Doklady Mathematics

Article	Citations
eco2AI: Carbon Emissions Tracking of Machine Learning Models as the First Step Towards Sustainable AI	15
Topological Modeling of Integrable Systems by Billiards: Realization of Numerical Invariants	15
Young Duality and Aggregation of Balances	11
On the Existence of a Global Solution of a Hyperbolic Problem	9
Classical Solutions of Hyperbolic Equations with Nonlocal Potentials	9
Force Evolutionary Billiards and Billiard Equivalence of the Euler and Lagrange Cases	9
Increased Integrability of the Gradient of the Solution to the Zaremba Problem for the Poisson Equation	9
Composition Operators on Weighted Sobolev Spaces and the Theory of $${{\mathcal{Q}}_{p}}$$-Homeomorphisms	9
Random Quantization of Hamiltonian Systems	9
Simulation of Seismic Waves in Anisotropic Media	9
Application of Pretrained Large Language Models in Embodied Artificial Intelligence	7
On L2-Dissipativity of a Linearized Explicit Finite-Difference Scheme with Quasi-Gasdynamic Regularization for the Barotropic Gas Dynamics System of Equations	7
On the Finiteness of the Number of Expansions into a Continued Fraction of $$\sqrt f $$ for Cubic Polynomials over Algebraic Number Fields	7
On the Generalized Gardner Problem for Phase-Locked Loops in Electrical Grids	7
On Global Classical Solutions of Hyperbolic Differential-Difference Equations	7
Uniqueness of Solutions of Initial-Boundary Value Problems for Parabolic Systems with Dini-Continuous Coefficients in Domains on the Plane	7
Schrödinger Quantization of Infinite-Dimensional Hamiltonian Systems with a Nonquadratic Hamiltonian Function	7
Arithmetic Properties of Euler-Type Series with a Liouvillian Polyadic Parameter	7
New Cases of Integrable Odd-Order Systems with Dissipation	6
Productive Education in Mathematical Schools	6
Many-Dimensional Zaremba Problem for an Inhomogeneous p-Laplace Equation	6
On the Zakharov–L’vov Stochastic Model for Wave Turbulence	6
Solution of the Fracture Detection Problem by Machine Learning Methods	6
Application of a Numerical-Asymptotic Approach to the Problem of Restoring the Parameters of a Local Stationary Source of Anthropogenic Pollution	6
On the Motion, Amplification, and Blow-up of Fronts in Burgers-Type Equations with Quadratic and Modular Nonlinearity	6

Estimate of the Number of Edges in Subgraphs of a Johnson Graph	6
On the Problem of Periodicity of Continued Fraction Expansions of $$\sqrt f $$for Cubic Polynomials over Number Fields	6
Combined Monotone Bicompact Scheme of Higher Order Accuracy in Domains of Influence of Nonstationary Shock Waves	6
Uniqueness of Solutions to Initial Boundary Value Problems for Parabolic Systems in Plane Bounded Domains with Nonsmooth Lateral Boundaries	6
Jacobi Stability of a Many-Body System with Modified Potential	5
Sub-Riemannian Engel Sphere	5
An Inverse Problem for a Semilinear Wave Equation	5
The Second Boundary Value Problem for Differential-Difference Equations	5
3D Filtering of Images Corrupted by Additive-Multiplicative Noise	5
Explicit Solutions for a Series of Optimization Problems with 2-Dimensional Control via Convex Trigonometry	5
Modeling of Radiative Heat Conduction on High-Performance Computing Systems	5
Bicompact Finite-Difference Scheme for Maxwell’s Equations in Layered Media	5
Hidden Boundary of Global Stability in a Counterexample to the Kapranov Conjecture on the Pull-In Range	5
Exact Solutions of Incompressible Navier–Stokes Equations in the Case of Oil and Gas Industrial Problems	4
Properties of an Aggregated Quasi-Gasdynamic System of Equations for a Homogeneous Gas Mixture	4
OntoMathPRO: An Ontology of Mathematical Knowledge	4
Two-Level Regression Method Using Ensembles of Trees with Optimal Divergence	4
Application of Special Function Spaces to the Study of Nonlinear Integral Equations Arising in Equilibrium Spatial Logistic Dynamics	4
On the Existence and Structure of Universal Functions	4
Minimal Self-Similar Peano Curve of Genus 5 × 5	4
Efficient Approximation of the Capacitated Vehicle Routing Problem in a Metric Space of an Arbitrary Fixed Doubling Dimension	4
Planning and Learning in Multi-Agent Path Finding	4
