline}$theta=frac12${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=40 HEIGHT=31 ALIGN=MIDDLE  SRC="img622.gif"  > |; 
$key = q/{_inline}$phi_U${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=20 HEIGHT=25 ALIGN=MIDDLE  SRC="img213.gif"  > |; 
$key = q/{_inline}$sigma^33${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=23 HEIGHT=14 ALIGN=BOTTOM  SRC="img538.gif"  > |; 
$key = q/{_inline}$sigma^11|_(0,0,0),;sigma^12_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=129 HEIGHT=29 ALIGN=MIDDLE  SRC="img456.gif"  > |; 
$key = q/{table}[htb]centertabular|l|l|l|l|l|hlineproperties;SPMamp;multicolumn2|cbad;SPMamp;multicolumn2c|good;SPMamp;multicolumn2|c_inline$longleftarrow$_inline;SPMamp;multicolumn2c|_inline$longrightarrow$_inlinehlinememory;SPMamp;GMRES;SPMamp;GMRESR;SPMamp;CGS;SPMamp;LSQRrobustness;SPMamp;CGS;SPMamp;GMRES;SPMamp;GMRESR;SPMamp;LSQRCPU-time;SPMamp;LSQR;SPMamp;GMRES;SPMamp;CGS;SPMamp;GMRESRhlinetabularcenterlabeltab82{table}/;
$cached_env_img{$key} = q| <IMG WIDTH=471 HEIGHT=111 ALIGN=BOTTOM  SRC="img671.gif"  > |; 
$key = q/{_inline}$sqrtgU^t${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=30 ALIGN=MIDDLE  SRC="img388.gif"  > |; 
$key = q/{_inline}$sigma^12|_(0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=66 HEIGHT=29 ALIGN=MIDDLE  SRC="img414.gif"  > |; 
$key = q/{_inline}$bmphi_j${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=18 HEIGHT=25 ALIGN=MIDDLE  SRC="img614.gif"  > |; 
$key = q/{_inline}$approx${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=12 HEIGHT=9 ALIGN=BOTTOM  SRC="img571.gif"  > |; 
$key = q/{_inline}$left(arrayc4+2-12arrayright)=10${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=146 HEIGHT=57 ALIGN=MIDDLE  SRC="img529.gif"  > |; 
$key = q/{_inline}$alpha=1;(U^1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=74 HEIGHT=30 ALIGN=MIDDLE  SRC="img502.gif"  > |; 
$key = q/{_inline}$(0,pm1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=49 HEIGHT=27 ALIGN=MIDDLE  SRC="img82.gif"  > |; 
$key = q/{_inline}$nablaphi${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=24 HEIGHT=25 ALIGN=MIDDLE  SRC="img194.gif"  > |; 
$key = q/{_inline}$sigma^nt_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=14 ALIGN=BOTTOM  SRC="img439.gif"  > |; 
$key = q/{_inline}$V^1_(0,-2,-1),V^2_(0,-3,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=147 HEIGHT=29 ALIGN=MIDDLE  SRC="img546.gif"  > |; 
$key = q/{_inline}$relaxcdotrelax${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=3 HEIGHT=3 ALIGN=BOTTOM  SRC="img8.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^1|_(0,1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=59 HEIGHT=36 ALIGN=MIDDLE  SRC="img429.gif"  > |; 
$key = q/{_inline}$mboxsmall$Phi$=2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=42 HEIGHT=12 ALIGN=BOTTOM  SRC="img224.gif"  > |; 
$key = q/{_inline}$L^-1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=14 ALIGN=BOTTOM  SRC="img682.gif"  > |; 
$key = q/{_inline}$sigma^33|_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=67 HEIGHT=29 ALIGN=MIDDLE  SRC="img488.gif"  > |; 
$key = q/{_inline}$V^2_(-2,i)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=45 HEIGHT=29 ALIGN=MIDDLE  SRC="img527.gif"  > |; 
