This is TeX, C Version 3.141 (format=lplain 93.6.8) 26 OCT 1995 23:26 **26063_images.tex (26063_images.tex LaTeX Version 2.09 <14 January 1992> (/usr/local/lib/tex/inputs/article.sty Standard Document Style `article' <14 Jan 92>. (/usr/local/lib/tex/inputs/art12.sty) \c@part=\count79 \c@section=\count80 \c@subsection=\count81 \c@subsubsection=\count82 \c@paragraph=\count83 \c@subparagraph=\count84 \c@figure=\count85 \c@table=\count86 ) \c@theorem=\count87 \c@lemma=\count88 \c@corollary=\count89 \c@proposition=\count90 \c@conjecture=\count91 (26063_images.aux) [1 ] [2 ] [3 ] [4 ] [5 ] [6 ] [7 ] [8 ] [9 ] [10 ] [11 ] [12 ] [13 ] [14 ] [15 ] [16 ] [17 ] [18 ] [19 ] [20 ] [21 ] [22 ] [23 ] [24 ] [25 ] [26 ] [27 ] [28 ] [29 ] [30 ] [31 ] [32 ] [33 ] [34 ] [35 ] [36 ] [37 ] [38 ] [39 ] [40 ] [41 ] [42 ] [43 ] [44 ] [45 ] [46 ] [47 ] [48 ] [49 ] [50 ] [51 ] [52 ] [53 ] [54 ] [55 ] [56 ] [57 ] [58 ] [59 ] [60 ] [61 ] [62 ] [63 ] [64 ] [65 ] [66 ] [67 ] [68 ] [69 ] [70 ] [71 ] [72 ] [73 ] [74 ] [75 ] [76 ] [77 ] [78 ] [79 ] [80 ] [81 ] [82 ] [83 ] [84 ] [85 ] [86 ] [87 ] [88 ] [89 ] [90 ] [91 ] [92 ] [93 ] [94 ] [95 ] [96 ] [97 ] [98 ] [99 ] ! Display math should end with $$. { \p ->{ \bf p} l.703 ...egin{lemma}Suppose \begin{displaymath}$\p \end{displaymath} is a pro... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.703 ...e \begin{displaymath}$\p\end{displaymath} is a probability vector \... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Display math should end with $$. { l.703 ... probability vector \begin{displaymath}${ \bf p} = (p_0,\ldots,p_K)\... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.703 ... vector \begin{displaymath}${\bf p} = (p_ 0,\ldots,p_K)\end{displaym... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.703 ...bf p} = (p_0,\ldots,p_K)\end{displaymath} and let Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.703 ...bf p} = (p_0,\ldots,p_K)\end{displaymath} and let I've inserted something that you may have forgotten. (See the 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 $$. \psi l.704 \begin{displaymath}$\psi (u,{\bf p}) = \sum p_j \exp(iju)\end{displayma... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.704 \begin{displaymath}$\psi (u,{\bf p}) = \sum p_j \exp(iju)\end{displayma... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.704 ...p}) = \sum p_j \exp(iju)\end{displaymath} be the corresponding char... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.704 ...p}) = \sum p_j \exp(iju)\end{displaymath} be the corresponding char... I've inserted something that you may have forgotten. (See the 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 $$. | l.705 Then \begin{displaymath}$| \psi(u,{\bf p})| \end{displaymath} is maximi... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.705 Then \begin{displaymath}$|\psi (u,{\bf p})| \end{displaymath} is maximi... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.705 ...math}$|\psi(u,{\bf p})| \end{displaymath} is maximized subject to \... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.705 ...math}$|\psi(u,{\bf p})| \end{displaymath} is maximized subject to \... I've inserted something that you may have forgotten. (See the 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 $$. \mathop \max ->\mathop {\rm max} l.705 ...mized subject to \begin{displaymath}$\max \{p_j\} \le 1-\delta\end{d... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \max ->\mathop {\rm max} l.705 ...mized subject to \begin{displaymath}$\max \{p_j\} \le 1-\delta\end{d... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.705 ...\max\{p_j\} \le 1-\delta\end{displaymath} by Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.705 ...\max\{p_j\} \le 1-\delta\end{displaymath} by I've inserted something that you may have forgotten. (See the 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 $$. p l.706 \begin{displaymath}$p _0=1-\delta\end{displaymath} and \begin{displayma... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.706 \begin{displaymath}$p_ 0=1-\delta\end{displaymath} and \begin{displayma... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.706 ...isplaymath}$p_0=1-\delta\end{displaymath} and \begin{displaymath}$\... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.706 ...isplaymath}$p_0=1-\delta\end{displaymath} and \begin{displaymath}$\... I've inserted something that you may have forgotten. (See the 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 $$. { \p ->{ \bf p} l.706 ...d{displaymath} and \begin{displaymath}$\p _{k_0} = \delta\end{displa... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.706 ...{displaymath} and \begin{displaymath}$\p_ {k_0} = \delta\end{display... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.706 ...ymath}$\p_{k_0} = \delta\end{displaymath} where \begin{displaymath}... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.706 ...ymath}$\p_{k_0} = \delta\end{displaymath} where \begin{displaymath}... I've inserted something that you may have forgotten. (See the 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 $$. k l.706 ...{displaymath} where \begin{displaymath}$k _0 \in \{1,\ldots,K\}\end{... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.706 ...displaymath} where \begin{displaymath}$k_ 0 \in \{1,\ldots,K\}\end{d... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.706 ...