Local groups in Delone sets: a conjecture and results

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1070/RM10037

N. Dolbilin, M. Shtogrin

引用次数: 1

Abstract

In the framework of a new approach to the concept of local symmetry in arbitrary Delone sets we obtain new results for such sets without any restrictions. These results have important consequences for lattices and regular systems. A conjecture about the crystal kernel is stated, which generalises significantly the classical theorem on the non-existence of a five-fold symmetry in three-dimensional lattices. The following theorems related to the foundations of geometric crystallography are proved.

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德龙集合中的局部群:一个猜想与结果

在对任意Delone集合局部对称概念的一种新方法的框架下，我们得到了不受任何限制的任意Delone集合的新结果。这些结果对晶格和规则系统具有重要意义。提出了一个关于晶体核的猜想，它极大地推广了三维晶格中五重对称不存在的经典定理。证明了下列与几何晶体学基础有关的定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.