$key = q/{_inline}$sigma^22_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=47 HEIGHT=29 ALIGN=MIDDLE  SRC="img457.gif"  > |; 
$key = q/{_inline}$0leqalphaleq1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=74 HEIGHT=25 ALIGN=MIDDLE  SRC="img317.gif"  > |; 
$key = q/{table}[htb]centertabular|c|c|c|hline;SPMamp;multicolumn2|c|boundaryconditiontypecline2-3combination;SPMamp;leftboundary;SPMamp;bottomboundary;SPMamp;_inline$(xi^2=0)$_inline;SPMamp;_inline$(xi^3=0)$_inlinehline(i);SPMamp;1;SPMamp;1(ii);SPMamp;1;SPMamp;2(iii);SPMamp;1;SPMamp;3(iv);SPMamp;1;SPMamp;4(v);SPMamp;2;SPMamp;2(vi);SPMamp;2;SPMamp;3(vii);SPMamp;2;SPMamp;4(viii);SPMamp;3;SPMamp;3(ix);SPMamp;3;SPMamp;4(x);SPMamp;4;SPMamp;4hlinetabularcenterlabeltab51{table}/;
$cached_env_img{$key} = q| <IMG WIDTH=390 HEIGHT=284 ALIGN=BOTTOM  SRC="img530.gif"  > |; 
$key = q/{_inline}$u_tau=sqrttau_wrho${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=94 HEIGHT=31 ALIGN=MIDDLE  SRC="img364.gif"  > |; 
$key = q/{_inline}$M_21${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=25 ALIGN=MIDDLE  SRC="img26.gif"  > |; 
$key = q/{_inline}$bmxi${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=25 ALIGN=MIDDLE  SRC="img330.gif"  > |; 
$key = q/{_inline}$kappaneqfrac13${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=41 HEIGHT=31 ALIGN=MIDDLE  SRC="img231.gif"  > |; 
$key = q/{_inline}$U=diag;(A)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=99 HEIGHT=27 ALIGN=MIDDLE  SRC="img676.gif"  > |; 
$key = q/{_inline}$DM^-1G${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=64 HEIGHT=15 ALIGN=BOTTOM  SRC="img652.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig511a.eps,height=8.3cmlabelfig511a{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=336 HEIGHT=379 ALIGN=BOTTOM  SRC="img521.gif"  > |; 
$key = q/{_inline}$xi^1=constant${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=106 HEIGHT=30 ALIGN=MIDDLE  SRC="img17.gif"  > |; 
$key = q/{_inline}$g_nt_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=26 HEIGHT=17 ALIGN=MIDDLE  SRC="img481.gif"  > |; 
$key = q/{_inline}$sigma^12_(0,0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=57 HEIGHT=29 ALIGN=MIDDLE  SRC="img556.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig82.eps,height=10cmvspace*-1,5cmlabelfig82{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=283 HEIGHT=284 ALIGN=BOTTOM  SRC="img669.gif"  > |; 
$key = q/{_inline}$V^1_(0,-3,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=68 HEIGHT=29 ALIGN=MIDDLE  SRC="img549.gif"  > |; 
$key = q/{_inline}$sigma_k${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=16 ALIGN=MIDDLE  SRC="img283.gif"  > |; 
$key = q/{_inline}$p_0,1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=27 HEIGHT=17 ALIGN=MIDDLE  SRC="img425.gif"  > |; 
$key = q/{_inline}$c_tau1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=17 ALIGN=MIDDLE  SRC="img273.gif"  > |; 
$key = q/{_inline}$bmS_dc,i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=33 HEIGHT=25 ALIGN=MIDDLE  SRC="img616.gif"  > |; 
$key = q/{_inline}$xi^2=0${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=48 HEIGHT=30 ALIGN=MIDDLE  SRC="img21.gif"  > |; 
$key = q/{_inline}$frac51cdot319=8${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=58 HEIGHT=31 ALIGN=MIDDLE  SRC="img668.gif"  > |; 
