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 article, several theorems were proved concerning the asymptotic behavior of Stieltjes transforms as |z| approaches infinity, in a sector of the complex z plane which does not include the cut in the transform.
Abstract: Several theorems are proved concerning the asymptotic behavior of Stieltjes transforms as |z| approaches infinity, in a sector of the complex z plane which does not include the cut in the transform. The asymptotic behavior of the transform is related to the asymptotic behavior, for large values of the argument, of the function whose transform is taken.
8 citations
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TL;DR: In this article, the Haag-Brenig theorem translated into operator language was used to obtain the asymptotic fields for a nonrelativistic self-coupled field.
8 citations
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TL;DR: In this paper, a nonstandard finite difference scheme for the Airy equation leads to a linear, second-order difference equation for which the theorems of Poincare and Perron do not apply if asymptotic representations of the solutions are desired.
Abstract: A nonstandard finite difference scheme for the Airy equation leads to a linear, second—order difference equation for which the theorems of Poincare and Perron do not apply if asymptotic representations of the solutions are desired. Using the method of dominant balance, a suggested form for the asymptotic solutions is obtained. This relation is then used to construct the required asymptotic representations for the two linearly independent solutions
8 citations
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TL;DR: In this paper, the authors considered the oscillatory and asymptotic behavior of solutions of the nonlinear difference equation of the form (1) has been considered by Thandapani and Selvaraj.
Abstract: where ∆ is the forward difference operator defined by ∆xn = xn+1 −xn, α and β are positive constants, {pn} and {qn} are positive real sequences defined for all n ∈ N(n0) = {n0, n0 + 1, ...}, and n0 a nonnegative integer. By a solution of equation (1), we mean a real sequence {xn} that satisfies equation (1) for all n ∈ N(n0). If any four consecutive values of {xn} are given, then a solution {xn} of equation (1) can be defined recursively. A nontrival solution of equation (1) is said to be nonoscillatory if it is either eventually positive or eventually negative, and it is oscillatory otherwise. The oscillatory and asymptotic behavior of solutions of the nonlinear difference equation of the form (1) has been considered by Thandapani and Selvaraj
8 citations
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TL;DR: In this paper, the authors investigated the equivalence of the concepts of strong stability and t∞-similarity for nonlinear differential systems and showed that they are equivalent under strong stability.
8 citations