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Эквивариантные пополнения аффинных пространств
Успехи математических наук. 2022. Т. 77. № 4(466). С. 3–90.
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
Dymov A. V., Математические заметки 2026 Т. 119 № 4 С. 539–545
Из результатов, полученных в работе Хис-Брауна 1996 года, следует, что число $N_L$ целых нулей невырожденной квадратичной формы, лежащих в шаре большого радиуса $L$ в $R^d$, $d\ge 5$, растет как $N_L\sim L^{d−2}$. Эта асимптотика, получающаяся нетривиальными вычислениями с помощью кругового метода, нередко вызывает удивление у специалистов из анализа и математической физики, где она в последние годы используется все интенсивнее. В данной заметке ...
Added: May 8, 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
Arzhantsev I., Shakhmatov K., Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas 2026 Vol. 120 Article 55
We give a criterion of factoriality of a suspension. This allows to construct many examples of flexible affine factorial varieties. In particular, we find a homogeneous affine factorial 3-fold that is not a homogeneous space of an algebraic group. ...
Added: March 24, 2026
Ivan Arzhantsev, Roman Avdeev, Yulia Zaitseva, International Mathematics Research Notices 2026 Vol. 2026 No. 4 Article rnag007
We complete the classification of algebraic monoid structures on the affine 3-space. The result is based on a reduction of the general case to that of commutative monoids. We also study various algebraic properties of all monoids appearing in the classification. ...
Added: February 24, 2026
Arzhantsev I., Beldiev I., Zaitseva Y., Journal of Algebraic Combinatorics 2025 Vol. 62 Article 42
We study projective hypersurfaces X admitting an induced additive action, i.e., an effective action of the vector group G_a^m with an open orbit that can be extended to an action on the ambient projective space. A criterion for normality of such a hypersurface X is given. Also, we prove that for any projective hypersurface Z there exists a hypersurface X with an induced additive ...
Added: October 29, 2025
Ghosh P., Gupta N., Pal A., / Series arXiv "math". 2024.
Hypersurfaces over a field k, defined by polynomials which are linear in one variable, have been playing a central role in the study of some of the challenging problems on affine spaces. Breakthroughs on such problems have occurred by examining two difficult questions on polynomials of the form H := α(X_1, . . . , ...
Added: October 7, 2025
Beldiev I., Bulletin of the Malaysian Mathematical Sciences Society 2025 Vol. 48 Article 195
We study induced additive actions on projective hypersurfaces, i.e. effective regular actions of the algebraic group G_a^m with an open orbit that can be extended to a regular action on the ambient projective space. It is known that the degree of a hypersurface X in the n-dimensional projective space P^n admitting an induced additive action cannot ...
Added: September 29, 2025
Rassolov K., Математические заметки 2025 Т. 118 № 4 С. 575–593
Рассматривается наиболее тонкая градуировка на алгебре регулярных функций триномиального многообразия, относительно которой однородны все координатные функции. Получен явный вид однородных относительно этой градуировки локально нильпотентных дифференцирований. ...
Added: September 19, 2025
D. A. Matveev, Siberian Mathematical Journal 2025 Vol. 66 No. 3 P. 715–727
We consider an affine algebraic variety with a torus action of complexity one. It is known
that in this case homogeneous locally nilpotent derivations on the algebra of functions of this variety
are defined in terms of a polyhedral divisor. In the present paper, a formula is obtained for multiple
commutators of two homogeneous locally nilpotent derivations with ...
Added: July 21, 2025
Arzhantsev I., МЦНМО, 2025.
Учебное пособие посвящено действиям групп на множествах. Обсуждаются кратно транзитивные группы
перестановок, в том числе исключительные группы Матьё. Рассматривается свойство бесконечной транзитивности для групп автоморфизмов аффинных пространств и, в большей общности,
аффинных алгебраических многообразий.
Материал доступен студентам младших курсов. Изложение сопровождается большим количеством задач. ...
Added: July 21, 2025
Dasgupta N., Gayfullin S., Математический сборник 2025 Т. 216 № 4 С. 3–34
В этой работе мы изучаем локально нильпотентные дифференцирования на алгебре многочленов от трех переменных над полем нулевой характеристики. Мы вводим итерационную конструкцию, дающую все локально нильпотентные дифференцирования ранга 2. Эта конструкция позволяет нам построить примеры нетриангуляризуемых локально нильпотентных дифференцирований ранга 2. Также мы показываем, что известный пример локально нильпотентного дифференцирования ранга 3, построенный Фройденбургом, может быть включен в большое ...
Added: July 1, 2025