Mathematical study of Mpemba effect?

Try this reference:

O:H-O Bond Anomalous Relaxation Resolving Mpemba Paradox, by Xi Zhang Yongli Huang, Zengsheng Ma and Chang Q Sun http://arxiv.org/abs/1310.6514

P.S. I see you have already found this reference. Some useful information about Mpemba effect can be found here http://math.ucr.edu/home/baez/physics/General/hot_water.html By the way it seems the competition already has a winner: http://www.rsc.org/mpemba-competition/mpemba-winner.asp

Since this question is still open, I take the liberty of pointing to a recent survey of the status of the Mpemba effect, Pathological Water Science -- Four Examples and What They Have in Common, which draws the following conclusion:

If confounding factors (such as evaporation, dissolved gases, mixing by convective currents, inefficient thermal contacts) are removed, hot water may indeed freeze earlier than cold water, but not because it cools off more quickly: the hot water remains warmer than the cold water during the cooling process.

Nucleation sites in the container may lower the freezing temperature to anywhere between $0$ and $-45^\circ$ C and it may happen that the container filled with the cold water needs to be supercooled to a much lower temperature before the water freezes than the container filled with the hot water. The freezing temperature is a reproducible but unpredictable property of the container. If it would be possible to have two containers with identical nucleation sites, then cold water would freeze earlier than hot water.

Try:

X. Zhang, Y. Huang, Z. Ma, Y. Zhou, J. Zhou, W. Zheng, Q. Jiang, and C.Q. Sun, Hydrogen-bond memory and water-skin supersolidity resolving the Mpemba paradox. PCCP, 2014. 16(42): 22995-23002.

X. Zhang, Y. Huang, Z. Ma, Y. Zhou, W. Zheng, J. Zhou, and C.Q. Sun, A common supersolid skin covering both water and ice. PCCP, 2014. 16(42): 22987-22994.