\batchmode
\documentclass{article}
\RequirePackage{ifthen}




\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{multirow}
\usepackage{rotating}


\makeindex{}


\makeatletter
\textheight 625pt
\textwidth 460pt
\oddsidemargin 0pt
\evensidemargin 0pt
\marginparwidth 50pt
\topmargin 0pt
\brokenpenalty=10000

%
\providecommand{\ie}{{\em i.e.}}%
\providecommand{\eg}{{\em e.g.}}%
\providecommand{\cf}{cf.} 

%
\providecommand{\gildas}{\mbox {\bf GILDAS}}%
\providecommand{\sic}{\mbox {\bf SIC}}%
\providecommand{\greg}{\mbox {\bf GREG}}%
\providecommand{\otfcal}{\mbox {\bf OTFCAL}}%
\providecommand{\mira}{\mbox {\bf MIRA}}%
\providecommand{\class}{\mbox {\bf CLASS}}%
\providecommand{\oldclass}{\mbox {\bf CLASS77}}%
\providecommand{\newclass}{\mbox {\bf CLASS90}} 

%
\providecommand{\analyse}{\texttt{ANALYSE}}%
\providecommand{\fit}{\texttt{FIT}}%
\providecommand{\fort}{\texttt{F90}}%
\providecommand{\plait}{\texttt{PLAIT}}%
\providecommand{\ave}{\texttt{AVERAGE}}%
\providecommand{\accu}{\texttt{ACCUMULATE}} 

%
\providecommand{\emm}[1]{\ensuremath{#1}}    % Ensures math mode%
\providecommand{\emr}[1]{\ensuremath{\mathrm{#1}}}  % Uses math roman fonts


\pagestyle{fancy}


\fancyhf{} % Clears all fields.


\lhead{\scshape Averaging spectra with \mbox {\bf CLASS}}
\rhead{\scshape \nouppercase{\rightmark}}   %
\fancyfoot[C]{\bfseries\thepage {}}


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\renewcommand{\footrulewidth}{0pt}    %


%
\renewcommand{\sectionmark}[1]{%
  \markright{\thesection. \MakeLowercase{#1}}}
%
\renewcommand{\subsectionmark}[1]{}




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\textsf{Averaged channel intensity and weight (aligned spectra):}
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$\displaystyle \sum_{ j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}}
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay2572}%
$\displaystyle \frac{1}{\beta^2}
                       \sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} f_R(j)^2 \, w_R(j)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath314}%
\begin{displaymath}
 \ensuremath{\mathrm{var}} (aX+bY) = a^2 \ensuremath{\mathrm{var}}(X) + b^2 \ensuremath{\mathrm{var}}(Y)
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1695}%
$a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1697}%
$b$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1699}%
$X$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1701}%
$Y$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2223}%
\fbox{
\begin{minipage}[t]{12cm}
\textsf{Resampled channel weight (weights {\tt TIME} and {SIGMA}):}
\begin{equation}
  
   w_{R'}(i) = \frac{ \left( \sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} f_R(j) w_R(j) \right) ^2}
                    {\sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} f_R(j)^2 \, w_R(j)}
\end{equation}
\end{minipage}
}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1705}%
${R'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1707}%
$0.0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1709}%
$0.25$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1711}%
$0.5$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1717}%
$x_{\ensuremath{\mathrm{val}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1719}%
$w_{R'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1721}%
$\sigma_{R'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1723}%
$x_{\ensuremath{\mathrm{val}}} \rightarrow x_{\ensuremath{\mathrm{val}}}+0.00$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1725}%
$w_{R'} = w_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1727}%
$\sigma_{R'} = \sigma_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1729}%
$x_{\ensuremath{\mathrm{val}}} \rightarrow x_{\ensuremath{\mathrm{val}}}+0.25$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1731}%
$w_{R'} = 1.6 \times w_R$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1733}%
$\sigma_{R'} = \sigma_R / \sqrt{1.6}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1735}%
$x_{\ensuremath{\mathrm{val}}} \rightarrow x_{\ensuremath{\mathrm{val}}}+0.50$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1737}%
$w_{R'} = 2 \times w_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1739}%
$\sigma_{R'} = \sigma_R / \sqrt{2}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1743}%
$\sigma_R(j)$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1745}%
$w_{R'}/w_{R}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1747}%
$\sqrt{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1755}%
$R' \rightarrow R''$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2259}%
\fbox{
\begin{minipage}[t]{12cm}
\textsf{Resampled channel weight (weight {\tt EQUAL}):}
\begin{equation}
  
   w_{R'}(i) = \frac{ \sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} f_R(j) w_R(j) }
                    { \sum_{j=j_{\ensuremath{\mathrm{min}}}}^{j_{\ensuremath{\mathrm{max}}}} f_R(j) }
\end{equation}
\end{minipage}
}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1759}%
$w_R(j)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1761}%
$1.0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1763}%
$T_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1765}%
$w_S$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2263}%
\fbox{
\begin{minipage}[t]{12cm}
\textsf{Averaged channel intensity and weight (non-aligned spectra):}
\begin{eqnarray}
  
