scispace - formally typeset
Search or ask a question

Showing papers on "Asymptotology published in 1997"


Journal ArticleDOI
Bruce E. Hansen1
TL;DR: In this paper, numerical approximations to the asymptotic distributions of recently proposed tests for structural change are presented, which enables easy yet accurate calculation of asymPTotic p values.
Abstract: Numerical approximations to the asymptotic distributions of recently proposed tests for structural change are presented. This enables easy yet accurate calculation of asymptotic p values. A GAUSS program is available to perform the computations.

730 citations


Book
01 Jan 1997
TL;DR: In this article, the boundary layer method is used for diffraction expansion of integrals, and the Fock functions reciprocity principle is used to obtain the surface impedance generalization of the notion of impedance.
Abstract: Ray optics search for solutions in the form of asymptotic expansions the boundary layer method spectral theory of diffraction uniform solutions integral methods surface field and physical theory of diffraction calculation of the surface impedance generalization of the notion of impedance. Appendices: canonical problems differential geometry complex rays asymptotic expansion of integrals Fock functions reciprocity principle.

88 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the asymptotic analysis for spectral densities arising from elliptic pseudodifferential operators is equivalent to the Cesaro and parametric behaviours of distributions at infinity.
Abstract: Modulo the moment asymptotic expansion, the Cesaro and parametric behaviours of distributions at infinity are equivalent. On the strength of this result, we construct the asymptotic analysis for spectral densities, arising from elliptic pseudodifferential operators. We show how Cesaro developments lead to efficient calculations of the expansion coefficients of counting number functionals and Green functions. The bosonic action functional proposed by Chamseddine and Connes can more generally be validated as a Cesaro asymptotic development.

52 citations


Journal ArticleDOI
TL;DR: In this article, two methods for computing the coefficients of the asymptotic series near the transition point are discussed, and auxiliary functions that can be computed more efficiently than the coefficients in the first method, and do not need the tabulation of many coefficients.
Abstract: Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal.

32 citations



Journal ArticleDOI
TL;DR: In this article, an asymptotic expansion for locally (at infinity) outgoing functions on Euclidian spaces is proved for N -body scattering where the two-body interactions are one-step polyhomogeneous symbols of order −1 or −2 (hence long-range and short-range respectively).

23 citations


01 Jan 1997
TL;DR: In this article, a summary of several talks given in 1990-1993 discusses the problem of asymptotic expansions of multiloop Feynman diagrams in masses and external momenta, a central problem in perturbative quantum field theory.
Abstract: This summary of several talks given in 1990-1993 discusses the problem of asymptotic expansions of multiloop Feynman diagrams in masses and external momenta - a central problem in perturbative quantum field theory Basic principles of the theory of asymptotic operation -- the most powerful tool for that purpose -- are discussed Its connection with the conventional methods is explained (the BPHZ theory, the method of leading logarithmic approximation etc) The problem of non-euclidean asymptotic regimes is discussed as well as ways of its solution

22 citations



Book ChapterDOI
01 Jan 1997
TL;DR: The quantum propagation of N-body systems is asymptotically constrained to Lagrangian manifolds corresponding to particular solutions of the free Hamilton-Jacobi equation as mentioned in this paper.
Abstract: The quantum propagation of N-body systems is asymptotically constrained to Lagrangian manifolds corresponding to particular solutions of the free Hamilton-Jacobi equation. This is used to give a proof of asymptotic completeness for short-range interactions.

13 citations


Journal ArticleDOI
TL;DR: In this article, a new notion about the asymptotic stability of Riemann entropy solutions of conservation laws is introduced, and corresponding analytical frameworks are developed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in L ∞.
Abstract: We are concerned with the asymptotic behavior of entropy solutions of conservation laws. A new notion about the asymptotic stability of Riemann solutions is introduced, and corresponding analytical frameworks are developed. The correlation between the asymptotic problem and many important topics in conservation laws and nonlinear analysis is recognized and analyzed, such as zero dissipation limits, uniqueness of entropy solutions, entropy analysis, and divergence-measure fields in \(L^\infty\). Then this theory is applied to understanding the asymptotic behavior of entropy solutions for many important systems of conservation laws.

10 citations



Journal ArticleDOI
TL;DR: In this article, the authors studied the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation and constructed formal approximations on a long timescale O(∣e∣−1).
Abstract: This paper is devoted to studying the asymptotic theory of initial value problems for a semilinear perturbed telegraph equation. The asymptotic theory and validity of formal approximations are constructed on long timescale O(∣e∣−1. As an application of the asymptotic theory, the initial value problems for a special telegraph equation are studied and two asymptotic solutions of order O(∣e∣−1 are presented.



