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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.
The Journal of Physical Chemistry Letters 2026 Vol. 17 No. 18 P. 5386–5394
We demonstrate and rationalize the effect of Au nanoparticles (NPs) on the hierarchical g-C3N4/CeO2 heterojunction. g-C3N4/CeO2 decorated with monodispersed plasmonic Au NPs was synthesized. Detailed analyses showed that CeO2 nanocubes and monodispersed Au NPs were evenly distributed over the 2D g-C3N4 surface, forming a robust interface enriched with abundant active sites. The structure enabled efficient separation of photogenerated charge ...
Added: May 16, 2026
Das A., Paul R., Sharma N. et al., Colloids and Surfaces A: Physicochemical and Engineering Aspects 2026 Vol. 728 P. 138830
Niobium-doped TiO2 (Nb-TiO2), demonstrates dual functionality as an efficient photocatalyst for dye degradation and a promising photoelectrocatalyst for water oxidation. Nb incorporation via a facile hydrothermal method was confirmed by XRD (Rietveld refinement), XPS, TEM, FT-IR, Raman, and BET analyses, indicating successful lattice doping and structural modification. Photocatalytic dye degradation experiments were conducted using a model ...
Added: May 16, 2026
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Kolokolov I., Lebedev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 113 Article 054117
We theoretically investigate the correlation functions of the phase of a light wave propagating through a
turbulent medium. We use an equation for the logarithm of a wave packet envelope, which includes a secondorder
nonlinear term. Based on this equation, we develop a diagrammatic technique to calculate corrections
to the correlation function obtained in the linear approximation. We ...
Added: May 15, 2026
Гущина В. А., / Series chemrxiv-2023-vpzhz-v2 "ChemRxiv". 2023.
All-inorganic perovskite CsPbBr3 and Cs4PbBr6 nanoparticles are being intensively studied due to their unique properties and wide range of applications; however, however, the nature of their optical properties is not yet fully understood due to the difficulty of synthesis of singlephase nanoparticles. In this article we describe the features of the synthesis of single-phase particles ...
Added: May 14, 2026
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
Гущина В. А., Mendeleev Communications 2025 Vol. 35 No. 2 P. 193–195
All-inorganic perovskite CsPbBr3 and Cs4PbBr6 nanoparticles are intensively studied for their unique optical properties, though synthesizing single-phase nanoparticles has posed challenges. Detailed synthesis method of CsPbBr3 and Cs4PbBr6 single-phase nanoparticles and their chemical and phase analysis are described. Distinctive optical characteristics, such as photoluminescence, optical band gap and the Urbach tail region, are revealed and explained within the current ...
Added: May 14, 2026
Гущина В. А., Physics of Complex Systems, Russia 2026 Vol. 7 No. 1 P. 3–15
Heterostructures based on ZnO nanorods and CsPbBr3 nanocrystals were investigated for their potential as semiconductor SERS substrates. We found that ZnO morphology governs the efficiency of interfacial energy transfer, leading to enhanced photoluminescence under 390 nm excitation and a noticeable reduction of the bandgap in the composites. Raman analysis revealed a pronounced intensity enhancement and ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Bisnovatyi-Kogan G., Kondratyev I., Moiseenko S. G., International Journal of Modern Physics A 2025 Vol. 40 No. 7 Article 2550018
Bright transient objects in different wave bands have been discovered in recent years.
To explain these short (from ms to s), and very powerful events, different models, galactic and
extragalactic, have been considered. One of the popular models is based on the suggestion of
transformation of the magnetized plasma blob, presumably a magnetohydrodynamic (MHD)
shock wave, moving with relativistic ...
Added: May 11, 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