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Showing papers on "Asymptotology published in 1986"


Book
01 Aug 1986

76 citations


Journal ArticleDOI
TL;DR: A general ODE model is proposed to describe epidemic systems that includes many epidemic systems already analyzed via different methods by various authors and is carried out with applications to several models.
Abstract: In this paper a general ODE model is proposed to describe epidemic systems. The mathematical structure of such a model is so general that it includes many epidemic systems already analyzed via different methods by various authors. The asymptotic analysis of the general system is carried out with applications to several models.

72 citations


Journal ArticleDOI
TL;DR: In this article, an approach to conditional inference for nonergodic stochastic process models by considering asymptotic properties was developed, and the context for most of the analysis is that of Le Cam's LAMN theory.

14 citations


Journal ArticleDOI
TL;DR: In this article, the need for a complete asymptotic analysis of these functions is discussed in the context of one-dimensional diffusion with random trapping sites and the necessary analysis is carried out.
Abstract: The solution of various diffusion problems, in both continuous and discrete systems, can be expressed in terms of a Laplace transform of the exponential function of a fractional power. In this Brief Report the need for a complete asymptotic analysis of these functions is discussed in the context of one-dimensional diffusion with random trapping sites and the necessary asymptotic analysis is carried out.

13 citations


Journal ArticleDOI
01 Dec 1986
TL;DR: Sufficient conditions for finite difference equations with a solution behaving in a precisely specified way like a given polynomial are given in this paper, and sufficient conditions for polynomials with a similar solution are also given.
Abstract: Sufficient conditions for somem-th order finite difference equations are presented which have a solution behaving in a precisely specified way like a given polynomial.

11 citations



Journal ArticleDOI
TL;DR: In this paper, the eigenvalues for the convolution operator of u where u is between 0 and 1 were found for the CNN operator with respect to the parameters of u.
Abstract: The eigenvalues are found for the convolution operator of u where u is between 0 and 1.(AIP)

7 citations



Journal ArticleDOI
TL;DR: In this article, the authors studied the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the real parts of their Laplace and Fourier transforms in a neighborhood of the origin.
Abstract: This paper studies the connection between the asymptotic and quasi-asymptotic properties at infinity of slowly increasing generalized functions with supports on the half-line and the asymptotic and quasi-asymptotic properties of the real parts of their Laplace and Fourier transforms in a neighborhood of the origin. The study is caried out in the scale of regularly varying self-similar functions. The results are applied to the study of the asymptotic properties of solutions of linear passive systems, and also to the study of the connection between Abel and Ces?ro convergence (with respect to a self-similar weight) of the Fourier-Stieltjes series of nonnegative measures. Bibliography: 13 titles.

4 citations



Journal ArticleDOI


Journal ArticleDOI
S. M. Roberts1
TL;DR: In this article, the boundary value technique is used to solve singular perturbation problems that may or may not succumb to asymptotic methods, such as the method of Carrier and Pearson.
Abstract: Singular perturbation problems not amenable to solution by asymptotic methods require special treatment, such as the method of Carrier and Pearson. Rather than devising special methods for these problems, this paper suggests that there may be a uniform way to solve singular perturbation problems, which may or may not succumb to asymptotic methods. A potential mechanism for doing this is the author's boundary-value technique, a nonasymptotic method, which previously has only been applied to singular perturbation problems that lend themselves to asymptotic techniques. Two problems, claimed by Carrier and Pearson to be insoluble by asymptotic methods, are solved by the boundary-value method.

Book ChapterDOI
01 Jan 1986
TL;DR: In this article, the authors established the asymptotic behavior of a class of discrete solutions of the Burgers' Equation and discussed the role of smoothing and filtering and the need of computing near some (hR)opt.
Abstract: Based on a Nonlinear Equivalence Theorem and a general method of error analysis, we established the asymptotic behavior of a class of discrete solutions of the Burgers’ Equation. As a model of fluid flow equations in CFD, we discussed the role of smoothing and filtering and the need of computing near some (hR)opt. for reasonable asymptotic approximations.

Journal ArticleDOI
TL;DR: In this article, the existence and convexity of a limit outputs set is proved and some asymptotic version of Lagrange's multipliers method is established, and estimates of optimal values to particular stochastic control problems are given.

Book ChapterDOI
R. Seneor1
01 Jan 1986
TL;DR: In this article, the degeneracy of the action in gauge theory has been studied in the context of logarithmic correction to the mean field picture in statistical mechanics models, which can be applied to any asymptotically free field theory provided one overcomes the difficulties linked to the formalism.
Abstract: As I said in the introduction, this method can clearly be extended to any asymptotically free field theory provided one overpasses the difficulties linked to the formalism (as for example the degeneracy of the action in gauge theory). It can also be applied to study logarithmic correction to the mean field picture in statistical mechanics models.


Journal ArticleDOI
TL;DR: In this paper, three basic asymptotic normality conditions for limiting discrete distributions are given in terms of differencing operators, which can be used to establish normality by directly dealing with the limiting behaviors of distribution functions themselves.
Abstract: Three basic asymptotic normality conditions for limiting discrete distributions are given in terms of differencing operators. Under these conditions one can establish asymptotic normality by directly dealing with the limiting behaviors of distribution functions themselves without resorting to the central limit theorem.