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Дифференциальные уравнения и их приложения в математическом моделировании: материалы XIII Международной научной конференции (Саранск, 12–16 июля 2017 г.)
Saransk :
Средневолжское математическое общество (СВМО), 2017.
Chapters
Zhukova N., В кн.: Дифференциальные уравнения и их приложения в математическом моделировании: материалы XIII Международной научной конференции (Саранск, 12–16 июля 2017 г.).: Саранск: Средневолжское математическое общество (СВМО), 2017. С. 403–407.
Complete affine foliations (i.e., foliations admitting the affine geometry as the transversal structure) are investigated. The strong transversal equivalence of complete affine foliations is considered, which is a more refined notion than the transverse equivalence of foliations in the sense of Molino. The classification of complete affine foliations with respect to the strong transversal equivalence ...
Added: November 13, 2017
Kruglov V., Pochinka O., В кн.: Дифференциальные уравнения и их приложения в математическом моделировании: материалы XIII Международной научной конференции (Саранск, 12–16 июля 2017 г.).: Саранск: Средневолжское математическое общество (СВМО), 2017. Гл. 59 С. 418–427.
A lot of many sorts of graphs (directed, multicolored, bipartite, etc.) were
repeatedly used to describe and realize systems with regular dynamics on surfaces. For
example, Morse-Smale flows are completely described by a directed graph equipped
with a subgraph system. In addition, their dynamics can be described by three-color
graphs. Four-color graphs describe the dynamics of some non structurally ...
Added: November 15, 2017
Pochinka O., Nozdrinova E., В кн.: Дифференциальные уравнения и их приложения в математическом моделировании: материалы XIII Международной научной конференции (Саранск, 12–16 июля 2017 г.).: Саранск: Средневолжское математическое общество (СВМО), 2017. С. 408–417.
В настоящей работе рассматриваются полярные диффеоморфизмы поверхности, то есть диффеоморфизмы, имеющие единственную стоковую и единственную источниковую периодические орбиты. Классическим примером такого диффеоморфизма является диффеоморфизм источник-сток'', который не имеет седловых точек и существует только на двумерной сфере. Однако, добавление даже одной седловой орбиты значительно расштряет класс полярных диффеоморфизмов на поверхностях. В частности в этой работе авторами ...
Added: November 14, 2017
Language:
Russian
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций,
включенных в программу Воронежской зимней матаматической школы С. Г. Крейна - 2026. ...
Added: June 25, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Androsov I., Proceedings of the Institute for System Programming of the RAS 2026 Vol. 38 No. 3 P. 87–114
This paper examines echo state networks (ESNs), one of the most prevalent approaches to
implementing reservoir computing. An ESN consists of a recurrent neural network with fixed (untrained)
weights and a readout layer that is typically linear and trainable. This approach enables the creation of energyefficient and computationally efficient neural networks capable of real-time learning. However, since ...
Added: May 26, 2026
Гущина В. А., / Series chemrxiv-2023-vpzhz-v2 "ChemRxiv". 2023.
All-inorganic perovskite CsPbBr3 and Cs4PbBr6 nanoparticles are being intensively studied due to their unique properties and wide range of applications; however, however, the nature of their optical properties is not yet fully understood due to the difficulty of synthesis of singlephase nanoparticles. In this article we describe the features of the synthesis of single-phase particles ...
Added: May 14, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...
Added: December 3, 2025
Bogomolov F. A., Schrandt S., / Series arXiv "math". 2025.
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree. ...
Added: December 1, 2025
Koltsov S., Ignatenko V., Surkov A. et al., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 527 С. 311–319
В данной работе рассматривается способность малых рассуждающих языковых моделей к построению аналитических решений дифференциальных уравнений. Компьютерные эксперименты проводятся на таких моделях, как DeepSeek-R1-Distill-Qwen-1.5B, Qwen2.5-1.5B и Open-Reasoner-Zero-1.5B. Для извлечения финального ответа из рассуждений моделей используется постобработка на основе двух языковых моделей – Qwen2.5.latest и llama3.2.latest. Затем извлеченные ответы сравниваются с эталонными решениями с помощью метрики BLEU. ...
Added: November 27, 2025
М.: ФГБУ «Российская академия наук», 2025.
СПЕЦИАЛЬНЫЙ ВЫПУСК: ТЕХНОЛОГИИ ИСКУССТВЕННОГО ИНТЕЛЛЕКТА И МАШИННОГО ОБУЧЕНИЯ ...
Added: November 27, 2025
Ignatenko V., Surkov A., Zakharov V. et al., Sci 2025 Vol. 7 No. 3 Article 130
Large language models (LLMs) have recently demonstrated remarkable capabilities in natural language processing, mathematical reasoning, and code generation. However, their potential for solving differential equations—fundamental to applied mathematics, physics, and engineering—remains insufficiently explored. For the first time, we applied LLMs as translators from the textual form of an equation into the textual representation of its ...
Added: October 10, 2025