deletions | additions       diff --git a/begin_equation_sigma__xy_v__.tex b/begin_equation_sigma__xy_v__.tex  index c6eee0d..621adce 100644  --- a/begin_equation_sigma__xy_v__.tex  +++ b/begin_equation_sigma__xy_v__.tex 
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\end{equation}  \begin{equation}  v=\frac{1}{2\pi}\int_{BZ}d^2kb_z(k)  \end{equation} This "$v$" number is called TKNN number or Chern number.