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Showing papers on "Asymptotology published in 1980"



Journal ArticleDOI
TL;DR: In this article, a method based on the use of certain asymptotic initial conditions together with the compound matrix method is presented for the numerical solution of the Orr-Sommerfeld equation on infinite intervals.

37 citations


Journal ArticleDOI
A. Ahmed1
TL;DR: In this article, a sufficient condition for asymptotic stability based on the state-space representation is developed for two-dimensional discrete linear systems in the case of 2-D separable systems.
Abstract: A sufficient condition for asymptotic stability based on the state-space representation is developed for two-dimensional discrete linear systems In the case of 2-D separable systems, necessary and sufficient conditions for asymptotic stability are obtained Necessary conditions for asymptotic stability are also given

36 citations


Journal ArticleDOI
TL;DR: In this paper, the authors extend the theory to provide stability criteria for periodic solutions which are known to exist but for which the first term of the asymptotic expansion does not determine stability.

20 citations


Journal ArticleDOI
TL;DR: In this article, the authors demonstrate that well-constructed error bounds for asymptotic approximations can provide useful analytical insight into the nature and reliability of the approximati...
Abstract: The purpose of this paper is to demonstrate that well-constructed error bounds for asymptotic approximations can provide useful analytical insight into the nature and reliability of the approximati...

17 citations



Journal ArticleDOI
TL;DR: Asymptotic expansions for the solution to hyperbolic systems with different time scales in one space dimension were derived in this paper for the general case with singular coefficients at the boundary.
Abstract: Asymptotic expansions are derived for the solution to hyperbolic systems with different time scales in one space dimension. The derivation is made for the general case with singular coefficients at the boundary.

14 citations



Book ChapterDOI
01 Jan 1980
TL;DR: In this paper, a certain class of continuous time parameter Markov processes is considered, whose probability law depends on a k-dimensional parameter, and under suitable regularity conditions, several asymptotic results are devived.
Abstract: In this paper, a certain class of continuous time parameter Markov processes is considered, whose probability law depends on a k-dimensional parameter. Then, under suitable regularity conditions, several asymptotic results are devived. These results are sufficient to allow us to draw statistical inferences about the stochastic processes in question.

10 citations


Journal ArticleDOI
TL;DR: In this paper, the occurrence of complicated or erratic asymptotic behavior in non-conservative dynamical systems has been linked by Ruelle and Takens to the appearance of strange attractors.
Abstract: The occurrence of complicated or erratic asymptotic behavior in nonconservative dynamical systems has been linked by Ruelle and Takens to the appearance of strange attractors.' While there are numerical mcthods that indicate the presence of these attractors (e.g.. exponential growth of tangent vectors or continuous frequency spectrums2). there are very few results to date that actually prove the existence of such attractors. Indeed, this has only been done in highly specialized cases (e.g., perturbation of quasi-periodic motion'). One is faced with two fundamental and largely unsolved problems:

10 citations



Journal ArticleDOI
TL;DR: In this article, the asymptotic expansions of a wide class of Gaussian function space integrals are described and analyzed for both the nondegenerate case and the degenerate case.
Abstract: Function space integrals are useful in many areas of mathematics and physics. Physical problems often give rise to function space integrals depending on a parameter and the asymptotics with respect to the parameter yield important information about the original problem. The purpose of this note is to describe the asymptotic expansions of a wide class of Gaussian function space integrals. Related work has been done by [Varadhan], [Schilder], [Pincus], [Donsker-Varadhan], and [Castro]. All asymptotic expansions previously obtained assume a nondegeneracy condition which assures that one never strays too far from the realm of Gaussian processes. Our results cover both the nondegenerate case and the degenerate case, the analysis of the latter being much more subtle. In the degenerate case, the leading asymptotic behavior is non-Gaussian. Let PA be a mean zero Gaussian probability measure with covariance operator A on a separable Hubert space tf. Our methods can also handle certain Banach spaces, such as C[0, 1], which are important in applications. Let # and F be suitably bounded, real C°° functionals on H. We study the asymptotics of



Journal ArticleDOI
TL;DR: In this article, the consistency of the Maximum Likelihood Estimator (MLE) of the unknown system parameter of a stochastic differential equation system with constant coefficients is proved.
Abstract: In this paper the consistency of the Maximum-Likelihood-Estimator of the unknown system parameter of a inhomogeneous stochastic differential equation system with constant coefficients is proved. Sufficient conditions are given for the asymptotic normality and asymptotic efficiency of the MLE in the stable case.

