Victor Pavlovich Maslov

We consider the construction of asymptotic solutions of linear equations related to equations of classical mechanics: the Hamilton–Jacobi equation and the transport equation. We show that these methods and also the theory of the mechanics of an infinitely narrow beam as a whole can be applied to some objects in bioenergy if the thin organic objects of the type of wood splinters, straw, pellets, and so on are approximated by infinitely narrow beams.

Рассматриваются конструкции асимптотических решений линейных уравнений, связанных с уравнениями классической механики - уравнением Гамильтона-Якоби и уравнением переноса. Показано, что эти методы, а также теория механики бесконечно узких пучков в целом применимы к некоторым объектам биоэнергетики, если тонкие биологические объекты типа древесных лучин, соломы, пеллетных гранул и т. п. аппроксимировать бесконечно узкими пучками.

The notions of “tropical mathematics” and “subtropical mathematics” are studied. The main principles of tropical analysis and examples of their application to various problems are considered.

The analysis of different physical models describing the cooling of the active zone in the accident ChAPP block required a large amount of detailed estimations and calculations, demanded the physical modelling of cooling processes and special experiments in the accident block, after which the scheme of convective filtering cooling of the ChAPP accident block was accepted as the base model. Subsequent analysis showed that the filtration cooling model of the pile-up completely explains all the phenomena taking place in the reactor after the accident. The behaviour of the pile-up was influenced by melting and evaporation processes of materials volatile at the temperature level in the active zone of the reactor at the beginning of the accident. When the temperature increases, the pile-up should be loosened artificially, otherwise, as the results of modelling show, nature can take care of it itself. The new results obtained were unexpected, since similar problems were never considered in technical applications.

In the present paper, we discuss the notion of “tropical mathematics” in view of the fact that, up to the present time, there is no generally accepted correct understanding of this notion. The paper presents, rather than mathematical proofs, humanitarian and social justification of the correct understanding of the term. The author proposes to describe the term “tropical mathematics” by means of a frame based on linguistic, psychological, and cognitive considerations. As an example of the new reality to which tropical mathematics can be applied, one can consider the group of the richest men on our planet, say those who appear in the corresponding lists of the American financial journal “Forbes.” Once a person has joined this group, he has reached a different state and will have special relationships with the rest of the world. To support the claim that tropical mathematics is in a sense “fantastic”, we shall present some unexpected viewpoints of this science. It will also be shown that in tropical mathematics such classical mathematical principles as the Duhamel principle or the Fredholm alternative remain valid.

The analogy between knots in mathematical knot theory and “knots” in medicine is studied for the example of a certain invariant of Legendrian knots. The connection between the “Chern class” and the “Maslov class” is analyzed. A conjecture on the connection between the “Connes-Chern character” and the “Maslov class” is proposed.

The paper deals with uncertainty relations for time and energy operators, and the aftermath of the Chernobyl catastrophe is considered as an example. The mathematical approach developed by Holevo is analyzed, which allows us to assign the corresponding observables to non-self-adjoint operators and to establish uncertainty relations for nonstandard canonical conjugate pairs. Relations for calculating the minimal time interval in which the energy jump can be discovered are given. Based on the intensity parameter introduced by the author, which is related to a special statistics called Gentile statistics and to the polylogarithm function, properties of stable chemical elements, such as time fluctuations and the jump of specific energy in the transition from the Bose—Einstein distribution to the Fermi—Dirac distribution, are mathematically described with regard to experimental data. The obtained data are arranged in a table for 255 stable chemical elements. The mathematical approach developed by the author of the present paper allows one to describe the “antipode” (in a certain sense) of the standard thermodynamics, i.e., the thermodynamics of nuclear matter. This field of nuclear physics is very important for the study of properties of radioactive elements and, accordingly, from the standpoint of ensuring nuclear safety.

The notions of “hole” and “vacuum” in various branches of science are considered. A philosophical generalization of these notions on the basis of examples from physics, history, and linguistics is...

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint using experimental values of the binding energy for the nucleus of the given substance. A nucleon...