### Volume 7, Issue 2, Summer 2010, Page 13-188

##### The Effects of Correlated Data and Correction Procedures for F-Test in Unbalanced Two Way Model

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 13-28

DOI:
10.33899/csmj.2010.163875

Independence of observations is one of the standard assumption in analysis of Variance (ANOVA) table. Where the error terms in the model are independent, identically distributed normal variables with null means and homogeneous variances. In this paper investigate the effect of dependence of observations in ANOVA for unbalanced 2-way nested fixed model and developing a method for adjusting it. When the error terms are correlated and focus on the effects of departures from independence assumptions on hypothesis testing by determining the expect mean squares for errors as well as treatments for this model and correcting the F statistics for testing the factor effect. The model considered is one in which all measurements have same variance, and the covariance matrix enjoy a structure defined as follows: every pair of measurements comes from:

i) The same experimental observation and the same experimental unit;

ii) Different experimental observation, but in the same experimental unit;

ii) Different experimental unit;

has covariance and respectively.

##### Stability Analysis of Reaction-Diffusion Equations with Double Diffusivity System

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 29-37

DOI:
10.33899/csmj.2010.163882

Stability analysis for steady state solution of reaction-diffusion equations with double diffusivity discuss and arise in the solution of problems of flow of homogeneous liquids and heat conduction involving air-temperature and a grain-temperature , the resulting of this analysis shows that the system is stable when:

##### New Hybrid (Oren- Al-Bayati) Self-Scaling Algorithm With Armijo Line-Search

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 39-47

DOI:
10.33899/csmj.2010.163883

In this paper the development, and numerical testing of a class of self-scaling Quasi-Newton update with adaptive step - size are presented . In our work a new combined (Oren-Al-Bayati) self-scaling algorithm is presented with a modified Armijo line search procedure.

This algorithm has implemented both theoretically and numerically and tested on some well-known test cases. Numerical experiments indicate that this new algorithm is effective and superior to the standard, with respect to the number of functions evaluations (NOF) and number of iterations (NOI).

##### The Existence, Uniqueness And Upper Bounds For Errors Of Six Degree Spline Interpolating The Lacunary Data (0,2,5)

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 49-57

DOI:
10.33899/csmj.2010.163884

The object of this paper is to obtain the existence, uniqueness and upper bounds for errors of six degree spline interpolating the lacunary data (0,2,5). We also showed that the changes of the boundary conditions and the class of spline functions has a main role in minimizing the upper bounds for error in lacunary interpolation problem. For this reason, in the construction of our spline function which interpolates the lacunary data (0,2,5), we changed the boundary conditions and the class of spline functions which are given by [1] from first derivative to third derivative and the class of spline function from to .

##### MGP and EGP Rings

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 59-65

DOI:
10.33899/csmj.2010.163885

The purpose of this paper is to study the rings in which every maximal (essential) right ideal is a left GP- ideal. Such rings will be called right MGP- rings (EGP- rings). We give the basic properties of such rings and their connection with strongly - regular rings, fully left idempotent rings, and - weakly regular rings.

##### Flow of Soap Films on Inclined Plane

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 67-78

DOI:
10.33899/csmj.2010.163886

In this paper a mathematical model is constructed to describe a two dimensional flow for an inclined films with an inclination angle to the horizontal that is drainage under the action of gravity. An asymptotic analysis is employed with the use of lubrication approximation. The film is assumed to be supported by wire frame elements at the ends. We apply the Navier–Stokes equations for flow of an incompressible fluid in two dimensions with specified boundary conditions. We obtain the equations representing the film thickness, the surface concentration, and the surface velocity. We obtain the similarity solutions for extensional flow of the simplified forms of these equations by using Lagrangian coordinate and then we approximate this equation by using Taylor series to obtain another similarity equation that can be used for different values of time.

##### A Suggested Point Search Algorithm for Circle Detection in Binary Images

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 79-94

DOI:
10.33899/csmj.2010.163887

Detecting circles is very important in the application of image processing especially in determining the object locations. In this paper, a new algorithm is proposed for circle detection, called Point Search Circle Detection (PSCD), which detects points and assumes them as inspection points on the circle circumference by using them to create a virtual circle to match it with the original image. Using matching operation leads to reduce computational operations and reduce the complexity and the running time of the algorithm. The proposed algorithm is highly accurate, has high speed and low storage requirements in comparing with other related algorithms. The proposed algorithm can precisely detect circles with various scales, crossed and nested circles in the binary images.

The proposed algorithm was compared with Hough Transform (HT) method for circle detection by using many images with different numbers and radius of circles and different image dimensions. The proposed algorithm was more efficient, where the average ratio of the running time for the proposed algorithm to HT method was 1:646, and the accuracy of the proposed algorithm was 100% for circles detection. Both the proposed and HT algorithms are applied by using Matlab 7.2 language, PC equipment with 1.8MHz Pentium IV processor and 512MB RAM.

