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Hyperbolic Singular Value Decomposition in the Study of Yang–Mills and Yang–Mills–Proca Equations
Computational Mathematics and Mathematical Physics. 2022. Vol. 62. No. 6. P. 1007–1019.
The hyperbolic singular value decomposition is used for studying the Yang–Mills equations with SU(2) gauge symmetry and the Yang–Mills–Proca equations in a pseudo-Euclidean (or Euclidean) space of an arbitrary finite dimension and signature. An explicit form of all constant solutions to the system of Yang–Mills–Proca equations in the case of the Lie group SU(2) is obtained. Nonconstant solutions to the Yang–Mills–Proca equations are considered as perturbation theory series.
Dudakov S., Lobachevskii Journal of Mathematics 2025 Vol. 46 No. 12 P. 6092–6102
We study the additive theory of arbitrary figures in linear spaces, that is, the theory of
addition extended to sets of vectors. Our main result is the following: if a linear space is infinite,
then the additive theory of figures admits interpreting second-order arithmetic and, therefore, it has
such or higher degree of undecidability. For countably infinite spaces, ...
Added: May 1, 2026
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
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
Domrin V. I., Malova H. V., V. Yu. Popov et al., Cosmic Research 2026 Vol. 64 No. 2 P. 238–252
During magnetospheric perturbations a relatively thin current sheet with thickness about several
proton gyroradii forms in the Earth’s magnetotail. In a framework of the kinetic model describing current
sheet thinning in the magnetotail, the processes of its formation are investigated depending on the normal
magnetic field magnitude which affects both the current sheet structure and particle dynamics within ...
Added: April 27, 2026
Tsareva O. O., Malova H. V., V. Yu. Popov et al., Plasma Physics Reports 2026 Vol. 52 No. 2 P. 179–185
The influence of asymmetry of plasma sources on the structure and spatial localization of a superthin
current sheet (STCS) supported by demagnetized electrons is studied using a self-consistent model. The
simulation takes into account the presence of a single plasma source in the northern hemisphere, which
makes the plasma flow asymmetric. It is demonstrated that the asymmetry of ...
Added: April 27, 2026
Pochinka O., Yakovlev E., Shmukler V., Russian Journal of Nonlinear Dynamics 2026
Every discrete dynamical system (cascade) generated by a homeomorphism induces a continuous
dynamic system (flow) — a suspension. However, not every flow is equivalent to a suspension
over a cascade, a necessary and sufficient condition for this is the existence of a global
section for the flow. In the case of the existence, the flow is equivalent to ...
Added: April 24, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 25
We revise the notion of the blobbed topological recursion by extending it to the setting of generalized topological recursion as well as allowing blobs which do not necessarily admit topological expansion. We show that the so-called non-perturbative differentials form a special case of this revisited version of blobbed topological recursion. Furthermore, we prove the KP ...
Added: April 23, 2026
Kazaryan M., Lando S., Kodaneva N., Journal of Geometry and Physics 2026 No. 225 Article 105841
Weight systems associated to the Lie algebras 𝔤𝔩(N) for N = 1,2,... can be unified into auniversal one. The construction is based on an extension of the 𝔤𝔩(N) weight systems to permutations. This universal weight system takes values in the algebra of polynomials C[N;C1,C2,...] in infinitely many variables. We show that under the substitution Cm ...
Added: April 23, 2026
Kychkin A., Chernitsin I., Прикладная информатика 2026 Т. 21 № 1 С. 40–58
The results of the development of a software microservice embedded in atmospheric air quality monitoring systems to support the identification of industrial pollution sources are presented. The emission and subsequent spread of harmful substances in the lower layers of the atmosphere is dynamic and characterized by high uncertainty due to the specific features of technological ...
Added: April 23, 2026
IEEE, 2026.
Added: April 21, 2026
Galkin O., Galkina S., Ястребова И. Ю., Журнал Средневолжского математического общества 2026 Т. 28 № №1 С. 11–30
Polynomials of least deviation from zero play an important role in the theory and practice of numerical methods. They can be used to solve problems of optimizing the properties of various computational algorithms. Our work is devoted to the study of polynomials of least deviation from zero on a ray in the exponential norm. In ...
Added: April 20, 2026
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
Petrov I., Doklady Mathematics 2026 Vol. Volume 112 P. S103–S110
This paper examines games on networks with linear best responses, which allow for the analysis of how interaction structures influence agents’ strategic behavior. Special attention is given to intervention issues in such models, particularly in selecting optimal intervention strategies aimed at maximizing the central planner’s objective function. Two main control policies are analyzed: individual agent ...
