Received (received date) Revised (revised date) Accepted (accepted date) We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider become very much involved even for a small number of players, which has hindered a ...

and Applied Analysis 3

In this paper, we establish some Harnack type inequalities satisfied by positive solutions of nonlocal inhomogeneous equations arising in the description of various phenomena ranging from population dynamics to micro-magnetism. For regular domains, we also derive an inequality up to the boundary. The main difficulty in such context lies in a precise control of the solutions outside a compact se...

Based on the elegant properties of the Thompson metric, we prove that the following two kinds of nonlinear matrix equations X = m ∑ i=1 AiX iAi and X = m ∑ i=1 (AiXAi) δi , (0 < |δi| < 1) always have a unique positive definite solution. Iterative methods are proposed to compute the unique positive definite solution. We show that the iterative methods are more effective as δ = max{|δi|, i = 1, 2...

Water resource management involves public investments with long-ranging impacts that traditional prediction approaches cannot address. These are increasingly being critiqued because (1) there is an absence of feedbacks between water and society; (2) the models are created by domain experts who hand them to decision makers to implement; and (3) they fail to account for global forces on local wat...