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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Vol 521, No 1 (2025)
MATHEMATICS
5-10
ON THE EXTRACTION OF RANDOM BIT SEQUENCES IN QUANTUM RANDOM NUMBER GENERATORS WITH SEVERAL INDEPENDENT MARKOV SOURCES
Abstract
The paper presents a method for extracting provably random bit sequences from several independent trajectories of circuits Markov, each of which has an arbitrary finite order. The combined use of several trajectories makes it possible in practice, when implementing quantum randomnumber generators, to significantly increase the speed of generating output bit sequences.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):11-22
11-22
23-27
NOTES ON THE RECURRENCE OF THE BIRKHOFF SUMS
Abstract
The measure-preserving, but not necessarily invertible, ergodic transformations of the compact metric space with the Caratheodory measure are considered. The behavior of the Birkhoff sums for integrable and almost everywhere bounded functions with zero mean value in terms of the Caratheodory measure is studied. It is shown that for almost all points of the metric space there is an infinite sequence of "moments of time"; along which the Birkhoff sums tend to zero and at the same moments the trajectory points approach their initial position as close as possible (as in the Poincare return theorem). As an example, we consider the transformation ; of the single segment; closely related to Bernoulli tests.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):28-31
28-31
DERIVING HYDRODYNAMIC EQUATIONS FOR A HAMILTONIAN “FIELD–LATTICE” SYSTEM
Abstract
We give the rigorous derivation of hydrodynamic equations for an infinite harmonic crystal coupled to the Klein–Gordon field. These equations hold in the hydrodynamic limit, and they should be considered as the analog of the Euler and Navier–Stokes equations for the model under consideration.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):32-37
32-37
38-42
ON THE DETERMINISM OF PATHS ON SUBSTITUTION COMPLEXES
Abstract
The work is devoted to the study of the combinatorial properties of determinism for a family of substitution complexes consisting of quadrangles glued together side-to-side. These properties are useful in constructing algebraic structures with a finite number of defining relations. In particular, this method was used to construct a finitely defined infinite nilsemigroup satisfying the identity x9 = 0. This construction solves the problem of L.N. Shevrin and M.V. Sapir. In this paper, we study the possibility of coloring the entire family of complexes in a finite number of colors, for which the weak determinism property is satisfied: if the colors of the three vertices of a certain quadrilateral are known, then the color of the fourth side is uniquely determined, except in some cases of a special arrangement of the quadrilateral. Even weak determinism is enough to construct a finitely defined nilsemigroup; when using this construction, the proof is reduced in scope. The properties of determinism were studied earlier within the framework of the theory of tessellations; in particular, Kari and Papasoglu constructed a set of square tiles that allowed only aperiodic tessellations of the plane and had determinism: the colors of the two adjacent edges were uniquely determined by the colors of the two remaining edges.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):43-62
43-62
DYNAMICS OF THE SYSTEM IN THE PRESENCE OF INVARIANT RELATIONSHIPS
Abstract
The possibility of the existence of an invariant measure with smooth density is discussed in two cases related to invariant sets — at the levels of particular integrals and at the joint invariant level of two or more functions. Conditions are investigated when the invariant sets represent a two-dimensional torus on which an invariant measure with smooth density is defined, which means that Kolmogorov’s theorem is applicable, and the motion after the appropriate coordinate replacement is conditionally periodic.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):63-71
63-71
COMPANION MATRIX FOR SUPERPOSITION OF POLYNOMIALS AND ITS APPLICATION TO KNOT THEORY
Abstract
The note provides a new formula for the companion matrix of the superposition of two polynomials over a commutative ring. The results obtained are used to provide a constructive proof of Plans’ theorem for two-bridge knots, which states that the first homology group of an odd-sheeted cyclic covering of a three-dimensional sphere branched over a given knot is the direct sum of two copies of some Abelian group. A similar result is also true for the homology of even-sheeted coverings factored by the reduced homology group of a two-sheeted covering. The structure of the above mentioned Abelian groups is described through Chebyshev polynomials of the second and fourth kind.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):72-80
72-80
THE VANDERMONDE MATRIX IN THE GENERAL CASE
Abstract
In an arbitrary complex Banach algebra, the Vandermonde matrix is considered. With the help of the accompanying Frobenius matrix, a connection is established between the coefficients of the algebraic equation and the Vandermonde matrix constructed from the roots, a definition of a divided difference of arbitrary order is given based on the invertible Vandermonde matrix. An analogue of the Hermite formula of the integral representation of the divided difference is given. An inclusion for the spectrum of the divided difference and an analogue of Dunford’s theorem on the mapping of spectra are given.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):81-87
81-87
NUMERICAL SOLUTION OF INTEGRO-DIFFERENTIAL EQUATIONS OF THE THEORY OF VISCOELASTICITY WITH KERNELS OF EXPONENTIAL AND RABOTNOV TYPES
Abstract
In differential equations describing the behavior of continuous media with creep, in accordance with Volterra’s linear theory, applicable to a wide range of materials with amorphous and heterogeneous structure, integral type operators are present. In these equations, the kernel of the integral operator is represented as a sum of exponentials, or as a weakly singular kernel (the Rabotnov function). Obtaining an analytical solution for the equations in question is problematic in some cases, hence the need to develop a numerical method and algorithm for solving such equations, taking into account the memory of the medium in question. To solve these equations, the paper uses the grid-characteristic method and the coordinate splitting method (for multidimensional problems). The approximation and stability of the proposed method are numerically investigated.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):88-95
88-95
NEW CASES OF INTEGRABLE CONSERVATIVE AND DISSIPATIVE SYSTEMS OF ANY ODD ORDER
Abstract
New cases of integrable dynamical systems of any odd order homogeneous in terms of variables are presented, in which a system on a tangent bundle to a even-dimensional manifold can be distinguished. In this case, the force field (shift generator in the system) is divided into an internal (conservative) and an external one, which has a dissipation of a different sign. The external field is introduced using some unimodular transformation and generalizes the previously considered fields. Complete sets of both first integrals and invariant differential forms are given.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):96-106
96-106
MODAL LOGICS WITH THE INTERSECTION MODALITY
Abstract
We give a simple proof of a recently obtained in [12] result on the completeness of modal logics with the modality that corresponds to the intersection of accessibility relations in a Kripke model. In epistemic logic, this is the so-called distributed knowledge operator. We prove completeness for the logics in the modal languages of two types: one has the modalities □1,...,□n for the relations R1,...,Rn that satisfy a unimodal logic L, and the modality □n+1 for the intersection Rn+1=R1 ∩...∩ Rn; the other language has the modalities □i (i ∈ Σ) for the relations Ri that satisfy the logic L, and, for every nonempty subset of indices I ⊆ Σ, the modality □I for the intersection ∩i∈I Ri. While in [12] the completeness is proved only for the logics over K, KD, KT, K4, S4, and S5, here we give a "uniform" construction that enables us to obtain completeness for the logics with intersection over the 15 so-called "traditional" modal logics KΛ, for Λ ⊆ {D, T, B, 4, 5}. The proof method is based on unravelling of a frame and then taking the Horn closure of the resulting frame.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):107-123
107-123
ERRATUM
POPRAVKA K STAT'E “OBZOR MUL'TIMODAL'NYKh SRED DLYa OBUChENIYa S PODKREPLENIEM”, 2024, TOM 520, № 2, S. 124–130
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;521(1):124-124
124-124