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О новом подходе к реконструкции лекции Феодора (Tht. 147d)
Платоновские исследования. 2016. № 2. С. 258–278.
In Theaetetus (145a–148a), Plato brings up Theaetetus’ retelling of a lesson by Theodorus of Cyrene, in which the latter demonstrated the incommensurability of the sides of squares containing three, five, and up to seventeen square feet with the side of one square foot. In this paper, we analyse modern scholarly attempts to reconstruct the exact content of the lesson. Our understanding of the fifth-century mathematics in general (and the early Pythagorean one in particular) may vary significantly depending on which methodology Theodorus actually used.
Priority areas:
humanitarian
Language:
Russian
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
Ермоленко Г. А., Кожевников С. Б., Вестник Московского городского педагогического университета. Серия: Философские науки 2026 № 1(57) С. 9–18
This article explores the phenomenon of social capital in the context of contemporary media communications and its relationship with the phenomenon of cancellation ethics. The authors examine the mechanisms by which social capital functions in the digital space and how it is transformed by cancellation practices. The research methodology draws
on theoretical approaches to understanding the ...
Added: September 11, 2026
Филатова А. А., Эпистемология и философия науки 2026 Т. 63 № 2 С. 154–171
intelligence (hereafter, AI), particularly in the form of large lan guage models, has prompted a renewed wave of philosophical debates concerning the semantic competences of technical sys tems and the criteria for evaluating the outputs they generate, especially textual outputs. This article examines a set of central problem areas and their treatment in contemporary philosophical ...
Added: September 10, 2026
Faul B., Эпистемология и философия науки 2026 Т. 63 № 2 С. 41–50
In the article “Knowledge in the Digital Age: The Redundancy of Romanticism”, a critical analysis is offered of Konstantin Ocheretyany’s argumentation as presented in his essay “Epistemic Nihilism and Existential Romanticism: Knowledge in the Digital Age”. Two scenarios proposed by the author – techno-pessimistic and techno-optimistic – are examined, and it is shown that the ...
Added: September 9, 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
Малышкин Е. В., Логос 2024 Т. 34 № 6 (163) С. 217–232
In his main works, René Descartes, in addition to such an impressive metaphysical construction, over and over again gives promises of happiness, which must certainly accompany the study of philosophy according to a new model. What exactly is this happiness and is the Cartesian construction capable of fulfilling this promise? For whom can it come? ...
Added: September 8, 2026
Малышкин Е. В., Эпистемология и философия науки 2026 Т. 63 № 2 С. 64–69
The article begins with several critical remarks about Konstantin Ocheretyany's paper. The conclusion of these remarks is that the dangers presented in the article under discussion, in the spirit of epistemic pessimism, are not frightening, and the problems raised are much older than the emergence of language models. The article is conceived in terms of ...
Added: September 8, 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
Ермоленко Г. А., Гришин С. Е., Дугарова С. Б. et al., М.: Издательство "Перо", 2026.
The monograph outlines the subject and problem fields of media research, highlights the role of media in modern society and the influence of media on social processes, and examines the main theoretical approaches and empirical methods for studying media in a digital society. The monograph is addressed to a wide range of researchers in the ...
Added: September 8, 2026
Ермоленко Г. А., Ахмадуллин В. А., Базилико Э. А. et al., М.: Издательско-торговая корпорация «Дашков и Ко», 2026.
The monograph is devoted to reconstructing the uniqueness of Russia’s historical path — its culture, social system, and religious, philosophical, and political thought. Based on a synthesis of various sciences and approaches, the authors summarize and comprehensively demonstrate the distinctiveness of Russian traditions.
The uniqueness of Russia is revealed through a vast body of factual material as a ...
Added: September 8, 2026
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
Kudriavtseva E., / РЦИС. Серия № 0148-756-286. 2026.
The content of the work is the system is a system for identifying four types of written speech structures. A set of 11 calculated parameters, statistical standards, and semantic characteristics allows for the identification of a text's structure as the result of a specific cognitive schema (scene, event, story, evaluation). The method has been verified ...
Added: June 2, 2026
Vorchik A., / SSRN. Серия Social Science Research Network "Social Science Research Network". 2026.
This work is devoted to a theoretical explanation of the Easterlin paradox, according to which long-term economic growth does not make average level of people's happiness increasing. By happiness, we mean the intensity of emotions people experience while comparing their new income with its expected value, or the target income with its original value. In the first case, ...
Added: May 31, 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