This is TeX, Version 3.1415 (C version 6.1) (format=lplain 94.6.16)  5 JUL 1996 11:44
**&latex209 images.tex
(images.tex
LaTeX Version 2.09 <25 March 1992>

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Standard Document Style `article' <14 Jan 92>.
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\captionwidth=\skip41
! You can't use `\long' or `\outer' with `\catcode'.
\makeatother ->\catcode 
                        `\@ =12\relax 
l.25 \makeatother
                 
I'll pretend you didn't say \long or \outer here.

\c@algorithm=\count87
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(images.aux)
! Undefined control sequence.
l.492 \samepage \setbox\sizebox=\hbox{${\fam \tw
                                                @ P}$}\lthtmltypeout{latex2h...
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Missing number, treated as zero.
<to be read again> 
                   @
l.492 \samepage \setbox\sizebox=\hbox{${\fam \tw@
                                                  P}$}\lthtmltypeout{latex2h...
A number should have been here; I inserted `0'.
(If you can't figure out why I needed to see a number,
look up `weird error' in the index to The TeXbook.)

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\hbox(0.0+0.0)x455.24408
.\glue(\tabskip) 0.0 plus 1000.0
.\unsetbox(0.0+0.0)x455.24408
.\glue(\tabskip) 0.0
.\unsetbox(0.0+0.0)x10.0
.\glue(\tabskip) 0.0
.etc.

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\hbox(0.0+0.0)x455.24408
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.\glue(\tabskip) 0.0
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.etc.

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! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.757 
      
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \par 
l.757 
      
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   \par 
l.757 
      
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.757 
      
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
<to be read again> 
                   \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.757 
      
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endtemplate 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.757 
      
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $$ inserted.
<to be read again> 
                   \par 
l.757 
      
Displays can use special alignments (like \eqalignno)
only if nothing but the alignment itself is between $$'s.

! Misplaced alignment tab character &.
\@tempa ->&
            & &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.759 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& &
              &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.759 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& & &
               
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.759 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.759 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endeqnarray ->\@@eqncr \egroup 
                                \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.759 \end{eqnarray}
                    
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.759 \end{eqnarray}
                    
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.759 \end{eqnarray}
                    
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

[39

]
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]
! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.783 
      
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \par 
l.783 
      
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   \par 
l.783 
      
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.783 
      
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
<to be read again> 
                   \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.783 
      
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endtemplate 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.783 
      
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $$ inserted.
<to be read again> 
                   \par 
l.783 
      
Displays can use special alignments (like \eqalignno)
only if nothing but the alignment itself is between $$'s.

! Misplaced alignment tab character &.
\@tempa ->&
            & &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.785 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& &
              &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.785 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& & &
               
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.785 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.785 \end{eqnarray}
                    
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endeqnarray ->\@@eqncr \egroup 
                                \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.785 \end{eqnarray}
                    
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.785 \end{eqnarray}
                    
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.785 \end{eqnarray}
                    
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

[43

]
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[44

] [45

]
! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.811 
      
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \par 
l.811 
      
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   \par 
l.811 
      
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.811 
      
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
<to be read again> 
                   \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.811 
      
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endtemplate 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.811 
      
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $$ inserted.
<to be read again> 
                   \par 
l.811 
      
Displays can use special alignments (like \eqalignno)
only if nothing but the alignment itself is between $$'s.

! Misplaced alignment tab character &.
\@tempa ->&
            & &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.812 \end{eqnarray*}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& &
              &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.812 \end{eqnarray*}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& & &
               
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.812 \end{eqnarray*}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.812 \end{eqnarray*}
                     
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endeqnarray ->\@@eqncr \egroup 
                                \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.812 \end{eqnarray*}
                     
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.812 \end{eqnarray*}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.812 \end{eqnarray*}
                     
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

[46

]
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! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.1132 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \in 
l.1133 \mbox{~for~}i\in
                       \{1,2,\ldots n\}$}\lthtmltypeout{latex2htmlSize :tex2...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

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! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.1309 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \par 
l.1309 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   \par 
l.1309 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1309 
       
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
<to be read again> 
                   \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1309 
       
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endtemplate 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1309 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $$ inserted.
<to be read again> 
                   \par 
l.1309 
       
Displays can use special alignments (like \eqalignno)
only if nothing but the alignment itself is between $$'s.

! Misplaced alignment tab character &.
\@tempa ->&
           
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1311 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1311 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endeqnarray ->\@@eqncr \egroup 
                                \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1311 \end{eqnarray}
                     
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.1311 \end{eqnarray}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.1311 \end{eqnarray}
                     
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

[123

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]
! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.1331 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \par 
l.1331 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   \par 
l.1331 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1331 
       
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
<to be read again> 
                   \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1331 
       
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endtemplate 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1331 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $$ inserted.
<to be read again> 
                   \par 
l.1331 
       
Displays can use special alignments (like \eqalignno)
only if nothing but the alignment itself is between $$'s.

