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: Asymptotic property C for metric spaces was introduced by Dranishnikos as generalization of finite asymptotics -asdim as discussed by the authors, and it turns out that this property can be viewed as transfinite extension of the original metric dimension.
Abstract: Asymptotic property C for metric spaces was introduced by Dranishnikos as generalization of finite asymptotic dimension - asdim. It turns out that this property can be viewed as transfinite extension of asymptotic dimension. The original definition was given by Radul. We introduce three equivalent definitions, show that asymptotic property C is closed under products (open problem stated "Open problems in topology II") and prove some other facts, i.e. by defining dimension of a family of metric spaces. Some examples of spaces enjoying countable trasfinite asymptotic dimension are given. We also formulate open problems and state "omega conjecture", which inspired most part of this paper.
11 citations
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07 Sep 2007
TL;DR: In this article, an asymptotic expansion of the well-known Szasz-Mirakyan operators is presented, which is based on an expansion of a well known Hungarian algorithm.
Abstract: We obtain an asymptotic expansion of the well‐known Szasz‐Mirakyan operatorsWe obtain an asymptotic expansion of the well‐known Szasz‐Mirakyan operators
11 citations
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TL;DR: In this paper, the authors give a rigorous justification of the asymptotic expansion of Green's function for the diffraction problem on a smooth convex contour in the shadow zone.
Abstract: In the paper we give a rigorous justification of the asymptotic expansion of Green's function for the diffraction problem on a smooth convex contour γ in the shadow zone. We assume that one of the source and observation points is on the boundary γ and the other one outside γ. We consider the case of the Dirichlet problem.
11 citations
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TL;DR: By formulating quantum field theory with an extended object in terms of the asymptotic condition, the correlation between the extended object and the quanta is studied and several new results are derived.
Abstract: By formulating quantum field theory with an extended object in terms of the asymptotic condition, we derive several new results such as the asymptotic Hamiltonian, the asymptotic field, the generalized coordinates, etc. In this derivation no approximation (such as the tree approximation, etc.) is used. The correlation between the extended object and the quanta is studied.
11 citations
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11 citations