?
Toric objects associated with the dodecahedron
Filomat. 2020. Vol. 34. No. 7. P. 2329–2356.
Baralic D., Grbic J., Limonchenko I., Vucic A.
In this paper we illustrate a tight interplay between homotopy theory and combinatorics
within toric topology by explicitly calculating homotopy and combinatorial invariants of toric objects
associated with the dodecahedron. In particular, we calculate the cohomology ring of the (complex and
real) moment-angle manifolds over the dodecahedron, and of a certain quasitoric manifold and of a related
small cover. We finish by studying Massey products in the cohomology ring of moment-angle manifolds
over the dodecahedron and how the existence of nontrivial Massey products influences the behaviour of
the Poincar´e series of the corresponding Pontryagin algebra.
Keywords: Massey productsмомент-угол-комплексквазиторическое многообразиеQuasitoric manifoldsпроизведение Массиmoment-angle-complex
Publication based on the results of:
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
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Bahri A., Limonchenko I., Panov T. et al., Discrete and Computational Geometry 2026 Vol. 76 P. 313–338
We define bigraded persistent homology modules and bigraded barcodes of a finite pseudo-metric space X using the ordinary and double homology of the moment-angle complex associated with the Vietoris–Rips filtration of X. We prove a stability theorem for the bigraded persistent double homology modules and barcodes. ...
Added: October 26, 2025
Buchstaber V. M., Popelensky T., Успехи математических наук 2024 Т. 79 № 4(478) С. 5–94
Развита теория триградуированной спектральной последовательности Бухштабера Bss для градуированных алгебр Хопфа. Показано, что ее дифференциалы задают возрастающую исчерпывающую фильтрацию как новую структуру в когомологиях этих алгебр. Для ряда известных алгебр Хопфа введенная структура описана в явном виде. На тензорной алгебре T(sExt1,∗A(k,k))надстройки над пространством одномерных когомологий алгебры Хопфа A, заданной над полем k, дана конструкция частичных и многозначных операций Bssp, p⩾1, в терминах которых описаны дифференциалы ...
Added: June 30, 2025
Fedor Vylegzhanin, Yakov Veryovkin, / Series math "arxiv.org". 2025.
Added: April 15, 2025
Limonchenko I., Sergeev M., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 326 С. 275–292
Вычислены вещественные и комплексные числа Бухштабера для всех сфер Бира. В размерности 22 найдены все 13 различных комбинаторных типов сфер Бира, и показано, что 12 из них представимы нерв-комплексами нестоэдров, а оставшийся — нерв-комплексом обобщенного пермутоэдра. В качестве приложения полученных результатов построен нормальный веер для каждого из найденных 13 многогранников Дельзанта, вычислены кольца когомологий соответствующих неособых проективных торических многообразий и ...
Added: January 16, 2025
Ivan Limonchenko, Taras Panov, Song J. et al., Advances in Mathematics 2023 Vol. 432 Article 109274
We put a cochain complex structure CH*(Z_K) on the cohomology of a moment-angle complex Z_K and call the resulting cohomology the double cohomology, HH*(Z_K). We give three equivalent definitions for the differential, and compute HH*(Z_K) for a family of simplicial complexes containing clique complexes of chordal graphs. ...
Added: October 25, 2023
Khovanskii A., Limonchenko I., Monin L., Filomat 2022 Vol. 36 No. 19 P. 6513–6537
The classical BKK theorem computes the intersection number of divisors on toric variety in terms of volumes of corresponding polytopes. It was observed by Pukhlikov and the first author that the BKK theorem leads to a presentation of the cohomology ring of toric variety as a quotient of the ring of differential operators with constant ...
Added: June 1, 2023
Panov T., Зейникешева И. К., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 317 С. 157–167
We compute the equivariant cohomology $H^*_{T_I}(Z_K)$ of moment-angle complexes $Z_K$ with respect to the action of coordinate subtori $T_I \subset T^m$. We give a criterion for the equivariant formality of $Z_K$ and obtain specifications for the cases of flag complexes and graphs. ...
Added: November 11, 2022