\batchmode
%
\documentclass[10pt,letterpaper,oneside,onecolumn]{article}
\makeatletter
\usepackage[]{fontenc}
\usepackage[dvips]{epsfig}


\makeatletter












\makeatother


\pagestyle{plain}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}

\def\LyX{L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\spacefactor1000}

\newcommand {\lyxtitle}[1] {\thispagestyle{empty}
\global\@topnum\z@
\section*{\LARGE \centering \sffamily \bfseries \protect#1 }
}

\newcommand {\lyxline}[1]{
{#1 \vspace{1ex} \hrule width \columnwidth \vspace{1ex}}
}

\newenvironment {lyxbibliography}
{
\begin{thebibliography}{99}}
{\end{thebibliography}}

\def\lxq{"}

\newenvironment {lyxcode}
{\list{}{
\rightmargin\leftmargin
\raggedright
\itemsep 0pt
\parsep 0pt
\ttfamily
}\item[]
}
{\endlist}

\newcommand {\lyxlabel}[1]{#1 \hfill}

\newenvironment {lyxlist}[1]
{\begin{list}{}
{\settowidth{\labelwidth}{#1}
\setlength{\leftmargin}{\labelwidth}
\addtolength{\leftmargin}{\labelsep}
\renewcommand  {\makelabel}{\lyxlabel}}}
{\end{list}}

\newcommand {\lyxletterstyle}{
\setlength\parskip{0.7em}
\setlength\parindent{0pt}
}

\newcommand {\lyxaddress}[1]{
\par {\raggedright #1 
\vspace{1.4em}
\noindent\par}
}

\newcommand {\lyxrightaddress}[1]{
\par {\raggedleft \begin{tabular}{l}\ignorespaces
#1
\end{tabular}
\vspace{1.4em}
\par}
}

\newcommand {\lyxformula}[1]{
\begin{eqnarray*}
#1
\end{eqnarray*}
}

\newcommand {\lyxnumberedformula}[1]{
\begin{eqnarray}
#1
\end{eqnarray}
}

\makeatother
\newenvironment{tex2html_wrap}{}{}
\newwrite\lthtmlwrite
\def\lthtmltypeout#1{{\let\protect\string\immediate\write\lthtmlwrite{#1}}}%
\newbox\sizebox
\begin{document}
\pagestyle{empty}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}
{\newpage
\clearpage
\samepage \( w,n\in \Omega ^{r} \)
}

{\newpage
\clearpage
\samepage \( (w,n)=\int _{M}w\wedge *n \)
}

{\newpage
\clearpage
\samepage \( w\wedge *n=\frac{1}{r!}w_{u_{1}..u_{r}}n^{u_{1}...u_{r}}\Omega _{M} \)
}

{\newpage
\clearpage
\samepage \( (w,n)=(n,w) \)
}

{\newpage
\clearpage
\samepage \( (w,w)>0 \)
}

{\newpage
\clearpage
\samepage \( \forall w\neq 0 \)
}

{\newpage
\clearpage
\samepage \( w\in \Omega ^{r},n\in \Omega ^{r-1} \)
}

{\newpage
\clearpage
\samepage \( (w,dn)=(d^{\dagger }w,n) \)
}

{\newpage
\clearpage
\samepage \( \partial M=0 \)
}

{\newpage
\clearpage
\samepage \( (d^{\dagger }w,n)= \)
}

{\newpage
\clearpage
\samepage \( (n,d^{\dagger }w)= \)
}

{\newpage
\clearpage
\samepage \( \int _{M}n\wedge d^{\dagger }w \)
}

{\newpage
\clearpage
\samepage \( =(w,dn)=(dn,w)=\int _{M}dn\wedge *w \)
}

{\newpage
\clearpage
\samepage \( =\int _{M}[d(n\wedge *w)-(-1)^{r-1}n\wedge d(*w)] \)
}

{\newpage
\clearpage
\samepage \( =\int _{M}-(-1)^{r-1}n\wedge d(*w) \)
}

{\newpage
\clearpage
\samepage \( **d^{\dagger }w=(-1)^{r}*d(*w) \)
}

{\newpage
\clearpage
\samepage \( =(-1)^{(r-1)(m-r-1)}d^{\dagger }w \)
}

{\newpage
\clearpage
\samepage \( d^{\dagger }w=(-1)^{m(r+1)+1}*d*w \)
}

{\newpage
\clearpage
\samepage \( *:r\rightarrow m-r \)
}

{\newpage
\clearpage
\samepage \( d:m-r\rightarrow m-r+1 \)
}

{\newpage
\clearpage
\samepage \( *:m-r+1\rightarrow r-1 \)
}

{\newpage
\clearpage
\samepage \( d^{\dagger } \)
}

{\newpage
\clearpage
\samepage \( (d^{\dagger })^{\dagger }=d \)
}

{\newpage
\clearpage
\samepage \( (d^{\dagger })^{2}=0 \)
}

{\newpage
\clearpage
\samepage \( d^{\dagger }w=0 \)
}

{\newpage
\clearpage
\samepage \( w=d^{\dagger }n \)
}


\end{document}
