N. Dolbilin

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20182023

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math.MG2023

Bounds for the Regularity Radius of Delone Sets

Nikolay Dolbilin, Alexey Garber, Egon Schulte +1

Delone sets are discrete point sets $X$ in $R^{d}$ characterized by parameters $(r, R)$ , where (usually) $2 r$ is the smallest inter-point distance of $X$ , and $R$ is the radi…

math.MG2020

Local Groups in Delone Sets

Nikolay Dolbilin

In the paper, we prove that in an arbitrary Delone set $X$ in $3 D$ space, the subset $X_{6}$ of all points from $X$ at which local groups have axes of the order not greater than 6 is…

math.MG2018

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 $X$ to be a regular or multi-regular system. One of the main goals…