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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 article, the authors define a notion of system of sets with multiplicative asymptotic density and define a criterion and one necessary condition for a given system i = 1∞ to be a system with multiscale density.
Abstract: The authors define a notion of system of sets with multiplicative asymptotic density in this paper. A criterion and one necessary condition for a given system {Ai}i=1∞ to be a system with multiplicative asymptotic density is given. Properties of certain special types of systems of sets with multiplicative asymptotic density are treated.

2 citations

01 Jan 2016
TL;DR: In this paper, it was shown that the set A = ∪3 i=0 Ag(Wi) is a minimal asymptotic basis of order four, where i = 0, 1, 2, 3, and Wi = {n ∈ N | n ≡ i (mod 4)}.
Abstract: Abstract Let N denote the set of all nonnegative integers and A be a subset of N. Let W be a nonempty subset of N. Denote by F∗(W ) the set of all finite, nonempty subsets of W . Fix integer g ≥ 2, let Ag(W ) be the set of all numbers of the form ∑ f∈F afg f where F ∈ F∗(W ) and 1 ≤ af ≤ g − 1. For i = 0, 1, 2, 3, let Wi = {n ∈ N | n ≡ i (mod 4)}. In this paper, we show that the set A = ∪3 i=0 Ag(Wi) is a minimal asymptotic basis of order four.

2 citations

Journal ArticleDOI
TL;DR: In this paper, a simple analytical approach for defining the asymptotic behavior of shell elements is proposed to define and analyse the deformation modes of selected benchmark problems suitable for the evaluation of the shell elements.

2 citations

Journal ArticleDOI
TL;DR: In this article, three lemmas are provided for additive correlation involving the Asymptotic Linearity Theorems, which were constructed for a study of the correlation between structure and properties in molecules having many identical moieties.
Abstract: The present article provides three lemmas that initiate the generalization of the theory of additive correlation involving the Asymptotic Linearity Theorems, which were constructed for a study of the correlation between structure and properties in molecules having many identical moieties. The new tools provided here also help to pave the way to linking the above theory with a theoretical framework developed for the asymptotic analysis of certain chemical kinetic network systems.

2 citations


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