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Showing papers on "Asymptotology published in 2004"


Journal ArticleDOI
TL;DR: In this article, the harmonic potential of a random walk has been shown to have arbitrary precision asymptotics, and two algorithms that allow to obtain arbitrary precision harmonic potentials for random walks are given.
Abstract: We give two algorithms that allow to get arbitrary precision asymptotics for the harmonic potential of a random walk.

38 citations




Book ChapterDOI
07 Jun 2004

16 citations


Journal ArticleDOI
Markus Scholz1
TL;DR: In this paper, the authors apply the methods of the above authors to discuss asymptotic behaviour of capillarities in cusps, which is a corner with opening angle 0.
Abstract: Concus and Finn [2] discovered that capillary surfaces rise to infinity in corners with sufficiently small opening angle. They also found the leading term of an asymptotic expansion. Miersemann [5] improved this result to obtain a complete asymptotic expansion. In the present paper we will apply the methods of the above authors to discuss asymptotic behaviour of capillarities in cusps, which is a corner with opening angle 0. A large variety of asymptotic formulas will be provided. The general comparison theorem from Concus and Finn will play an important role in the proofs.

8 citations


Journal ArticleDOI
TL;DR: In this paper, transient and asymptotic behaviors of general Markov fluid models are studied and analyzed, and methods to apply to a general MarkOV fluid model and the numerical results are interpreted.
Abstract: In this paper, transient and asymptotic behaviors of general Markov fluid models are studied and analyzed. The input and output rates are assumed to be modulated by a finite state irreducible Markov process, which can admit states with zero effective input rate. The main advantage of the proposed methods is their accuracy and their numerical stability. For the transient solution, properties of stationary detection lead to reduce considerably the computational complexity of the algorithm. As for the asymptotic solution, it is derived from the transient one's. We apply these methods to a general Markov fluid model and we interpret the numerical results.

8 citations



Journal ArticleDOI
TL;DR: A differential calculus for the non-operator norms of m-times continuously differentiable matrix function χ(t), t ≥ t 0 is presented and combined with the study of the asymptotic behavior of the evolution Φ(t, t 0) for periodic linear dynamical systems.
Abstract: In this paper, a differential calculus for the non-operator norms |·|1 and |·|∞ of m-times continuously differentiable matrix function χ(t), t ≥ t 0, is presented and combined with the study of the asymptotic behavior of the evolution Φ(t, t 0) for periodic linear dynamical systems. The upper bound describing the asymptotic behavior (for short, asymptotic bound or asymptotic estimate) is based on Floquet's theory and on a bound containing the spectral abscissa of a constant matrix; it compares favorably with other asymptotic bounds. The minimal constant in the asymptotic estimate is computed by the differential calculus of norms. As far as we are aware, the achieved result cannot be obtained by other methods.

7 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that for autoresonance to appear, the pump amplitude must exceed some threshold value, i.e., the amplitude of the pump is larger than a threshold value.
Abstract: Autoresonance is one of the most interesting phenomena in nonlinear oscillations. The energy of forced oscillations of a nonlinear system substantially increases in the course of time, although the driving force remains small. This phenomenon, observed in various physical systems [1–8], is used, for example, for accelerating relativistic particles [9–12]. Numerical experiments based on various mathematical models have shown that, for autoresonance to appear, it is necessary that the pump amplitude exceed some threshold value [13, 14]. In the present paper, we obtain a result of this sort analytically by an asymptotic analysis of the equations

5 citations




Posted Content
TL;DR: Asymptotic expansions for a wide class of distribution are studied in this paper, where simple method for the computation of the series coefficients i s suggested The case when regularization parameter of distribution depends on the asymptotics parameter is considered
Abstract: Asymptotic expansions for a wide class of distribution are studied Simple method for the computation of the series coefficients i s suggested The case when regularization parameter of distribution depends on the asymptotic parameter is considered

Journal ArticleDOI
TL;DR: In this paper, a new approach is proposed to problems of asymptotic parameter estimation in stochastic switching systems, which allows one to investigate the properties of estimates of parameters constructed from observed trajectories.
Abstract: A new approach is proposed to problems of asymptotic parameter estimation in stochastic switching systems. In this approach, results on the asymptotic behavior of solutions of stochastic equations and theorems of the type of averaging are used for switching processes. This approach allows one to investigate asymptotic properties of estimates of parameters constructed from observed trajectories for a numerous class of stochastic systems with regular behaviors of trajectories under stationary and transient conditions.

01 Jan 2004
TL;DR: Asymptotic properties and equivalence of some Volterra dierence equations are investigated in this article, where the equivalence is shown to be asymptotically tight.
Abstract: Asymptotic properties and asymptotic equivalence of some Volterra dierence equations are investigated.


Journal ArticleDOI
TL;DR: In this article, asymptotic analysis of the mathematical model of two-composite materials has been studied and the main result is the deduction of the extended Stefan problem being a singular limit of the initial problem.
Abstract: The paper is devoted to asymptotic analysis of the mathematical model of two-composite materials. The main result is the deduction of the extended Stefan problem being a singular limit of the initial problem.

Journal ArticleDOI
TL;DR: In this article, the properties of asymptotic soliton-like solutions to the 1-D nonstationary nonlinear Schrodinger equation with the external-field potential of a special form are studied.
Abstract: The properties of asymptotic soliton-like solutions to the 1-D nonstationary nonlinear Schrodinger equation with the external-field potential of a special form are studied. A comparative analysis of the asymptotic solutions and simulation results is performed to show the range of parameter values where asymptotic and numerical soliton-like solutions are in agreement, the localization being preserved.