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Showing papers on "Asymptotology published in 1993"



BookDOI
01 Jan 1993
TL;DR: This paper presents a meta-modelling of Complex Systems with Asymptotic-Enhanced Numerical Methods and its applications in Scientific Computing and Symbolic Manipulation Tools for AsymPTotic Analysis.
Abstract: Preface. Part 1: Modeling of Complex Systems with Asymptotic-Enhanced Numerical Methods. Part 2: Asymptotic-Induced Domain Decomposition Methods. Part 3: Multiple-Scale Problems in Scientific Computing. Part 4: Applied and Asymptotic Analysis. Part 5: Symbolic Manipulation Tools for Asymptotic Analysis. Part 6: Numerical Methods, Algorithms, and Architectures. Index.

97 citations


Journal ArticleDOI
TL;DR: In this paper, a description of the asymptotic development of a family of minimum problems is proposed by a suitable iteration of Γ-limit procedures, and an example of the development of functionals related to phase transformations is also given.
Abstract: A description of the asymptotic development of a family of minimum problems is proposed by a suitable iteration of Γ-limit procedures. An example of asymptotic development for a family of functionals related to phase transformations is also given.

90 citations


Journal ArticleDOI
TL;DR: The problem of asymptotic expansion of Green functions in perturbative QFT is studied in this paper for the class of Euclidean asymPTotic regimes, and it is shown that the problem reduces to the expansion of products of a class of singular functions.
Abstract: The problem of asymptotic expansion of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem. It is shown that the problem reduces to studying asymptotic expansion of products of a class of singular functions in the sense of the distribution theory. Existence, uniqueness and explicit expressions for such expansions. (As-operation for products of singular functions) in dimensionally regularized form are obtained using the so-called extention principle.

47 citations



Book
01 Jul 1993
TL;DR: Probability and measure random variables and distributions in statistics concepts of asymptotic convergence further asymPTotic theory with applications in regression likelihood and associated concepts of maximum likelihood, metric spaces and stochastic processes Brownian motion and weak convergence applications of dependent random variables as mentioned in this paper.
Abstract: Probability and measure random variables and distributions in statistics concepts of asymptotic convergence further asymptotic theory with applications in regression likelihood and associated concepts maximum likelihood and asymptotic theory metric spaces and stochastic processes Brownian motion and weak convergence applications of weak convergence dependent random variables and mixing dependent sequences and martingales.

26 citations


Journal ArticleDOI
TL;DR: The asymptotic distribution of the least squares estimators in the random walk model was first found by White [17] and is described in terms of functional of Brownian motion with no closed form expression known as discussed by the authors.
Abstract: The asymptotic distribution of the least-squares estimators in the random walk model was first found by White [17] and is described in terms of functional of Brownian motion with no closed form expression known. Evans and Savin [5,6] and others have examined numerically both the asymptotic and finite sample distribution. The purpose of this paper is to derive an asymptotic expansion for the distribution. Our approach is in contrast to Phillips [12,13] who has already derived some terms in a general expansion by analyzing the functionals. We proceed by assuming that the errors are normally distributed and expand the characteristic function directly. Then, via numerical integration, we invert the characteristic function to find the distribution. The approximation is shown to be extremely accurate for all sample sizes ≥25, and can be used to construct simple tests for the presence of a unit root in a univariate time series model. This could have useful applications in applied economics.

12 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the asymptotic mean squared error for predicting the integral of a weakly stationary spatial process over a unit cube based on a centered systematic sample.
Abstract: This paper studies the asymptotic mean squared error for predicting the integral of a weakly stationary spatial process over a unit cube based on a centered systematic sample. For processes whose spectral density decays sufficiently slowly at infinity, the asymptotic mean squared error takes a form similar to that obtained by letting the cube increase in size with the number of observations. However, if the spectral density decays faster than a certain critical rate, then the asymptotic mean squared error takes on a completely different form. By adjusting the weights given to observations near an edge of the cube, it is possible to obtain asymptotic results for the fixed cube that again resemble those for the increasing cube.

11 citations


Journal ArticleDOI
TL;DR: For the two-level version of boundary integral equations applied to the analysis of oscillations of composite thin-shelled constructions in an acoustic medium, asymptotic analysis and simplification of equations in several characteristic excitation bands is carried out within the framework of the plane problem.

