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Анатолий Гордеевич Костюченко
Успехи математических наук. 2010. Т. 65. № 4. С. 179–190.
Agranovich M. S., Buchstaber V. M., Ismagilov R. S., Kashin B. S., Mityagin B. S., Novikov S. P., Sadovnichii V. A., Sergeev A. G., Sinai Y. G., Shkalikov A. A.
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 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
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 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
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 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
Алексеева Е. С., Рассадин А. Э., Вестник Дагестанского государственного университета 2020 Т. 35 № 3 С. 7–11
Approximate conformal mapping of the exterior of the domain on phase plane restricted by phase trajectory of the weakly nonlinear oscillator on the exterior of the unit disk is calculated in the paper. The aim of this consideration is to clarify the interrelation of Hamiltonian systems on plane with discovered at the beginning of our ...
Added: December 16, 2022
V. I. Bogachev, T. I. Krasovitskii, S. V. Shaposhnikov, Doklady Mathematics 2020 Vol. 102 No. 3 P. 464–467
We give a solution to the Kolmogorov problem on uniqueness of probability solutions to a parabolic Fokker–Planck–Kolmogorov equation. ...
Added: October 31, 2022
Smirnova A., Журнал Средневолжского математического общества 2022 Т. 24 № 3 С. 297–303
The paper considers the Cauchy problem for a parabolic partial differential equation in a Riemannian manifold of bounded geometry. A formula is given that expresses arbitrarily accurate (in the Lp-norm) approximations to the solution of the Cauchy problem in terms of parameters - the coefficients of the equation and the initial condition. The
manifold is not assumed to be ...
Added: October 24, 2022
Брауэр О., Buryak A., Функциональный анализ и его приложения 2021 Т. 55 № 4 С. 22–39
In a recent paper, given an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space of local functionals, which conjecturally gives a second Hamiltonian structure for the double ramification hierarchy associated to the CohFT. In this paper we prove this conjecture in ...
Added: September 14, 2022
Vedenin A., Voevodkin V., Galkin V. et al., Mathematical notes 2020 Vol. 108 No. 3 P. 451–456
Short communication is presented without abstract ...
Added: December 29, 2021
Arsie A., Buryak A., Lorenzoni P. et al., Communications in Mathematical Physics 2021 Vol. 388 P. 291–328
We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat F-manifold possesses a (homogeneous) integrable dispersive deformation at all orders in the dispersion parameter. The proof is based on the reconstruction of an F-CohFT starting from a semisimple ...
Added: October 29, 2021
Buryak A., Rossi P., Shadrin S., Letters in Mathematical Physics 2021 Vol. 111 Article 13
We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field theory. Various checks are presented to support the conjecture. ...
Added: October 29, 2021
Andreev N. A., Smirnov S. N., Computational Mathematics and Modeling 2021 Vol. 32 P. 22–44
We consider a guaranteed deterministic approach to discrete-time super-replication for guaranteed coverage of contingent claims on options for all possible asset-price scenarios. Price increases during a period are assumed to be contained in a priori specified compacta dependent on price history. A game problem is stated and reduced to the solution of the corresponding Bellman–Isaacs ...
Added: September 30, 2021
Buryak A., Rossi P., Bulletin of the London Mathematical Society 2021 Vol. 53 No. 3 P. 843–854
In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic DR integrals are the main ingredients for the computation of the DR hierarchy associated to the ...
Added: February 1, 2021
Brauer Gomez O., Buryak A., Journal of High Energy Physics 2021 Vol. 2021 P. 1–15
The paper is devoted to the open topological recursion relations in genus 1, which are partial differential equations that conjecturally control open Gromov-Witten invariants in genus 1. We find an explicit formula for any solution analogous to the Dijkgraaf-Witten formula for a descendent Gromov-Witten potential in genus 1. We then prove that at the approximation ...
Added: February 1, 2021
Malovichko M., Koshev N., Yavich N. et al., IEEE Transactions on Biomedical Engineering 2021 Vol. 68 No. 6 P. 1811–1819
Objective: This paper develops a novel approach for fast and reliable reconstruction of EEG sources in MRI-based head models. Methods: The inverse EEG problem is reduced to the Cauchy problem for an elliptic partial-derivative equation. The problem is transformed into a regularized minimax problem, which is directly approximated in a finite-element space. The resulting numerical method is efficient and easy ...
Added: November 10, 2020
Smirnov S. N., Математическая теория игр и ее приложения 2020 Т. 12 № 3 С. 50–88
Для задачи суперрепликации с дискретным временем рассматривается гарантированная детерминистская постановка: задача состоит в гарантированном покрытии обусловленного обязательства по опциону при всех допустимых сценариях. Эти сценарии задаются при помощи априорно заданных компактов, зависящих от предыстории цен: приращения цены в каждый момент времени должны лежать в соответствующих компактах. Предполагается отсутствие транзакционных издержек. Постановка задачи носит теоретико-игровой характер ...
Added: November 6, 2020