Doklady Mathematics

Article	Citations
eco2AI: Carbon Emissions Tracking of Machine Learning Models as the First Step Towards Sustainable AI	23
Topological Modeling of Integrable Systems by Billiards: Realization of Numerical Invariants	16
Young Duality and Aggregation of Balances	11
Increased Integrability of the Gradient of the Solution to the Zaremba Problem for the Poisson Equation	10
Simulation of Seismic Waves in Anisotropic Media	10
Force Evolutionary Billiards and Billiard Equivalence of the Euler and Lagrange Cases	10
Schrödinger Quantization of Infinite-Dimensional Hamiltonian Systems with a Nonquadratic Hamiltonian Function	9
Classical Solutions of Hyperbolic Equations with Nonlocal Potentials	9
Random Quantization of Hamiltonian Systems	9
Composition Operators on Weighted Sobolev Spaces and the Theory of $${{\mathcal{Q}}_{p}}$$-Homeomorphisms	9
On the Existence of a Global Solution of a Hyperbolic Problem	9
On Optimal Rotation of a Rigid Body by Applying Internal Forces	8
Application of a Numerical-Asymptotic Approach to the Problem of Restoring the Parameters of a Local Stationary Source of Anthropogenic Pollution	8
On the Finiteness of the Number of Expansions into a Continued Fraction of $$\sqrt f $$ for Cubic Polynomials over Algebraic Number Fields	8
Application of Pretrained Large Language Models in Embodied Artificial Intelligence	8
On the Generalized Gardner Problem for Phase-Locked Loops in Electrical Grids	7
Many-Dimensional Zaremba Problem for an Inhomogeneous p-Laplace Equation	7
Estimate of the Number of Edges in Subgraphs of a Johnson Graph	7
Uniqueness of Solutions of Initial-Boundary Value Problems for Parabolic Systems with Dini-Continuous Coefficients in Domains on the Plane	7
Combined Monotone Bicompact Scheme of Higher Order Accuracy in Domains of Influence of Nonstationary Shock Waves	7
Arithmetic Properties of Euler-Type Series with a Liouvillian Polyadic Parameter	7
Productive Education in Mathematical Schools	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 Motion, Amplification, and Blow-up of Fronts in Burgers-Type Equations with Quadratic and Modular Nonlinearity	7
Dependence of the Dynamics of a Model of Coupled Oscillators on the Number of Oscillators	6

Sub-Riemannian Engel Sphere	6
On the Problem of Periodicity of Continued Fraction Expansions of $$\sqrt f $$for Cubic Polynomials over Number Fields	6
Uniqueness of Solutions to Initial Boundary Value Problems for Parabolic Systems in Plane Bounded Domains with Nonsmooth Lateral Boundaries	6
Two-Level Regression Method Using Ensembles of Trees with Optimal Divergence	5
Planning and Learning in Multi-Agent Path Finding	5
Problem of Acoustic Diagnostics of a Damaged Zone	5
Hidden Boundary of Global Stability in a Counterexample to the Kapranov Conjecture on the Pull-In Range	5
Explicit Solutions for a Series of Optimization Problems with 2-Dimensional Control via Convex Trigonometry	5
3D Filtering of Images Corrupted by Additive-Multiplicative Noise	5
Accuracy of MUSCL-Type Schemes in Shock Wave Calculations	5
An Inverse Problem for a Semilinear Wave Equation	5
The Second Boundary Value Problem for Differential-Difference Equations	5
Bicompact Finite-Difference Scheme for Maxwell’s Equations in Layered Media	5
OntoMathPRO: An Ontology of Mathematical Knowledge	4
Integral Estimates of Derivatives of Rational Functions in Hölder Domains	4
On the Existence and Structure of Universal Functions	4
Properties of an Aggregated Quasi-Gasdynamic System of Equations for a Homogeneous Gas Mixture	4
Problem of Determining the Anisotropic Conductivity in Electrodynamic Equations	4
Application of Special Function Spaces to the Study of Nonlinear Integral Equations Arising in Equilibrium Spatial Logistic Dynamics	4
On the Existence of Focus Singularities in One Model of a Lagrange Top with a Vibrating Suspension Point	4
Efficient Approximation of the Capacitated Vehicle Routing Problem in a Metric Space of an Arbitrary Fixed Doubling Dimension	4
Phaseless Problem of Determination of Anisotropic Conductivity in Electrodynamic Equations	4
