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Смешанные задачи в липшицевой области для сильно эллиптических систем 2-го порядка
Функциональный анализ и его приложения. 2011. Т. 45. № 2. С. 1–22.
Agranovich M. S.
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
Agranovich M. S., Селицкий А. М., Функциональный анализ и его приложения 2013 Т. 47 № 2 С. 2–17
Пусть \omega — ограниченная липшицева область в R^n и пусть в ней задан матричный сильно эллиптический оператор 2-го порядка, записанный в дивергентной форме. Обширная литература посвящена изучению областей определения дробных степеней операторов, отвечающих задачам для уравнения , прежде всего Дирихле и Неймана, c однородными граничными условиями, включая решение проблемы Като, возникшей в 1961 г. Охвачены ...
Added: August 30, 2013
Agranovich M. S., Functional Analysis and Its Applications 2011 Vol. 45 No. 2 P. 81–98
We consider mixed problems for strongly elliptic second-order systems in a bounded domain with Lipschitz boundary in the space Rn. For such problems, equivalent equations on the boundary in the simplest L2-spaces Hs of Sobolev type are derived, which permits one to represent the solutions via surface potentials. We prove a result on the regularity ...
Added: April 12, 2012
Agranovich M. S., Functional Analysis and Its Applications 2011 Vol. 45 No. 1 P. 1–12
We consider boundary value problems and transmission problems for strongly elliptic second-order systems with boundary conditions on a compact nonclosed Lipschitz surface S with Lipschitz boundary. The main goal is to find conditions for the unique solvability of these problems in the spaces Hs , the simplest L2-spaces of the Sobolev type, with the use ...
Added: April 12, 2012
Agranovich M. S., Современная математика. Фундаментальные направления 2011 Т. 39 С. 11–45
Статья посвящена спектральным задачам для сильно эллиптических систем 2-го порядка в ограниченных липшицевых областях. Рассматриваются спектральные задачи Дирихле и Неймана, а также три задачи со спектральным параметром в условиях на границе: задача Пуанкаре-Стеклова
и две задачи сопряжения. В порядке обзора обсуждаются основные свойства этих задач, самосопряженных и несамосопряженных. Предварительно объясняется ряд фактов общей теории основных задач ...
Added: April 12, 2012
Agranovich M. S., Функциональный анализ и его приложения 2011 Т. 45 № 1 С. 1–15
Рассматриваются граничные задачи и задачи сопряжения для сильно эллиптических систем 2-го порядка с граничными условиями на компактной незамкнутой липшицевой поверхности S с липшицевым краем. Основная цель - выяснение условий однозначной разрешимости этих задач в пространствах Hs - простейших L2 -пространствах типа Соболева - с использованием операторов типа потенциала на S. Обсуждаются вопросы о регулярности решений ...
Added: April 12, 2012