In-home Smart Grid (SG), the integration of Renewable Power Systems (RPSs) with Conventional Power Systems (CPSs), calls for cost-effective management for the electricity usages of end users' household appliances. In this paper, by taking the charging process of RPSs and multiple types of household appliances in to consideration, we have developed… (More)
We present the small-scale limits for the homogenization of a class of spatial-temporal random fields; the field arises from the solution of a certain fractional kinetic equation and also from that of a related two-equation system, subject to given random initial data. The space-fractional derivative of the equation is characterized by the composition of… (More)
The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding an asymptotic regime of accurate approximation comparable to that for the spectral vector method.