Operator Theory and Harmonic Analysis

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Operator Theory and Harmonic Analysis

* 2: Probability-Analytical Models, Methods and Applications. Cham : Springer, 2021.

Under the general editorship: A. Karapetyants, I. Pavlov, A. Shiryaev

Introduces new results in methods, problems and applications of operator theory and harmonic analysis by leading researchers

Presents the fundamentals of theory followed by recent developments in PDE’s, mathematical modelling, bioinformatics, and a discussion of real-world problems

Focuses on the very new trends in operator theory and function spaces theory, such as variable exponent spaces and objects of variable nature

Single Jump Filtrations: Preservation of the Local Martingale Property with Respect to the Filtration Generated by the Local Martingale

Gushchin A. A., Zhunussova A., , in: Operator Theory and Harmonic Analysis* 2: Probability-Analytical Models, Methods and Applications.: Cham: Springer, 2021. P. 219–231.

Let M be a local martingale with respect to a so-called single jump filtration F = F(г ,F ) generated by a random time г on a probability space (Omega,F ,P). It was recently mentioned by Herdegen and Herrmann (2016) that M is also a local martingale with respect to the filtration H = F^M that it generates if ...

Added: December 25, 2022

Research target: Mathematics

Language: English

DOI

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Keywords: mathematical modelling

Wave dynamics within the Whitham-Ostrovsky equation

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

On structural stability of 3-diffeomorphisms with the Smale solenoid attractor–repeller dynamics

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

A model exhibiting all possible types of hyperbolic chaos on the 2-torus

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

Об эквивалентности по надстройке декартовых произведений регулярных гомеоморфизмов с гомеоморфизмами Данжуа

Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89

Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...

Added: June 3, 2026

Случайные блуждания на симметрических пространствах некомпактного типа ранга 1

Gnetov F., Konakov V., Успехи математических наук 2026 Т. 81 № 3 (489) С. 161–162

Пусть M обозначает симметрическое пространство некомпактного типа ранга 1. Опираясь на фундаментальную работу [1], в [2] было показано, что плотность соответствующим образом нормированной суммы независимых Hn-значных случайных величин, определенная через сложение Мёбиуса в модели шара Пуанкаре, сходится к фундаментальному решению соответствующего уравнения теплопроводности. Пределом являлся нормальный закон на Hn, соответствующий ядру теплопроводности, определяемому оператором Лапласа–Бельтрами. ...

Added: June 2, 2026

Electrical networks and data analysis in phylogenetics

Gorbounov Vassily, Kazakov A., Data Analytics and Topology 2025 Vol. 1 No. 1 P. 33–45

A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set. For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response ...

Added: May 28, 2026

Generalizing the Brady-Yong Algorithm: Efficient Fast Hough Transform for Arbitrary Image Sizes

Kazimirov D., Rybakova E., Vitalii V. Gulevskii et al., IEEE Access 2025 Vol. 13 P. 20101–20132

The Hough (discrete Radon) transform (HT/DRT) is a digital image processing tool that has become indispensable in many application areas, ranging from general image processing to neural networks and X-ray computed tomography. The utilization of the HT in applied problems demands its computational efficiency and increased accuracy. The de facto standard algorithm for the fast ...

Added: May 28, 2026

Universal Comparison Methodology for Hough Transform Approaches

Kazimirov D., Vitalii Gulevskii, Kroshnin A. et al., Mathematics 2026 Article 1136

The Hough transform (HT) is widely used in computer vision, tomography, and neural networks. Numerous algorithms for HT computation have been proposed, making their systematic comparison essential. However, existing comparative methodologies are either non-universal and limited to certain HT formulations, or task-oriented, relying on application-specific criteria that do not fully capture algorithmic properties. This paper ...

Added: May 28, 2026

Non-linear in-band interference cancellation on base of conjugate gradients method

Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6

This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...

Added: May 26, 2026

New Numerical Invariants of an Unfolding of a Polycycle “Tears of the Heart”

Yu.S. Ilyashenko, S. Minkov, I. Shilin, Russian Journal of Mathematical Physics 2026 Vol. 33 No. 1 P. 89–106

In this paper, new numerical invariants of structurally unstable vector fields in the plane are found. One of the main tools is an improved asymptotics of sparkling saddle connections that occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological invariant of two arithmetic progressions, both perturbed and unperturbed, on the ...

