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Random eigenvalues of graphenes and the triangulation of plane
Journal of Physics A: Mathematical and Theoretical. 2025. Vol. 58. No. 2. Article 025212.
We analyze the numbers of closed paths of length on two important regular lattices: the hexagonal lattice (also called graphene in chemistry) and its dual triangular lattice. These numbers form a moment sequence of specific random variables connected to the distance of a position of a planar random flight (in three steps) from the origin. Here, we refer to such a random variable as a random eigenvalue of the underlying lattice. Explicit formulas for the probability density and characteristic functions of these random eigenvalues are given for both the hexagonal and the triangular lattice. Furthermore, it is proven that both probability distributions can be approximated by a functional of the random variable uniformly distributed on increasing intervals as . This yields a straightforward method to simulate these random eigenvalues without generating graphene and triangular lattice graphs. To demonstrate this approximation, we first prove a key integral identity for a specific series containing the third powers of the modified Bessel functions In nth order, . Such series play a crucial role in various contexts, in particular, in analysis, combinatorics, and theoretical physics.
Keywords: combinatoricstheoretical physicsModified Bessel functionhexagonal latticedual triangular lattice.
Publication based on the results of:
Avdeev R., Zaitseva Y., Mediterranean Journal of Mathematics 2026 Vol. 23 No. 7 Article 224
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
Added: October 17, 2026
Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...
Added: October 16, 2026
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Gusein-Zade S., Campillo A., Delgado F., Mathematische Zeitschrift 2026 Vol. 314 No. 1 P. 1–22
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coefficients in $\K$. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a (discrete, rank one) valuation on it. ...
Added: October 13, 2026
Mishuris G., Meylan M. H., Pelinovsky E., Journal of Fluid Mechanics 2026 Vol. 1045 Article A4
In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...
Added: October 12, 2026
Gusein-Zade S., М.: МЦНМО, 2026.
Книга содержит курс лекций по дифференциальной геометрии и топологии, читавшихся автором на механико-математическом факультете МГУ в разные годы. В дополнениях приводятся некоторые сюжеты (связности в расслоениях, теорема Фробениуса, производные Ли и др.), которые были включены в курс в отдельные годы либо содержались в аналогичных курсах лекций в Независимом московском университете.
Для студентов математических и физических специальностей. ...
Added: October 12, 2026
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
М.: Юрайт, 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Springer, 2025.
The second edition of this 5-volume handbook is intended to be a basic yet comprehensive reference work in combinatorial optimization that will benefit newcomers and researchers for years to come. This multi-volume work deals with several algorithmic approaches for discrete problems as well as with many combinatorial problems. The editors have brought together almost every aspect ...
Added: January 18, 2026
Khestanov R., Suvalko A., Социологическое обозрение 2025 Т. 24 № 2 С. 164–189
The article examines the genesis of the concept of novelty and argues that modern difficulties in defining and identifying the new are a symptom of a semantic crisis, which is based on the loss of strategic normativity of novelty in modern culture. Three historical-semantic models of novelty are identified and analyzed: cyclical (characteristic of prehistoric ...
Added: June 29, 2025
Уфа: Башкирский государственный педагогический университет им. М. Акмуллы, 2024.
The collection contains abstracts of reports published following the work of sections of the II All-Russian Youth School Conference. The articles were reviewed and grouped according to the thematic areas of the conference. The collection contains abstracts of oral and poster presentations by students, masters, postgraduates, university professors, teachers and school students. ...
Added: March 5, 2025
Уфа: Издательство БГПУ, 2023.
The collection contains abstracts of reports published following the work of sections of the II All-Russian Youth School Conference. The articles were reviewed and grouped according to the thematic areas of the conference. The collection contains abstracts of oral and poster presentations by students, masters, postgraduates, university professors, teachers and school students. ...
Added: March 5, 2025
Уфа: РИЦ УУНиТ, 2023.
The presented conference materials discuss in detail the latest results and open problems of complex analysis and theory of functions, spectral theory of operators, mechanics, theoretical physics and radiophysics, electronics and nanophysics, materials science and nanomaterials, geophysics and applied physics, as well as the problems of modern teaching methods. The materials of the collection are ...
Added: March 3, 2025
М.: Математический институт им. В. А. Стеклова РАН, 2024.
This volume is dedicated to the 80th birthday of Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences. The volume includes articles on topology, geometry, combinatorics, and mathematical physics, the areas in which V. M. Buchstaber is a recognized world leader and the head of an active scientific school. Most of the articles are written ...
Added: January 15, 2025