### Volume 5, Issue 1, Winter and Spring 2008, Page 11-195

##### An Approximate Solution of Non-Linear System of Volterra Integral Equation

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 11-19

DOI:
10.33899/csmj.2008.163945

A Taylor series expansion is developed and applied to evaluate an approximate solution of the non-linear system of Volterra integral equation of the second kind for both Urysohn and Hammerstein types. The solution is based on substituting for the unknown function after differentiating both sides of the integral equation. Program associated with above methods is written in Matlab, finally, by using various examples, the accuracy of this method will be shown.

##### Maximal Generalization of Pure Ideals

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 21-27

DOI:
10.33899/csmj.2008.163946

The purpose of this paper is to study the class of the rings for which every maximal right ideal is left GP-ideal. Such rings are called MGP-rings and give some of their basic properties as well as the relation between

MGP-rings, strongly regular ring, weakly regular ring and kasch ring.

##### A New Numerical Procedure to Compute the Residues of a Complex Functions

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 29-46

DOI:
10.33899/csmj.2008.163947

In this paper, we are going to deal with computations of **Residues and Poles** for the complex functions **. **We are also going to investigate a **new **numerical procedure theoretically and its implementation numerically to compute the **residue **of complex analytic functions with high order poles. The paper needs the knowledge of computing the complex improper integrations.

##### On Centrally Prime and Centrally Semiprime Rings

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 47-56

DOI:
10.33899/csmj.2008.163948

In this paper, centrally prime and centrally semiprime rings are defined and the relations between these two rings and prime (resp. semiprime) rings are studied.Among the results of the paper some conditions are given under which prime (resp. semiprime) rings become centrally prime (resp.centrally semiprime) as in:1-A nonzero prime (resp. semiprime) ring which has no proper zero divisors is centrally prime (resp.centrally semiprime).Also we gave some other conditions which make prime (resp. semiprime) rings and centrally prime (resp.centrally semiprime) rings equivalent, as in :2-A ring which satisfies the-for multiplicative systems is prime (resp. semiprime) if and only if it is centrally prime (resp.centrally semiprime).3-A ring with identity in which every nonzero element of its center is a unit is prime (resp. semiprime) if and only if it is centrally prime (resp.centrally semiprime).

##### Application of Polyalphabetic Substitution Cipher using Genetic Algorithm

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 57-68

DOI:
10.33899/csmj.2008.163949

Several Genetic Algorithms have been developed for applications of cryptography problem; the primary distinction among all of them being the G.A. used for decryption problem and obtains the plain text. In this paper a new approach is proposed using Genetic Algorithm with cryptography. G.A. is used to obtain a best secret key in polyalphabetic substitution cipher. This key will be used then for encryption and decryption with a high level of security. The program is written in Matlab language (6.5).

##### A New Family of Spectral CG-Algorithm

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 69-80

DOI:
10.33899/csmj.2008.163950

A new family of CG –algorithms for large-scale unconstrained optimization is introduced in this paper using the spectral scaling for the search directions, which is a generalization of the spectral gradient method proposed by Raydan [14].

Two modifications of the method are presented, one using Barzilai line search, and the others take at each iteration (where is step- size). In both cases tested for the Wolfe conditions, eleven test problems with different dimensions are used to compare these algorithms against the well-known Fletcher –Revees CG-method, with obtaining a robust numerical results.

##### Limit Cycles of Lorenz System with Hopf Bifurcation

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 81-99

DOI:
10.33899/csmj.2008.163951

We prove that near the bifurcation point unstable limit cycle arises from the Lorenz system. In the analysis, we use the method of local bifurcation theory, especially the center manifold and the normal form theorem. A computer algebra system using Maple to derive all the formulas and verify the results presented in this paper.

##### Convergence Analysis of the Finite Difference Solution for the Nonlinear Klein-Gordon Equation

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 101-113

DOI:
10.33899/csmj.2008.163952

This paper is devoted to drive the matrix algebraic equation for the one-dimensional nonlinear Klein-Gordon equation which is obtained from using the implicit finite difference method. The convergence analysis of the solution is discussed. Numerical computations are conducted and the solutions are stable and convergent when the sine function is used as an initial condition.

##### Hosoya Polynomials of Steiner Distance of Complete m-partite Graphs and Straight Hexagonal Chains(*)

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 115-126

DOI:
10.33899/csmj.2008.163953

The Hosoya polynomials of Steiner distance of complete m-partite graphs and Straight hexagonal chains are obtained in this paper. The Steiner *n*-diameter and Wiener index of Steiner n-distance of and are also obtained.

##### Stability Conditions of Zero Solution for Third Order Differential Equation in Critical Case

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 127-138

DOI:
10.33899/csmj.2008.163955

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

##### Priority Dispatching Rules for Virtual Manufacturing Using Genetic Algorithm

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 139-164

DOI:
10.33899/csmj.2008.163956

The current research concentrates on designing and applying an intelligent information system by the use of (Oracle) language based Multi- Agents manufacturing process to produce a new product. Every agent (user) has its own *roles and privileges*. The research focuses on determining the ** delivery date** through using genetic algorithms to simulate Shop floor and specify priorities for

**according to specific rules which determine the lead time of the product. The importance of the research stems from designing software in c++ to simulate manufacturing processes in the genetic algorithm to realize the following :**

*dispatching orders*Attain the best sequences in implementing jobs according to the required rules.

Decreasing the queuing time for products and their components in the production processes.

Perfect utilization of the available resources.

