Relations of the Genetic Code with Algebraic Codes and Hypercomplex Double Numbers

2020 ◽  
pp. 558-570
Author(s):  
Sergey V. Petoukhov
Keyword(s):  
Genetic Code ◽  
Double Numbers ◽  
Algebraic Codes

scholarly journals The Genetic Code, Algebraic Codes and Double Numbers

2020 ◽  
Author(s):  
Sergey V. Petoukhov
Keyword(s):  
Genetic Code ◽  
Communication Technologies ◽  
Structural Features ◽  
Rna Molecules ◽  
Doubly Stochastic ◽  
Dna And Rna ◽  
Double Numbers ◽  
Algebraic Codes ◽  
Living Organisms ◽  
Algebraic Code

The article shows materials to the question about algebraic features of the genetic code and about the dictatorial influence of the DNA and RNA molecules on the whole organism. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Structural features of the genetic systems are associated with hypercomplex double (or hyperbolic) numbers and with bisymmetric doubly stochastic matrices. The received results confirm that represented matrix approaches are effective for modeling genetic phenomena and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities where structures of genetic molecules have the dictatorial influence on inherited structures of the whole organism. New described algebraic approaches and results are discussed.

scholarly journals The Genetic Code, Algebraic Codes and Double Numbers

2019 ◽  
Author(s):  
Sergey V. Petoukhov
Keyword(s):  
Genetic Code ◽  
Wide Class ◽  
Communication Technologies ◽  
Hyperbolic Numbers ◽  
Double Numbers ◽  
Algebraic Codes ◽  
Structural Relations ◽  
Living Organisms ◽  
Algebraic Code

The article shows materials to the question on algebraic features of the genetic code. Presented results testify in favor that the genetic code is an algebraic code related with a wide class of algebraic codes, which are a basis of noise-immune coding of information in communication technologies. Algebraic features of the genetic code are associated with hypercomplex double (or hyperbolic) numbers. The article also presents data on structural relations of some genetically inherited macrobiological phenomena with double numbers and with their algebraic extentions. The received results confirm that multidimensional numerical systems is effective for modeling and revealing the interconnections of structures of biological bodies at various levels of their organization. This allows one to think that living organisms are algebraically encoded entities.

Multidimensional Numbers and the Genomatrices of Hydrogen Bonds

2010 ◽  
pp. 193-206
Author(s):  
Sergey Petoukhov ◽  
Matthew He
Keyword(s):  
Hydrogen Bonds ◽  
Genetic Code ◽  
Structural Features ◽  
Hyperbolic Type ◽  
Complex Numbers ◽  
Hypercomplex Numbers ◽  
Molecular Systems ◽  
Natural Systems ◽  
Double Numbers ◽  
Mathematical Properties

This chapter returns to the kind of numeric genetic matrices, which were considered in Chapter 4-6. This kind of genomatrices is not connected with the degeneracy of the genetic code directly, but it is related to some other structural features of the genetic code systems. The connection of the Kronecker families of such genomatrices with special categories of hypercomplex numbers and with their algebras is demonstrated. Hypercomplex numbers of these two categories are named “matrions of a hyperbolic type” and “matrions of a circular type.” These hypercomplex numbers are a generalization of complex numbers and double numbers. Mathematical properties of these additional categories of algebras are presented. A possible meaning and possible applications of these hypercomplex numbers are discussed. The investigation of these hyperbolic numbers in their connection with the parameters of molecular systems of the genetic code can be considered as a continuation of the Pythagorean approach to understanding natural systems.

Ideology and Science (based on the discussion in CEMI RAS)

2019 ◽  
pp. 55-68
Author(s):  
V.L. Makarov ◽  
V.G. Grebennikov ◽  
V.E. Dementyev ◽  
E.V. Ustyuzhanina
Keyword(s):  
Genetic Code ◽  
Mathematical Institute ◽  
Tea Party ◽  
Russian Academy Of Sciences ◽  
Academy Of Sciences ◽  
Central Economic

The debating society “Makarov’s tea party” chaired by the academician V.L. Makarov met on the 18th April 2019 in the Central Economic Mathematical Institute of the Russian Academy of Sciences in order to discuss the interrelationship between ideology and science. The society raised such issues as opposition and interpenetration of science and ideology; ideology and the genetic code of a nation; ideology and manipulation of conscience; numbers and facts as tools of ideological intervention. Here we present the most interesting points of the discussion. The authors of the reports: Makarov Valery, Doctor of Phys.-math., member of the Russian Academy of Sciences; Dementiev Victor, Doctor of Economics, Corr. RAS; Grebennikov Valery, Doctor of Economics; Ustyuzhanina Elena, Doctor of Economics.

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