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Polynomial and non-polynomial first integrals of projective structures and geodesic flows
Journal of Geometry and Physics. 2025. Vol. 216. Article 105596.
Maria V. Demina, Anna R. Ishchenko
We develop a method based on the Darboux theory of integrability that is able to produce first integrals of geodesic equations on 2-surfaces. We present local explicit examples of two-dimensional metrics with polynomial in momenta first integrals of arbitrary degrees. We also find metrics admitting transcendental first integrals. In particular, we express some first integrals via the hypergeometric function. Our metrics are parameterized by an arbitrary function of one variable.
Mishuris G., Meylan M. H., Pelinovsky E., Journal of Fluid Mechanics 2026 Vol. 1045 Article A4
In this paper, we revisit the classic problem of a wave field on a sloping beach of an arbitrary angle and propose a general approach that allows the computation of regular solutions of the problem regardless of the angle. We use the Mellin-transform technique, reducing the problem to singular integral equations with fixed-point singularities of ...
Added: October 12, 2026
Gusein-Zade S., М.: МЦНМО, 2026.
Книга содержит курс лекций по дифференциальной геометрии и топологии, читавшихся автором на механико-математическом факультете МГУ в разные годы. В дополнениях приводятся некоторые сюжеты (связности в расслоениях, теорема Фробениуса, производные Ли и др.), которые были включены в курс в отдельные годы либо содержались в аналогичных курсах лекций в Независимом московском университете.
Для студентов математических и физических специальностей. ...
Added: October 12, 2026
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
Maria V. Demina, Varvara G. Nechitailo, Qualitative Theory of Dynamical Systems 2025 Vol. 24 No. 1 Article 29
We classify generalized Liénard differential equations, sometimes called Liénard type equations, that have integrating factors of a special form. We present first integrals of the related equations. Our families of equations contain almost all known integrable generalized Liénard equations as partial cases. We find the necessary and sufficient conditions of the Liouvillian integrability for the ...
Added: April 7, 2025
Ulitin, B., Babkin, E., Babkina, T., , in: Model-Driven Organizational and Business Agility: Second International Workshop, MOBA 2022, Leuven, Belgium, June 6–7, 2022, Revised Selected PapersIssue 457: Model-Driven Organizational and Business Agility. MOBA 2022.: Switzerland: Springer, 2022. P. 110–124.
The use of intelligent systems with advanced AI algorithms is a key aspect of enterprise digitalization. The railway domain is not an exception. We argue, that the quality of any AI-based system greatly depends on the methods of computer-human interaction. We propose an approach to organize the interaction of the end user with the AI-based ...
Added: October 25, 2022
Ulitin B., Babkina T. S., , in: Lecture Notes in Business Information ProcessingIssue 423: Advanced Information Systems Engineering Workshops. CAiSE 2021.: Switzerland: Springer, 2021. P. 81–92.
The process of implementing agile technologies in an enterprise is an example of a highly demanding and challenging topic both for practitioners and academy. Speaking about agility, we basically mean various kinds of automation. A higher degree of automation results in a more agile enterprise. However, in practice, even in the case of complete automation ...
Added: June 9, 2021
Korotyaev Evgeny, Saburova N., Mathematische Annalen 2020 Vol. 337 P. 723–758
We consider a Laplacian on periodic discrete graphs. Its spectrum consists of a finite
number of bands. In a class of periodic 1-forms, i.e., functions defined on edges of
the periodic graph, we introduce a subclass of minimal forms with a minimal number
I of edges in their supports on the period. We obtain a specific decomposition of ...
Added: February 5, 2021
Boris Ulitin, Eduard Babkin, , in: Lecture Notes in Information Systems and OrganisationIssue 40: Digital Transformation and New Challenges. Digitalization of Society, Economics, Management and Education.: Switzerland: Springer, 2020. P. 37–48.
The research is related to the problem of coherent evolution of a domain-specific language (DSL) in response to evolution of the application domain and users’ capabilities. We offer a solution of that problem based on a particular model-driven approach. We give the whole definition of DSL in terms of model-oriented approach. Such definition allows us ...
Added: June 10, 2020
Boris Ulitin, Eduard Babkin, Tatiana Babkina et al., , in: Lecture Notes in Business Information ProcessingIssue 365: Perspectives in Business Informatics Research.: Switzerland: Springer, 2019. P. 59–73.
The article is devoted to the problem of automated formal verification of modeling artifacts during engineering of digital transformations. Automation significantly increases the quality of model transformations since many manual errors are eliminated. However, the formal checking the correctness of such automation remains an open question. One more problem is the dependence of the procedure ...
Added: September 30, 2019