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: A turning-point theory is developed for the second-order difference equation where the coefficients An and Bn have asymptotic expansions of the form θ≠0 being a real number and it is shown how the Airy functions arise in the uniform asym PT expansion of the solutions to this three-term recurrence relation.
Abstract: A turning-point theory is developed for the second-order difference equation
$$$$
where the coefficients An and Bn have asymptotic expansions of the form
$$$$
θ≠0 being a real number. In particular, it is shown how the Airy functions arise in the uniform asymptotic expansions of the solutions to this three-term recurrence relation. As an illustration of the main result, a uniform asymptotic expansion is derived for the orthogonal polynomials associated with the Freud weight exp(−x4), xℝ.
53 citations
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TL;DR: In this article, the asymptotic form of fixed-point solutions in functional truncations, in particular the f(R) approximation, has been studied both physically and mathematically.
Abstract: As already hinted at in Sect. 1.4.3, in order to understand fixed point solutions of the RG equation both physically and mathematically it is necessary to study their asymptotic behaviour. In this chapter we explain how to find the asymptotic form of fixed-point solutions in functional truncations, in particular the f(R) approximation.
53 citations
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TL;DR: In this paper, a general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems.
Abstract: A general asymptotic method based on the work of Krylov-Bogoliubov is developed to obtain the response of nonlinear over damped systems. A second-order system with both roots real is treated first and the method is then extended to higher-order systems. Two illustrative examples show good agreement with results obtained by numerical integration.
53 citations
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18 Jul 2005
TL;DR: Asymptotic methods provide considerable physical insight and understanding of diffraction mechanisms and are very useful in the design of electromagnetic devices such as radar targets and antennas.
Abstract: Asymptotic methods provide considerable physical insight and understanding of diffraction mechanisms and are very useful in the design of electromagnetic devices such as radar targets and antennas. However, difficulties can arise when trying to solve problems using multipole and asymoptotic methods together, such as in radar cross section objects.
53 citations
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TL;DR: In this article, it was shown that the asymptotic analysis for spectral densities arising from elliptic pseudodifferential operators is equivalent to the Cesaro and parametric behaviours of distributions at infinity.
Abstract: Modulo the moment asymptotic expansion, the Cesaro and parametric behaviours of distributions at infinity are equivalent. On the strength of this result, we construct the asymptotic analysis for spectral densities, arising from elliptic pseudodifferential operators. We show how Cesaro developments lead to efficient calculations of the expansion coefficients of counting number functionals and Green functions. The bosonic action functional proposed by Chamseddine and Connes can more generally be validated as a Cesaro asymptotic development.
52 citations