}$k_0 \in \{1,\ldots,K\}\end{displaymath} is chosen to Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.706 ...}$k_0 \in \{1,\ldots,K\}\end{displaymath} is chosen to I've inserted something that you may have forgotten. (See the 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 $$. | l.707 minimize \begin{displaymath}$| | \exp\{ik_0 u\} - 1||\end{displaymath}.... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \exp ->\mathop {\rm exp}\nolimits l.707 minimize \begin{displaymath}$|| \exp \{ik_0 u\} - 1||\end{displaymath}.... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.707 ...$|| \exp\{ik_0 u\} - 1||\end{displaymath} . Moreover, for \begin{di... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.707 ...$|| \exp\{ik_0 u\} - 1||\end{displaymath} . Moreover, for \begin{di... I've inserted something that you may have forgotten. (See the 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 $$. \delta l.707 ... Moreover, for \begin{displaymath}$\delta \le 1/2\end{displaymath} ... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \delta l.707 ... Moreover, for \begin{displaymath}$\delta \le 1/2\end{displaymath} ... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.707 ...playmath}$\delta \le 1/2\end{displaymath} we have Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.707 ...playmath}$\delta \le 1/2\end{displaymath} we have I've inserted something that you may have forgotten. (See the 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. [100 ] [101 ] ! Display math should end with $$. \protect \bf ->\protect \pbf l.732 ...mepage \clearpage \begin{displaymath}$\bf p\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.732 ...begin{displaymath}$\bf p\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [102 ] ! Display math should end with $$. \mathop \max ->\mathop {\rm max} l.738 ...epage \clearpage \begin{displaymath}$\max {p_i} \le 1- \log n/(n(1-\... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \max ->\mathop {\rm max} l.738 ...epage \clearpage \begin{displaymath}$\max {p_i} \le 1- \log n/(n(1-\... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.738 ... n/(n(1-\cos(\epsilon)))\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.738 ... n/(n(1-\cos(\epsilon)))\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [103 ] ! Display math should end with $$. A l.744 {\samepage \clearpage \begin{displaymath}$A _j\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.744 {\samepage \clearpage \begin{displaymath}$A_ j\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.744 ... \begin{displaymath}$A_j\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.744 ... \begin{displaymath}$A_j\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [104 ] ! Display math should end with $$. B l.750 {\samepage \clearpage \begin{displaymath}$B _j = \{u: |u-t_j| < a_n\}\... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.750 {\samepage \clearpage \begin{displaymath}$B_ j = \{u: |u-t_j| < a_n\}\... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.750 ... = \{u: |u-t_j| < a_n\}\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.750 ... = \{u: |u-t_j| < a_n\}\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [105 ] ! Display math should end with $$. A l.756 {\samepage \clearpage \begin{displaymath}$A _j \setminus B_j\end{displa... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.756 {\samepage \clearpage \begin{displaymath}$A_ j \setminus B_j\end{displa... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.756 ...ymath}$A_j \setminus B_j\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.756 ...ymath}$A_j \setminus B_j\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [106 ] ! Display math should end with $$. a l.762 {\samepage \clearpage \begin{displaymath}$a _n\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.762 {\samepage \clearpage \begin{displaymath}$a_ n\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.762 ... \begin{displaymath}$a_n\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.762 ... \begin{displaymath}$a_n\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [107 ] [108 ] ! Display math should end with $$. B l.775 {\samepage \clearpage \begin{displaymath}$B _j\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.775 {\samepage \clearpage \begin{displaymath}$B_ j\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.775 ... \begin{displaymath}$B_j\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.775 ... \begin{displaymath}$B_j\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [109 ] ! Display math should end with $$. \psi l.781 ...epage \clearpage \begin{displaymath}$\psi (u,{\bf p})^n \end{display... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.781 ...epage \clearpage \begin{displaymath}$\psi (u,{\bf p})^n \end{display... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.781 ...math}$\psi(u,{\bf p})^n \end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.781 ...math}$\psi(u,{\bf p})^n \end{displaymath} I've inserted something that you may have forgotten. (See the 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. [110 ] ! Display math should end with $$. t l.787 {\samepage \clearpage \begin{displaymath}$t _j\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.787 {\samepage \clearpage \begin{displaymath}$t_ j\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.787 ... \begin{displaymath}$t_j\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.787 ... \begin{displaymath}$t_j\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [111 ] ! Display math should end with $$. X l.794 Suppose \begin{displaymath}$X \end{displaymath} is an integer valued ra... