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Showing papers on "Asymptotology published in 1966"




Journal ArticleDOI
TL;DR: The importance of asymptotic analysis in applied mathematics was discussed in this article, where the authors discuss the importance of the Asymptotics in the application of applied mathematics.
Abstract: (1966). The Importance of Asymptotic Analysis in Applied Mathematics. The American Mathematical Monthly: Vol. 73, No. 1, pp. 7-14.

12 citations





Journal ArticleDOI
TL;DR: In this paper, a proof of their main asymptotic results is given, which depends on substantially weakened hypotheses and is based on the mathematical basis of their method of inequalities.
Abstract: Ho & Meyer [1] have sketched an argument for arriving at asymptotic properties of solutions of a pair of non-linear conservation laws with floating, shocktype boundary condition of importance in gas dynamics and oceanography. To clarify the mathematical basis of their method of inequalities, a proof of their main asymptotic results is given here. It depends on substantially weakened hypotheses.

7 citations



Journal ArticleDOI
TL;DR: In this paper, the derivation of asymptotic expansions for functions of a certain class is studied, which satisfy a differential equation in a variablez and a recursion in a parametern and include most of the classical functions of Mathematical Physics.
Abstract: The paper deals with the derivation of asymptotic expansions for functions of a certain class. The functions concerned satisfy a differential equation in a variablez and a recursion in a parametern and include most of the classical functions of Mathematical Physics.

3 citations



Journal ArticleDOI
01 Oct 1966-Nature
TL;DR: In the case of normal diffusion, the distribution of the overflow may be found by evaluating its moment generating function, and there is an alternative and more general method, which is useful when only the expected overflow is required.
Abstract: IN a previous communication1, an asymptotic theory was outlined for the probabilistic behaviour of a finite dam or reservoir subject to random input and output. A further problem raised by Herman Rubin—that of the amount of water lost by overflow—may be solved by similar methods. In the case of normal diffusion which is treated here, the distribution of the overflow may be found by evaluating its moment generating function. There is an alternative and more general method, which is useful when only the expected overflow is required. The alternative, suggested by R. Morton, is discussed in the succeeding communication.

Book ChapterDOI
John M. Gormally1
TL;DR: In this paper, the authors summarized comments by the author on the asymptotic foundations of some perturbation methods that have been applied to problems in satellite theory and used Van der Corput's theory as a consistent basis for the perturbations.
Abstract: This paper summarizes invited comments by the author on the asymptotic foundations of some perturbation methods that have been applied to problems in satellite theory. Van der Corput's theory of asymptotic series is proposed as a consistent basis for the perturbation methods and used to establish that the perturbation series are asymptotic representations of the solutions to the applicable differential equations. It is pointed out that this asymptotic theory is concerned primarily with the existence of mathematical order of magnitude error bounds and that error bounds for practical application must be derived by independent means.

Journal ArticleDOI
TL;DR: In this article, the authors studied the production amplitudes asymptotic behavior in perturbation theory for scalar particles in λ Φ 3 topology when the number of the external lines is 6.
Abstract: In this paper we study the production amplitudes asymptotic behaviour in perturbation theory for scalar particles inλΦ3 topology when the number of the external lines is 6. The choice of independent invariants is complicated by a geometric equation expressed by the annihilation of a Grammian. We give an asymptotic solution in some particular cases (quasi-elastic processes). Some Eden's and Tiktopoulos' theorems aboutC andD properties are generalized. The calculation is performed for energies going to infinity and momentum transfers small and fixed. This can be considered a particular way to approach the multiperipheral model. The two methods of λ-transform and Mellin transform are used. We found, as expected, in some cases a Regge asymptotic behaviour.