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Inverse resonance scattering for massless Dirac operators on the real line
Asymptotic Analysis. 2023. Vol. 132. No. 1-2. P. 83–130.
Korotyaev E., Mokeev D.
We consider massless Dirac operators on the real line with compactly supported potentials. We solve two inverse problems: in terms of zeros of reflection coefficient and in terms of poles of reflection coefficients (i.e. resonances). Moreover, we prove the following: 1) a zero of the reflection coefficient can be arbitrarily shifted, such that we obtain the sequence of zeros of the reflection coefficient for another compactly supported potential, 2) the set of “isoresonance potentials” is described, 3) the forbidden domain for resonances is estimated, 4) asymptotics of the resonances counting function is determined, 5) these results are applied to canonical systems.
Cham: Springer Publishing Company, 2026.
The four-volume set LNCS 16483-16486 constitutes the refereed conference proceedings of the 48th European Conference on Information Retrieval, ECIR 2026, held in Delft, The Netherlands, during March 29–April 2, 2026.
The 46 full papers and 37 short papers presented together with 10 findings papers, 9 reproducibility papers, 17 resource papers, 11 workshop papers, 7 tutorial papers, ...
Added: June 18, 2026
Poddiakov A., Троицкий вариант. Наука 2026 № 12 С. 24–25
В научно-популярной заметке представлен обзор содержания поста филдсовского медалиста Тимоти Гауэрса о возможностях ИИ в математике и содержания комментариев под постом. Обзор сделан в основном чат-ботом DeepSeek. В заключение обсуждается возможность не только решения задач искусственным интеллектом, но и их постановки. ...
Added: June 18, 2026
Garzón J., Mora Rodríguez J., Moreno-Franco H. A., Applied Mathematics and Optimization 2026 Vol. 94 No. 10 P. 1–43
We study an optimal extraction problem where the agent’s actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, evolve according to a drifted Brownian motion with jumps. The agent’s primary aim is to identify an optimal extraction strategy ...
Added: June 17, 2026
Nesterov A. S., Журнал Новой экономической ассоциации 2026
В этой статье рассматривается целевой приём в вузы в России с точки зрения науки об устройстве рынков сочетания и экономических механизмов (matching market and mechanism design), ключевого направления современной теории игр. Мы изучаем механизм целевого приёма -- набор правил, по которым устраивается трёхстороннее сочетание между абитуриентом, заказчиком и образовательной программой. Используемый в России механизм имеет ...
Added: June 16, 2026
Kh. Kh. Abdullin, D. B. Mokeev, D. S. Taletskii, Mathematical notes 2026 Vol. 119 No. 1 P. 3–7
By the Ramsey number R(K1,s,Pt) one means the least positive integer n such that, for every n-vertex graph G, the following condition holds: either G contains a vertex of degree at least s or the complement of G contains a simple t-path. In this paper, we fi nd precise values of R(K1,s,Pt) for certain values ...
Added: June 10, 2026
Springer, 2026.
The book presents the proceedings of the 13th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA 2024), held at Intelligent Systems Research Group (ISRG), London Metropolitan University, London, United Kingdom, during June 6–7, 2025. Researchers, scientists, engineers and practitioners exchange new ideas and experiences in the domain of intelligent computing theories with ...
Added: June 8, 2026
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Kazakov A., Mints D., Petrova I. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
Added: June 4, 2026
Derkach D., Efremenko D., Чупров И. А. et al., / Series Computer Science "arxiv.org". 2025. No. 2503.18849.
Added: March 25, 2025
Belomestny D., Morozova E., Panov V., / Series arXiv.org "math.ST". 2024. No. 2405.05419.
This study focuses on statistical inference for compound models of the form \(X=\xi_1+\ldots+\xi_N\), where \(N\) is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables \(\xi_1, \xi_2, \ldots\). The paper addresses the problem of reconstructing the distribution of \(\xi\) from observed samples of \(X\)'s distribution, a process ...
Added: May 10, 2024
Korotyaev E., Mantile A., Mokeev D., SIAM Journal on Mathematical Analysis 2024 Vol. 56 No. 2 P. 2115–2148
We consider Schrödinger equations with energy-dependent potentials that are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under suitable regularity assumptions. Then, we consider a specific class of energy-dependent Schrödinger equations without eigenvalues, defined with Miura potentials and boundary conditions at the origin. ...
Added: March 7, 2024
Mokeev D., Алгебра и анализ 2022 Т. 34 № 6 С. 197–216
В работе исследуется оператор Дирака на полуоси с потенциалом, имеющим компактный носитель. Пусть $(k_n)_{n≥1}$ — последовательность его резонансов, взятых с учетом кратности и упорядоченных так, что $|k_n|$ не убывают с ростом $n$. Мы докажем, что для любой такой последовательности $(r_n)_{n≥1} \in \ell_1$, что точки $k_n+r_n$ остаются в нижней полуплоскости для всех $n≥1$, последовательность $(k_n+r+n)_{n≥1}$ тоже ...
