In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

The research aims to characterize the strategic plan of the Educational Professional Development Center, to reveal the most important training needs for teachers from this center, to reveal the extent to which this center meets those needs, and to identify the differences between teacher responses about the degree of importance, availability of those needs according to variables of sex, specialization, and years of experience. This descriptive study adopted a questionnaire applied to (256) teachers in the K.S.A. The results of the study showed that all training needs ranged in the degree of importance from large to very large and that the most important were the skills associated with communicating with members of the learning community.

In this paper, the effective computational method (ECM) based on the standard monomial polynomial has been implemented to solve the nonlinear Jeffery-Hamel flow problem. Moreover, novel effective computational methods have been developed and suggested in this study by suitable base functions, namely Chebyshev, Bernstein, Legendre, and Hermite polynomials. The utilization of the base functions converts the nonlinear problem to a nonlinear algebraic system of equations, which is then resolved using the Mathematica^®12 program. The development of effective computational methods (D-ECM) has been applied to solve the nonlinear Jeffery-Hamel flow problem, then a comparison between the methods has been shown. Furthermore, the maximum

في هذا البحث، تم تنفيذ الطريقة الحسابية الفعالة (ECM) المستندة إلى متعددة الحدود القياسية الأحادية لحل مشكلة تدفق جيفري-هامل غير الخطية. علاوة على ذلك، تم تطوير واقتراح الطرق الحسابية الفعالة الجديدة في هذه الدراسة من خلال وظائف أساسية مناسبة وهي متعددات الحدود تشيبشيف، بيرنشتاين، ليجندر، هيرمت. يؤدي استخدام الدوال الأساسية إلى تحويل المسألة غير الخطية إلى نظام جبري غير خطي من المعادلات، والذي يتم حله بع

The aim of the research is to evaluate the response of the researched leaders towards practicing the concept of the lens, which is its dimensions with (stakeholders, resource mobilization, knowledge development, culture management) and the nature of its relationship to tax pioneer performance represented in its dimensions (strategic direction, leadership indicators, growth, renewal and modernization, efficiency, Effectiveness) The questionnaire was approved as a main tool in collecting data and information from the sample members in the General Authority of Taxes, which number (91) Who are on (M. General Manager, Division Director, Deputy Director, Senior Division Director, Deputy Director, Second Division, Division Officer, M. D

Background. The use of modern aids and technology has contributed greatly to football development, the goalkeeper is the most important position in the team, and the use of devices gave objective readings about the goalkeeper's ability in terms of skill and physical aspects. Objectives. The research aimed to prepare exercises using an electronic device to measure the knee bending angle because of its great importance in developing the skill of catching and dimensions of the high ball for football goalkeepers. Methods. The researchers used the experimental method, and the sample consisted of (4) male goalkeepers under 15 years of age, one of the research procedures was to determine the biomechanical variables affecting the development of the

This study aimed at some of the criteria used to determine the form of the river basins, and exposed the need to modify some of its limitations. In which, the generalization of the elongation and roundness ratio coefficient criterion was modified, which was set in a range between (0-1). This range goes beyond determining the form of the basin, which gives it an elongated or rounded feature, and the ratio has been modified by making it more detailed and accurate in giving the basin a specific form, not only a general characteristic. So, we reached a standard for each of the basins' forms regarding the results of the elongation and circularity ratios. Thus, circular is (1-0.8), and square is (between 0.8-0.6), the blade or oval form is (0.6-0

We have provided in this research model multi assignment  with  fuzzy function goal has been to build programming model is correct Integer Programming fogging  after removing the case from the objective function data and convert it to real data .Pascal triangular graded mean using Pascal way to the center of the triangular.

The data processing to get rid of the case fogging which is surrounded by using an Excel 2007 either model multi assignment  has been used program LNDO to reach the optimal solution, which represents less than what can be from time to accomplish a number of tasks by the number of employees on the specific amount of the Internet, also included a search on some of the