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卷 526, 编号 1 (2025)
MATHEMATICS
BOUNDARY VALUE PROBLEM FOR THE STATIONARY THERMAL DIFFUSION MODEL WITH VARIABLE COEFFICIENTS
摘要
The global solvability and local uniqueness of a new boundary value problem for a stationary thermal diffusion model with variable coefficients, taking into account the Soret effect, are proven. A priori estimates of the norms of the main components of the solution are derived and analyzed, depending on the norms of the problem data and the leading coefficients of the model. A special dependence of the solution on the modulus of the Soret coefficient is established.
Doklady Mathematics. 2025;526(1):3-7
3-7
ORLICZ TYPE SPACES RELATED WITH NONLINEAR NONLOCAL FUNCTIONALS
摘要
In the work we introduce the Orlicz spaces on the base of nonlinear nonlocal functionals. We study the main properties of such spaces. We prove that these spaces are Banach, separable and the set of compactly supported infinitely differentiable functions is dense in these spaces. We describe the structure of dual spaces and obtain the representations for the linear functionals.
Doklady Mathematics. 2025;526(1):8-15
8-15
SURVEY OF MODERN SMOOTH OPTIMIZATION ALGORITHMS WITH COMPARISON ORACLE
摘要
Modern optimization methods often encounter limited access to the values of the objective function, leading to the development of works dedicated to comparative oracles. This review provides an overview of contemporary algorithms for smooth, multivariate optimization that utilize only information about the order of the function values, rather than their numerical magnitudes. Both non-accelerated and accelerated methods are considered, including the latest advancements in optimization with comparative oracles. Special attention is paid to the diversity of approaches for designing algorithms that achieve convergence rates comparable to first-order methods (coordinate algorithms), as well as the first accelerated method within this oracle framework. Additionally, stochastic generalizations of the comparative oracle and their theoretical guarantees are discussed.
Doklady Mathematics. 2025;526(1):16-23
16-23
THEORIES OF BOOLEAN ALGEBRAS WITH A DISTINGUISHED SUBALGEBRA THAT DO NOT HAVE A PRIME MODEL
摘要
Boolean algebras in a signature enriched with a distinguished subalgebra are investigated. The question of the existence of complete theories of Boolean algebras with a distinguished subalgebra that do not have a prime model is studied. A continuum of Boolean algebras with a distinguished subalgebra is constructed, the elementary theories of which are different and do not have prime models, and for a fairly narrow class of very simply structured algebras. Namely, these are superatomic Boolean algebras with a distinguished subalgebra that is isomorphic to the Boolean algebra itself and almost coincides with it.
Doklady Mathematics. 2025;526(1):24–29
24–29
ON THE EXISTENCE OF POLYNOMIALS f OF ODD DEGREE DEFINING A HYPERELLIPTIC FIELD WITH FUNDAMENTAL S-UNIT OF DEGREE 13 AND PERIODIC EXPANSION √f
摘要
We proved that there are no polynomials f ∈ ℚ[x], deg f is odd, deg f ≥ 7, deg f ≠ 11,13, for which the corresponding hyperelliptic field ℚ(x)(√f) has a fundamental S-unit of degree 13 and for which the expansion of √f into a functional continued fraction is periodic. In the case deg f = 11,13, all polynomials f with the indicated properties are obtained. It is also proved that there exist at most finitely many pairwise nonequivalent polynomials f(x) ∈ ℚ[x] of degree 5 with such properties. Symbolic computations with Grobner bases play a significant role in proving the main results.
Doklady Mathematics. 2025;526(1):30–35
30–35
ON FITTING’S MODIFICATION OF KRIPKE’S THEORY OF TRUTH
摘要
In [3], inspired by some ideas from logic programming, Melvin Fitting proposed his own modification of Kripke’s theory of truth. Let J*
denote the corresponding monotone operator. We show that: 1) the closure ordinal of J*
is ω1
СК, i.e. the least non-constructive ordinal; 2) the collection of all sentences true according to J*
is Π1
1-complete.
Doklady Mathematics. 2025;526(1):36-39
36-39
GREEN FUNCTION OF THE ZAREMBA PROBLEM FOR THE HEAT OPERATOR
摘要
A parabolic initial-boundary value problem with homogeneous Zaremba boundary conditions in a cylinder whose base is a strictly Lipschitz bounded domain is considered, for which a theorem of the existence and uniqueness of the Green’s function is proved.
Doklady Mathematics. 2025;526(1):40–45
40–45
MATHEMATICAL MODELING OF THE PHYSICO-CHEMICAL PROCESS IN THE CATALYST LAYER
摘要
The article presents developed by the author mathematical model of an unsteady physico-chemical process in a catalyst layer with a cylindrical grain shape. The computational algorithm used to solve equations based on the splitting by physical processes is described. The accuracy order of the algorithm is defined. His verification was carried out on a problem with a known analytical solution. Based on the developed model and the constructed algorithm, three modes of the flow of an unsteady process are investigated, and confirmation of the dynamic mode effectiveness in comparison with the static one is obtained.
Doklady Mathematics. 2025;526(1):46–53
46–53
COMPUTER SCIENCE
STATE REGULATION OF DIGITAL BUSINESS
摘要
Digital technologies and the expansion of their application open up new opportunities for the development of the Russian economy, also form competitive advantages. However, the widespread adoption of digital technologies and the based digital business processes often entails the socio-economic complexities and challenges. The paper examines the information business as a new digital phenomenon. Also the paper examines the development of some regulate and support actions that provide relationship within the transition of digital transformations to a new technological level. Authors used the following scientific methods: system analysis, content analysis, sociological survey, comparative analysis, cluster analysis, mathematical modeling methods. The purpose of the paper is to substantiate and simulate the directions of state regulation of economic relations arising in the context of digital transformations. The result of the paper is a predictive economic and mathematical model of state regulation of the information business in Russia.
Doklady Mathematics. 2025;526(1):54-60
54-60