Problem of Determining the Anisotropic Conductivity in Electrodynamic Equations	4
Problem of Acoustic Diagnostics of a Damaged Zone	4
Accuracy of MUSCL-Type Schemes in Shock Wave Calculations	4
On Dividing Sets into Parts of Smaller Diameter	4
Dependence of the Dynamics of a Model of Coupled Oscillators on the Number of Oscillators	4
Differential Equations in Banach Algebras	4
Phaseless Problem of Determination of Anisotropic Conductivity in Electrodynamic Equations	4
Nonlocal Problems with Generalized Samarskii–Ionkin Condition for Some Classes of Nonstationary Differential Equations	3
Optimal Control and “Strange” Term Arising from Homogenization of the Poisson Equation in the Perforated Domain with the Robin-type Boundary Condition in the Critical Case	3
On Optimal Rotation of a Rigid Body by Applying Internal Forces	3
Classical Solutions of the First Boundary Value Problem for Parabolic Systems on the Plane	3
Computers as a Novel Mathematical Reality: I. A Personal Account	3
Regular Boundary Value Problems for the Dirac Operator	3
On the Maximal Cut in a Random Hypergraph	3
On the Periodicity Problem for the Continued Fraction Expansion of Elements of Hyperelliptic Fields with Fundamental S-Units of Degree at Most 11	3
Integral Estimates of Derivatives of Rational Functions in Hölder Domains	3
Stability Analysis of Artificial Ice Islands by Methods of Mathematical Modeling	3
Plans’ Periodicity Theorem for Jacobian of Circulant Graphs	3
Quantum Graphs with Small Edges: Holomorphy of Resolvents	3
Uniqueness of a Probability Solution to the Kolmogorov Equation with a Diffusion Matrix Satisfying Dini’s Condition	3
Analogues of Classical Goodness-of-Fit Tests for Distribution Tails	3
Representation of Synthesizable Differentiation-Invariant Subspaces of the Schwartz Space	3
Periodic Time-Optimal Controls on Two-Step Free-Nilpotent Lie Groups	2
On a Family of Complex-Valued Stochastic Processes	2
Asymptotics of the Number of Threshold Functions and the Singularity Probability of Random {±1}-Matrices	2
One Problem of Extremal Functional Interpolation and the Favard Constants	2
Generalization of the Landau and Becker–Pommerenke Inequalities	2
Covering Planar Sets	2

Markov Approximations of the Evolution of Quantum Systems	2
Modeling Formation and Removal of Limescale in Water Treatment Systems	2
Estimation of the Growth of the Degree of Nonconvexity of Reachable Sets in Terms of α-Sets	2
Numerical Analysis of Laminar–Turbulent Transition by Methods of Chaotic Dynamics	2
On the Spectrum of a Non-Self-Adjoint Quasiperiodic Operator	2
New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Two-Dimensional Manifolds	2
The Problem of Trajectories Avoiding a Sparse Terminal Set	2
Forecasting a Cyclical Downturn (Recession) in the US Economy Using a Mathematical Model of Hyman Minsky’s Theory of Financial Instability	2
New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Three-Dimensional Manifolds	2
On Derivation of Equations of Electrodynamics and Gravitation from the Principle of Least Action, the Hamilton–Jacobi Method, and Cosmological Solutions	2
Mathematical Structures Related to the Description of Quantum States	2
Tensor Invariants of Geodesic, Potential, and Dissipative Systems on Tangent Bundles of Two-Dimensional Manifolds	2
Group Structures on Algebraic Varieties	2
The Kolmogorov Problem on Uniqueness of Probability Solutions of a Parabolic Equation	2
Anisotropy-Based Approach to Communication Tuning for a Time-Varying Sensor Network System	2
Optimal Trajectory of an Observer Tracking the Motion of an Object Equipped with a Striking Device	2
Operator Spectrum Transformation in Hartree–Fock and Kohn–Sham Equations	2
On Gaussian Transition Operators	2
Zero Preservation for a Family of Multivalued Functionals, and Applications to the Theory of Fixed Points and Coincidences	2
On Oscillation Properties of Self-Adjoint Boundary Value Problems of Fourth Order	2
Densities of distributions of homogeneous functions of Gaussian random vectors	2
On Second-Order Parabolic and Hyperbolic Perturbations of a First-Order Hyperbolic System	2
Uniqueness and Existence Theorems for Solving Problems of Scattering Electromagnetic Waves by Anisotropic Bodies	2
