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Об интерпретациях арифметики Пресбургера в арифметиках Бюхи
Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2023. Т. 510. С. 3–7.
Büchi arithmetics BAn, , are extensions of Presburger arithmetic with an unary functional symbol
denoting the largest power of n that divides x. Definability of a set in BAn is equivalent to its recognizability
by a finite automaton receiving numbers in their n-ary expansion. We consider the interpretations of Presburger
Arithmetic in the standard model of BAn and show that each such interpretation has an internal model
isomorphic to the standard one. This answers a question by A. Visser on the interpretations of certain weak
arithmetical theories in themselves.
Брычков М. Е., Незнанов А.А., Программирование 2026 № 4 С. 50–66
The matrix profile (MP) quickly became one of the most important time series preprocessing methods when it was introduced in 2016, facilitating the solution of a wide range of time series analysis problems, in particular anomaly and pattern detection problems. The high significance has led to the emergence of various tools for MP calculating, but ...
Added: October 9, 2026
ООО "Издательство Юрайт ", 2026.
The Collection of Olympiad Problems (COP) in Probability Theory and Mathematical Statistics (PTMS) is offered as a teaching aid primarily for university students and faculty as a developmental supplementary resource, expanding the range of problems to be solved in lectures, seminars, and out-of-class independent work with students in various formats, including (as the title suggests) ...
Added: October 9, 2026
Aleskerov F. T., Вайншток А. П., Делахова А. М. et al., Информационные процессы 2026 Т. 26 № 3 С. 895–913
The development and effective management of territorial entities are priority issues for all states, particularly in the context of the digital transformation of public administration. Over the past decade, the integration of information technologies into municipal and regional planning has significantly altered approaches to strategic development, service delivery, and public engagement. This paper describes the ...
Added: October 9, 2026
Kupavskii A., Noskov F., Forum of Mathematics, Sigma 2026 Vol. 14 Article 124
We call a family of $s$ sets $\{F_1, \ldots, F_s\}$ a sunflower with $s$ petals if, for any distinct $i, j \in [s]$, one has $F_i \cap F_j = \cap_{u = 1}^s F_u$. The set $C = \cap_{u = 1}^s F_u$ is called the {\it core} of the sunflower. It is a classical result of ...
Added: October 8, 2026
Flamarion M. V., Pelinovsky E., Chaos, Solitons and Fractals 2026 Vol. 213 No. 2 Article 119245
This article concerns the study of modulational instability in the rotated-modified Gardner–Whitham (rmGW) equation. This model incorporates both quadratic and cubic nonlinearities, similarly to the Gardner equation, while also retaining the fully dispersive character of the Whitham equation together with a large-scale dispersive term analogous to that in the Ostrovsky equation. Using a classical multiple-scale asymptotic expansion, we ...
Added: October 8, 2026
Люксембург А. А., УРСС, 2005.
Изучается возможность автоматизированного построения математических теорий. Рассматривается дедуктивная система, основанная на языке логики предикатов первого порядка, объектами системы являются математические выражения или формулы, которые описывают математические объекты или их свойства. В дедуктивной системе выводятся математические определения и теоремы. Для доказательства теорем используются методы автоматического доказательства. Разработан алгоритм, выводящий часть формул системы. Для решения задачи используется аппарат математической ...
Added: October 7, 2026
Aleskerov F. T., Chaika E., Дерендяев А. Б. et al., Procedia Computer Science 2026 No. 287 P. 590–595
Under conditions of dynamic socio-economic changes, effective planning and decision-making are key factors in ensuring a high quality of life for the population in territories. This paper presents a decision support system for territorial administrations for the development and implementation of sustainable development strategies, using one of the regions of the Russian Federation – the ...
Added: October 7, 2026
Bernardin C., Gonçalves P., Olla S., Mathematical Physics Analysis and Geometry 2024 Vol. 27 No. 7
We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space. ...
Added: October 6, 2026
Bernardin C., Chhaibi R., Najnudel J. et al., Probability Theory and Related Fields 2026 Vol. 195 P. 1823–1875
We study the celebrated Shiryaev-Wonham filter (Wonham, W.M., in J. Soc. Ind. Appl. Math. 347–369, 1964) in its historical setup, where the hidden Markov jump process has two states. We are interested in the weak noise regime for the observation equation. Interestingly, this becomes a strong noise regime for the filtering equations. Earlier results of ...
Added: October 5, 2026
Ismailov A., Spiridonov V., Успехи математических наук 2026 Т. 81 № 5 С. 183–184
Получена новая формула для цепной дроби Аски–Вильсона в форме отношения двух q-гипер-геометрических рядов. ...
Added: October 5, 2026
Abdulkhaev K., Shirokov D., Advances in Applied Clifford Algebras 2026 Vol. 36 P. 1–21
In this paper, we present explicit formulas for the inverse and determinant in geometric (Clifford) algebras over vector spaces of dimension n = 7. The derivation of these formulas is made possible by generalizing the concept of conjugation to basis conjugation operations. We further develop a general method for constructing such formulas over odd-dimensional spaces ...
