In this paper, a least squares group finite element method for solving coupled Burgers' problem in   2-D is presented. A fully discrete formulation of least squares finite element method is analyzed, the backward-Euler scheme for the time variable is considered, the discretization with respect to space variable is applied as biquadratic quadrangular elements with nine nodes for each element. The continuity, ellipticity, stability condition and error estimate of least squares group finite element method are proved.  The theoretical results  show that the error estimate of this method is . The numerical results are compared with the exact solution and other available literature when the convection-dominated case to illustrate the effic

Western Scholars have criticized al the material on the point of reliability . Some have taken the unduly Sceptical view that nothing is to be trusted except Quran . The present study is based on opposing view that at least the material in the early biographers is to be accepted as true , except where there are particular reasons for thinking that an anecdote has been distorted ( or invented ) through legal or political motives. It is also assumed that most of the background material culled from a large number of vaired works , is sound . This standpoint .I would claim , leads to a coherent view of Muhammad's life and achievement.

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

This paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.

         The issue of penalized regression model has received considerable critical attention to variable selection. It plays an essential role in dealing with high dimensional data. Arctangent denoted by the Atan penalty has been used in both estimation and variable selection as an efficient method recently. However, the Atan penalty is very sensitive to outliers in response to variables or heavy-tailed error distribution. While the least absolute deviation is a good method to get robustness in regression estimation. The specific objective of this research is to propose a robust Atan estimator from combining these two ideas at once. Simulation experiments and real data applications show that the proposed LAD-Atan estimator

In this work, the effect of the addition of bright nickel plating and silver carried out by the electroplating method has been studied, on the coating of copper nanoparticles on the copper base metal via the process of thermal evaporation. The improvement of the solar absorber using CuNP in combination with the bright nickel and silver was obtained to be better than copper nanoparticles individually. A bright nickel enhanced the absorbed thermal stability. Also, other optical properties, absorptions, and emissivity slightly decreased from (93% to 87%), while the existence of silver had a slight impact on absorption of about (86.50%). On the other hand, thermal conductivity was evaluated using hot disk analyzer. The results showed a good

In this work, chemical spray pyrolysis deposition (CSP) technique was used to prepare a mixed In2O3-CdO thin films with different CdO content (10, 30 and 50)%volume ratio on glass substrates at 150 ᵒC substrate temperature. The surface morphology and structural properties were measured to find the optimum conditions to improve thin films properties for using as photo detector. Current –Time, the sensitivity and response speed vary for each mixture. Samples with 10% vol. CdO content has square pulse response with average rise time nearly 1s and fall time 1s.