This paper is devoted to the asymptotic stability region estimation for nonlinear discrete polynomial systems. An algebraic method is derived for the enlargement of a guaranteed stability region in which the asymptotic stability is ensured. The advantages of the proposed method are the accuracy of determination of the largest stability boundary, its numerical and theoretical robustness and its ...

An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self–similar approximation theory, being its variant where control functions are defined from asymptotic crossover conditions. Several examples from statistical physics demonstrate...

Abstract. We develop a new asymptotic method for the analysis of matrix Riemann-Hilbert problems. Our method is a generalization of the steepest descent method first proposed by Deift and Zhou; however our method systematically handles jump matrices that need not be analytic. The essential technique is to introduce nonanalytic extensions of certain functions appearing in the jump matrix, and to...

For the quintom models with arbitrary potential V = V (φ, σ), the asymptotic value of equation of state parameter ω is obtained by a new method. In this method, ω of stable attractors are calculated by using the ratio d lnV/d ln a in asymptotic region. All the known results, have been obtained by other methods, are reproduced by this method as specific examples.

This paper presents a new control variate method for general multi-dimensional stochastic differential equations (SDEs) including jumps in order to reduce the variance of Monte Carlo method. Our control variate method is based on an asymptotic expansion technique, and does not require an explicit characteristic function of SDEs. This is an extension of previous researches using asymptotic expan...

The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding an asymptotic regime of accurate approximation comparable to that for the spectral vector method.

In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for...

2014 We analyse the scattered light and specific heat data on xenon using the recent nonlinear renormalization group calculations obtained in the ~4 theory in three dimensions. The minimal set of free parameters that the theory imposes is sufficient to describe these data even for the case where, in the usual analysis, many correction terms to scaling are needed. We show that it will be very di...

Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian nite elements with straight edges. These elements are allowed to have diameters with diierent asymptotic behaviour in diierent space directions. The case of aane elements (parallelepipeds) with arbitrarily high degree of the shape functions is considered rst. Then, a careful examination of th...

We calculate the large quantum level asymptotic expansion of the RT–invariants associated to SU(2) of all oriented Seifert 3–manifolds X with orientable base or non-orientable base with even genus. Moreover, we identify the Chern–Simons invariants of flat SU(2)– connections on X in the asymptotic formula thereby proving the so-called asymptotic expansion conjecture (AEC) due to J. E. Andersen [...