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Бутерброды и носки в курсе высшей алгебры
Математика в высшем образовании. 2014. № 12. С. 9–14.
Г.М. Полотовский, Ремизов. И. Д.
Some examples of application of the models constructed of «household» objects, useful to an explanation to students of some abstract structures of modern mathematics are given.
Priority areas:
mathematics
Language:
Russian
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Chronopoulos D., Вестник Омского университета. Серия: Исторические науки 2027 № 1
В 1863 г. в России отметили тысячелетие славянской письменности. Имперские власти и церковные деятели осознавали общеславянский характер праздника и его важность для «славянского вопроса». В общественной дискуссии фигуры Кирилла и Мефодия были мобилизованы для осмысления ключевых вопросов — от народного просвещения до обострившегося в связи с восстанием «Польского вопроса». Парадоксальным образом обращение к «общеславянскому» прошлому ...
Added: September 24, 2026
Sokolov V., Adler V. E., Journal of Geometry and Physics 2026 Vol. 227 Article 105860
The group reduction procedure is applied to vector generalizations of the NLS, mKdV,
and KdV equations. The resulting ODE systems admit isomonodromic Lax representations
and are multicomponent generalizations of the Painlevé equations P 1, P 2, P 34, and P 4.
Some of them can be interpreted as nonautonomous deformations of well-known systems
integrable in the Liouville sense, in ...
Added: September 24, 2026
Sokolov V., BALAKHNEV M. Y., Ufa Mathematical Journal 2026 Vol. 18 No. №3 P. 85–93
A collection of miscellaneous continuous, semi-discrete, and discrete integrable
systems can be associated with each integrable evolution equation of the KdV type. We provide them for the Schwarz — KdV equation and generalize to the vector case. The existence
of these vector generalizations is a non-trivial found fact, no mathematical explanation of
which is known yet. ...
Added: September 24, 2026
Yakovlev E., Maksimov D. A., Mathematical notes 2026 Vol. 120 No. 3 P. 483–496
Smooth principal bundles whose total spaces and bases are time oriented Lorentzian manifolds and whose projections are Lorentzian submersions preserving time orientations are studied. Previously, the authors showed that the chronologicity, causality, and stable causality always lift from the base to the space of a Lorentzian bundle. For strong causality and global hyperbolicity, this holds ...
Added: September 24, 2026
Sokolov V., Shabat G. B., Tsiganov A. V., Journal of Geometry and Physics 2026 Vol. 220
We consider Novikov equations for commutative ring generated by differential operators of
orders 3,4,5. We present an explicit Hamiltonian form of these equations. Using the method
of compatible Poisson brackets, we find a separation of variables on a hyperelliptic curve
of genus 2 for the Novikov equations ...
Added: September 24, 2026
Marshakov A., Yung A., Ievlev E. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 No. 114 P. 1–22
We continue the study of non-Abelian vortex string in 4D N ¼ 2 supersymmetric QCD (SQCD) as critical superstring, and extend this analysis to UðNÞ gauge theory with arbitrary even N and Nf ¼ 2N number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by ...
Added: September 24, 2026
Demina M.V., Nechitailo V., Analysis and Mathematical Physics 2026 Vol. 16 No. 5 P. 1–25
We present a method of finding non-Liouvillian first integrals of rational two-dimensional differential systems. The method is based on the existence of two independent invariants that satisfy a linear second-order ordinary differential equation with respect to one of the variables. We call systems with this property R-integrable. These invariants are not necessarily polynomial; they can ...
Added: September 24, 2026
Bitter I., Konakov V., Mathematical notes 2026 Vol. 120 No. 4 P. 599–615
The paper provides a generalization of the local limit theorem on the convergence
of inhomogeneous Markov chains to the diffusion limit for the case in which the corresponding
coefficients of the process satisfy weak regularity conditions and coincide only asymptotically.
In particular, the drift coefficients under consideration can be unbounded with at most linear
growth, and the bounds reflect ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Pochekaev R. Y., Тутаев И. В., Христианское чтение 2026 № 3 С. 254–269
The article presents an attempt to clarify the general trends and analyze some specific examples of how the form and content of canon law documents in the 13th-15th centuries were affected by the fact that Russian lands were under the rule of the Golden Horde khans. The discussion covers such aspects as the types of ...
Added: September 24, 2026
Stoyanov R., Ancient Civilizations from Scythia to Siberia 2026 Vol. 32 No. 1 P. 1–13
This study examines the fragment of an architectural block adorned with vegetal ornamentation which was discovered at the ancient settlement of Kepoi, situated in the Asiatic Bosporus on the northern coast of the Black Sea (fig. 1). The block’s façade features a spiraling vegetal motif rendered in high relief with exceptional detail (fig. 2). The ...
Added: September 23, 2026
Ivantchik A., Зайцев А. В., Vestnik Drevnei Istorii 2026 Vol. 86 No. 1 P. 141–152
This article publishes the inscriptions preserved on the funerary stele from Parion, discussed in the preceding article. The stele was used twice, and the Greek inscription, carved at the same time as the stele was created in the late second – early first century BC, was partly erased when it was re-used. It was reconstructed ...
Added: September 23, 2026
Istanbul: Ege Yayınları, 2025.
This volume presents the results of the first season of a Turkish–Russian–French research project at Parion, one of the most important Greek poleis on the southern shore of the Propontis, in the northern Troad. Archaeological excavations were carried out in July and August 2021 as part of an international project devoted to the multidisciplinary study ...
Added: September 23, 2026
Данилочкина К. С., Индоевропейское языкознание и классическая филология 2026 Т. 1 № 30 С. 537–546
The article examines the issue of naming the wooden writing tablets from the Roman fort Vindolanda (late 1st - first quarter of the 2nd century AD), which represent a unique corpus of epistolary and documentary sources for the history of Roman Britain. Since their discovery in the 1970s, over a thousand specimens have been found, ...
Added: September 23, 2026
Щавелев А. С., Электронный научно-образовательный журнал "История" 2026 Т. 17 № 6(164) Статья 3
The present study considers a suite of insignia recovered from the large burial mound C‐74 (Serg‐1900) within the Gnezdovo archaeological complex, dated to the 10th century. The interment was performed in situ according to the cremation‐in‐boat rite. The richness of the grave assemblage, notably the presence of several paired high‐status items (two sets of horse ...
Added: September 21, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., Муллабаева А. У., Уфимский математический журнал 2010 Т. 2 № 1 С. 52–58
В данной статье введены обобщённые пространства Фока и рассмотрены основные свойства этих пространств. Найдена операция, сопряженная к операции умножения на переменную в обобщенном пространстве Фока. Также определены собственные функции сопряженного оператора. Изучены обобщенное преобразование Лапласа и задача построения базиса для введенных пространств. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 855–862
Tasks related to the automation of medical data processing are becoming more urgent. Particular attention is paid to systems for monitoring and analyzing human physiological parameters. Such systems often use specialized sensors to capture biomedical images, such as infrared cameras. This article describes our study of the problem of segmenting the eye pupil and iris ...
Added: September 21, 2026
Aleksei Samarin, Nazarenko A., Alexander Savelev et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 844–854
Improving image quality is becoming an increasingly popular task, especially when working with mobile devices. One common approach to image enhancement is the use of convolutional neural networks. However, to achieve good results, such networks must be large enough, otherwise there is a risk of unwanted artifacts. In addition, large convolutional neural networks require significant ...
Added: September 21, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
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
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