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: The equichordal problem was first raised by Klee as discussed by the authors, who pointed out that the existence of a simple closed curve with two equichoral points is very unlikely, but no proof demonstrating the nonexistence has yet been given.
Abstract: The equichordal problem asks whether there exists an equichordal curve, i.e. a simple closed curve in the plane with two equichordal points. An equichordalpoint of a simple closed curve is a point such that every line passing through the point meets the curve in exactly two points and all chords determined in this way have the same length. According to Klee [5] the problem was first raised by Fujiwara [4] in 1916 and independently by Blaschke, Rothe and Weitzenb ck [1] in 1917. The problem has been investigated by S ss [10], Dirac [2], Wirsing [11], Ehrhart [3] and others. Several of these authors pointed out that the existence of an equichordal curve is very unlikely but no proof demonstrating the nonexistence has been given so far.
10 citations
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TL;DR: In this article, a matched asymptotic expansion for the eigenvalues arising in perturbations about the Blasius solution was proposed, and good agreement was obtained with the numerical results of Libby.
Abstract: A further term is found in the asymptotic expansion suggested by Stewartson for the eigenvalues arising in perturbations about the Blasius solution. The method employed is that of matched asymptotic expansions, and good agreement is obtained with the numerical results of Libby.
10 citations
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TL;DR: In this article, the authors consider systems of the form (1) on the semiaxis, where is a column vector with components, is an matrix, and is a parameter.
Abstract: In this paper we consider systems of the form (1)on the semiaxis , where is a column vector with components, is an matrix, and is a parameter. We pose the problem of finding the asymptotic behavior of the solutions of equation (1) as and .
10 citations
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10 citations
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TL;DR: In this article, the junction problem on the union of two bodies: a thin cylinder and a massive body with an opening into which this cylinder has been inserted was considered, and the asymptotic behaviour of a solution was studied.
Abstract: We consider the junction problem on the union of two bodies: a thin cylinder and a massive body with an opening into which this cylinder has been inserted. The equations on and contain the operators and (where is a large parameter and is the Laplacian): Dirichlet conditions are imposed on the ends of and Neumann conditions on the remainder of the exterior boundary. We study the asymptotic behaviour of a solution as . The principal asymptotic formulae are as follows: on and on , where is a solution of the Neumann problem in and the Dirac function is distributed along the interval with density . The functions and , depending on the axis variable of the cylinder, are found as solutions of a so-called resulting problem, in which a second-order differential equation and an integral equation (principal symbol of the operator ) are included. In the resulting problem the large parameter remains. Various methods of constructing its asymptotic solutions are discussed. The most interesting turns out to be the case ) (even the principal terms of the functions and are not found separately). All the asymptotic formulae are justified; the remainders are estimated in the energy norm.
10 citations