In this chapter we introduce the fundamental concepts behind the Green Function Theory. We start from a description of the second quantization method and then, after introducing the ensemble average of an operator, we define the main object of the theory, the Green function. Further on, after obtaining the equation of motion for the Green function, we introduce the self-energy operator and we d...

A formal way to obtain a recently found solution of the problem of nonlinear interaction of two non-concentric spherical waves in terms of quasi-linear approach is described.

Introduction. The purpose of this paper is to describe an effective construction of Greene and Neumann's functions for a general class of linear, second-order partial differential equations of elliptic type in terms of a set of continuously differentiable functions, complete and orthonormal with respect to the domain considered. This result completes a previous paper by us in which an analogous...

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

This paper proposes a hybrid method to find cumulative distribution function (CDF) of completion time of GERT-type networks (GTN) which have no loop and have only exclusive-or nodes. Proposed method is cre-ated by combining an analytical transformation with Gaussian quadrature formula. Also the combined crude Monte Carlo simulation and combined conditional Monte Carlo simulation are developed a...

This paper presents a novel Interpolated Factored Green Function method (IFGF) for the accelerated evaluation of integral operators in scattering theory and other areas. Like existing acceleration methods these fields, IFGF algorithm evaluates action function-based at cost O(Nlog⁡N) operations an N-point surface mesh. The strategy, which leads to extremely simple algorithm, capitalizes on slow ...

In this paper, we consider generalized space-time fractional cable equation in presence of external source. By using the Fourier-Laplace transform we obtain the Green function in terms of infinite series in H-functions. The fractional moments of the fundamental solution are derived and their asymptotic behavior in the short and long time limit is analyzed. Some previously obtained results are c...

A static mixed boundary value problem of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard boundary-domain integro-differential formulation of the problem is presented, with respect to the displacements and their gradients. Using a cut-off fu...