This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

This study is dedicated to solving multicollinearity problem for the general linear model by using Ridge regression method. The basic formulation of this method and suggested forms for Ridge parameter is applied to the Gross Domestic Product data in Iraq. This data has normal distribution. The best linear regression model is obtained after solving multicollinearity problem with the suggesting of 10 k value.

        In this paper, double Sumudu and double Elzaki transforms methods are used to compute the numerical solutions for some types of fractional order partial differential equations with constant coefficients and explaining the efficiently of the method by illustrating some numerical examples that are computed by using  Mathcad 15.and graphic in Matlab R2015a.

This manuscript presents several applications for solving special kinds of ordinary and partial differential equations using iteration methods such as Adomian decomposition method (ADM), Variation iterative method (VIM) and Taylor series method. These methods can be applied as well as to solve nonperturbed problems and 3rd order parabolic PDEs with variable coefficient. Moreover, we compare the results using ADM, VIM and Taylor series method. These methods are a commination of the two initial conditions.

In wireless broadband communications using single-carrier interleave division multiple access (SC-IDMA) systems, efficient multiuser detection (MUD) classes that make use of joint hybrid decision feedback equalization (HDFE)/ frequency decision-feedback equalization (FDFE) and interference cancellation (IC) techniques, are proposed in conjunction with channel coding to deal with several users accessing the multipath fading channels. In FDFE-IDMA, the feedforward (FF) and feedback (FB) filtering operations of FDFE, which use to remove intersymbol interference (ISI), are implemented by Fast Fourier Transforms (FFTs), while in HDFE-IDMA the only FF filter is implemented by FFTs. Further, the parameters involved in the FDFE/

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

We study the physics of flow due to the interaction between a viscous dipole and boundaries that permit slip. This includes partial and free slip, and interactions near corners. The problem is investigated by using a two relaxation time lattice Boltzmann equation with moment-based boundary conditions. Navier-slip conditions, which involve gradients of the velocity, are formulated and applied locally. The implementation of free-slip conditions with the moment-based approach is discussed. Collision angles of 0°, 30°, and 45° are investigated. Stable simulations are shown for Reynolds numbers between 625 and 10 000 and various slip lengths. Vorticity generation on the wall is shown to be affected by slip length, angle of incidence,

في هذا البحث نحاول تسليط الضوء على إحدى طرائق تقدير المعلمات الهيكلية لنماذج المعادلات الآنية الخطية والتي تزودنا بتقديرات متسقة تختلف أحيانا عن تلك التي نحصل عليها من أساليب الطرائق التقليدية الأخرى وفق الصيغة العامة لمقدرات K-CLASS. وهذه الطريقة تعرف بطريقة الإمكان الأعظم محدودة المعلومات "LIML" أو طريقة نسبة التباين الصغرى"LVR

     Bimetallic Au –Pt catalysts supporting TiO2 were synthesised using two methods; sol immobilization and impregnation methods. The prepared catalyst underwent a thermal treatment process at 400◦ C, while the reduction reaction under the same condition was done and the obtained catalysts were identified with transmission electron microscopy (TEM) and energy-dispersive spectroscopy (EDS). It has been found that the prepared catalysts have a dimension around 2.5 nm and the particles have uniform orders leading to high dispersion of platinum molecules .The prepared catalysts have been examined as efficient photocatalysts to degrade the Crystal violet dye under UV-light. The optimum values of Bimetallic Au –Pt catalysts supp

     Bimetallic Au –Pt catalysts supporting TiO₂ were synthesised using two methods; sol immobilization and impregnation methods. The prepared catalyst underwent a thermal treatment process at 400^◦ C, while the reduction reaction under the same condition was done and the obtained catalysts were identified with transmission electron microscopy (TEM) and energy-dispersive spectroscopy (EDS). It has been found that the prepared catalysts have a dimension around 2.5 nm and the particles have uniform orders leading to high dispersion of platinum molecules .The prepared catalysts have been examined as efficient photocatalysts to degrade the Crystal violet dye under UV-light. The optimum values of Bimetallic Au –