LINE INTEGRATION AND SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS OVER CAYLEY-DICKSON ALGEBRAS
2011jqw | Ludkovsky S.V.  // Moscow State Technical University MIREA, Moscow, Russia, sludkowski@mail.ru

This article presents some results of investigation of the multi-level system of moleculargenetic alphabets by means of matrix methods from theory of noise-immunity coding. These studies have revealed links of the system of alphabets with some systems of hypercomplex numbers (Hamilton quaternions and Cockle split-quaternions and their extensions), Kronecker families of matrices, orthogonal systems of Rademacher functions and Walsh functions, Hadamard matrices etc. Structural parallels are shown between molecular-genetic alphabets and a system of inheritance of traits in holistic organisms, which obeys the Mendel laws and which is reflected in genetic Punnett squares. The system of molecular-genetic alphabets, common to all living organisms, possesses algebraic properties which lead to a new - algebraic - way of cognition of living matter. This cognition is related with development of algebraic biology associated with hypercomplex numbers. Living matter, providing the transmission of hereditary information in the chain of generations, is presented as information entity deeply algebraic in its nature.

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