?
On the Probability of Co-primality of two Natural Numbers Chosen at Random: From Euler identity to Haar Measure on the Ring of Adeles
Bernoulli News. 2017. Vol. 24. No. 1. P. 7–13.
Abramovich S., Nikitin Y. Y.
The paper describes the rich history of remarkable problem lying at the confluence of number theory and probability. What is the probability of co-prima;lity of two randomly selected random numbers? In russian literature this problem and its solution is attributed to P.L.Chebyshev, but we show that before Chebyshev the solution was given by P. Dirichlet, who probably learned the paper from the great Gauss. We describe three main approaches to the solution of this problem and give numerous generalizations of it.
Priority areas:
mathematics
Language:
English
Боголюбов Е. А., Вестник Российского университета дружбы народов. Серия: История России 2026 Т. 25 № 2 С. 373–385
The attitude of the Soviet government towards the palaces of former reigning personages in the early years was ambiguous. In their article, the author focuses on the palaces of the Emir of Bukhara, which had not previously been considered as symbolic objects. In 1926, the Uzbek SSR attempted to take over the palace of the ...
Added: June 30, 2026
Springer, 2026.
This book presents established and new research on the close connections between graph games and systems of logic, particularly existing and newly designed modal logics. The volume utilizes two graph games – the sabotage game and the hide-and-seek game – to demonstrate the natural interplay between designing new graph games and exploring new kinds of ...
Added: June 30, 2026
Pochinka O., Barinova M., Journal of Geometry and Physics 2026 Vol. 228 P. 1–8
In the present paper we consider an Ω-stable 3-diffeomorphism with a solid or thickened surfaced non-trivial basic set. Such basic sets include, for instance, all one-dimensional expanding attractors and those two-dimensional basic sets that are not expanding. We prove that the chain recurrent set of every such a diffeomorphism necessarily contains at least two non-trivial ...
Added: June 30, 2026
М.: ИСАА МГУ имени М.В. Ломоносова, 2023.
Издание представляет собой сборник материалов I Международной научно-образовательной конференция «Пейсиковские чтения: проблемы современного академического востоковедения», проведённой 21 апреля 2023 года в ИСАА МГУ имени М.В. Ломоносова. В книге представлены работы сотрудников Института и приглашённых специалистов из ряда ведущих институтов России и зарубежных стран
Сборник в электронном виде можно скачать по ссылке http://iranistika.iling-ran.ru/Sbornik/ ...
Added: June 30, 2026
Gromova A., Научный вестник Крыма (Россия, ISSN: 2499-9911) 2021 № 2 (31) С. 1–13
The Iranian ‘Teleschool’ that was launched in 2020 on the base of standard schoolbooks published by the Ministry of Education, reflects the common vision of the glorious history of Ancient Iran and promotes the national cultural heritage. The present article aims to describe a comprehensive selection of new learning materials such as original texts and ...
Added: June 30, 2026
Gromova A., М.: КноРус, 2023.
Учебное пособие по лингвострановедению предназначено для востоковедов, изучающих персидский язык в рамках различных специализаций: регионоведение, филология, история и политология, экономическое развитие стран Ближнего и Среднего Востока. Пособие знакомит с реалиями современной иранской жизни и национальными новостными ресурсами, широко использует материалы Интернета. Книга оставляет известную свободу в выборе материала для занятий в зависимости от уровня владения ...
Added: June 29, 2026
German O., Illarionov A., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 3–18
Пусть симплекс с целочисленными вершинами - содержащий ровно одну целочисленную точку, отличную от своих вершин. В работе доказывается, что если точка находится во внутренности симплекса или в относительной внутренности некоторой гиперграни симплекса, то объем симплекса ограничен величиной, зависящей только от размерности, в противном случае объем симплекса может быть сколь угодно большим. Этот результат применяется для вывода асимптотической формулы для среднего числа вершин полиэдров ...
Added: June 29, 2026
Boltunova E., Edelman O., Herald of the Russian Academy of Sciences 2025 Vol. 95 No. 7 P. 753–765
The primary work currently available that examines the negotiations between the Decembrists of the Southern Society and members of Polish secret societies is P.N. Olshansky’s monograph The Decembrists and the Polish National Liberation Movement (1959). Consistent with Soviet ideological expectations, Olshansky proposed an interpretation of the relations between Russian and Polish conspirators in the spirit ...
