Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
ISSN (print): 2686-9543
Media registration certificate: PI No. FS 77 - 77121 dated 06.11.2019
Founder: Russian Academy of Sciences
Editor-in-Chief Semenov Alexey Lvovich
Number of issues per year: 6
Indexation: RISC, list of Higher Attestation Commissions, CrossRef, White List (level 4)
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卷 522, 编号 1 (2025)
MATHEMATICS
ON SOME CLASS OF EXTREME POINTS OF THE UNIT BALL OF A HARDY-LORENTZ SPACE
摘要
The problem of a characterization of the set of extreme points of the unit ball in the Hardy-Lorentz space H(Λ(φ)), posed by E.M. Semenov in 1978, is considered. New necessary and sufficient conditions, under which a normalized function f in H(Λ(φ)) belongs to this set, are found. The most complete results are obtained in the case when f is the product of an outer analytic function and a Blaschke factor.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):3-6
3-6
ORDINARY DIFFERENTIAL EQUATIONS OF EVEN ORDER WITH INTEGRAL CONDITIONS
摘要
We consider an even-order ordinary differential operator with a spectral parameter and integral conditions. An a priori estimate of the solutions to the problem is obtained for sufficiently large values of the spectral parameter. The discreteness and the sectoral structure of the spectrum of the corresponding operators are proved.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):7-10
7-10
MATHEMATICS OF ACCELERATED EXPANSION OF THE UNIVERSE AND LOBACHEVSKY SPACE
摘要
In classical works, the Hubble constant is defined via the metric. Here we define it, as it should be, via matter, according to Milne and McCrea, extending their theory of the expanding universe to the relativistic case. This allows us to explain the accelerated expansion as a simple relativistic effect without Einstein’s lambda, dark energy and new particles as an exact consequence of the classical Einstein action. The well-verified fact of accelerated expansion allows us to determine the sign of the curvature in the Friedmann model: it turns out to be negative, and we live in Lobachevsky space.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):11-18
11-18
UNIQUE STRONG SOLVABILITY OF THE INITIAL BOUNDARY VALUE PROBLEM FOR THE INHOMOGENEOUS INCOMPRESSIBLE KELVIN–VOIGT FLUID MODEL
摘要
The paper proves the existence and uniqueness theorem of a strong solution for a inhomogeneous incompressible Kelvin-Voigt fluid motion model. It is not assumed that the initial condition for the fluid density is separated from zero. To prove the existence of a solution, an approximation problem is considered, its solvability and strong a priori estimates for its solutions, independent of the approximation parameter, are established. After that, a passage to the limit is carried out as the approximation parameter tends to zero and it is shown that solutions to the approximation problem converge to a strong solution of the original problem as the approximation parameter tends to zero. The uniqueness of the solution is established using the Gronwall–Bellman inequality.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):19-24
19-24
GENERALIZATION OF THE JULIA–CARATHE´ODORY THEOREM TO THE CASE OF SEVERAL BOUNDARY FIXED POINTS
摘要
Holomorphic self-maps of the unit disc with boundary fixed points are investigated. In 1982, Cowen and Pommerenke established an interesting generalization of the classical Julia— Carathe´odory theorem, which allowed them to derive an exact estimate for the derivative at the Denjoy—Wolff point on a class of functions with an arbitrary finite set of boundary fixed points. In this paper, we obtain a new generalization of the Julia—Carathe´odory theorem, which contains Cowen—Pommerenke result as a special case, moreover, it is an effective tool for solving various problems on classes of functions with fixed points.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):25-32
25-32
ON A TOPOLOGICAL STRUCTURE OF A SOLUTION SET TO A CAUCHY PROBLEM FOR FRACTIONAL DIFFERENTIAL INCLUSIONS WITH A UPPER SEMICONTINUOUS RIGHT-HAND SIDE
摘要
In this paper, we study the topological structure of a solution set to the Cauchy problem for semilinear differential inclusions of fractional order α ∈ (1, 2) in Banach spaces. It is assumed that the linear part of the inclusions is a linear closed operator generating a strongly continuous and uniformly bounded family of cosine operator functions. The nonlinear part is represented by a upper semicontinuous multivalued operator of Caratheodory type. It is established that the set of solutions to the problem is an Rδ-set.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):33-39
33-39
