Duality of Presentation of Information Signals in Biological Systems: Generalized Kotel''nikov Theorem
This article presents a conceptual approach to the substantiation of a factor of duality of information presentation, and it signals in biological systems. The purpose is to study relations between discrete and continuous bio-informational signals, which provide all the aspects of functioning of biosystems. Strict physical-mathematical and biophysical evidence of a generalized Kotelnikov theorem for biological systems is formulated. This material is essentially important in the context of the development of the information biophysical models. This aim is realized by the decision of the following tasks. It is shown that a structured living organism is a complex, organized in its hierarchy functional system in which information exchange is carried out set of discrete and continuous (analog) signals of various physical nature: from simple and electrochemical to magnetic and electromagnetic. Their analysis are developed, theorem of duality of presentation of information in biological systems is formulated. Basic generalized theorem Kotelnikov - Yashin (see explanation in the text) with the use of physical and mathematical apparatus of integral equations, the Lebesgue integral, the Fourier and Hilbert transforms etc. is formulated and proved. This theorem states that in the biosystem information-containing signal has the quality of dualism, which combines quantum potentiality of the wave function and discreteness of collapsing. This paper contains useful application.