Babylonian Journal of Mathematics

Some Results on Commutativity for Alternative Rings With 2, 3-Torsion Free.

Abubakar Salisu — 2024-03-25

ABSTRACT

In this article, we establish and proof some theorem on commutativity of alternative ring with 2, 3 –torsion free satisfy the following properties (Identities):

(P₁) [x²y²+y²x²,x]=0

(p₂) [x(xy)²+(xy)²x,x]=0

(p₃) [x(x²y²),x]=0

(p₄) [x(xy),x]=0 for every x,y in R.

Keywords: .

A Survey of MCDM-Based Software Engineering Method

sahar Mohammed — 2024-02-18

Multi-criteria decision making (MCDM) is an operation research subfield (OR). Decision-making is primarily a process involving various actors, including individuals, groups of individuals, institutions, and the state. As a discipline, multi-criteria decision-making is relatively new Many researchers have devoted their time to developing new MCDM models and techniques since the 1950s and 1960s, when the foundations of modern multi-criteria decision-making methods were laid. Research and development in the area have intensified recently and appear to be developing tremendously. Few attempts have been made to systematically convey the theoretical foundations and advancements of multi-criteria decision-making systems, despite the widespread and intense development. The framework for evaluating judgments and the methodological options are still up for debate. In this paper reviews of MCDM/MADM technologies will be included describing their scenarios. Making a decision that is more appropriate than others to solve a particular problem is the goal of decision-making (DM), so this study presents a review of the advantages and disadvantages of different decision-making techniques, specifically in the field of software engineering.

Nearly Endo Quasi Prime Sub-modules

Wafaa H. Hanoon — 2024-10-15

In this paper, the notion of nearly Endo quasi prime sub-modules is introduced together with several fundamental features and theorems. It provides several properties and descriptions of these ideas, and additional diagrams and examples are used to show how the study's findings translate into nearly Endo quasi prime and nearly Endo prime sub-modules

UTLIZATION OF GENERALIZED HEAT FLUX MODEL ON THERMAL TRANSPORT OF POWELL-EYRING MODEL VIA OHAM WITH HEAT GENEARTION ASPECTS

Esha Rafique — 2024-02-20

The focus of this work is on the flow of a spinning Powell-Eyring nanofluid in the boundary layer in three dimensions using magnetohydrodynamics (MHD). The research simulates mass transfer processes and heat transfer processes using non-Fick's mass flux theory and non-Fourier heat flux theory, respectively. Heat transport phenomena are analyzed by the integration of non-linear heat generation/absorption and thermal radiation properties. The boundary layer method is employed to solve a system of nonlinear partial differential equations (PDE) in the mathematical formulation. These equations are converted into nonlinear ordinary differential equations (ODES), and then the optimal OHAM with convergence control parameters is used to solve them. The impact of various physical movement circumstances on concentration and temperature profiles is visually represented through the generation of diagrams. This study provides important new understandings for both applied and scholarly research on complex heat transfer and fluid dynamics mechanisms in the context of three-dimensional MHD boundary layer flows of rotating Powell-Eyring nanofluids.

Bio-Convective Thermally Radiated Casson Fluid Model PDEs Past over a Darcy-Forchheimer Porous Stretched Sheet via OHAM Strategy

