Volume 10, 2005. 1 - 4. 
Marshall Hampton, Andrea Peterson, Heather Stoller, Albert Wang
On the Nonexistence of Singular Equilibria in the Four-Vortex Problem.

Abstract In this paper, we provide a partial answer to a question recently posed by Hassan Aref et. al. in their article Vortex Crystals, namely whether there are certain singular equilibria of point vortices. We prove that there are no such equilibria in the four-vortex case.

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Furman University Electronic Journal of Undergraduate Mathematics