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Brian Jackson edited Thus_begin_equation_label_eqn__.tex
over 8 years ago
Commit id: 6013b7fb053ee7cb45d140414e5791a58ae7163c
deletions | additions
diff --git a/Thus_begin_equation_label_eqn__.tex b/Thus_begin_equation_label_eqn__.tex
index 834a53d..17f46f6 100644
--- a/Thus_begin_equation_label_eqn__.tex
+++ b/Thus_begin_equation_label_eqn__.tex
...
\rho({\rm act}) = \left[ 4 b_{\rm max}^2\ \Gamma_{\rm obs}^{-2}\ f(b)^{-1}\ P_{\rm obs} \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]_{\rm obs \rightarrow act} \\
\Rightarrow \rho(\Gamma_{\rm act}, P_{\rm act}) =
k k\ \Gamma_{\rm act}^{-11/3} \left( \dfrac{P_{\rm min}}{P_{\rm act} - P_{\rm min}} \right)^{1/2} \left[ \dfrac{\partial \rho(\Gamma_{\rm obs}, P_{\rm obs})}{\partial P_{\rm obs}} - \left( \dfrac{\Gamma_{\rm obs}}{2 P_{\rm obs}} \right) \dfrac{\partial \rho(\Gamma_{\rm obs}, P_{\rm obs})}{\partial \Gamma_{\rm obs}} \right]_{\rm obs \rightarrow act},
\end{equation}
where
$k^\prime $k = 4 b_{\rm max}^2 A_{\rm max} \kappa^{-1}\ \upsilon^{-1}$, $\partial \Gamma_0/\partial P_{\rm obs} = 0$, and ${\rm obs \rightarrow act}$ indicates that ${\rm obs}$ quantities should be replaced with ${\rm act}$ quantities after the derivatives are taken.