Added: June 29, 2026
Masagutova M., Антропологический форум 2026 № 69 С. 361-375
The book by Page Herrlinger constitutes the most comprehensive existing historical research on the movement of Brother Ioann Churikov’s teetotalers (trezvenniki), encompassing the period from the dawn of the community up to our day. Using an extensive array of documents, Herrlinger demonstrates the process of the development of the teetotalers’ identity and proposes some possible ...
Added: June 29, 2026
Gromova A., КноРус, 2026.
Предназначено для востоковедов, изучающих персидский язык в рамках различных специализаций, таких как история, политология, регионоведение, филология, экономическое развитие стран Ближнего и Среднего Востока. Рассчитано на студентов востоковедных вузов второго курса, знакомит с основными этапами истории Древнего Ирана, туристским потенциалом этой многоликой страны, с национальными новостными и тематическими онлайн-ресурсами. Книга оставляет известную свободу в выборе материала ...
Added: June 29, 2026
Egorov E., Quaestio Rossica 2026 Т. 14 № 2 С. 505–522
This article examines the diplomatic practices of the Russian Empire in northern Europe during the mid-nineteenth century, with particular focus on the methods of observation and interpretation of political events as reflected in official dispatches. The focus is on the limitations of observation practices and how visual metaphors, comparisons and the stylistic features of diplomatic ...
Added: June 28, 2026
Alexandrov B., Индоевропейское языкознание и классическая филология 2026 Т. 30 № 1 С. 42–60
The article examines the system of political institutions of Emar during the Old Babylonian period (20th–16th centuries B.C.). The epistolary texts published in the last three volumes of the Archives royales de Mari series (ARM XXXIII, XXXIV, XXXV, 2019–2024) contain several dozen references to this ancient city in the Middle Euphrates valley. Unlike the era of the ...
Added: June 28, 2026
ДВАДЦАТЬ ПЯТЬ ЗАСЕДАНИЙ НАУЧНОГО СЕМИНАРА «ФЕНОМЕН РУССКОЙ МЕДИЕВИСТИКИ: ЛЮДИ, КОНЦЕПЦИИ, ИНСТИТУТЫ»
Klyuev A., Средние века 2026 Т. 87 № 2 С. 160–170
The article presents some results of the work of the scientific seminar «The Phenomenon of Russian Medieval Studies: People, Concepts, Institutions», established in February 2023 as a non-institutional specialized historiographic platform aimed at a comprehensive study of the phenomenon of Russian medieval studies. ...
Added: June 28, 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
Antonova N., Амброджий А. В., В кн.: XII Международный Форум Ассоциации Когнитивно-Поведенческой Психотерапии CBTFORUM: сборник научных статей.: СПб.: Международный институт развития когнитивно-поведенческой терапии, 2026. С. 21–29.
With the digitalization of higher education, the importance of student independence in learning is increasing. Online learning formats increase the demands on self-regulation, metacognitive skills, and intrinsic motivation of students (Köse, 2016; Sorokin, 2022). The aim of this study was to develop and empirically test a cognitive-behavioral coaching program based on the self-regulated learning (SRL) ...
Added: May 31, 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
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Semenov P., Математика в школе 2024 № 4 С. 34–40
Simple examples are given to show that
the independence of two random events is a very
rare circumstance. It is shown how to estimate its
frequency. Open questions are posed ...
Added: March 14, 2026
Koreshnikova Y., Afanaseva I., Solominova D., Мониторинг общественного мнения: Экономические и социальные перемены 2026 № 1 С. 182–207
The study presented in this article aims to create a socio-demographic profile of the agentic individual. By "agency," the authors define a person's ability to act as an active participant in changing the environment, rather than passively following it. The authors believe that the demand for such qualities is heightened in a highly volatile world. ...
Added: March 2, 2026
Семаков С. Л., Автоматика и телемеханика 2025 № 12 С. 104–118
This paper considers the problem of estimating the probability of the following event: a continuous random process will first reach a given level at some time from a given variation interval of the independent variable. The general results obtained previously are specified for a smooth Gaussian process. The estimates are calculated for different values of ...
Added: February 23, 2026