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In this paper, we found an approximate solution for solving linear Fredholm integro-differential equation, by using Aitken's method with the help of the successive iteration method. Some numerical example were presented to show the accuracy of this method.

A ring R is said to be right(left) sπ-weakly regular if for each a ∈ R and a positive integer n, a n ∈ a n R a n 2 R (a n ∈ R a n 2 R a n ). In this paper, we continue to study sπ-weakly regular rings due to R. D. Mahmood and A. M. Abdul-Jabbar (8). We first consider properties and basic extensions of sπ-weakly regular rings, and we give the connection of s π-weakly regular, semi π-regular and π-biregular rings.

The aim of the project is to develop parallel approaches for Gaussian Elimination Methods that are used in linear programming to solve linear module systems. Most of these models are time-consuming when executed and processed in the sequential microprocessor computers. During the project, we try to decrease this time and increase the efficiency of the algorithm for the Gaussian Elimination Method, through developing parallel methods appropriate to be executed on MIMD type computers. In this paper, three algorithms were suggested for paralleling a developed algorithm of Gaussian Elimination Method and a comparison was made between the three algorithms and the original. As we have been able to accelerate the three parallel methods and the speedup was one of the following: Speedup = , no. of processor is (50) In general, the practical results and the suggested programs for these new algorithms proved to be better in performance than their analogues that are executed in computers of sequential processor in view of the two elements of execution time and algorithm time.

In this paper we give some properties of the zero commut idempotent matrices ,and give some properties of non-singular matrices .

In this paper we used successive approximate method (S.A.M.) to solve Fredholm integral equation of the first kind (F.I.E.1st. K.) with symmetric kernel. And also suggested an algorithm for this method the computer programming is given for the algorithm. The method and algorithm are tested on several numerical examples. After comparing the results with exact solution see tables (1, 2), it occurred that the results are good. (in this work Matlab programming used).

In this Paper, we studied the stability analysis of steady state solutions of Gray-Scott Model in one-dimension using Fourier mode and we showed that the solutions are conditionally stable.

In this paper we used the improved least square method presented to solve Fredholm integral equation of the second kind .This method combines, forward and backward factorial polynomial and quasi orthogonal polynomial. These polynomials improved the above method and getting it to a strong convergence property .The numerical results are agreeable in comparison with exact solution .

This paper has a dual purpose. One purpose is to introduce a method consists of repeatedly applying Riemann-Liouville operator of appropriate order until the equation , ( ) , (q is integer) is transformed into an ordinary differential equation.A second purpose is to apply the Adomian decomposition method for the solution of fractional differential equation an alternative method of Laplace transform.

In this paper we investigate the existence and approximation of the periodic solution for a system of nonlinear integro-differential equations of Volterra type. The numerical-analytic method has been used to study the periodic solutions of the non-linear ordinary differential equations that were introduced by A.M. Samoilenko.

In this paper, we study the conditions under which the zero solution is stable in the semi- liner case for certain third order differential equation of the form : Where , s = 1,2,3 , , , The characteristic equation of the above differential equation has complex roots of the form : and the other root has the following , . property

The aim of this paper is to establish a new formula of generalized curvature discussed with the help of decomposition theorem which is used to obtain generalized curvature for algebraic curves by using some concepts of nonstandard analysis given by Robinson A. and axiomatized by Nelson E.

In this paper we study the existence and approximation of the periodic solutions for a system of first order nonlinear differential equations by assuming that each of the functions are measurable at t and bounded by Lebesgue integrable functions. The numerical-analytic method has been used to study the periodic solutions of ordinary differential equations which were introduced by A. M. Samoilenko.

