Present paper demonstrates on application aspect of Haar wavelets and method of moments for computing performance characteristics in electromagnetic field. In this paper, some significant results including performance characteristics relevant to application of the Haar wavelets as the expansion function in the method of moments have been successfully explored. The present analysis for performance evaluation has been focused for three different electromagnetic materials-finite straight, thin plane plate and eddy current problem. The main results explored are described in the main text and also concluded at the end with discussions.

In this paper some general transportation models have been discussed and particularly a multi-choice cost stochastic transportation problem (STP) has been reviewed in the light of progressive research works of previous noteworthy researchers. In addition, an analytical approach for the optimal solution (OS) of the proposed stochastic transportation problem has been demonstrated. The analytical method proposed by us is not only heuristic but also a generalization in threefold. We remark here that some unnecessary complications involved previously have been removed in our proposed method. Finally, by way of demonstrating a numerical illustration some significant conclusive observations have also been drawn in order to highlight the threefold feature.

In this paper, we present that the propositional proof system R(lin) (Resolution over Linear Equations) established by Ran Raz and Iddo Tzameret is not a super system, there exists a sequence of tautologies, which require proof complexity exponential in size of tautologies. We show that there are the sequence of unsatisfiable collections of disjuncts of linear equations, which require exponential lower bounds in R(lin) and have polynomially bounded refutations by incorporating renaming inference rule to R(lin) system. Some additional properties of R(lin) have been described that many of the "hard" provable in R outstanding examples of propositional tautologies (contradictions) have polynomially bounded proofs in R(lin).