in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...

this paper proposes a stochastic framework for demand response (dr) aggregator to procure dr from customers and sell it to purchasers in the wholesale electricity market. the aggregator assigns fixed dr contracts with customers based on three different load reduction strategies. in the presented problem the uncertainty of market price is considered and the risk of aggregator participation is ma...

prediction of mechanical properties of carbon nanotube-based composite is one of the important issues which should be addressed reasonably. a proper modeling approach is a multi-scale technique starting from nano scale and lasting to macro scale passing in-between scales of micro and meso. the main goal of this research is to develop a multi-scale modeling approach to extract mechanical propert...

let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...