$key = q/{_inline}$phi_i,foralliin{1,..,N}${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=128 HEIGHT=27 ALIGN=MIDDLE  SRC="img636.gif"  > |; 
$key = q/{_inline}$bme^T_1=[1;;0]${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=79 HEIGHT=31 ALIGN=MIDDLE  SRC="img504.gif"  > |; 
$key = q/{_inline}$Gamma_b${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=25 ALIGN=MIDDLE  SRC="img563.gif"  > |; 
$key = q/{_inline}$Re_mboxtinyT${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=29 HEIGHT=25 ALIGN=MIDDLE  SRC="img348.gif"  > |; 
$key = q/{table}[htb]centertabular|l|c|c|c|c|hlineAEVM;SPMamp;_inline$c_mu$_inline;SPMamp;_inline$c_tau1$_inline;SPMamp;_inline$c_tau2$_inline;SPMamp;_inline$c_tau3$_inlinehlineSpeziale;SPMamp;0.09;SPMamp;0.1512;SPMamp;0.1512;SPMamp;0hlineRubinstein-Barton;SPMamp;0.085;SPMamp;0.68;SPMamp;0.14;SPMamp;-0.56hlineNisizima-Yoshizawa;SPMamp;0.09;SPMamp;-0.7881;SPMamp;0.1769;SPMamp;1.0675hlineMyong-Kasagi;SPMamp;0.09;SPMamp;0.275;SPMamp;0.2375;SPMamp;0.05hlinetabularcenterlabeltabaniso{table}/;
$cached_env_img{$key} = q| <IMG WIDTH=437 HEIGHT=113 ALIGN=BOTTOM  SRC="img276.gif"  > |; 
$key = q/{_inline}$alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=8 ALIGN=BOTTOM  SRC="img35.gif"  > |; 
$key = q/{_inline}$dGamma${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=18 HEIGHT=12 ALIGN=BOTTOM  SRC="img77.gif"  > |; 
$key = q/{_inline}$bmtau_1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=17 ALIGN=MIDDLE  SRC="img393.gif"  > |; 
$key = q/{_inline}$rho${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=17 ALIGN=MIDDLE  SRC="img129.gif"  > |; 
$key = q/{_inline}$R_y${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=20 HEIGHT=26 ALIGN=MIDDLE  SRC="img349.gif"  > |; 
$key = q/{_inline}$eta=sqrtP_krhoc_muvarepsilon${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=110 HEIGHT=39 ALIGN=MIDDLE  SRC="img290.gif"  > |; 
$key = q/{_inline}$alpha=0.85${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=64 HEIGHT=13 ALIGN=BOTTOM  SRC="img318.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig515.epslabelfig515{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=639 HEIGHT=635 ALIGN=BOTTOM  SRC="img557.gif"  > |; 
$key = q/{_inline}$Q^alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=31 HEIGHT=32 ALIGN=MIDDLE  SRC="img319.gif"  > |; 
$key = q/{_inline}$alpha=1,2,3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=75 HEIGHT=25 ALIGN=MIDDLE  SRC="img464.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig54.eps,height=6cmlabelfig54{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=456 HEIGHT=272 ALIGN=BOTTOM  SRC="img437.gif"  > |; 
$key = q/{_inline}$sigma_varepsilon${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=15 HEIGHT=17 ALIGN=MIDDLE  SRC="img284.gif"  > |; 
$key = q/{_inline}$n_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=14 HEIGHT=17 ALIGN=MIDDLE  SRC="img656.gif"  > |; 
$key = q/{_inline}$barsigma^ij${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=21 HEIGHT=15 ALIGN=BOTTOM  SRC="img737.gif"  > |; 
$key = q/{displaymath}left(arraycccM_11;SPMamp;M_12;SPMamp;M_13M_21;SPMamp;M_22;SPMamp;M_23M_31;SPMamp;M_32;SPMamp;M_33arrayright)left(arraycu_1u_2u_3arrayright)=left(arraycf_1f_2f_3arrayright);.{displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=412 HEIGHT=67 ALIGN=BOTTOM  SRC="img662.gif"  > |; 
