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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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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.
2 citations
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TL;DR: In this paper, a reformulation of the asymptotic solution of the coupledmode equations with a periodic variation of the refractive index along the propagation length is presented, and a first-order correction using the solution and Piccard's method are also determined.
Abstract: A reformulation of the asymptotic solution of the coupledmode equations with a periodic variation of the refractive index along the propagation length is presented. A first-order correction using the asymptotic solution and Piccard’s method are also determined. It is found that the first-order solution compares very well with the numerical solution throughout a wide range of coupling parameters. The key differences between the method presented here and elsewhere reside in the derivation of the asymptotic solution as well as in the carefull derivation of the higher order corrections.
2 citations
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2 citations
01 Jan 2015
TL;DR: This part II-C of this work completes the factorizational theory of asymptotic expansions in the real domain by presenting two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymPTotic scale at an endpoint.
Abstract: This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymptotic scale at an endpoint. These algorithms arise quite naturally in our asymptotic context and prove very simple in special cases and/or for scales with a small numbers of terms. All the results in the three Parts of this work are well illustrated by a class of asymptotic scales featuring interesting properties. Examples and counterexamples complete the exposition.
2 citations