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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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Journal ArticleDOI
TL;DR: The asymPTotic expansion technique is applied to verify the order of accuracy of asymptotic expansion of linear and nonlinear initial value problems.

4 citations

Journal ArticleDOI
TL;DR: In this paper, a uniform asymptotic approximation of the solution of a boundary-value problem is constructed and justified up to an arbitrary power of a small parameter, where the parameter is a collection of two-dimensional elliptic equations in 2D domains depending on one parameter.
Abstract: A second order elliptic equation with a small parameter at one of the highest order derivatives is considered in a three-dimensional domain. The limiting equation is a collection of two-dimensional elliptic equations in two-dimensional domains depending on one parameter. By the method of matching of asymptotic expansions, a uniform asymptotic approximation of the solution of a boundary-value problem is constructed and justified up to an arbitrary power of a small parameter. §

4 citations

Journal ArticleDOI
TL;DR: Diverse problems arising in economics, engineering, the social sciences, medicine, physics, chemistry, and other areas can be modelled in such a way that the central limit theorem comes into play.
Abstract: 1. INTRODUCTION. In his 1974 book entitled \" The Life and Times of the Central Limit Theorem, \" Adams [1] describes this theorem as \" one of the most remarkable results in all of mathematics \" and \" a dominating personality in the world of probability and statistics. \" More than three decades later, his description is not only still pertinent but has also been corroborated and reinforced by developments in different branches of knowledge. In fact, the central limit theorem owes much of its importance to its proven application well beyond the field of probability. Diverse problems arising in economics, engineering, the social sciences, medicine, physics, chemistry, and other areas can be modelled in such a way that the central limit theorem comes into play. Empirically, one observes that a great many natural phenomena, such as the heights of individuals in a given population, obey an approximately normal distribution, that is, a symmetric bell-shaped distribution with scores more concentrated in the middle than in the tails (see Figure 1). One explanation suggested for this is that these phenomena are sums of a large number of independent random effects, none of which is predominant. Actually, the classical version of the central limit theorem asserts that the sum of many independent random variables is asymptotically normally distributed provided that each summand is small with high probability.

4 citations

Journal ArticleDOI
01 Dec 1962-Nature
TL;DR: Asymptotic approximations by Prof Harold Jeffreys Pp 144 (Oxford: Clarendon Press; London: Oxford University Press, 1962) 30s net as mentioned in this paper.
Abstract: Asymptotic Approximations By Prof Harold Jeffreys Pp 144 (Oxford: Clarendon Press; London: Oxford University Press, 1962) 30s net

4 citations


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