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Optimal Data Splitting in Distributed Optimization for Machine Learning Dokl. Math. (IF 0.6) Pub Date : 2024-03-25 D. Medyakov, G. Molodtsov, A. Beznosikov, A. Gasnikov
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Barcodes as Summary of Loss Function Topology Dokl. Math. (IF 0.6) Pub Date : 2024-03-25 S. A. Barannikov, A. A. Korotin, D. A. Oganesyan, D. I. Emtsev, E. V. Burnaev
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On Barenblatt–Zeldovich Intermediate Asymptotics Dokl. Math. (IF 0.6) Pub Date : 2024-03-14 V. A. Kostin, D. V. Kostin, A. V. Kostin
Abstract The concept of intermediate asymptotics for the solution of an evolution equation with initial data and a related solution obtained without initial conditions was introduced by G.N. Barenblatt and Ya.B. Zeldovich in the context of extending the concept of strict determinism in statistical physics and quantum mechanics. Here, according to V.P. Maslov, to axiomatize the mathematical theory,
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On Derivation of Equations of Gravitation from the Principle of Least Action, Relativistic Milne–McCrea Solutions, and Lagrange Points Dokl. Math. (IF 0.6) Pub Date : 2024-03-14 V. V. Vedenyapin, A. A. Bay, A. G. Petrov
Abstract Equations of gravitation in the form of Vlasov–Poisson relativistic equations with Lambda term are derived from the classical principle of least action. Hamilton–Jacobi consequences are used to obtain cosmological solutions. The properties of Lagrange points are investigated.
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Existence of a Maximum of Time-Averaged Harvesting in the KPP Model on Sphere with Permanent and Impulse Harvesting Dokl. Math. (IF 0.6) Pub Date : 2024-03-14 E. V. Vinnikov, A. A. Davydov, D. V. Tunitsky
Abstract A distributed renewable resource of any nature is considered on a two-dimensional sphere. Its dynamics is described by a model of the Kolmogorov–Petrovsky–Piskunov–Fisher type, and the exploitation of this resource is carried out by constant or periodic impulse harvesting. It is shown that, after choosing an admissible exploitation strategy, the dynamics of the resource tend to limiting dynamics
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Rotation Functions of Integrable Billiards As Orbital Invariants Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 G. V. Belozerov, A. T. Fomenko
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Artificially Generated Text Fragments Search in Academic Documents Dokl. Math. (IF 0.6) Pub Date : 2024-03-11
Abstract Recent advances in text generative models make it possible to create artificial texts that look like human-written texts. A large number of methods for detecting texts obtained using large language models have already been developed. However, improvement of detection methods occurs simultaneously with the improvement of generation methods. Therefore, it is necessary to explore new generative
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Neural Networks for Coordination Analysis Dokl. Math. (IF 0.6) Pub Date : 2024-03-11
Abstract This paper is dedicated to the development of a novel method for coordination analysis (CA) in English using the neural (deep learning) methods. An efficient solution for the task allows identifying potentially valuable links and relationships between specific parts of a sentence, making the extraction of coordinate structures an important text preprocessing tool. In this study, a number of
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Algorithms with Gradient Clipping for Stochastic Optimization with Heavy-Tailed Noise Dokl. Math. (IF 0.6) Pub Date : 2024-03-11
Abstract This article provides a survey of the results of several research studies [12–14, 26], in which open questions related to the high-probability convergence analysis of stochastic first-order optimization methods under mild assumptions on the noise were gradually addressed. In the beginning, we introduce the concept of gradient clipping, which plays a pivotal role in the development of stochastic
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On the Structure of Laplacian Characteristic Polynomial of Circulant Graphs Dokl. Math. (IF 0.6) Pub Date : 2024-03-11
Abstract The present work deals with the characteristic polynomial of Laplacian matrix for circulant graphs. We show that it can be decomposed into a finite product of algebraic function evaluated at the roots of a linear combination of Chebyshev polynomials. As an important consequence of this result, we get the periodicity of characteristic polynomials evaluated at the prescribed integer values.
