The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

In this paper, numerical and experimental studies on the elastic behavior of glass fiber reinforced ‎polymer (GFRP) with stiffeners in the GFRP section's web (to prevent local buckling) are presented. ‎The GFRP profiles‎ were connected to the concrete deck slab by shear connectors. Two full-scale simply supported ‎composite beams (with and without stiffeners) were tested under impact load (three-point load) to ‎assess its structural response. The results ‎proved that the maximum impact force, maximum ‎deflection, damping time, and ‎damping ratio of the composite beam were affected by the GFRP ‎stiffeners‎. The experimental results indicated that the damping ratio and deflection were diminished compare

This research seeks the effects of dubbed Turkish TV series on Iraqi audiences. The chosen sample is about 600 Iraqi students at Baghdad and al-Anbar Universities. This study consists of four sections: section one deals with the theoretical framework of the study. Section two studies the dubbed Turkish TV series. The third section explores the role of mass media in forming tendencies, and the last section seeks the field study by analyzing the tendencies if Iraqi viewers of these series.
The goal of this study is to know the role these series played in affecting the behavior and attitudes of Iraqi people and how it can change their morals.
The research ends with the number of results like the negative effect of these series on the

priorities of materials research due to their promising properties, especially in the field of thermoelectricity. The efficiency or performance of thermoelectric devices is expressed in terms of the thermoelectric figure-of-merit (ZT) – a standard indicator of a material’s thermoelectric properties for use in cooling systems. The evaluation of ZT is principally determined by the thermoelectric characteristics of the nanomaterials. In this paper, a set of investigative computations was performed to study the thermoelectric properties of monolayer TMDCs according to the semiclassical treatment of the Boltzmann transport equation. It was confirmed that the thermoelectric properties of 2D materials can be greatly improved compared with thei