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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.
Filippova A. V., Yurchenko N. Y., Smirnov S. A. et al., Journal of Alloys and Compounds 2026 No. 1074 Article 189162
This study investigates the effects of post-processing heat treatment at 300–500 °C on the microstructure, hardness, and tensile properties of laser powder bed fusion (PBF-LB) processed Al-bronze processed with energy densities (ED) in the range of 125–938 J/mm3. In the as-printed state, sharp needle-like α + β′ laths form at lower ED whereas with increasing ED, the β′ ...
Added: June 12, 2026
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
Спонтанное образование скин-слоя в воде с деформацией ОН-полосы КР вкладом компоненты льда 3200 см-1
Першин С. М., Степанов Е. В., Артемова Д. Г. et al., Письма в Журнал экспериментальной и теоретической физики 2026 Т. 123 № 6 С. 383–390
Открыто спонтанное образование в течение 4 ч скин-слоя дистиллированной воды толщиной до 3 мм при комнатной температуре с новыми свойствами. Обнаружены деформация ОН-полосы комбинационного рассеяния вкладом компоненты льда ( 3200 см-1), снижение коэффициента упругого рассеяния и его флуктуаций, а также увеличение на 20 капиллярах. Восстановление слоя после обогащения воздухом в результате перемешивания указывает на стабильность ...
Added: June 8, 2026
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
N.S. Artekha, D.R. Shklyar, Physics of Plasmas 2026 Vol. 33 No. 6 Article 062105
The peculiarities of resonant interaction between slow extraordinary (SE) waves and relativistic electrons have been studied. General equations of motion of relativistic electrons in the field of SE wave and a uniform ambient magnetic field are derived. Conditions of applicability of the isolated resonance approximation are elucidated. In this approximation, the equations of motion are reduced to one-dimensional set of ...
Added: June 6, 2026
Zirnik G., Ostovari Moghaddam A., Zhukov S. et al., Journal of Materials Science: Materials in Electronics 2026 Vol. 37 Article 738
In regards to the advances in InGaZnO for flexible transistors applications, herein for the first time we measure the broadband radio-frequency range (10 Hz to 1 MHz) dielectric permittivity ε′ and electrical conductivity σ of InGaZnO4 nanoparticle layers at different temperatures ranging from 10 to 300 K. The InGaZnO4 nanoparticles prepared by metal–nitrate–glycol gel decomposition method exhibited ...
Added: June 6, 2026
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
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
Kurnosov N., Soldatenkov A., Verbitsky M., Advances in Mathematics 2019 Vol. 351 P. 275–295
Let M be a simple hyperkähler manifold. Kuga-Satake
construction gives an embedding of H^2(M, C) into the
second cohomology of a torus, compatible with the Hodge
structure. We construct a torus T and an embedding of the
graded cohomology space H^•(M, C) → H^{•+l}(T, C) for some
l, which is compatible with the Hodge structures and the
Poincaré pairing. Moreover, this ...
Added: June 3, 2019
V.A.Vassiliev, Doklady Mathematics 2018 Vol. 98 No. 1 P. 330–333
Stable rational cohomology groups of spaces of non-resultant homogeneous polynomial systems of growing degree in R^n are calculated ...
Added: December 7, 2018
В.А.Васильев, Известия РАН. Серия математическая 2016 Т. 80 № 4 С. 163–184
Rational homology groups of spaces of non-resultant (that is, having only trivial common zeros) systems of homogeneous quadratic polynomial systems in R^3 are calculated ...
Added: March 3, 2018
Chebochko N.G., / Series math "arxiv.org". 2017. No. 1712.01810.
The description of global deformations of Lie algebras is important since it is related to unsolved problem of the classification of simple Lie algebras over a field of small characteristic.
In this paper we study global deformations of Lie algebras of type ${D}_{l}$ over an algebraically closed field K of characteristic 2. It is proved that ...
Added: December 8, 2017