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Aperiodical Isoperimetric Planar Homogenization with Critical Diameter: Universal Non-local Strange Term for a Dynamical Unilateral Boundary Condition Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 J. I. Díaz, T. A. Shaposhnikova, A. V. Podolskiy
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eco4cast: Bridging Predictive Scheduling and Cloud Computing for Reduction of Carbon Emissions for ML Models Training Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 M. Tiutiulnikov, V. Lazarev, A. Korovin, N. Zakharenko, I. Doroshchenko, S. Budennyy
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Text Reuse Detection in Handwritten Documents Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 A. V. Grabovoy, M. S. Kaprielova, A. S. Kildyakov, I. O. Potyashin, T. B. Seyil, E. L. Finogeev, Yu. V. Chekhovich
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Towards Efficient Learning of GNNs on High-Dimensional Multilayered Representations of Tabular Data Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 A. V. Medvedev, A. G. Djakonov
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Towards Discovery of the Differential Equations Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 A. A. Hvatov, R. V. Titov
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Graph Models for Contextual Intention Prediction in Dialog Systems Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 D. P. Kuznetsov, D. R. Ledneva
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Solvability Analysis of the Nonlinear Integral Equations System Arising in the Logistic Dynamics Model in the Case of Piecewise Constant Kernels Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 M. V. Nikolaev, A. A. Nikitin, U. Dieckmann
Abstract A nonlinear integral equation arising from a parametric closure of the third spatial moment in the single-species model of logistic dynamics of U. Dieckmann and R. Law is analyzed. The case of piecewise constant kernels is studied, which is important for further computer modeling. Sufficient conditions are found that guarantee the existence of a nontrivial solution to the equilibrium equation
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On a Paradoxical Property of the Shift Mapping on an Infinite-Dimensional Tori Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 S. D. Glyzin, A. Yu. Kolesov
Abstract An infinite-dimensional torus \({{\mathbb{T}}^{\infty }} = {{\ell }_{p}}{\text{/}}2\pi {{\mathbb{Z}}^{\infty }},\) where \({{\ell }_{p}},\) \(p \geqslant 1\), is a space of sequences and \({{\mathbb{Z}}^{\infty }}\) is a natural integer lattice in \({{\ell }_{p}},\) is considered. We study a classical question in the theory of dynamical systems concerning the behavior of trajectories of a
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Common Digital Space of Scientific Knowledge as an Integrator of Polythematic Information Resources Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 N. E. Kalenov, A. N. Sotnikov
Abstract The goals, objectives, and structure of the ontology of the Common Digital Space of Scientific Knowledge (CDSSK) are considered. The CDSSK is an integrated information structure that combines state scientific information systems presented on the Internet (the Great Russian Encyclopedia, the National Electronic Library, the State Catalog of Geographical Names, etc.) with industry information
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Accessible Russian Large Language Models: Open-Source Models and Instructive Datasets for Commercial Applications Dokl. Math. (IF 0.6) Pub Date : 2024-03-11
Abstract This paper presents an approach to developing and fine-tuning large language models for Russian language that are capable of following instructions across domains. As base models, XGLM-4.5B, LLaMA-1 7B, LLaMA-1 13B, LLaMA-2 7B, LLaMA-2 13B, and ruGPT-3.5 13B are used. This work compares two main fine-tuning techniques: fine-tuning all model parameters and fine-tuning using LoRA layers. To
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Operator Estimates for Problems in Domains with Singularly Curved Boundary: Dirichlet and Neumann Conditions Dokl. Math. (IF 0.6) Pub Date : 2024-03-11
Abstract We consider a system of second-order semilinear elliptic equations in a multidimensional domain with an arbitrarily curved boundary contained in a narrow layer along the unperturbed boundary. The Dirichlet or Neumann condition is imposed on the curved boundary. In the case of the Neumann condition, rather natural and weak conditions are additionally imposed on the structure of the curving
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Artificial Intelligence in Society Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 A. L. Semenov
Abstract This article is the author’s review of the singularity in which events in the field of artificial intelligence (AI) are developing. A general view is offered on the role of revolutions in information technology as they expand the human personality. The current stage of personal expansion is considered, covering the last decade, especially 2023. The most important and common socially significant
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Hierarchical Method for Cooperative Multiagent Reinforcement Learning in Markov Decision Processes Dokl. Math. (IF 0.6) Pub Date : 2024-03-11 V. E. Bolshakov, A. N. Alfimtsev
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Attack against Layered Defense Dokl. Math. (IF 0.6) Pub Date : 2024-03-04 V. V. Morozov
Abstract An attack–defense model is considered in which the defense party at each point of defense has several lines and uses a target allocation of its forces. The average damage caused by attack forces breaking through all defense points is used as a criterion for attack effectiveness. The problem of optimizing the defense force distribution over defense lines is solved, and optimal strategies of
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Individual Stability of Pareto Equilibrium of Threats and Counterthreats in a Coalition Differential Game without Side Payments Dokl. Math. (IF 0.6) Pub Date : 2024-03-04 V. I. Zhukovskiy, K. N. Kudryavtsev, L. V. Zhukovskaya, I. S. Stabulit
Abstract The notion of individual stability of a Pareto equilibrium of threats and counterthreats in a three-person linear-quadratic differential game without side payments is used. The corresponding equilibrium is found in explicit form.