##### Develop Parallel Arithmetic Operations for Binary Modified Signed-Digit System Using Two-Step Algorithm

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 95-105

DOI:
10.33899/csmj.2010.163888

An optical computing system is expected to be a powerful information processing system that takes full advantage of optics, such as parallelism, high speed, and large information capacity. Therefore many suitable optical number systems have been developed by many research to exploit the inherent parallelism of optics to developed parallel arithmetic operations .

In this paper we used binary modified signed-digit (BMSD) number system and available recoding method to generate a simplified binary MSD addition/subtraction truth table to obtained a parallel two-step algorithm in which the carry chain was generated during the addition operation and the borrowing chain was generated during the subtraction operation that will be stopped after two steps, the addition and subtraction operations will be completed independent of the number of digits in each operand. Also this paper involve limitation for the minterms that used in the logical processing for the addition/subtraction truth table.

##### Voice Security Using Hybrid Algorithm

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 107-118

DOI:
10.33899/csmj.2010.163889

This research deals with constructing and implementing a new digital voice security Algorithm based on hiding large amount of data (sound file) in a 24 bits host color image (RGB image). The proposed method starts with speech compression to convert human speech into an efficiently encoded representation that can later be decoded to produce a close approximation of the original signal. The process of compression is achieved by first computing Discrete Wavelet Transform (DWT), truncating small-valued coefficients and then efficiently encoding them. The stream bits output from coder are encrypted using Linear Feedback Shift Register (LFSR) algorithm. These enciphered bits are then embedded into the image blocks. A binary key matrix and weight matrix are used as a secret key to protect the hidden information. The algorithm can hide as many as bits of data in the image by changing one bit in each block of size . High security algorithm was achieved using three layers to make it difficult to break by attacker. The algorithm has been implemented using MATLAB.

##### Unsteady Flow near the Junction Zone of Three Liquids

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 119-128

DOI:
10.33899/csmj.2010.163890

In this paper we consider the motion near the junction zone of three approximately plane liquid films of semi–infinite extent in two dimensional polar coordinate system with negligible inertia. We use Stokes equation to describe such flow. The pressure in the region of large curvature is less than that on the surface of bulk fluid and this pressure gradient ensures that this problem is unsteady state case. The equation that governs such flow is solved analytically, the shape and the thickness are determined for some liquids.

##### Design a Fuzzy Expert System for Liver and Pancreas Diseases Diagnosis

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 129-141

DOI:
10.33899/csmj.2010.163891

Fuzzy logic is a branch of artificial intelligence techniques, it deals with uncertainty in knowledge that simulates human reasoning in incomplete or fuzzy data. Fuzzy relational inference that has applied in medical diagnosis was used within the medical knowledge base system to deals with diagnostic activity, treatment recommendation and patient's administration.

In this research, a medical fuzzy expert system named (Liv&PanFES) has been developed for diagnosis and decision making of general Liver and Pancreas diseases.

The (Liv&PanFES) is a rule based fuzzy expert system, results of laboratory analysis are inserted into the system. This system can define the probable diagnosis on these data, and later on it can pick out the most probable one for disease.

##### New bounds for mr(2,37) and tr(2,37) in PG(2,37)

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 143-150

DOI:
10.33899/csmj.2010.163892

In this paper we find the nearest complete (n,r)-arcs to the maximum bound and the minimum sizes for m_{r}(2,37) where and t_{r}(2,37)** **where .Also we show that not exists (1236,34)-arc and some other arcs in PG(2,37).

##### Multistage Hiding Image Techniques

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 151-166

DOI:
10.33899/csmj.2010.163893

In the few recent years computer sciences have been widely developed especially in communication spaces and Internet, therefore, a great need appear for security and safety of our information. Steganography is the science of hiding information or data (like a secret message) in other cover (like a digital image) in such a way that a normal person can't sense it.

In this paper, four new methods were suggested in steganography systems to embed secret data in compressed images. Two methods are working in spatial domain, known as moving window and odd/even LSB, others are working in transform domain, known as odd/even DCT and DCT+DWT.

The comparison results present that new methods are better than traditional methods in many characteristics, like (efficiency, security level, imperceptibility and robustness). The work was implemented using Matlab.

