# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/:d_{00}=0:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$ \:d_{00} = 0 \:$">|; 

$key = q/,d_{00}=-1;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$ \,d_{00} = -1\;$">|; 

$key = q/displaystyle-x^2-y^2-1,=,0hspace{1cm}Longleftrightarrowhspace{1cm}x^2+y^2+1,=,0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="425" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$\displaystyle -x^2-y^2-1 \,=\,0 \hspace{1cm}\Longleftrightarrow \hspace{1cm}
x^2+y^2+1 \,=\,0.
$">|; 

$key = q/{displaymath}left{array{{l}x''=displaystylefrac{x}{sqrt{a_{11}}}<row_mark>,<row_<row_mark>,<row_mark>z''=z<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="167" BORDER="0"
 SRC="img24.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x'' = \displaystyle\frac{x}{\sqr...
...-2{a_{02}}} \\\\
\, \\\\
z'' = z \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/,a_{11}>0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.gif"
 ALT="$ \,a_{11} &gt; 0 \,$">|; 

$key = q/{displaymath}array{{ll}x^2+y^2+z^2-1,=,0;hspace{1cm}<col_mark>x^2+y^2+z^2+1,=,0;1cm}<col_mark>x^2-y^2-z^2-1,=,0.<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="416" HEIGHT="90" BORDER="0"
 SRC="img7.gif"
 ALT="\begin{displaymath}
\begin{array}{ll}
x^2+y^2+z^2-1 \,=\,0; \hspace{1cm} &amp; x^2...
...,=\,0; \hspace{1cm} &amp; x^2-y^2-z^2-1 \,=\,0. \\\\
\end{array}
\end{displaymath}">|; 

$key = q/displaystylex^2+y^2,=,0;hspace{1cm}x^2-y^2,=,0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$\displaystyle x^2+y^2 \,=\,0; \hspace{1cm} x^2-y^2 \,=\,0.
$">|; 

$key = q/{displaymath}array{{ll}x^2-1,=,0hspace{2cm}<col_mark>mbox{se}:a_{11}>0;<row_mark2cm}<col_mark>mbox{se}:a_{11}<0.<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="90" BORDER="0"
 SRC="img22.gif"
 ALT="\begin{displaymath}
\begin{array}{ll}
x^2 - 1 \,=\,0 \hspace{2cm} &amp; \mbox{se} ...
...,=\,0 \hspace{2cm} &amp; \mbox{se} \:a_{11} &lt; 0.\\\\
\end{array}
\end{displaymath}">|; 

$key = q/displaystyle:d_{00}=0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$\displaystyle \:d_{00} = 0;
$">|; 

$key = q/,-1:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$ \,-1\:$">|; 

$key = q/,c_{00}neq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$ \,c_{00} \neq 0
\,$">|; 

$key = q/{displaymath}left{array{{l}x'=displaystylefrac{x}{sqrt{|a_{11}|}}<row_mark>,<row}<row_mark>,<row_mark>z'=z<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="179" BORDER="0"
 SRC="img11.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x' = \displaystyle\frac{x}{\sqrt...
..._{22}\vert}} \\\\
\, \\\\
z' = z \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/,d_{00}neq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$ \,d_{00} \neq 0 \,$">|; 

$key = q/,A^3(mathbb{R});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img26.gif"
 ALT="$ \,A^3(\mathbb {R})$">|; 

$key = q/displaystylex^2-y,=,0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img25.gif"
 ALT="$\displaystyle x^2-y \,=\,0.
$">|; 

$key = q/displaystylex^2+y^2+z^2,=,0;hspace{1cm}x^2+y^2-z^2,=,0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="343" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$\displaystyle x^2+y^2+z^2 \,=\,0; \hspace{1cm} x^2+y^2-z^2 \,=\,0.
$">|; 

$key = q/,d_{00}=1,,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.gif"
 ALT="$ \,d_{00} =
1,\,$">|; 

$key = q/displaystylex^2+y^2-z,=,0;hspace{1cm}x^2-y^2-z,=,0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$\displaystyle x^2+y^2-z \,=\,0; \hspace{1cm} x^2-y^2-z \,=\,0.
$">|; 

$key = q/,c_{00},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$ \,c_{00} \,$">|; 

$key = q/,-c_{00}^{-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$ \,-c_{00}^{-1} \,$">|; 

$key = q/{displaymath}left{array{{l}x'=displaystylefrac{x}{sqrt{|a_{11}|}}<row_mark>,<rowplaystylefrac{z}{-2a_{03}}<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="185" BORDER="0"
 SRC="img16.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x' = \displaystyle\frac{ x}{\sqr...
... = \displaystyle\frac{z}{-2a_{03}} \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/displaystylex^2,=,0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$\displaystyle x^2 \,=\,0$">|; 

$key = q/{displaymath}left{array{{l}x'=displaystylefrac{x}{sqrt{|a_{11}|}}<row_mark>,<rowylefrac{z}{sqrt{|a_{33}|}}<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="190" BORDER="0"
 SRC="img6.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x' = \displaystyle\frac{x}{\sqrt...
...\frac{z}{\sqrt{\vert a_{33}\vert}} \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/displaystylex^2+y^2-1,=,0;hspace{1cm}hspace{1cm}x^2-y^2-1,=,0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$\displaystyle x^2+y^2-1 \,=\,0; \hspace{1cm} \hspace{1cm} x^2-y^2-1 \,=\,0;
$">|; 

$key = q/,mathcal{Q},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$ \,\mathcal{Q} \,$">|; 

$key = q/:c_{00}=0:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$ \:c_{00} = 0 \:$">|; 

1;