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Equilibrium in Secure Strategies As a Development of the Concept of Nash Equilibrium Dokl. Math. (IF 0.6) Pub Date : 2024-03-04 M. B. Iskakov, A. B. Iskakov
Abstract As its main goal, the article advocates the rationality of the concept of equilibrium in secure strategies (EinSS) and the organic proximity of the logic of this concept to the logic underlying the classical approach to solving game-theory problems through Nash equilibrium. The article examines in detail the system of EinSS definitions through the prism of the Nash equilibrium concept. Based
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Average Tree Solution in Multi-Agent Systems with Network Structure Dokl. Math. (IF 0.6) Pub Date : 2024-03-04 A. V. Tur, L. A. Petrosyan
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Application of Bargaining Schemes for Equilibrium Determination in Dynamic Games Dokl. Math. (IF 0.6) Pub Date : 2024-03-04 V. V. Mazalov, A. N. Rettieva
Abstract Cooperation plays an important role in dynamic games related to resource management problems. To construct cooperative behavior in asymmetric (when players possess different discount factors) and multicriteria (when players have vector payoff functions) dynamic games, the standard approaches are not applicable. The paper presents methods based on bargaining schemes to determine cooperative
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Ramond and Neveu–Schwarz Algebras and Narrow Lie Superalgebras Dokl. Math. (IF 0.6) Pub Date : 2024-02-29 D. V. Millionshchikov, F. I. Pokrovsky
Abstract Two one-parameter families of positively graded Lie superalgebras generated by two elements and two relations that are narrow in the sense of Zelmanov and Shalev are considered. The first family contains the positive part R+ of the Ramond algebra, while the second one contains the positive part NS+ of the Neveu–Schwarz algebra. The results of the article are super analogues of Benoist’s theorem
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On Derivation of Vlasov–Maxwell–Einstein Equations from the Principle of Least Action, the Hamilton–Jacobi Method, and the Milne–McCrea Model Dokl. Math. (IF 0.6) Pub Date : 2024-02-29 V. V. Vedenyapin
Abstract In classical texts equations for gravitation and electromagnetic fields are proposed without deriving their right-hand sides [1–4]. In this paper, we derive the right-hand sides and analyze the energy–momentum tensor in the framework of Vlasov–Maxwell–Einstein equations and Milne–McCrea models. New models of accelerated expansion of the Universe without Einstein’s lambda are proposed.