##### A New Algorithms in Mixed Integer Programming Problems

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 13-29

DOI:
10.33899/csmj.2010.163894

**ABSTRACT**

In this paper we have studied two new algorithms for solving mixed IPP. In the 1^{st} algorithm we have investigated a new short technique for searching to the efficient cut in the standard cutting plane procedure to obtain the same optimal solution by using a number of test problems in this field. In the 2^{nd} new algorithm we have put certain numerical conditions to obtain the global solution instead of the local solution by using cutting-plane and Al-Zobaidyi [1] algorithms. Our numerical results indicate that our new suggestions are efficient both numerically and theoretically compared with Al-Zobaidyi algorithm.

##### Wiener Polynomials of the Width Distance for Compound Graphs of G1 ☒ G2

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 31-46

DOI:
10.33899/csmj.2010.163895

For a connected vertex disjoint graphs G_{1} and G_{2} , we define G1 ☒ G2 as the graph obtained from the union of G_{1 }and G_{2 }with four edges joining the vertices of an edge of G_{1 }to the vertices of an edge of G_{2 }.In this paper we obtain Wiener polynomials of the width distance-2 for K_{s} ☒ K_{t} , K_{s} ☒ G_{t} and G_{s} ☒ G_{t}.The Wiener index of each such composite graph is also obtained.

##### Numerical Solution for Sine-Gordon System in One Dimension

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 47-59

DOI:
10.33899/csmj.2010.163896

This paper has studied the numerical solution for Sine-Gordon system in one dimensions using finite difference methods. We have used Explicit method and Crank-Nicholson method.A comparison between results of the two methods has been done and we obtained that Crank-Nicholson method is more accurate than the Explicit method but the Explicit method is easer .

We also studied the stability analysis for each method by using Fourier(Von-Neumann) method and obtained that Crank-Nicholson method is unconditionally stable while the Explicit method is stable under the condition and .

##### A Proposed Method to Minimize the Flow Time Average and the Due Date Average in Sequence Problem

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 61-75

DOI:
10.33899/csmj.2010.163897

The problem tackled in this research is to propose a method to minimize the flow time average and the due date average to resolve the sequence problem. Assuming that we have a set of jobs, and every job has processing time and due date required to running by method that satisfy balance and minimize the flow time average and the due date average. The research presents the methods used to solve the former. The paper compares the new method with the Critical ratio (CR) method on a set of data generated by simulation by system (MATLAB). The results show a high efficiency and ease of use.

##### The Minimal Blocking Set Of Size 22 In PG ( 2 , 13 )

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 77-88

DOI:
10.33899/csmj.2010.163898

A blocking set B in projective plane PG (2, ) in a set of points such that every line in the plane intersect B in at least one point and there exist a line intersect B in only one point, we say that B is minimal if B has no minimal blocking subset. In this project we proved the non-existence of minimal blocking set of size 22 contains 8-secant and not contains 9-secant in PG (2, 13). Also we have proved the existence of minimal blocking set of the size 22 of redei-type. Also we give some properties of such blocking set.

##### Integration of Multispectral Images Using Two-Dimensional Wavelet Transformation

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 89-99

DOI:
10.33899/csmj.2010.163899

Image fusion is an effective tool to integrate multi-source image, where the purpose of the process access to information integration concept, and make the resulting image more suited to human vision, as well as digital processing. This integration leads to a technology that joins the resources in order to increase and clarify the information that serve the visual and automatic interpretation.

The current research aims to use wavelet transformation with two dimensions (2D-DWT) in the integration of multispectral images (images taken by visible band) and others taken by IR (Infrared band) to obtain a single and clear image, and shows in accurate details of the original images.

This algorithm programmed by MATLAB tools (MATLAB R2008a) is applied to the two images, the dimensions of each image 512×512 pixels. Where the fusion process depends on two types of mathematical models, the Maximum, and Average. High pass Combination and Low pass Combination filters were used. Using filters db4, coif4 and sym4 and then the Entropies of images were calculated to measure the amount of information in the resulting image.

This paper shows that the 2D-DWT is used to integrate images using the image fusion ,and it gives good results in increasing the amount of generated information, increase the efficiency of the image , increase reliability , and reduce the uncertainty-surrounding some of the features in the images which are not clear.

##### Some Results in the Theory of Fractional Order Integro-Differential Equation with Boundary Conditions

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 101-114

DOI:
10.33899/csmj.2010.163900

This paper deals with the existence and uniqueness of the solution for a boundary value problem of fractional order integro-differential equation, when using Banach fixed point theorem and Shafer’s fixed point theorem. This investigation based on the well known Riemann-Liouville fractional differential operator.

##### Representation of a Standard Continuous Function by a Microscope

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 115-124

DOI:
10.33899/csmj.2010.163901

The aim of this paper is to provide a representation of a standard continuous function and a standard differentiable function by mean of a microscope.

More precisely, under certain conditions, the following results have been obtained.

