Journal of Hyperstructures
Volume:6 Issue: 1, Winter and Spring 2017

Let R be a vector space ( on C) and ϕ be an element of R∗ (the dual space of R), the product r·s = ϕ(r)s converts R into an associative algebra that we denote it by Rϕ. We characterize the nilpotent, idempotent and the left and right zero divisor elements of Rϕ[[x]]. Also we show that the set of all nilpotent elements and also the set of all left zero divisor elements of Rϕ[[x]] are ideals of Rϕ[[x]].

Let n ≥ 2 be a positive integer, R be a commutative ring with identity and M be a unitary R-module . In this paper we study the (n−1,n)-weakly prime submodules of direct product of modules. Also, we show that for some special cases, every proper submodule is (n−1,n)-weakly prime.

Let A be a symmetric positive definite (n)×(n) real matrix for n ≥ 1 and S ∈ Rn be a hypersurface. We are supposed to determine the tangent space TpS in an arbitrary point p ∈ S in the case that the whole space Rn admits the inner product with matrix A. Among other things, some maximum and minimum properties for the vector fields perpendicular to tangent spaces of hypersurfaces, the compatibility of the image or inverse image of a hypersurface and its tangent space under an embedding, an isometry, and a submersion are also pointed out.

In this paper, we give a necessary and sufficient condition for the product of two derivations on the triangular Banach algebra to be a derivation. We also study the case where the product of derivations is commutative.

This paper presents new analytical approximate methods such as local fractional variational iteration method and local fractional decomposition method for a family of the linear and nonlinear integral equations of the second kind within local fractional derivative operators. Some examples are presented to illustrate the efficiency and accuracy of the proposed methods. The obtained results reveal that the proposed methods are very efficient and simple tools for solving local fractional integral equations.

In this study, a new fourth-order method to compute the Moore-Penrose inverse is proposed. Convergence analysis along with the error estimates of the method is investigated. Every iteration of the method involves four matrix multiplications. A wide set of numerical comparisons of the proposed method with nine higher order methods shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.

In this paper we compute some geometric quantities of Schwarzschild Robertson-Walker space time by using MATLAB platform to construct functions that compute These quantities.