### Volume 4, Issue 2, Summer and Autumn 2007, Page 11-174

##### Investigation on Scaled CG-Type Algorithms for Unconstrained Optimization

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 11-23

DOI:
10.33899/csmj.2007.164012

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.

##### sπ-Weakly Regular Rings

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 25-32

DOI:
10.33899/csmj.2007.164013

The purpose of this paper is to study a new class of rings R in which, for each a Î R, aÎ aR aR, for some positive integer n. Such rings are called sp-weakly regular rings and give some of their basic properties as well as the relation between sp-weakly regular rings, strongly p-regular rings and division rings.

##### Weighted Points and Lines in Projective Plane of order 17

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 33-41

DOI:
10.33899/csmj.2007.164014

In the current research ,the points and lines of the projective plane of the seventeenth (17th)order were constructed ,this was followed by examining the arcs designated (k,n;f)- in the plane type (m,n).As a result, it is concluded that these arcs do exist having all their points of the order one or two ,but the order of their lines are m or n only .A further result was arriving at proving the theorems being concluded. The research also included a study of Monoidal arcs with some given examples.

##### An Implementation of an Initial Scale in Solving Binary Knapsack Problem Using a Genetic Algorithm

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 43-57

DOI:
10.33899/csmj.2007.164015

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.

##### Interleaving between Ant Colony Optimization and Tabu Search for Image Matching

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 59-77

DOI:
10.33899/csmj.2007.164016

**Image matching **plays an important role in many applications such as multi-modality medical imaging and multi-spectral image analysis. The role of matching is to integrate multiple sources of object information into a single image. The matching problem consists of determining the unknown transform parameters required to map one image to match the other image(20). Different non – traditional methods are used for solving this kind of problem. Among these methods are the Genetic Algorithms, Neural Networks & Simulating Annealing.

** Swarm Intelligence** (SI) algorithms take their inspiration from the collective behavior of natural, for example, ant colonies, flocks of birds, or fish shoals, a particularly successful strandant colony optimization (ACO)(1). **Ant Colony Optimization** is a population-based general search technique, proposed by Dorigo(1992,1996), for the solution of difficult combinatorial problems)4). The studies show that, in nature, the ant colony is able to discover the shortest paths between the nest and food sources very efficiently, such a deposit substance is called ** pheromone **during talking and another ants can smell it, if one of ants find a short path, it feedback on the same path and the value of pheromone on this path increases and a another ants gradually chose this path.(22)

**Tabu search**is one of the best known heuristic to choose the next neighbor to move on. At each step, one chooses the best neighbor with respect to specific function (23).

The basic idea in this paper is using Ant Colony Optimization(ACO) & Tabu Search(TS) as a success strategy for matching two images. The suggestion algorithm evaluation is a good promising solution, by providing an optimal algorithm which is executed by optimal time and coast, I believe that there is no prior research conjoining the two topics in this way. The program is written in Matlab language (6.5).

##### Free Convection Flow of Viscous Dissipative Fluid in a Rectangular Cavity

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 79-88

DOI:
10.33899/csmj.2007.164017

Free convection flow of incompressible viscous fluid with dissipation in a rectangular cavity has been studied, a finite difference technique based on **ADI **scheme is adopted in the solution of the problem. The effect of dissipation parameter (), which usually appears as a term in the energy equation, has been taken into account.The results indicated that the effect of dissipation number () was very small which is accepted with the fact of neglecting the dissipation function in the energy equation of most convection problems.

##### The Numerical Range of 6 Χ 6 Irreducible Matrices

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 89-98

DOI:
10.33899/csmj.2007.164018

In this paper, we consider the problem of characterizing the numerical range of 6 by 6 irreducible matrices which have line segments on their boundary.

