A numerical method for solving the model Boltzmann equation using arbitrary order polynomials is presented. The S-model is solved by a discrete ordinate method with velocity space discretized with a truncated Hermite polynomial expansion. Physical space is discretized according to the Conservative Flux Approximation scheme with extension to allow non-uniform grid spacing. This approach, which u...

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive C0-semigroups under topology uniform weak operator convergence on compact subsets R+. Eisner and Serény raised in [6] [3] open problem: Does this constitute a Baire space? Observing that subspace unitary semigroups is completely metrisable appealing to known density resul...

The paper under discussion [2] states that its main result is as follows. It considers several of the usual parameter adaptive control schemes for fully actuated mechanical systems and proves that persistency of excitation of the regressor matrix along the desired trajectory is a necessary and sufficient condition for uniform global asymptotic stability (UGAS) of the closed loop system. While t...

in this paper we discuss on the fixed points of asymptotic contractions and boyd-wong type contractions in uniform spaces equipped with an e-distance. a new version ofkirk's fixed point theorem is given for asymptotic contractions and boyd-wong type contractions is investigated in uniform spaces.

The considered problem is uniform convergence of sequences of hypergeometric series. We give necessary and sufficient conditions for uniformly dominated convergence of infinite sums of proper bivariate hypergeometric terms. These conditions can be checked algorithmically. Hence the results can be applied in Zeilberger type algorithms for nonterminating hypergeometric series.

A necessary and sufficient condition for the uniform convergence of a family of reversed martingales converging to a degenerated limiting process is given. The condition is expressed by means of regular convergence (in Hardy’s sense) of corresponding means. It is shown that the given regular convergence is equivalent to Hoffmann-Jørgensen’s eventually total boundedness in the mean which is nece...

the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...