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Accounting for Phase Limitations During Intense Acceleration of a Mobile Robot and Its Motion in Drift Mode Dokl. Math. (IF 0.6) Pub Date : 2024-02-29 S. A. Reshmin, M. T. Bektybaeva
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Deep Learning Approach to Classification of Acoustic Signals Using Information Features Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 P. V. Lysenko, I. A. Nasonov, A. A. Galyaev, L. M. Berlin
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SpiderNet: Fully Connected Residual Network for Fraud Detection Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 S. V. Afanasiev, A. A. Smirnova, D. M. Kotereva
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Spectral Neural Operators Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 V. S. Fanaskov, I. V. Oseledets
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A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraints Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 A. V. Konstantinov, L. V. Utkin
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Solving Large-Scale Routing Optimization Problems with Networks and Only Networks Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 A. G. Soroka, A. V. Meshcheryakov
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Adaptive Spectral Normalization for Generative Models Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 E. A. Egorov, A. I. Rogachev
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Automating the Temperament Assessment of Online Social Network Users Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 V. D. Oliseenko, A. O. Khlobystova, A. A. Korepanova, T. V. Tulupyeva
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Optimization of Physics-Informed Neural Networks for Solving the Nolinear Schrödinger Equation Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 I. Chuprov, Jiexing Gao, D. Efremenko, E. Kazakov, F. Buzaev, V. Zemlyakov
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An Explained Artificial Intelligence-Based Solution to Identify Depression Severity Symptoms Using Acoustic Features Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 S. Shalileh, A. O. Koptseva, T. I. Shishkovskaya, M. V. Khudyakova, O. V. Dragoy
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Deep Metric Learning: Loss Functions Comparison Dokl. Math. (IF 0.6) Pub Date : 2024-02-09 R. L. Vasilev, A. G. D’yakonov
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Probability Calibration with Fuzzy Set Theory to Improve Early Cancer Detection Dokl. Math. (IF 0.6) Pub Date : 2024-02-09
Abstract Cancer is the leading cause of death before the age of 70 years. An important step for reducing the cancer mortality can be its early detection. To improve the early diagnosis of cancer, we propose a novel probability calibration method based on the fuzzy set theory. Our approach was tested on the detection of female breast cancer and lung cancer. These are complicated by a small data set
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On the Integral Convergence of Numerical Schemes Calculating Gas-Dynamic Shock Waves Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 V. V. Ostapenko, E. I. Polunina, N. A. Khandeeva
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Fokker–Planck–Kolmogorov Equations with a Parameter Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 V. I. Bogachev, S. V. Shaposhnikov
Abstract For Fokker–Planck–Kolmogorov equations with coefficients depending measurably on a parameter we prove the existence of solutions that are measurable with respect to this parameter.
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Principle of Dynamic Balance of Demographic Process and the Limits of World Population Growth Dokl. Math. (IF 0.6) Pub Date : 2024-01-31
Abstract A new model of world population growth, including discrete equations for the dynamics of percentage increases in integral inflows and outflows and a balance equation for the population size, is proposed. The principle of dynamic balance of a demographic process and the condition of interval dynamic consistency based on this principle are formulated. A sample example of forecasting world population
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Countable Models of Complete Ordered Theories Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 T. S. Zambarnaya, B. S. Baizhanov
Abstract The article consists of observations regarding complete theories of countable signatures and their countable models. We provide a construction of a countable linearly ordered theory that has the same number of countable non-isomorphic models as the given countable, not necessarily linearly ordered, theory.
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Study of Volterra Integro-Differential Equations by Methods of Semigroup Theory Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 N. A. Rautian
Abstract Abstract Volterra integro-differential equations that are operator models of viscoelasticity problems are investigated. The class of equations under consideration also includes the Gurtin–Pipkin integro-differential equations describing heat propagation in media with memory. As kernels of integral operators, it is possible to use, in particular, sums of decreasing exponents or sums of Rabotnov
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On Attractors of Ginzburg–Landau Equations in Domain with Locally Periodic Microstructure: Subcritical, Critical, and Supercritical Cases Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 K. A. Bekmaganbetov, A. A. Tolemys, V. V. Chepyzhov, G. A. Chechkin
Abstract In the paper we consider a problem for complex Ginzburg–Landau equations in a medium with locally periodic small obstacles. It is assumed that the obstacle surface can have different conductivity coefficients. We prove that the trajectory attractors of this system converge in a certain weak topology to the trajectory attractors of the homogenized Ginzburg–Landau equations with an additional
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Optimization Spectral Problem for the Sturm–Liouville Operator in a Vector Function Space Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 V. A. Sadovnichii, Ya. T. Sultanaev, N. F. Valeev
Abstract An inverse spectral optimization problem is considered: given a matrix potential \({{Q}_{0}}(x)\) and a value \(\lambda {\kern 1pt} \text{*}\), find a matrix function \(\hat {Q}(x)\) closest to \({{Q}_{0}}(x)\) such that the kth eigenvalue of the Sturm–Liouville matrix operator with potential \(\hat {Q}(x)\) matches \(\lambda {\kern 1pt} \text{*}\). The main result of the paper is the proof
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Dirac Electron Free Field Anticommutator and Its Zeros on Time Intervals Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 E. A. Karatsuba
Abstract Estimates are obtained for time intervals containing a zero of the Pauli–Jordan–Dirac anticommutator in a discrete representation in the one- and three-dimensional cases.
