Hyperbolic Numbers in Modeling Genetic Phenomena

Sergey Petoukhov

doi:10.20944/preprints201908.0284.v1

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preprints.org > biology and life sciences > biochemistry and molecular biology > doi: 10.20944/preprints201908.0284.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Hyperbolic Numbers in Modeling Genetic Phenomena

Sergey Petoukhov

Version 1 : Received: 26 August 2019 / Approved: 27 August 2019 / Online: 27 August 2019 (11:39:59 CEST)
Version 2 : Received: 18 September 2019 / Approved: 19 September 2019 / Online: 19 September 2019 (11:21:42 CEST)
Version 3 : Received: 14 January 2020 / Approved: 16 January 2020 / Online: 16 January 2020 (12:07:48 CET)
Version 4 : Received: 12 April 2020 / Approved: 13 April 2020 / Online: 13 April 2020 (11:04:05 CEST)

How to cite: Petoukhov, S. Hyperbolic Numbers in Modeling Genetic Phenomena. Preprints 2019, 2019080284. https://doi.org/10.20944/preprints201908.0284.v1 Petoukhov, S. Hyperbolic Numbers in Modeling Genetic Phenomena. Preprints 2019, 2019080284. https://doi.org/10.20944/preprints201908.0284.v1

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MDPI and ACS Style

Petoukhov, S. Hyperbolic Numbers in Modeling Genetic Phenomena. Preprints 2019, 2019080284. https://doi.org/10.20944/preprints201908.0284.v1

APA Style

Petoukhov, S. (2019). Hyperbolic Numbers in Modeling Genetic Phenomena. Preprints. https://doi.org/10.20944/preprints201908.0284.v1

Chicago/Turabian Style

Petoukhov, S. 2019 "Hyperbolic Numbers in Modeling Genetic Phenomena" Preprints. https://doi.org/10.20944/preprints201908.0284.v1

Abstract

The article is devoted to applications of 2-dimensional hyperbolic numbers and their algebraic 2ⁿ-dimensional extensions in modeling some genetic phenomena. Mathematical properties of hyperbolic numbers and their matrix representations are described in a connection with alphabets of DNA nucleobases and with inherited phyllotaxis phenomena. Known data on using hyperbolic rotations, which are particular cases of hyperbolic numbers, in physics and in some biological phenomena, including phyllotaxis laws and structural features of locomotions, are discussed. Applications of hyperbolic numbers reveal hidden interrelations between structures of different biological and physical phenomena. They lead to new approaches in mathematical modeling genetic phenomena.

Keywords

hyperbolic numbers, genetics, tensor product, Fibonacci numbers, phyllotaxis

Subject

Biology and Life Sciences, Biochemistry and Molecular Biology

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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