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

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

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

Semi-Interlaced Polytopes

Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187

Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems. Motivated by relaxing the bound dim(F)+1 to dim(F), we ...

Added: August 31, 2026

A new spin on polynomial relations among kappa classes

Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., International Mathematics Research Notices 2026 Vol. 14 Article rnag146

We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...

Added: August 31, 2026

Any Topological Recursion on a Rational Spectral Curveis KP Integrable

Kazaryan M., Dunin-Barkowski P., Bychkov B. et al., Communications in Mathematical Physics 2026 Vol. 407 No. 69

We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...

Added: August 31, 2026

Сплетенный мир: кошка перевернулась. Доклад Римскому клубу

Gromov V., Переслегин С. Б., Переслегина Е. Б. et al., СПб.: Полакс, 2026.

Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...

Added: August 31, 2026

Multiplicity-free products of Schubert divisors

Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786

Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...

Added: August 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