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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 derived asymptotic expansions of the electric dipole (E1) differential excitation function for large values of the adiabaticity parameter ξ and for all value of the eccentricity (e) of the projectile orbit.
Abstract: We have obtained asymptotic expansions of the electric dipole (E1) differential excitation function for large values of the adiabaticity parameter ξ and for all values of the eccentricity (e) of the projectile orbit. To accomplish this, we have developed a new asymptotic power series of exponential integrals related to the Airy integrals, introduced originally in a paper by Brussaard et al. [Ann. Phys. (N.Y.) 7, 47 (1962)], in which asymptotic expansions of the total excitation function were derived.

2 citations

Journal ArticleDOI
TL;DR: In this paper, a perturbation method, the Lindstedt-Poincare method, was used to obtain the asymptotic expansions of the solutions of a nonlinear differential equation arising in general relativity.
Abstract: A perturbation method, the Lindstedt-Poincare method, is used to obtain the asymptotic expansions of the solutions of a nonlinear differential equation arising in general relativity. The asymptotic solutions contain no secular term, which overcomes a defect in Khuri’s paper. A technique of numerical order verification is applied to demonstrate that the asymptotic solutions are uniformly valid for small parameter.

2 citations

01 Jan 1990
TL;DR: The theorem is called Hajek-Le Cam because it was proved by Hâjek (1972) for the asymptotically normal (more precisely LAN) case and how the theorem can be applied to problems recently studied by Donoho and Liu (1990), by M. Low (1989) and by Golubev and Nussbaum (1990).
Abstract: One of the simplest results in asymptotic theory of estimation is the Hajek-Le Cam asymptotic minimax theorem. Besides being simple, it has many applications. We review the theorem and give brief indications on some applications. The theorem is called Hajek-Le Cam because it was proved by Hâjek (1972) for the asymptotically normal (more precisely LAN) case. There was a previous theorem by Le Cam (1953). Hajek's result was substantially extended in Le Cam (1979). Section 2 below gives a summary of definitions and notation. Section 3 reviews the asymptotic minimax theorem. Section 4 indicates how the theorem can be applied to problems recently studied by Donoho and Liu (1990), by M. Low (1989) and by Golubev and Nussbaum (1990). For further applications of the asymptotic minimax theorem, see Millar (1983).

2 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526