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The σ− Cohomology Analysis for Symmetric Higher-Spin Fields
Symmetry. 2021. Vol. 13. No. 8. Article 1498.
In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective σ − cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in A d S 4 . In the d-dimensional case H p ( σ − ) is computed for any p and interpretation of H p ( σ − ) is given both for the original Fronsdal system and for the associated systems of higher form fields.
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Ivchenko A., Nigmatullin R. R., Dorokhin S. V., Mathematics 2026 Vol. 9 No. 4 Article 381
n this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors become impossible. We consider ...
Added: June 27, 2026
Ivchenko A., Шестопёров А. И., Фомина Е. В., Microgravity Science and Technology 2025 Vol. 37 No. 19 P. 1–19
The paper is dedicated to the analysis of medico-biological data obtained during locomotor testing of astronauts. Accurate data interpretation plays a crucial role in locomotion system monitoring, prophylaxis of long-duration spaceflight negative effects and thus in the development of an autonomous medical support system for deep space expeditions. During the locomotor testing the astronaut changes ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., 2023 3rd International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET) Mohammedia, Morocco 2023 P. 1–6
The article proposes the architecture for eventdriven Emergency Operation Center with Machine Vision Component. Sources of information are analyzed and approaches to machine vision events for tactical situations detection and estimation are discussed. Messages from Machine Vision Components are converted to Common Alerting Protocol and processed by Operation Center environment for tactical situations recognition. ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., Лукьянченко П. П., Computer Research and Modeling 2023 Vol. 15 No. 1 P. 129–140
In this article we propose a new approach to the analysis of econometric industry parameters for the industry consolidation level. The research is based on the simple industry automatic control model. The state of the industry is measured by quarterly obtained econometric parameters from each industry’s company provided by the tax control regulator. An approach ...
Added: June 26, 2026
Gadzhimirzaev S., Хельвас А. В., International Frequency Sensor Association (IFSA) Publishing, 19-21 February 2025 Granada, Spain 2025 P. 172–176
The paper presents models for an innovative fully robotic warehouse for storing boxed goods. A discrete multiagent simulation of the movement of shuttles in a warehouse for a given sequence of pallet shipments has been implemented. Different strategies for placement of boxes in various areas of a warehouse are evaluated, as well as optimal routing ...
Added: June 26, 2026
Никонов В. Д., Никитин С. С., Патракеев М. В., Ionics 2025 Vol. 31 No. 1 P. 675–687
Modification of perovskite-type oxides is an effective way to develop functional materials with advanced properties. The effects of cerium introduction into the A sublattice of La0.5Sr0.5FeO3−δ and variation of La:Sr ratio on the defect structure and charge transfer characteristics were studied in this work. The LaxSr0.85−xCe0.15FeO3−δ oxides were found to be single-phase with cubic (x = 0.1) and orthorhombic ...
Added: June 26, 2026
Fedorov Timofey, Moscow Mathematical Journal 2026 Vol. 26 No. 1 P. 73–85
We obtain a complete list of smooth projective threefolds over C for which the dimension of the space of vanishing cycles (in H2(Y,Q) of the smooth hyperplane section Y) equals 2. We also obtain a complete list of rank 2 very ample vector bundles E on smooth projective surfaces with c2(E)=3. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций, включенных в программу весенней математической школы. ...
Added: June 25, 2026
Воронеж: Издательский дом ВГУ, 2026.
В сборнике представлены материалы докладов и лекций,
включенных в программу Воронежской зимней матаматической школы С. Г. Крейна - 2026. ...
Added: June 25, 2026
Buryak A., Shadrin S., Epijournal de Geometrie Algebrique 2024 Vol. 8
We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus g with n marked points. A large part of these relations has a surprisingly simple form: the tautological classes involved in the relations are given by stable graphs that are trees and that are decorated only by powers ...
Added: June 23, 2026
Popov V., Успехи математических наук 2025 Т. 80 № 3(483) С. 189–190
It is proved that for any positive integers d and c, the set of isomorphism classes of all d-dimensional reductive algebraic groups with exactly c connected components is finite. As a corollary, the set of isomorphism classes of all d-dimensional compact real Lie groups with exactly c connected components is proved to be finite. To ...