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.794 ...se \begin{displaymath}$X\end{displaymath} is an integer valued rand... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Display math should end with $$. M l.794 ...variable bounded by \begin{displaymath}$M \end{displaymath} and The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.794 ...by \begin{displaymath}$M\end{displaymath} and Your command was ignored. Type I to replace it with another command, or to continue without it. ! Display math should end with $$. K l.795 fix an integer \begin{displaymath}$K \end{displaymath}. Let \begin{dis... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.795 ...er \begin{displaymath}$K\end{displaymath} . Let \begin{displaymath}... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Display math should end with $$. \sigma l.795 ...laymath}. Let \begin{displaymath}$\sigma ^2\end{displaymath} denote... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \sigma l.795 ...laymath}. Let \begin{displaymath}$\sigma ^2\end{displaymath} denote... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.795 ...in{displaymath}$\sigma^2\end{displaymath} denote the variance of \b... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.795 ...in{displaymath}$\sigma^2\end{displaymath} denote the variance of \b... I've inserted something that you may have forgotten. (See the 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 $$. X l.795 ...ote the variance of \begin{displaymath}$X \end{displaymath} and \beg... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.795 ...of \begin{displaymath}$X\end{displaymath} and \begin{displaymath}$\... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Display math should end with $$. \psi l.795 ...displaymath} and \begin{displaymath}$\psi \end{displaymath} the The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.795 ...displaymath} and \begin{displaymath}$\psi \end{displaymath} the I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.795 ...\begin{displaymath}$\psi\end{displaymath} the Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.795 ...\begin{displaymath}$\psi\end{displaymath} the I've inserted something that you may have forgotten. (See the 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 $$. X l.796 ...eristic function of \begin{displaymath}$X \end{displaymath}. If \be... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.796 ...of \begin{displaymath}$X\end{displaymath} . If \begin{displaymath}$... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Display math should end with $$. t l.796 ...d{displaymath}. If \begin{displaymath}$t _j = 2 \pi j / K\end{displ... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.796 ...{displaymath}. If \begin{displaymath}$t_ j = 2 \pi j / K\end{displa... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.796 ...ymath}$t_j = 2 \pi j / K\end{displaymath} for some \begin{displayma... Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.796 ...ymath}$t_j = 2 \pi j / K\end{displaymath} for some \begin{displayma... I've inserted something that you may have forgotten. (See the 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 $$. j l.796 ...splaymath} for some \begin{displaymath}$j \end{displaymath} then\beg... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.796 ...me \begin{displaymath}$j\end{displaymath} then\begin{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Display math should end with $$. | l.798 for all \begin{displaymath}$| u|\end{displaymath} less than the positiv... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.798 ... \begin{displaymath}$|u|\end{displaymath} less than the positive co... Your command was ignored. Type I to replace it with another command, or to continue without it. [112 ] [113 ] ! Display math should end with $$. | l.819 {\samepage \clearpage \begin{displaymath}$| \psi(t_j)|\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.819 ...page \clearpage \begin{displaymath}$|\psi (t_j)|\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.819 ...displaymath}$|\psi(t_j)|\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.819 ...displaymath}$|\psi(t_j)|\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [114 ] ! Display math should end with $$. | l.825 {\samepage \clearpage \begin{displaymath}$| \psi(t_j)| = 1\end{displaym... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.825 ...page \clearpage \begin{displaymath}$|\psi (t_j)| = 1\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.825 ...laymath}$|\psi(t_j)| = 1\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.825 ...laymath}$|\psi(t_j)| = 1\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [115 ] ! Display math should end with $$. B l.831 {\samepage \clearpage \begin{displaymath}$B _0\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.831 {\samepage \clearpage \begin{displaymath}$B_ 0\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.831 ... \begin{displaymath}$B_0\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.831 ... \begin{displaymath}$B_0\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [116 ] ! Display math should end with $$. { \p ->{ \bf p} l.837 {\samepage \clearpage \begin{displaymath}$\p \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.837 ...e \begin{displaymath}$\p\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [117 ] [118 ] ! Display math should end with $$. l.857 {\samepage \clearpage \begin{displaymath}$ |\psi(t_j,{\bf p})| \le C ... