?
Ещё раз об определении предмета математики и о периодизации её истории
Семь искусств. 2014. № 5(52).
Аbout approaches to the definition of a subject of mathematics and about a periodization of its history
Priority areas:
mathematics
Language:
Russian
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
Рязанов П. А., Софронова Л. В., Диалог со временем 2026 № 94 С. 36–50
Among the Roman pontiffs who proclaimed crusades against the Turks, Pius II (1458-1464) stands out for having publicly declared his intention to go to war and backed it up with concrete actions. His death in Ancona, from where he was about to set sail for the East, can be perceived as a feat of faith ...
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
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
Филянов Н. А., Вестник древней истории 2026 Т. 86 № 2 С. 388–408
Данная статья посвящена вопросу о возможном влиянии законопроекта плебейского трибуна 126 г. до н.э. М. Юния Пенна об изгнании перегринов из Рима на гракханскую политику в т.н. италийском вопросе, которая была представлена рогацией консула 125 г. до н.э. М. Фульвия Флакка о предоставлении союзникам (латинам) прав римского гражданства или права провокации (provocatio ad populum). По ...
Added: September 6, 2026
Voloshina S., Логос 2025 Т. 35 № 2 (165) С. 193–233
Статья посвящена исследованию маскарадов как социального и культурного феномена в эпоху правления Николая I. Автор рассматривает маскарады не только как развлекательные мероприятия, но и как сложные ритуалы, совмещающие властные сценарии, гендерные роли, социальные иерархии и индивидуальные характеры. Основное внимание уделяется трем типам маскарадов: придворным, аристократическим и публичным. Придворные маскарады (новогодние и июльские) служили инструментом демонстрации ...
Added: September 4, 2026
Voloshina S., СПб.: Владимир Даль, 2016.
Представленная книга - первый опыт "полной" биографии Николая Платоновича Огарёва, попытка объемного описания этой разносторонней, талантливой личности, его многочисленных и неоднозначных интересов и занятий, политических, поэтических, дружеских и финансовых связей с современниками (А. И. Герценом, М. А. Бакуниным, Н. А. Некрасовым и многими другими). Тесная связь биографии Н. П. Огарёва с современными ему социальными, политическими ...
Added: September 4, 2026
Voloshina S., М.: Издательский дом «Дело» РАНХиГС, 2022.
Книга посвящена взаимоотношениям власти и журналистики 1830–1855 гг. – времени правления Николая I и одновременно периода журналистской деятельности Андрея Александровича Краевского. Это годы профессионализации журналистики и литературы, попыток общественного мнения выразить себя в печати посредством завуалированных общественно-политических высказываний в условиях жесточайшей цензуры. Один из фокусов исследования в книге – профессиональная биография Краевского, талантливого редактора и предпринимателя, ...
Added: September 4, 2026
Потехина И. П., СПб.: Евразия, 2026.
В центре внимания этой книги развитие папской власти в период с середины VIII до конца XII в. — в эпоху, когда римская церковь из локального религиозного центра, пусть и засвидетельствовавшего свое апостольское происхождение, постепенно превращалась в одну из главных политических сил европейского континента. Автор показывает, как выстраивались отношения преемников ап. Петра с франкскими правителями, византийскими ...
Added: September 3, 2026
Потехина И. П., Вестник Санкт-Петербургского университета. Серия 2. История 2026 Т. 71 № 2 С. 525–533
The review is dedicated to the fourth volume of the “History of the Roman Popes” (2024), which represents a continuation of the long-term scholarly project lead by the philosopher and historian Vitaly L. Zadvorny. The volume itself is dedicated to the popes of the 11th - early 13th centuries and generally continues the traditions laid down in ...
Added: September 3, 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
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 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
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026