The Law of Conservation of Incidents in the Space of Nanoworld

Abstract

This article first establishes the existence of integral equality relatively to the issue of the transmission of information by elements of lower and higher dimensions in the polytopes of the higher dimension that describe natural objects in the nanoworld. This integral equality is called the law of conservation of incidents. There is the incidence interpreted as the transfer of information from one material body to another. The fulfillment of the law of conservation of incidents for the n - simplex of the n - golden - hyper - rhombohedron and the n - cross - polytope is proved in general terms. It is shown that the law of conservation of incidents is valid for both regular bodies and irregular bodies, which can be clusters of chemical compounds. The incident conservation law can serve as a mathematical basis for the recently discovered epigenetic principle of the transmission of hereditary information without changing the sequence of genes in DNA and RNA molecules.