New Problems in the Theory of Transcendental Polyadic Numbers	2
A Time-Dependent Strange Term Arising in Homogenization of an Elliptic Problem with Rapidly Alternating Neumann and Dynamic Boundary Conditions Specified at the Domain Boundary: The Critical Case	2
On the Period Length of a Functional Continued Fraction over a Number Field	2
On Large Deviations of a Sum of Independent Random Variables with Rapidly Decreasing Distribution Tails	2
Asymptotic Efficiency of Maximum Entropy Estimates	2
Constructive Solution of One Vector Equilibrium Problem	2
Kirchhoff Index for Circulant Graphs and Its Asymptotics	2
Method for Reduced Basis Discovery in Nonstationary Problems	2
Pólya–Schur Inequality and the Green Energy of a Discrete Charge	2
Applications of Zvonkin’s Transform to Stationary Kolmogorov Equations	2
Problem of Safely Tracking an Object Avoiding Observation in $${{\mathbb{R}}^{2}}$$	2
Mathematical Modeling of the Consumer Loan Market in Russia under Sanctions	2
Coarea Formula for Functions on 2-Step Carnot Groups with Sub-Lorentzian Structure	2
Optimization of Oscillations of Mechanical Systems	2
Randomization and Entropy in Machine Learning and Data Processing	2
On the Homogenization of an Optimal Control Problem in a Domain Perforated by Holes of Critical Size and Arbitrary Shape	2
On the Existence of Focus Singularities in One Model of a Lagrange Top with a Vibrating Suspension Point	2
Improving the Quality of Tomographic Images of a Medium Using Irradiation with Pulses of Different Duration	2
Refined Mathematical Model of Economic Dynamics under High Inflation and Unstable Development	1
On Numerical Modeling of Fiber Deformation and Destruction under Impact Load	1
Fundamental Research and Developments in the Field of Applied Artificial Intelligence	1
Space-Likeness of Classes of Level Surfaces on Carnot Groups and Their Metric Properties	1
Terminal Invariance of Jump Diffusions	1
Minimax-Maximin Relations for the Problem of Vector-Valued Criteria Optimization	1
ruSciBERT: A Transformer Language Model for Obtaining Semantic Embeddings of Scientific Texts in Russian	1
On the Existence of B-Root Subgroups on Affine Spherical Varieties	1
Extremum Conditions for Constrained Scalar Control of Two Nonsynchronous Oscillators in the Time-Optimal Control Problem	1
Correct Solvability and Exponential Stability for Solutions of Volterra Integro-Differential Equations	1
Functions of Pairs of Unbounded Noncommuting Self-Adjoint Operators under Perturbation	1
Coadjoint Orbits of Three-Step Free Nilpotent Lie Groups and Time-Optimal Control Problem	1
Identification of Nodal Points of an Elastic Inclusion in Elastic Plane	1
Adaptive Gauss–Newton Method for Solving Systems of Nonlinear Equations	1
Asymptotic Structure of Eigenvalues and Eigenvectors of Certain Triangular Hankel Matrices	1
On Kantorovich Problems with a Parameter	1
Suppression of Speckle Noise in Medical Images via Segmentation-Grouping of 3D Objects Using Sparse Contourlet Representation	1
Absence of Global Periodic Solutions for a Schrödinger-Type Nonlinear Evolution Equation	1
On the Strong Chromatic Number of Random Hypergraphs	1
Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws	1
Limiting Characteristics of Queueing Systems with Vanishing Perturbations	1
On Some Properties of Superreflexive Besov Spaces	1
Construction of Effective Randomized Projective Estimates for Solutions of Integral Equations Based on Legendre Polynomials	1
Suppression of Multiplicative Noise in Images via Grouping of Similar Objects	1
Binary Orlicz Spaces	1
SpiderNet: Fully Connected Residual Network for Fraud Detection	1
New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Four-Dimensional Manifolds	1
On the Chromatic Numbers of Random Hypergraphs	1
Methods for Calculating Zero-Level Instability of Electronic Circuits under Variations in Parameters and External Disturbances	1
Operator Estimates for the Steklov Problem in an Unbounded Domain with Rapidly Changing Conditions on the Boundary	1
On Implementation of Boolean Functions by Contact Circuits with a Constant Uniform Width	1
