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\begin{document}
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{\newpage
\clearpage
\samepage \begin{equation}f(\log a) ={\rm const}\,,\qquad \max~\{10~ {\rm R}_\odot,~\hbox{Roche Lobe}~
(M_1)\} < \log a < 10^4~{\rm R}_\odot.
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{equation}\null\,\vcenter{\openup\jot\m@th
\ialign{\strut$\displaystyle{##}$\hfil&$\displaystyle{{}##}$\hfil
\crcr
f(M_1) \propto  M_1^{-2.35}\,,&~10~{\rm M}_\odot < M_1< 120~{\rm M}_\odot
\,;       \cr
f(q)   \propto  q^{\alpha_q}\,,& q\equiv M_2/M_1<1 \,.   \cr
\crcr}}\,
\end{equation}
}

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{\newpage
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\samepage \begin{eqnarray}f(\log\mu)=~{\rm const}\,,~~
	  10^{28} \le \mu \le 10^{32}~ \hbox{G cm}^3\,,
\end{eqnarray}
}

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\clearpage
\samepage \begin{equation}\alpha_{CE}\left({GM_aM_c\over 2a_f}-{GM_aM_d\over 2a_i}\right) =
	{GM_d \left(M_d-M_c\right) \over R_d}\,,
\end{equation}
}

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\samepage \begin{equation}M(r)=3.4\times 10^6~ {\rm M}_\odot\,
\left(1+\frac{R}{1\, {\rm pc}}\right)\, .
\end{equation}
}

{\newpage
\clearpage
\samepage \begin{equation}\ln {r\over  r_0}={1\over 2.94}\left(v_0^2-v^2\right)~,
\end{equation}
}

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\end{document}
