deletions | additions       diff --git a/oscillationTheory.tex b/oscillationTheory.tex  index 5effcf1..7d54ff6 100644  --- a/oscillationTheory.tex  +++ b/oscillationTheory.tex 
...
\end{split}  \end{equation}  Where U_{\alpha \beta} is a unitary matrix called the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix. matrix \cite{Kopp_2006}.  This matrix \begin{equation}  U_{i \alpha} = \begin{bmatrix}