Anosova, Olga and Kurlin, Vitaliy 
ORCID: 0000-0001-5328-5351
(2023)
Density functions of periodic sequences of continuous events.
[Preprint]
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Abstract
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 change due to small noise in measurements. For any integer k>=0, the density function of a periodic set S was previously defined as the fractional volume of all k-fold intersections (within a minimal cell) of balls that have a variable radius t and centers at all points of S. This paper introduces the density functions for periodic sets of points with different initial radii motivated by atomic radii of chemical elements and by continuous events occupying disjoint intervals in time series. The contributions are explicit descriptions of the densities for periodic sequences of intervals. The new densities are strictly stronger and distinguish periodic sequences that have identical densities in the case of zero radii.
| Item Type: | Preprint |
|---|---|
| Additional Information: | 16 pages, 12 figures, the latest version is maintained at http://kurlin.org/projects/periodic-geometry/densities-sequences-intervals.pdf. arXiv admin note: text overlap with arXiv:2205.02226 |
| Uncontrolled Keywords: | cs.CG, cs.CG, math.MG, 68U05, 51K05, 51N20, 51F30, 51F20 |
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 04 Oct 2023 08:07 |
| Last Modified: | 14 Mar 2024 17:32 |
| DOI: | 10.48550/arxiv.2301.05137 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3173403 |
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