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We study, on the entire space ℝN(N [ges ] 1), the diffusive logistic equationand its generalizations. Here p > 1 is a constant. Problem (1.1) plays an important role in understanding various population models and some other problems in applied mathematics. When λ = 1 and p = 2, it is also known as the Fisher equation and KPP equation, due to the pioneering works of Fisher [8] and Kolmogoroff, Petrovsky and Piscounoff [18].

This paper mainly focuses on the energy management of microgrids (MGs) consist of combined heat and power (CHP) and photovoltaic (PV) prosumers. A multi-party energy management framework is proposed for joint operation of CHP and PV prosumers with the internal price-based demand response. In particular, an optimization model based on Stackelberg game is designed where the microgrid operator (MGO) acts as the leader and PV prosumers are the followers. The properties of the game are studied and it is proved that the game possesses a unique Stackelberg equilibrium. The heuristic algorithm based on differential evolution is proposed that can be adopted by the MGO, and nonlinear constrained programming can be adopted by each prosumer to reach the Stackelberg equilibrium. Finally, via a practical example, the effectiveness of the model is verified in terms of determining MGO's prices and optimizing net load characteristic, etc.Index Terms-microgrid, combined heat and power, energy management, demand response, Stackelberg game. 1

In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is invariant under the flow in dimension three (similar results hold in higher dimension with more assumptions). A consequence of this result is the following. Let (M, g) be an ALE manifold of dimension n = 3. If m(g) = 0, then the Ricci flow starting at g can not have Euclidean space as its (uniform) limit.

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