TENSOR PRODUCT OF MATRICES IN STUDYING THE ORGANISM AS A GENETIC SYSTEM OF RESONANCES
2015jdv | S.V. Petoukhov  // Institutes for Machines Science, RAS, Moscow, Russia, spetoukhov@gmail.com

The article is devoted to the new modeling approach to study the role of wave and vibration processes in genetically inherited organization of living bodies. This approach is based on matrix analysis and uses the well-known property of matrices for displaying resonances. Emphasis is placed on systems of resonances in families tensor matrices based on the tensor product. The concept of inheritance tables eigenvalues of the matrices of these families is introduced. Their analogies are shown with Punnet’s squares of Poly-hybrid crosses of organisms under the Mendel’s laws.Matrix analysis gives evidences in favor of the following: alphabets of the genetic code are alphabets of resonances; respectively, the genetic code is the code of resonances, and genetic texts, which are based on these alphabets, are written in the language of resonances; alleles of genes, which are represented in Mendel’s laws, can be interpreted as resonances (the eigenvalues of matrices) of some oscillatory systems. The conception of resonance genome is formulated. Ideas of vibrational genetic biomechanics are under development taking into account connections between inherited biological processes and phenomena of vibrational mechanics.

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