This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

The research addresses the importance of reading and writing for sura Al-alaq and Al-qalam as they represent the main sources for all the sciences as well as ethical values. The researcher seeks to define the educational and ethical values in these two texts which related to reading and writing. To do this, the author went through different relevant literature to show the similarities and related points between them, she also shows the significant of reading and writing and the learning and teaching worth to be consider. The result revealed that the both texts assert on the educational and ethical values, and the vital role of reading and writing.  

The current research deals with studying the aesthetics of symbolic values in the design of internal spaces and their connotations through their existence as a material value, as well as the symbolic meanings and their connotations that touch the spiritual and emotional side of the human being as an intangible value, and the research included four chapters, so the research problem was embodied by the following question (What is the role of values Symbolism and aesthetics in the design of interior spaces)? Therefore, the aim was to clarify the role of symbolic values and their aesthetics in the design of internal spaces. The first chapter included the importance of research, the need for it, the limits of the research and its terminology.

This research aims to identify the effectiveness of modern media technologies represented by satellite TV in the development of good citizenship values when students. To achieve this purpose were selected a sample of 44 students in the Department of Electrical technologies in Technical Institute in Nasiriyah in southern Technical University during the school year (2015-2016).
Was determined the general objectives of the use of modern media techniques represented satellite TV is to promote the values of good citizenship among the sample of students in order to make them good citizens in the community could contribute to the development and upgrading it. And put the general plan of research. Promising researchers measure of good citizen

The avoidance of failure in construction projects is not an easy task, which makes the failure of the construction project to achieve its objectives a major problem experienced by all countries in the world, especially Iraq. Where nearly two-thirds of the construction projects in the world have been suffered by significant problems as an increase in the cost of the project, delay in the specified duration for execution, and stopping the project. Therefore it is required to study and apply new methods for managing the construction project to ensure its success and achieve its objectives. The aim of this study is to study the Agile project management method and its impact on the construction project. In addition, to identi

current research Cares about study patterns of optical and aesthetic values in the halls of occasions (weddings) because of their importance in providing an atmosphere of joy. The problem was through the study of light and its impact on the receiver and found a researcher that interior spaces allocated to the halls inappropriate in terms of functional and aesthetic so necessitated the need to study this phenomenon in order to be addressed through the study of light and its impact on the users of those spaces where research aims to current detection properties patterns optical in the internal spaces of the halls and identify some of the aesthetic values of the lighting for the interior spaces.The search consists of four chapters, the firs