\batchmode
                                                    

\documentclass[10pt]{article}
\makeatletter

\usepackage[dvips,dvipsnames]{color}

\usepackage{latexsym} 

\usepackage{wasysym}    
\let\wasyiint\iint
\let\wasyiiint\iiint
\let\iint\relax
\let\iiint\relax
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{amsmath} 
\usepackage{amsfonts} 
\usepackage{amsthm} 
\usepackage[mathscr]{eucal} 
\usepackage[dvips]{graphics}
\usepackage{psfrag}
\usepackage{html,htmllist,makeidx,longtable}

\advance\hoffset by -20mm  
\setlength{\topmargin}{1.0cm}   
\numberwithin{equation}{section}  
	\setlength{\textwidth}{165mm}   

\providecommand{\squareroot}{\sqrt{1+i \bar \omega/{(k^2\nu)}}}

\providecommand{\Real}{\mbox{Re}}
 \providecommand{\Imag}{\mbox{Im}}

\providecommand{\hatb}{\hat b}
 \providecommand{\hatR}{\hat R}
 \providecommand{\hatphi}{\hat \phi}
 \providecommand{\hatpsi}{\hat \psi}
 \providecommand{\hatzeta}{\hat \zeta}
\providecommand{\hatx}{\hat x}
\providecommand{\haty}{\hat y}
\providecommand{\hatr}{\hat r}
\providecommand{\hattheta}{\hat theta}
\providecommand{\hatz}{\hat z}

\providecommand{\bB}{\vec{B}}
 \providecommand{\btu}{\vec{\tilde {\bf u}}}
 \providecommand{\bu}{\vec{u}}

\providecommand{\bs}{\boldsymbol}
\providecommand{\csch}{\mbox{ cosech}}
\providecommand{\cross}{\mathbf{\times}}
\providecommand{\dd}{\partial}
\providecommand{\deriv}[2]{ \ensuremath {\frac{d #1}{d #2}} }
\providecommand{\derivp}[2]{ \ensuremath {\frac {\partial #1}{\partial #2}} }
\providecommand{\definedas}{\equiv}
\providecommand{\eps}{\epsilon}

\providecommand{\half}{\frac{1}{2}}
\providecommand{\third}{\frac{1}{3}}
\providecommand{\fourth}{\frac{1}{4}}
\providecommand{\fifth}{\frac{1}{5}}
\providecommand{\sixth}{\frac{1}{6}}
\providecommand{\seventh}{\frac{1}{7}}
\providecommand{\eighth}{\frac{1}{8}}
\providecommand{\ninth}{\frac{1}{9}}
\providecommand{\tenth}{\frac{1}{10}}

\providecommand{\lam}{\ensuremath{\lambda} }
\providecommand{\nab}{\mathbf{\nabla}}
\providecommand{\sech}{\mbox{ sech}}
\providecommand{\sign}{\mbox{sign}}
\providecommand{\n}{\rho}

\providecommand{\np}{\rho_+}
\providecommand{\nm}{\rho_-}
 \providecommand{\tchi}{\tilde \chi}

\providecommand{\tf}{\tilde f}
\providecommand{\tu}{\tilde {\bf u}}
\providecommand{\tn}{\tilde \rho}
\providecommand{\tp}{\tilde p}
\providecommand{\tphi}{\tilde \phi}
\providecommand{\tpsi}{\tilde \psi}
\providecommand{\trho}{\tilde \rho}

\providecommand{\bkap}{\vec \kappa}
\providecommand{\bn}{\tilde{\bar n}}
\providecommand{\bphi}{\tilde{\bar \phi}}
\providecommand{\bpsi}{\tilde{\bar \psi}}

\providecommand{\wbar}{\bar \omega}

\providecommand{\sig}{\sigma}
\providecommand{\viz}{\emph{viz. }}
\providecommand{\w}{\omega}
\providecommand{\W}{\Omega}

\providecommand{\kunit}{\left(\frac{\rho_-}{\rho_+} \frac{g}{\nu^2}\right)^{1/3}}

\providecommand{\gammaunit}{\left(\frac{\rho_-^2}{\rho_+^2}
\frac{g^2}{\nu}\right)^{1/3} }

\providecommand{\shearunit}{\left(\frac{\rho_+}{\rho_-}
\frac{g^2}{\nu}\right)^{1/3}}

\providecommand{\nmnp}{\frac{\rho_-}{\rho_+}}
\providecommand{\npnm}{\frac{\rho_+}{\rho_-}}
\providecommand{\npbnmb}{\frac{\rho_+^2}{\rho_-^2}}

\providecommand{\cm}{\mbox{cm}}
\providecommand{\rps}{\mbox{revs}/\mbox{s}}
\providecommand{\second}{\mbox{s}}
\par\pagecolor[gray]{.7}


\makeatletter
\count@=\the\catcode`\_ \catcode`\_=8 
\newenvironment{tex2html_wrap}{}{} \catcode`\_=\count@
\makeatother
\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
\newbox\sizebox
\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
\setlength{\textwidth}{349pt}
\newwrite\lthtmlwrite
\makeatletter
\let\realnormalsize=\normalsize
\global\topskip=2sp
\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
\def\@float{\let\@savefreelist\@freelist\real@float}
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
\let\@largefloatcheck=\relax
\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
 \parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}\normalsize}%
\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}%
\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup}%
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup%
 \let\ifinner=\iffalse }%
\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
 \expandafter\box\next\egroup}%
\newcommand\lthtmlmathtype[1]{\def\lthtmlmathenv{#1}}%
\newcommand\lthtmllogmath{\lthtmltypeout{l2hSize %
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
       \lthtmlmathtype{#1}\lthtmlvboxmathA}%
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
       \global\let\@freelist\@savefreelist}%
\newcommand\lthtmldisplayA[1]{\lthtmlmathtype{#1}\lthtmlvboxmathA}%
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
  \lthtmldisplayA{#1}\let\@eqnnum\relax}%
\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
\newcommand\lthtmlinlinemathA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA  \vrule height1.5ex width0pt }%
\newcommand\lthtmlinlineA[1]{\lthtmlmathtype{#1}\lthtmlhboxmathA}%
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
  \expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
\def\lthtmlsetinline{\hbox{\vrule width.1em\vtop{\vbox{%
  \kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
\def\lthtmlsetmath{\hbox{\vrule width.1em\setbox1=\vtop{\vbox{%
  \kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
  \ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
  \ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}\message{ht\the\ht1: dp\the\dp1}\box1}}
\def\centerinlinemath{%\dimen1=\ht\sizebox
  \dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
  \advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1 
 \dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}

\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize\expandafter\vfill
  \else\expandafter\vss\fi}%
\makeatletter \tracingstats = 1 


\begin{document}
\pagestyle{empty}\thispagestyle{empty}%
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}%
\lthtmltypeout{latex2htmlLength vsize=\the\vsize}%
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}%
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}%
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}%
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}%
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}%
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}%
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}%
\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}%
\makeatletter
\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
\makeatother
\stepcounter{section}
\stepcounter{section}
\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline190}%
$\mbox{$\bullet$}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}


\end{document}
