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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.
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 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
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2025 Vol. 12 No. 1 P. 1–40
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Novikov R., Sivkin V., Inverse Problems 2026 Vol. 42 No. 4 Article 045009
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
the Helmholtz equation in an exterior region in Rd, d ⩾ 2. In this region, we consider a hyperplane X with sufficiently large distance s from the origin in Rd. We give two-point local formulas
for approximate recovering the radiation ...
Added: May 11, 2026
Hecht M., Hofmann P., Wicaksono D. et al., IMA Journal of Numerical Analysis 2026 Vol. 00 P. 1–30
Recent advances in Bernstein—Walsh theory have extended Bernstein’s Theorem to multiple dimensions, stating that a multivariate function can be approximated with a geometric rate in a downward-closed polynomial space if and only if it is analytic in a generalized Bernstein polyellipse. To compute approximations of this class of functions—which we term Bos–Levenberg–Trefethen–(BLT) functions—we extend the ...
Added: May 11, 2026
Kelbert M., Kalimulina E. Y., Entropy 2026 Vol. 28 Article 536
We study binary hypothesis testing for i.i.d. observations under a multiplicative context
weight. For the optimal weighted total loss, defined as the sum of weighted type-I and typeII losses, we prove the logarithmic asymptotic L∗n = exp{−nDwC (P,Q) + o(n)}, n →∞, where Dw
C is the weighted Chernoff information. The single-letter form of the exponent
relies on ...
Added: May 7, 2026
Белоусов Н. М., Черепанов Л. К., Деркачов С. Э. et al., Selecta Mathematica, New Series 2026 Vol. 32 Article 44
We prove equivalence of two integral representations for the wave functions of hyperbolic Calogero–Sutherland system. For this we study two families of Baxter operators related to hyperbolic Calogero–Sutherland and rational Ruijsenaars models; the first one as a limit from hyperbolic Ruijsenaars system, while the second one independently. Besides, computing asymptotics of integral representations and also ...
Added: May 6, 2026
Муравьев М. Ю., Annales Mathematiques du Quebec 2025
Recently Rohleder proposed a new variational approach to an inequality between the Neumann and Dirichlet eigenvalues in the simply connected planar case using the language of classical vector analysis. Interpreting his approach in terms of differential forms permits to generalize these results to a much broader context. The spectrum of the absolute boundary problem for ...
Added: May 6, 2026
Цыганов А. В., Порубов Е. О., Теоретическая и математическая физика 2026 Т. 227 № 2 С. 336–355
Теория тензорных инвариантов обыкновенных дифференциальных уравнений и классификация Картана простых алгебр Ли используется для установления изоморфизма задачи Козлова о движении ферромагнетика в магнитном поле и задачи Шоттки о движении четырехмерного твердого тела. Найдены новые полиномиальные и рациональные бивекторы Пуассона, инвариантные либо относительно пары коммутирующих фазовых потоков, либо относительно одного из пары потоков. ...
Added: May 5, 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
Maksim V. Kukushkin, Axioms 2021 Vol. 10 No. 2 Article 64
In this paper, we consider a norm based on the infinitesimal generator of the shift semigroup
in a direction. The relevance of such a focus is guaranteed by an abstract representation of a uniformly
elliptic operator by means of a composition of the corresponding infinitesimal generator. The main
result of the paper is a theorem establishing equivalence of ...
Added: November 27, 2023
Maksim V. Kukushkin, International Journal of Applied Mathematics 2021 Vol. 34 No. 1 Article 1
In this paper we aim to construct an abstract model of a differential
operator with a fractional integro-differential operator composition in final
terms, where modeling is understood as an interpretation of concrete differential
operators in terms of the infinitesimal generator of a corresponding semigroup.
We study such operators as a Kipriyanov operator, Riesz potential, difference
operator.
Along with this, we consider ...
Added: November 27, 2023