deletions | additions       diff --git a/Thus_begin_eqnarray_label_eqn__.tex b/Thus_begin_eqnarray_label_eqn__.tex  index 366b098..f19afe9 100644  --- a/Thus_begin_eqnarray_label_eqn__.tex  +++ b/Thus_begin_eqnarray_label_eqn__.tex 
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\left( \dfrac{2}{\Gamma_{\rm obs}} \right) \left( \dfrac{P_{\rm obs} - P_{\rm min}}{P_{\rm min}} \right)^{1/2} 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) & = & b_{\rm max}^{-2}\ f(b)\ \rho({\rm act}(b))\ b \\  &  \Rightarrow &  \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} \\ \rho(\Gamma_{\rm act}, P_{\rm act}) & = & k\ \Gamma_{\rm act}^{-11/3} \left( P_{\rm act} - P_{\rm min} \right)^{-1/2} \left[ P_{\rm obs} \dfrac{\partial \rho(\Gamma_{\rm obs}, P_{\rm obs})}{\partial P_{\rm obs}} - \left( \dfrac{\Gamma_{\rm obs}}{2 } \right) \dfrac{\partial \rho(\Gamma_{\rm obs}, P_{\rm obs})}{\partial \Gamma_{\rm obs}} \right]_{\rm obs \rightarrow act},