$key = q/{_inline}$p_0,0,1${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=37 HEIGHT=17 ALIGN=MIDDLE  SRC="img461.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig58.eps,height=5cmlabelfig58{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=428 HEIGHT=227 ALIGN=BOTTOM  SRC="img514.gif"  > |; 
$key = q/{_inline}$(sqrtgsigma^12)_(0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=98 HEIGHT=29 ALIGN=MIDDLE  SRC="img495.gif"  > |; 
$key = q/{_inline}$bmp${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=11 HEIGHT=17 ALIGN=MIDDLE  SRC="img608.gif"  > |; 
$key = q/{_inline}$tau_w${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=17 ALIGN=MIDDLE  SRC="img365.gif"  > |; 
$key = q/{_inline}$fracpartialU^2partialxi^3|_(0,0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=70 HEIGHT=36 ALIGN=MIDDLE  SRC="img471.gif"  > |; 
$key = q/{_inline}$phi_(i+1,j-1,k)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=79 HEIGHT=25 ALIGN=MIDDLE  SRC="img244.gif"  > |; 
$key = q/{_inline}$Y_mboxtinyP${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=25 ALIGN=MIDDLE  SRC="img359.gif"  > |; 
$key = q/{_inline}$U^2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=15 ALIGN=BOTTOM  SRC="img18.gif"  > |; 
$key = q/{_inline}$phi_(i,j-1,k)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=62 HEIGHT=25 ALIGN=MIDDLE  SRC="img243.gif"  > |; 
$key = q/{_inline}$frac13cdot29=3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=58 HEIGHT=31 ALIGN=MIDDLE  SRC="img667.gif"  > |; 
$key = q/{_inline}$bmx${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=9 HEIGHT=8 ALIGN=BOTTOM  SRC="img184.gif"  > |; 
$key = q/{_inline}$bmx(bmxi)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=32 HEIGHT=27 ALIGN=MIDDLE  SRC="img238.gif"  > |; 
$key = q/{_inline}$bmucdotbmn${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=37 HEIGHT=8 ALIGN=BOTTOM  SRC="img380.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig51.eps,height=5cmlabelfig51{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=306 HEIGHT=226 ALIGN=BOTTOM  SRC="img385.gif"  > |; 
$key = q/{_inline}$xi^n${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=16 HEIGHT=25 ALIGN=MIDDLE  SRC="img390.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=fig514.epslabelfig514{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=571 HEIGHT=559 ALIGN=BOTTOM  SRC="img536.gif"  > |; 
$key = q/{_inline}$V^3V^3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=41 HEIGHT=15 ALIGN=BOTTOM  SRC="img486.gif"  > |; 
$key = q/{_inline}$fracpartialU^1partialxi^1|_(0,0,0),;fracpartialU^1partialxi^2|_(0,0,0),${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=160 HEIGHT=36 ALIGN=MIDDLE  SRC="img465.gif"  > |; 
$key = q/{_inline}$t=t^n+thetaDeltat${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=95 HEIGHT=25 ALIGN=MIDDLE  SRC="img645.gif"  > |; 
$key = q/{_inline}$(i+frac12,j,k)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=81 HEIGHT=31 ALIGN=MIDDLE  SRC="img237.gif"  > |; 
$key = q/{_inline}$bma_(1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=28 HEIGHT=17 ALIGN=MIDDLE  SRC="img81.gif"  > |; 
$key = q/{_inline}$bmV^n+theta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=40 HEIGHT=17 ALIGN=BOTTOM  SRC="img650.gif"  > |; 
