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Topology of the isometry group of the Urysohn space

Julien Melleray (2010)

Fundamenta Mathematicae

Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space ℓ²(ℕ). The proof is based on a lemma about extensions of metric spaces by finite metric spaces, which we also use to investigate (answering a question of I. Goldbring) the relationship, when A,B are finite subsets of the Urysohn space, between the group of isometries fixing A pointwise, the group...

Towards Sub-cellular Modeling with Delaunay Triangulation

G. Grise, M. Meyer-Hermann (2010)

Mathematical Modelling of Natural Phenomena

In this article a novel model framework to simulate cells and their internal structure is described. The model is agent-based and suitable to simulate single cells with a detailed internal structure as well as multi-cellular compounds. Cells are simulated as a set of many interacting particles, with neighborhood relations defined via a Delaunay triangulation. The interacting sub-particles of a cell can assume specific roles – i.e., membrane sub-particle, internal sub-particle, organelles, etc –,...

Towards the determination of the regular n -covers of P G 3 , q

Martin Oxenham, Rey Casse (2003)

Bollettino dell'Unione Matematica Italiana

A set of lines S of P G 3 , q is said to cover a point P of P G 3 , q n times if there are exactly n lines of S incident with P . An n -cover of P G 3 , q is a set of lines of P G 3 , q which covers each point of P G 3 , q n times. In this paper, the properties and known examples of n -covers...

Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

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