##### Curtain Coating Flow of an Inclined Thin Liquid Films

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 99-111

DOI:
10.33899/csmj.2007.164019

The mechanism of thin liquid films on solid surfaces is fundamental to a wide variety of phenomena such as surface coatings in paint. A mathematical model is constructed to describe the two dimensions of steady thin liquid films flow on an inclined plane with the use of lubrication approximation, we have applied Navier-Stokes equations in two dimensional coordinates for flow of incompressible fluid with the specified boundary conditions, and the solution of the film thickness equation has been drawn for flow for several inclination angles which modify the shape of the emerging patterns and also we derived the third order differential equations that govern such flow. Finally the equations have been solved analytically.

##### Numerical Solution of Non-Linear Prey-Predator System using Finite Elements Method

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 113-133

DOI:
10.33899/csmj.2007.164020

A non-linear prey-predator system solved numerically by Galerkin method, and we compare these results with the results of Pius Peter Nyaanga[6] who used finite difference methods, we found that Galerkin finite elements method is faster than finite difference method to reach equilibrium state where the density for the prey and the predator are equals for all the values for and , also we found that Galerkin method converges towards the steady state solutions faster than finite difference method with less steps in time.

##### Solving System of a Linear Fractional Differential Equations by Using Laplace Transformation

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 135-142

DOI:
10.33899/csmj.2007.164021

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.

##### Latin Character Recognition using Neural Networks

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 143-155

DOI:
10.33899/csmj.2007.164022

The aim of this work is to recognize the printed Latin's characters. In this work two methods for constructing the feature space are used. These methods are Variance and Fractal dimension methods, as a result they have real values for every character in the Latin's language, and from these values they constructed the feature space extractions for every character in the Latin's language. After that, these features are given to the Back Propagation network for recognizing the characters.

The result is a highest recognition for the characters is obtained, it is about 82.75% characters while the unrecognized characters are 17.25.

##### Image Compression Based on Clustering Fuzzy Neural Network

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 157-174

DOI:
10.33899/csmj.2007.164023

The problem inherent to any digital image is the large amount of bandwidth required for transmission or storage. This has driven the research area of image compression to develop algorithm that compress images to lower data rates with better quality.

This research present, a new approach to image compression based on clustering. This new approach includes new objective function, and its minimization by energy function based on unsupervised two dimensional fuzzy Hopfield neural network. New objective function consists of a combination of classification entropy function and average distance between image pixels and cluster centers. After applying new method on gray scale sample images at different number of clusters, better compression ratio and signal to noise ratio was observed. The new method is also a new clustering analysis method, and it provides more compact and separate clustering.

##### Stability Analysis of Steady State Solutions of Sine–Gordon Equation

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 11-29

DOI:
10.33899/csmj.2007.164024

The stability analysis of steady state solutions of Sine–Gordon equation using Fourier mode stability analysis in two cases has been considered : Firstly when the amplitude is constant and secondly when the amplitude is variable in the two cases the results were found to be : The steady state solutions and are unconditionally stable . In the second case the comparison between the analytical solution and the numerical solution of Galerkin technique has been done . This comparison showed that the analytical solution and the numerical solution of Galerkin technique are the same.

##### Wiener Polynomials for Multi-Rings Paraffin Structures

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 31-40

DOI:
10.33899/csmj.2007.164025

The distance between any two vertices u and v in a connected graph G is defined as the length of the shortest path between them, and it is denoted by d(u,v).The sum of distances for all unordered pairs of distinct vertices in G represents Wiener index.

The number of pairs of vertices G which are distance k apart is denoted by d(G,k), it is clear that the number of d(G,k) is graphical invariant, and the Wiener polynomial of graph G is a generating function of the sequence d(G,k).

In this paper, we find the Wiener polynomial of multi-circles of paraffin structural, and this formula which we obtained is better than the formula prove in [5] , because we are able to evaluate coefficients for any limited power of x without depending on the number of circles , and we find the Wiener index and average distance for this structural.

Lastly, we contracted a MATLAB program to evaluate the Wiener polynomial coefficient ,Wiener index and average distance.

