Journal of Mathematical Extension
Volume:7 Issue: 4, Autumn 2013

Recently, a new algebraic structure, namely grouplike, has been introduced and studied by the first author. A grouplike is something between semigroup and group with so close relations to groups. The grouplike axioms are generalizations of the four group axioms. In this paper, we study regular and irregular grouplikes as a class of semigroups. The motivation of this study lies in some interesting properties of regular proper grouplikes.

We show how we can obtain the general solution of rank one perturbed linear Diophantine systems (A + uvT )x = b using only information from the application of the Hermite normal form algorithm to the corresponding linear Diophantine system Ax = b. The empirical results show that use of the proposed algorithm may result in saving considerable computing time.

In this paper, a new algorithm is presented to approximate the solution of a singularly perturbed boundary value problem with leftlayer based on the homotopy perturbation technique and applying the Laplace transformation. The convergence theorem and the error bound of the proposed method are proved. The method is examined by solving two examples. The results demonstrate the reliability and efficiency of the proposed method.

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and Serre classes of R-modules. Let R be a commutative Noetherian ring, I , J be two ideals of R and M be an R-module. Let a 2 ˜W (I, J) and t 2 N0 be such that Extt R(R/a,M) 2 S and Extj R(R/a,Hi I,J (M)) 2 S for all i < t and all j > 0. Then for any submodule N of Ht I,J (M) such that Ext1 R(R/a,N) 2 S, we obtain HomR(R/a,Ht I,J (M)/N) 2 S.

The well-known formulas for divided differences in the case of one and two dimensional with multiple knots have played an important role in applied mathematics, particularly in numerical analysis, polynomial and lagrange interpolations. In this article we obtain a new formula for two dimensional divided differences in the case of multiple knots. This formula has a simpler form than the known formula given in literature. It is friendly using for computations and analysis.

The asymptotic distribution for the ratio of the sample correlations in two independent populations is established. The presented method can be used to derive the asymptotic confidence interval and hypothesis testing for the ratio of population correlations. The performance of the new interval is comparable with similar metho

In this paper, we generalize the construction of a pullback diagram in the framework of Hilbert modules over locally C-algebras and we explore some conditions under which diagrams of Hilbert modules over the corresponding C-algebras are pullback.

In this paper, weakly supercyclicity and weakly hypercyclicity of composition operators on some Hilbert spaces of analytic functions, especially on some weighted Hardy spaces are investigated.