Exact Solutions of Incompressible Navier–Stokes Equations in the Case of Oil and Gas Industrial Problems	4
On Dividing Sets into Parts of Smaller Diameter	4
Plans’ Periodicity Theorem for Jacobian of Circulant Graphs	3
Nonlocal Problems with Generalized Samarskii–Ionkin Condition for Some Classes of Nonstationary Differential Equations	3
On the Period Length of a Functional Continued Fraction over a Number Field	3
Uniqueness of a Probability Solution to the Kolmogorov Equation with a Diffusion Matrix Satisfying Dini’s Condition	3
Stability Analysis of Artificial Ice Islands by Methods of Mathematical Modeling	3
On Oscillation Properties of Self-Adjoint Boundary Value Problems of Fourth Order	3
Tensor Invariants of Geodesic, Potential, and Dissipative Systems on Tangent Bundles of Two-Dimensional Manifolds	3
On the Maximal Cut in a Random Hypergraph	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
Anisotropy-Based Approach to Communication Tuning for a Time-Varying Sensor Network System	3
Representation of Synthesizable Differentiation-Invariant Subspaces of the Schwartz Space	3
Computers as a Novel Mathematical Reality: I. A Personal Account	3
Regular Boundary Value Problems for the Dirac Operator	3
On Derivation of Equations of Electrodynamics and Gravitation from the Principle of Least Action, the Hamilton–Jacobi Method, and Cosmological Solutions	3
Quantum Graphs with Small Edges: Holomorphy of Resolvents	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
Analogues of Classical Goodness-of-Fit Tests for Distribution Tails	3
Classical Solutions of the First Boundary Value Problem for Parabolic Systems on the Plane	3
Mathematical Modeling of the Consumer Loan Market in Russia under Sanctions	2
Periodic Time-Optimal Controls on Two-Step Free-Nilpotent Lie Groups	2
On Second-Order Parabolic and Hyperbolic Perturbations of a First-Order Hyperbolic System	2
Asymptotics of the Number of Threshold Functions and the Singularity Probability of Random {±1}-Matrices	2
Terminal Invariance of Jump Diffusions	2
Improving the Quality of Tomographic Images of a Medium Using Irradiation with Pulses of Different Duration	2
Generalization of the Landau and Becker–Pommerenke Inequalities	2
Operator Spectrum Transformation in Hartree–Fock and Kohn–Sham Equations	2

Problem of Safely Tracking an Object Avoiding Observation in $${{\mathbb{R}}^{2}}$$	2
Markov Approximations of the Evolution of Quantum Systems	2
New Correlative Randomized Algorithm for Estimating the Influence of the Medium Stochasticity on Particle Transport	2
On the Strong Chromatic Number of Random Hypergraphs	2
Refinement of Optimal Control Problem for Practical Implementation of Its Solution	2
The Problem of Trajectories Avoiding a Sparse Terminal Set	2
On Gaussian Transition Operators	2
New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Three-Dimensional Manifolds	2
New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Two-Dimensional Manifolds	2
On a Family of Complex-Valued Stochastic Processes	2
Forecasting a Cyclical Downturn (Recession) in the US Economy Using a Mathematical Model of Hyman Minsky’s Theory of Financial Instability	2
Asymptotic Efficiency of Maximum Entropy Estimates	2
One Problem of Extremal Functional Interpolation and the Favard Constants	2
On the Homogenization of an Optimal Control Problem in a Domain Perforated by Holes of Critical Size and Arbitrary Shape	2
The Kolmogorov Problem on Uniqueness of Probability Solutions of a Parabolic Equation	2
Expanded Personality As the Main Entity and Subject of Philosophical Analysis: Implications for Education	2
Zero Preservation for a Family of Multivalued Functionals, and Applications to the Theory of Fixed Points and Coincidences	2
Examples of Differential Systems with Contrasting Combinations of Lyapunov, Perron, and Upper-Limit Properties	2
Kirchhoff Index for Circulant Graphs and Its Asymptotics	2
Optimal Trajectory of an Observer Tracking the Motion of an Object Equipped with a Striking Device	2
