The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

shoulder joint by preparing special exercises for the youth-category wrestling, and through the researchers' follow-up to the wrestling game and their work in the field of rehabilitation and physical therapy, noticing that most of the wrestling players suffer from the shoulder joint pain despite their visit to the specialist doctor and take Treatment, so the researchers saw to study this problem and restore the recovery of the injured through special exercises and a suitable qualification program for the shoulder joint muscles, the goal of research in preparing special exercises and knowing its effect on the rehabilitation of the background muscle of the shoulder for the youth wrestling category. The researchers assumed that there are stati

Economic organizations operate in a dynamic environment, which necessitates the use of quantitative techniques to make their decisions. Here, the role of forecasting production plans emerges. So, this study aims to the analysis of the results of applying forecasting methods to production plans for the past years, in the Diyala State Company for Electrical Industries.

The Diyala State Company for Electrical Industries was chosen as a field of research for its role in providing distinguished products as well as the development and growth of its products and quality, and because it produces many products, and the study period was limited to ten years, from 2010 to 2019. This study used the descriptive approa

The research explain the analysis of finance investments through  analyze the finance tables for commercial banks, by using the pointers to indicate the limits of economical benefit for these investments, and fix the negative deviations and as well positive, for the purpose of  diagnostic the negative (disadvantage) and develop the advantage deviation, For the importance of finance investments in the development operation and economical growth, further to that the finance investments is represent one of the most activities in the commercial banks in which aim the adequate incomes as a result of the commercial banks act to receipt the banks deposits and then make it growth and develop through  commercial advantage o

      The aim of this study is to investigate the nature of the relationship between domestic savings and domestic investment, or rather the efficiency of domestic savings in financing development in Algeria, in order to explain this relationship, identify the challenges to investment, and finance and accelerate economic growth. The economic measurement methodology has estimated the relationship between the savings rate and the local investment rate in the Algerian economy. We have annual data for the period 1970-2014. One of the most important conclusions is that there is no relationship between savings and investment, nor even an integration between them. To illustrate this, the use of some statistical tools, a

  The research aims to presenting a number of scenarios for the investment of the marshes. The problem of research problem was that there is no in-depth analysis of the marshes  environment. The traditional methods of  the environmental analysis are insufficient. The research community is represented by the decision makers in Maysan Governorate. The research led to proposing of three scenarios with statement  the requirements for the success of each one. The most important conclusions are that the three proposed scenarios for marshes investment depend on the availability of the required volunteers for each scenario. The higher the availability of the requirements, the more optimistic the scenario becomes. If t

This deals with estimation of Reliability function and one shape parameter (?) of two- parameters Burr – XII , when ?(shape parameter is known) (?=0.5,1,1.5) and also the initial values of (?=1), while different sample shze n= 10, 20, 30, 50) bare used. The results depend on empirical study through simulation experiments are applied to compare the four methods of estimation, as well as computing the reliability function . The results of Mean square error indicates that Jacknif estimator is better than other three estimators , for all sample size and parameter values

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.