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О числе вечного доминирования планарных графов диаметра 2
Дискретный анализ и исследование операций. 2025. Т. 32. № 1. С. 122–144.
Keywords: планарный графдоминирующее множествовечное доминирующее множествочисло вечного доминирования
Publication based on the results of:
Ермолаев Е. С., Chernyshev V. L., Skripchenko A., Journal of Nonlinear Science 2026 Vol. 36 No. 122 (2026) P. 1–37
We study upper bounds for the moment of permanent -saturation in finite metric graphs. The dynamics is generated by moving points travelling with unit speed along edges and branching into all outgoing directions whenever they reach a vertex. We first reformulate this branched dynamics in terms of birth times at vertices and prove a sufficient ...
Added: November 12, 2026
Alfimov Mikhail, Kurakin Andrey, Journal of High Energy Physics 2026 Vol. 2026 Article 99
We continue studying regularization scheme dependence of the 𝒩 = 2 supersymmetric sigma models. In the present work the previous result for the four loop β-function is extended to the five loop order. Namely, we find the renormalization scheme, in which the fifth loop contribution is completely eliminated, while the fourth loop contribution is represented ...
Added: November 12, 2026
Ignatev M., Vilkin T., Mediterranean Journal of Mathematics 2026 Vol. 23 No. 2 Article 70
Trinomial varieties are affine varieties given by a system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal varieties with torus action of complexity one. For an affine variety X, we consider the subgroup SAut(X) of the automorphism group generated by all algebraic subgroups isomorphic to the additive ...
Added: November 12, 2026
Maksaev A., Promyslov V., Тишутин П. С., Записки научных семинаров ПОМИ РАН 2026 Т. 554 С. 218–235
Let K be an algebraically closed field and let ℰₖ be the set of n × n matrices over K with exactly k distinct eigenvalues. Previously, the classification of linear maps T: Mₙ(K) → Mₙ(K) satisfying T(ℰₙ) ⊆ ℰₙ was obtained for invertible maps over fields of characteristic 0. In this paper, the classification is ...
Added: November 11, 2026
Barinova M., Tirskaya Karina, Владикавказский математический журнал 2026 Vol. 28 No. 3 P. 25–43
In this paper, the problem of the existence of an energy function for discrete dynamical systems defined by structurally stable diffeomorphisms is studied. For the considered class of dynamical systems, such a function is defined as a continuous function that decreases along the orbits of the system outside the non-wandering set and remains constant on ...
Added: November 11, 2026
Illarionov A., Математический сборник 2026 Т. 217 № 11 С. 56–87
Let $b(\alpha;T)$ be the number of best simultaneous Diophantine approximations with common denominator $\le T$ to the point $\alpha \in {\Bbb R}^n$. We derive asymptotic formulas for the mean value of this quantity (averaging is performed over all rational points of the form $\alpha = (k_1/N,\ldots, k_n/N)$, $N\le R$), as well as for its mathematical ...
Added: November 10, 2026
Vereshchagin N., Математический сборник 2026 Т. 217 № 10 С. 3–46
Теорема Гудмана-Штрауса утверждает, что для “почти всякой” подстановки семейство подстановочных замощений софично, т.е. может быть задано локальными правилами для некоторой раскраски плиток. Условия на подстановку, гарантирующие софичность, довольно сложные.
В настоящей работе мы предлагаем версию теоремы Гудмана-Штрауса с более простыми условиями на подстановку. Хотя эти условия достаточно ограничительны, мы показываем, что в сочетании с двумя простыми приемами (взятием достаточно ...
Added: November 10, 2026
Aleksei Samarin, Belous F., Торопов А. Г. et al., Technologies 2026 Vol. 14 No. 11 P. 1–21
Abstract
Automated interpretation of magnetic flux leakage (MFL) data is central to condition assessment of long-distance oil and gas pipelines. Yet, full-resolution panoramas are difficult to process without either suppressing small anomalies through resizing or fragmenting elongated objects at sliding-window boundaries. We propose MFL-ScrollNet, a recurrent sliding-window detector that formulates panoramic analysis as an ordered sequence ...
