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О концентрации значений чисел независимости случайных гиперграфов
Дискретная математика. 2021. Т. 33. № 4. С. 32–46.
Денисов И. О., Shabanov D. A.
The paper deals with asymptotic behavior of the general independence numbers of random hypergraphs in the binomial model. We prove that there is a concentration of the values of the independence numbers in two consecutive numbers under the certain conditions on the parameters.
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 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
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., V. N. Sivkin, Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
N. Belousov, L. Cherepanov, Derkachov S. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Кошелев М. М., Shabanov D. A., Шайхеева Т. М., Успехи математических наук 2025 Т. 80 № 1(481) С. 161–162
In the paper we obtain new estimates of threshold probabilities for the properties of fractional (r:2)-colorings of a random hypergraph in the binomial model H(n,k,p). ...
Added: February 4, 2025
Popova S., Discrete Applied Mathematics 2024 Vol. 345 P. 215–225
The notion of spectrum for first-order properties introduced by J. Spencer for Erdős–Rényi random graph is considered in relation to random uniform hypergraphs. In this work we study the set of limit points of the spectrum for first-order formulae with bounded quantifier depth and obtain bounds for its maximum value. Moreover, we prove zero–one k-laws for ...
Added: February 3, 2024
Tiapkin D., Shabanov D. A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 512 № 1 С. 52–57
The paper deals with the structure of the set of panchromatic colorings with three colors of a random hypergraph in the uniform model $H(n,k,m)$. It is well known that the property of the existence of a panchromatic coloring with given number of colors $r$ has the sharp threshold, i.e. there exists the threshold value $\widehat{m}_r=\widehat{m}_r(n)$ ...
Added: November 30, 2023
Zakharov P., Shabanov D. A., Успехи математических наук 2023 Т. 78 № 6 (474) С. 183–184
We obtain very accurate estimates for the threshold probability of fractional (4:2)-colorability property in a random k-uniform hypergraph in the binomial model H(n,k,p). ...
Added: November 30, 2023
Денисов И. О., Shabanov D. A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 509 № 1 С. 28–35
The paper deals with the study of the limit distribution of the j-chromatic numbers of a random k-uniform hypergraph in the binomial model H(n,k,p). We consider the sparse case when the expected number of edges is a linear function of the number of vertices n, i.e. is equal to cn for c>0 not depending on n. We ...
Added: October 25, 2023
Alina Khuzieva, Matveeva T., Dmitry Shabanov, Moscow Journal of Combinatorics and Number Theory 2023 Vol. 12 No. 1 P. 57–88
The paper deals with strong r-colorings of a random k-uniform hypergraph in the binomial model H(n,k,p). A vertex coloring is said to be strong for a hypergraph if any two vertices that share a common edge are colored with distinct colors. We consider the sparse case when the expected number of edges is equal to cn and the values r≥k≥3, c>0 remain constant ...
Added: April 10, 2023
Демидович Ю. А., Shabanov D. A., Теория вероятностей и ее применения 2022 Т. 67 № 2 С. 223–246
Работа посвящена изучению предельной концентрации значений хроматического числа случайного гиперграфа в биномиальной модели H(n,k,p). Доказано, что при фиксированном k>2 и не слишком быстро растущем значении n^{k-1}p хроматическое число H(n,k,p) с вероятностью, стремящейся к 1, принадлежит множеству из некоторых двух соседних значений. Кроме того, показано, что при чуть более сильных ограничениях на рост n^{k-1}p данные значения ...
Added: January 11, 2023
Матвеева Т. Г., Khuzieva A., Shabanov D. A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2022 Т. 502 С. 37–41
The paper deals with the study of the probability threshold for the property of strong colorability with given number of colors of the random k-uniform hypergraph in the binomial model H(n,k,p). A vertex coloring of a hypergraph is said to be strong if any edge does not have two vertices of the same color under ...
Added: January 11, 2023
Семенов А. С., Shabanov D. A., Проблемы передачи информации 2022 Т. 58 № 1 С. 80–111
We study the threshold probability for the property of existence of a special-form r-coloring for a random k-uniform hypergraph in the H(n, k, p) binomial model. A parametric set of j-chromatic numbers of a random hypergraph is considered. A coloring of hypergraph vertices is said to be j-proper if every edge in it contains no ...
Added: April 20, 2022
Zakharov P., Shabanov D. A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2021 Т. 501 С. 26–30
This paper deals with the problem of finding the max-cut for random hypergraphs. We consider the classical binomial model H(n,k,p) of a random k-uniform hypergraph on n vertices with probability p=p(n). The main results generalize previously known facts for the graph case and show that in the sparse case (when the expected number of edges ...
Added: April 20, 2022