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Showing papers on "Asymptotology published in 1996"


Book
25 Apr 1996
TL;DR: Asymptotic expansion and linear extrapolation methods have been studied in this article for philosophy error bounds, stopping rules and monotonicity generalizations, with a focus on linear expansion.
Abstract: Part 1 Asymptotic expansion: asymptotic systems and expansions geometric asymptotic expansions logarithmic asymptotic expansions. Part 2 Linear extrapolation methods: fundamental concepts and general philosophy error bounds, stopping rules and monotonicity generalizations and final remarks.

54 citations




Journal ArticleDOI
TL;DR: A technique is presented that uses numerical solutions to verify the order of the accuracy of an asymptotic expansion for several types of problems.
Abstract: A technique is presented that uses numerical solutions to verify the order of the accuracy of an asymptotic expansion for several types of problems. This technique may be introduced in any beginning course on asymptotic or perturbation methods, but is equally suited to verifying advanced asymptotic results.

47 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derive asymptotic expansion of the probability distributions of statistics for systems perturbed by small noises by means of the Malliavin calculus, and apply it to the problem of the second order efficiency of the maximum likelihood estimator.

23 citations


Book
01 Feb 1996
TL;DR: In this paper, asymptotic problems for non-linear elliptic equations in cylindrical domains and homogenization problems are studied. But the authors focus on homogenisation problems.
Abstract: Preface 1. Asymptotic problems for non-linear elliptic equations 2. On the asymptotic behaviour of solutions of some non-linear elliptic equations in cylindrical domains 3. On the asymptotic behaviour of solutions of non-linear elliptic equations in a neighbourhood of a conic point of the boundary 4. On some homogenization problems Index.

18 citations


Journal ArticleDOI
TL;DR: In this paper, existence theorems and asymptotic formulas for the solutions of a class of delay-differential equations with time-state dependent lag have been proved and shown to exist.

15 citations


Journal ArticleDOI
TL;DR: In this article, the junction problem on the union of two bodies: a thin cylinder and a massive body with an opening into which this cylinder has been inserted was considered, and the asymptotic behaviour of a solution was studied.
Abstract: We consider the junction problem on the union of two bodies: a thin cylinder and a massive body with an opening into which this cylinder has been inserted. The equations on and contain the operators and (where is a large parameter and is the Laplacian): Dirichlet conditions are imposed on the ends of and Neumann conditions on the remainder of the exterior boundary. We study the asymptotic behaviour of a solution as . The principal asymptotic formulae are as follows: on and on , where is a solution of the Neumann problem in and the Dirac function is distributed along the interval with density . The functions and , depending on the axis variable of the cylinder, are found as solutions of a so-called resulting problem, in which a second-order differential equation and an integral equation (principal symbol of the operator ) are included. In the resulting problem the large parameter remains. Various methods of constructing its asymptotic solutions are discussed. The most interesting turns out to be the case ) (even the principal terms of the functions and are not found separately). All the asymptotic formulae are justified; the remainders are estimated in the energy norm.

10 citations


Journal ArticleDOI
TL;DR: In this article, an asymptotic solution of the magnetic induction equation in a given velocity field is constructed for large magnetic Reynolds numbers, and the expansion of the leading term of the equation is proved to be rigorously valid over a finite time interval.
Abstract: An asymptotic solution of the magnetic induction equation in a given velocity field is constructed for large magnetic Reynolds numbers. Initially localized distributions of the magnetic field are considered. The leading term of the asymptotics is found. The expansions are proved to be rigorously valid over a finite time interval. Estimates for the residuals are given. The results are illustrated by some examples: the Hubble flow with a linear dependence of the velocity on coordinates, and ABC type flows. The solutions in these cases are expressed in terms of elementary functions.

7 citations


Journal ArticleDOI
TL;DR: It is shown that this asymptotic behavior of a class of functional differential equations with state-dependent delays can be numerically observed by computing corresponding solutions of approximating equations with piecewise constant arguments.

7 citations



Journal ArticleDOI
TL;DR: In this paper, the analysis of asymptotic waves for the hydrodynamical model of semiconductors is presented, based on the reduction-perturbation method, and numerical solutions show the possible formation of strong gradients from a smooth initial profile.



