Showing papers on "Asymptotology published in 1978"
20 citations
19 citations
TL;DR: In this article, a ray method is presented for obtaining short time asymptotic solutions of diffusion equations in several dimensions, where the solutions are valid for $t \ll N$ generation times, where t is time and N is the population size.
Abstract: A variety of stochastic models in population genetics, which lead to diffusion equations in several dimensions, are described. Because these equations are difficult to solve, a ray method is presented for obtaining short time asymptotic solutions of them. The solutions are valid for $t \ll N$ generation times, where t is time and N is the population size. The method is applied to a general two dimensional boundary value problem with densities on the boundaries and at the corners. Then the resulting asymptotic solution is specialized to cases of independent traits. For a particular equation, this asymptotic solution is shown to agree with the asymptotic expansion of the exact solution. The method permits the analysis of models with more than two alleles at a locus, and with many loci. It was previously used by Voronka and Kelley [20] on problems in one dimension, and the results were in good agreement with some known exact solutions for t as large as N generation times
13 citations
TL;DR: A short review of the various problems which arise in connection with the use of asymptotic methods in the optimal control of distributed systems is presented.
13 citations
TL;DR: In this article, a new high-frequency asymptotic theory of propagation in ducts with continuously varying refractive index is presented, based on local wave fields with complex phase and constitutes a special application of the evanescent wave tracking theory developed by the authors.
Abstract: A new high‐frequency asymptotic theory of propagation in ducts with continuously varying refractive index is presented. The theory is based on local wave fields with complex phase and constitutes a special application of the evanescent wave tracking theory developed by the authors. It is shown, for analytic profiles and for refractive indexes that vary only transversely to the duct direction, how the coefficients in the asymptotic expansion are evaluated explicitly. When the method is applied to parabolic and hyperbolic secant profiles for which exact solutions of the wave equation are available, the asymptotic expansions so generated agree term by term with the asymptotically expanded exact results. The method is then applied to a class of polynomial profiles for which exact results in terms of known functions are not available.
8 citations
TL;DR: In this article, various asymptotic phenomena exhibited by solutions of singularly perturbed Robin boundary value problems are studied in the case when the right-hand side grows faster than the square of the derivative.
7 citations
7 citations
6 citations
6 citations
TL;DR: In this article, the authors studied uniform approximation of functions in a fixed subset of OFnOD by functions holomorphic in D. The method of proof will depend on the results in [10] where the special case E = 8FnSD is studied.
Abstract: If h exists whenever f and e are given, F is called a set of uniform approximation for H(D). Arakelian [1] has given a complete geometrical description of these sets: \"F is a set of uniform approximation for H(D) if and only if D*\\ F is connected and locally connected, where D* denotes the one point compactification of D\". If E is a fixed subset of OFnOD, let A~F) denote all continuous functions f on FuE such that flee A(F). (We assume F carries the induced spherical metric.) In § 1 we study uniform approximation of functions in AE(F) by functions holomorphic in D. The sets of uniform approximation are given a geometrical description which coinsides with Arakelians if E is empty. The method of proof will depend on the results in [10] where the special case E= 8FnSD is studied. Consider now a set F which is a set of uniform approximation for H(D). Given f and e we can then seek a better approximant hlEH(D ) such that If(z)-hl(z)l
TL;DR: In this article, the construction of uniform asymptotic expansions of parabolic cylinder functions based on integral representations and the theory of linear differential equations has been studied, and some previous errors in the literature are corrected.
Abstract: Methods are discussed for the construction of uniform asymptotic expansions of parabolic cylinder functions of large order, based on integral representations and the theory of linear differential equations. Some previous errors in the literature are corrected.
TL;DR: In this article, a simple "asymptotic dynamics" for four-dimensional gauge theories is obtained allowing an explicit construction of asymptotic spaces, and the structure of these spaces is studied; and in particular one proves that for Abelian theories they contain states with an arbitrary number of particles and antiparticles.
Abstract: Rigorous methods are used to analyze the asymptotic (large time) behavior of gauge-theory Hamiltonians in the interaction picture. A simple ''asymptotic dynamics'' for four-dimensional gauge theories is obtained allowing an explicit construction of asymptotic spaces. The structure of these spaces is studied; and in particular one proves that for Abelian theories they contain states with an arbitrary number of particles and antiparticles, whereas for non-Abelian theories either the symmetry is spontaneously broken or the asymptotic space contains no states with observable charges.
TL;DR: In this paper, a uniform asymptotic approximation for the Fourier integral for all qh > 0 was developed for the first L + 2 derivatives of f(y) for q > 0.
Abstract: A uniform asymptotic approximation which can be used for all qh > 0 is developed for the Fourier integral z (-,/Y2_ q2) 1(h) = 2 2 1/2 sin yhdy (Y -q ) under the assumptions that hz >> 1, that the first L + 2 derivatives of f(y) are continuous for 0 > q.
TL;DR: In this article, two nonlinear ordinary differential systems, one of which contains impulses are considered, and assuming the existence of bounded solutions, some results on asymptotic equivalence type correspondence between them are obtained.
Abstract: Two nonlinear ordinary differential systems, one of which contains impulses are considered in this note, and assuming the existence of bounded solutions, some results on asymptotic equivalence type correspondence between them are obtained. At the end an open question is posed.
01 Jan 1978
01 Jan 1978
01 Jan 1978
TL;DR: The aim of this paper is to provide a tool for an analysis of the asymptotic behaviour (in shorts asymptic analysis) of dynamical systems by using a discrete time, state space description of the system.
Abstract: The aim of this paper is to provide a tool for an analysis of the asymptotic behaviour (in shorts asymptotic analysis) of dynamical systems. I shall use a discrete time,state space description of the system (cf. section 1). Let us assume that some properties of the asymptotic behaviour of a particular system are expected on heuristic grounds — a situation that may arise in two different ways:
1)
The behaviour of the system has been observed thoroughly for a long time,
2)
The system has been designed to achieve a certain goal asymptotically.
TL;DR: In this article, it was shown that integral functions have regular asymptotic behaviour outside a set of circles with centers and radii of radius t and radius t for which it is possible to obtain a regular integral function that has regular behavior outside a circle.
Abstract: Let/(z) be an integral function satisfying ,+ dr /\"{logm(r,f) cos wp log M(r,/)}\" -^-¡ and . ,. log M(r,f) 0< hm-< oo f-»0O *\" for some p: 0 < p < 1. It is shown that such functions have regular asymptotic behaviour outside a set of circles with centres £¡ and radii t¡ for which