Added: February 14, 2023
Stepanova I., Salnikov A., Batov A., , in: Proceedings of 2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), STAB 2020.: IEEE, 2020. P. 1–3.
The paper discusses a new block method for solving ill-conditioned systems of linear algebraic equations of large and extra-large dimensions. Systems of this kind often arise in inverse problems of geophysics and geodesy. ...
Added: October 30, 2022
Korotyaev E., Леонова Е. О., / Series arXie "Statistical mechanics". 2022.
We solve the inverse problem for Jacobi operators on the half lattice with finitely supported perturbations, in particular, in terms of resonances. Our proof is based on the results for the inverse eigenvalue problem for specific finite Jacobi matrices and theory of polynomials. We determine forbidden domains for resonances and maximal possible multiplicities of real ...
Added: September 26, 2022
Evgeny Korotyaev, Mokeev D., Analysis and Mathematical Physics 2021 Vol. 11 Article 32
We consider massless Dirac operators on the half-line with compactly supported potentials. We solve the inverse problems in terms of Jost function and scattering matrix (including characterization). We study resonances as zeros of Jost function and prove that a potential is uniquely determined by its resonances. Moreover, we prove the following: (1) resonances are free ...
Added: April 18, 2021
Людмила Ивановна Кузьмина, ОСИПОВ Ю. В., ЦАРЕВА В. И., Промышленное и гражданское строительство 2020 № 6 С. 64–68
Filtration problem for a suspension in a porous medium characterize the injection of a liquid grout into porous rock to strengthen loose soil or create waterproof partitions during the construction of tunnels and underground structures. The suspension is injected under pressure into an empty homogeneous porous medium and moves from inlet to outlet. Some particles ...
Added: July 2, 2020
Pospelov I. G., Zhukova A., Сагирова А. Р., В кн.: Труды IX Московской международной конференции по исследованию операций (ORM2018)Т. 2.: М.: ООО «Макс Пресс», 2018. С. 221–226.
Работа посвящена решению проблемы идентификации параметров модели банковского сектора Российской Федерации на имеющихся статистических данных и является дальнейшим развитием исследований, посвященных моделированию банковского сектора Российской Федерации. Для идентификации параметров применяется метод решения обратной задачи для системы нелинейных дифференциальных уравнений при известных начальных данных и дополнительной информации о значениях внешних переменных. Численное решение возникающих в работе систем ...
Added: December 9, 2019
Pogrebkov A., Symmetry 2019 Vol. 11 No. 436 P. 1–11
We considered the relation between two famous integrable equations: The Hirota difference equation (HDE) and the Darboux system that describes conjugate curvilinear systems of coordinates in R3. We demonstrated that specific properties of solutions of the HDE with respect to independent variables enabled introduction of an infinite set of discrete symmetries. We showed that degeneracy ...
Added: May 2, 2019
Klemashev N., Шананин А. А., Journal of Inverse and Ill-posed problems 2016 Vol. 24 No. 4 P. 367–391
According to Pareto's theory of consumer demand a rational representative consumer should choose their consumption bundle as the solution of mathematical programming problem of maximization of utility function under their budget constraint. The inverse problem of demand analysis is to recover the utility function from the demand functions. The answer to the question of solvability ...
Added: March 5, 2019
Inverse problems in Pareto’s demand theory and their applications to analysis of stock market crises
Klemashev N., Shananin A. A., Zhang S., Journal of Inverse and Ill-posed problems 2016 Vol. 26 No. 1 P. 95–108
We develop an approach to analysis of stock market crises based on the generalized nonparametric method. The generalized nonparametric method is based on solvability and regularization of ill-posed inverse problem in Pareto's demand theory. Our approach allows one to select a few companies that may be considered as the main reason for the crisis. We ...
Added: March 5, 2019
Джо Й. С., Satanin A., Варгиамидис В. et al., Journal of Experimental and Theoretical Physics 2018 Vol. 153 No. 6 P. 851–858
new scenario for the occurrence of a Fano resonance in the transmission probability of electron waveguides is investigated using a coupled-channel theory. Both a quantum dot and an antidot with either short- or finite-range interaction are embedded in the electron waveguide. Particularly, when the Fano resonance occurs close to the mobility edge (channel threshold), it ...
Added: February 21, 2019
Pogrebkov A., Boiti M., Pempinelli F., Theoretical and Mathematical Physics 2015 Vol. 185 No. 2 P. 1599–1613
We describe the properties of the Cauchy–Jost (also known as Cauchy–Baker–Akhiezer) function of the
Kadomtsev–Petviashvili-II equation. Using the ∂-method, we show that for this function, all equations
of the Kadomtsev–Petviashvili-II hierarchy are given in a compact and explicit form, including equations
for the Cauchy–Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential
of the ...
Added: September 9, 2016