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On algebraic and topological semantics of the modal logic of common knowledge S4CI
Logic Journal of the IGPL. 2024. Vol. 32. No. 1. P. 164–179.
For the modal logic S4CI, we identify the class of completable S4IC-algebras and prove for them a Stone-type representation theorem. As a consequence, we obtain strong algebraic and topological completeness of the logic S4CI in the case of local semantic consequence relations. In addition, we consider an extension of the logic S4CI with certain infinitary derivations and establish the corresponding strong completeness results for the enriched system in the case of global semantic consequence relations.
Богатырев А. Б., Математический сборник 2023 Т. 214 № 3 С. 106–119
Рассматривается клеточное разбиение пространства модулей вещественных кривых рода 2 с отмеченной точкой на единственном вещественном овале. Клетки перечисляются определенными графами, веса которых описывают комплексную структуру на кривой. Показано, что стягивание ребра графа приводит к корневой особенности естественного отображения из весов графа в пространство модулей кривых. ...
Added: August 14, 2026
Богатырев А. Б., Gendron Q., Успехи математических наук 2023 Т. 78 № 1 С. 209–210
Уравнение Пелля-Абеля — это функциональное уравнение вида P²-DQ² = 1, с заданным многочленом D, свободным от квадратов, и неизвестными многочленами P и Q. Мы показываем, что пространство уравнений Пелля-Абеля с фиксированными степенями D и примитивным решением P является комплексным многообразием. Мы описываем его связные компоненты с помощью эффективно вычислимого инварианта. ...
Added: August 14, 2026
Богатырев А. Б., Transactions of the Moscow Mathematical Society 2024 Vol. 85 No. 2 P. 323–337
The best uniform rational approximation of the Sign function on two intervals separated by zero was explicitly found by E. I. Zolotarëv in 1877. The natural extension of this problem to three bands was solved by E. Stiefel in 1961. We indicate the solutions overlooked by the prominent geometer and study their properties. ...
Added: August 14, 2026
Богатырев А. Б., Успехи математических наук 2026 Т. 81 № 3(489) С. 159–160
Предложена простая и эффективно реализуемая формула для изменения абелевых интегралов (включая их периоды) при вариации образующих классической группы Шоттки, представляющей риманову поврехность. ...
Added: August 14, 2026
Gendron Q., Compositio Mathematica 2025 Vol. 161 No. 7 P. 1483–1511
A Pell–Abel equation is a functional equation of the form P^2-DQ^2=1 , with a given polynomial D free of squares and unknown polynomials P and Q. We show that the space of Pell–Abel equations with the degrees of D and of the primitive solution P fixed is a complex manifold. We describe its connected components ...
Added: August 14, 2026
Yu Z., Wang J., Wang Z. et al., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2026 Vol. 384 P. 1–16
The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation to fuse heterogeneous data and diverse knowledge. The framework facilitates structured reasoning and hypothesis generation through a task-adaptable, five-stage cycle: representation, reasoning, ...
Added: August 13, 2026
Speranski S. O., Математические заметки 2026 Т. 120 № 3 С. 470–483
We show that, in terms of closure ordinals, many infinitary calculi for ‘first-order’ logics of probability (i.e., for languages similar to those in [Abadi & Halpern 1994]) are as hard as possible: the corresponding closure ordinals coincide with the least non-constructive ordinal, denoted by $\omega_1^{\mathrm{CK}}$. ...
Added: August 12, 2026
Ali S., Bocharnikov V., Ratnikov F. et al., Sensors 2026 Vol. 26 No. 16 Article 5024
Large distributed sensor arrays require repeated recalibration as radiation damage, material aging, gain variation, and readout drift alter channel responses. We studied a high-granularity calorimeter as a large sensor array and addressed unsupervised recalibration from two unpaired datasets: a nominal reference response and an aged response with attenuated cell-wise signals. Aging was modeled by a ...
Added: August 11, 2026
Грегор Э. Д., СПб.: Владимир Даль, 2026.
Фашизм традиционно считался иррациональным и антиинтеллектуальным феноменом, ведомым мистицизмом и приверженным хаосу и грубой жестокости. Настоящее издание — итог почти четырех десятилетий исследований одного из ведущих экспертов по этому вопросу, американского историка Энтони Джеймса Грегора. Он утверждает, что итальянский фашизм был не более и не менее иррациональным, чем другие революционные идеологии XX века. Грегор прослеживает историю ...
