Volume 516, Nº 1 (2024)

We obtain broad sufficient conditions for reconstructing the coefficients of a Kolmogorov operator by means of a solution to the Cauchy problem for the corresponding Fokker–Planck–Kolmogorov equation. 

This paper is dedicated to studying of the algorithmic properties of unars with an injective function. We prove that the theory of every such unar admits quantifier elimination if the language is extended by a countable amount of predicate symbols. Necessary and sufficient conditions are established for the quantifier elimination to be effective, and a criterion of decidability of theories of such unars is formulated. Using this criterion we build a unar such that its theory is decidable, but the theory of the unar of its subsets is undecidable.

Under minimal conditions on the right side of the wave equation, a generalized solution of the mixed problem is constructed. The solution is presented as a series from the Fourier method, its sum is found. The form of a generalized solution of a mixed problem for an inhomogeneous telegraphic equation is given.

In a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper On the interpretation of intuitionistic logic “was written in hope that with time, the logic of solution of problems [i.e., intuitionistic logic] will become a permanent part of a [standard] course of logic. A unified logical apparatus was intended to be created, which would deal with objects of two types – propositions and problems.” We construct such a formal system as well as its predicate version, QHC, which is a conservative extension of both the intuitionistic predicate calculus QH and the classical predicate calculus QC. The axioms of QHC are obtained as a result of a simultaneous formalization of two well-known alternative explanations of intiuitionistic logic: 1) Kolmogorov's problem interpretation (with familiar refinements by Heyting and Kreisel) and 2) the proof interpretation by Orlov and Heyting, as clarified and extended by Gödel.

The article proves the following statement: in any hyperelliptic field L defined over the field of algebraic numbers K which having non-trivial units of the ring of integer elements of the field L, there is an element for which the period length of the continued fraction is greater any pre-given number.

This article considers an extremal problem for positive definite functions on ${ℝ}^n$ with a fixed support and a fixed value at the origin (the class 𝔉 _r (${ℝ}^n$)). It is required to find the least upper bound of a special form functional over  𝔉 _r (${ℝ}^n$). This problem is a generalization of the Turán problem for functions with support in a ball. We have obtained a general solution to this problem for $n\ne 2$. As a consequence, new sharp inequalities are obtained for derivatives of entire functions of exponential spherical type. 

We prove that a.a.s. for any $\epsilon >0$ and $n^{-\frac{e-2}{3e-2}+\epsilon }\le p=o\left(1\right)$ the maximum size of an induced subtree of the binomial random graph $G\left(n,p\right)$ is concentrated in 2 consecutive points.

This paper is devoted to some questions of inversion for the classical and generalized integral Radon transform. The main question is to determine information about the integrand functions if the values of some integrals are known. A feature of the work of the authors of this message is an analysis of the case when the function is integrated according to hyperplanes in finite-dimensional Euclidean space, and the integrands depend not only on the variables of integration, but also on some of the variables characterizing the hyperplanes. At the same time, the number of independent variables describing known integrals are smaller than those of the unknown integrand. We consider discontinuous integrands defined specifically introduced pseudo-convex sets. A Stefan-type problem is posed about finding surfaces discontinuities of the integrand function. The work provides formulas based on the application special integro-differential operators to known data and allowing you to solve the assigned tasks.

The paper considers the application of machine learning methods for optimal resource management for Network Powered by Computing (NPC) – a new generation computing infrastructure. The relation between the proposed computing infrastructure and the GRID concept is considered. It is shown how machine learning methods applied to computing infrastructure management make it possible to solve the problems of computing infrastructure management that did not allow the GRID concept to be fully implemented. As an example, the application of multi-agent optimization methods with reinforcement learning for network resources management is considered. It is shown that the application of multi-agent machine learning methods makes it possible to increase the speed of distribution of transport flows and ensure optimal NPC network channel load according to the criterion of uniform load distribution, and that such management of network resources is more effective than a centralized approach.