Added: November 8, 2026
Retinsky V., Функциональный анализ и его приложения 2026 Т. 60 № 4 С. 83–100
Приведено обобщение матричной теоремы о деревьях на случай перечисления пар остовных деревьев. Это обобщение включает в качестве частных случаев и унифицирует сразу несколько известных ранее результатов, в частности классическую теорему Кирхгофа, теорему Масбаума–Вайнтроба о перечислении 3-деревьев, а также аналог матричной теоремы о деревьях для перечисления 4-элементов Кирхгофа. ...
Added: November 5, 2026
Levashev V., Математические заметки 2026 Т. 120 № 5 С. 843–846
Пусть 𝐴 – коммутативное ассоциативное кольцо с единицей и 𝐴((𝑡)) = 𝐴[[𝑡]][𝑡−1] – кольцо рядов Лорана над 𝐴. Алгебра 𝐴((𝑡)) имеет естественную топологию, где 𝐴 – подмодули вида 𝑡𝑚𝐴[[𝑡]] образуют базу окрестностей нуля. Пусть также Ω1𝐴((𝑡))/𝐴 – модуль кэлеровых 1-дифференциалов 𝐴((𝑡)) над 𝐴. ...
Added: November 5, 2026
Алексеев О. В., Letters in Mathematical Physics 2026 Vol. 116 No. 5 Article 132
We study the mixed Hessian of the dispersionless Toda \(\tau\)-function for the one-harmonic \(s\)-fold symmetric conformal map \(f(w)=r\bigl(w+\zeta w^{1-s}\bigr)\), where \(r>0\) is the exterior conformal radius and \(\zeta>0\) is the dimensionless shape parameter. This Hessian is the susceptibility matrix generated by the inverse conformal map. Our spectral statements are formulated for its weighted symmetry-block realizations ...
Added: November 5, 2026
Levin A., Sakharova N., / Series arXiv "math". 2024. No. 2412.17795.
The modular curves serve as excellent objects for testing conjectures in arithmetic geometry. They possess a natural geometric definition in contrast with rather nontrivial structure. On the other hand, they are well-studied from the perspective of number theory. Furthermore, there is a well-developed and powerful analytic technique available. We will use the square of the ...
Added: November 4, 2026
Zhuzhoma E. V., Medvedev V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 732–742
We study Axiom A diffeomorphisms (in the sense of Smale) on a closed orientable $n$-manifold $M^n$, $n\ge 4$, whose non-wandering sets consist of codimension one orientable attractors, repellers, and isolated saddle periodic orbits with the same Morse index. Such systems combine chaotic dynamics on basic sets with regular dynamics near trivial periodic orbits. We prove ...
Added: November 3, 2026
Zhuzhoma E. V., Medvedev V., Yu B. et al., Chaos 2026 Vol. 36 No. 6 P. 063111–063118
We show that any orientable closed 3-manifold $M$ admits structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of a 2-dimensional expanding attractor and finitely many repelling periodic trajectories. For $M=\mathbb{S}^3$, we prove that the set of repelling periodic trajectories can be an arbitrary link provided that this link contains the figure eight knot. ...
Added: November 3, 2026
Zhuzhoma E. V., Zhirov A. Y., Russian Journal of Nonlinear Dynamics 2026 Vol. 22 No. 2 P. 403–414
On a closed orientable surface, we consider the set of axiom A diffeomorphisms whose non-wandering sets consist of connected one-dimensional expanding attractors and contracting repellers (any attractor/repeller is locally homeomorphic to the product of segment and Cantor set). This set consists of $\Omega$-stable diffeomorphisms and structurally unstable diffeomorphisms. We classify such diffeomorphisms up to the ...
