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Теоремы о редукции в теории коллективного выбора
Итоги науки и техники. Современная математика и ее приложения. Тематические обзоры. 2020. Т. 174. С. 46–51.
Polyakov N. L., Шамолин М. В.
In the paper, combinatorial theorems relating to the theory of social choice are obtained.These theorems describe general conditions under which theproblem on the preserving the preferencesetDby an arbitrary aggregation rulefand the problem on the compatibility of the preference setDwith a pair(f,C)can be reduced to similar problems for two specific aggregation rules: the majority rulemaj and the “counting rhyme” rule cog. Results are obtained within the framework ofclone approachin the theory of social choice proposed by S. Shelah and developed by the authors.
Language:
Russian
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
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Kuznetsov A. P., Sataev I. R., Stankevich N., Chaos 2026 Vol. 36 No. 8 Article 083131
A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
Added: August 30, 2026
Ustyuzhanin V., Zinkina J. V., Korotayev A., / Series "SocArXiv". 2026.
“Leaderlessness” is widely held to be a defining feature of contemporary mass mobilization, yet the claim rests on a handful of recent cases. We offer the first systematic cross-national analysis of this phenomenon from 1791 to 2019. We show that the absence of leadership is real but older and more modest than claimed: the share ...
Added: August 29, 2026
Shirokov N. A., Rozenblum G., Israel Journal of Mathematics 2026 P. 1–30
We establish that a generalized H\¨older continuous function on an (m−2)-Ahlfors regular compact set in Rm can be approximated by solutions of an elliptic equation, with the rate of approximation determined by the continuity modulus of the function ...
Added: August 29, 2026
Tikhomirova A., Professional Discourse & Communication 2026 Vol. 8 No. 3 P. 66–84
Given China’s rise as the world’s leading automotive producer and the radical
transformation of the Russian market, societal acceptance of new market entrants remains a dif
ficult communicative task. Against the backdrop of growing sales and persistent consumer am
bivalence, this study examines how Russian consumers discursively construct, challenge, and
renegotiate the legitimacy of Chinese automobile brands in online ...
Added: August 28, 2026
Avdoshin S.M., Patrushev K. A., Proceedings of the Institute for System Programming of the RAS 2026 No. 4 часть 2 P. 245–256
The cardinality-constrained Markowitz problem is NP-hard and traditionally solved with commercial MIQP solvers. Following the 2022 export restrictions that rendered both commercial MIQP software and cloud quantum platforms (IBM Quantum, D-Wave Leap) inaccessible from the Russian Federation, practitioners require open-source alternatives. This paper systematically compares three solver families for the discrete mean-variance problem: two open-source ...
Added: August 27, 2026
Zaikin A., Vlasenko D., Zakharov D. et al., Diagnostics 2026 Vol. 16 No. 17 P. 1–15
Background/Objectives: Synolitic graphs (SGs) were developed for task-based fMRI, where
edge weights encode the discriminative power of pairwise regional features; whether similar
information can be recovered from resting-state data was untested. We benchmarked
SGs for autism spectrum disorder (ASD) classification using the multisite ABIDE-I dataset
(871 subjects: 403 subjects with ASD, 468 typical controls; 17 sites; CC200 atlas). Methods:
Using ...
Added: August 27, 2026
Melnikov I., Pelinovsky E., Nonlinear Dynamics 2026 No. 114 Article 934
Pyramidal solitons (solitons with more than two inflection points) of the generalized Korteweg–de Vries (KdV) equation are investigated. Necessary and sufficient conditions for the existence of such structures are presented. Within the framework of the generalized Gardner equation — the simplest model that admits pyramidal solitons as solutions — it is shown that these solutions ...
Added: August 27, 2026
Тула: Тульский государственный педагогический университет им. Л.Н. Толстого, 2025.
Сборник содержит материалы, представленные на XXIV Международной конференции «Алгебра, теория чисел, дискретная геометрия и многомасштабное моделирование: современные проблемы, приложения и проблемы истории», посвящённой 110-летию со дня рождения академика Юрия Владимировича Линника и 110-летию со дня рождения профессора Андрея Борисовича Шидловского и 80-летию со дня рождения профессора Геннадия Ивановича Архипова. Материалы конференции будут полезны научным работникам, ...
Added: August 27, 2026
Nesterenko A., Чирский В. Г., Матвеев В. Ю., Чебышевский сборник 2026 Т. 27 № 2 С. 118–127
The article presents the results of a practical study of the statistical properties of some sequences that are values of functions of a special type. ...
Added: August 26, 2026
Medushevsky A. N., Liberal.ru 2026
The Liberal Mission Foundation continues to introduce readers to new concepts of democracy and relevant publications. This discussion focuses on the challenges facing democracy in the era of globalization, as addressed in two recent books: *The Backsliders: Why Leaders Undermine Their Own Democracies* by S.C. Stokes (2025) and *Critical Theories and the Postsocialist Challenge: Race, ...
Added: August 26, 2026
Medushevsky A. N., Liberal.ru 2026
Today, more than ever before, the contribution of new technologies shapes the conditions of humanity's existence as a biological species, prompting a debate about its prospects for survival. This process of transformation—which spans every sphere of social and moral regulation, from family relations and child-rearing to the very meaning of life—is dividing public opinion between ...
Added: August 26, 2026
Medushevsky A. N., Сравнительное конституционное обозрение 2026 Т. 35 № 2 (167) С. 4–29
In the context of the rapid changes in the modern world associated with globalization, informatiza tion, and the revision of ethical standards of mass behavior, legal theory faces a number of problems — the loss of consensus in understanding global constitutionalism, growing disagreements regard ing its values and principles, and unclear prospects for the future. ...
Added: August 26, 2026
Medushevsky A. N., Сравнительное конституционное обозрение 2026 Т. 35 № 1 С. 53–77
Judges should be independent of politics, yet they are constantly ensnared by it. Politics haunts judges even where the full scope of constitutional guarantees for the separation of powers and an in dependent judiciary is in place, infiltrating the courtroom through variable interpretations of the val ues, principles, and norms of the constitution, the selection ...
Added: August 26, 2026
Medushevsky A. N., Вопросы теоретической экономики 2026 № 2 С. 146–164
It is generally accepted that the basis of social and legal stability in any society is a consensus on vir tue — the fundamental values of proper behavior, ways of maintaining and reproducing them. And, conversely, the destruction of this consensus is a sign of the loss of stability and divergence of positions of social ...
Added: August 26, 2026
Eduard Sopin, Nazarin A., Begishev V. et al., IEEE Transactions on Vehicular Technology 2026 Vol. 75 No. 6 P. 10995–11007
Aimed at rate-greedy applications having extreme requirements for the data rate at the air interface, 5G New Radio (NR) systems may experience problems when the number of user equipment (UE) in the coverage of the cell increases due to limited capacity of the physical downlink control channel (PDCCH).The aim of this study is to explore ...
Added: August 26, 2026
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
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