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.857 ...age \clearpage \begin{displaymath}$ |\psi (t_j,{\bf p})| \le C \log... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.857 ...f p})| \le C \log n /n \end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.857 ...f p})| \le C \log n /n \end{displaymath} I've inserted something that you may have forgotten. (See the 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. [119 ] [120 ] ! Display math should end with $$. l.871 {\samepage \clearpage \begin{displaymath}$ |\psi(t_j, {\bf p})| \ge 1-... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.871 ...age \clearpage \begin{displaymath}$ |\psi (t_j, {\bf p})| \ge 1- C \... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.871 ... p})| \ge 1- C \log n /n\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.871 ... p})| \ge 1- C \log n /n\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [121 ] [122 ] ! Display math should end with $$. | l.884 {\samepage \clearpage \begin{displaymath}$| u| \le a_n\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.884 ...ge \clearpage \begin{displaymath}$|u| \le a_n\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.884 ...displaymath}$|u| \le a_n\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.884 ...displaymath}$|u| \le a_n\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [123 ] [124 ] [125 ] Overfull \hbox (43.92079pt too wide) detected at line 907 \twlmi \twlrm (\twlmi t[] \twlrm + \twlmi u\twlrm )[] [](\twlsy ^^@\twlmi i\tw lrm (\twlmi tK\twlrm ! + \twlmi r\twlrm )(\twlmi t[] \twlrm + \twlmi u\twlrm )) = \twlmi \twlrm (\twlmi t[]\twlrm )[] [](\twlsy ^^@\twlmi irt[]\twlrm ) [](\t wlmi ^^P[]u \twlsy ^^@ \twlmi ^^P[]u[]=\twlrm 2 + \twlmi ^^P[]u[]=\twlrm 6 + \t wlmi R\twlrm (\twlmi u\twlrm )) \hbox(10.11026+3.35555)x390.0, glue set - 1.0 .\twlmi .\kern0.43056 .\twlrm ( .\twlmi t .\hbox(5.2887+1.55556)x4.39859, shifted 1.79999 ..\egtmi j .etc. [126 ] [127 ] [128 ] [129 ] ! Display math should end with $$. n l.937 {\samepage \clearpage \begin{displaymath}$n \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.937 ...ge \begin{displaymath}$n\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [130 ] ! Display math should end with $$. ( l.943 {\samepage \clearpage \begin{displaymath}$( 1- C \log n /n)^4 > 2\end{... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \log ->\mathop {\rm log}\nolimits l.943 ...clearpage \begin{displaymath}$( 1- C \log n /n)^4 > 2\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.943 ...$( 1- C \log n /n)^4 > 2\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.943 ...$( 1- C \log n /n)^4 > 2\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [131 ] [132 ] [133 ] [134 ] ! Display math should end with $$. | l.970 {\samepage \clearpage \begin{displaymath}$| I(u)| \le 1\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.970 ...\clearpage \begin{displaymath}$|I(u)| \le 1\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.970 ...isplaymath}$|I(u)| \le 1\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.970 ...isplaymath}$|I(u)| \le 1\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [135 ] [136 ] ! Display math should end with $$. N l.987 {\samepage \clearpage \begin{displaymath}$N _0\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.987 {\samepage \clearpage \begin{displaymath}$N_ 0\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.987 ... \begin{displaymath}$N_0\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.987 ... \begin{displaymath}$N_0\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [137 ] ! Display math should end with $$. K l.993 {\samepage \clearpage \begin{displaymath}$K \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.993 ...ge \begin{displaymath}$K\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [138 ] ! Display math should end with $$. d l.999 {\samepage \clearpage \begin{displaymath}$d \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.999 ...ge \begin{displaymath}$d\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [139 ] ! Display math should end with $$. | l.1005 {\samepage \clearpage \begin{displaymath}$| \zeta_3 u^3/6| \end{displa... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \zeta l.1005 ...ge \clearpage \begin{displaymath}$|\zeta _3 u^3/6| \end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1005 ...ymath}$|\zeta_3 u^3/6| \end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1005 ...ymath}$|\zeta_3 u^3/6| \end{displaymath} I've inserted something that you may have forgotten. (See the 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. [140 ] ! Display math should end with $$. ? l.1011 {\samepage \clearpage \begin{displaymath}$? M^3 \lambda_n^3/\sqrt{n}\e... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ ^ l.1011 ...epage \clearpage \begin{displaymath}$?M^ 3 \lambda_n^3/\sqrt{n}\end... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1011 ...