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On Smoothness of the Solution to the Abel Equation in Terms of the Jacobi Series Coefficients
Axioms. 2020. Vol. 9. No. 3. Article 81.
Maksim V. Kukushkin
In this paper, we continue our study of the Abel equation with the right-hand side belonging
to the Lebesgue weighted space. We have improved the previously known result— the existence and
uniqueness theorem formulated in terms of the Jacoby series coefficients that gives us an opportunity
to find and classify a solution by virtue of an asymptotic of some relation containing the Jacobi series
coefficients of the right-hand side. The main results are the following—the conditions imposed on
the parameters, under which the Abel equation has a unique solution represented by the series, are
formulated; the relationship between the values of the parameters and the solution smoothness is
established. The independence between one of the parameters and the smoothness of the solution
is proved.
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 ...
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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 ...
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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. ...
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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. ...
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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 ...
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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. ...
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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 ...
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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 ...
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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
Kuksin S., Dynamical Systems 2026
We study the mixing properties of discrete-time and continuous-time dissipative dynamical systems driven by bounded mixing random forces. The continuous-time systems are
reduced to discrete-time random dynamical systems generated by time-one maps, so that
the main analysis is carried out in the discrete setting. We introduce a class of mixing random forcings whose regular conditional distributions with ...
Added: October 1, 2026
Kuksin S., Shirikyan A., Journal of Dynamics and Differential Equations 2026 P. 1098–1100
The paper deals with the problem of large-time behaviour of trajectories for discrete-time dynamical systems driven by a random noise. Assuming that the phase space is finite-dimensional and compact, and the noise is a Markov process with a transition probability satisfying some regularity hypotheses, we prove that all the trajectories converge to a unique measure ...
Added: October 1, 2026
Издательский дом ВГУ, 2025.
В сборнике представлены материалы докладов и лекций, включенных в программу Воронежской весенней
математической школы. ...
Added: June 15, 2025
Maksim V. Kukushkin, Математические заметки СВФУ 2020 Vol. 27 No. 3 P. 39–51
In this paper we aim to generalize results obtained in the framework of
fractional calculus due to reformulating them in terms of operator theory. In its own
turn, the achieved generalization allows us to spread the obtained technique on practical
problems connected with various physical and chemical processes. More precisely, a class
of existence and uniqueness theorems is covered, ...
Added: December 1, 2023
Maksim V. Kukushkin, Electronic Journal of Differential Equations 2018 Vol. 2018 No. 29 P. 1–24
We consider fractional differentiation operators in various senses
and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds
for differential operators second order with a fractional derivative in the final
term, we explore a location of the spectrum and resolvent sets and show that
the spectrum ...
Added: December 1, 2023
Maksim V. Kukushkin, Axioms 2019 Vol. 8 No. 2 Article 75
In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study
the Riemann–Liouville fractional integral and derivative operators on a compact of the real axis.
This approach has some advantages and allows us to complete the previously known results of the
fractional calculus theory by means of reformulating them in a new ...
Added: November 30, 2023
Maksim V. Kukushkin, Fractional Calculus and Applied Analysis 2019 Vol. 22 No. 3 P. 658–680
In this paper we deal with a linear combination of a second order uniformly
elliptic operator and the Kipriyanov fractional differential operator.
We use a novel method based on properties of a real component to study
such type of operators. We conduct the classification of the operators by
belonging of their resolvent to the Schatten-von Neumann class and formulate
the ...
Added: November 30, 2023
Maksim V. Kukushkin, Abstract and Applied Analysis 2020 Vol. 2020 Article 1461647
In this paper, we explore a certain class of Non-selfadjoint operators acting on a complex separable Hilbert space. We consider a
perturbation of a nonselfadjoint operator by an operator that is also nonselfadjoint. Our consideration is based on known
spectral properties of the real component of a nonselfadjoint compact operator. Using a technique of the sesquilinear forms
theory, ...
Added: November 30, 2023
M. V. Kukushkin, Lobachevskii Journal of Mathematics 2023 Vol. 44 No. 8 P. 3411–3429
This paper is partly a historical survey of various approaches and methods in the
fractional calculus, partly a description of the Kipriyanov extraordinary theory in comparisonwith the
classical one. The significance and outstanding methods in constructing the independent Kipriyanov
fractional calculus theory are convexly stressed, also we represent modern results involving the
Kipriyanov operator and corresponding generalization under the ...
Added: November 27, 2023