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Dergiler / Journal of Mathematical Sciences and Modelling / 2018 / Cilt: 1 - Sayı: 2

Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes

James F. PETERS
Sayfa
56–72
Yayın Tarihi
2018-09-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Several main results are given in this paper, namely, a Whitehead CW topology and a Leader uniform topology are outcomes of having a collection of vortex cycles (or nerves) equipped with a connectedness proximity and the case where each cluster of closed, convex vortex cycles and the union of the vortex cycles in the cluster have the same homotopy type.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively.
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Temel Bulgular & Veri:A vortex cycle is a collection of non-concentric, nesting 1-cycles with nonempty interiors i.e., a collection of 1-cycles that share a nonempty set of interior points and which may or may not overlap).
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Sonuç & Katkı:Several main results are given in this paper, namely, a Whitehead CW topology and a Leader uniform topology are outcomes of having a collection of vortex cycles (or nerves) equipped with a connectedness proximity and the case where each cluster of closed, convex vortex cycles and the union of the vortex cycles in the cluster have the same homotopy type.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Connectedness Proximity · CW Topology · Vortex Cycle

Abstract

This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's smoke rings. A vortex cycle is a collection of non-concentric, nesting 1-cycles with nonempty interiors i.e., a collection of 1-cycles that share a nonempty set of interior points and which may or may not overlap). Overlapping 1-cycles in a vortex yield an Edelsbrunner-Harer nerve within the vortex. Overlapping vortex cycles constitute a vortex nerve complex. Several main results are given in this paper, namely, a Whitehead CW topology and a Leader uniform topology are outcomes of having a collection of vortex cycles (or nerves) equipped with a connectedness proximity and the case where each cluster of closed, convex vortex cycles and the union of the vortex cycles in the cluster have the same homotopy type.

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Bu Makaleye Atıf Yap

PETERS, J. F. (2018). Proximal vortex cycles and vortex nerve structures. Non-concentric, nesting, possibly overlapping homology cell complexes. Journal of Mathematical Sciences and Modelling, Cilt: 1 - Sayı: 2, 56–72. https://ajindex.com/articles/777570

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Kaynakça (10)

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