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Инвариант Арфа-Кервера как препятствие к вложимости
AAPP Atti della Accademia Peloritana dei Pericolanti, Classe di Scienze Fisiche, Matematiche e Naturali. 2022. Vol. 100. No. 2. P. A10-1–A10-17.
CENCELJ M.
Translator: D. REPOVŠ
We prove that no 14-connected (resp. 30-connected) stably parallelizable
manifold N^{30} (resp. N^{62{) of dimension 30 (resp. 62) with the Arf-Kervaire invariant 1 can
be smoothly embedded into R36 (resp. R83)
Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438
In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...
Added: September 7, 2026
Ismailov A., Constructive Approximation 2026
The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f is bounded from below by the Motzkin density.
We generalize the bound to polynomials in several variables and almost periodic functions.
We then use these generalizations to extend known results on Taikov’s problem. ...
Added: September 7, 2026
Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401
В работе изучаются перестановки, возникающие при упорядочивании по возрастанию дробных долей произведений элементов фиксированной целочисленной последовательности на вещественный параметр. Исследуется количество различных перестановок, которые можно получить таким образом при изменении этого параметра от нуля до единицы. ...
Added: September 7, 2026
Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146
Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...
Added: September 3, 2026
Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80
Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026
We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems.
Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146
We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
Added: August 31, 2026
Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69
We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.
Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Journal fuer die reine und angewandte Mathematik 2026 Vol. 2026 No. 836 P. 111–162
We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
Added: August 30, 2026
Bayer A., Kuznetsov A., Macrì E., Compositio Mathematica 2026 Vol. 162 No. 1 P. 59–99
We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Guseva L., Novikov A., Advances in Mathematics 2026 Vol. 503 Article 111211
We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
Added: August 30, 2026
Polishchuk A., Rains E., Journal of the Institute of Mathematics of Jussieu 2026 Vol. 25 No. 1 P. 339–373
We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
Added: August 30, 2026
Kazhdan D., Polishchuk A., Pure and Applied Mathematics Quarterly 2026 Vol. 22 No. 3 P. 1115–1166
We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
Added: August 30, 2026
Nebolsin D., Логос 2026 Т. 36 № 1 С. 113–134
The article addresses the problem of theorizing the relationship between sound and visuality on the material of the more specific topics of recorded sound and visual image. The text is organized as a playlist: throughout the eight sound examples, it identifies the concepts of current image theory that are relevant for theoretical problems of sound ...
Added: May 23, 2026
Akhmetiev Petr M., , in: Essays on Topology Dedicated to Valentin Poénaru.: Switzerland: Springer, 2025. Ch. 12 P. 189–236.
The Kervaire Problem in Stable Homotopy Theory is a problem to classify framed immersions with Arf-invariant one. The first interesting example is in dimension 30. There exists a closed stably-parallelizable manifold ˜M 30
\protect\tilde{M}^{ with Arf–Kervaire invariant 1. The goal of the chapter is to recall various geometrical constructions concerning the Kervaire Problem. In particular, we ...
Added: February 11, 2026
Кузьмин Д. О., В кн.: Многомерность общества: человек в социальном взаимодействии : 2-й молодежный конвент : материалы международной студенческой конференции 29–31 марта 2018 года.: Екатеринбург: Издательство Уральского университета, 2018. С. 462–464.
The article's topic is studying videogames as alternate realities that allow for existential experiences. This is possible due to immersion and player-game communication via the player character. To study these phenomenas, narratological and ANT methods were utilized. ...
Added: June 7, 2022
Obukhov A., Kosaretsky S., Можаева М. В. et al., Исследователь/Researcher 2021 № 1-2 С. 32–51
The article presents the theoretical foundations and examples of the use of project and research activity methods, media resources and e-learning technologies for the formation and development of environmental literacy and environmentally responsible behavior in additional education programs. A model of three levels of student involvement in activities for the development of environmental literacy is ...
Added: October 11, 2021
Delazari I., Genre 2021 Vol. 54 No. 2 P. 221–244
This article explores the “encyclopedic” properties of Madeleine Thien’s Do Not Say We Have Nothing (2016), seeking to define the novel as inherently comparative—that is, providing, in Edward Said’s words, “a comparative or, better, a
contrapuntal perspective” on the world with no need for a second counterpart text to draw cross-literary parallels. Written from a transpacific ...
Added: December 10, 2020
Staruseva-Persheeva A., Fadeeva T., В кн.: Proceedings of the 3d International Conference on Art Studies: “Science, Experience, Education” (ICASSEE 2019).: Atlantis Press, 2020.
This article focuses on media art (and specifically - virtual reality) as a powerful tool which allows transforming social agenda into personal meaning for a participating viewer. VR has recently become an intriguing medium which makes one feel present in the artistic “text”; to maximize the effect of immersion many VR projects give the viewer ...
Added: October 6, 2020
Aristova U., Rolich A., Staruseva-Persheeva A. et al., , in: Digital Transformation and Global Society. Third International Conference, DTGS 2018, St. Petersburg, Russia, 2018, Revised Selected Papers. Part II. Communications in Computer and Information Science 859Issue 859.: Springer, 2018. Ch. CCIS 859 P. 146–161.
The article presents an analysis of the possibilities and limitations of the use of information and communication technologies, in particular the Internet of things as an effective tool for artistic and sociocultural practices in the context of transformations of cultural industries. It is revealed that such radical transformations lead to a change in the formats ...
Added: December 15, 2018
Novikova A., Kiriya I., В кн.: Эстетика журналистики.: СПб.: Алетейя, 2018. С. 39–54.
В статье рассматриваются изменения в журналистике как способе производства символических форм. Анализируются новые эстетические и технологические подходы к созданию журналистских проектов в мультимедийных и многоплатформенных средах, а также используемые ими методы воздействия на аудиторию. Эти изменения, по мнению авторов статьи, в первую очередь обусловлены тем, что журналистика все меньше стремится удовлетворять когнитивные потребности аудитории (эти ...
Added: October 5, 2018