Volume 3, Issue 2, Summer and Autumn 2006, Page 11-143

A Hyperbolic Rational Model for Unconstrained Non-Linear Optimization

Nidhal H. Al-Assady; Basim A. Hassan

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 11-22
DOI: 10.33899/csmj.2006.164047

We consider a class of invariant Hyperbolic scaling of a strictly convex quadratic function, to extend the family of the conjugate gradient methods for solving unconstrained minimization problems. An algorithm is derived and evaluated numerically. The results indicate that, in general, the new algorithm is superior to the classical standard CG-algorithm.

Techniques of Finding Lower Bounds in Multi Objective Functions

Ayad M. Ramadhan; Adil K. Jabbar

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 23-29
DOI: 10.33899/csmj.2006.164048

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 () and sum of completion times with the maximum tardiness (), 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.

EPS & EPUS Step-size Control for Linear Multistep Method

Abbas Y. Al-Bayati; Ann J. Al-Sawoor; Abbas H. Taqi

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 31-39
DOI: 10.33899/csmj.2006.164049

In this paper we consider step-size control in one class of Adams linear multi-step methods for Ordinary differential equation.   Theoretical results are presented for Adam-Bashforth-Moulton formula using both Error-per-step (EPS)  & Error-per-Unit -Step (EPUS) controls. These obtained by considering a 2D system of the form:
 where  and

A Crank-Nicolson Method of Autocatalytic Reaction-Diffusion Systems

Abbas Y. Al-Bayati; Saad A. Manaa; Abdulghafor M. Al-Rozbayani

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 41-52
DOI: 10.33899/csmj.2006.164050

In this paper we used two numerical methods to investigate propagating heat solutions of PDEs. The explicit and Crank-Nicolson methods and the results show that Crank-Nicolson method is more accurate than the explicit method. As an illustration, we used the above method to an autocatalytic reaction diffusion equations involving two diffusing chemicals in one dimension.

A Generalization of A Contra Pre Semi-Open Maps

Abdullah M. Abdul-Jabbar

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 59-68
DOI: 10.33899/csmj.2006.164052

The concept of  q-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 qs-open maps, the maps whose images of a q-semi-open sets is q-semi-closed. Also, we introduce and study a new type of closed maps called contra pre qs-closed maps, which is stronger than contra pre semi-closed due to Caldas [2], the maps whose image of a q-semi-closed sets is q-semi-open.1991 Math. Subject Classification: 54 C10, 54 D 10.

Parallel Newtonian Optimization without Hessian Approximation

Khalil K. Abbo

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 69-82
DOI: 10.33899/csmj.2006.164053

The purpose of this paper is to introduce parallel algorithms based on the Newton method for solving non-linear unconstrained optimization problem in (MIMD) parallel computers by solving linear system in parallel using Gaussian Elimination method rather than finding inverse Hessian matrix to avoid the errors caused by evaluating the inverse matrix and also to increase computing power and reduce run time.

On the Generalized Curvature

Tahir H. Ismail; Ibrahim O. Hamad

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 83-98
DOI: 10.33899/csmj.2006.164054

By using methods of nonstandard analysis given by Robinson, A., and axiomatized by Nelson, E., we try in this paper to establish the generalized curvature of a plane curve at regular points and at points infinitely close to a singular point. It is known that the radius of curvature of a plane curve is the limit of the radius of a circle circumscribed to a triangle ABC, where B and C are points ofinfinitely close to A. Our goal is to give a nonstandard proof of this fact. More precisely, if A is a standard point of a standard curve  and B, C are points of  defined by  and where  and  are infinitesimals, we intend to calculate the quantity in the cases where A is biregular, regular, singular or singular oforder p.

Image Compression Technique Using a Hierarchical Neural Network

Rafid A. Khalil; Mohammed C. Younis

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 99-112
DOI: 10.33899/csmj.2006.164055

This paper present a Resilient Backpropagation (RBP) algorithm based on hierarchical neural network for image compression. The proposed technique includes steps to break down large images into smaller blocks for image compression/ decompression process. Furthermore, a Linear Backpropagation (LBP) algorithm is also used to train hierarchical neural network, and both training algorithms are compared. A number of experiments have been achieved, the results obtained, are the compression rate and Peak Signal to Noise Ratio of the compressed/ decompressed images which are presented in this paper.

