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Формы поверхностей дель Пеццо степеней 5 и 6
Математический сборник. 2023. Т. 214. № 6. С. 69–86.
Зайцев А. В.
Publication based on the results of:
Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 P. 1–16
A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
Added: May 21, 2026
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
Gonchenko S., Lerman L., Turaev D., 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., Khutorskaya O., Stepochkina A. 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 2026 Vol. 12 No. 1 P. 60–110
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
Н. Я. Амбург, Л. Бриль, Фундаментальная и прикладная математика 2024 Т. 25 № 2 С. 63–77
Ю. И. Манин и М. Марколли предложили новый способ построения инвариантов действия абсолютной группы Галуа на детских рисунках Гротендика. В частности, они сформулировали гипотезу о том, что многочлен Татта является примером такого инварианта. В этой заметке мы приводим контрпример, опровергающий эту гипотезу. ...
Added: May 26, 2025
Cheltsov I., Математический сборник 2021 Т. 212 № 3 С. 139–156
We answer a question of Ciliberto's about cylinders in rational surfaces obtained by blowing up the plane at points in general position. © 2021 Russian Academy of Sciences (DoM) and London Mathematical Society. ...
Added: September 24, 2021
Perepechko A., Forum Mathematicum 2021 Vol. 33 No. 2 P. 339–348
Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on ...
Added: January 15, 2021
Loughran D., Trepalin A., Mathematical Research Letters 2020 Vol. 27 No. 3 P. 845–853
We completely solve the inverse Galois problem for del Pezzo surfaces of degree 2 and 3 over all finite fields. ...
Added: October 28, 2020
Vyugin I. V., Gontsov R. R., Arnold Mathematical Journal 2015 Vol. 1 No. 4 P. 445–471
The paper conserns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with non-resonant irregular ones and propose some criteria of solvability for systems whose exponents (respectively, so-called formal exponents in the irregular case) are ...
Added: June 22, 2015
Fedor Bogomolov, Tschinkel Y., Communications on Pure and Applied Mathematics 2013 Vol. 66 No. 9 P. 1335–1359
We explore connections between birational anabelian geometry and abstract projective geometry. One of the applications is a proof of a version of the birational section conjecture. ...
Added: December 27, 2013
Vyugin I. V., Гонцов Р. Р., Успехи математических наук 2012 Т. 67 № 3 (405) С. 183–184
Получено обобщение результата Ильяшенко-Хованского, утверждающего, что разрешимость в квадратурах фуксовой системы с малыми коэффициентами эквивалентна ее треугольности. В работе этот результат обобщен на случай систем с малыми собственными значениями матриц вычетов. ...
Added: February 21, 2013