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Semiproducts, Products, and Modal Predicate Logics: Some Examples Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 V. B. Shehtman, D. Shkatov
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Dynamics of a System of Two Equations with a Large Delay Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 S. A. Kashchenko, A. O. Tolbey
Abstract The local dynamics of systems of two equations with delay is considered. The main assumption is that the delay parameter is large enough. Critical cases in the problem of the stability of the equilibrium state are identified, and it is shown that they are of infinite dimension. Methods of infinite-dimensional normalization are used and further developed. The main result is the construction
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On the Finiteness of the Set of Generalized Jacobians with Nontrivial Torsion Points over Algebraic Number Fields Dokl. Math. (IF 0.6) Pub Date : 2024-01-31 V. P. Platonov, V. S. Zhgoon, G. V. Fedorov
Abstract For a smooth projective curve \(\mathcal{C}\) defined over an algebraic number field k, we investigate the finiteness of the set of generalized Jacobians \({{J}_{\mathfrak{m}}}\) of \(\mathcal{C}\) associated with modules \(\mathfrak{m}\) defined over \(k\) such that a fixed divisor representing a class of finite order in the Jacobian J of \(\mathcal{C}\) provides the torsion class in the
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Invariant Forms of Geodesic, Potential, and Dissipative Systems on Tangent Bundles of Finite-Dimensional Manifolds Dokl. Math. (IF 0.6) Pub Date : 2023-12-03 M. V. Shamolin
Abstract It is well known [1–3] that a system of differential equations can be exactly integrated if a sufficient number of its tensor invariants (not only first integrals) are found. For example, if there is an invariant differential form of the phase volume, the number of required first integrals can be reduced. For conservative systems, this fact is natural, but for systems with attracting or repelling
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On Solution Existence for a Singular Nonlinear Burgers Equation with Small Parameter and p-Regularity Theory Dokl. Math. (IF 0.6) Pub Date : 2023-12-03 B. Medak, A. A. Tret’yakov
Abstract In this paper we study a solution existence problem for the singular nonlinear Burgers equation \(F(u,\varepsilon ) = {{u}_{t}} - {{u}_{{xx}}} + u{{u}_{x}} + \varepsilon {{u}^{2}} = f(x,t),\) where \(F:\Omega \to C([0,\pi ] \times [0,T])\) and \(\Omega = {{C}^{2}}([0,\pi ] \times [0,T]) \times \mathbb{R}\), with small parameter ε under the boundary conditions \(u(0,t) = u(\pi ,t) = 0\) and
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On Subspaces of an Orlicz Space Spanned by Independent Identically Distributed Functions Dokl. Math. (IF 0.6) Pub Date : 2023-12-03 S. V. Astashkin
Abstract Subspaces of an Orlicz space LM generated by probabilistically independent copies of a function \(f \in {{L}_{M}}\), \(\int_0^1 {f(t){\kern 1pt} dt} = 0\), are studied. In terms of dilations of f, we get a characterization of strongly embedded subspaces of this type and obtain conditions that guarantee that the unit ball of such a subspace has equi-absolutely continuous norms in LM. A class
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Method for False Extrema Localization in Global Optimization Dokl. Math. (IF 0.6) Pub Date : 2023-12-03 Yu. G. Evtushenko, A. A. Tret’yakov
Abstract The problem of finding the global minimum of a nonnegative function on a positive parallelepiped in n-dimensional Euclidean space is considered. A method for localizing false extrema in a bounded domain near the origin is proposed, which allows one to separate the global minimum from the false ones by moving the former away from the latter. With a suitable choice of the starting point in the
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On Asymptotics of Attractors of the Navier–Stokes System in Anisotropic Medium with Small Periodic Obstacles Dokl. Math. (IF 0.6) Pub Date : 2023-12-03 K. A. Bekmaganbetov, A. M. Toleubay, G. A. Chechkin
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On Higher Integrability of the Gradient of Solutions to the Zaremba Problem for p-Laplace Equation Dokl. Math. (IF 0.6) Pub Date : 2023-12-03 Yu. A. Alkhutov, C. D’Apice, M. A. Kisatov, A. G. Chechkina
Abstract A higher integrability of the gradient of a solution to the Zaremba problem in a bounded Lipschitz plane domain is proved for an inhomogeneous p-Laplace equation.