^3 \lambda_n^3/\sqrt{n}\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1011 ...^3 \lambda_n^3/\sqrt{n}\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [141 ] [142 ] [143 ] [144 ] [145 ] [146 ] [147 ] [148 ] [149 ] [150 ] [151 ] [152 ] [153 ] [154 ] [155 ] [156 ] [157 ] [158 ] [159 ] [160 ] [161 ] [162 ] [163 ] [164 ] [165 ] [166 ] [167 ] [168 ] [169 ] [170 ] [171 ] [172 ] [173 ] [174 ] [175 ] [176 ] [177 ] [178 ] [179 ] [180 ] [181 ] [182 ] [183 ] [184 ] [185 ] [186 ] [187 ] [188 ] [189 ] [190 ] [191 ] [192 ] [193 ] [194 ] [195 ] [196 ] [197 ] [198 ] [199 ] [200 ] [201 ] [202 ] [203 ] [204 ] [205 ] [206 ] [207 ] [208 ] [209 ] [210 ] [211 ] [212 ] [213 ] [214 ] [215 ] [216 ] [217 ] [218 ] [219 ] [220 ] [221 ] [222 ] [223 ] [224 ] [225 ] [226 ] [227 ] [228 ] [229 ] [230 ] [231 ] [232 ] [233 ] [234 ] [235 ] [236 ] [237 ] [238 ] [239 ] [240 ] [241 ] [242 ] [243 ] [244 ] [245 ] [246 ] [247 ] [248 ] [249 ] [250 ] [251 ] [252 ] Overfull \hbox (6.23259pt too wide) in paragraph at lines 1790--1795 [] []\twlit Suppose $\twlbf p$ \twlit is a prob-a-bil-ity vec-tor $\twlbf p \tw lrm = (\twlmi p[]; [] ; p[]\twlrm )$ \twlit and let $\twlmi \twlrm (\twlmi u; \twlbf p\twlrm ) = \hbox(9.0+3.0)x390.0, glue set - 1.0 .\hbox(0.0+0.0)x17.62482 .\glue -17.62482 .\hbox(8.23334+0.0)x60.45827 ..\glue 0.0 ..\glue 0.0 ..\glue -5.87494 ..\hbox(8.23334+0.0)x60.45827 ...\glue 5.87494 ...\twlbf L ...\twlbf e ...\twlbf m ...\twlbf m ...etc. ..\glue 5.87494 .\penalty 0 .\twlit S .etc. [253 ] ! Display math should end with $$. \psi l.1810 ...page \clearpage \begin{displaymath}$\psi (u,{\bf p})\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \psi l.1810 ...page \clearpage \begin{displaymath}$\psi (u,{\bf p})\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1810 ...aymath}$\psi(u,{\bf p})\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1810 ...aymath}$\psi(u,{\bf p})\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [254 ] ! Display math should end with $$. \delta l.1816 ...ge \clearpage \begin{displaymath}$\delta \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \delta l.1816 ...ge \clearpage \begin{displaymath}$\delta \end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1816 ...gin{displaymath}$\delta\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1816 ...gin{displaymath}$\delta\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [255 ] ! Display math should end with $$. 1 l.1822 {\samepage \clearpage \begin{displaymath}$1 -\delta\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \delta l.1822 ... \clearpage \begin{displaymath}$1-\delta \end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1822 ...n{displaymath}$1-\delta\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1822 ...n{displaymath}$1-\delta\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [256 ] ! Display math should end with $$. \mathop \exp ->\mathop {\rm exp}\nolimits l.1828 ...page \clearpage \begin{displaymath}$\exp (i\ell_1 u)\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \exp ->\mathop {\rm exp}\nolimits l.1828 ...page \clearpage \begin{displaymath}$\exp (i\ell_1 u)\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1828 ...aymath}$\exp(i\ell_1 u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1828 ...aymath}$\exp(i\ell_1 u)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [257 ] ! Display math should end with $$. \mathop \exp ->\mathop {\rm exp}\nolimits l.1834 ...page \clearpage \begin{displaymath}$\exp (i\ell_2u)\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \exp ->\mathop {\rm exp}\nolimits l.1834 ...page \clearpage \begin{displaymath}$\exp (i\ell_2u)\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1834 ...laymath}$\exp(i\ell_2u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1834 ...laymath}$\exp(i\ell_2u)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [258 ] ! Display math should end with $$. \mathop \exp ->\mathop {\rm exp}\nolimits l.1840 ...page \clearpage \begin{displaymath}$\exp (i(\ell_1-ell_2)u)\end{dis... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \exp ->\mathop {\rm exp}\nolimits l.1840 ...page \clearpage \begin{displaymath}$\exp (i(\ell_1-ell_2)u)\end{dis... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1840 ...$\exp(i(\ell_1-ell_2)u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1840 ...$\exp(i(\ell_1-ell_2)u)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [259 ] ! Display math should end with $$. X l.1846 {\samepage \clearpage \begin{displaymath}$X ^*\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ ^ l.1846 ...mepage \clearpage \begin{displaymath}$X^ *\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1846 ...\begin{displaymath}$X^*\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1846 ...\begin{displaymath}$X^*\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [260 ] ! Display math should end with $$. X l.1852 {\samepage \clearpage \begin{displaymath}$X \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1852 ...e \begin{displaymath}$X\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [261 ] ! Display math should end with $$. Y l.1858 {\samepage \clearpage \begin{displaymath}$Y =X-X^*\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ ^ l.1858 ...ge \clearpage \begin{displaymath}$Y=X-X^ *\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1858 ...in{displaymath}$Y=X-X^*\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1858 ...in{displaymath}$Y=X-X^*\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [262 ] ! Display math should end with $$. 