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

Space-Time Fluctuations in a Quasi-static Limit

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

To spike or not to spike: the whims of the Wonham filter in the strong noise regime

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

Цепная дробь Аски–Вильсона при qN=1

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. ...

Added: October 5, 2026

Explicit Formula for Inverse and Determinant in Geometric Algebras over Odd-dimensional Vector Spaces

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 ...

Added: October 4, 2026

On Practical Aspects of Constructing Quasi-Cyclic Subfield Subcodes of Dual Elliptic Codes and Their Application in McEliece-type Cryptosystems

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. ...

Added: October 3, 2026

Graphon spin systems as exactly solvable models

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 ...

Added: October 2, 2026

Планетарное зацепление трилистника

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

A quantum–analogue formalism for modeling supraliminal information processing

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

Консервативные энтропийно и энергетически корректные разностные методы для одномерных квазигазодинамических систем уравнений

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 ...

Added: October 1, 2026

On some arithmetic conditions of recurrent sequences modulo prime p

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

Long-time behaviour of dynamical systems driven by bounded mixing noises

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

Markovian reduction and exponential mixing in total variation for random dynamical systems

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

Bounds on the derivatives of the log-cumulative distribution function of the multivariate normal distribution

Potanin B., Dolgikh S., Statistics and Probability Letters 2027 Article 110984

We derive bounds on the gradient and Hessian of the log-CDF, ln F(x), of the multivariate normal distribution. These bounds scale linearly and quadratically in ‖x‖ , respectively, with constants depending only on the covariance matrix. We demonstrate the usefulness of these bounds by proving asymptotic normality of the maximum-likelihood estimator of the multivariate probit ...

Added: October 1, 2026

Asymptotics of Spectrum and Quantum Averages of the Hydrogen Atom in a Magnetic Field Near the Upper Boundaries of Spectral Clusters

A. V. Pereskokov, Journal of Mathematical Sciences 2026 Vol. 302 No. 4 P. 531–545

We consider the Zeeman effect problem for the hydrogen atom in a magnetic field using irreducible representations of the Karasev–Novikova algebra with quadratic commutation relations. We find the asymptotics of a series of eigenvalues and the corresponding asymptotic eigenfunctions near the upper boundaries of spectral clusters. ...

Added: October 1, 2026

Simultaneous approximation of the score function and its derivatives by deep neural networks

Yakovlev K., Puchkin N., Journal of Complexity 2026 Vol. 97

We present a theory for simultaneous approximation of the score function and its derivatives, enabling the handling of data distributions with low-dimensional structure and unbounded support. Our approximation error bounds match those in the literature while relying on assumptions that relax the usual bounded support requirement. Crucially, our bounds are free from the curse of ...

Added: September 30, 2026

Conservative Entropy and Energy Correct Difference Methods for One-Dimensional Quasi-Gasdynamic Systems of Equations

Zlotnik A., Mathematical notes 2026 Vol. 120 No. 6 P. 1174–1178

Numerical methods for solving systems of gas dynamic equations are the subject of a vast literature. A special family of spatially symmetric conservative difference methods based on preliminary kinetic, or quasi-gasdynamic (QGD), regularization of these equations was constructed and successfully tested. A pressing issue is the construction of numerical methods that are not only conservative ...

Added: September 30, 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

Site-specific photolabile roadblocks for the study of transcription elongation in biologically complex systems

Nadon J., Epshtein V., Cameron E. et al., Communications Biology 2022 Vol. 5 No. 1 Article 457

Transcriptional pausing is crucial for the timely expression of genetic information. Biochemical methods quantify the half-life of paused RNA polymerase (RNAP) by monitoring restarting complexes across time. However, this approach may produce apparent half-lives that are longer than true pause escape rates in biological contexts where multiple consecutive pause sites are present. We show here ...

Added: May 13, 2022

Effect of current density, concentration of ternary electrolyte and type of cations on the monovalent ion selectivity of surface-sulfonated graft anion-exchange membranes: modelling and experiment

Golubenko D. V., Yaroslavtsev A. B., Journal of Membrane Science 2021 Vol. 635 Article 119466

The dependence of monovalent-ion selectivity of surface-sulfonated anion exchange membranes (s-AEMs) on the electrodialysis (ED) desalination current density, the concentration of equimolar ternary electrolyte (XCl + X2SO4) in the total concentration range 0.04–0.2 M, and the type of cations (X = H, Cs, Na) has been studied. The membrane current-voltage characteristics and values of the diffusion permeability coefficients in electrolyte solutions and their mixtures ...

Added: September 23, 2021