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B14

11 bytes removed, 17:37, 28 April 2014
== Equation ==
The paper main equation 50<br><math>R_{2, needs following definitions\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2}-\frac{N_{\textrm{CYC}}}{T_{\textrm{rel}}}\cosh{}^{-1}(v_{1c}) - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D \right)} \\= R_{2,\textrm{eff}}^{\textrm{CR72}} - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D \right)}</math>
Which have these following definitions
<math>
v_{1c} = F_0\cosh{\left(\tau_{\textrm{CP}}E_0\right)}-F_2\cosh{\left(\tau_{\textrm{CP}}E_2\right)} \\
The term <math>p_D</math> is based on product of the off diagonal elements in the CPMG propagator (Supplementary Section 3).
 
Equation 50 is then <br>
<math>
R_{2,\textrm{eff}} = \frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2}-\frac{N_{\textrm{CYC}}}{T_{\textrm{rel}}}\cosh{}^{-1}(v_{1c}) - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D \right)} \\
= R_{2,\textrm{eff}}^{\textrm{CR72}} - \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D \right)}
</math>
It is interesting to consider the region of validity of the Carver Richards result. The two results are equal when the correction is zero, which is true when<br>

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