Journal of Mathematical Extension
Volume:17 Issue: 5, May 2023

One of the most well-known issues in Data Envelopment Analysis (DEA) literature is to identify the anchor points of the production possibility set (PPS). Each extreme efficient unit which is located on the intersection of the strong and weak efficient frontiers of the PPS, is called an anchor point. In the other word, a decision making unit (DMU) is an anchor point, if there is at least one supporting hyperplane at the unit under consideration, in the situation that some components of its gradient vector are equal to zero, and so some input or output factors do not play any role in the performance of that unit. This study presents a new method to identify the anchor points of the PPS under the variable returns to scale (VRS) assumption and in the presence of the uncertain data. The proposed method is based on the robust optimization technique and finding the weak and strong defining supporting hyperplanes passing through the unit under evaluation. The potentially of the proposed method is illustrated by a data set, includes 20 banks in Iran.

Discrete fractional calculus (DFC) is continuously spreading in the neural networks, chaotic maps, engineering practice, and image encryption, which is appropriately assumed for discrete-time modelling in continuum problems. For solving problems including difference operators (classic and fractional), we employ a discrete version of the Adomian decomposition method (ADM). This method help to find the solutions of linear and nonlinear classic and fractional difference problems (CDPs and FDPs). Examples are given to clarify and confirm the obtained results and some of particular cases of CDPs and FDPs are highlighted.

The purpose of this paper is to introduce the concept ofsoft multiplicative linear functional in soft Banach algebras. Then the notions of soft spectrum and soft spectral radius of an element in soft Banach algebras are introduced. Furthermore we discuss some important characterizations and theorems of them.

The main purpose of this paper is the comparison between an ideal and its integral closure and how to obtain the integral closure of ideals in diferent ways. We know that integral closure of a monomial ideal is again a monomial ideal and monomial ideals are associated to graphs. As graphs are widely used in computer science and cryptography in which there are only binary numbers, we introduced the associated matrix to a graph only with digits of 0 and 1. Moreover, we compared and computed the index of stability of associated prime ideals with index of stability of the integral closure of associated prime ideals.

In this paper, we establish a new Carlson type integral inequality with the best constant factor. The equivalent Beurling-Kjellberg type inequality and discrete form are considered.

The paper deals with the mathematical programming problems with switching constraints that are defined with continuously differentiable functions. The main results are the upper approximations of the Fr`echet Normal Cone of the feasible set for the problem. As applications of the main results, we present some stationary conditions of the considered problem.