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On fields of meromorphic functions on neighborhoods of rational curves
Arnold Mathematical Journal. 2025. Vol. 11. No. 2. P. 133–153.
Suppose that 𝐹 is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve with positive selfintersection. We prove that if there exists a non-constant meromorphic function on 𝐹, then the field of meromorphic functions on 𝐹 is isomorphic to the field of rational functions in one or two variables over ℂ.
Kuninets A., Malygina E., Cryptography and Communications 2026
In this paper, we determine explicit bases for Riemann–Roch spaces associated with various families of elliptic codes. We establish the feasibility and provide exact algorithms for constructing bases of Riemann–Roch spaces corresponding to arbitrary divisors on elliptic curves, including the non-effective case. These results are subsequently applied to derive bases for quasi-cyclic elliptic codes and ...
Added: September 17, 2026
Kazakov A., Koryakin V., Safonov K. et al., Journal of Differential Equations 2026 Vol. 480 Article 114626
We study a family of one-dimensional maps that models the dynamics of a system of differential equations with a Lorenz attractor near a bifurcation curve where the system has a pair of homoclinic loops with zero separatrix value. Of particular interest is the region of the parameter plane where the map has a robust chaotic ...
Added: September 16, 2026
Letellier C., Stankevich N., Houri S. et al., Chaos 2026 Vol. 36 No. 9 Article 093128
Toroidal chaos designates a chaotic solution that is structured in the neighborhood of a torus. For being chaotic, such a torus needs to be discontinuously fractalized to present a Cantor set, ensuring the great sensitivity to initial conditions required for chaos. A fractal is related to self-similarity and a non-integer dimension. In fact, although clearly ...
Added: September 16, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Смирнов С. В., Миллионщиков Д. В., Уфимский математический журнал 2021 Т. 13 № 2 С. 44–73
В данной работе изучаются характеристические алгебры для систем экспоненциального типа, соответствующих вырожденным матрицам Картана. Эти системы обобщают хорошо известные в теории интегрируемых систем гиперболические уравнения синус-Гордон и Цицейки. Для таких систем, соответствующих матрицам Картана ранга 2, характеристические алгебры описаны явно в терминах образующих и соотношений, и доказано, что они имеют линейный рост. Исследуется связь между ...
Added: September 11, 2026
Смирнов С. В., Glasgow Mathematical Journal 2026 Vol. 68 No. 2 P. 299–316
In the second half of the 19th century Darboux obtained determinant formulae that provide the general solution for a linear hyperbolic second order PDE with finite Laplace series. These formulae played an important role in his study of the theory of surfaces and, in particular, in the theory of conjugate nets. During the last three ...
Added: September 11, 2026
Смирнов С. В., Journal of Physics A: Mathematical and Theoretical 2023 Vol. 56 No. 26 Article 265204
There are different methods of discretizing integrable systems. We consider semi-discrete analog of two-dimensional Toda lattices associated to the Cartan matrices of simple Lie algebras that was proposed by Habibullin in 2011. This discretization is based on the notion of Darboux integrability. Generalized Toda lattices are known to be Darboux integrable in the continuous case ...
Added: September 11, 2026
Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 132–138
In schemes S for placing r particles in n distinguishable cells, their placement in selected m cells – schemes S∗ is studied, for which the analysis is carried out by a new enumerative method (EM) in extended areas of enumerative combinatorics: finding the number of outcomes and, based on the construction of a model of ...
Added: September 11, 2026
Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 139–147
The class of particle cell arrangements under consideration is characterized by the introduction of an upper limit on the filling levels of the cells, which must be achieved in at least one cell of each outcome of each arrangement. The circuits are distinguished by the paired qualities of their constituent elements (cells and particles) according ...
Added: September 11, 2026
Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 8 С. 110–123
Для многокритериальных задач принятия решений по аналогии с качественной вероятностью введены понятия полной и частичной качественной важности как бинарных отношений, обладающих постулируемыми
свойствами. Предложено новое определение отношения нестрогого предпочтения на множестве вариантов решений, порождаемое качественной
важностью. Исследованы его свойства. Указаны аналитические правила,
позволяющие попарно сравнивать варианты по предпочтительности. Проведено сравнение новых отношений предпочтения с разработанными ранее для задач, ...
Added: September 9, 2026
Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 7 С. 113–126
Рассматриваются задачи принятия решений, когда предпочтения оцениваются в порядковой шкале, а возможности реализации значений
неопределенного фактора описываются качественной вероятностью (полной или только частичной). Вводятся определения отношений предпочтения и безразличий на множестве стратегий. Предлагаются простые
решающие правила, позволяющие сравнивать стратегии по предпочтительности, и приводятся иллюстративные примеры. ...
Added: September 9, 2026
Chemical Papers 2026
Benzenoid hydrocarbons are structurally regular aromatic compounds, which makes them well suited for quantitative structure–property relationship (QSPR) studies. This study presents a QSPR analysis of nineteen benzenoid hydrocarbon species using degree-based topological co-indices. We developed a Python program to compute eleven degree-based topological co-indices from molecular graphs and evaluated their ability to explain variations in ...
Added: September 8, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Glutsyuk A., / Series arXiv "math". 2026.
A planar dual billiard is a planar curve γ equipped with a family (σP)|P∈γ of projective involutions of the projective lines LP tangent to γ at P that fix P. A dual billiard is called rationally integrable, if there exists a rational function R(x,y) of two variables (called first integral) whose restriction to each tangent ...
Added: September 8, 2026
Alexandrov A., Glutsyuk A., Journal of Differential Equations 2026 Vol. 465 Article 114178
The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on ...
Added: September 8, 2026
Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058
A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conjecture, studied by many mathematicians, states that if the billiard boundary has an inner neighborhood foliated by closed caustics, then it is an ellipse. In the paper we study ...
Added: September 8, 2026
Kubrak D., Prikhodko A., 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
Kelbert M., Statistics 2026 Vol. 60
We present variational representations for the weighted divergencies
and exponential error function, and discuss implications for the
statistical inference and entropic optimal transport. ...
Added: September 7, 2026
Kucheryavyy P., Математические заметки 2026 Т. 120 № 3 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
Lvovsky S., Moscow Mathematical Journal 2024 Vol. 24 No. 3 P. 391–405
We prove that for any d>0 there exists an embedding of the Riemann sphere P^1 in a smooth complex surface, with self-intersection d, such that the germ of this embedding cannot be extended to an embedding in an algebraic surface but the field of germs of meromorphic functions along C has transcendence degree 2 over the field of complex numbers. We give ...
Added: September 1, 2024
Obolonsky A. V., Политическая концептология: журнал метадисциплинарных исследований 2022 № 4 С. 14–26
Статья посвящена классификации негативных явлений в современных общественных науках – их причинам, проявлениям и последствиям. Их общей мета причиной представляется эскалация бюрократических методов управления наукой. Рассматриваются две группы факторов такого рода – социальные и морально-психологические и факторы методологические. К числу первых относятся: отсутствие заинтересованности у бизнеса и власти в поддержке фундаментальной науки; разного рода зависимость ...
Added: February 7, 2023
Serge Lvovski, Manuscripta Mathematica 2022 Vol. 169 No. 1-2 P. 325–326
In the proof of Proposition 2.3 of the paper [1] I referred to a result form the paper [2] which is valid only in characteristic zero, while later in the paper I use Proposition 2.3 for varieties over an arbitrary algebraically closed field. What follows is a proof of this proposition that is valid in ...
Added: August 25, 2022