! Misplaced alignment tab character &.
\@tempa ->&
           
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1333 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1333 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endeqnarray ->\@@eqncr \egroup 
                                \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1333 \end{eqnarray}
                     
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.1333 \end{eqnarray}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.1333 \end{eqnarray}
                     
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

[126

]
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]
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[147

]
! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.1473 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \par 
l.1473 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   \par 
l.1473 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1473 
       
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
<to be read again> 
                   \cr 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1473 
       
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endtemplate 
<to be read again> 
                   }
<to be read again> 
                   \par 
l.1473 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $$ inserted.
<to be read again> 
                   \par 
l.1473 
       
Displays can use special alignments (like \eqalignno)
only if nothing but the alignment itself is between $$'s.

! Misplaced alignment tab character &.
\@tempa ->&
            & &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1474 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& &
              &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1474 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& & &
               
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1474 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1474 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten \endgroup.
\endeqnarray ->\@@eqncr \egroup 
                                \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1474 \end{eqnarray}
                     
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.1474 \end{eqnarray}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Display math should end with $$.
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.1474 \end{eqnarray}
                     
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.

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]
! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Missing \cr inserted.
<inserted text> 
                \cr 
<to be read again> 
                   }
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
I'm guessing that you meant to end an alignment here.

! Missing { inserted.
<inserted text> 
                {
<to be read again> 
                   \cr 
<to be read again> 
                   }
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
I've put in what seems to be necessary to fix
the current column of the current alignment.
Try to go on, since this might almost work.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endtemplate 
<to be read again> 
                   }
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing $$ inserted.
<to be read again> 
                   \@@par 
\par ->\if@newlist \else {\@@par 
                                 }\fi 
l.1771 
       
Displays can use special alignments (like \eqalignno)
only if nothing but the alignment itself is between $$'s.

! Extra }, or forgotten \endgroup.
\par ->\if@newlist \else {\@@par }
                                  \fi 
l.1771 
       
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \mathaccent 
\tilde ->\mathaccent 
                     "707E 
l.1772  = {\tilde
                 {p} }
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Extra }, or forgotten $.
l.1772  = {\tilde{p} }
                      
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Misplaced alignment tab character &.
\@tempa ->&
           
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\@xeqncr [#1]->\ifnum 0=`{\fi }\@@eqncr 
                                        \noalign {\penalty \@eqpen \vskip \j...
<to be read again> 
                   \label 
l.1774 \label
             {eq:iscaling}
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\@xeqncr [#1]->\ifnum 0=`{\fi }\@@eqncr 
                                        \noalign {\penalty \@eqpen \vskip \j...
<to be read again> 
                   \label 
l.1774 \label
             {eq:iscaling}
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \noalign.
\@xeqncr [#1]->\ifnum 0=`{\fi }\@@eqncr \noalign 
                                                 {\penalty \@eqpen \vskip \j...
<to be read again> 
                   \label 
l.1774 \label
             {eq:iscaling}
I expect to see \noalign only after the \cr of
an alignment. Proceed, and I'll ignore this case.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \vskip 
\@xeqncr ...ncr \noalign {\penalty \@eqpen \vskip 
                                                  \jot \vskip #1\relax }
<to be read again> 
                   \label 
l.1774 \label
             {eq:iscaling}
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \vskip 
\@xeqncr ...ncr \noalign {\penalty \@eqpen \vskip 
                                                  \jot \vskip #1\relax }
<to be read again> 
                   \label 
l.1774 \label
             {eq:iscaling}
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

! Misplaced alignment tab character &.
l.1775 {\rm where} &
                    ~&f^{\#}
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
l.1775 {\rm where} &~&
                      f^{\#}
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   ^
l.1775 {\rm where} &~&f^
                        {\#}
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Misplaced alignment tab character &.
\@tempa ->&
            & &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1779 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& &
              &
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1779 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced alignment tab character &.
\@tempa ->& & &
               
\@@eqncr ...& &}\else \def \@tempa {&}\fi \@tempa 
                                                  \if@eqnsw \@eqnnum \stepco...

\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1779 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
here. If you just want an ampersand, the remedy is
simple: Just type `I\&' now. But if some right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Misplaced \cr.
\@@eqncr ...l \@eqnswtrue \global \@eqcnt \z@ \cr 
                                                  
\endeqnarray ->\@@eqncr 
                        \egroup \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1779 \end{eqnarray}
                     
I can't figure out why you would want to use a tab mark
or \cr or \span just now. If something like a right brace
up above has ended a previous alignment prematurely,
you're probably due for more error messages, and you
might try typing `S' now just to see what is salvageable.

! Extra }, or forgotten $.
\endeqnarray ->\@@eqncr \egroup 
                                \global \advance \c@equation \m@ne $$\global...

\end #1->\csname end#1\endcsname 
                                 \@checkend {#1}\expandafter \endgroup \if@e...
l.1779 \end{eqnarray}
                     
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \endgroup 
\end ...ndafter \endgroup \if@endpe \@doendpe \fi 
                                                  \if@ignore \global \@ignor...
l.1779 \end{eqnarray}
                     
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.

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LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.
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Here is how much of TeX's memory you used:
 378 strings out of 11977
 3352 string characters out of 87272
 31136 words of memory out of 262141
 2328 multiletter control sequences out of 9500
 18996 words of font info for 72 fonts, out of 100000 for 255
 14 hyphenation exceptions out of 607
 12i,15n,15p,201b,343s stack positions out of 300i,40n,60p,3000b,4000s

Output written on images.dvi (285 pages, 36256 bytes).