Added: November 3, 2026
Elena R. Loubenets, Sergey Kuznetsov, Quantum Information Processing 2026 Vol. 25 Article 358
The optimal implementation of quantum gates for closed $N$-qubit systems is one of the key challenges for practical realization of many quantum information processing tasks. In the present article, based on the generalized Bloch vectors formalism [J. Phys. A: Math. Theor. 54, 195301 (2021)] for a finite-dimensional quantum system, we develop a new \emph{general} model for the ...
Added: November 3, 2026
Zhuzhoma E. V., Medvedev V. S., Yu B., Mathematical notes 2025 Vol. 118 No. 2 P. 421–423
We show that given any orientable closed 3-manifold $M^3$ admits structurally stable non-singular flow $f^t$ whose non-wandering set $NW(f^t)$ consists of 2-dimensional expanding attractor and finitely many repelling periodic trajectories. For $M^3=\mathbb{S}^3$, we prove that the set of repelling periodic trajectories can be an arbitrary link provided this link contains the figure eight knot. ...
Added: November 3, 2026
Kazakov A., Kulagin N., Lerman L. et al., Chaos 2026 Vol. 36 No. 11 P. 1–24
We study perturbations of an integrable Hamiltonian system with two degrees of freedom that possesses a saddle-focus equilibrium with a homoclinic skirt—a one-parameter family of homoclinic orbits of the saddle-focus whose stable and unstable invariant manifolds coincide. The perturbations are dissipative, and we consider those that split the skirt completely (i.e., no intersections remain). We are interested ...
Added: November 2, 2026
Дахно Г. С., Malyshev D., Математические заметки 2025 Т. 117 № 1 С. 62–78
Наследственный класс — множество обыкновенных графов, замкнутое относительно удаления вершин, каждый такой класс задается множеством своих минимальных запрещенных порожденных подграфов. Задача о доминирующем множестве для заданного графа состоит в том, чтобы определить, а имеется ли в нем такое подмножество вершин заданного размера, что каждая вершина вне подмножества имеет хотя бы одного соседа в данном подмножестве. ...
Added: December 3, 2024
Taletskii D., Дискретный анализ и исследование операций 2024 Т. 31 № 1 С. 109–128
The set of graph vertices J_k is called k-dominating independent (k > 1) if its vertices are pairwise adjacent and every vertex not from J_k is adjacent to at least k vertices from J_k. In the presentb paper we obtain new upper bounds for the number of k-dominating independent sets for k > 2 in ...
Added: March 25, 2024
Taletskii D., Математический сборник 2023 Т. 214 № 11 С. 133–156
Сформулирована следующая гипотеза: если средняя степень вершин графа не превосходит натурального числа k ⩾ 1, то количество его k-доминирующих множеств не превосходит количества его независимых множеств, при этом равенство возможно, если и только если граф является k-регулярным. Эта гипотеза доказана для случая k ∈ {1,2}. ...
Added: November 2, 2023
G. S. Dakhno, D. S. Malyshev, Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2023 Vol. 17 No. 1 P. 25–31
A hereditary class is a set of simple graphs closed under deletion of vertices; every such class is defined by the set of its minimal forbidden induced subgraphs. If this set is finite, then the class is said to be finitely defined. The concept of a boundary class is a useful tool for the analysis ...
Added: December 6, 2022
Sirotkin D., Malyshev D., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 4 P. 760–766
The vertex 3-colourability problem is to verify whether it is possible to split the vertex set of a given graph into three subsets of pairwise nonadjacent vertices or not. This problem is known to be NP-complete for planar graphs of the maximum face length at most 4 (and, even, additionally, of the maximum vertex degree ...
Added: June 5, 2021
Sirotkin D., Журнал Средневолжского математического общества 2018 Т. 20 № 2 С. 199–205
The vertex 3-colourability problem is to determine for a given graph whether one can divide its vertex set into three subsets of pairwise non-adjacent vertices. This problem is NP-complete in the class of planar graphs, but it becomes polynomial-time solvable for planar triangulations, i.e. planar graphs, all facets of which (including external) are triangles. Additionally, ...
Added: July 2, 2018