Geometrical Problems Related to Crystals, Fullerenes and Nanoparticles Structure

Bouniaev, Mikhail; Musin, Oleg R.; Долбилин, Николай Петрович; Tarasov, A.S.

doi:10.5176/2251-1911_cmcgs14.06

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“…[7], [8], [10], [12], [13], [16]). Though the statements of the theorems are almost identical for both Delone sets and t-bonded sets the main challenge of the proofs is related to the rank of the clusters, which as we have already mentioned is d for 2R-clusters in Delone sets, however, in case of t-bonded sets it may not be equal to d for ρ-clusters when ρ is equal to t. The cluster's rank naturally affects the structure of the group S x (ρ) of the cluster's symmetries.…”

Section: And It Is Connected To the Center X By A T-chain Contained Imentioning

confidence: 99%

Regular and Multi-regular <i>t</i>-bonded Systems

Bouniaev

Долбилин

2017

Journal of Information Processing

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Abstract:The concept of t-bonded sets was briefly introduced by the second author in 1976 under the name of dconnected sets, though it has not received due consideration. This concept is a generalization of the concept of Delone (r, R)-systems. In light of the developments in the local theory for crystals that occurred since 1976 and demands in chemistry and crystallography, we believe the local theory for t-bonded sets deserves to be developed to describe materials whose atomic structures is multi-regular "microporous" point set. For a better description of such "microporous" structures it is worthwhile to take into consideration a parameter that represents atomic bonds within the matter. The overarching goal of this paper is to prove that analogous local conditions that guarantee that a Delone set is a regular (or multi-regular) system also guarantee that a t-bonded set is a regular (or multi-regular) t-bonded system.

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Section: And It Is Connected To the Center X By A T-chain Contained Imentioning

confidence: 99%