Trusted, Bureaucrats
4,223
edits
Changes
Jump to navigation
Jump to search
CR72
,→Equation: Added some phantom goodness :)
<math>
R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-))\\\phantom{R_{2,\textrm{eff}}} = R_2 + \frac{k_{\textrm{EX}}}{2} - \nu_{\textrm{cpmg}} \cosh^{-1} (D_+\cosh(\eta_+) - D_-\cos(\eta_-))
</math>
<math>
\zeta = 2 \Delta \omega \, (R_2^A - R_2^B - p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}}) \\\phantom{\zeta} = - 2 \Delta \omega \, ( p_A k_{\textrm{EX}} - p_B k_{\textrm{EX}}) \\\phantom{\zeta} = - 2 \Delta \omega \, ( k_{\textrm{BA}} - k_{\textrm{AB}}) \\\phantom{\zeta} = - 2 \Delta \omega \, k_{\textrm{EX}} ( 2p_A - 1) \\\Psi = (p_B k_{\textrm{EX}} - p_A k_{\textrm{EX}})^2 + 4 p_A p_B k_{\textrm{ex}}^2 - \Delta \omega^2\\\phantom{\Psi} = ( p_A k_{\textrm{EX}} + p_B k_{\textrm{EX}} )^2 - \Delta \omega^2 \\\phantom{\Psi} = k_{\textrm{ex}}^2 - \Delta \omega^2 \\
\eta_+ = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{+\Psi + \sqrt{\Psi^2 + \zeta^2}} \\
\eta_- = \frac{1}{2\sqrt{2} \, \nu_{\textrm{cpmg}}}\sqrt{-\Psi + \sqrt{\Psi^2 + \zeta^2}} \\
