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 exactness of asymptotic expansions of the central limit theorem has been studied, and new explicit estimates of exactness for expansions of this theorem have been given.
Abstract: This paper gives new explicit estimates of exactness for asymptotic expansions in the central limit theorem.
2 citations
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TL;DR: In this paper, a simplified asymptotic expansion for large positive values of s is constructed for the integral transform, where the modified Bessel function of the third kind of purely imaginary order is defined.
Abstract: A simplified asymptotic expansion valid for large positive values of s is constructed for the integral transform ^dx m = Kis{x)f{x) ^ where Ki,{x) denotes the modified Bessel function of the third kind of purely imaginary Order. The expansion applies to functions f{x) that are analytic in some sector containing the half plane Re{x) > 0 and are exponentially damped as a: —̂ oo in this half plane.
2 citations
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TL;DR: In this article, the problem of asymptotic equivalence of non-homogeneous differential equations with exponentially equivalent right-hand sides was studied, and with the help of this result, the behavior of solutions to nonhomogeneous solutions to nonsmooth differential equations was described.
Abstract: This paper is devoted to the problem of asymptotic equivalence of $n$-th order differential equations with exponentially equivalent right-hand sides. With the help of this result asymptotic behavior of solutions to nonhomogeneous differential equations is described.
2 citations
01 Jan 2011
2 citations
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TL;DR: In this paper, the Galerkin and compactness method in approximate Sobolev spaces with weight was used to prove the existence of a unique weak solution of the boundary value problem, and the asymptotic behavior of the solution u/ depending on /i as ft 0+.
Abstract: We study the following nonlinear boundary value problem (*) ^£(xV(x) | p \"V(x) ) + /(*,«(«)) = *•(*),<> < X < 1, | lim xPu'ix)I < +oo, |w ' ( l ) | p ~V( l ) + hu(l) = g, s—»0_|_ where 7 > 0,p > 2,h > 0,g axe given constants, / , F are given functions. In this paper, we use the Galerkin and compactness method in approximate Sobolev spaces with weight to prove the existence of a unique weak solution of the problem (*). Afterwards, we also study the asymptotic behavior of the solution u/, depending on /i as ft 0+. We also obtain that the function h 1—> |u h ( l ) | is nonincreasing on (0, +00).
2 citations