Comparison of Edge Detection Methods in Gray Images

Sobhi H. Hamdoun; Afzal A. Hassan

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 11-28
DOI: 10.33899/csmj.2006.164056

The methods of edge detection play an important role in many image processing applications as edge detection is regarded as an important stage in image processing and the extraction of certain information from it.
Therefore, this subject was the focus of many studies performed by many authors. Many new techniques of edge detection which search into the discontinuity in color intensity of the image leading to the features of the image components were suggested.
Despite of the presence of many methods of edge detection which proved their efficiency in certain fields and gave good results on application, the performance of one method differs from one application to another, thus there was a need to carry out an evaluation of performance for each method to show its efficiency. The aim of this research is to evaluate the performance of edge detection by choosing five methods known as (Canny, Laplacian of Gaussian,Prewitt, Scobel, Roberts) and the application of each method on images with grayscale to find out the performance of each of them and writing down computer programs for each. Also, a subjective evaluation to compare the performance of these five methods using Partt Figure of Merit, calculating the increase percent in the detected edges, decrease percent in the edge points and the correct position of the edge in each method.

Stability Analysis of Fisher Equation Using Numerical Galerkin Techniques

Saad A. Manna; Ahmed F. Qassem

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 29-42
DOI: 10.33899/csmj.2006.164057

We studied the stability of the steady state solutions for Fisher Equation in two cases, the First one with constant amplitude and we show that the steady state solution is always stable under any condition, but the other two solutions and  are conditionally stable.
In the Second case, we studied the steady state solutions for various amplitude by using two Methods. The First is analytically by direct Method and the second is numerical method using Galerkin technique which shows the same results, that is the steady state solution  is always stable under any conditions, but the other two solutions and are conditionally stable.

Encryption Binary Images by Using Template Matching

Sundus Khaleel Ebraheem

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 43-69
DOI: 10.33899/csmj.2006.164058

Text encryption is a very important field in application of data transformation through the digital networks, and the Internet, so it is very necessary to do encryption operation on the text data to get more security in data transformation.
In this paper, we present a method -Template Matching- to encrypt data which is represented in form of image with BMP extension by using Mono Digital Images method with partial compression for the data by using RLE method which increases the security of the method and reduces the file size.
The application results is efficient for the printed or handwritten text in Arabic or English or any other language, and for the maps or sketches images. The method gives a good ability for data encryption. It is suitable for data transformation through the Internet networks.

Numerical Solution of the Problem of Heat Transfer by Convection

Ahmed M. Juma’a; Ashraf S. Aboudi

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 71-88
DOI: 10.33899/csmj.2006.164059

In this paper we have presated a heat transfer by convection in rectangular cavity filled with static fluid.  Differentially heated end vertical walls. Two-dimensional motions are assumed. The governing vorticity and energy transport equations are solved by an alternating direction implicit finite- difference method. We transference heat equation into two finite- difference equations. The time interval has been deviled into two equal halves, alternating to compute an intermediate point in the first step and final value at T time. We get by result analysis, that we can reach the steady – state from Un steady –state after some iteration.

Compression of Satellites Images Using Embedded Zero Tree Wavelet

Ahmed Kh. Al-Selifani; Faten A. Mustafa

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 89-102
DOI: 10.33899/csmj.2006.164060

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 .

Weiner Polynomials for Generalization of Distance for Some Special Graphs

Ali Aziz Ali; Ahmed M. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 103-120
DOI: 10.33899/csmj.2006.164061

The minimum distance of a vertex v to an set of vertices of a graph G is defined as :
The n-Wiener polynomial for this distance of a graph G is defined as
where  is the number of order pairs (v,S), , such that
and  is the diameter for this minimum n-distance.
In this paper, the n-Wiener polynomials for some types of graphs such as complete graphs, bipartite graphs, star graphs, wheel graphs, path and cycle graphs are obtained .The n-Wiener index for each of these special graphs is given. Moreover, some properties of the coefficients of   are established.

Using ANN and Decision Tree in Diagnoses Mouth Dseaise

Adebaa esmaeel al_ sakal; Ghada Mohammad Tahir Qasim

AL-Rafidain Journal of Computer Sciences and Mathematics, Volume 3, Issue 2, Pages 121-143
DOI: 10.33899/csmj.2006.164062

The research includes construction of hybrid system from decision tree and artificial neural networks in order to classify the special treatment for some dental diseases .The work is achieved in two stages; the first uses the velocity as one of the decision tree characteristics by binary regular decision tree to determine the treatment for each case. The second implies the artificial neural network characteristic and its ability in classification and pattern recognition. The aware network with supervised training is used in this classification to determine the treatment class or pattern for each disease case. This network is used in two ways; the treatment's type according to treatment symbol, and the treatment's class according the x-ray of the case. In the last way, several photos are chosen and then transformed into BMP with 256 gray level and 100*100 dimensions. The hybrid system gives an excellent result in velocity and accuracy of classification.