In this paper, we used a new operation in a Genetic Algorithm for solving the binary Knapsack problem depending on it 's LP Relaxation solution after eliminating the fractional part of the non-binary values. The benefit is to make a filter to the initial random population from the farness of the optimal solution and unsuitable chromosomes. This good property will be fixed automatically in all generations in the Genetic Algorithm until reaching the optimal binary solution. 1. Introduction to Genetic Algorithm: A Genetic Algorithm (GA) was first introducted by John Holland for the formal investigation of the mechanisims of natural adaptation but the algorithm has been since modified to solve computational search problems, GA has been used to solve the NP-hard combinatorial problems effectively such as Knapsack Problem.(2) GA is a heuristic search algorithm for the solution of optimization problems in which starting from a random initial guess solution, better descendants are tried in an attempt to find one that is the best under some criteria and conditions.(5) GA is a computer algorithm that searches for good solutions to a problem from among a large number of possible solutions. It begins with a set of candidate solutions (chromosomes) called population. A new population is created from solutions of an old population in hope of getting a better population. Solutions which are chosen to the new solutions

In this paper, we provide a solution to the system of non-integer differential equation of order 0 < q < 1, by the technique of Laplace transformation and with interest to property of Mittag-Leffler function, with the help of the programming technique of Maple.

In this paper, we describe two new algorithms which are modifications of the Hestens-stiefl CG-method. The first is the scaled CG- method (obtained from function and gradient-values) which improves the search direction by multiplying to a scalar obtained from function value and its gradient at two successive points along the iterations. The second is the Preconditioned CG-method which uses an approximation at Hessein of the minimizing function. These algorithms are not sensitive to the line searches. Numerical experiments indicate that these new algorithms are effective and superior especially for increasing dimensionalities.

This paper contains two main results relating to the size of eight and fourth blocking set in PG(2,16). First gives new example for (129,9)-complete arc. The second result we prove that there exists (k,13)- complete arc in PG(2,16), k≤197. We classify the minimal blocking sets of size eight in PG(2,4).We show that Rédei –type minimal blocking sets of size eight exist in PG(2, 4). Also we classify the minimal blocking sets of size ten in PG(2, 5), We obtain an example of a minimal blocking set of size ten with at most 4-secants.We show that Rédei –type minimal blocking sets of size ten exists in PG(2, 5).

In this paper we investigate the existence and approximation for nonlinear system of differential equations with boundary conditions by using the numerical-analytic method for investigate of a periodic solutions which is given by Samoilenko A. M. and also these investigations lend us to the improving and extending the above method.

In this paper we will study the (G,H)- posets , to give a condition of freeness on colouring maps . Also we will look at the group – posets from the view point of the category theory . That is to give some results on semi-direct product poset groupoid.

The compression technique is an optimal solution for decreasing the amount of information sents out from satellites to earth station with rate transmission. In this paper, a study for the application of embedded zero tree wavelet (EZW) in image compression is incorporated. The study is implemented using the image processing toolbox of Matlab ver 6.5 .The performance of the proposed algorithm is executed and tested using the standard image of Barbara with size 512×512 pixels in bmp format. Different threshold values are used in the proposed algorithm to specify the compression ratio CR. The quality of reconstructed image is measured in terms of PSNR .The recorded results show that there are a trade off between the PSNR and CR and depends on the type of used image .In this work the extraction of the results are focused on two types of local area satellites images .The first image is the Mosul dam area with simple and limited topography .The second image is the Singar area with different and difficult topography .The results show that at threshold of 16 , the CR is a round 1:60 with PSNR more than 34 dB ,for the tested image .

In this paper, the problm of sequencing n jobs on one machine is considered with a multi objective function.Two problems have been studied, sum of completion times added with the maximum tardiness i i T c max ) and sum of completion times with the maximum tardiness ( ∑ ∈N i i T and c max ), the first one has optimal solution solved by Branch and bound technique, the second has efficient solutions founded by Van Wassenhove algorithm.A theorem is presented to show a relation between the number of efficient solutions, lower bound (LB) and optimal solution.This theorem restricts the range of the lower bound, which is the main factor to find the optimal solution.Also the theorem opens algebraic operations and concepts to find new lower bounds.

The concept of θ-semi-open sets in topological spaces was introduced in 1984 and 1986 by T. Noiri (9, 10). In this paper we introduce and study a generalization of a contra pre semi-open maps due to (Caldas and Baker) (3), it is called contra pre θs-open maps, the maps whose images of a θ-semi-open sets is θ-semi-closed. Also, we introduce and study a new type of closed maps called contra pre θs-closed maps, which is stronger than contra pre semi-closed due to Caldas (2), the maps whose image of a θ- semi-closed sets is θ-semi-open.1991 Math. Subject Classification: 54 C10, 54 D 10.