Syed Tehseen Abbas — 2024-06-20

The current study examines the topic of continuous flow of nanofluids over two-directional boundary level employing Casson heat transmission across a linearly stretched sheet. Firstly, the partial differential equations are transformed into non-linear ordinary differential equations with the help of similarity parameters. These non-linear ordinary differential equations are solved with the given boundary conditions by applying the BVPh2.0 method on Mathematica software. The effects of magnetic impact, radiation parameter, porosity number, Brownian motion parameter, thermophoresis parameter, Casson fluid parameter, Schmidt number, Prandtl number, peclet number, bioconvection on Velocity, temperature and concentration profiles is observed. It is noted that the concentration and temperature profiles increase by expanding values of thermophoresis parameter also the temperature increase by increment in Brownian motion while a reverse result obtained on concentration profile. Also, the influence of Casson fluid, thermophoresis and Brownian motion on skin friction, Sherwood number and Nusselt number is noted and check the behavior of these numbers by increasing or decreasing values of thermophoresis parameter, Casson fluid parameter and Brownian motion. And, calculated that by increment in thermophoresis and Brownian motion, the Nusselt number decreases. The graphs of temperature profile, velocity profile and concentration profile are drawn and also other results are tabulated.

Restricted visible submodules and fully restricted visible module

Mahmood S. Fiadh — 2024-04-24

In this article, the concept of Restricted visible (for short; Res-visible) submodule and fully restricted visible (for short fully Res-visible) module have been introduced which are considered the generalizations of the concepts of visible submodules and fully visible module respectively where every visible submodule (fully visible module) is Res-visible submodule (fully Res-visible) module, but the converse is not be true. Examples have been presented illustrating those relationships.

Numerical Solution of Burgers’-Type Equations Using Modified Variational Iteration Algorithm-I

Amir Muhammad — 2024-03-25

In this paper, we present modified variational iteration algorithm-I for the numerical solution of Burger's equations. In this recently developed technique, an auxiliary parameter is introduced which speed up the convergence rate of the series solutions. The suggested technique gives approximate and exact solutions with easily computable terms to linear and nonlinear PDEs without the Adomian polynomials, small perturbation, discretization or linearization.
In order to assess the precision, reliability and compactness, results of the proposed procedure are compared with the variational iteration method, which reveals that the MVIA-I exceptionally productive, computationally attractive and has more accuracy than the others methods. Two numerical test problems are given to judge the behaviour of the modified algorithms and absolute errors are used to evaluate the accuracy of the method. Numerical results are carried out for different values of the parameters.

Substitutional Based Gauss-Seidel Method For Solving System of Linear Algebraic Equations

Tuljaram Meghwar — 2024-01-10

In this research paper a new modification of Gauss-Seidel method has been presented for solving the system of linear algebraic equations. The systems of linear algebraic equations have an important role in the field of science and engineering. This modification has been developed by using the procedure of Gauss-Seidel method and the concept of substitution techniques. Developed modification of Gauss-Seidel method is a fast convergent as compared to Gauss Jacobi’s method, Gauss-Seidel method and successive over-relaxation (SOR) method. It works on the diagonally dominant as well as positive definite symmetric systems of linear algebraic equations. Its solution has been compared with the Gauss Jacobi’s method, Gauss-Seidel method and Successive over-Relaxation method by taking different systems of linear algebraic equations and found that, it was reducing to the number of iterations and errors in each problem.

Modified Technique to Solve Degeneracy in Linear Programming Problems

Sadia Qureshi — 2024-09-15

This paper addresses degeneracy that has been analyzed in the simplex method in Linear programming (LP) issues. The newly changed technique is proposed for choosing particular pivot rows from leaving variables. This method offers greater beneficial and faster consequences in the assessment of the prevailing classical approach. The proposed set of rules is a higher preference to avoid the confusion of taking an arbitrary ratio to pick out leaving variables and for this reason, the proposed method is robust to solve degeneracy in linear programming (LP) problems.

On commutativity of alternative rings with [xy^n x±yx^n y,x]=0

Abubakar Salisu — 2024-05-21

Let R be a n-torsion free with identity 1 ,In this article we investigate and prove the commutativity of alternative ring of the property(p_1 ), (p_2) and(p_3 ) under suitable constraints.

(p_1 ) [xy^n x±yx^n y,x]=0

(p_2 ) [xy^n x±yx^n y,y]=0

(p_3) [x(〖xy)〗^2+(〖xy)〗^2 x,x] = 0. ∀ x,y ∈R.