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\begin{eqnarray*}
   \epsilon_{ab} &=& \sqrt{\epsilon_{a}\epsilon_{b}} \\
   R_{m,ab} &=& \frac{R_{m,a}+R_{m,b}}{2} \\ 
   \alpha_{ab} &=& \sqrt{\alpha_{a}\alpha_{b}} \\
\end{eqnarray*}                           

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