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In this paper we introduce and study a relation “~” between projections, a relation “ ” on positive operators and a relation "~G" (G-group) on projections in extended factor algebras. The main results in this paper state that these relations are indeed an equivalence relation (Theorem 2.1) and (Theorem 2.2). Finally, we determine the relation between these concepts.

In this paper we consider parameter estimation in a linear regression setting with inequality linear constraints on the regression parameters. Most other research on this topic has typically been addressed from a Bayesian perspective. In this paper we apply Bayesian approach with Gibbs sampler to generate samples from the posterior distribution. However, these implementations can often exhibit poor mixing and slow convergence. This paper overcomes these limitations with a new implementation of the Gibbs sampler. In addition, this procedure allows for the number of constraints to exceed the parameter dimension and is able to cope with equality linear constraints.

The aim of this paper is to establish a new method for calculating generalized curvature and generalized torsion. This method depends on at least three points infinitely close to the considered point. The established method is characterize from other methods by using only dot and cross product of vectors combined from this points, without any parameter that interacts in the defined curve by using some concepts of nonstandard analysis given by Robinson A. and axiomatized by Nelson E. 1- Introduction: - In this paper the problem of obtaining the generalized curvature(6), (7), and generalized torsion(8), is considered and studied by using three points infinitely close to the given point. This method is different from the two methods given in (7), (8) and (9), and it has an advantage that it does not depend on any parameter which interact with the curve.

An Optical Character Recognition (OCR) approach for printed Arabic script is presented in this paper, Which is one of the most popular scripts in the world. Development of an OCR system. For Arabic script it is difficult because Arabic characters are distinct and many structurally similar characters exist in the character set. In the proposed approach, the technique can be divided into three major steps. The first step is digitization then do some pre-processing like segmentation to detect the slant of character and correct it .Second, feature extraction , using gray-level matrices. Finally, the K-Nearest-Neighbors is used for classification. This method was tested using 45 patterns for each Arabic character with different fonts (simplified Arabic, tahoma, traditional Arabic), The sample images were divided into 20 training and 25 test images. Images in the test set did not appear in the training sets. This method performs extremely well with recognition rates .90.3%. This is a very good performance. All of this demonstrates that the new method is able to handle printed Arabic character task efficiently. It is a promising technique for recognition printed Arabic character. 1. Introduction Optical character recognition (OCR), deals with the recognition of optically processed character rather magnetically processed ones. In a typical OCR system, input characters are read and digitized by an optical scanner. Each character is then located, segmented and the resulting matrix is fed into a preprocessor. Off-line recognition can de considered the most general case: no special device is required for writing and signal interpretation is independent of signal generation, as in human recognition [6]. The recognition of Arabic character has been an area of great interest for many years, and a number of research papers and reports have already been published in this area. There are several major problems with Arabic character recognition: Arabic characters are distinct and ideographic, many structurally similar character exist in the character set Table (1). Thus, classification criteria are difficult to generate [1 J[3j[6]. The Arabic language has a rich vocabulary. More than 200 million people speak this language as their native speaking, and over 1 billion people use its character set, such as Persian and Urdu, Due to the cursive nature of the script, there are several characteristic that make recognition of Arabic distinct from the recognition of Latin script or Chinese The study of Arabic character recognition has been regarded since 1980s. However, in comparison with the other languages, such as Latin, Chinese and Japanese, there is a little work has been conducted on the automatic recognition of Arabic character [4][5].

In this paper, a new conjugate gradient formula using Kafaki and Gambry is proposed. And we give the global convergence of new method.Also we give descent and sufficient descent conditions.Numerical results, show that this new formula is more efficient for solving unconstrained optimization problems comparing with other method (H/S),depending on the iterations and the number of functions evaluation.

In this paper we applied new geometric methods for prove existence three dimensional linear [97,3 ,87]11 and [143,3,131]13 codes theorems [(1.4.4), (1.5.5)].

Let R be a ring. The ring is called right almost WJCP-injective. If for any , (right non singular) there exists a left ideal of such that . In this paper, we give some characterization and properties of almost WJCP-injective rings, which are proper generalization of JCP-injective ring and almost AP-injective ring. Then, we study the regularity of the right almost WJCP-injective ring and some important results which are known for the right JCP-injective rings to be hold for the right almost WJCP-injective rings.