Journal ArticleDOI
TL;DR: Genera t ing functions for the number of fanout-free and cascade networks and a set of symmetric gates are studied, finding that the average number of gates in n-input networks grows near ly with n, in contrast to the situation when a much larger set of gates is al lowed.
Abstract: Genera t ing functions for the number o f fanout-free and cascade networks buil t f rom an a rb i t ra ry set of symmetric gates are studied Recurslons and asymptot ic estimates are obtained. The average number o f gates in n-input networks .s studied It grows hnear ly with n, in contrast to the situation when a much larger set o f gates is al lowed

Book ChapterDOI
F. Rothe1
TL;DR: For Fisher's diffusion model which describes the advance of an advantageous gene, the following two questions are discussed: Existence of travelling fronts and convergence to travelling fronts as mentioned in this paper. And there are striking differences between the heterozygote intermediate and the heter-ozygote inferior case.
Abstract: For Fisher’s diffusion model which describes the advance of an advantageous gene, the following two questions are discussed: Existence of travelling fronts and convergence to travelling fronts. There are striking differences between the heterozygote intermediate and the heterozygote inferior case.




Book ChapterDOI
01 Jan 1980

Journal ArticleDOI
TL;DR: One general and three specialized models of the Bush-Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced as discussed by the authors, and the random sequences of response probabilities and of responses associated with the different models are considered.
Abstract: One general and three specialized models of the Bush–Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced. Inhomogeneity is admitted. The random sequences of response probabilities and of responses associated with the different models are considered. Information about the existence and the distribution of asymptotic response probabilities is provided. The stress is on sufficient and necessary conditions for convergence (a.s. or with positive probability) of the response sequence, which is what ‘learning' means.

Journal ArticleDOI
TL;DR: In this paper, the existence and the asymptotic behavior of solutions of a class of singularly perturbed second-order Robin boundary value problems are studied by means of nonlinear stability theory.
Abstract: : The existence and the asymptotic behavior of solutions of a class of singularly perturbed second-order Robin boundary value problems are studied by means of nonlinear stability theory. Several examples are discussed in detail. (Author)

Book ChapterDOI
01 Jan 1980


Book ChapterDOI
01 Jan 1980
TL;DR: In this article, the problem of proving asymptotic completeness in N-body quantum scattering is reduced to the proof of existence of certain strong limits closely related to the adjoints of the wave operators and certain spectral information about the M-body subsystems with 2 ~< M ~< N-1.
Abstract: The present work is motivated by the paper of DEIFT and SIMON [1] in which the problem of proving asymptotic completeness in N-body quantum scattering is reduced to the proof of existence of certain strong limits closely related to the adjoints of the wave operators and certain spectral information about the M-body subsystems with 2 ~< M ~< N-1. This "geometric" approach is time-dependent in character as contrasted with the time-independent character of the more customary approach involving resolvents. DEIFT and SIMON describe the difficulties involved in the application of the latter approach and we refer to their paper for these details as well as for references to recent work.

Journal ArticleDOI
TL;DR: In this article, the authors derived a uniformly valid asymptotic approximation of the periodic solution of a self-excited system given by the differential equation, where β1,β2, is a positive constant.
Abstract: In this paper we derive a uniformly valid asymptotic approximation of the periodic solution of a self-excited system given by the differential equation and β1,β2, are positive constants. By uniformly valid asymptotic approximation we mean that no secular terms are present. Our procedure makes use of a nonlinear change of independent variable that transforms the problem from one in which the discontinuities are ϵ dependent to one in which the discontinuities are ϵ independent. We obtain an asymptotic approximation up to order ϵ of the periodic solution and an asymptotic approximation up to order ϵ2 of the period. Some comparisons between our asymptotic results and numerically derived results are given. Application of our technique to other examples of self-excited systems is discussed. The equation is investigated in detail.