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Tropical semimodules of dimension two
St Petersburg Mathematical Journal. 2015. Vol. 26. P. 341–350.
Shitov Y.
In the paper, the concept of a semimodule is discussed, which is rather ill-behaved in tropical mathematics. The semimodules S in R^n having topological dimension two are studied, and it is shown that any such S has a finite weak dimension not exceeding n. For a fixed k, a polynomial time algorithm is constructed that decides whether S is contained in some tropical semimodule of weak dimension k or not. This result provides a solution of a problem that has been open for eight years.
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 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
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 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
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
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
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
Panov T., М.: МЦНМО, 2024.
Книга основана на лекционном курсе, который автор регулярно читает на механико-математическом факультете МГУ им. М. В. Ломоносова. Это современный курс линейной алгебры, отражающий геометрический взгляд на предмет. Необходимые предварительные сведения входят в курсы аналитической геометрии и алгебры первого семестра. В конце приводится список теоретических задач, которые можно использовать при сдаче экзамена. ...
Added: January 15, 2025
Kirill V. Kaymakov, Dmitry S. Malyshev, Optimization Letters 2024 Vol. 18 P. 1273–1283
For given edge-capacitated connected graph and two its vertices s and t, the bottleneck (or max min ) path problem is to find the maximum value of path-minimum edge capacities among all paths, connecting s and t. It can be generalized by finding the bottleneck values between s and all possible t. These problems arise ...
Added: April 18, 2024
Plotnikova E. G., Ivanov A. P., Loginova V. V. et al., М.: Юрайт, 2024.
Данный курс предназначен в помощь студентам-бакалаврам, изучающим линейную алгебру и аналитическую геометрию в качестве базовой дисциплины математического и научного цикла. В простой и наглядной форме изложены основные математические понятия, методы решения задач. Каждая тема содержит необходимый теоретический материал, иллюстрированный примерами, контрольные вопросы, задания для самостоятельного решения. Отдельные подтемы посвящены экономическим приложениям рассмотренных математических понятий и ...
Added: April 6, 2024
Malyshev D., Duginov O. I., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2023 Vol. 17 No. 4 P. 791–801
For a given graph, the edge-coloring problem is to minimize the number of colors sufficient to color all the graph edges so that any adjacent edges receive different colors. For all classes defined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem is known. In this paper, we obtain ...
Added: February 16, 2024
Gerasimova O., Makarov I., Severin N., IEEE Access 2023 Vol. 11 P. 88074–88086
The problem of query answering over incomplete attributed graph data is a challenging field of database management systems and artificial intelligence. When there are rules on data structure expressed in the form of the ontology, the theoretical complexity of finding exact solution satisfying ontology constraints increases. Logic-based methods use theoretical constructions to obtain efficient rewritings ...
Added: January 5, 2024
Sergei Valentinovich Fedorenko, IEEE Access 2023 Vol. 11 P. 62771–62779
The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. The methods are based on a binary trace calculation over the finite field and use the cyclotomic DFT. The direct DFT computational complexity has been reduced due to using the binary trace function over the finite field and ...
Added: July 19, 2023
Смирнов И. А., Разумов П. В., Сафарьян О. А. et al., Изд-во ВлГУ, 2019.
В данной статье представлен проект модификации и оптимизации ρ – метода факторизации Полларда с помощью рекурсивного метода подсчета факторизации чисел, работающий быстрее стандартного алгоритма на 27%, что сможет значительно облегчить работу по расшифрованию и криптографическому анализу различных шифров типа RSA. Были рассмотрены и использованы алгоритм факторизации, алгоритм Эвклида для нахождения НОД, подсчитана алгоритмическая сложность, матрица ...
Added: May 11, 2023
Черкесова Л. В., Сафарьян О. А., Смирнов И. А., Молодой исследователь Дона 2018 Т. 3 (12) С. 111–121
The paper presents the project implementation of ρ-factor Pollard factorization in C ++, which works faster than the standard algorithm by 27%, which can significantly facilitate the work in deciphering and cryptanalysis of various ciphers such as RSA ...
Added: May 9, 2023
Complexity function and complexity of validity of modal and superintuitionistic propositional logics
Rybakov M., Shkatov D., Journal of Logic and Computation 2023 Vol. 33 No. 7 P. 1566–1595
We consider the relationship between the algorithmic properties of the validity problem for a modal or superintuitionistic propositional logic and the size of the smallest Kripke countermodels for non-theorems of the logic. We establish the existence, for every degree of unsolvability, of a propositional logic whose validity problem belongs to the degree and whose every ...
Added: January 6, 2023
Malyshev D., Duginov O. I., Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций") 2022 Vol. 16 P. 276–291
The edge-coloring problem is to minimize the number of colors sufficient to color all the edges of a given graph so that any adjacent edges receive distinct colors. The complexity status of this problem is known for all the classes defined by the sets of forbidden subgraphs with 7 edges each. In this paper, we ...
Added: December 31, 2022
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