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\begin{document}
\begin{varwidth}{50in}
  \begin{equation}
    \vec{F}^{i} = -\sum_{j}^{Neighbor} \left( \vec{s}_{i}\times \vec{s}_{j} \right)
    \times \vec{E} ~~{\rm and}~~ \vec{\omega}^{i} = -\frac{1}{\hbar} 
    \sum_{j}^{Neighbor} \vec{s}_j \times \left(\vec{E}\times r_{ij} \right),\nonumber
  \end{equation}
\end{varwidth}
\end{document}
