# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/displaystylefrac{epsilon-bar{epsilon}}{xi}-gamma'-beta^2-lnfrac{xi}{E_{{rm{max}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="51" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$\displaystyle \frac{\epsilon -\bar{\epsilon} }{\xi}
- \gamma' - \beta^2 - \ln \frac{\xi} {E_{\rm max}}$">|; 

$key = q/a^2+b^2=c^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$ a^2+b^2=c^2$">|; 

$key = q/n>2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$ n&gt;2$">|; 

$key = q/{subequations}align{B_{ij}^alpha<col_mark>=left(B_{ij}^alpharight)_0+left(B_{ij}}{{d{X_i}frac{{d{N_k^alpha}{{d{X_j}right)align{{subequations};MSF=1.6;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="559" HEIGHT="159" ALIGN="BOTTOM" BORDER="0"
 SRC="img21.gif"
 ALT="\begin{subequations}\begin{align}B_{ij}^\alpha &amp; = \left(B_{ij}^\alpha\right)_0 ...
...\beta}{\d X_i} \frac{\d N_k^\alpha}{\d X_j} \right)\end{align}\end{subequations}">|; 

$key = q/y=B(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$ y=B(x)$">|; 

$key = q/displaystyle=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$\displaystyle =$">|; 

$key = q/mathcal{N}(A)=mathcal{R}(B);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$ \mathcal{N}(A) = \mathcal{R}(B)$">|; 

$key = q/displaystylelambda;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$\displaystyle \lambda$">|; 

$key = q/displaystyle0.577215dotsmathrm{hspace{5mm}(Euler'sconstant)};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$\displaystyle 0.577215\dots \mathrm{\hspace{5mm}(Euler's\ constant)}$">|; 

$key = q/displaystylegamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$\displaystyle \gamma$">|; 

$key = q/displaystyleleft<sum_iM_imathbf{V}_imathbf{V}_i+sum_isum_{j>i}mathbf{R}_{ij}mathbf{F}_{ij}right>;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$\displaystyle \left&lt; \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+ \sum_i \sum_{j&gt;i} \mathbf{R}_{ij} \mathbf{F}_{ij}\right&gt;$">|; 

$key = q/displaystylegamma';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$\displaystyle \gamma'$">|; 

$key = q/a^n+b^n=c^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$ a^n+b^n=c^n$">|; 

$key = q/displaystyleepsilon,bar{epsilon};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$\displaystyle \epsilon , \bar{\epsilon}$">|; 

$key = q/displaystyleleft<sum_iM_imathbf{V}_imathbf{V}_i+sum_{i}sum_{j>i}sum_alphasum_betalphajbeta}-sum_isum_alphamathbf{p}_{ialpha}mathbf{f}_{ialpha}right>;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="418" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$\displaystyle \left&lt; \sum_i M_i \mathbf{V}_i \mathbf{V}_i
+ \sum_{i}\sum_{j&gt;i}\...
... j\beta}
- \sum_i \sum_\alpha \mathbf{p}_{i\alpha} \mathbf{f}_{i\alpha} \right&gt;$">|; 

$key = q/displaystylecgeq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$\displaystyle c \geq 0$">|; 

$key = q/deltamathbf{c};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="img12.gif"
 ALT="$ \delta\mathbf{c}$">|; 

$key = q/displaystyle0.422784dots=1-gamma;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="28" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$\displaystyle 0.422784\dots = 1 - \gamma$">|; 

$key = q/displaystylefrac{1}{2pii}int^{c+iinfty}_{c-iinfty}expleft(ulnu+lambdauright)du;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$\displaystyle \frac{1} {2 \pi i}\int^{c+i\infty}_{c-i\infty}
\exp \left( u \ln u + \lambda u \right ) du$">|; 

$key = q/displaystylephi(lambda);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$\displaystyle \phi(\lambda)$">|; 

$key = q/displaystyleVmathbf{pi}^{sr};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$\displaystyle V \mathbf{\pi}^{sr}$">|; 

1;