Journal of Mathematical Extension
Volume:9 Issue: 4, Autumn 2015

The main aim of this paper is to illustrate and discuss consistent Fuzzy Linear Matrix Equations (shown as FLME) of the form Pl i=1(AiXiBi) = C for finding its fuzzy number solutions. Similar equation is studied in [12] based on Friedman’s method [5]. Recently, Mikaeilvand et al. [13] proposed a novel method based on Ezzati’s method [4] for solving fuzzy linear systems, which is better than Friedman’s method numerically. In this article, we used this method for finding the general solutions of consistent FLME. The parametric form of fuzzy numbers is used. The embedding method is profited to transform fuzzy linear matrix equations to parametric linear equations, and a numerical procedure for calculating the solutions is designed.

This paper is concerned with the problem of synchronization of the Harb-Zohdy chaotic system using the back-stepping. Based on the stability theory, the control for the synchronization of chaotic systems Harb-Zohdy is considered without unknown parameters. Next, an adaptive back-stepping control law is derived to generate an error signal between the drive and response systems Harb-Zohdy with an uncertain parameter asymptotically synchronized. Finally, this method is extended to synchronize the system with two unknown parameters. Note that the method presented here needs only one controller to realize the synchronization. Numerical simulations indicate the effectiveness of the proposed chaos synchronization scheme.

In this paper, a new class of distributions called the weighted Lindley (WL) distribution is proposed. Different properties of the distribution are investigated. This new family has two unknown parameters. It is observed that the maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms and they have to be obtained by solving some numerical methods. One real data application illustrates the performance of the distribution.

In this paper we establish necessary and sufficient optimality conditions for a nondifferenriable, nonconvex semi-infinite vector optimization problem involving locally Lipschitz functions, whose constraints are required to depend continuously on an index j belonging to a compact set J.

In this paper it is shown that T and I have a unique common fixed point on a compact subset C of a metric space X, where T and I are two self maps on C, I is non-expansive and the pair (T, I) is weakly commuting. In [3] Fisher and Sessa verified the same problem but with C closed subset. Further we show this result by replacing compatibility with weakly commutativity of pair (T, I) and continuity with non-expansiveness of I.

The boundary element methos is applied to the Helholtltz equation. To this end we discretized the Helmholtz equation over the boundary and conclude a system of equations. By applying the boundary condition we get a new system which gives the solution of the equation.

Let A and B be unital Banach algebras and M be a left A-module and right B-module. We consider generalized derivations associate with Hochschild 2-cocycles on triangular Banach algebra T (related to A, B and M). We characterize this new version of generalized derivations on triangular Banach algebras and we obtain some results for l1 − direct summands of Banach algebras.

Let R be a commutative Noetherian ring. We prove that every R-module N of finite Gorenstein injective dimension has a Gorenstein injective envelope : N ! G where injective dimension of Ker is finite and is injective.