r23103 - /trunk/docs/latex/dispersion.tex -- May 08, 2014 - 20:07

Author: bugman
Date: Thu May  8 20:07:06 2014
New Revision: 23103

URL: http://svn.gna.org/viewcvs/relax?rev=23103&view=rev
Log:
Converted all complex numbers 'i' in the B14 dispersion model section of the 
manual ti \imath.


Modified:
    trunk/docs/latex/dispersion.tex

Modified: trunk/docs/latex/dispersion.tex
URL: 
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion.tex?rev=23103&r1=23102&r2=23103&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex     (original)
+++ trunk/docs/latex/dispersion.tex     Thu May  8 20:07:06 2014
@@ -590,18 +590,18 @@
 The ground state ensemble evolution frequency $f_{00}$ expressed in 
separated real and imaginary components, in terms
 of definitions $\zeta , \Psi , h_3 , h_4$ is
 \begin{equation}
-       f_{00} = \frac{1}{2}(\RtwozeroA + \RtwozeroB + \kex) + 
\frac{1}{2}(\dw - h_4) i .
+       f_{00} = \frac{1}{2}(\RtwozeroA + \RtwozeroB + \kex) + 
\frac{\imath}{2}(\dw - h_4) .
 \end{equation}
 
 Define substutions for `stay' and `swap' factors are
 \begin{subequations}
 \begin{align}
-       N & = h_3 + h_4 i , \\
+       N & = h_3 + \imath h_4 , \\
        NN^* & = h_3^2 + h_42 , \\
        F_0 & = (\dw^2 + h_3^2) / NN^* , \\
        F_2 & = (\dw^2 - h_4^2) / NN^* , \\
-       F_1^b & = (\dw + h_4) (\dw - h_3 i) / NN^* , \\
-       F_1^{a+b} & = (2\dw^2 + \zeta i) / NN^* .
+       F_1^b & = (\dw + h_4) (\dw - \imath h_3) / NN^* , \\
+       F_1^{a+b} & = (2\dw^2 + \imath \zeta) / NN^* .
 \end{align}
 \end{subequations}
 
@@ -610,7 +610,7 @@
 \begin{align}
        E_0 & =  2 \taucpmg \cdot h_3 , \\
        E2 & =  2 \taucpmg \cdot  h_4 , \\
-       E1 & = (h_3 - h_4 i) \cdot \taucpmg .
+       E1 & = (h_3 - \imath h_4) \cdot \taucpmg .
 \end{align}
 \end{subequations}
 
@@ -619,10 +619,10 @@
 \begin{subequations}
 \begin{align}
        \nu_{1c} & = F_0  \cosh(E_0) - F_2 \cos(E_2) , \\
-       \nu_{1s} & = F_0  \sinh(E_0) - F_2 \sin(E_2)i , \\
+       \nu_{1s} & = F_0  \sinh(E_0) - \imath F_2 \sin(E_2), \\
        \nu_{3} & = \sqrt{\nu_{1c}^2 - 1} , \\
-       \nu_{4} & = F_1^b (-\alpha_- - h_3 ) + F_1^b (\dw - h_4) i , \\
-       \nu_{5} & =(-\Delta \Rtwozero + \kex + \dw i) \nu_{1s} + 2 (\nu_{4} + 
\kAB F_1^{a+b}) \sinh(E_1) , \\
+       \nu_{4} & = F_1^b (-\alpha_- - h_3 ) + \imath F_1^b (\dw - h_4) , \\
+       \nu_{5} & =(-\Delta \Rtwozero + \kex + \imath \dw) \nu_{1s} + 2 
(\nu_{4} + \kAB F_1^{a+b}) \sinh(E_1) , \\
        y & = \left( \frac{\nu_{1c} - \nu_{3}}{\nu_{1c} + \nu_{3}} \right) ^ 
{N_{\textrm{CYC}}} , \\
        T & = \frac{1}{2}(1 + y) + \frac{(1 - y)\nu_{5}}{2 \nu_{3}N} , \\
        \RtwoeffCR & = \frac{(\RtwozeroA + \RtwozeroB + \kex)}{2} - 
\frac{N_{\textrm{CYC}}}{\taucpmg} \, \textrm{arcosh}(\, 
\operatorname{Re}(\nu_{1c}) \, ) , \\