Zobrazeno 1 - 10
of 101
pro vyhledávání: '"51F20"'
Publikováno v:
Published in IUCrJ, v.11 (4), 2024
This paper was motivated by the articles "Same or different - that is the question" in CrystEngComm (July 2020) and "Change to the definition of a crystal" in the IUCr newsletter (June 2021). Experimental approaches to crystal comparisons require rig
Externí odkaz:
http://arxiv.org/abs/2406.12894
Autor:
Banakh, Taras
Following Will Brian, we define a metric space $X$ to be $Banakh$ if all nonempty spheres of positive radius $r$ in $X$ have cardinality $2$ and diameter $2r$. Standard examples of Banakh spaces are subgroups of the real line. In this paper we study
Externí odkaz:
http://arxiv.org/abs/2305.07354
Autor:
Widdowson, Daniel, Kurlin, Vitaliy
Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances. Rigid patterns
Externí odkaz:
http://arxiv.org/abs/2303.15385
Autor:
Kurlin, Vitaliy
A finite set of unlabelled points in Euclidean space is the simplest representation of many real objects from mineral rocks to sculptures. Since most solid objects are rigid, their natural equivalence is rigid motion or isometry maintaining all inter
Externí odkaz:
http://arxiv.org/abs/2303.14161
Autor:
Kurlin, Vitaliy
This paper solves the continuous classification problem for finite clouds of unlabelled points under Euclidean isometry. The Lipschitz continuity of required invariants in a suitable metric under perturbations of points is motivated by the inevitable
Externí odkaz:
http://arxiv.org/abs/2303.13486
Autor:
Anosova, Olga, Kurlin, Vitaliy
Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are determined in a rigid form but any minimal cells can discontinuously c
Externí odkaz:
http://arxiv.org/abs/2301.05137
Autor:
Lebedeva, Nina, Petrunin, Anton
Publikováno v:
Algebra i Analiz 35:3 (2023), 52--56
A metric space is said to be all-set-homogeneous if any of its partial isometries can be extended to a genuine isometry. We give a classification of a certain subclass of all-set-homogeneous length spaces.
Comment: English+Russian, 4+4 pages, 1+
Comment: English+Russian, 4+4 pages, 1+
Externí odkaz:
http://arxiv.org/abs/2211.09671
Autor:
Kurlin, Vitaliy
Publikováno v:
MATCH Communications in Mathematical and in Computer Chemistry, v.91 (2024), p.79-108
The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalence between clouds of atoms is rigid motion, which is a composition of t
Externí odkaz:
http://arxiv.org/abs/2207.08502
Autor:
Wahlberg, Mats
This thesis presents the strong and weak forms of the Banach-Tarski paradox based on the Hausdorff paradox. It provides modernized proofs of the paradoxes and necessary properties of equidecomposable and paradoxical sets. The historical significance
Externí odkaz:
http://arxiv.org/abs/2206.13512
Autor:
Heidari, Fahimeh, Honari, Bijan
In this paper, we introduce the notion of a total polar for an arbitrary subspace of a Cayley-Klein space in an analytical framework. We show that the set of all total polars of a subspace is a Schubert variety. The notion of total polar gives a defi
Externí odkaz:
http://arxiv.org/abs/2201.10330