A theorem on generalized nonions and their properties for the applied structures in physics
- Authors: Frątczak E.Z.1, Ławrynowicz J.1, Nowak-Kępczyk M.2, Polatoglou H.M.3, Wojtczak L.1
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Affiliations:
- Faculty of Physics and Applied Informatics
- Institute of Mathematics and Informatics
- Aristotle University of Thessaloniki
- Issue: Vol 38, No 2 (2017)
- Pages: 255-261
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/198939
- DOI: https://doi.org/10.1134/S199508021702007X
- ID: 198939
Cite item
Abstract
The central part of the paper consists of a theorem on generalized nonions governing dynamical systems modelling of special ternary, quaternary, quinary, senary, etc. structures, due to the third named author. Let Mn(C), n ≥ 2, be the set of n × n-matrices with complex entries. The theorem states that in Mn(C) there exists a basis such that PQ− λsQP = 0, s = 0, 1, 2,.., n − 1, where {P,Q,}, u, v are specified in Section 1, formulae (1) and (2).The particular cases n = 2, 3, 4 with other choices of u, v were discussed by James Joseph Sylvester (1883, 1884) and by Charles Sanders Peirce (1882).In particular, λ = j, j3 = 1, j ≠ 1, generates nonions. Before the section on the above theorem and its visualization on a two-sheeted Riemann surface, we give three physical motivations for the topic: controlled noncommutativity: Sylvester–Peirce approach vs. Max Planck approach (1900), supersonic flow of a ternary alloy in gas, and changing hexagonal to pentagonal structure in pentacene.
Keywords
About the authors
E. Z. Frątczak
Faculty of Physics and Applied Informatics
Author for correspondence.
Email: ewelinazofia@gmail.com
Poland, Łódź
J. Ławrynowicz
Faculty of Physics and Applied Informatics
Email: ewelinazofia@gmail.com
Poland, Łódź
M. Nowak-Kępczyk
Institute of Mathematics and Informatics
Email: ewelinazofia@gmail.com
Poland, Chełm
H. M. Polatoglou
Aristotle University of Thessaloniki
Email: ewelinazofia@gmail.com
Greece, Thessaloniki
L. Wojtczak
Faculty of Physics and Applied Informatics
Email: ewelinazofia@gmail.com
Poland, Łódź