2 l.1864 {\samepage \clearpage \begin{displaymath}$2 M\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1864 ... \begin{displaymath}$2M\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [263 ] ! Display math should end with $$. \tau l.1870 ...page \clearpage \begin{displaymath}$\tau ^2 = 2\sigma^2\end{display... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \tau l.1870 ...page \clearpage \begin{displaymath}$\tau ^2 = 2\sigma^2\end{display... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1870 ...ath}$\tau^2 = 2\sigma^2\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1870 ...ath}$\tau^2 = 2\sigma^2\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [264 ] ! Display math should end with $$. Y l.1876 {\samepage \clearpage \begin{displaymath}$Y \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1876 ...e \begin{displaymath}$Y\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [265 ] ! Display math should end with $$. \chi l.1882 ...page \clearpage \begin{displaymath}$\chi (s) = | \psi(s)|^2\end{dis... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \chi l.1882 ...page \clearpage \begin{displaymath}$\chi (s) = | \psi(s)|^2\end{dis... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1882 ...$\chi(s) = | \psi(s)|^2\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1882 ...$\chi(s) = | \psi(s)|^2\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [266 ] [267 ] ! Display math should end with $$. | l.1895 {\samepage \clearpage \begin{displaymath}$| u| \le C(M,K)\end{displaym... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.1895 ...e \clearpage \begin{displaymath}$|u| \le C(M,K)\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1895 ...laymath}$|u| \le C(M,K)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1895 ...laymath}$|u| \le C(M,K)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [268 ] ! Display math should end with $$. \chi l.1901 ...page \clearpage \begin{displaymath}$\chi \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \chi l.1901 ...page \clearpage \begin{displaymath}$\chi \end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1901 ...begin{displaymath}$\chi\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1901 ...begin{displaymath}$\chi\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [269 ] [270 ] ! Display math should end with $$. \theta l.1919 $\theta \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \theta l.1919 $\theta \end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1919 $\theta\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1919 $\theta\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [271 ] ! Display math should end with $$. t l.1925 {\samepage \clearpage \begin{displaymath}$t _j+u\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.1925 ...mepage \clearpage \begin{displaymath}$t_ j+u\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1925 ...egin{displaymath}$t_j+u\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1925 ...egin{displaymath}$t_j+u\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [272 ] ! Display math should end with $$. c l.1931 {\samepage \clearpage \begin{displaymath}$c (u)\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1931 ...begin{displaymath}$c(u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [273 ] ! Display math should end with $$. R l.1937 {\samepage \clearpage \begin{displaymath}$R (u)\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1937 ...begin{displaymath}$R(u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [274 ] [275 ] ! Display math should end with $$. 1 l.1951 {\samepage \clearpage \begin{displaymath}$1 -x \le \exp(-x)\end{displa... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.1951 ...e \clearpage \begin{displaymath}$1-x \le \exp(-x)\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1951 ...ymath}$1-x \le \exp(-x)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1951 ...ymath}$1-x \le \exp(-x)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [276 ] ! Display math should end with $$. c l.1957 {\samepage \clearpage \begin{displaymath}$c (0) =\chi(t_j) > 0\end{dis... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \chi l.1957 ...clearpage \begin{displaymath}$c(0) =\chi (t_j) > 0\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1957 ...th}$c(0) =\chi(t_j) > 0\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1957 ...th}$c(0) =\chi(t_j) > 0\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [277 ] ! Display math should end with $$. \chi l.1963 ...page \clearpage \begin{displaymath}$\chi (t_j+u) =\chi(t_j) -u E(Y\... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \chi l.1963 ...page \clearpage \begin{displaymath}$\chi (t_j+u) =\chi(t_j) -u E(Y\... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1964 \sigma |u|\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1964 \sigma |u|\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [278 ] ! Display math should end with $$. | l.1970 {\samepage \clearpage \begin{displaymath}$| u| \le 1/(2M)\end{displaym... