Committee: International Scientific Committee of Mathematical and Computational Sciences
University: University of Kufa
Department: Department of Mathematics
Research Fields: Fractal, Singular Value Decomposition, Image Encryption, Applied Numerical Mathematics

## Publications

##### 6 Laplace Technique to Find General Solution of Differential Equations without Initial Conditions

Abstract:

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.

##### 5 Encryption Image via Mutual Singular Value Decomposition

Abstract:

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.

##### 4 Some Applications of Transition Matrices via Eigen Values

Abstract:

In this short paper, 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.

##### 3 Calculus Logarithmic Function for Image Encryption

Abstract:

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.

Keywords: Linear Systems, Calculus, Image Encryption

##### 2 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem

Abstract:

In this paper, 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.

##### 1 Cantor Interpolating Spline to Design Electronic Mail Boxes

Abstract:

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.