Let 12F"> be a standard continuous function define on 12R"> , and 12Â°G"> the shadow of it's graph. If there exists a standard point 12X0âˆˆR"> and an interval 12I0"> about 12X0"> such that : 12âˆ€XâˆˆI0,X,FX limited âŸ¹Xâ‰ƒX0"> .

(i) Furthermore If there exist 12X1"> , 12X2"> limited in 12I0"> such that 12FX1"> , 12FX2"> are infinitely large with opposite sign, then 12Â°G"> contains the vertical line 12âˆ†"> of the equation 12Â°X=X0"> .

(ii) If there exist a standard number 12Î±"> , 12XâˆˆI0"> and if 12FX"> is limited such that 12Â°FXâ‰¤Î±"> (resp. 12 Â°FXâ‰¥Î±"> ). Also if there exist 12X1"> , 12 X2"> limited in 12I0"> such that 12FX1<0"> is infinitely large (resp. 12 FX1>0"> ) and 12FX2â‰ƒÎ±"> ,then 12Â°G"> contains the half line 12âˆ†Î±"> defined by :

12âˆ†Î±=X,YâˆˆR2:Â°X=X0 , Â°Yâ‰¤Î± resp.Â°Yâ‰¥Î± ">

Let 12f"> be a standard function defined at a neighborhood at a standard point 12x0"> , then 12f"> is differentiable at 12x0"> **if and only if** under every microscope of power 12Îµ"> ,centered at 12x0,fx0"> ,the representation of 12f"> is not a vertical line at 12x0,fx0"> .

##### Hybrid intelligent watermark System

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 125-138

DOI:
10.33899/csmj.2010.163902

As a result of the development in data transfer technology a cross multimedia and internet, it has became possible to access and copy these information in unauthentical manner . This leads to penetrate digital multimedia security problem.

In this research a hybrid method is designed to protect product from unauthentication access using watermark technique with digital images, these images represent the important part in information systems and many applications. The method indicates hiding the watermark in both spatial and frequency domains using Artificial Intelligent techniques, such as neural networks and genetic algorithms by dividing the watermark depending on the important information contents. The basic important part hides in frequency domain and the second part in spatial domain using *Discreet Cosine Transform DCT* and *Least Significant Bit LSB*.

The method efficiency is measured using *Peak Signal –to-Noise Ratio** PSNR* and *Normalized Correlation Coefficient* *NC* , Also many attacks is used to measured the watermark robustness and feasibility.

##### Studying the Stability of Some Models Combinatory with Application

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 139-157

DOI:
10.33899/csmj.2010.163903

In this paper we find the statistical properties (Moments) of the harmonic model with additive noise, The stability of the mixed spectra (linear and non-linear models) for special case (low order) by using the Ozaki linear approximation method is found .The time series of the mean monthly temperature of Bege City is applied in order to explain the studied method. A mathematical model SARIMA(1,0,0)(2,0,0)s is suggested by the NBIC criterion and other statistical tools (auto-correlation and the residual variance). A one year ahead prediction is made for the studied time series by using the proposed model .

##### Application of Traditional Denoising Algorithms to Zoom-In the Color Images

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 159-171

DOI:
10.33899/csmj.2010.163904

In this paper many algorithmswere applied to" zoom –in" the images, like traditional algorithms which is used (Linear Averaging) algorithm, (Convolution) algorithm and the proposed algorithms to be the new algorithms in this paper. These algorithms are obtained from another application which involves in Enhancement Smoothing Algorithms and will be used as a (zooming-in) color images algorithms which are include (Median) Algorithm and (Max & Min) Algorithm and sometimes called (Conservative Smoothing Algorithm). The obtained results of these algorithms were compared together. The MATLAB language is used to apply the algorithms.

##### Recognition of Printed Text Based on Hidden Markov Model

*AL-Rafidain Journal of Computer Sciences and Mathematics*,
Volume 7, Issue 2, Pages 173-188

DOI:
10.33899/csmj.2010.163905

Automatic recognition of printed text is of high importance in modern IT applications. Recognition of text for lateen scripted language is readily in use for a long time. For cursive script languages (such as Arabic language) recognition of text is not available as a robust one with a reliable performance. More improvements still exist to reduce average of incorrect words, rather then no constraints on the limit of words of a specific language.

Numerous approaches were tried in recognition of text but recognition of Arabic text based on Hidden Markov model seems to be the most promising one because of its ability to discriminate cursive scripts.

This paper provides an off-line system to recognize printed Arabic text by using hidden Markov model with the aid of the algorithm that segment the text lines into connected parts then into characters.

By looking on the results given by the designed recognition system it is found that a recognition rate (94.9 %) can be achieved. Such rate is in the same order of rates of recognition researches viewed in previous studies. This rate can still be improved. The language used in building the system is Matlab V7.6 (R2008a).

** **