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.1970 ...e \clearpage \begin{displaymath}$|u| \le 1/(2M)\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1970 ...laymath}$|u| \le 1/(2M)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1970 ...laymath}$|u| \le 1/(2M)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [279 ] ! Display math should end with $$. \tau l.1976 ...page \clearpage \begin{displaymath}$\tau ^2 = 2\sigma^2 \le 2M^2\en... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \tau l.1976 ...page \clearpage \begin{displaymath}$\tau ^2 = 2\sigma^2 \le 2M^2\en... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1976 ...^2 = 2\sigma^2 \le 2M^2\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1976 ...^2 = 2\sigma^2 \le 2M^2\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [280 ] [281 ] ! Display math should end with $$. 1 l.1989 {\samepage \clearpage \begin{displaymath}$1 /(2M) > C(M,K)\end{display... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1989 ...aymath}$1/(2M) > C(M,K)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [282 ] ! Display math should end with $$. l.1995 {\samepage \clearpage \begin{displaymath}$ (1-\tau^2 u^2/2 ) - c(u)\e... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \tau l.1995 ... \clearpage \begin{displaymath}$ (1-\tau ^2 u^2/2 ) - c(u)\end{disp... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.1995 ...1-\tau^2 u^2/2 ) - c(u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.1995 ...1-\tau^2 u^2/2 ) - c(u)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [283 ] ! Display math should end with $$. u l.2001 {\samepage \clearpage \begin{displaymath}$u =0\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2001 ...\begin{displaymath}$u=0\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [284 ] ! Display math should end with $$. c l.2007 {\samepage \clearpage \begin{displaymath}$c (0) = 1\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2007 ...n{displaymath}$c(0) = 1\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [285 ] ! Display math should end with $$. \mathop \cos ->\mathop {\rm cos}\nolimits l.2013 ...page \clearpage \begin{displaymath}$\cos (t_jY) = 1\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \cos ->\mathop {\rm cos}\nolimits l.2013 ...page \clearpage \begin{displaymath}$\cos (t_jY) = 1\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2013 ...laymath}$\cos(t_jY) = 1\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2013 ...laymath}$\cos(t_jY) = 1\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [286 ] ! Display math should end with $$. \mathop \sin ->\mathop {\rm sin}\nolimits l.2019 ...page \clearpage \begin{displaymath}$\sin (t_jY)= 0\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \sin ->\mathop {\rm sin}\nolimits l.2019 ...page \clearpage \begin{displaymath}$\sin (t_jY)= 0\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2019 ...playmath}$\sin(t_jY)= 0\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2019 ...playmath}$\sin(t_jY)= 0\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [287 ] ! Display math should end with $$. c l.2025 {\samepage \clearpage \begin{displaymath}$c (u) = 1 - \tau^2 u^2 /2 \e... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \tau l.2025 ...page \begin{displaymath}$c(u) = 1 - \tau ^2 u^2 /2 \end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2025 ...u) = 1 - \tau^2 u^2 /2 \end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2025 ...u) = 1 - \tau^2 u^2 /2 \end{displaymath} I've inserted something that you may have forgotten. (See the 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. [288 ] ! Display math should end with $$. u l.2031 {\samepage \clearpage \begin{displaymath}$u \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2031 ...e \begin{displaymath}$u\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [289 ] ! Display math should end with $$. c l.2037 {\samepage \clearpage \begin{displaymath}$c (0) < 1\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2037 ...n{displaymath}$c(0) < 1\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [290 ] ! Display math should end with $$. - l.2043 {\samepage \clearpage \begin{displaymath}$- r_-\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.2043 ...epage \clearpage \begin{displaymath}$-r_ -\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2043 ...begin{displaymath}$-r_-\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2043 ...begin{displaymath}$-r_-\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [291 ] ! Display math should end with $$. r l.2049 {\samepage \clearpage \begin{displaymath}$r _+\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.2049 ...mepage \clearpage \begin{displaymath}$r_ +\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2049 ...\begin{displaymath}$r_+\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2049 ...