deletions | additions       diff --git a/untitled.tex b/untitled.tex  index ce93f88..16ae855 100644  --- a/untitled.tex  +++ b/untitled.tex 
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G^>_{\beta q}(\epsilon) = \sum_\gamma [G_{\beta\gamma}^r(\epsilon) V_{\gamma q} g^{>}_{q}(\epsilon)+ G_{\beta\gamma}^>(\epsilon) V_{\gamma q} g^{a}_{q}(\epsilon)]  \end{eqnarray}  \begin{eqnarray}  G^{<,h}_{\gamma k}(\omega+\epsilon) = \sum_\beta [G_{\gamma\beta}^r(\omega+\epsilon) V^*_{\beta k} g^{<,h}_{k}(\omega)+ g^{<,h}_{k}(\omega+\epsilon)+  G_{\gamma\beta}^<(\omega+\epsilon) V^*_{\beta k} g^{a,h}_{k}(\omega+\epsilon)] \end{eqnarray}  Then, we have  \begin{eqnarray}