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, it was shown that the conclusion of Theorem 1 will follow from Lemma 1 when applied to equation (15) if we assume, instead of (6), The hypothesis given in Trench's theorem is sufficient to imply ( * ) but not (6).
Abstract: Remarks 1, 3 and 5 are incorrect as stated. They should be supplemented by the following observations: (i) In case the perturbing term is linear in y , i.e. f(t, y) = B(t)y , the conclusion of Theorem 1 will follow from Lemma 1 when applied to equation (15) if we assume, instead of (6), The hypothesis given in Trench's theorem is sufficient to imply ( * ) but not (6). A similar comment applies to Remark 5.
2 citations
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TL;DR: In this paper, a mathematical foundation for the law of gas-parameter stabilization during near-sonic flow of a stream around bodies, which is known in experimental aerodynamics, is presented.
Abstract: A mathematical foundation is presented for the law of gas-parameter stabilization during near-sonic flow of a stream around bodies, which is known in experimental aerodynamics. The quantitative formulation of this law relies on a simple asymptotic analysis of the solutions of the Karman equations. The numerical computation performed for the velocity field around a body of revolution whose meridian section is a Chaplygin profile confirmed the deductions of asymptotic theory to high accuracy.
2 citations
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TL;DR: In this article, a method to obtain asymptotic evaluations for double sums from the asymPTotic evaluations of a single sum was proposed. But this method requires the assumption that the Euler totient function is a function of the divisor.
Abstract: In this paper, we indicate a method to obtain asymptotic evaluations for double sums from the asymptotic evaluations of a single sum. As applications, we show that all results in the recent paper [New extensions of some classical theorems in number theory, J. Number Theory 133(13) (2013) 3771–3795] can be used to obtain some asymptotic evaluations for double sums. Further, we give asymptotic evaluations for double sums which involve the divisor and the Euler totient function.
2 citations
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TL;DR: In this article, an asymptotic approximation is applied to study the instability of slow hydromagnetic waves with magnetic diffusion, where the waves are short in some directions other than the azimuthal, and vary slowly in those directions.
2 citations