1. Abstract We study the stochastic quantization of two-dimensional nonlinear sigma model in the large N limit. Our main tool is the effective Langevin equation with which we investigate nonperturbative phenomena and derive the results which are same as the path integral approach gives.

In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra  integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on wavelets, then we apply the Chebyshev wavelets to solve the integral equation. Numerical implementation of the method is illustrated by two ben...

In this paper, a numerical method for solving fuzzy Fredholm integral equations of the second kind is introduced. We apply the trapezoidal rule to compute the Riemann integrals.This kind of integral equations convert to a linear system. Then, by solving the linear system , unknowns are determined. Finally, an algorithm is presented to solve the fuzzy integral equation by using the trapezoidal r...

A direct method for determining powder diffraction data at specific depths from angle-dependent diffraction data is described. The method is non-destructive and only traditional data collections, where the angle of incidence is varied, are required. These angle-dependent spectra are transformed to give diffraction data arising from different depths, which may then be exploited using any convent...

In this paper an expansion method, based on Legendre or any orthogonal polynomials, is developed to find numerical solutions of two-dimensional linear Fredholm integral equations. We estimate the error of the method, and present some numerical examples to demonstrate the accuracy of the method. 2000 Mathematics subject classification: 65R20.

Abstract In this article we make an improvement in the Banach contraction using a controlled function metric like spaces, which generalizes many results literature. Moreover, present application on Fredholm type integral equation.

This article deals with the mathematical and the numerical aspects of the Fredholm integral equation of the second kind arising as a result of the heat energy exchange inside a convex and non-convex enclosure geometries. Some mathematical results concerning the integral operator are presented. The Banach fixed point theorem is used to guarantee the existence and the uniqueness of the solution o...