In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modifications are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.

    Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking f

Given a matrix, the Consecutive Ones Submatrix (C1S) problem which aims to find the permutation of columns that maximizes the number of columns having together only one block of consecutive ones in each row is considered here. A heuristic approach will be suggested to solve the problem. Also, the Consecutive Blocks Minimization (CBM) problem which is related to the consecutive ones submatrix will be considered. The new procedure is proposed to improve the column insertion approach. Then real world and random matrices from the set covering problem will be evaluated and computational results will be highlighted.

When scheduling rules become incapable to tackle the presence of a variety of unexpected disruptions frequently occurred in manufacturing systems,  it is necessary to develop a reactive schedule which can absorb the effects of such disruptions. Such responding requires efficient strategies, policies, and methods to controlling production & maintaining high shop performance. This can be achieved through rescheduling task which defined as an essential operating function to efficiently tackle and response to uncertainties and unexpected events. The framework proposed in this study consists of rescheduling approaches, strategies, policies, and techniques, which represents a guideline for most manufacturing companies operatin

Neurolinguistics is a new science, which studies the close relationship between language and neuroscience, and this new interdisciplinary field confirms the functional integration between language and the nervous system, that is, the movement of linguistic information in the brain in receiving, acquiring and producing to achieve linguistic communication; Because language is in fact a mental process that takes place only through the nervous system, and this research shows the benefit of each of these two fields to the other, and this science includes important topics, including: language acquisition, the linguistic abilities of the two hemispheres of the brain, the linguistic responsibility of the brain centers, and the time limit for langua