$key = q/{_inline}$h_mboxtinyR${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE  SRC="img587.gif"  > |; 
$key = q/{_inline}$sigma^33|_(0,0,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=77 HEIGHT=29 ALIGN=MIDDLE  SRC="img512.gif"  > |; 
$key = q/{_inline}$c_varepsilon3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=19 HEIGHT=17 ALIGN=MIDDLE  SRC="img296.gif"  > |; 
$key = q/{_inline}$M_ii,;i=1,2,3${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=110 HEIGHT=25 ALIGN=MIDDLE  SRC="img663.gif"  > |; 
$key = q/{_inline}$V^1_(0,-2,-1)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=68 HEIGHT=29 ALIGN=MIDDLE  SRC="img548.gif"  > |; 
$key = q/{figure}[htb]centerlinepsfigfigure=ndist.eps,height=8cmlabelndist{figure}/;
$cached_env_img{$key} = q| <IMG WIDTH=438 HEIGHT=361 ALIGN=BOTTOM  SRC="img354.gif"  > |; 
$key = q/{_inline}$Deltat${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=20 HEIGHT=12 ALIGN=BOTTOM  SRC="img619.gif"  > |; 
$key = q/{displaymath}sign(bma^(n)cdotbmn){g_t_1t_2sigma^nt_1+g_t_2t_2sigma^nt_2+g_nt_2sigma^nn}=sqrtg^nnS^ntau(alpha_1g_t_1t_2+alpha_2gt_2t_2){displaymath}/;
$cached_env_img{$key} = q| <IMG WIDTH=576 HEIGHT=21 ALIGN=BOTTOM  SRC="img752.gif"  > |; 
$key = q/{_inline}$V^alpharightarrowprightarrowphi_1rightarrow,..,rightarrowphi_Nrightarrowkrightarrowvarepsilonmboxoromega${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=307 HEIGHT=25 ALIGN=MIDDLE  SRC="img639.gif"  > |; 
$key = q/{_inline}$bmtau_i${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=15 HEIGHT=17 ALIGN=MIDDLE  SRC="img717.gif"  > |; 
$key = q/{_inline}$V^1_(0,0)${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=37 HEIGHT=29 ALIGN=MIDDLE  SRC="img515.gif"  > |; 
$key = q/{table}[htb]centertabular|l|c|c|c|c|c|c|hline_inline$k$_inline-_inline$varepsilon$_inlinevariant;SPMamp;_inline$c_mu$_inline;SPMamp;_inline$sigma_k$_inline;SPMamp;_inline$sigma_varepsilon$_inline;SPMamp;_inline$c_varepsilon1$_inline;SPMamp;_inline$c_varepsilon2$_inline;SPMamp;_inline$c_varepsilon3$_inlinehlineStandard;SPMamp;0.09;SPMamp;1.0;SPMamp;1.3;SPMamp;1.44;SPMamp;1.92;SPMamp;-hlineRNG;SPMamp;0.085;SPMamp;0.7179;SPMamp;0.7179;SPMamp;1.42;SPMamp;1.68;SPMamp;-hlineExted;SPMamp;0.09;SPMamp;0.75;SPMamp;1.15;SPMamp;1.35;SPMamp;1.9;SPMamp;0.05hlinetabularcenter{table}/;
$cached_env_img{$key} = q| <IMG WIDTH=447 HEIGHT=91 ALIGN=BOTTOM  SRC="img294.gif"  > |; 
$key = q/{_inline}$xi^alpha${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=17 HEIGHT=25 ALIGN=MIDDLE  SRC="img105.gif"  > |; 
$key = q/{_inline}$underlineucdotunderlinetau_2${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=38 HEIGHT=16 ALIGN=MIDDLE  SRC="img396.gif"  > |; 
$key = q/{_inline}$omega${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=11 HEIGHT=8 ALIGN=BOTTOM  SRC="img277.gif"  > |; 
$key = q/{_inline}$knablaphi${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=33 HEIGHT=25 ALIGN=MIDDLE  SRC="img193.gif"  > |; 
$key = q/{_inline}$G=S^alphabetaS_alphabeta${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=94 HEIGHT=32 ALIGN=MIDDLE  SRC="img367.gif"  > |; 
$key = q/{_inline}$V^alphasqrtg${_inline}/;
$cached_env_img{$key} = q| <IMG WIDTH=55 HEIGHT=28 ALIGN=MIDDLE  SRC="img154.gif"  > |; 

1;