ON A СOMBINATORIAL APPLICATION OF ULTRAFILTER THEORY: A NEW CONSTRUCTION OF TRIANGLE-FREE GRAPHS WITH ARBITRARILY LARGE CHROMATIC NUMBER
摘要
The paper describes a new method for constructing triangle-free graphs with an arbitrarily large chromatic number. The method is substantiated using properties of various types of ultrafilter extensions of functions and predicates.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):40-49
40-49
EXACT SOLUTIONS AND REDUCTIONS OF THE NONLINEAR SCHRO¨ DINGER EQUATION OF THE GENERAL FORM
摘要
The nonlinear Schro¨dinger equation of a general form is investigated, in which the chromatic dispersion and the potential are given by two arbitrary functions. The equation under consideration is a natural generalization of a wide class of related nonlinear equations that are often encountered in various sections of theoretical physics, including nonlinear optics, superconductivity, and plasma physics. Exact solutions of the nonlinear Schro¨dinger equation of general form are found, which are expressed in quadratures. One-dimensional reductions are described, which reduce the studied partial differential equation to simpler ordinary differential equations or systems of such equations. The exact solutions obtained in this work can be used as test problems intended to assess the accuracy of numerical methods for integrating nonlinear equations of mathematical physics.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):50-55
50-55
FORMATION OF STOCHASTIC BEHAVIOR AND EXPLOSIVE SOLUTIONS IN THE INFINITELY REMOTE PHASE SPACE OF DYNAMIC SYSTEMS
摘要
The article examines the conditions under which phase variables undergo a blow-up regime, tending toward the Poincare´ circle in finite time. It also explores systems where, alongside explosive solutions, stochastic behavior of trajectories is observed in some cases. The role of separatrices and separatrix cycles is analyzed both before perturbation and under non-autonomous small periodic perturbations of the right-hand sides of the original dynamic systems. These perturbations give rise to homoclinic structures in the phase space, leading to stochastic trajectory behavior. Various cases of soliton formation during trajectory bifurcations are also considered.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):56-61
56-61
PROBLEMS AND METHODS OF THE THEORY FUNCTIONAL-DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS RIGHT HAND PART
摘要
The main methods and approaches of the theory of discontinuous systems are applied to the construction of the theory of functional-differential equations with a discontinuous right-hand side. In particular, methods for describing sets of discontinuity points and sliding modes of discontinuous systems with delay by using a special class of invariantly differentiable functionals are considered.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):62-69
62-69
COMPUTER SCIENCE
THE DIPOLARCALC SOFTWARE SYSTEM FOR ASSESSING THE POLARIZATION OF BIOLOGICAL MOLECULAR STRUCTURES
摘要
The unique DipolarCalc software system is presented, which makes it possible to calculate the polarization of biomolecules through the total dipole moment of chemical bonds of “functional topological atoms” (FTA). The program implements a user-friendly interface that provides intuitive data entry and visualization of calculation results, as well as uses analytical expressions that allow accurate calculations to be performed in real time. The presented software package is aimed at use in computational biology and provides researchers with a convenient tool for modeling intramolecular and intermolecular interactions of biological molecular structures.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):70-75
70-75
ПРОЦЕССЫ УПРАВЛЕНИЯ
DIFFERENTIATION, EFFICIENCY AND INFLATION IN ECONOMIC THEORY
摘要
The paper proposes four parameters to measure the efficiency of investments and their inflation. These parameters were calculated for relatively large 49 countries with a fairly advanced level of economic development separately, and for the rest of the world within the framework of 3 international economic associations (OECD, Old EU countries and New EU countries) and the World (as a whole) for two-time ranges (1996–2008) and (2009–2023). Based on the calculated parameters, ratings of the efficiency of investments and broad money supply (M3 aggregate) and their inflation for these 53 subjects, which include all countries of the world, are constructed. The necessary conditions for ensuring the growth rate of GDP of modern Russia above the world average while maintaining macroeconomic stability are shown.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;522(1):76-80
76-80