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News
September 11, 2026
How to Assess Students Knowledge in the Age of AI
A researcher at HSE University has proposed a flowchart to help lecturers decide how to assess students who use artificial intelligence. It shows where the use of AI should be restricted and where it can be incorporated into the learning process. The article has been published in IT Professional.
September 9, 2026
‘Balkan Hospitality Opens Doors: Studying Dialects on the Verge of Extinction
You cannot study spoken dialects from books. Instead, you need to go to a village, seek out its elders, and earn the trust of local residents before you can record hours of spontaneous stories. This is how Natalia Muravleva, Associate Professor at the Faculty of Humanities, conducts her research. Her internship in Serbia continued her long-standing study of dialects spoken by Macedonian settlers. In this interview, she discusses how diaspora cultural centres help researchers reach informants, why native speakers need to be interviewed only in their own language (otherwise, as she puts it, they may 'break'), and how a single field season helped her finalise her monograph. She also shares warm memories of autumn in Belgrade and of colleagues with whom grammar can be discussed in three languages at once.
September 9, 2026
Scientists Train Neural Network to Generate Process Plans from 3D Models
Researchers at the HSE FCS AI and Digital Science Institute have developed CAD2TechSpec, a framework that converts 3D models of mechanical parts into machining process plans—step-by-step instructions for machine tools. The solution aims to reduce the time required for the design and preparation of technical process documentation in mechanical engineering, aircraft manufacturing, and other high-tech industries. The study findings have been published in PeerJ Computer Science.

 

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?

Асимптотическая формула для свертки обобщенной функции делителей

Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2015. Т. 465. № 2. С. 137–140.
Frolenkov D., Быковский В. А.
Priority areas: mathematics
Language: Russian
DOI
Keywords: Euclidian algorithmsалгоритм Евклидаconvolution formulaформула свертки
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On phase-lock area parquet in a special slow-fast limit of model of Josephson junction.
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Infinitely many graph manifolds with unique geometrical piece that admit arbitrarily many Anosov flows
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the study of geodesic flows in negative curvature surface by Anosov and Sinai. Not every closed manifold admits an Anosov flow for well-known reasons: the fundamental group of a 3-manifold M admitting an Anosov flow must have exponential growth, and M must be universally covered by R3. Nevertheless, there ...
Added: August 31, 2026
New bound on S1× S2-setting Bell locality of a nonseparable Werner state
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a  nonseparable Werner state with a ...
Added: July 21, 2026
On functional equations for Chow polylogarithms
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity. To prove this, we study ...
Added: July 16, 2026
On Goncharov’s conjecture in next to Milnor degree
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond
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
Strong Approximations for Markov Chains Weakly Converging to Diffusions
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
Bifurcations and Structural Stability of Generic PC-HC Families
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
On the minimum number of maximal distance-k independent sets in trees
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
On Arithmetic Mirror Symmetry for smooth Fano fourfolds
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
On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization
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
On the dimension of the space of static potentials on three-manifolds
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
Using predefined vector systems to speed up neural network multimillion class classification
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
Homogeneous maximizers of the Blaschke-Santalo-type functionals
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
Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection
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
On finding formal power-logarithmic expansions of solutions to q-difference equations
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
Асимптотическое поведение первого и второго моментов для числа шагов в алгоритме Евклида
Ustinov A., Известия РАН. Серия математическая 2008 Т. 72 № 5 С. 189–224
We prove asymptotic formulae with two significant terms for the expectation and variance of the random variable s(c/d) when the variables c and d range over the set 1≤c≤d≤R and R→∞, where s(c,d)=s(c/d) is the number of steps in the Euclidean algorithm applied to the numbers c and d. ...
Added: October 11, 2025
О числе решений сравнения xy≡l (mod q) под графиком дважды непрерывно дифференцируемой функции
Ustinov A., Алгебра и анализ 2008 Т. 20 № 5 С. 186–216
A result by V. A.Bykovskiĭ (1981) on the number of solutions of the congruence xy≡l (modq) under the graph of a twice continuously differentiable function is refined. As an application, Porter's result (1975) on the mean number of steps in the Euclid algorithm is sharpened and extended to the case of Gauss–Kuzmin statistics. ...
Added: October 11, 2025
О среднем числе шагов в алгоритме Евклида с выбором минимального по модулю остатка
Ustinov A., Математические заметки 2009 Т. 85 № 1 С. 153–156
The article proves an asymptotic formula for the average number of steps in the Euclidean algorithm with centered division. ...
Added: October 10, 2025
О среднем числе шагов в алгоритме Евклида с нечетными неполными частными
Ustinov A., Математические заметки 2010 Т. 88 № 4 С. 594–604
The length of the continued-fraction expansion of a rational number with odd incomplete quotients is expressed via the Gauss–Kuzmin statistics for the classical continued fraction. This has made it possible to prove asymptotic formulas, similar to those already known for the classical Euclidean algorithm, for the mean length of the Euclidean algorithm with odd incomplete ...
Added: October 9, 2025
О статистиках Гаусса — Кузьмина в коротких интервалах
Ustinov A., Дальневосточный математический журнал 2011 Т. 11 № 1 С. 93–98
The article is devoted to investigation of Gauss — Kuz'min statistics for rational numbers a/b, where b is fixed, 1⩽a⩽b, (a,b)=1. New asymptotic formula for the mean value of Gauss — Kuz'min statistics is proved. It sharpens previous result which is similar to the Porter's theorem. ...
Added: October 9, 2025
Лекции по алгебре для учителей математики
Paramonova I., М.: МЦНМО, 2017.
The book contains a transcript of lecture notes of the first part of the course on Algebra read at the training courses for math teachers. Topics close to the school program in algebra are discussed. The author’s goal was to show how the school algebra  can be included in  a more general context  of algebra as a ...
Added: December 7, 2018
Асимптотическое поведение первого момента для числа шагов в алгоритме Евклида по избытку и недостатку
Frolenkov D., Математический сборник 2012 Т. 203 № 2 С. 143–160
В  работе рассматриваются первые моменты для числа шагов в различных алгоритмах Евклида. Для них, используя улучшенные оценки сумм дробных долей и идеи из элементарного доказательства А.Сельберга асимптотического закона распределения простых чисел, получены асимптотические формулы с новыми остаточными членами ...
Added: November 3, 2014
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