in this paper, a stochastic two-stage model is offered for optimization of the day-ahead scheduling of the microgrid. system uncertainties including dispatchable distributed generation and energy storage contingencies are considered in the stochastic model. for handling uncertainties, monte carlo simulation is employed for generation several scenarios and then a reduction method is used to d...

Abstract Consider $$(X_{i}(t))$$ (Xi(t)) solving a system of N stochastic differential equations interacting through random matrix $${\mathbf {J}} ...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...

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We prove new modularity lifting theorems for p-adic Galois representations in situations where the methods of Wiles and Taylor–Wiles do not apply. Previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology. In practice, this imposes several restrictions – one must be in a Shimura variety settin...