The following open problem stated that, if T: A⟶B is a dense range homomorphism between Banach algebras A and B such that B is semi-simple. Is T automatically continuous? (see [1]). In [3] given a partial solution of the above problem as follows: Let A and B be Fréchet algebras such that B is semi simple, the spectral radius rB is continuous on B and the spectral radius rA is continuous at zero. If T : A ⟶ B is a dense range homomorphism, then T is automatically continuous. In this paper, we prove the following result : If T : A+ ⟶ B+ is a dense range homomorphism between Jordan – Banach algebras A+ and B+ such that B+ is semi simple, the spectral radius rB+ is continuous on B+ and the spectral rA+ is continuous at zero, then T is automatically continuous.

The purpose of this paper is using a class of open sets called i-open sets [9] to study some classes of separating axioms spaces for open,  -open and semi-open sets. Further, we studied the relations between such spaces.

In this paper, we are concerned with the conjugate gradient method for solving unconstrained optimization problems due to its simplicity and don’t store any matrices. We proposed two spectral modifications to the conjugate descent (CD). These two proposed methods produces sufficient descent directions for the objective function at every iteration with strong Wolfe line searches and with inexact line search, and also they are globally convergent for general non-convex functions can be guaranteed. Numerical results show the efficiency of these two proposed methods.

The following open problem state that: If is a dense range homomorphism from Banach algebra into Banach algebra such that is semisimple. Is automatically continuous? (see[1]) In [5] given a partial solution of the above problem as follows: Let and be a Fréchet algebras such that is semisimple, the spectral radius is continuous on and the spectral radius is continuous at zero. If is a dense range homomorphism, then is automatically continuous. In this paper, we prove the following result: If is a dense range homomorphism from a complete normed nonassociative algebrainto a complete normed nonassociative algebra such that is semisimple and multiplication algebra of is also semisimple, the spectral radius is continuous on and the spectral radius is continuous at zero, then is automatically continuous.

In this paper we have generalized the extended Dai-Yuan conjugate Gradient method by Considering the parameter in the denominator of as a convex combination. Three values of are computed in three different ways namely by assuming descent property, Pure Conjugacy and using Newton direction. The descent property and global convergence for the proposed algorithms are established. Our numerical experiments on some standard test functions show that there are considerable improvement on other classical methods in this field.

This paper deals with finding outliers in a multivariate linear regression model after assuming a model of normal – Wishart distribution. This method is based on the estimation of probability of an outlier for each observation by mixed Bernoulli model with shifting location outlier. We show how to obtain the posterior distribution in the mixed model by Gibbs sampler algorithm. Also the determination of the number of outliers is done by criterion of marginal likelihood distribution. The theoretical results of this research are applied to real data of multivariate linear regression. The results obtained are so encouraging in determining the outliers in these data.

The main purpose of this paper is to study Ɣ-regular rings, and the connection between such rings and weakly regular, π-regular, strongly π-regular, semi π-regular and SNI-rings. We also study P-injective modules, and to find it's relation with Ɣ-regular rings.

This paper deals with the treatment of trend seasonality of time series by using the method of exponential smoothing, indeed the triple exponential method (Winter's Method) which includes two procedures of analysis, the first one is (multiplicative seasonal model) and second (additive seasonal model), we conclude the forecasting for future data for multiplicative model is better than additive model by using many criterions .MAD, MAPE, MSE.

In this paper we investigate the existence and approximation solution for nonlinear system of an integro-differential equation of the second order with boundary conditions by using the numerical-analytic method for investigating a system of nonlinear differential equation with boundary conditions which is given by Samoilenko A. M. And also these investigations lead us to generalized the above method.

This paper conclude the study of the weights of points and lines of (k,n)-arcs from until , since the number of points and lines of this plane is very large, so we divide this search in to three parts. The first part contained the existence of these arcs from to and we show that when the (210,39;f)-arc of type (20,39) exist and all the other cases from to does not exist. In the second part we studied these arcs from to and we saw that there are two types of these arcs when and which are respectively (39,21;f)- arc of type (2,21) and (20,20;f)- arc of type (1,20), then proved the theorem of these special cases are given. Finally in the last step we prove that (k,n;f)- arc of type (n-19,n) does not exist in PG(2,19) for all values of from 362 to 381.

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.

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 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.

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.

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.

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 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