In this paper, we have investigated a new initial parameter in the nonlinear constrained optimization method. The aim of this new method is to make a balance between interior and exterior method for constrained optimization. The new technique has been programmed to solve some of standard problems in the non-linear optimization. The results are too effective when compared with other standard optimization methods like interior and exterior methods.

In this paper, the present algorithm [4] to solve fractional programming problem for multi objective functions, investigate the algorithm to solve linear programming problem for multiobjective functions [2], the computer application of algorithm was tested on a number of numerical examples and modify the approach by using mean and median for values of objective functions, to combine objective function from objective functions for linear programming problem for multi objective functions then it has been improved the above algorithm to solve the problem and computer application of improvement algorithm has been demonstrated by a flow chart and solving numerical examples on the computer then the good results have been often, as compared to the previous method [2].

This paper presents the development and implementation of a new numberical based on a non-quadratic Triangular rational function model. For solving non-linear optimization problem .The algorithm is implemented in one version, employing exact line search. This version is compared numberically against versions of the CG-method. The results indicate that in general the new algorithm is superior to the previon algorithm.

In this paper we used Hermite polynomial with Galerkin , collocation and least square methods for solving fredholm integral equations of the first kind (F.I.E.F.K) with degenerated kernel .The algorithms and computer applications of the algorithms are given for the methods which have tested through numerical exaples and compared the results with exact solutions as indecated in tables (1,2,3,4), (used Matlab programmong in this work).

This paper deals with the study of solvability condition for certain boundary value problem with boundary conditions by .using perturbation method [5] . Since w, kw are constants, and e is a small parameter .

In this paper, we study the comparison among many methods to solve a system of linear equations based on the principle of wavelet methods as a Daubechies wavelet, Haar wavelet, Meyer wavelet, Symlet wavelet, Mexican Hat wavelet, Morlet wavelet. As a result, the Haar wavelet method can be considered the best method to solve the linear equations compared with the other methods especially for the dense and sparse matrix. For the three diagonal matrices the Meyer wavelet gave a good results. Other conclusion was found that the Symlet wavelet needs a long time to solve this system of equations and for all types of the matrix.

In this paper we investigate the existence and approximation for nonlinear system of integro-differential equation with boundary integral conditions by using the numerical-analytic method for investigating of a periodic solutions which is given by Samoilenko A.M. and Also these investigations lend us to the improving and extending the above method.

In this paper we study the existence and approximation of the periodic solutions for system of nonlinear integro-differential equations of Volterra type by Lebesque integrable function, By using weaker conditions of the function F(t,s,x,x) to be measurable in t and bounded by Lebesque integrable function.

In this paper we have modified a new extended generalized conjugate gradient steps with self-scaling variable metric updates for unconstrained optimization. The new proposed algorithm is based on the inexact line searches and it is examined by using different non-linear test functions with various dimensions.

In this paper, we find the algebra of quotients with bounded evaluation for operator algebras on a complex Hilbert space, namely: Hilbert - Schmidt and trace -class operators. Also, we study the behavior in computing the algebra of quotients with bounded evaluation for totally prime associative algebra

The main objective of this paper is the development of a new technique for solving stiff Linear Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs), The new Technique consists of combining the linear superposition principle with the principle of Multiple shooting. We have applied the new technique successfully for solving hard stiff IVPs. Also we have studied the ability of the new technique for controlling the stability of the numerical solution of IVPs and how the new technique prevents the accumulation of round off errors.

This paper examined 1122 statistical tests found in 55 master theses accredited during 1995-2000 at Mu'tah University. It tried to answer two main questions: First, do researchers still relying on the level of significance (a) as the only criterion to judge the importance of relations and differences? Second, to what extent practical significance can be found along with statistical significance? Results showed that researchers do consider statistical significance as the only criterion to judge the importance of their findings. 74.33% of the statistically significant tests were having a small practical significance, and only 10.27% were of large practical significance.