Densities of distributions of homogeneous functions of Gaussian random vectors	2
Applications of Zvonkin’s Transform to Stationary Kolmogorov Equations	2
Uniqueness and Existence Theorems for Solving Problems of Scattering Electromagnetic Waves by Anisotropic Bodies	2
On the Spectrum of a Non-Self-Adjoint Quasiperiodic Operator	2
Noise-Immune Communication with Orthogonal Frequency Division Multiplexing Using Kravchenko Weight Function Processing	2
Nonstationary Venttsel Problem with VMOx Leading Coefficients	2
Mathematical Structures Related to the Description of Quantum States	2
New Problems in the Theory of Transcendental Polyadic Numbers	2
ruSciBERT: A Transformer Language Model for Obtaining Semantic Embeddings of Scientific Texts in Russian	2
Group Structures on Algebraic Varieties	2
Pólya–Schur Inequality and the Green Energy of a Discrete Charge	2
Modeling Formation and Removal of Limescale in Water Treatment Systems	2
Covering Planar Sets	2
Method for Reduced Basis Discovery in Nonstationary Problems	2
Optimization of Oscillations of Mechanical Systems	2
Randomization and Entropy in Machine Learning and Data Processing	2
Estimation of the Growth of the Degree of Nonconvexity of Reachable Sets in Terms of α-Sets	2
Numerical Modeling of Acoustic Processes in Gradient Media Using the Grid-Characteristic Method	2
Double Potential Method for Modeling the Internal Flow of a Viscous Incompressible Liquid	1
Construction of Effective Randomized Projective Estimates for Solutions of Integral Equations Based on Legendre Polynomials	1
Quotients of Severi–Brauer Surfaces	1
Mathematical Modeling of Vibrational Combustion	1
Methods for Calculating Zero-Level Instability of Electronic Circuits under Variations in Parameters and External Disturbances	1
Sharp Dimension Estimates for the Attractors of the Regularized Damped Euler System	1
On Attractors of Reaction–Diffusion Equations in a Porous Orthotropic Medium	1
Semiproducts, Products, and Modal Predicate Logics: Some Examples	1
Spectral Neural Operators	1
Deviation of an Object with a Striking Device from a Visibility Area of an Observer in $${{\mathbb{R}}^{3}}$$	1
Geometry of Factorization Identities for Discriminants	1
Coadjoint Orbits of Three-Step Free Nilpotent Lie Groups and Time-Optimal Control Problem	1
Self-Affine Tiling of Polyhedra	1
On One Approach to the Estimation of a Triangular Element Degeneration in a Triangulation	1
Adaptive Gauss–Newton Method for Solving Systems of Nonlinear Equations	1
Combined Multidimensional Bicompact Scheme with Higher Order Accuracy in Domains of Influence of Nonstationary Shock Waves	1
Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws	1
On Asymptotics of Attractors of the Navier–Stokes System in Anisotropic Medium with Small Periodic Obstacles	1
Digital Ark of Knowledge	1
Hybrid Grid-Characteristic Schemes for Arctic Seismic Problems	1
Computational Complexity of Theories of a Binary Predicate with a Small Number of Variables	1
Fundamental Research and Developments in the Field of Applied Artificial Intelligence	1
New Cases of Homogeneous Integrable Systems with Dissipation on Tangent Bundles of Four-Dimensional Manifolds	1
On Stabilization of the Poisson Integral and Tikhonov–Stieltjes Means: Two-Sided Estimate	1
The Work of a Mathematician As a Prefiguring of Mastering Mathematics by Students: The Role of Experiments	1
Adaptive Mesh Refinement Simulations of Gas Dynamic Flows on Hybrid Meshes	1
Identification of Nodal Points of an Elastic Inclusion in Elastic Plane	1
Mathematical Modeling of 3D Dynamic Processes near a Fracture Using the Schoenberg Fracture Model	1
Minimax-Maximin Relations for the Problem of Vector-Valued Criteria Optimization	1
Schur Complement and Continuous Spectrum in a Kinetic Plasma Model	1
Extremum Conditions for Constrained Scalar Control of Two Nonsynchronous Oscillators in the Time-Optimal Control Problem	1
Linear System of Differential Equations with a Quadratic Invariant as the Schrödinger Equation	1
Binary Orlicz Spaces	1
