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On the Number of Minimum Total Dominating Sets in Trees
Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций"). 2023. Vol. 17. No. 1. P. 213–224.
The minimum total dominating set (MTDS) of a graph is a vertex subset D of
minimum cardinality such that every vertex of the graph is adjacent to at least one vertex of D.
In this paper we obtain a sharp upper bound for the number of MTDSs in the class
of n-vertex 2-caterpillars. We also show that for all n ≥ 1 every n-vertex tree has less than (√2)^n MTDSs.
Prokofev V., Zabrodin A., Proceedings of the Steklov Institute of Mathematics 2020 Vol. 309 P. 225–239
We consider solutions of the matrix Kadomtsev-Petviashvili (KP) hierarchy that are trigonometric functions of the first hierarchical time t1 = x and establish the correspondence with the spin generalization of the trigonometric Calogero-Moser system at the level of hierarchies. Namely, the evolution of poles xi and matrix residues at the poles aαibβi of the solutions with respect to the kth hierarchical time of the ...
Added: July 14, 2026
Prokofev V., Zabrodin A., Journal of Physics A: Mathematical and Theoretical 2021 Vol. 54
We consider solutions of the Kadomtsev–Petviashvili hierarchy which are elliptic functions of x = t1. It is known that their poles as functions of t2 move as particles of the elliptic Calogero–Moser model. We extend this correspondence to the level of hierarchies and find the Hamiltonian Hk of the elliptic Calogero–Moser model which governs the dynamics of poles with respect to the kth ...
Added: July 14, 2026
Prokofev V., Zabrodin A., Theoretical and Mathematical Physics 2021 Vol. 208 P. 1093–115
We consider solutions of the 2D Toda lattice hierarchy which are elliptic functions of the zeroth time t_0=x. It is known that their poles as functions of t_1 move as particles of the elliptic Ruijsenaars-Schneider model. The goal of this paper is to extend this correspondence to the level of hierarchies. We show that the ...
Added: July 14, 2026
Prokofev V., Zabrodin A., Теоретическая и математическая физика 2023 Т. 217 № 2 С. 299–316
We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B), which can be regarded as a discretization of the BKP hierarchy. We introduce the tau function of the B-Toda hierarchy and obtain bilinear equations for it. Examples of soliton tau functions are presented in explicit form. ...
Added: July 14, 2026
Шиманогов И. Н., Vyalyi M., Дискретный анализ и исследование операций 2025 Т. 32 № 4 С. 213–230
A well-studied class of algorithmic problems is that of regular realizability: checking the non-emptiness of the intersection of a regular language with a given language. This problem has a natural algebraic interpretation: verifying whether an element of a Boolean algebra belongs to the kernel of a certain homomorphism. This motivates the consideration of an analogous ...
Added: July 12, 2026
Rybakov M., Annals of Pure and Applied Logic 2026 Vol. 177 Article 103811
The paper presents a solution to the question about the decidability of the two-variable fragment of the superintuitionistic predicate logic QLC defined by the class of linear Kripke frames, which is also the ‘superintuitionistic’ fragment of the modal predicate logic QS4.3, under the Gödel translation. We prove that the fragment is undecidable. The result remains true for the ...
Added: July 11, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular
L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings
between the links and a bounded length of the maximum link that does not depend on the network
size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in
the ...
Added: July 8, 2026
Pilé I., Deng Y., Shchur L., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 1 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 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
Gurvich V., Krnc M., Vyalyi M., Results in Mathematics 2025 Vol. 80 Article 117
An amoeba is a tree together with instructions how to iteratively grow trees by adding paths of a fixed length . This paper analyses such a growth process. An amoeba is mortal if all versions of the process are finite, and it is immortal if they are all infinite. We obtain some necessary and some ...
Added: August 24, 2025
Qian X., Guan X., Jia J. et al., Journal of Optimization Theory and Applications 2024 Vol. 200 P. 524–554
Given an undirected tree T = (V, E) and a value σ > 0, every edge e ∈ E has a lead time l(e) and a capacity c(e). Let Pst be the unique path connecting s and t. A transmission time of sending σ units data from s to t ∈ V is Q(s, t,σ) ...
Added: January 18, 2024
D. S. Taletskii, Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2023 Vol. 17 No. 3 P. 664–677
The set of vertices of a graph is called distance-k independent if the distance between any two of its vertices is greater than some integer k ≥ 1. In this paper, we describe n-vertex trees with a given diameter d that have the maximum and minimum possible number of distance-k independent sets among all such ...
Added: November 8, 2023
Taletskii D., Дискретный анализ и исследование операций 2023 Т. 30 № 3 С. 111–131
The set of vertices of a graph is called distance-k independent if the distance between any two of its vertices is greater than some integer k ⩾ 1. In this paper we describe n-vertex trees with a given diameter d which have maximum and minimum possible number of distance-k independent sets among all such trees. The ...
Added: June 13, 2023
Zhang Q., Guan X., Jia J. et al., Journal of Global Optimization 2023 Vol. 86 P. 251–284
We consider the restricted inverse optimal value problem on shortest path under weighted l1 norm on trees (RIOVSPT1). It aims at adjusting some edge weights to minimize the total cost under weighted l1 norm on the premise that the length of the shortest root-leaf path of the tree is lower-bounded by a given value D, ...
Added: June 2, 2023
D. S. Taletskii, Mathematical notes 2023 Vol. 113 P. 552–566
The class of trees in which the degree of each vertex does not exceed an integer 𝑑 is considered. It is shown that, for 𝑑=4, each 𝑛-vertex tree in this class contains at most (√2)^𝑛 minimum dominating sets (MDS), and the structure of trees containing precisely (√2)^𝑛 MDS is described. On the other hand, for 𝑑=5, an 𝑛-vertex tree containing more than (1/3)⋅1.415^𝑛 MDS is ...
Added: April 25, 2023
Taletskii D., Математические заметки 2023 Т. 113 № 4 С. 577–595
The class of trees in which the degree of each vertex does not exceed an integer d is considered. It is shown that, for d = 4, each n-vertex tree in this class contains at most (√2)^n minimum dominating sets (MDS), and the structure of trees containing precisely (√2)^n MDS is described. On the other hand, ...
Added: April 25, 2023