Added: December 16, 2025
Alexey S. Bychkov, Ushakov K., Vasiliev M., Symmetry 2024 Vol. 16 No. 9 Article 1115
In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective σ− cohomology both in ...
Added: October 14, 2025
Alhussein H., Kolesnikov P., Lopatkin V., Journal of Geometry and Physics 2025 Vol. 217 Article 105617
We apply discrete algebraic Morse theory to the computation of Hochschild cohomologies of associative conformal algebras. As an example, we evaluate the dimensions of the Hochschild cohomology groups with scalar coefficients of the universal associative conformal envelope U(3) of the Virasoro Lie conformal algebra relative to the associative locality bound N=3 on the generator. In contrast to the Weyl ...
Added: September 18, 2025
Buryak A., Hernandez Iglesias F., Shadrin S., Epijournal de Geometrie Algebrique 2022 Vol. 6 Article 8595
We propose a conjectural formula for DR_g(a,−a)\lambda_g and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Guéré and Rossi, and we prove that the two conjectures are in fact equivalent, though in a quite non-trivial way. ...
Added: September 14, 2022
Lopatkin V., Kolesnikov P., Alhussein H., / Series arXiv "math". 2022.
We apply discrete algebraic Morse theory to the computation of Hochschild cohomologies of associative conformal algebras. As an example, we evaluate the dimensions of the universal associative conformal envelope U(3) of the Virasoro Lie conformal algebra relative to the associative locality N=3 on the generator with scalar coefficients. ...
Added: May 5, 2022
Lopatkin V., Дальневосточный математический журнал 2011 Т. 11 № 2 С. 181–189
In this paper, we introduce the cohomology rings of asynchronous transition systems. We'll show that dierent asynchronous transition systems which have isomorphic homology groups may have nonisomorphic cohomology rings. ...
Added: October 29, 2021
Lopatkin V., Известия Саратовского университета. Новая серия. Серия: Математика. Механика. Информатика 2010 Т. 10 № 2 С. 3–10
The aim of this paper is to define the structure of the ring over the graded cohomology group of a semicubical set with coefficients in a ring with unit. ...
Added: October 29, 2021
Lopatkin V., Nam T. G., Journal of Algebra 2017 No. 481 P. 273–292
In this paper, we give sharp bounds for the homological dimensions of the Leavitt path algebra LK(E) of a finite graph E with coefficients in a commutative ring K, as well as establish a formula for calculating the homological dimensions of LK(E) when K is a commutative unital algebra over a field. ...
Added: October 29, 2021
Podkopaev O., Вестник Санкт-Петербургского университета. Серия 1. Математика. Механика. Астрономия 2018 Т. 5(63) № 4 С. 631–636
The goal of this note is to give a proof of the following proposition. Let π be a profinite group and K∗ be a bounded complex of discrete Fp[π]-modules. Assume all Hi (K∗) are finite abelian groups. Then there exists a quasiisomorphism L∗ −→ K∗, where L∗ is a bounded complex of discrete Fp[π]-modules such ...
Added: April 18, 2021
Przyjalkowski V., Shramov K., Collectanea Mathematica 2020 Vol. 71 P. 549–574
We give lower bounds for Hodge numbers of smooth well formed Fano weighted complete intersections. In particular, we compute their Hodge level, that is, the maximal distance between non-trivial Hodge numbers in the same row of the Hodge diamond. This allows us to classify varieties whose Hodge numbers are like that of a projective space, ...
Added: November 13, 2020
Buryak A., Shadrin S., Zvonkine D., Journal of the European Mathematical Society 2016 Vol. 18 No. 12 P. 2925–2951
We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus g curves with n marked points. ...
Added: September 27, 2020
Guere J., Rossi P., Buryak A., Geometry and Topology 2019 Vol. 23 No. 7 P. 3537–3600
We present a family of conjectural relations in the tautological ring of the moduli spaces of stable curves which implies the strong double ramification/Dubrovin–Zhang equivalence conjecture introduced by the authors with Dubrovin. Our tautological relations have the form of an equality between two different families of tautological classes, only one of which involves the double ...
Added: April 21, 2020
Брудный Ю. А., Зайденберг М. Г., Лин В. Я. et al., Успехи математических наук 2019 Т. 74 № 5 С. 170–180
A detailed review of the scientific activities of the remarkable domestic mathematician E. A. Gorin and his results ...
Added: March 17, 2020