This work is concerned with studying the optimal classical continuous control quaternary vector problem. It is consisted of; the quaternary nonlinear hyperbolic boundary value problem and the cost functional. At first, the weak form of the quaternary nonlinear hyperbolic boundary value problem is obtained. Then under suitable hypotheses, the existence theorem of a unique state quaternary vector solution for the weak form where the classical continuous control quaternary vector is considered known is stated and demonstrated by employing the method of Galerkin and the compactness theorem. In addition, the continuity operator between the state quaternary vector solution of the weak form and the corresponding classical continuous control qua

Many of the elementary transformations of determinants which are used in their evaluation and in the solution of linear equations may by expressed in the notation of matrices. In this paper, some new interesting formulas of special matrices are introduced and proved that the determinants of these special matrices have the values zero. All formulation has been coded in MATLAB 7.

The flexible joint robot (FJR) typically experiences parametric variations, nonlinearities, underactuation, noise propagation, and external disturbances which seriously degrade the FJR tracking. This article proposes an adaptive integral sliding mode controller (AISMC) based on a singular perturbation method and two state observers for the FJR to achieve high performance. First, the underactuated FJR is modeled into two simple second-order fast and slow subsystems by using Olfati transformation and singular perturbation method, which handles underactuation while reducing noise amplification. Then, the AISMC is proposed to effectively accomplish the desired tracking performance, in which the integral sliding surface is designed to reduce cha

In the present work, a z-scan technique was used to study the nonlinear optical properties, represented by the nonlinear refractive index and nonlinear absorption coefficients of nanoparticles cadmium sulfide thin film. The sample was prepared by the chemical bath deposition method. Several testing were done including, x-ray, transmission and thickness of thin film. z-Scan experiment was performed at two wavelengths (1064 nm and 532 nm) and different energies. The results showed the effect of self-focusing in the material at higher intensities, which evaluated n2 to be (0.11-0.16) cm2/GW. The effect of two-photon absorption was studied, which evaluated β to be (24-106) cm/GW. In addition, the optical limiting behavior has been studied.

    This paper deals with finding the approximation solution of a nonlinear parabolic boundary value problem (NLPBVP) by using the Galekin finite element method (GFEM) in space and Crank Nicolson (CN) scheme in time, the problem then reduce to solve a Galerkin nonlinear algebraic system(GNLAS). The predictor and the corrector technique (PCT) is applied here to solve the GNLAS, by transforms it to a Galerkin linear algebraic system (GLAS). This GLAS is solved once using the Cholesky method (CHM) as it appear in the matlab package and once again using the Cholesky reduction order technique (CHROT) which we employ it here to save a massive time. The results, for CHROT are given by tables and figures and show

The aim of this study to identify the effect of using two strategies for active learning ( Jigsaw Strategy & Problems Solving) in learning some balanced beam's skills in artistic gymnastics for women , as well as to identify the best of the three methods (jigsaw strategy , problems solving and the traditional method) in learning some skills balance beam , the research has used the experimental methodology, and the subject included the students of the college of Physical Education and Sports Sciences / University of Baghdad / third grade and by the lot was selected (10) students for each group of groups Search three and The statistical package for social sciences (SPSS) was used means, the standard deviation and the (T.test), the one way a n