Added: October 4, 2026
Kuninets A., IEEE Transactions on Information Theory 2026 P. 1–1
In this work we study the applicability of Quasi-Cyclic Subfield Subcodes of Dual Elliptic (QC-SSDE) codes for integration into code-based cryptographic schemes. Detailed algorithms are provided for constructing parity-check matrices as well as block-circulant parity-check matrices for this family of codes, accompanied by empirical results that enable the construction of QC-SSDE codes with predetermined dimensions. ...
Added: October 3, 2026
Medvedev G., Alexandrov Artem, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 114 Article 044102
Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include ...
Added: October 2, 2026
Pochinka O., Baranov D., Nozdrinova E., Теоретическая и математическая физика 2026 Т. 229 № 1 С. 3–14
The Birman–Williams problem on describing the planetary link of a fibered knot K in S^3 has been partially solved. Using Nielsen's theory for the classification of periodic surface homeomorphisms and its close relationship with the theory of gradient-like diffeomorphisms, it is proved that the planetary link of the trefoil (the unique periodic fibered knot of genus ...
Added: October 2, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 2026
Zlotnik A., Математические заметки 2026 Т. 120 № 6 С. 1005–1009
Численным методам решения систем газодинамических уравнений посвящена обширная литература. Ранее было разработано и успешно апробировано специальное семейство симметричных по пространству консервативных разностных методов, основанных на предварительной кинетической, точнее, квазигазодинамической (КГД), регуляризации этих уравнений. Актуальной задачей является построение численных методов, которые обладают не только свойством консервативности по массе, импульсу и полной энергии, но и удовлетворяют условиям энтропийной ...
Added: October 1, 2026
Vyugin I. V., Sashadhar D., Algebra and Number Theory 2026 P. 1–10
We study the K-Fibonacci sequence Fp modulo prime p. Cardinalities of sets |Fp+Fp| and |Fp⋅Fp| are estimated. We present the method of estimating doubling constant of some m-dimensional recurrent sets in Fp. ...
Added: October 1, 2026
Pahomov F., Zapryagaev A., Logic Journal of the IGPL 2026 Vol. 34 No. 4 Article jzag045
We prove the linear orders first-order definable in the standard model (Z;<,+) of Presburger arithmetic are exactly those that are (Z;<,+)-definably embeddable into the lexicographic ordering on Z^n for some n. ...
Added: July 16, 2026
Dudakov S., Вестник Тверского государственного университета. Серия: Прикладная математика 2024 № 2 С. 27–38
In our previous works, we have proved for various associative algebras that the finite subsets theory allows to interpret elementary arithmetic, in particular, such theory is undecidable. For example, this is proved for all infinite Abelian groups. A natural question arises: can we generalize this result to a wider class of algebras, for example, all ...
Added: March 18, 2026
Благовещенская Е. А., Павлова Н. Г., Гарбарук В. В. et al., Международная конференция по мягким вычислениям и измерениям 2018 Т. 1 С. 684–686
Abelian torsion-free groups, being one of the primary algebraic structures, admit an algorithmic approach to the study of their various direct decompositions. The graphs used are of the line-parallel form and they are applicable to parallelization problems. ...
Added: January 13, 2026
Благовещенская Е. А., Гарбарук В. В., Кузнецова И. В. et al., , in: IEEE International Conference on Electrical Engineering and Photonics (EExPolytech).: St. Petersburg: IEEE, 2021. P. 128–131.
Added: January 13, 2026
Благовещенская Е. А., Филимонов А. В., Трифонов А. Е., Journal of Mathematical Sciences 2021 Vol. 259 No. 4 P. 394–402
Added: January 13, 2026
Карпов В. Е., Speranski S. O., Математические заметки 2025 Т. 118 № 1 С. 77–90
Строится $\Sigma_1$-интерпретация класса BiG-fin всех конечных двудольных графов в классе 2Eq-fin всех пар отношений эквивалентности на общем конечном носителе; это даёт наследственную неразрешимость $\Sigma_2$-теории 2Eq-fin. Далее, строится $\Sigma_1$-интерпретация 2Eq-fin в классе LEq-fin всех пар, состоящих из линейного порядка и отношения эквивалентности на общем конечном носителе; это даёт наследственную неразрешимость $\Sigma_2$-теории LEq-fin. Полученные результаты являются в известном ...
Added: December 26, 2025
Гугнин Д. В., Алгебра и анализ 2025 Т. 37 № 6 С. 90–99
В работе В. М. Бухштабера, А. П. Веселова и А. А. Гайфуллина 2022 года была получена практически полная классификация инволютивных коммутативных двузначных групп. В работе А. А. Гайфуллина 2024 года была доказана автоматическая коммутативность произвольной инволютивной двузначной группы. Единственный вопрос о классификации инволютивных двузначных групп, который оставался открытым после этих публикаций, заключается в следующем: Верно ли, что если две ...
Added: November 13, 2025