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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, asymptotic behavior of the eigenvalues of the φ-laplacian was studied. But the π-la placian is not a convex polytope.
Abstract: (1989). Asymptotic behaviour of the eigenvalues of the φ—laplacian. Communications in Partial Differential Equations: Vol. 14, No. 8-9, pp. 1059-1069.

47 citations

Journal ArticleDOI
TL;DR: The problem of asymptotic expansion of Green functions in perturbative QFT is studied in this paper for the class of Euclidean asymPTotic regimes, and it is shown that the problem reduces to the expansion of products of a class of singular functions.
Abstract: The problem of asymptotic expansion of Green functions in perturbative QFT is studied for the class of Euclidean asymptotic regimes. Phenomenological applications are analyzed to obtain a meaningful mathematical formulation of the problem. It is shown that the problem reduces to studying asymptotic expansion of products of a class of singular functions in the sense of the distribution theory. Existence, uniqueness and explicit expressions for such expansions. (As-operation for products of singular functions) in dimensionally regularized form are obtained using the so-called extention principle.

47 citations

Book
30 Oct 2009
TL;DR: This chapter discusses Stochastic processes: an overview, asymptotic distributions, categorical data models, and Regression models, which describe weak convergence and Gaussian processes.
Abstract: Exact statistical inference may be employed in diverse fields of science and technology. As problems become more complex and sample sizes become larger, mathematical and computational difficulties can arise that require the use of approximate statistical methods. Such methods are justified by asymptotic arguments but are still based on the concepts and principles that underlie exact statistical inference. With this in perspective, this book presents a broad view of exact statistical inference and the development of asymptotic statistical inference, providing a justification for the use of asymptotic methods for large samples. Methodological results are developed on a concrete and yet rigorous mathematical level and are applied to a variety of problems that include categorical data, regression, and survival analyses. This book is designed as a textbook for advanced undergraduate or beginning graduate students in statistics, biostatistics, or applied statistics but may also be used as a reference for academic researchers.

47 citations

Journal ArticleDOI
TL;DR: In this article, a vector-valued version of the asymptotic expansion is constructed, which allows us to determine the order of a Levin-type method with highly oscillatory kernels, such as Airy functions or Bessel functions.
Abstract: We present a method for the efficient approximation of integrals with highly oscillatory vector-valued kernels, such as integrals involving Airy functions or Bessel functions. We construct a vector-valued version of the asymptotic expansion, which allows us to determine the asymptotic order of a Levin-type method. Levin-type methods are constructed using collocation, and choosing a basis based on the asymptotic expansion results in an approximation with significantly higher asymptotic order.

46 citations

Journal ArticleDOI
TL;DR: In this article, a new technique is proposed for the analysis of shape optimization problems using the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains.
Abstract: A new technique is proposed for the analysis of shape optimization problems. The technique uses the asymptotic analysis of boundary value problems in singularly perturbed geometrical domains. The asymptotics of solutions are derived in the framework of compound and matched asymptotics expansions. The analysis involves the so–called interior topology variations. The asymptotic expansions are derived for a model problem, however the technique applies to general elliptic boundary value problems. The self–adjoint extensions of elliptic operators and the weighted spaces with detached asymptotics are exploited for the modelling of problems with small defects in geometrical domains. The error estimates for proposed approximations of shape functionals are provided.

46 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526