  T_S(i) & = & \frac{w_{R'}(i) \times T_{R'}(i) + w_{T'}(i) \times T_{T'}(i) }
                    {w_{R'}(i)                  + w_{T'}(i)} \\
  
  w_S(i) & = & w_{R'}(i) + w_{T'}(i)
\end{eqnarray}
\end{minipage}
}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1777}%
$f \ne 0$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1779}%
$^{\prime\prime}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1781}%
$obs$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1783}%
$S_{\ensuremath{\mathrm{in}}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1785}%
$S_{\ensuremath{\mathrm{out}}}$%
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\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1789}%
$t_{S_{\ensuremath{\mathrm{out}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath456}%
\begin{displaymath}
        
        t_{S_{\ensuremath{\mathrm{out}}}} = t_{S_{\ensuremath{\mathrm{in}}}} + t_{\ensuremath{\mathrm{obs}}}
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1791}%
$T_{\ensuremath{\mathrm{sys}},S_{\ensuremath{\mathrm{out}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1793}%
$t \times |r| / T_{\ensuremath{\mathrm{sys}}}^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1795}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath465}%
\begin{displaymath}
         \frac {t_{S_{\ensuremath{\mathrm{out}}}} \times |r_{S_{\ensuremath{\mathrm{out}}}}|}
               {T_{\ensuremath{\mathrm{sys}},S_{\ensuremath{\mathrm{out}}}}^2}
         =
         \frac {t_{S_{\ensuremath{\mathrm{in}}}}  \times |r_{S_{\ensuremath{\mathrm{in}}}}|}
               {T_{\ensuremath{\mathrm{sys}},S_{\ensuremath{\mathrm{in}}}}^2} +
         \frac {t_{\ensuremath{\mathrm{obs}}}     \times |r_{\ensuremath{\mathrm{obs}}}|}
               {T_{\ensuremath{\mathrm{sys}},\ensuremath{\mathrm{obs}}}^2}
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1805}%
$f_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1807}%
$f_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{out}}}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1809}%
$f_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{in}}}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1811}%
$f_{\ensuremath{\mathrm{off}}}$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1813}%
$(f_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{out}}}} -
            x_{\ensuremath{\mathrm{val}},S_{\ensuremath{\mathrm{out}}}}) /
            f_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1819}%
$f(i_{\ensuremath{\mathrm{chan}}}) = f_{\ensuremath{\mathrm{res}}} \times
             (i_{\ensuremath{\mathrm{chan}}}-r_{\ensuremath{\mathrm{chan}}}) + f_{\ensuremath{\mathrm{off}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1821}%
$i_{\ensuremath{\mathrm{chan}}} = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1823}%
$x_{\ensuremath{\mathrm{val}}}     = f_{\ensuremath{\mathrm{res}}} \times
             (0       -r_{\ensuremath{\mathrm{chan}}}) + f_{\ensuremath{\mathrm{off}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1825}%
$v_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1827}%
$ -c \times f_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}} /
            f_{\ensuremath{\mathrm{rest}},S_{\ensuremath{\mathrm{out}}}} $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1829}%
$c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1831}%
$f_{\ensuremath{\mathrm{rest}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1833}%
$v_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{out}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1835}%
$v_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{in}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1841}%
$v_{\ensuremath{\mathrm{off}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1845}%
$(v_{\ensuremath{\mathrm{off}},S_{\ensuremath{\mathrm{out}}}}-x_{\ensuremath{\mathrm{val}},S_{\ensuremath{\mathrm{out}}}}) / v_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1853}%
$ - f_{\ensuremath{\mathrm{rest}},S_{\ensuremath{\mathrm{out}}}} \times v_{\ensuremath{\mathrm{res}},S_{\ensuremath{\mathrm{out}}}} / c $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
\stepcounter{subsubsection}
\stepcounter{subsection}
\stepcounter{section}
\stepcounter{section}

\end{document}
