• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Closed Classes of Three-Valued Logic Generated by Systems Containing Symmetric Functions
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
June 22, 2026
‘In Science, You Are Your Own Boss
Polina Nasledskova is interested in identifying gaps in linguistics and topics that have been overlooked by other researchers. In an interview for the  Young Scientists of HSE University project, she spoke about rare ordinal numerals in Nakh-Daghestanian languages, the benefits of knitting for concentration, and the beauty of the Patriarshy Bridge.
June 19, 2026
HSE Researchers Determine Which Internet Users Are More Likely to Fact-Check
Researchers at HSE University examined the strategies employed by Russian internet users to verify unreliable information and the factors that motivate them to do so. The study found that more than half of users who encounter potentially false information online attempt to verify it by locating the original source. The likelihood of fact-checking is influenced by several factors, including age, place of residence, social status, information literacy skills, and the use of AI. The findings have been published in Monitoring of Public Opinion: Economic and Social Changes.
June 5, 2026
'Im Used to Producing Distilled Knowledge'
Ivan Rubachev works in a HSE University laboratory established jointly with Yandex Research, where he focuses on machine learning with tabular data. In this interview with the HSE Young Scientists project, he discusses why following a vibe can be better than goal-setting, explains the concept of the Neural Turing Machine, and argues why withholding scientific knowledge is counterproductive.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Closed Classes of Three-Valued Logic Generated by Systems Containing Symmetric Functions

Moscow University Mathematics Bulletin. 2012. Vol. 67. No. 1. P. 41–45.
Mikhailovich A.

Closed classes of functions of three-valued logic whose generating systems include nonmonotone symmetric functions taking values in the set {0,1} are studied. It is shown that in some cases the problems of existence of a basis and existence of a finite basis can be reduced to a similar problem for reduced generated systems.