Book ChapterDOI
01 Jan 1997
TL;DR: In this article, the concept of local asymptotic efficiency of estimators can be made precise in several ways, e.g., by applying Le Cam's admissibility theorem and Hajek's uniqueness theorem to semiparametric problems.
Abstract: The concept of local asymptotic efficiency of estimators can be made precise in several ways. In semiparametric theory most authors are using local asymptotic minimaxity or asymptotic convolution theorems. We will show how Le Cam’s asymptotic admissibility theorem and Hajek’s asymptotic uniqueness result can be applied to semiparametric problems.



Journal ArticleDOI
TL;DR: In this article, the authors present three different asymptotic studies of the second Painleve equation involving, or unbounded initial data, and show how the direct method, which is in the spirit of Boutroux, can be naturally applied to each of the three cases.
Abstract: We present three different asymptotic studies of the second Painleve equation involving , or unbounded initial data. We show how the direct method, which is in the spirit of Boutroux, can be naturally applied to each of the three cases.

Journal ArticleDOI
TL;DR: In this paper, a reformulation of the asymptotic solution of the coupledmode equations with a periodic variation of the refractive index along the propagation length is presented, and a first-order correction using the solution and Piccard's method are also determined.
Abstract: A reformulation of the asymptotic solution of the coupledmode equations with a periodic variation of the refractive index along the propagation length is presented. A first-order correction using the asymptotic solution and Piccard’s method are also determined. It is found that the first-order solution compares very well with the numerical solution throughout a wide range of coupling parameters. The key differences between the method presented here and elsewhere reside in the derivation of the asymptotic solution as well as in the carefull derivation of the higher order corrections.

Book ChapterDOI
01 Jan 1997

Journal ArticleDOI
TL;DR: In this article, the authors deal with the asymptotic theory of initial value problems for semilinear wave equations in three dimensions, and the well-posedness and validity of formal approximations on a long time scale of order ∣e∣−1 are discussed in the classical sense of C 2.
Abstract: This paper deals with the asymptotic theory of initial value problems for semilinear wave equations in three space dimensions. The well-posedness and validity of formal approximations on a long time scale of order ∣e∣−1 are discussed in the classical sense of C 2. This result describes accuratively the approximations of solutions. At the end of this paper, an application of the asymptotic theory is given to analyze a special model for a perturbed wave equation.


Journal ArticleDOI
01 Mar 1997
TL;DR: In this article, the asymptotic expansion of the singular Fourier integral with respect to the large real parameter k is presented, where k is the number of real parameters.
Abstract: This paper presents the asymptotic expansion, with respect to the large real parameter k, of the singular Fourier integral I(k) B fp & b

Journal ArticleDOI
TL;DR: In this article, a new algorithm was proposed to compute the asymptotic solutions of a linear differential system. But the algorithm is not suitable for the case of periodic coefficients.

Journal ArticleDOI
TL;DR: In this article, the Dirichlet problem for the Poisson equation is considered in a nonperiodic framelike domain that consists of thin short strips or cylinders, and an estimate for the difference between the exact solution and the asymptotic one is obtained.
Abstract: In this paper, the Dirichlet problem for the Poisson equation is considered in a nonperiodic framelike domain that consists of thin short strips or cylinders. We construct a complete asymptotic expansion for the solution. We obtain an estimate for the difference between the exact solution and the asymptotic one. Bibliography: 9 titles.


Journal ArticleDOI
TL;DR: The method of successive approximation is used to establish the results and it is shown that the asymptotic behaviour of the solutions of the fuzzy differential equations is similar to that of the real world.


DOI
01 Jan 1997
TL;DR: In this paper, the phase separation of a binary mixture in the presence of a mass constraint is analyzed asymptotically and numerically in a two-dimensional domain, and the slow motion behavior of a semi-circular interface intersecting a at boundary segment is also analyzed.
Abstract: The Allen-Cahn equation with a mass constraint is analyzed asymptotically and numerically in a two-dimensional domain. This problem models the phase separation of a binary mixture in the presence of a mass constraint. Solutions develop internal layers, or interfaces, that propagate depending on the curvature of the interfaces while keeping the area they enclose constant. Small interfaces attached to the boundary of the domain are shown to move along the boundary in the direction of increasing boundary curvature. The motion of the interfaces is simulated numerically to verify these asymptotic results. The slow motion behavior of a semi-circular interface intersecting a at boundary segment is also analyzed. The projection method is used to derive an explicit ordinary di erential equation for the location of the center of such a semi-circular interface. ii Table of

Journal ArticleDOI
TL;DR: Recently, recent developments in the asymptotic theory of statistics are, surprisingly, shedding new light on this debate, and may have the potential to provide a common middle ground as discussed by the authors.
Abstract: Statistics in the 20th century has been enlivened by a passionate, occasionally bitter, and still vibrant debate on the foundations of statistics and in particular on Bayesian vs. frequentist approaches to inference. In 1975 D. V. Lindley predicted a Bayesian 21st century for statistics. This prediction has often been discussed since, but there is still no consensus on the probability of its correctness. Recent developments in the asymptotic theory of statistics are, surprisingly, shedding new light on this debate, and may have the potential to provide a common middle ground.