Discrete Geometry and Mathematical Morphology - Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24-27, 2022, Proceedings
Discrete Geometry and Mathematical Morphology - Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24-27, 2022, Proceedings
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离散几何与数学形态学 - 第二届国际联合会议，DGMM 2022，法国斯特拉斯堡，2022 年 10 月 24-27 日，论文集
DOI：
10.1007/978-3-031-19897-7_31
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Anosova O
中科院分区：
文献类型：
--
作者：
Anosova O
本文为周期几何的新兴领域做出了贡献，该领域通过度量几何的新方法研究固体晶体材料（晶体）的连续空间。由于晶体结构是以刚性形式确定的，因此它们最强的实际等效性是刚性运动或保持点间距离的等距。任何晶体最基本的模型都是所有原子中心的周期性点集。之前的工作引入了密度函数的无限序列，它们是周期点集的连续等距不变量。事实证明，即使在 1 维中，对于直线上的点的周期序列，这些密度函数也非常重要。本文全面描述了任意周期序列的密度函数及其对称性。明确的描述证实了先前通过有限样本计算的密度函数的一致性。
This paper contributes to the emergent area of Periodic Geometry, which studies continuous spaces of solid crystalline materials (crystals) by new methods of metric geometry. Since crystal structures are determined in a rigid form, their strongest practical equivalence is rigid motion or isometry preserving inter-point distances. The most fundamental model of any crystal is a periodic set of points at all atomic centers. The previous work introduced an infinite sequence of density functions that are continuous isometry invariants of periodic point sets. These density functions turned out to be highly non-trivial even in dimension 1 for periodic sequences of points in the line. This paper fully describes the density functions of any periodic sequence and their symmetry properties. The explicit description confirms coincidences of density functions that were previously computed via finite samples.