عادل محمد حسن رزاق الرماحي

a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

Digital images became very important in our digital life. So, the operations of rearrangement image are very obligated for protection, compression, saving, gaming, and testing of image. In this paper, a new approach of digital image encryption is proposed based on the solution of low order linear systems and modular numbers technique. For each row of given digital image matrix, a linear system was built from two successive elements where the principle diagonal elements are imposed for value one, and the other represents the image values. The system matrix ( )was multiplied by public key ( ) to deduce linear system ,where is a cipher of the two given image values .For more complexity against attacker ,and for more integrity with decoder, a repeated modular numbers are implemented in order to transform three encryption images.

when we prefer to make the data secure from various attacks and fore integrity of data, we must encrypt the data before it is transmitted or stored. This paper introduces a new effective and lossless image encryption algorithm using a natural logarithmic function. The new algorithm encrypts an image through a three stage process. In the first stage, a reference natural logarithmic function is generated as the foundation for the encryption image. The image numeral matrix is then analyzed to five integer numbers, and then the numbers’ positions are transformed to matrices. The advantages of this method is useful for efficiently encrypting a variety of digital images, such as binary images, gray images, and RGB images without any quality loss. The principles of the presented scheme could be applied to provide complexity and then security for a variety of data systems such as image and others.

new properties of transition matrix were introduced. Eigen values for small order transition matrices are calculated in flexible method. For benefit of these properties applications of these properties were studied in the solution of Markov's chain via steady state vector, , and information theory via channel entropy. The implemented test examples were promised for usages.

In this study we will provide a new way of images compression based on two mathematic concepts, these two concepts are Singular Value Decomposition (SVD) and Block Truncation Coding. The input image either is in JPEG format or in BMP format and the current way suitable for both color and gray scale images. The input image will be compressed first by reducing the image matrix rank, which achieved by using the SVD process and then the result matrix compressed by using BTC. The proposed algorithm gives further lossless compression to JPEG compression process and the rate of compression reach more than 99%.

Nowadays, text encryption is recommendable when it is transmitted or stored on insecure channels as Internet. In this paper we introduced novel method to encrypt text based on SVD. Up to our knowledge this is the first paper encrypted text by using SVD. The message is the composition of some character. Every character of the message can be represented as an ASCII value, and then we can build numeric matrix for each text. We suggested using other text as key and using with plaintext to scramble the plaintext prior to use the SVD process which makes cryptanalyst’s job difficult. There are many difficulties in using the SVD to encrypt text. The decrypted text was the same as the plaintext without loss any character. Encryption and decryption time were reasonable. One of the important features of this work is the ability to produce encrypted text with language differ from the plaintext language which make add more complixity of decrypt the encrypted text from third party.

Laplace transformations have wide applications in engineering and sciences. All previous studies of modified Laplace transformations depend on differential equation with initial conditions. The purpose of our paper is to solve the linear differential equations (not initial value problem) and then find the general solution (not particular) via the Laplace transformations without needed any initial condition. The study involves both types of differential equations, ordinary and partial.

Image or document encryption is needed through egovernment data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files.

Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. The roots of spline function versus Cantor sets used as the controller admin. The roots calculated by the numerical Newton – Raphson's method. The result of this algorithm was promised.

Image encryption is one of the most methods of information hiding. A novel secure encryption method for image encryption is presented in this study. The proposed algorithm based on using singular value decomposition SVD. In this study we start to scramble the image data according to suggested keys (two sequence scrambling process with two different keys) to finally create two different matrices. The diagonal matrix from the SVD will be interchanged with the resulted matrices. Another scrambling and diagonal matrices interchange will apply to increase the complexity. The resulted two matrices combine to one matrix according to predefined procedure. The encrypted image is a meaningfull image. The suggested method tested with many images encryption and gives promised results.

To study the Lyapunov Stability of Linear Large Scale Systems with programmed procedure

To detect Fake ImageSingular via Value Decomposition

To Solve Partial Differential Equations via B-Splines Method with applications

To study the solutions of Differential Equations via B-Splines Method.

To study Lyapunov Stability using Definite and Permutation Matrices.

To study the Stability of Differential Equations and its systems using Lyapunov Method. the family of stable method was added and introduced.

To study New proposed methods for coding Information Using Direct Product of Symmetric Matrices and Contraction Functions via new properties of Hermitian Matrices

To introduce the Relation between Fractal Interpolating Functions and some Physical Parameters.

To study Liayapunov Stability of Large Scale Dynamic Systems via the matrices of Definite and Permutation

to study the relation between Information Function and Evolution

to study the Application Of Discrete Logarithms In Information Hiding And Knapsack Problem With New Properties Of Sk Sets ,

to study Stability And Instability Of Interconnected Systems Using Symmetric Test Matrix via Liapunov Methods

to study and constructing Magic Squares With Genetic Algorithm

to study The Application Of Fractal Geometry In Coding Information.

to study the Direct Product of Hermitian and Symmetric Matrices With Application,

to study Stability Of Interconnected Systems Using Reducible Test Matrix via Liapunov Methods ,

bhe modification of RSA cryptography was introduced using the composition of functions

to study new properties of Positive And Negative Definite Matrices

to stydy the Liapunov Stability Of Composite Systems Using Two Definite Matrices

to study the Procedure For Stability Of Large Scale Dynamic Systems Using Directness And Reduction Of Definite Matrices

to study Stability Of Large Scale Dynamic Systems Using Direct Sum And Direct Product Of Mitzler Matrices

To study Bezer Numeric Method for interpolating data and On Analyzing the method. An application were added foe digital image

Important documents must be secured via communication. Steganography and cryptography are the virtual information of security. With the growth of data communication over computer network, the security of information has become a major issue. In this paper a proposed method which combines between encrypted text words message and plain digital image is studied. A novel encrypted method named as Assignment Significant Bit is introduced. In our method each word transformed to 26-digits grey level numbers. Then all message represented as a border of plain image. A comparison between the famous method referred as Least Significant Bit and proposed method is studied for many cover images. It is showed that the proposed method needs less operations than the method of Least Significant Bit. Also the test mathematical test tools provides the goodness of proposed method.

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لبيان مدى الاستفادة من الرياضيات في الحياة

لبيان اهمية الاعداد في القران الكريم ومعنى وجودها والدلالات المترتبة

لطرح مسالة الفلسفة المحايدة التي انشاها عالم الراضبات سمارانداكه في 1995

لبيان الدراسات المهمة للاعداد في الحضارة الاسلامية

لبيان العلاقة بي الرياضيات و العبقرية

ندوة حول عرض الدراسات للمسلمين بشأن الاعداد وتطويرها وتمثيلها

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