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Inverse Resonance Problems for Energy-Dependent Potentials on the Half-Line
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. We solve the inverse resonance problem in this case and describe sets of isoresonance potentials and boundary condition parameters. Our strategy consists of exploiting a correspondence between Schrödinger and Dirac equations on the half-line. As a byproduct, we describe similar sets for Dirac operators and show that the scattering problem for a Schrödinger equation or Dirac operator with an arbitrary boundary condition can be reduced to the scattering problem with the Dirichlet boundary condition.
Naumov A., Рубцов А. С., Samsonov S. et al., Успехи математических наук 2026 Т. 81 № 4 (490) С. 161–162
Краткое сообщение рассматривает Моментные оценки для стохастической аппроксимации ...
Added: October 17, 2026
Avdeev R., Zaitseva Y., Mediterranean Journal of Mathematics 2026 Vol. 23 No. 7 Article 224
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
Added: October 17, 2026
Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...
Added: October 16, 2026
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Gusein-Zade S., Campillo A., Delgado F., Mathematische Zeitschrift 2026 Vol. 314 No. 1 P. 1–22
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coefficients in $\K$. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a (discrete, rank one) valuation on it. ...
Added: October 13, 2026
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
М.: 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
Korotyaev E., Mokeev D., Asymptotic Analysis 2023 Vol. 132 No. 1-2 P. 83–130
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 ...
Added: March 8, 2023
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
Filonov N. D., Алгебра и анализ 2021 Т. 33 № 5 С. 176–192
Рассмотрим оператор Шрёдингера −Δ+V(x,y) в евклидовом пространстве. Предположим, что потенциал V периодичен по части переменных, а по оставшимся переменным убывает быстрее первой степени. Показано, что в спектре такого оператора нет собственных значений. Аналогичный результат установлен для оператора Максвелла. ...
Added: October 31, 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
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