8 citations


Book ChapterDOI
01 Jan 1993
TL;DR: In this article, the authors proved the asymptotic completeness of long-range quantum systems with respect to the clustering for N -body long-term quantum systems.
Abstract: It is well-known that the asymptotic completeness holds for short-range quantum systems. The first proof was given by Sigal-Soffer in reference [13] of Part I [9], which we refer to as reference [I.13], and the alternative proofs were obtained by Graf [I.8], Kitada [9], Derezinski [3], Tamura [I.17], and Yafaev [18]. In the present paper we shall prove the asymptotic clustering for N -body long-range quantum systems

8 citations



Journal ArticleDOI
TL;DR: In this paper, regular and singular asymptotic methods are applied to one-and two-dimensional integral equations of the first kind that arise in the treatment of various 2D axisymmetrical and 3D problems with mixed boundary conditions in the mechanics of continuous media.



Journal ArticleDOI
TL;DR: In this paper, the authors applied the asymptotic method of Belinskii, Khalatnikov and Lifshitz to the study of the behavior near singularities of generic Bianchi IX cosmological models in the framework of the R2 theory of gravity.
Abstract: The asymptotic method of Belinskii, Khalatnikov and Lifshitz is applied to the study of the behavior near singularities of generic Bianchi IX cosmological models in the framework of the R2 theory of gravity Three main kinds of asymptotic forms for the metric are obtained: a de Sitter geometry, a monotonic fall on a curvature singularity after a finite number of oscillations, an infinite sequence of regular oscillations No chaos appears

Book ChapterDOI
01 Jan 1993
TL;DR: The theory of generalized functions and their applications in solving different mathematical models have pointed at the need of the adequate theory of the asymptotic behaviour of distributions as mentioned in this paper. But this theory has not yet been developed.
Abstract: Development of the theory of generalized functions and their applications in solving different mathematical models have pointed at the need of the adequate theory of the asymptotic behaviour of distributions. Let us point at integral transforms of distributions, Abelian and Tauberian type theorems, asymptotic behaviour of solutions of partial differential equations,... These and many other problems have pushed on the elaboration of a theory of asymptotic behaviours of generalized functions.

Journal ArticleDOI
TL;DR: In this paper, it was shown that an infinity of different uniform asymptotic expansions can be constructed for each type of development for the Kouyoumjian and Pathak formulation on a rigorous basis.
Abstract: By exhibiting the development of the Pauli-Clemmow method in a new manner, it is shown that the two uniform asymptotic expansions commonly used are different. Next it is shown that an infinity of different uniform asymptotic expansions can be constructed for each type of development. This allows us to set the Kouyoumjian and Pathak formulation on a rigorous basis. © 1993 John Wiley & sons, Inc.

Book
01 Jan 1993
TL;DR: Aida et al. as mentioned in this paper analyzed the support of Wiener functionals and proposed an elementary approach to Malliavin fields, K. Ito and S. Mauabe studied the regularity of solution to S.D.
Abstract: Part 1 Analysis of Wiener functionals: on the support of Wiener functionals, S. Aida, et al an elementary approach to Malliavin fields, K. Ito on the regularity of solution to S.D.E., S. Kusuoka. Part 2 Asymptotics: Schilder's large deviation principle without topology, G. Ben Arons and M. Ledoux on a precise Laplace-type asymptotic formula for sums of independent random vectors, T. Chiyonobu asymptotic formulae for stochastic oscillatory integrals, N. Ikeda and S. Mauabe some problems related to a one-dimensional stochastic wave equation, R. Leandre and F. Russo the asymptotic distributimons of the eigenvalues for the Schroedinger operators with magnetic fields, H. Matsumoto asymptotic expansion formulas of the Shilder type for a class of conditional Wiener functional integrations, S. Takanobu and S. Watanabe.

Journal ArticleDOI
TL;DR: In this paper, simple analytic expressions for the stresses in an elastic half-space when the load is applied at times near the starting time are derived and error bounds worked out for the principal terms of the asymptotic series, subject to certain assumptions.