Suppression of Speckle Noise in Medical Images via Segmentation-Grouping of 3D Objects Using Sparse Contourlet Representation	1
Intelligent Technologies for Digital Transformation of Industrial Production	1
Bicompact Schemes for Compressible Navier–Stokes Equations	1
A Method of Defining Central and Gibbs Measures and the Ergodic Method	1
On Stability of Continuous Extensions of Mappings with Respect to Nemytskii Operator	1
Mathematical Modeling of Melting Tungsten Exposed to Pulsed Laser Beam	1
Reachable Sets and Integral Funnels of Differential Inclusions Depending on a Parameter	1
Asymptotic Structure of Eigenvalues and Eigenvectors of Certain Triangular Hankel Matrices	1
Stationary Spherically Symmetric Solutions of the Vlasov–Poisson System in the Three-Dimensional Case	1

Absence of Global Periodic Solutions for a Schrödinger-Type Nonlinear Evolution Equation	1
Computer Experiment in Teaching Mathematics	1
On Linear-Quadratic Differential Games for Fractional-Order Systems	1
Neural Network Approach to the Problem of Predicting Interest Rate Anomalies under the Influence of Correlated Noise	1
Accelerated Gradient Sliding for Minimizing a Sum of Functions	1
On the Problem of Describing Elements of Elliptic Fields with a Periodic Expansion into a Continued Fraction over Quadratic Fields	1
Suppression of Multiplicative Noise in Images via Grouping of Similar Objects	1
Solvability of the Initial-Boundary Value Problem for the Kelvin–Voigt Fluid Motion Model with Variable Density	1
On the Chromatic Numbers of Random Hypergraphs	1
On the Existence of B-Root Subgroups on Affine Spherical Varieties	1
On Kantorovich Problems with a Parameter	1
SpiderNet: Fully Connected Residual Network for Fraud Detection	1
Dynamics of a Chain of Logistic Equations with Delay and Antidiffusive Coupling	1
On Alternating Quasipositive Links	1
Operator Estimates for the Steklov Problem in an Unbounded Domain with Rapidly Changing Conditions on the Boundary	1
Space-Likeness of Classes of Level Surfaces on Carnot Groups and Their Metric Properties	1
On Some Properties of Superreflexive Besov Spaces	1
Estimate for the Domain of Univalence in the Class of Holomorphic Self-Maps of a Disk with Two Boundary Fixed Points	1
On Stable Random Variables with a Complex Stability Index	1
Features of the Statistical Distribution of a Quasi-Harmonic Signal Phase	1
Functions of Pairs of Unbounded Noncommuting Self-Adjoint Operators under Perturbation	1
Correct Solvability and Exponential Stability for Solutions of Volterra Integro-Differential Equations	1
Refined Mathematical Model of Economic Dynamics under High Inflation and Unstable Development	1
The Lattice of Definability: Origins, Recent Developments, and Further Directions	1
An Inverse Problem for Electrodynamic Equations with Nonlinear Conductivity	1
Foundations of Mathematical Education in the Digital Age	1
Trusted Artificial Intelligence: Challenges and Promising Solutions	1
Asymptotics of Eigenvalues in the Orr–Sommerfeld Problem for Low Velocities of Unperturbed Flow	1
Mathematical Modeling of Overcoming the COVID-19 Pandemic and Restoring Economic Growth	1
Equiconvergence of Spectral Decompositions for Sturm–Liouville Operators with a Distributional Potential in Scales of Spaces	1
System of Equations for the Marangoni Boundary Layer in Media with Ladyzhenskaya Rheological Law	1
Rigidity Theorem for Self-Affine Arcs	1
On Convergence of Finite-Difference Shock-Capturing Schemes in Regions of Shock Waves Influence	1
Limiting Characteristics of Queueing Systems with Vanishing Perturbations	1
On the Bellman Function Method for Operators on Martingales	1
On Numerical Modeling of Fiber Deformation and Destruction under Impact Load	1
Orthogonal Elements in Nonseparable Rearrangement Invariant Spaces	1
Asymptotics of the Independence Number of a Random Subgraph of the Graph G(n, r, < s)	1
On Implementation of Boolean Functions by Contact Circuits with a Constant Uniform Width	1
On the Correct Solvability of the Dirichlet Boundary Value Problem for the Generalized Helmholtz Equation in a Strip	1