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The Local Theory For Regular Systems In The Context Of T-Bonded Sets, Mikhail M. Bouniaev, Nikolay Dolbilin
The Local Theory For Regular Systems In The Context Of T-Bonded Sets, Mikhail M. Bouniaev, Nikolay Dolbilin
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
The main goal of the local theory for crystals developed in the last quarter of the 20th Century by a geometry group of Delone (Delaunay) at the Steklov Mathematical Institute is to find and prove the correct statements rigorously explaining why the crystalline structure follows from the pair-wise identity of local arrangements around each atom. Originally, the local theory for regular and multiregular systems was developed with the assumption that all point sets under consideration are (r,R)" role="presentation">(r,R) -systems or, in other words, Delone sets of type (r,R)" role="presentation">(r,R) in d-dimensional Euclidean space. In this paper, we will …