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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TL;DR: In this paper, the authors studied the asymptotic behavior of solutions of a Schrodinger-type equation with oscillating potential, which was studied by A. Its.
Abstract: We are interested in the asymptotic behavior of solutions of a Schrodinger-type equation with oscillating potential which was studied by A. Its. Here we use a different technique, based on Levinson's Fundamental Lemma, to analyze the asymptotic behavior, and our approach leads to a complete asymptotic representation of the solutions. We also discuss formal simplifications for differential equations with what might be called “regular/irregular singular points with periodic coefficients”. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
4 citations
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TL;DR: In this article, a double asymptotic limit theory for the persistent parameter in explosive continuous time models driven by Levy processes with a large number of time span (N) and a small number of sampling interval (h) is presented.
Abstract: This paper develops a double asymptotic limit theory for the persistent parameter (k) in explosive continuous time models driven by Levy processes with a large number of time span (N) and a small number of sampling interval (h). The simultaneous double asymptotic theory is derived using a technique in the same spirit as in Phillips and Magdalinos (2007) for the mildly explosive discrete time model. Both the intercept term and the initial condition appear in the limiting distribution. In the special case of explosive continuous time models driven by the Brownian motion, we develop the limit theory that allows for the joint limits where N -> infinity and h -> 0 simultaneously, the sequential limits where N -> infinity is followed by h -> 0, and the sequential limits where h -> 0 is followed by N -> infinity. All three asymptotic distributions are the same.
4 citations
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4 citations
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TL;DR: In this paper, asymptotic expansions for the Schrodinger equation of the diamagnetic Coulomb problem with infinite nuclear mass were obtained for the non-adiabatic approximation and for finding non-trivial auto-ionizing states.
Abstract: The paper deals with asymptotic expansions in cylindrical coordinates for the Schrodinger equation of the diamagnetic Coulomb problem with infinite nuclear mass. The basis functions introduced by Liu and Starace are analysed: analytical asymptotic expansions are given for the basis functions and eigenvalues belonging to them. Using these, analytical asymptotic expansions are obtained for the coupling coefficients and solutions of the system of second-order ordinary differential equations which arise if the wavefunction is expanded in terms of the Liu - Starace basis functions. The role of the asymptotic expansions is elucidated for the numerical solution of the non-adiabatic approximation and for finding non-trivial auto-ionizing states.
4 citations