Theoretically, an eight-term chaos system is presented. The effect of changing the initial conditions values on behavior Chen system was studied. The basic dynamical properties of system are analyzed like time series, attractor, FFT spectrum, and bifurcation. Where the system appears steady state behavior at initial condition x_{i ,} y_i , z_i equal (0, 0, 0) respectively and it convert to quasi-chaotic at x_i ,y_i ,z_i  equal (-0.1, 0.5,-0.6). Finally, the system become hyper chaotic at x_i ,y_i ,z_i equal(-0.5, 0.5,-0.6 ) that can used it in many applications like secure communication.

A computational investigation is carried out in the field of charged –particle optics with the aid of numerical analysis method using the personal computer. The work is concerned with the design of electron gun with space-charge effect. The Finite element method (FEM) used in the solution of Poison's equation for determine the axial potential distribution of the two-electrode immersion lens operated under zero magnification condition , and from the solution of the paraxial ray equation the optical properties such as the focal length , spherical and chromatic aberration coefficients are determined, also a calculation of the brightness and perveance for the lens. The electrodes geometry was determined in two and three dimensi

    In this article, we introduce and study two new families of analytic functions by using strong differential subordinations and superordinations associated with Wanas differential operator/. We also give and establish some important properties of these families.

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

     In this paper, we introduce and discuss an extended subclass〖 Ą〗_p^*(λ,α,γ) of meromorphic multivalent functions involving Ruscheweyh derivative operator. Coefficients inequality, distortion theorems, closure theorem for this subclass are obtained.

This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

The primary purpose of this paper is to introduce the, 2- coprobabilistic normed space, coprobabilistic dual space of 2- coprobabilistic normed space and give some facts that are related of them