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Конечно-гладкая локальная эквивалентность автономных систем с одним нулевым корнем
Математические заметки. 2010. Т. 88. № 2. С. 275–287.
In a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations for which one eigenvalue of the matrix of the linear part is zero and the remaining eigenvalues do not belong to the imaginary axis. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.
Keywords: обыкновенные дифференциальные уравненияordinary differential equationsautonomous systemsingular pointzero eigenvaluetaylor seriesnormal formN-jet of a functionавтономная системаособая точкаряды Тейлоранормальная формаfinitely smooth equivalenceлокальная гладкая эквивалентностьнулевое собственное значениеN-струя функции
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 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
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
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
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
Deviatov R., Baek S., / Series arXiv "math". 2025.
The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for the torsion index of half-spin groups, the only remaining case in the calculation of ...
Added: December 1, 2025
Amerik E., Verbitsky M., Sao Paulo Journal of Mathematical Sciences 2024 Vol. 18 P. 540–557
Let M be a holomorphically symplectic complex manifold, not necessarily compact or quasiprojective, and a compact Lagrangian submanifold. We construct a deformation to the normal cone, showing that a neighbourhood of X can be deformed to its neighbourhood in. This is used to study Lagrangian submanifolds which can be bimeromorphically contracted to a point. We ...
Added: December 3, 2024
Бляхман Л.Г., Громов Е.М., ISBN 978-5-907868-27-4, 2024.
Приводится банк задач контрольных работ по математическому анализу для студентов международного бакалавриата по бизнесу и экономики. С примерами решений нулевых выариантов. ...
Added: May 17, 2024
Lomonosov T., , in: Abstracts of the 9th International Conference on Differential and Functional Differential Equations.: [б.и.], 2022. P. 77–78.
An algebraic approach to solving certain nonhomogeneous ODEs is studied. The approach is also extendable to solving certain nonhomogeneous difference equations. The approach is based on representing the right-hand side of the equation as an element of a certain vector space, the restriction of the d/dx operator on which is an automorphism space. ...
Added: July 5, 2022
Springer, 2020.
This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019.
First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. ...
Added: November 1, 2020
Kondratieva L. A., A.V. Romanov, Electronic Journal of Qualitative Theory of Differential Equations 2019 No. 96 P. 1–11
We show that the presence of a two-dimensional inertial manifold for an ordinary differential equation in Rn permits reducing the problem of determining asymptotically orbitally stable limit cycles to the Poincaré–Bendixson theory. In the case n = 3 we implement such a scenario for a model of a satellite rotation around a celestial body of ...
Added: December 22, 2019
Rabinowitch A., Московский технологический университет (МИРЭА), 2018.
В учебно-методическом пособии рассмотрены основные методы решения обыкновенных дифференциальных уравнений. Даются общие подходы к решению линейных и нелинейных дифференциальных уравнений первого порядка. Подробно излагаются основные методы решения линейных дифференциальных уравнений порядка выше первого и систем линейных дифференциальных уравнений. Рассматриваются также численные методы решения обыкновенных дифференциальных уравнений. Приводятся многочисленные примеры решения рассмотриваемых классов дифференциальных уравнений и ...
Added: October 5, 2019
Гурарий М. М., Жаров М. М., Русаков С. Г. et al., Наноиндустрия 2018 № 82 С. 410–411
The paper considers the problems of envelope following method construction for determining transient response and steady state of integrated circuits. The envelope following algorithms based on using one-step high order integration methods have been offered. ...
Added: February 12, 2019