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Remarks on Number Theory and Thermodynamics Underlying Statistical Distributions in Languages
Mathematical notes. 2017. Vol. 101. No. 4. P. 660–665.
In the paper “The relationship between the Fermi–Dirac distribution and statistical
distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac
distributions are considered in connectionwith frequency distributions in languages in the context of
the author’s approach to thermodynamics and number theory problems. The present article presents
certain clarifications of certain notions used in that approach, in particular, the identity of particles,
the Poisson adiabat, thematching of number theory formulas with those given by the Bose–Einstein
distribution, nonstandard analysis, and others.
Priority areas:
mathematics
Language:
English
Vlasenko D., Saranskaia I., Zakharov D., European Physical Journal: Special Topics 2026 P. 1–16
Hypergraphs provide a natural framework for representing neurophysiological interactions distributed across sets of sensors. A key methodological question is how hyperedges should be defined from frequency-resolved electroencephalography/magnetoencephalography (EEG/MEG) data. We demonstrate a construction strategy in which hyperedges are obtained from canonical coherence (caCOH), an extension of coherence that estimates coupling between multidimensional signal spaces. To ...
Added: August 18, 2026
Borisov D., Katzarkov Ludmil, Sheshmani A. et al., American Journal of Mathematics 2026 Vol. 148 No. 4 P. 1075–1101
It is shown that there are globally defined Lagrangian distributions on the stable loci of derived \mathrm{Quot}-stacks of coherent sheaves on Calabi--Yau four-folds. Dividing by these distributions produces perfectly obstructed smooth stacks with globally defined -1-shifted potentials, whose derived critical loci give back the stable loci of smooth stacks of sheaves in global Darboux form. ...
Added: August 18, 2026
Belova P., Когнитивные исследования языка 2025 № 1 (62) С. 56–60
This article contains the results of studying the content of SPACE concept in the Russian language consciousness based on the material of literary prose texts of diff erent genres created in the second half of the XXth century and in the XXIst century and presented in th e Russian National Corpus (RNC). The analysis is ...
Added: August 16, 2026
Kanogina P., Когнитивные исследования языка 2026 Т. 3 № 68 С. 196–200
The article examines gender and age-related features of the conceptualization of space by native speakers of the Russian language based on subjective definitions. Gender differences manifest themselves in varying degrees of attention to the physical, functional, and emotional characteristics of space, while age affects the level of abstraction in the definitions. ...
Added: August 16, 2026
Kanogina P., Когнитивные исследования языка 2026 Т. 2 № 67 С. 118–122
This article is devoted to the study of the conceptualization of city streets in Russian fiction in the second half of the XXth century and in the first quarter of the XXIst century. The analysis of the selected object of open urban space in order to establish the features of its conceptualization was carried out ...
Added: August 16, 2026
Zinchenko S., Бейн П. В., Дубровская Д. В. et al., Институт востоковедения РАН, 2026.
Contrary to Antoine de Saint-Exupéry's assertion that "the most beautiful thing in the stars, houses, and deserts is what the eyes cannot see," the authors of this monograph dispassionately test the harmony of beauty in the East through the algebra
of scientific analysis, continuing the work of their first book, "The Beautiful and the Utilitarian: From ...
Added: August 14, 2026
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
Lavrentiev A., Preobrazhenskaya A., Вестник Санкт-Петербургского университета. Язык и литература. 2026 Т. 23 № 2 С. 419–437
Thе article examines the administrative and economic structure of the southern holdings of the Grand Princes of Ryazan in the Upper Don region and the origin of the well-known place name Epifan’. Based on a study of literary texts, toponymy, and historical material, the authors hypothesize a connection between the literary character, the Ryazan boyar ...
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
Dmitrova E., Буклина С. Б., Gronskaya N. E. et al., Вопросы нейрохирургии им. Н.Н. Бурденко 2026 № 90(4) С. 87–94
Effective intraoperative speech mapping requires specific test with standardized linguistic material. The last one should capture speech function supported by brain region targeted for resection. It is necessary to develop a test tailored to specific patient’s needs and document intraoperative linguistic support. The objective of this report was to describe the procedure of intraoperative speech testing and battery of intraoperative tests for Russian language. We correlated intraoperative tests with brain regions and speech functions, as well as presented an application ...
Added: August 12, 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
М.: Институт славяноведения РАН, 2023.
Более двадцати лет Институт славяноведения РАН отмечает День славянской
письменности и культуры традиционной научной конференцией. С 2014 г. она проходит в формате конференции молодых ученых. В 2023 г. участники из Мос квы,
Санкт-Петербурга, Воронежа, Казани, Калининграда, Нижнего Новгорода, Ростова-на-Дону, Смоленска, а также Белоруссии, Венгрии, Китая, Польши, Словакии
и Чехии продолжили эту традицию. Вновь обсуждался широкий круг проблем,
связанных с ...
Added: August 12, 2026
Nhà xuất bản Đại học quốc gia Hà Nội, 2026.
Added: August 11, 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
Arkhipov I., Клыгина Ю. А., Широкова М. А., Вестник древней истории 2026 Т. 86 № 1 С. 216–259
Первый русский перевод ARET 13 1, одного из наиболее пространных и необычных документов из Эблы (Сирия, XXIV в. до н.э.) с подробным историко-филологическим комментарием. Главными героям произведения являются правитель Эблы, не названный по имени, и царь соседнего государства Мари по имени Хинна-Даган. Царь и Хинна-Даган посещают дом божеств, обозначенных как Отец и Мать Богов, чтобы спросить ...
Added: August 11, 2026
Pimenova N., Satdarov K., Известия РАН. Серия литературы и языка 2026 № 3 С. 49–61
The article examines the emergence of a distinctive definiteness system in Faroese, featuring two free-standing definite “adjectival” articles, tann and hin. Unlike familiar systems that distinguish “weak” and “strong” definiteness through distinct forms, the distribution of tann and hin is typically attributed to register, with hin linked to formal usage and high style. Analysis of the Faroese Gospels reveals stable and variable contexts for ...
Added: August 10, 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