The results of the designed system application have revealed that the operations planning by the use of the GA philosophy will perform a great role in calculating the product's lead time at the manufacturing operations' stages. This role supports the VM philosophy in calculating the industrial part of the products lead time quickly. Also the application results have confirmed that the designed

*GA software*efficiency depends upon the

*number*; whenever the number of jobs is bigger, the software execution efficiency is better.

**of jobs available at the time of execution**##### Nonstandard Treatment of Two Dimensional Taylor Series with Reminder Formulas

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 165-176

DOI:
10.33899/csmj.2008.163957

The aim of this paper is to establish some new two dimensional Taylor series formulas using some concepts of nonstandard analysis given by **Robinson **and axiomatized by **Nelson**

** **

##### Numerical Solution for Linear Parabolic Reaction-Double Diffusivity System using the Operational Matrices of the Haar Wavelets Method

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 177-195

DOI:
10.33899/csmj.2008.163958

We are using the operational matrices of the Haar wavelets method for solving linear parabolic reaction-diffusion system with double diffusivity. A numerical method based on the Haar wavelets approach which has the property , we compared this result with the exact solution for reaction-diffusion system, we found that high accuracy of the results in this method in the solution double diffusivity system even in the case of a small number of grid points is used. However, the computation is simple because consists of the matrices which can be programmed by Matlab language, thes matrices which we got of the numerical solution are representing all time steps while the finite difference method and finite elements method need the iteration to get the needed time step, they are complicated and time-consuming.

##### w-Wiener Polynomials of the Width Distance of the Square of a Path and a Cycle and a m-Cubic

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 11-32

DOI:
10.33899/csmj.2008.163959

Let G be a k_{0}-connected graph ,and let , ,be the w- width distance between the two vertices u,v in G. The w-Wiener polynomial of the width distance of G is defined by:

The w-Wiener polynomials of the square of a path , the square of a cycle ,and of an m-cube are obtained in this paper . The diameter with respect to the width distance –w ,and the Wiener index for each such graphs are also obtained .

##### Vertical Flow in Viscous Thin Films

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 33-41

DOI:
10.33899/csmj.2008.163960

The aim of this paper is to investigate the vertical flow in thin films of an incompressible liquids with no inertia force. Continuity equation and Navier-Stokes equations are used to obtain the equation that governs this type of flow, this equation is solved by using numerical methods to find the thickness of film.

##### Hybrid Algorithm for Image Denoising

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 43-60

DOI:
10.33899/csmj.2008.163961

The development in life has made the need for using images very important in many fields like space, engineering and medicine. Due to the fact that such images are affected by various noises from different resources they require some kind of filtering. The new algorithm applied in this research is obtained from merging two available methods. The first method adopts the conservative smoothing filter while the second one uses the median filter. The result of each method is compared with the new result outcome from the application of the new hybrid algorithm.

##### Reduction of the Accompanying Noise when Hidding in an Audio File

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 61-79

DOI:
10.33899/csmj.2008.163962

The stereography which used to hide certain information using a host file is a science and an art. Such practice is usually done to keep away any thought in the presence of a hidden message in the host. Hiding is often done using sound, image or video files. The problem is that such hiding may cause some detectable changes in the host file .This study focuses on hiding in WAVE type sound file. Sound files are either one-byte sample or two- byte sample .The hiding idea involves the replacement of the original data by another data from a text file. The first four bits from each byte are used in wave file as a hiding domain.

Accordingly, a hiding system was designed for the reduction of the accompanying noise. In this research, it was depended on the human herring for group of people to calculate the reduction in the noise of the host file .It was also shown that hiding in 8-bit sample (1 byte) results in a clearly detectable noise. This jumping 10 bytes in each replacement process led to eliminate the noise .It was also concluded, that when using first and second bit from each byte the noise was completely eliminated by jumping 30 byte. On the other hand, hiding in 16-bit sample (2byte) has led to complete disappearance of the noise when jumping 10 byte at each data replacement process.

##### Numerical Solution to the Fluid Flow in a Bend Duct Equation

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 81-94

DOI:
10.33899/csmj.2008.163963

The Fluid Flow in a bend Duct equation had been solved numerically by using two methods. The first is **ADE** **(**Alternating Direction Explicit**)** method and the second is **ADI **(Alternating Direction Implicit**)** method. A comparison had been made between these two methods with the exact solution, and we find that the **ADI** method is the best and most accurate than the **ADE** method, the numerical solution is alternant and identical. This means that the solution is itself in every period. Therefore, we need lesser accounts and then to a short time.

##### Comparison on Color Quantization Techniques

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 95-115

DOI:
10.33899/csmj.2008.163965

Due to the fast and high development in computer technology and the reflection of this development on digital images ,many image processing algorithms became in need to initialization steps for the image before starting the actual operations of the algorithms and the program. Image quantization is one of the important operations in image processing field and it is the first step in many digital image applications.

This technique is based on taking the best colors from the original image and produce a new image with a new quality with less colors and with small error ratio. There are many image quantization methods ,but this research focuses on studying three different methods of image quantization and compares them. These methods are:

Quantization by mask

Uniform Quantization

Half toning Quantization

After programming the methods we could reach a high degree of clarity in image after reducing its color. The research was applied on different types of images to find the best method for each image with small error ratio and that depends on the contents and on color distributions in the image .(Matlab7) was used for programming these methods.

##### Using the Genetic Algorithm in Images Matching

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 5, Issue 1, Pages 117-128

DOI:
10.33899/csmj.2008.163966

The proposes of the present work is to suggest the use of a purely Genetic Algorithm(GA) as a search technique for the global optimum estimates of the transformation parameters. Because Genetic Algorithms search optimal solutions from the entire solution space, they often can obtain reasonable solutions in all situations. The program is written in Matlab language.