23 citations · 23 across the 4 of their papers we have counts for
6 papers
Bounds for the Regularity Radius of Delone Sets
Nikolay Dolbilin, Alexey Garber, Egon Schulte +1
Delone sets are discrete point sets in characterized by parameters , where (usually) is the smallest inter-point distance of , and is the radi…
Local Groups in Delone Sets
Nikolay Dolbilin
In the paper, we prove that in an arbitrary Delone set in space, the subset of all points from at which local groups have axes of the order not greater than 6 is…
On the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets
Igor A. Baburin, Mikhail Bouniaev, Nikolay Dolbilin +4
The local theory of regular or multi-regular systems aims at finding sufficient local conditions for a Delone set to be a regular or multi-regular system. One of the main goals…
Local Theory of t-bonded sets
Mikhail Bouniaev, Nikolay Dolbilin
The local theory for regular and multi-regular systems was developed in the assumption that these systems are Delone sets, or (r;R)-systems. The requirement for a set to be a (r;R)…
Delone Sets: Local Identity and Global Symmetry
Nikolay Dolbilin
In the paper we present a proof of the local criterion for crystalline structures which generalizes the local criterion for regular systems. A Delone set is called a crystal if it…
Functionals on Triangulations of Delaunay Sets
Nikolay P. Dolbilin, Herbert Edelsbrunner, Alexey Glazyrin +1
We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this…