Double Potential Method for Modeling the Internal Flow of a Viscous Incompressible Liquid	1
Refinement of Optimal Control Problem for Practical Implementation of Its Solution	1
Numerical Modeling of Acoustic Processes in Gradient Media Using the Grid-Characteristic Method	1
Geometry of Factorization Identities for Discriminants	1
Deviation of an Object with a Striking Device from a Visibility Area of an Observer in $${{\mathbb{R}}^{3}}$$	1
An Inverse Problem for Electrodynamic Equations with Nonlinear Conductivity	1
New Correlative Randomized Algorithm for Estimating the Influence of the Medium Stochasticity on Particle Transport	1
Orthogonal Elements in Nonseparable Rearrangement Invariant Spaces	1

Self-Affine Tiling of Polyhedra	1
Asymptotics of Eigenvalues in the Orr–Sommerfeld Problem for Low Velocities of Unperturbed Flow	1
On the Correct Solvability of the Dirichlet Boundary Value Problem for the Generalized Helmholtz Equation in a Strip	1
Stationary Spherically Symmetric Solutions of the Vlasov–Poisson System in the Three-Dimensional Case	1
Equiconvergence of Spectral Decompositions for Sturm–Liouville Operators with a Distributional Potential in Scales of Spaces	1
On Alternating Quasipositive Links	1
System of Equations for the Marangoni Boundary Layer in Media with Ladyzhenskaya Rheological Law	1
Examples of Differential Systems with Contrasting Combinations of Lyapunov, Perron, and Upper-Limit Properties	1
Hybrid Grid-Characteristic Schemes for Arctic Seismic Problems	1
Noise-Immune Communication with Orthogonal Frequency Division Multiplexing Using Kravchenko Weight Function Processing	1
On the Bellman Function Method for Operators on Martingales	1
Adaptive Mesh Refinement Simulations of Gas Dynamic Flows on Hybrid Meshes	1
Asymptotics of the Independence Number of a Random Subgraph of the Graph G(n, r, < s)	1
Rigidity Theorem for Self-Affine Arcs	1
Mathematical Modeling of 3D Dynamic Processes near a Fracture Using the Schoenberg Fracture Model	1
Linear System of Differential Equations with a Quadratic Invariant as the Schrödinger Equation	1
Mathematical Modeling of Vibrational Combustion	1
A Method of Defining Central and Gibbs Measures and the Ergodic Method	1
Solvability of the Initial-Boundary Value Problem for the Kelvin–Voigt Fluid Motion Model with Variable Density	1
On Stability of Continuous Extensions of Mappings with Respect to Nemytskii Operator	1
Intelligent Technologies for Digital Transformation of Industrial Production	1
On Attractors of Reaction–Diffusion Equations in a Porous Orthotropic Medium	1
Nonstationary Venttsel Problem with VMOx Leading Coefficients	1
On Stabilization of the Poisson Integral and Tikhonov–Stieltjes Means: Two-Sided Estimate	1
Reachable Sets and Integral Funnels of Differential Inclusions Depending on a Parameter	1
Combined Multidimensional Bicompact Scheme with Higher Order Accuracy in Domains of Influence of Nonstationary Shock Waves	1
Quotients of Severi–Brauer Surfaces	1
Mathematical Modeling of Overcoming the COVID-19 Pandemic and Restoring Economic Growth	1
Accelerated Gradient Sliding for Minimizing a Sum of Functions	1
Schur Complement and Continuous Spectrum in a Kinetic Plasma Model	1
Dynamics of a Chain of Logistic Equations with Delay and Antidiffusive Coupling	1
On Stable Random Variables with a Complex Stability Index	1
Sharp Dimension Estimates for the Attractors of the Regularized Damped Euler System	1
Invariant Forms of Geodesic, Potential, and Dissipative Systems on Tangent Bundles of Finite-Dimensional Manifolds	0
On Moment Methods in Krylov Subspaces	0
On the 4-Spectrum of First-Order Properties of Random Graphs	0
Mathematical Elements of Elementary Education	0
A Generalization of the First Beurling–Malliavin Theorem	0
Principle of Dynamic Balance of Demographic Process and the Limits of World Population Growth	0
Uniform, on the Real Line, Equiconvergence of Spectral Expansions for the Higher-Order Differential Operators	0
On the Finiteness of the Set of Generalized Jacobians with Nontrivial Torsion Points over Algebraic Number Fields	0
Conditions for Dissipativity of an Explicit Finite-Difference Scheme for a Linearized Multidimensional Quasi-Gasdynamic System of Equations	0