Added: August 10, 2026
Междуреченск: Кузбасский государственный технический университет им. Т.Ф. Горбачева, 2023.
В сборнике представлены материалы докладов по направлениям Международной научно-практической конференции «Современные тенденции и инновации в науке и производстве»: 1. Горное дело; 2. Экономика и управление; 3. Социально-гуманитарные знания: теория и практика; 4. Информационные системы и технологии; 5. Вопросы технических наук в свете современных исследований; 6. Юный исследователь. Целью этой конференции является обмен передовым опытом, повышения ...
Added: August 7, 2026
Kulev Y., Maksaev A., Promyslov V., Linear Algebra and its Applications 2026 Vol. 730 P. 51–72
The notion of λ-th upper scrambling index was introduced by Huang and Liu in 2010, as a generalization of a notion considered by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every λ vertices of D there exist directed paths of lengths k from these vertices to a common vertex. This ...
Added: August 7, 2026
Kanunnikov A., Promyslov V., Vassilieva E., Electronic Journal of Combinatorics 2024 Vol. 31 No. 3 Article P3.6
Introduced by Goulden and Jackson in their 1996 paper, the matchings-Jack conjecture and the hypermap-Jack conjecture (also known as the b-conjecture) are two major open questions relating Jack symmetric functions, the representation theory of the symmetric groups and combinatorial maps. They show that the coefficients in the power sum expansion of some Cauchy sum for ...
Added: August 7, 2026
Borzenko V., Театралис, 2025.
Творчество Бориса Васильевича Щукина – одна из интереснейших страниц в истории сценического искусства, а для Театра им. Вахтангова и вовсе целая веха, прославившая коллектив в 1920-е – 1930-е годы. Его судьба прослеживается подробно с самых первых лет интереса к театру, участия в любительских кружках подмосковной Каширы, поступления в Вахтанговскую студию и до последних лет жизни. ...
Added: August 6, 2026
М.: Ад Маргинем Пресс, 2026.
Это первое отдельное издание русского перевода самого известного эссе немецкого писателя и философа Эрнста Юнгера (1895–1998). «Замысел этой книги, — писал автор в предисловии к первому изданию, — состоит в том, чтобы по ту сторону теорий, политических партий и предрассудков показать гештальт Рабочего как действенную величину, которая уже со всей мощью вмешалась в историю и ...
Added: August 6, 2026
Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...
Added: August 3, 2026
Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129
Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...
Added: August 3, 2026
Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...
Added: August 3, 2026
A. Radomskii, Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Shamkanov D. S., Logic Journal of the IGPL 2024 P. 1–46
We consider an extension of the modal logic of transitive closure K+ with certain infinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. We establish continuous cut-elimination for the given calculus using fixed-point theorems for contractive mappings. The infinitary derivations mentioned above are well founded and countably branching, while the non-well-founded proofs ...
Added: January 29, 2025
Shamkanov D. S., / Series arXiv "math". 2023.
We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the cut-elimination theorem following the lines of so called continuous cut elimination. Our consideration also covers ordinary proofs of K+ since ...
Added: November 14, 2023
Vilinbakhova E., Escandell-Vidal V., Zevakhina N., Journal of Pragmatics 2022 Vol. 191 P. 55–66
In the literature on nominal tautologies, it is assumed that common knowledge is a crucial ingredient for their interpretation. This paper explores a different approach: we argue that invoking shared knowledge is at the same time too strict and too vague as a condition for the understanding of tautologies in context. More specifically, we claim ...
Added: February 8, 2022
Shamkanov D. S., , in: Advances in Modal LogicVol. 13.: College Publications, 2020. P. 581–596.
The provability logic GLP introduced by G. Japaridze is a propositional polymodal logic with important applications in proof theory, specificially, in ordinal analysis of arithmetic. Though being incomplete with respect to any class of Kripke frames, the logic GLP is complete for its neighbourhood interpretation. This completeness result, established by L. Beklemishev and D. Gabelaia, implies ...
Added: October 6, 2020