Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 2012TL;DR: In this article, several asymptotic methods have been developed for the derivation of the evolution equations which describe how some dynamical variables evolve in time and space, which are not integrable by analytic methods.
Abstract: Many physical systems involving nonlinear wave propagation include the effects of dispersion, dissipation, and/or the inhomogeneous property of the medium. The governing equations are usually derived from conservation laws. In simple cases, these equations are hyperbolic. However, in general, the physical processes involved are so complex that the governing equations are very complicated, and hence, are not integrable by analytic methods. So, special attention is given to seeking mathematical methods which lead to a less complicated problem, yet retain all of the important physical features. In recent years, several asymptotic methods have been developed for the derivation of the evolution equations which describe how some dynamical variables evolve in time and space.
1 citations
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TL;DR: In this article, an asymptotic expansion in integer nonnegative powers of small parameter for a solution of a discrete optimal control problem for one class of weakly controllable systems is constructed by substituting an assumed expansion into the problem conditions and obtaining a series of problems in the coefficients of the coefficients.
Abstract: An asymptotic expansion in integer nonnegative powers of small parameter for a solution of a discrete optimal control problem for one class of weakly controllable systems is constructed by substituting an assumed asymptotic expansion into the problem conditions and obtaining a series of problems in the coefficients of the asymptotics. Conditions of existence of a solution to the perturbed problem for sufficiently small values of the parameter are found. Estimates of closeness of the approximate and exact solutions in terms of trajectory, control, and functional are obtained. The values of the minimized functional are proven not to increase when higher-order asymptotic approximations of the optimal control are used. The discussion is illustrated by examples.
1 citations
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TL;DR: In this article, an integral statistic for the testing of the independence of the coordinates of a two-dimensional random vector is introduced, and with its aid one computes the Bahadur exact slope of the considered sequence of statistics for close noncontinual alternatives.
Abstract: One introduces an integral statistic for the testing of the independence of the coordinates of a two-dimensional random vector. One finds the coarse asymptotic behavior of the probabilities of large deviations of this statistic and with its aid one computes the Bahadur exact slope of the considered sequence of statistics for close noncontinual alternatives. One investigates the Bahadur efficiency and the structure of the domain of the local asymptotic optimality of this sequence.
1 citations
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TL;DR: In this paper, a survey of asymptotic expansions of Green's function of the Cauchy problem for the heat equation is presented, with the basic attention devoted to the first two terms of the logarithmic Asymptotics which are obtained locally by probabilistic methods and globally by convolution of the sequence of solutions over small time.
Abstract: In the survey results are presented related to the construction of asymptotic expansions of Green's function of the Cauchy problem for the heat equation. The basic attention is devoted to the first two terms of the logarithmic asymptotics which are obtained “locally” by probabilistic methods and “globally” by the method of convolution of the sequence of asymptotic solutions over small time.
1 citations