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Brian Jackson edited Thus_begin_eqnarray_label_eqn__.tex
over 8 years ago
Commit id: d90673efa7fcbaf167e65043bf4592fc249810d2
deletions | additions
diff --git a/Thus_begin_eqnarray_label_eqn__.tex b/Thus_begin_eqnarray_label_eqn__.tex
index 25668c7..064314f 100644
--- a/Thus_begin_eqnarray_label_eqn__.tex
+++ b/Thus_begin_eqnarray_label_eqn__.tex
...
Thus,
\begin{eqnarray}
\label{eqn:}
\dfrac{d}{db}
\bigg[ \bigg( \rho(\Gamma_{\rm obs}, P_{\rm obs}) - \rho(\Gamma_0, P_{\rm min})
\bigg] \bigg) = \dfrac{d}{db}
\left[ \left( \int_{b^\prime = 0}^{b} f\ \rho({\rm act}) \dfrac{2b^\prime\ db^\prime}{b_{\rm max}^2}
\right] \right) \\
\Rightarrow b^{-1}\ P_{\rm obs}
\left[ \left( \dfrac{\partial \rho({\rm obs})}{\partial P_{\rm obs}} - \left( \dfrac{\Gamma_{\rm obs}}{2 P_{\rm obs}} \right) \dfrac{\partial \rho({\rm obs})}{\partial \Gamma_{\rm obs}}
\right] \right) = b_{\rm max}^{-2}\ f(b)\ \rho({\rm act}(b))\ b
\end{eqnarray}