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Vol 523, No 1 (2025)
MATHEMATICS
ON PRIMARY SUBMODULES IN MODULES OF ENTIRE FUNCTIONS THAT ARE DUAL TO SPACES OF Ω-ULTRADIFFERENTIABLE FUNCTIONS
Abstract
We consider weighted modules of entire functions that are dual to general spaces of Ω-ultradifferentiable functions. We explore the local description problem for primary submodules in these modules. It is shown that there exist non-localisable primary submodules. We also obtain non-trivial conditions under which local description is possible. All assertions may be reformulated to the equivalent dual ones concerning with the spectral synthesis problem for differentiation invariant subspaces of Ω-ultradifferentiable functions.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):3–9
3–9
NEW FORMULAS FOR THE INVERSION OF THE RADON TRANSFORM
Abstract
For the integral Radon transform, classical formulas for inversion of the integrand function are known, provided that it is smooth. However, this restriction does not fully correspond to the application of the results in sounding theory, which is the main area of application of the Radon transform. It would be more natural to assume that discontinuities of the first kind are admissible for integrands. The paper presents a number of inversion formulas proved by the authors for piecewise continuous functions. A comparison of the obtained formula variants is carried out and preliminary recommendations on their use for numerical algorithms are given.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):10-14
10-14
TYPE-QUANTIFIER CALCULUS OF POSITIVELY-FORMED FORMULAS WITH NEGATIONS
Abstract
Type quantifier language and calculus as logical positively-constructed means of knowledge representation and automation of deductive inference have been developed. In them, the type conditions of quantifiers can contain negations, and the calculus has completeness with respect to derivability in the classical predicate calculus.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):15-20
15-20
ALGORITHMIC PROPERTIES OF BASIC CATEGORIAL GRAMMARS WITH UNIQUE CATEGORY ASSIGNMENT
Abstract
The work is devoted to basic categorial grammars with unique type assignment (BCGUTA). For this class, a number of algorithmic properties are examined. It is proven that, for an arbitrary context-free language L, the problem of verifying whether is generated by a grammar from the BCGUTA class is algorithmically undecidable. Furthermore, it is proven that for any two BCGUTA grammars, the problem of determining the emptiness of the intersection of the languages generated by these grammars is also algorithmically undecidable.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):21-26
21-26
ON THE SOLVABILITY OF THE CAUCHY PROBLEM IN GEVREY CLASSES FOR THE WEYL FRACTIONAL DERIVATIVE EQUATION
Abstract
An alternative definition of fractional-order Weyl derivatives is given and their effect on functions from the Gevrey classes is studied. Conditions for the solvability of the Cauchy problem in Gevrey classes are found for the Weyl partial differential equation.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):27-30
27-30
ERROR BOUNDS FOR INTERPOLATION IN THE MEAN INTEGRO QUADRATIC SPLINES AND SUPERCONVERGENCE POINTS
Abstract
The problem of interpolation in the mean of a function on known integrally averaged values by an integro quadratic spline is considered. It is shown that the integro quadratic spline can be defined via the interpolation cubic spline. Since the interpolation cubic spline is studied quite well, well-known error bounds for interpolation and some of its properties can be transferred to the integro quadratic spline. The points of superconvergence of the integro spline are found, i.e. the points at which the spline or its derivatives have a higher order of approximation.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):31-34
31-34
ON ONE APPROACH TO OBTAINING THE BOUNDARIES OF PERTURBATION OF HOMOGENEOUS MARKOV PROCESSES
Abstract
Homogeneous Markov chains with continuous time are considered. A new approach is proposed that makes it possible to obtain accurate estimates of stability for such chains with relation to perturbations of infinitesimal characteristics. The application of the results to stationary queuing systems of several classes, as well as to some non-stationary systems, is considered.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):35-43
35-43
ON THE NUMERICAL SOLUTION OF THE THREE-DIMENSIONAL NEUMANN PROBLEM FOR THE HELMHOLTZ EQUATION BY THE POTENTIAL METHOD
Abstract
The three-dimensional exterior Neumann problem for the Helmholtz equation is considered. Using the potential method, it is reduced to a boundary weakly singular Fredholm integral equation of the second kind, which is solved numerically. The accuracy is increased and the computational complexity of the numerical solution algorithm is reduced by averaging the kernel of the integral operator and localizing its singular part during discretization using simple analytical expressions. Examples of using this approach in the numerical solution of the original problem are given.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):44-49
44-49
MODIFICATION OF THE DISCONTINUOUS GALERKIN METHOD USING TIME-DEPENDENT BASIS FUNCTIONS
Abstract
In this paper, we propose a modification of the discontinuous Galerkin method using time-dependent basis functions. The use of such basis functions allows us to naturally and stably calculate strong discontinuities.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):50-58
50-58
ON THE ENERGY INTEGRALS OF A MIXED PROBLEM FOR A B-HYPERBOLIC EQUATION
Abstract
A mixed problem for the B-hyperbolic equation in Euclidean domains with different locations relative to singular coordinate hyperplanes is considered. In each of these domains, energy integrals with respect to the Lebesgue—Kipriyanov integral measure with weak and strong singularities are introduced. The absence of energy flow through coordinate singular hyperplanes, which are the internal boundary of mirror-symmetric regions in Euclidean space, is proven. If solutions to these problems exist, their uniqueness is proven.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):59–65
59–65
ON CERTAIN SPANNING SUBGRAPHS OF RANDOM GRAPHS
Abstract
Presented by Academician of the RAS V. V. Kozlov. An improvement of Riordan’s result on the threshold probability of the occurrence of a spanning subgraph in a random graph is obtained for some classes of subgraphs, which, in particular, implies an improved bound for the maximum power of a Hamiltonian cycle in a random graph. Moreover, the exact asymptotics of the threshold probability for the occurrence of spanning subgraphs from a wide class of k-degenerate graphs is found.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):66-70
66-70
ON THE SIZES OF k-SUBGRAPHS OF THE BINOMIAL RANDOM GRAPH
Abstract
Consider E(G, k) — the set of all sizes (numbers of edges) of induced subgraphs of size k in a given graph G with n vertices. For the binomial random graph G = G(n, p), we proved that, for each α > 0 and ε small enough, the set E(G, k) with high probability contains a large segment for all k such that (ln n)1+α < k < εn. We also found the asymptotic length of this segment.
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ. 2025;523(1):71-74
71-74