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

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Abstract

That the reduction of costs for products and services provided by economic units is one of the main concerns at the present time to keep pace with competition in the markets, economic units are always striving to stay competitive in a modern business environment and achieve a competitive advantage, (TDABC) in the General Company for Electrical and Electronic Industries / Air cooler engine plant to reduce the costs facing the economic units under the circumstances of the Iraqi environment, especially the industrial, and the need for development events in traditional methods (TDABC) as a technology for reducing costs by relying on time guidelines. The research also concluded that the financial and non-financ

The human being is a social being and human communication is a fundamental axis in the process of social interaction, and the characteristic of social shyness grows through the interaction of the individual with his environment. Identifying the level of shyness among university students, and identifying the differences in shyness among university students according to specialization (scientific, humanities). In order to achieve the objectives of the research, the researcher prepared a measure of shyness based on Zimbardo's theory, and the components that he identified are the (behavioral, cognitive, and emotional components). The validity and reliability were calculated using the Cronbach's alpha method, reaching (0.94), and the scale in

Technological development intersects with terrorism to a large extent, beyond the use of the Internet and social media, in order to spread ideas, obtain support and financing, and recruit new elements, to the area of tactics and techniques of terrorist attacks, and everything related to the arsenal of terrorist weapons in the present and future, while technology offers many benefits. In various fields, and contribute to achieving multiple gains for humanity, they provide extremist and terrorist organizations and elements with a set of weapons and means through which they attempt to bypass monitoring and control efforts and the restrictions imposed on the use of weapons. They also help in planning and implementing their terrorist operations,

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a thir

New designs of solar using ray tracing program, have been presented for improved the performance and the out put power of the silicon solar cell, as well as reducing the cost of system working by solar energy. Two dimensional solar concentrator (Fresnel lenses) and three dimensional concentrators (parabola dish and cassegrain) were used as concentrator for photovoltaic applications (CPV). The results show that the performance efficiency and out power for crystalline silicon solar cells are improved.