The eigen equation of pitch-angle distribution derived from the slowing-down with an energetic particle source term is solved by using Legendre series expansion method. An iteration matrix established when scattering terms become important. whole region separated into three parts, two passing regions, and one trapped area. for each finally obtained. method applied to solve equations that Maxwel...

A stochastic response of an elastic 3D half-space to random displacement excitations on the boundary plane is studied. We derive exact results for the case of white noise excitations which are then used to give convolution representations for the case of general finite correlation length fluctuations of displacements prescribed on the boundary. Solutions to this elasticity problem are random fi...

A method has been developed for deriving the approximate global optimum of a nonlinear objective function. First, the objective function is expanded into a linear equation for a moment vector, and the optimization problem is reduced to an eigen analysis problem in the wave coefficient space. Next, the process of the optimization is expressed using a Schrödinger-type equation, so global optimiza...

The classic formulation of the extended boundary condition method is revisited to inject regularization operators for unknown coefficients eigen-function expansions travelling and standing waves throughout dielectric scatterer. It shown that, using new definitions, existing algorithm scattering field calculation can be kept same its well-conditioned version. This exemplified scalar 2D problems ...

Cylindrically symmetric inhomogeneous magnetized string cosmological model is investigated with cosmological term Λ varying with time. To get the deterministic solution, it has been assumed that the expansion (θ) in the model is proportional to the eigen value σ 1 of the shear tensor σ j . The value of cosmological constant for the model is found to be small and positive which is supported by t...