A theoretical study has been proposed to investigate the effects of different laser radiations (Nd - glass, DF and C02) as a heating source on different glass samples (Optical glass, Bk - 7 and Soda - lime glass) and different waves lengths (10.6, 3.8, 1.6) ???. The heat changes as which are resulted due irradiation with laser sources have been determined by using the one dimension mathematical relation as a function of time (t) and depth (z). The results of the study show ed that the irradiation with C02 laser had a greater effect than DF laser, while the effects of Nd - glass laser were minimal with a power density of (1.8*10?? w/m2) within atime(l^sec).(Forboth Kinds) The change in the temperatures were not exceeded than (70"K) in all sa

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

This article aims to estimate the partially linear model by using two methods, which are the Wavelet and Kernel Smoothers. Simulation experiments are used to study the small sample behavior depending on different functions, sample sizes, and variances. Results explained that the wavelet smoother is the best depending on the mean average squares error criterion for all cases that used.

This paper deals with a new Henstock-Kurzweil integral in Banach Space with Bilinear triple n-tuple and integrator function Ψ which depends on multiple points in partition. Finally, exhibit standard results of Generalized Henstock - Kurzweil integral in the theory of integration.

The transportation model is a well-recognized and applied algorithm in the distribution of products of logistics operations in enterprises. Multiple forms of solution are algorithmic and technological, which are applied to determine the optimal allocation of one type of product. In this research, the general formulation of the transport model by means of linear programming, where the optimal solution is integrated for different types of related products, and through a digital, dynamic, easy illustration Develops understanding of the Computer in Excel QM program. When choosing, the implementation of the form in the organization is provided.