Journal ArticleDOI
TL;DR: In this paper, a function which involves a real parameter is introduced; the parameter can be specialized to produce all of these special cases, and the asymptotic behavior is obtained for this function for all real values of the parameter.
Abstract: The asymptotic behaviors of four closely related special cases of power series with ζ-functions in the coefficients have appeared in the literature. A function which involves a real parameter is introduced; the parameter can be specialized to produce all of these special cases. The asymptotic behavior is obtained for this function for all real values of the parameter.


Book ChapterDOI
01 Jan 1993
TL;DR: These tools are presented that permit the representation and automatic handling of general exp-log asymptotic expansions of a form more complicated than mere Puiseux series.
Abstract: In many applications, one encounters asymptotic expansions of a form more complicated than mere Puiseux series. Existing computer algebra systems lack good algorithms for handling such asymptotic expansions. We present tools that permit the representation and automatic handling of general exp-log asymptotic expansions.

Book ChapterDOI
01 Jan 1993
TL;DR: This paper summarizes some recent advances in numerical analysis for PDEs, particularly those in algebraic domain decomposition techniques, and demonstrates how such methods may be combined with asymptotic methods to provide robust and effective solvers.
Abstract: This paper summarizes some recent advances in numerical analysis for PDEs, particularly those in algebraic domain decomposition techniques, and demonstrates how such methods may be combined with asymptotic methods to provide robust and effective solvers.

Book ChapterDOI
H. Herwig1
01 Jan 1993
TL;DR: In this article, a new way of turbulence modeling is proposed, called indirect turbulence modeling, which may be characterized as an asymptotically motivated ad hoc model, and two examples are given for this kind of turbulence modelling: turbulent Couette flow with heat, transfer, and Couette-Poiseuille flow with zero shear stress at the lower wall.
Abstract: Turbulence modeling is put into the perspective of a general analysis of modeling in fluid mechanics. It is argued that modeling turbulence necessarily leads to a type of model called the ad hoc model, in contrast to a more systematically deduced asymptotic model. Based on these considerations, a new way of turbulence modeling is proposed, called indirect turbulence modeling, which may be characterized as an asymptotically motivated ad hoc model. Two examples are given for this kind of turbulence modeling: turbulent Couette flow with heat, transfer, and Couette-Poiseuille flow with zero shear stress at the lower wall.

01 Jan 1993
TL;DR: In this article, the authors investigated local asymptotic theory when there are multiple solutions of the likelihood equations due to non-identifiability arising as a consequence of incomplete information.
Abstract: This paper investigates local asymptotic theory when there are multiple solutions of the likelihood equations due to non-identifiability arising as a consequence of incomplete information. Local asymptotic results extend in a stochastic way the notion of a Frechet expansion, which is then used to prove asymptotic normality of the maximum likelihood estimator under certain conditions. The local theory, which provides simultaneous consistency and asymptotic normality results, is applied to a bivariate exponential model exhibiting non-identifiability. This statistical model arises as an approximation to the distribution of observable sojourn-times in the states of a two-state Markov model of a single ion channel and the non-identifiability is a consequence of an inability to record sojourns less than some small detection limit. For each of two possible estimates, confidence intervals are constructed using the asymptotic theory. Although it is not possible to decide between the two estimates on the basis of a single realization, an appropriate solution of the likelihood equations may be found using the additional information contained in data based on two different detection limits; this is investigated numerically and by simulation.

ReportDOI
01 Jul 1993
TL;DR: In this article, the basic concepts of asymptotic analysis are introduced, including the concept of order functions and regular asmptotic expansion of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D ϵ R{sup N}.
Abstract: In this note we introduce the basic concepts of asymptotic analysis. After some comments of historical interest we begin by defining the order relations O, o, and O{sup {number_sign}}, which enable us to compare the asymptotic behavior of functions of a small positive parameter {epsilon} as {epsilon} {down_arrow} 0. Next, we introduce order functions, asymptotic sequences of order functions and more general gauge sets of order functions and define the concepts of an asymptotic approximation and an asymptotic expansion with respect to a given gauge set. This string of definitions culminates in the introduction of the concept of a regular asymptotic expansion, also known as a Poincare expansion, of a function f : (0, {epsilon}{sub o}) {yields} X, where X is a normed vector space of functions defined on a domain D {epsilon} R{sup N}. We conclude the note with the asymptotic analysis of an initial value problem whose solution is obtained in the form of a regular asymptotic expansion.