##### Learing Visual Fox Pro Language with Audio, Video and Sharing

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 41-61

DOI:
10.33899/csmj.2007.164026

Recently, the need for learning programs is increased, especially after the fast propagation of computers in different areas and the essential use of computer as an assistant in learning process due to simplicity of this method of learning, and it is not restricted with time for the user.

In this research, a system including Enumeration and Interactive learning with user has been adopted for the visual programming language Visual FoxPro, where this language is a strong development programming language in Database that combines between features of visual development languages and Object Oriented Programming in addition to Database.

Two learning methods are used in this research: Enumeration learning where the user plays a video file containing the lecture while the user is listening, and the Interactive learning which instructs the user to build the application by himself by sound and pictures step-by-step until the application is finished. The lectures are divided into six branches and each branch contains from 1 to 3 lectures with interactive lectures included. In addition, a set of tests is added to the system to know how the user benefits from the system. The proposed system has been applied on a sample of 74 students from second stage in Database laboratory of computer science department and it gave excellent results in learning according to a questionnaire form that distributed to the students after using the system.

##### Speech Compression using Wavelet Transforms

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 63-75

DOI:
10.33899/csmj.2007.164027

In this research wavelet technique was used for speech compression. It was translated and scaled to groups which represent mother wavelet function.

Applying the adopted algorithm with MATLAB software using Daubechies filters family (with multi-scale for compression level) to compress speech signal for (N=1..9). When the compression level and the distortion level, a best compression level seen at level (5), with different type of wavelet and fixed compression ratio at level (5) with different type of Daubechies filters family.

Minimum signal distortion was seen when the adopted algorithm was applied. And with multi type of wavelet it was seen that the scale had direct proportional relation ship with the compression ratio, also speech compression does not need smoothing for the speech signal as compared to other compression methods.

##### Flow of Thin Liquid Film on an Inclined Solid Surface

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 77-86

DOI:
10.33899/csmj.2007.164028

In this paper, we consider flow of thin liquid film on an inclined solid surface with an inclination angle . We use the Navier-Stokes equations to obtain equations that govern such flow .We solve these equations analytically with an appropriate boundary conditions to determine the thickness of the film for different values of the inclined angle .

##### Copyright Protection for Text Documents

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 87-101

DOI:
10.33899/csmj.2007.164029

Due to the rapid development in communication and multimedia technology, different techniques are used for copyright protection and monitoring illegal copying of these media. One of the most important techniques is digital watermarking.

In this research, an algorithm for copyright protection of text documents was designed and implemented.

The algorithm includes three steps: Watermark generation using the original text, watermark embedding using space embedding approach and finally watermark extracting and comparing it with the original one using normalized correlation.

Experimental results are presented to demonstrate the robustness of the algorithm against common attacks which alter the embedded text like changing some letters of the text, changing structure of text sentences, or changing the number of spaces between the words …etc.

Matlab Ver. 6.5 was used to implement the algorithm under Windows.

##### w-Wiener Polynomials for Width Distance of Some Special Graphs

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 103-124

DOI:
10.33899/csmj.2007.164030

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:

W_{w}(G;x) is obtained in this paper for some special graphs G such as a cycle , a wheel, a theta graph , a straight hexagonal chain , and Wagner graph .The diameter with respect to the width distance – w, and the Wiener index for each such special graphs are also obtained in this paper.

##### Cryptanalysis of Knapsack Cipher Using Genetic Algorithm

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 4, Issue 2, Pages 125-136

DOI:
10.33899/csmj.2007.164031

This research offers a new method in Cryptanalysis of knapsack cipher. It focuses on the application of genetic algorithm as a modern way in solving complex problems (problems have a huge numbers of alternate solutions in appropriate time). One of these problems is knapsack problem which is considered one of the known problems in operation researches. Cryptanalysis is done by using a new algorithm that is different from known knapsack breaking algorithm. Genetic algorithm has recently been successfully applied to the cryptanalysis of ciphers, among them Substitution ciphers and Transposition ciphers. This research deals with another type of ciphers called Public-key ciphers, that are high secure ciphers because they are based on NP-Complete problems.