In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior

The term "semantic exchange" was popularized in Arabic, especially in derivatives, grammatical structures, etc., but it came under different names or terms, including deviation, deviation, transition, displacement, tooth breach, replacement, attention, etc. In the rooting of this term through its study in language and terminology, and among linguists, grammar and others, we have reached a number of results, including The existence of a harmonization between the lexical and idiomatic meaning of the term exchange, and the phenomenon of semantic exchange is a form of expansion in language, and that the first language scientists They had turned to this And studied under Cairo for different names, as noted above.

أثر تنوع الرؤى الاخراجية للاتجاهات والحركات المسرحية المعاصرة في أتساعالاشتراطات الجمالية لبنية الخطاب المسرحي + الامر الذي ادى الى انزياح مكوناتالعرض وعناصره ؛ ومنها المنظومة السردية للنص التي شكلت في بدايات المسرحجغرافية العرض المسرحي والمرتكز النظري والفكري الذي يمد العرض المسرحي أغلبتدفقه الجمالي وعنصر أستعلائي لعناصر العرض الاخرى ؛ وضمن التطورات اللاحقةأنسحب المخرج المسرحي من سطوة البنية النص

The research aims to build a training program to develop the willpower in the kindergarten children. In order to achieve the objective of the research, the two researchers have developed a Training Program according to the following steps:

- Determining the general objective of the Training Program.

- Determining the behavioral objectives of the Training Program.

- Determining the content of the Training Program.

- Implementing the content of the Training Program sessions.

- Evaluating the Training Program.

The training program consisted of (15) sessions, each session included a set of parts (title, general objective, methods, time and place to implement the sessions, behavioral goals, tool

This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela