Journal of Hyperstructures
Volume:4 Issue: 1, Winter and Spring 2015

We introduce and study clean hyperrings. A hyperring R is called a clean hyperring if for every element x of R, x 2 u + e where u is a unit and e is an idempotent. We also introduce GC-hyperring which is a proper generalization of clean hyperrings and obtain some related results of such hyperrings.

Throughout R is a commutative Noetherian ring and a an ideal of R.In this paper we study formal homology modules of Artinian R-modules. We obtain an expression of the formal homology interm of a certain local homology module. Also we consider their behavior with respect to the a-torsion functor, exact sequences for various situations and related ideas.

We introduce the notion of multiplicative hyperternary-rings, consider their regular equivalences and strongly regular equivalences and investigate their properties. As a consequences, three isomorphism theorems on multiplicative hyperternary-rings are obtained.

The object of the present paper is to appraise generalization of the Hyers-Ulam-Rassias stability theorem of the Pexider type functional equation f (2 x+y) - f (x+2 y) = 3 g (x) - 3 h (y). .. (1) in intuitionistic fuzzy Banach spaces. The stability results have been obtained by a fixed point method. This method shows that the stability is related to some fixed point of a suitable operator.

In this paper, we present some fixed point theorems for fundamentally nonexpansive mappings in Banach spaces and give one common fixed point theorem for a commutative family of demiclosed fundamentally nonexpansive mappings on a nonempty weakly compact convex subset of a strictly convex Banach space with the Opial condition and a uniformly convex in every direction Banach space, respectively; moreover, we show that the common fixed points set of such a family of mappings is closed and convex.

In this paper we use MATLAB platform to calculate some quantities of 3-manifold sol3 like Christoffel symbols, curvatures, Einstein tensor and plot the geodesics of this space.

In this paper an expansion method, based on two dimensional delta functions (2D-DFs), is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. The main characteristic behind this method is that this method reduce such problems to a system of algebraic equations. Since this approach does not need integration, all calculations can be easily implemented. Finally, we estimate the error of the method, and present two numerical examples to demonstrate the accuracy of the method.