Erratum to: On Thermal Boundary Layer in a Viscous Non-Newtonian Medium	0
Existence and Stability of Equilibrium Solutions of the Vlasov Equation with a Modified Gravitational Potential	0
Reciprocal Function Method for Cauchy Problems with First-Order Poles	0
Integrability of a Geodesic Flow on the Intersection of Several Confocal Quadrics	0
On One Approach to the Estimation of a Triangular Element Degeneration in a Triangulation	0
Construction of Infinite Finitely Presented Nilsemigroup	0
Interpolation of Spaces of Functions of Positive Smoothness on a Domain	0
The Lattice of Definability: Origins, Recent Developments, and Further Directions	0
WKB Method for Nonlinear Equations of Emden–Fowler Type	0
Equilibria in a Dynamic Model of Coordination of Two Firms with Nonfixed Prices	0
On the Dynamics of Systems with Two Degrees of Freedom	0
Axiomatic Definition of Small Cancellation Rings	0
Two-Colorings of Normed Spaces with No Long Monochromatic Unit Arithmetic Progressions	0
On Asymptotics of Attractors of the Navier–Stokes System in Anisotropic Medium with Small Periodic Obstacles	0
The Software System LingvoDoc and the Possibilities It Offers for Documentation and Analysis of Ob-Ugric Languages	0
Three Infinite Families of Shilla Graphs Do Not Exist	0
Foundations of Mathematical Education in the Digital Age	0
Mathematical Modeling of Melting Tungsten Exposed to Pulsed Laser Beam	0
Dynamics of a System of Two Equations with a Large Delay	0
Trajectory of an Observer Tracking Object Motion around Convex Obstacles in $${{\mathbb{R}}^{2}}$$ and $${{\mathbb{R}}^{3}}$$	0
On Procedures for Testing the Equivalence of Distribution Tails	0
On Fixed Points of Continuous Mappings Associated with Construction of Artificial Neural Networks	0
Numerical Solution of Scalar Diffraction Problems in Integral Statements on Spectra of Integral Operators	0
Construction of Families of Equations to Describe Irregular Solutions in the Fermi–Pasta–Ulam Problem	0
Inverse Problem for a Monoid with an Exponential Sequence of Primes	0
On Interpretations of Presburger Arithmetic in Büchi Arithmetics	0
Erratum to: Abductive Reasoning in Explanation Problems of an Observed Effect	0
On Polyadic Liouville Numbers	0
Solutions of Cooperative Differential Games with Partner Sets	0
Arithmetic Properties of the Values of Generalized Hypergeometric Series with Polyadic Transcendental Parameters	0
Simple Pursuit Problem with Phase Constraints of Two Coordinated Evaders on Time Scales	0
On Topological Classification of Regular Denjoy Type Homeomorphisms	0
On Subspaces of an Orlicz Space Spanned by Independent Identically Distributed Functions	0
Attractors of an Autonomous Model of Nonlinear Viscous Fluid	0
Sub-Riemannian Cartan Sphere	0
Optimization of Oscillations of Mechanical Systems with Friction	0
Contact Geometry in Optimal Control of Thermodynamic Processes for Gases	0
Scheduling in Multiagent Systems Using Reinforcement Learning	0
Interference-Based Logic Gates	0
Study of Volterra Integro-Differential Equations by Methods of Semigroup Theory	0
New Cases of Integrability of Systems of Geodesics and Potential and Dissipative Systems on Tangent Bundles of Finite-Dimensional Manifolds	0
Invariant Volume Forms of Variable Dissipation Systems with Three Degrees of Freedom	0
On Periodic Solutions of Quasilinear Parabolic Equations with Boundary Conditions of Bitsadze–Samarskii Type	0
Two-Stage Method for Solving Systems of Nonlinear Equations and Its Applications to the Inverse Atmospheric Sounding Problem	0
Proof of Stability in the Brower–Paul Problem	0
Polyadic Liouville Numbers	0
Minimum Clique-Free Subgraphs of Kneser Graphs	0
Estimation of Weighted Kloosterman Sums with the Help of Additive Shift	0
Periodicity Criterion for Continued Fractions of Key Elements in Hyperelliptic Fields	0
Individual Stability of Pareto Equilibrium of Threats and Counterthreats in a Coalition Differential Game without Side Payments	0
Behavior of Binomial Distribution near Its Median	0
Computers As a Novel Mathematical Reality: IV. The Goldbach Problem	0
Quasi-Normal Forms in the Problem of Vibrations of Pedestrian Bridges	0