In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

Abstract

This study highlights the importance of Iraq in the analysis of foreign trade and economic growth for the period (1980 - 2013) is an attempt to determine the equilibrium relationship long term and short term between these two variables were used ARDL model to explain the economic relationship between the two variables.

To achieve the objectives of the research has been the standard model estimate after testing the stability of exports X data series, and imports M, and GDP current prices, and exchange rate EXR, and verify the existence of a joint integration relationship between these variables.

In order to achieve the objectives of the research it

Artificial Intelligence Algorithms have been used in recent years in many scientific fields. We suggest employing artificial TABU algorithm to find the best estimate of the semi-parametric regression function with measurement errors in the explanatory variables and the dependent variable, where measurement errors appear frequently in fields such as sport, chemistry, biological sciences, medicine, and epidemiological studies, rather than an exact measurement.

The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent o

In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V. Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl. 316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition Method (ADM), does not require to calculate Lagrange multiplier a

The primary components of successful engineering projects are time, cost, and quality. The use of the ring footing ensures the presence of these elements. This investigation aims to find the optimum number of geogrid reinforcement layers under ring footing subjected to inclined loading. For this purpose, experimental models were used. The parameters were studied to find the optimum geogrid layers number, including the optimum geogrid layers spacing and the optimum geogrid layers number. The optimum geogrid layers spacing value is 0.5B. And as the load inclination angle increased, the tilting and the tilting improvement percent for the load inclination angles (5°,10°,15°) are (40%,28%, and 5%) respectively. The reduction percent of the

        In this paper, the Magnetohydrodynamic (MHD) for Williamson fluid with varying temperature and concentration in an inclined channel with variable viscosity has been examined. The perturbation technique in terms of the Weissenberg number  to obtain explicit forms for the velocity field has been used. All the solutions of physical parameters of the Darcy parameter , Reynolds number , Peclet number  and Magnetic parameter  are discussed under the different values as shown in plots.

  The theory of the epic theater has received wide attention by filmmakers around the world because of its great impact on the artistic work of the theater and its relationship with societies, and among these directors the Iraqi directors have been influenced by the epic theater and its applications in the show.
In order to find out the effectiveness of these influences on the Iraqi director, I found the need to do this study, which was divided into an introduction and a theoretical framework that included two topics. The first topic (Philosophical References and the Intellectual Foundations of the Epic Theater Theory) deals with the philosophical foundations that crystallized the epic theory of Burch and the mechanism of working