Added: April 17, 2026
A. V. Pereskokov, Theoretical and Mathematical Physics 2026 Vol. 226 No. 3 P. 470–484
We consider the spectral problem for a hydrogen atom in orthogonal electric and magnetic fields with
an additional self-consistent field. We obtain an asymptotic expansion of self-consistent energy levels.
We find an asymptotic expansion of asymptotic eigenfunctions near the sphere |q| = 2. We calculate the
asymptotics of their norm in the space L2(R3). ...
Added: April 12, 2026
Kolachev N., Адамский А. И., Drozdov D. et al., Моделирование и анализ данных 2026 Т. 16 № 1 С. 157–176
Context and relevance. Despite the widespread adoption of the competency-based approach in higher education, a gap remains between the understanding of competence as a dynamic process and the tools available for its design and management. Dominant practices of learning outcomes assessment rely on static “snapshots,” which limits the possibilities for forecasting and purposeful development of competence. ...
Added: April 10, 2026
Alexander S. Rabinowitch, Annals of Physics 2025 Vol. 480 Article 170149
In the present paper, transverse progressive waves in Yang-Mills fields with SU(2) symmetry propagating in the direction of the Cartesian z-axis are considered. In this case, the considered Yang-Mills equations are reduced to a system of six nonlinear partial differential equations. Field potentials satisfying them are sought in a special form. Substituting it in the ...
Added: July 14, 2025
Shirokov D., Advances in Applied Clifford Algebras 2024 Vol. 34 Article 23
In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in nondegenerate real and complexified Clifford geometric algebras of arbitrary dimension and signature. The new theorems involve only operations in geometric algebras and do not involve matrix operations. We naturally define these and other related ...
Added: August 23, 2024
Alexander S. Rabinowitch, Nuclear Physics B 2024 Vol. 1001 Article 116505
In the present paper, a new class of wave solutions to the Yang-Mills equations with SU(2) symmetry is considered. They describe the propagation of non-Abelian transverse progressive waves. In the case under consideration, the problem is reduced to six nonlinear partial differential equations. Their solutions are sought in a special form that allows them to be ...
Added: March 6, 2024
Shirokov D., Modern Physics Letters A 2023 Vol. 38 No. 20n21 Article 2350096
We present a classification and an explicit form of all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space ℝp,q of arbitrary finite dimension n=p+q. Using hyperbolic singular value decomposition and two-sheeted covering of orthogonal group by spin group, we solve the nontrivial system for constant solutions of the Yang-Mills ...
Added: October 5, 2023
A. S. Rabinowitch, Russian Journal of Mathematical Physics 2022 Vol. 29 No. 4 P. 576–580
In the present paper, the classical Yang-Mills equations with SU(2) symmetry are considered. The application of a generalized Wu-Yang form for field potentials results in a nonlinear differential equation of the second order . This equation is studied for a Yang-Mills field generated by a point-like source acting at the instant t = 0. In the examined case, ...
Added: January 25, 2023
Shirokov D., , in: Journal of Physics: Conference Series, Volume 2099Vol. 2099: International Conference «Marchuk Scientific Readings 2021» (MSR-2021) 4-8 October 2021, Novosibirsk, Russian Federation.: IOP Publishing, 2021. Ch. 012015 P. 1–7.
We study the Yang-Mills equations in the algebra of h-forms, which is developed in the works of N. G. Marchuk and the author. The algebra of h-forms is a special geometrization of the Clifford algebra and is a generalization of the Atiyah-Kahler algebra. We discuss an invariant subspace of the constant Yang-Mills operator in the ...
Added: October 11, 2022
Alexander S. Rabinowitch, European Physical Journal Plus 2021 Vol. 136:574 No. 5 P. 1–10
In the present paper, the Yang-Mills equations which play a leading role in modern physics are studied. For them, a new class of non-abelian wave solutions is found, This class of solutions describes axisymmetric reansverse progressive waves in Yang-Mills fields. The found wave solutions are represented in the form of absolutely convergent series. ...
Added: May 26, 2021
Marchuk N., Shirokov D., Physics of Particles and Nuclei 2020 Vol. 51 No. 4 P. 589–594
The paper considers plane-wave solutions of the Yang–Mills equations, which allow one to write out three systems of equations modeling the Yang–Mills system. An explicit form of all plane-wave solutions of the Yang–Mills equations with the SU(2) gauge symmetry and zero current in a (pseudo)Euclidean space of arbitrary finite dimension is presented. ...
Added: September 29, 2020
Shirokov D., Journal of Nonlinear Mathematical Physics 2020 Vol. 27 No. 2 P. 199–218
In this paper, we present all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in Euclidean space Rn of arbitrary finite dimension n. Using the invariance of the Yang-Mills equations under the orthogonal transformations of coordinates and gauge invariance, we choose a specific system of coordinates and a specific gauge fixing for ...
Added: October 8, 2019