Research target: Mathematics
Priority areas: IT and mathematics mathematics
Language: English
Full text
Keywords: функции многозначной логикизамкнутые классыпорождающие системыбазисmulti-valued logic functionscloses classesgenerating systemsbasisматематическая теория управляющих систем
Similar publications
Международная конференция «Математические идеи академика П.Л. Чебышёва, их приложения в естественных науках и технологи- ях искусственного интеллекта», приуроченная к 205-й годовщине со дня его рождения» : Материалы конференции. / (Обнинск, 14–16 мая 2026 г.): Материалы конференции. Под ред. акад. В.Б. Бетелина. — Калуга: Калужский печатный двор, 2026. — 232 с.
Калужский печатный двор, 2026.
Conference Proceedings INTERNATIONAL CONFERENCE “Mathematical Ideas of Academician P.L. Chebyshev, Their Applications in Natural Sciences and Artificial Intelligence Technologies” dedicated to the 205th anniversary of his birth ...
Added: June 20, 2026
Численное решение уравнений Блэка–Шоулза и конвекции-диффузии с определением положения свободной границы
Джанбекова А. Р., Shvedov A. S., Математическое моделирование 2026 Т. 38 № 3 С. 159–176
Boundary value problems for the Black–Scholes partial differential equation, which describes the value of a financial instrument, may contain a free boundary condition if the financial instrument allows for early exercise. This article considers free boundary value problems for the Black–Scholes equation and the convection diffusion equation. For the convection diffusion equation, a finite difference ...
Added: June 20, 2026
Open Hurwitz numbers and the mKP hierarchy
Buryak A., Tessler R., Troshkin M., Journal of Geometry and Physics 2026 Vol. 223 Article 105783
We give a natural definition of open Hurwitz numbers, where the weight of each ramified covering includes an integer parameter N taken to the power that is equal to the number of boundary components of a Riemann surface with boundary mapping to . We prove that the resulting sequence of partition functions, depending on , is a tau-sequence of ...
Added: June 19, 2026
Bihamiltonian structure of the DR hierarchy in the semisimple case
Buryak A., Rossi P., Communications in Mathematical Physics 2025 Vol. 406 Article 205
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second has the advantage of being very explicit. The Poisson operator of the DR hierarchy is , where  is the metric ...
Added: June 19, 2026
Advances in Information Retrieval: 48th European Conference on Information Retrieval, ECIR 2026, Delft, The Netherlands, March 29 – April 2, 2026, Proceedings, Part II. (LNCS, volume 16484)
Cham: Springer Publishing Company, 2026.
The four-volume set LNCS 16483-16486 constitutes the refereed conference proceedings of the 48th European Conference on Information Retrieval, ECIR 2026, held in Delft, The Netherlands, during March 29–April 2, 2026. The 46 full papers and 37 short papers presented together with 10 findings papers, 9 reproducibility papers, 17 resource papers, 11 workshop papers, 7 tutorial papers, ...
Added: June 18, 2026
Искусственный интеллект как роза научной деятельности: исследование Тимоти Гауэрса
Poddiakov A., Троицкий вариант. Наука 2026 № 12 С. 24–25
В научно-популярной заметке представлен обзор содержания поста филдсовского медалиста Тимоти Гауэрса о возможностях ИИ в математике и содержания комментариев под постом. Обзор сделан в основном чат-ботом DeepSeek. В заключение обсуждается возможность не только решения задач искусственным интеллектом, но и их постановки. ...
Added: June 18, 2026
Optimal Extraction with an Impact on Diffusion-Jump Pricing
Garzón J., Mora Rodríguez J., Moreno-Franco H. A., Applied Mathematics and Optimization 2026 Vol. 94 No. 10 P. 1–43
We study an optimal extraction problem where the agent’s actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, evolve according to a drifted Brownian motion with jumps. The agent’s primary aim is to identify an optimal extraction strategy ...
Added: June 17, 2026
Об устройстве целевого приёма в России.
Nesterov A. S., Журнал Новой экономической ассоциации 2026
В этой статье рассматривается целевой приём в вузы в России с точки зрения науки об устройстве рынков сочетания и экономических механизмов (matching market and mechanism design), ключевого направления современной теории игр. Мы изучаем механизм целевого приёма -- набор правил, по которым устраивается трёхстороннее сочетание между абитуриентом, заказчиком и образовательной программой. Используемый в России механизм имеет ...
Added: June 16, 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
On the Ramsey Number R(K_{1,s},P_t)
Kh. Kh. Abdullin, D. B. Mokeev, D. S. Taletskii, Mathematical notes 2026 Vol. 119 No. 1 P. 3–7
By the Ramsey number R(K1,s,Pt) one means the least positive integer n such that, for every n-vertex graph G, the following condition holds: either G contains a vertex of degree at least s or the complement of G contains a simple t-path. In this paper, we fi nd precise values of R(K1,s,Pt) for certain values ...
Added: June 10, 2026
Innovations in Information and Decision Sciences. Proceedings of the 13th International Conference on Frontiers in Intelligent Computing: Theory and Applications (FICTA 2025), Volume 4
Springer, 2026.
The book presents the proceedings of the 13th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA 2024), held at Intelligent Systems Research Group (ISRG), London Metropolitan University, London, United Kingdom, during June 6–7, 2025. Researchers, scientists, engineers and practitioners exchange new ideas and experiences in the domain of intelligent computing theories with ...
Added: June 8, 2026
Wave dynamics within the Whitham-Ostrovsky equation
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
ML-based Fast Simulation of FARICH Responses
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
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
Natural hazard database from Internet publications: text mining with a large language model
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
Algorithmic overlaps as thermodynamic variables: from local to cluster Monte Carlo dynamics in critical phenomena
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
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
Математические вопросы кибернетики. Вып. 22
Mikhailovich A., Kochergin V., М.: Физматлит, 2024.
Added: March 10, 2025
Prime avoiding numbers form a basis of order 2
Gabdullin M., A. O. Radomskii, Sbornik: Mathematics 2024 Vol. 215 No. 5 P. 612–633
For a positive integer $n$ we denote by $F(n)$ the distance of $n$ to the nearest prime number. Using the technique from the recent paper ``Long gaps in sieved sets'' by Ford, Konyagin, Maynard, Pomerance and Tao (J. Eur. Math. Soc., 23:2 (2021), 667--700) we prove that every sufficiently large positive integer $N$ can be ...
Added: September 22, 2024
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit