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

ВЕРОЯТНОСТНЫЕ МОДЕЛИ РАЗМЕЩЕНИЯ ПО ЯЧЕЙКАМ СЛУЧАЙНОГО ЧИСЛА ЧАСТИЦ

Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 132–138

In schemes S for placing r particles in n distinguishable cells, their placement in selected m cells – schemes S∗ is studied, for which the analysis is carried out by a new enumerative method (EM) in extended areas of enumerative combinatorics: finding the number of outcomes and, based on the construction of a model of ...

Added: September 11, 2026

КОМБИНАТОРНЫЙ АНАЛИЗ СХЕМ РАЗМЕЩЕНИЯ ЧАСТИЦ С ЗАДАННЫМ МАКСИМАЛЬНЫМ УРОВНЕМ ЗАПОЛНЕНИЯ ЯЧЕЕК

Enatskaya N., Труды Карельского научного центра РАН. Серия 10: Математическое моделирование и информационные технологии 2026 № 6 С. 139–147

The class of particle cell arrangements under consideration is characterized by the introduction of an upper limit on the filling levels of the cells, which must be achieved in at least one cell of each outcome of each arrangement. The circuits are distinguished by the paired qualities of their constituent elements (cells and particles) according ...

Added: September 11, 2026

Многокритериальные задачи с упорядоченными по важности группами критериев (II). Решающие правила

Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 8 С. 110–123

Для многокритериальных задач принятия решений по аналогии с качественной вероятностью введены понятия полной и частичной качественной важности как бинарных отношений, обладающих постулируемыми свойствами. Предложено новое определение отношения нестрогого предпочтения на множестве вариантов решений, порождаемое качественной важностью. Исследованы его свойства. Указаны аналитические правила, позволяющие попарно сравнивать варианты по предпочтительности. Проведено сравнение новых отношений предпочтения с разработанными ранее для задач, ...

Added: September 9, 2026

Теоретические основы и методы анализа решений в условиях неопределенности при качественных оценках вероятностей и предпочтений

Podinovskiy V. V., Нелюбин А. П., Автоматика и телемеханика 2026 № 7 С. 113–126

Рассматриваются задачи принятия решений, когда предпочтения оцениваются в порядковой шкале, а возможности реализации значений неопределенного фактора описываются качественной вероятностью (полной или только частичной). Вводятся определения отношений предпочтения и безразличий на множестве стратегий. Предлагаются простые решающие правила, позволяющие сравнивать стратегии по предпочтительности, и приводятся иллюстративные примеры. ...

Added: September 9, 2026

Degree-based topological co-indices for QSPR modelling of benzenoid hydrocarbons: a comparative computational study

Chemical Papers 2026

Benzenoid hydrocarbons are structurally regular aromatic compounds, which makes them well suited for quantitative structure–property relationship (QSPR) studies. This study presents a QSPR analysis of nineteen benzenoid hydrocarbon species using degree-based topological co-indices. We developed a Python program to compute eleven degree-based topological co-indices from molecular graphs and evaluated their ability to explain variations in ...

Added: September 8, 2026

On phase-lock area parquet in a special slow-fast limit of model of Josephson junction.

Glutsyuk A., / Series arXiv "math". 2026.

B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...

Added: September 8, 2026

On exotic rationally integrable dual billiards I. Complex geometry and type of dynamics.

Glutsyuk A., / Series arXiv "math". 2026.

A planar dual billiard is a planar curve γ equipped with a family (σP)|P∈γ of projective involutions of the projective lines LP tangent to γ at P that fix P. A dual billiard is called rationally integrable, if there exists a rational function R(x,y) of two variables (called first integral) whose restriction to each tangent ...

Added: September 8, 2026

Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking

Alexandrov A., Glutsyuk A., Journal of Differential Equations 2026 Vol. 465 Article 114178

The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on ...

Added: September 8, 2026

On rationally integrable planar dual and projective billiards

Glutsyuk A., Inventiones Mathematicae 2026 Vol. 245 P. 977–1058

A caustic of a strictly convex planar bounded billiard is a smooth curve whose tangent lines are reflected from the billiard boundary to its tangent lines. The famous Birkhoff Conjecture, studied by many mathematicians, states that if the billiard boundary has an inner neighborhood foliated by closed caustics, then it is an ellipse. In the paper we study ...

Added: September 8, 2026

Rational p-adic Hodge theory for d-de Rham-proper stacks

Prikhodko Artem, Kubrak D., Compositio Mathematica 2026 Vol. 162 No. 6 P. 1377–1438

In this follow-up paper we show that smooth Hodge-proper stacks over O𝐾 are ℚ𝑝-locally acyclic: namely the natural map between étale ℚ𝑝-cohomology of the algebraic and Raynaud generic fibers is an equivalence. This establishes the ℚ𝑝-case of general conjectures made in D. Kubrak and A. Prikhodko [p-adic Hodge theory for Artin stacks, Mem. Amer. Math. ...

Added: September 7, 2026

Lower Bounds on the Measure of the Support of Positive and Negative Parts of Trigonometric Polynomials

Ismailov A., Constructive Approximation 2026

The measure of the positivity set {x ∈ [0; 2π] | f (x) > 0} of a trigonometric polynomial f is bounded from below by the Motzkin density. We generalize the bound to polynomials in several variables and almost periodic functions. We then use these generalizations to extend known results on Taikov’s problem. ...

Added: September 7, 2026

Variational representation of weighted divergencies and error exponent function

Kelbert M., Statistics 2026 Vol. 60

We present variational representations for the weighted divergencies and exponential error function, and discuss implications for the statistical inference and entropic optimal transport. ...

Added: September 7, 2026

Конечные последовательности и перестановки, ими порождаемые

Kucheryavyy P., Математические заметки 2026 Т. 2026 № 120 С. 380–401

В работе изучаются перестановки, возникающие при упорядочивании по возрастанию дробных долей произведений элементов фиксированной целочисленной последовательности на вещественный параметр. Исследуется количество различных перестановок, которые можно получить таким образом при изменении этого параметра от нуля до единицы. ...

Added: September 7, 2026

Относительные аналитические законы взаимности

Осипов Д.В., Математический сборник 2026 Т. 217 № 9 С. 130–146

Изучаются законы взаимности, связанные с комплексными линейными расслоениями на расслоениях на ориентируемые окружности. В частности, доказывается следующий закон взаимности. Пусть B – комплексное многообразие и πi:Mi→B – расслоение на ориентируемые окружности, где индекс i пробегает конечное множество. Пусть Li и Ni – комплексные линейные расслоения на каждом многообразии Mi. Закон взаимности утверждает, что сумма всех элементов (πi)∗(c1(Li)∪c1(Ni)), где (πi)∗ – ...

Added: September 3, 2026

Orbifold Saito theory of A and D type singularities

Basalaev A., Rarovskii A., Journal of Singularities 2026 Vol. 30 P. 61–80

Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...

Added: September 1, 2026

Non-axiomatizability of modal predicate logics of Dedekind-complete linear orders with constant domains

Rybakov M., Shkatov D., Journal of Logic and Computation 2026 Vol. 36 No. 6 Article exag026

We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...

Added: September 1, 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