\begin{displaymath}$r_+\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [292 ] ! Display math should end with $$. G l.2055 {\samepage \clearpage \begin{displaymath}$G \end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]...finner \@badmath \else $$\fi \else \@badmath \fi \ignorespaces \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2055 ...e \begin{displaymath}$G\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. [293 ] ! Display math should end with $$. \mathop \cos ->\mathop {\rm cos}\nolimits l.2061 ...page \clearpage \begin{displaymath}$\cos (t_jY) \ne 1\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \mathop \cos ->\mathop {\rm cos}\nolimits l.2061 ...page \clearpage \begin{displaymath}$\cos (t_jY) \ne 1\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2061 ...ymath}$\cos(t_jY) \ne 1\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2061 ...ymath}$\cos(t_jY) \ne 1\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [294 ] [295 ] [296 ] ! Display math should end with $$. r l.2082 {\samepage \clearpage \begin{displaymath}$r _- > r_+ > C(M,K)\end{disp... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ _ l.2082 ...mepage \clearpage \begin{displaymath}$r_ - > r_+ > C(M,K)\end{displ... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2082 ...ath}$r_- > r_+ > C(M,K)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2082 ...ath}$r_- > r_+ > C(M,K)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [297 ] [298 ] ! Display math should end with $$. R l.2095 {\samepage \clearpage \begin{displaymath}$R (u) \le |u|^3 E(|Y|^3)/6\e... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.2095 ... \clearpage \begin{displaymath}$R(u) \le |u|^3 E(|Y|^3)/6\end{disp... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2095 ...u) \le |u|^3 E(|Y|^3)/6\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2095 ...u) \le |u|^3 E(|Y|^3)/6\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [299 ] [300 ] ! Display math should end with $$. | l.2108 {\samepage \clearpage \begin{displaymath}$| u| \le \min( C(M,K) , \tau... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.2108 ...e \clearpage \begin{displaymath}$|u| \le \min( C(M,K) , \tau^2/ E(... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2108 ...,K) , \tau^2/ E(|Y|^3))\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2108 ...,K) , \tau^2/ E(|Y|^3))\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [301 ] ! Display math should end with $$. E l.2114 {\samepage \clearpage \begin{displaymath}$E (|Y|^3) \le 2ME(Y^2) = 2M\... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ ^ l.2114 ...ge \clearpage \begin{displaymath}$E(|Y|^ 3) \le 2ME(Y^2) = 2M\tau^2... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2114 ...\le 2ME(Y^2) = 2M\tau^2\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2114 ...\le 2ME(Y^2) = 2M\tau^2\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [302 ] ! Display math should end with $$. l.2120 {\samepage \clearpage \begin{displaymath}$ \tau^2/ E(|Y|^3))\ge 1/(2M... The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \tau l.2120 ...age \clearpage \begin{displaymath}$ \tau ^2/ E(|Y|^3))\ge 1/(2M)\en... I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2120 ...^2/ E(|Y|^3))\ge 1/(2M)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2120 ...^2/ E(|Y|^3))\ge 1/(2M)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [303 ] ! Display math should end with $$. c l.2126 {\samepage \clearpage \begin{displaymath}$c (0) \le 0\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \le l.2126 ... \clearpage \begin{displaymath}$c(0) \le 0\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2126 ...displaymath}$c(0) \le 0\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2126 ...displaymath}$c(0) \le 0\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [304 ] ! Display math should end with $$. \chi l.2132 ...page \clearpage \begin{displaymath}$\chi (t_j+u)\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \chi l.2132 ...page \clearpage \begin{displaymath}$\chi (t_j+u)\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2132 ...isplaymath}$\chi(t_j+u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2132 ...isplaymath}$\chi(t_j+u)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [305 ] ! Display math should end with $$. - l.2138 {\samepage \clearpage \begin{displaymath}$- \chi(t_j+u)\end{displaymath} The `$' that I just saw supposedly matches a previous `$$'. So I shall assume that you typed `$$' both times. ! Missing $ inserted. $ \chi l.2138 ...age \clearpage \begin{displaymath}$-\chi (t_j+u)\end{displaymath} I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. LaTeX error. See LaTeX manual for explanation. Type H for immediate help. ! Bad math environment delimiter. \@latexerr ...for immediate help.}\errmessage {#1} \]->\relax \ifmmode \ifinner \@badmath \else $$\fi \else \@badmath \fi \igno... \enddisplaymath ->\] \global \@ignoretrue \end #1->\csname end#1\endcsname \@checkend {#1}\expandafter \endgroup \if@e... l.2138 ...splaymath}$-\chi(t_j+u)\end{displaymath} Your command was ignored. Type I to replace it with another command, or to continue without it. ! Missing $ inserted. $ \endgroup \end ...ndafter \endgroup \if@endpe \@doendpe \fi \if@ignore \global \@ignor... l.2138 ...splaymath}$-\chi(t_j+u)\end{displaymath} I've inserted something that you may have forgotten. (See the 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. [306 ] [307 ] (26063_images.aux) LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. ) Here is how much of TeX's memory you used: 245 strings out of 11981 2377 string characters out of 87214 28482 words of memory out of 262141 2199 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,7n,15p,251b,115s stack positions out of 300i,40n,60p,3000b,4000s Output written on 26063_images.dvi (307 pages, 53400 bytes).