Added: May 26, 2026

ADDITIVE AUTOMORPHISMS OF REGULAR MATRIX GRAPH

Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2025 Vol. 299 No. 6

The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...

Added: May 25, 2026

Coping with AI errors with provable guarantees

Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856

AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...

Added: May 23, 2026

Overcoming the Curse of Dimensionality with Synolitic AI

Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84

High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...

Added: May 23, 2026

Stable On-the-Fly Learning for Dynamic Neural Networks With Delayed Inputs

Chertopolokhov V., Mukhamedov A., Bugriy G. et al., IEEE Access 2026 Vol. 14 P. 14369–14392

This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...

Added: May 22, 2026

Analysis of the alternating minimization method for low-rank canonical polyadic decomposition in the Chebyshev norm

Stanislav Morozov, Calcolo 2026 Vol. 63 No. 2 Article 23

The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...

Added: May 22, 2026

B-facets in Dimension 4

Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 Article 18

A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...

Added: May 21, 2026

The VCG Mechanism, the Core, and Assignment Stages in Auctions

Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 Article 106192

The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders ...

Added: May 20, 2026

Upper bounds for Steklov eigenvalues of a hypersurface of revolution

Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407

In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...

Added: May 19, 2026

Оценка качества функционирования авиатранспортной системы как инструмент формирования требований к перспективной авиационной технике

Власенко А. О., Sukharev A., Урюпин И. В., Управление большими системами: сборник трудов 2023 № 104 С. 73–99

The aim of this article is to define and to describe the calculation methodology for both on-point and general quantitative indicators of air transportation system quality for a passenger. The indicators can be based on any of the three common measures of path-passing (time, cost, and distance). The pair of values that is proposed to ...

Added: January 12, 2024

Mathematic modelling of electronically controlled filters of microwave, SubTHz and THz–bands on the base of graphene–and–dielectric multilayer structure

Смирнов И. А., Черкесова Л. В., Поркшеян В. М. et al., IEEE, 2019.

In the offered examination the mathematical modelling of interaction processes of electromagnetic waves with composite substances nanostructures and electrodynamic structures on the base of graphene and carbon nanotubes is made. Models are grounded on solution of diffraction boundary-value 3D problems for Maxwell's equations with electrodynamic boundary conditions. Principles of subTHz and THz frequency bands controlled ...

Added: May 10, 2023

Reliability and Maintainability Assessment of Industrial Systems

Springer, 2022.

Presents the latest research in the field of reliability engineering applications. Signposts areas for useful future research. A Useful reference to engineers, researchers and advanced students in reliability engineering ...

Added: December 16, 2022

Оптимизация пунтков перевалки «морской порт – железная дорога»

Морозов Н. Ю., Гришин Е. М., Правдивец Н. А. et al., Управление большими системами: сборник трудов 2022 № 99 С. 135–156

В связи с ростом объема мультимодальных перевозок ОАО «РЖД» требуется более эффективное использование имеющихся ресурсов. В наши дни наиболее востребованной разновидностью международного грузооборота является доставка морским транспортом с последующей перегрузкой на железную дорогу для доставки до пункта назначения на материке. В настоящей статье предлагается комплексная математическая модель, включающая две подзадачи: задачу назначения причалов (BAP) и ...

Added: December 7, 2022

Modeling the process of capacitive deionization of solutions at supposing complex structure of the pores of the electrodes

Tikhonov N. A., Tokmachev M., Bakhia T. et al., Journal of Mathematical Chemistry 2021 Vol. 59 No. 4 P. 1054–1067

An electrochemical cell was created and experimentally tested and the process of intense capacitive deionization (CDI) of aqueous solutions in a cyclic mode was studied. The paper presents a developed mathematical model for CDI process on electrodes with complex structure of pore space. This allows to describe the process and obtain results that are in ...

Added: November 17, 2022

Pulse of the Nation: Observable Subjective Well-Being in Russia Inferred from Social Network Odnoklassniki

Sergey Smetanin, Mathematics 2022 Vol. 10 No. 16 Article 2947

Policymakers and researchers worldwide are interested in measuring the subjective well-being (SWB) of populations. In recent years, new approaches to measuring SWB have begun to appear, using digital traces as the main source of information, and show potential to overcome the shortcomings of traditional survey-based methods. In this paper, we propose the formal model for ...

Added: August 15, 2022