لقد أحدث ظهور الآلات الحاسبة ثورة في تكنولوجيا التعليم مما جعل المعلمين ينقسمون إلى فئتين بشأن استخدامها في تعليم الرياضيات. البعض يرى أن التكنولوجيا بصفة عامة ذات فوائد عديدة في عملية التعليم لعل أهمها هي أنها تقلل من جهد ووقت المعلم الذي يبذله في أعمال رتيبة مما يوفر له جهدا ووقتا لأعمال أكثر إبداعاً لصالح تلاميذه. وهم يرون في الآلة الحاسبة أداة تثير الحماس لدى المتعلمين وتقدم إثارة وتيسيرا لتدريس المفاهيم، كما تنمي الحس العددي، وتعمل على تقديم بعض المفاهيم والمهارات مبكراً قبل مفهوم الكسور العشرية ومهارات العمليات الحسابية عليها، أن الآلة الحاسبة يمكن أن تساعد المتعلمين على اكتشاف العلاقات المختلفة بين الأعداد بواسطة التجريب على الحالات المختلفة والتي يصعب التحقق منها باستخدام الورقة والقلم خاصة إذا كانت تتضمن عمليات حسابية معقدة، وإلى تجريب عدد كبير من الحالات حتى تتضح العلاقة المستهدفة. ومن ناحية أخرى يرى المعارضون لاستخدام الآلة الحاسبة أنها تقضي على الدافعية الذاتية لدى المتعلمين لتعلم وتذكر الحقائق الأساسية، كما قد تؤدي إلى ضعف قدرة المتعلمين على اكتشاف الأخطاء والذي يؤدي بدوره إلى ضعف التفكير الرياضي. ويرى المعارضون أن حصول المتعلم على الإجابات جاهزة من الآلة سوف يفقده حب الاستطلاع والتساؤل ومعرفة كيفية الحصول على الإجابة الصحيحة ومعرفة الأخطاء وهو ما يمارسه عندما يكون العمل باستخدام الورقة والقلم. من هذا المنطلق تجيء هذه الدراسة للتعرف على رأي المعلمين في هذا المجال مع تحديد البحث في أطار المرحلة المتوسطة بالكويت. The invention of calculators is considered a revolution in Education Technology. As a result of that, teachers of Mathematics are classified into two categories. On one hand, some of them believe that Technology in general has various advantages in Education practice. It saves the teacher's time and efforts, in his daily work. Also it enables him to be creative to the best for his pupils. They believe that Calculators are tools which arise pupils enthusiasm and make the teaching practice and concept more easier for them, and helps them to setup the numerical sensitivity, concepts and skills in their early stages before Fractional practice and other mathematical operations. They think that calculators enable pupils to find out the different relationships between numbers through practicing different cases which can't be realized by using a paper and pencil, especially if it includes complicated problems that requires many to reach the exact relationship. On the other hand, those who reject the usage of calculators, believe that this will terminate pupils self-motivation to discover their mistakes which leads to a lower mathematics thinking ability. Also, they believe that when pupils get the ready and correct answers, they will lose their curiosity and ability to discuss their difficulties. With reference to this study, we will explore teachers opinion toward this subject in the Intermediate stage in Kuwait schools.

Due to the latest attempt to change the Saudi Mathematics Curriculum many questions have been raised: Is the so-called "new mathematics" suitable to the Saudi students? How high is the level of abstraction of its new concepts? Does this level match the Saudi students' age and cognitive development? To answer these questions, much educational research must be conducted. This study is done in that direction; mainly, to examine where the Saudi mathematics curriculum stands when compared with some international curricula. In this study, fifty-two mathematical subjects introduced in the Saudi curriculum were statistically analyzed and compared with the corresponding subjects introduced in the curricula of twenty-three countries which participated in the Second International Mathematics Study conducted in the five year period from 1976 to 1983. Some useful results have been reached including: 1) The Saudi curriculum introduces twenty mathematical concepts earlier than what the international curricula specify. 2) There were three mathematical concepts introduced late in the Saudi curriculum when compared with the international standard. 3) Seventeen mathematical concepts were equally introduced timewise in the Saudi curriculum and in the studied curricula. 4) It was impossible to compare seven mathematical concepts due to lack of international agreement on where these concepts should come. 5) It was found that some subjects were ignored by the Saudi curriculum while some international curricula recognize them. Based on the findings of this paper several recommendations were made to improve the Saudi curriculum.