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 1995
6 citations
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TL;DR: In this article, Korn's inequalities are proved for star-shaped domains and it is shown how the constants in these inequalities depend on the dimensions of the domain, and these inequalities are then used to prove a generalisation of the Saint-Venant's Principle for nonlinear elasticity and additionally to establish the asymptotic behaviour of solutions to the traction boundary value problem for a non-prismatic cylinder.
Abstract: Korn's inequalities are proved for star-shaped domains and it is shown how the constants in these inequalities depend on the dimensions of the domain. These inequalities are then used to prove a generalisation of Saint-Venant's Principle for nonlinear elasticity and additionally to establish the asymptotic behaviour of solutions to the traction boundary value problem for a non-prismatic cylinder.
6 citations
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TL;DR: A framework that extends the look-ahead estimator to a broader range of applications is studied and a general asymptotic theory for the estimator is provided, where both L1 consistency and L2 asymPTotic normality are established.
Abstract: The look-ahead estimator is used to compute densities associated with Markov processes via simulation We study a framework that extends the look-ahead estimator to a broader range of applications We provide a general asymptotic theory for the estimator, where both L1 consistency and L2 asymptotic normality are established The L2 asymptotic normality implies √n convergence rates for L2 deviation
6 citations
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TL;DR: In this article, the authors developed asymptotic tests for the means of interval-valued population in the framework of random compact convex sets and derived analytical forms of the probability density functions for the limiting null distributions under both one-sample and two-sample settings.
6 citations
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TL;DR: In this paper, the authors discuss the asymptotic behavior of solutions to higher-order Emden-Fowler type equations with constant potential and present a classification of all solutions.
Abstract: We discuss the asymptotic behavior of solutions to a higher-order Emden–Fowler type equation with constant potential. Several author’s results are presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities. We discuss the existence and asymptotic behavior of “blowup” solutions. Results on the asymptotic behavior of oscillating solutions are formulated. For the third- and forth-order equations an asymptotic classification of all solutions is presented. Some applications of the results obtained are proposed
6 citations