Journal ArticleDOI
TL;DR: In this paper, asymptotic expansions for the Schrodinger equation of the diamagnetic Coulomb problem with infinite nuclear mass were obtained for the non-adiabatic approximation and for finding non-trivial auto-ionizing states.
Abstract: The paper deals with asymptotic expansions in cylindrical coordinates for the Schrodinger equation of the diamagnetic Coulomb problem with infinite nuclear mass. The basis functions introduced by Liu and Starace are analysed: analytical asymptotic expansions are given for the basis functions and eigenvalues belonging to them. Using these, analytical asymptotic expansions are obtained for the coupling coefficients and solutions of the system of second-order ordinary differential equations which arise if the wavefunction is expanded in terms of the Liu - Starace basis functions. The role of the asymptotic expansions is elucidated for the numerical solution of the non-adiabatic approximation and for finding non-trivial auto-ionizing states.

Journal ArticleDOI
TL;DR: In this paper, an asymptotic theory for a class of fourth-order differential equations is developed for a general class of four-order equations. But the theory is restricted to the case where the coefficients of the differential equation have different orders of magnitude for large x.
Abstract: An asymptotic theory is developed for a class of fourth-order differential equations. Under a general conditions on the coefficients of the differential equation we obtained the forms of the asymptotic solutions such that the solutions have different orders of magnitude for large x.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the analytic function can be reconstructed from the asymptotic expansion of a function at a boundary point of the domain of analyticity.
Abstract: Asymptotic expansions of analytic functions at a boundary point of their domain of analyticity arise in a variety of problems in Applied Mathematics and Mathematical Physics. Relying on a concept of an asymptotic expansion which is slightly more restrictive than that of Poincare, but still considerably weaker than that of a ‘strong asymptotic expansion’, it is shown when and how the analytic function can be reconstructed from the asymptotic expansion. As in the famous Watson-Nevanlinna reconstruction by Borel summability moment summation methods are used. We find an interesting new link between the growth rate of the expansion coefficients with n and the allowed geometrical form of the domain of analyticity near the expansion point. The general reconstruction result is illustrated by a class of special reconstructions, the Mittag-Leffler reconstructions.

Journal ArticleDOI
TL;DR: In this article, the existence theorems and conditions for solvability of the Neumann problem are presented based on the weighted Korn inequality, and the study of the asymptotic behavior of a solution to the last problem is simplified.
Abstract: Asymptotic representations of solutions to the boundary-value problems of elasticity theory are studied in domains with parabolic exit at infinity (or in bounded domains with singularities like polynomial zero sharpness). The procedure of derivating a formal asymptotic expansion looks like the algorithm of asymptotic analysis in domains. Under the Dirichlet conditions (displacements are prescribed on the boundary of a domain), it is not hard to justify the power asymptotic series. It follows from the theorem on the unique solvability of the problem in spaces of the type L2 containing degrees of distance r=|x| as weight multipliers. For the Neumann conditions (stresses are prescribed on the boundary of a domain) an asymptotic expansion is justified by introducing the Eiry function Φ transforming the Lame system to the biharmonic equation. Due to the appearance of the Dirichlet condition on Φ, the study of the asymptotic behavior of a solution to the last problem is simplified. The existence theorems and conditions for solvability of the “elastic” Neumann problem are presented. These results are based on the weighted Korn inequality. Bibliography: 29 titles.

Journal ArticleDOI
TL;DR: In this paper, the authors construct renormalization group invariant forms of the effective potential of massive Φ4 theory that yield its asymptotic behavior for large and small values of the field and mass variables.
Abstract: We construct renormalization group invariant forms of the effective potential of massive Φ4 theory that yield its asymptotic behavior for large and small values of the field and mass variables. Some consequences of these asymptotic formulas are discussed.

Journal ArticleDOI
TL;DR: In this article, the invariance principle in a Banach space with less restriction is used to study the asymptotic behavior of an integro-differential equation with infinite delay.
Abstract: Using the invariance principle in a Banach space with less restriction, we discuss the asymptotic behaviour of an integro-differential equation with infinite delay which is an infection disease model. It is proved that the equilibria are globally asymptotic stable if the parameters fit some relation and the integral kern satisfies a convergence condition.