Balonin N.A., Sergeev M.B. M-matrices and crystal structures

Abstract

This article provides an overview of Minimax orthogonal Hadamard, Mersenne, Fermat and Euler matrices. The elementary basis of these matrices and low-levels orthogonal matrices with the shown structures are considered. The models of chemical elements, based on the relationship of the periodic table of Men-deleev with the theory of numbers, and the advantage of bases, giving the spatial characteristics, are explained. Examples of mathematical models of alloys in the form of quasicrystals solving theoretical difficulties of the official crystallography are clarified.

Keywords

Crystal structures, orthogonal matrices, Hadamard matrices, Mersenne primes, Fermat numbers.

Balonin Nikolaj Alekseevich – D.Sc. (Eng.), professor Saint Petersburg State University of Aerospace Instrumentation (SUAI). E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Sergeev Mikhail Borisovich – D.Sc. (Eng.), professor, Director of Information and Control Systems Institute, Saint Petersburg National Research University of Information Technologies, Mechanics and Optics. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..

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Details: Published: 21 September 2015; Last Updated: 21 September 2015; Hits: 2420