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

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

Journal of Dynamics and Differential Equations. 2026. P. 1098–1100.

Kuksin S., Shirikyan A.

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 in the total variation metric. The proof is based on the Markovian reduction of the system in question and a result on mixing for Markov processes. Then we present an extension of this result to the case of systems driven by stationary noises. The results of this paper were announced in Kuksin-Shirikyan (Russian Math. Surveys 79:1098–1100, 2024).

Research target: Mathematics Physics

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

Исследование свойств оптического покрытия на основе упрощенного симулятора процесса напыления

Isaev T. F., Шаров А. Н., Журнал вычислительной математики и математической физики 2026 Т. 66 № 1 С. 83–93

Исследуются свойства оптических покрытий на основе использования упрощенного симулятора ошибок в толщинах слоев покрытий при их напылении. Обосновывается возможность такого подхода. Выводятся аналитические оценки среднеквадратичного значения нормы вектора ошибок и степени коррелированности ошибок в толщинах слоев покрытия. Изучается зависимость среднеквадратичного значения нормы вектора ошибок и свойств покрытия от уровня случайных ошибок в слоях. ...

Added: October 5, 2026

Prospects for an independent measurement of the l = 1, 2, 3 CMB anisotropy multipoles using the anisotropic Sunyaev-Zel’dovich effect

Осипова А. М., Пилипенко С. В., Novikov D. I. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 063522

We investigate the prospects for observing a specific spectral distortion of the cosmic microwave background, which occurs due to the anisotropy of the radiation when it is scattered by hot plasma of galaxy clusters. Detection of this anisotropic Sunyaev-Zel’dovich effect would enable an independent measurement of the CMB anisotropy multipoles with l 1⁄4 1, 2, 3, allow the ...

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

Nanometer thick iron garnet films with high Faraday rotation

Gribova N. I., Osmanov S. V., Lyashko S. D. et al., Journal of Magnetism and Magnetic Materials 2025 No. 614 P. 1–8

Here we demonstrate nanometer thick iron garnet films with high specific Faraday rotation suitable for the magneto-optical applications. Bismuth-substituted iron garnet films of compositions Bi1Y2Fe5O12 and Bi1Tm2Fe5O12 deposited on gadolinium gallium garnet substrate are fabricated and characterized. Their thicknesses range from 2 to 10 nm, which corresponds to just a few crystal lattice constants. Spectacularly, Faraday rotation of the ...

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

Enhancement of superconductivity by polarization of magnetic impurities in disordered films

Seleznev G., Fominov Yakov V., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 7 Article 074505

Dirty superconducting films with magnetic impurities can exhibit nontrivial behavior in a magnetic field that polarizes the impurity spins. As predicted by Kharitonov and Feigelman (KF) [JETP Lett. 82, 421 (2005)], this polarization reduces the exchange scattering rate. Consequently, a parallel magnetic field can enhance the critical temperature Tc when magnetic-field pair breaking is weak, as realized for ...

Added: October 2, 2026

Advances in colloidal anisotropic nanocrystals for high-efficiency light-emitting diodes

Zhukov A., Chen F., Zeng Y. et al., Nanoscale 2026 Vol. 18 No. 36 P. 19223–19253

Colloidal semiconductor nanocrystals have emerged as promising materials for next-generation light-emitting diodes (LEDs) owing to their solution processability, tunable emission wavelengths, narrow emission linewidths, and high photoluminescence quantum yields. Among them, anisotropic nanocrystals, including one-dimensional nanorods (NRs) and two-dimensional nanoplatelets (NPLs), offer additional opportunities for controlling transition dipole moment orientation and light out-coupling efficiency. These ...

Added: October 2, 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

Improved measurement of Born cross sections for chi_bJ omega and chi_bJ (pi+ pi- pi0)non-omega (J = 0, 1, 2) at Belle and Belle II

Uglov T., Pakhlov P., Bodrov D. et al., Journal of High Energy Physics 2026 Vol. 04 Article 101

We study the processes chi_bJ omega and chi_bJ (pi+ pi- pi0)non-omega (J = 0, 1, 2) at center-of-mass energies sqrt(s) from 10.73 to 11.02 GeV using a 142.5 fb^-1 data sample collected with the Belle detector at the KEKB asymmetric-energy e+e- collider; and at sqrt(s) ~ 10.75 GeV using a 19.8 fb^-1 sample collected with ...

Added: October 2, 2026

Observation of e+e- -> eta Upsilon(2S) and search for e+e- -> eta Upsilon(1S), gamma X_b at sqrt(s) near 10.75 GeV

Uglov T., Pakhlov P., Bodrov D. et al., Physical Review Letters 2026 Vol. D No. 113 Article L051102

We present an analysis of the processes e+ e- -> eta Upsilon(1S), eta Upsilon(2S), and gamma X_b with X_b -> pi+ pi- chi_bJ, chi_bJ -> gamma Upsilon(1S) (J = 1, 2) reconstructed from gamma gamma pi+ pi- l+ l- (l = e, mu) final states in 19.6 fb^-1 of Belle II data collected at four ...

Added: October 2, 2026

First Search for B -> Xs nu nubar Decays

Bodrov D., Pakhlova G., Aushev Т. et al., Physical Review Letters 2026 Vol. 136 No. 23 Article 231801

We report the first search for the flavor-changing neutral-current decays B -> Xs nu nubar, where Xs is a hadronic system with strangeness equal to 1, in data collected with the Belle II detector at the SuperKEKB asymmetric-energy e+ e- collider. The data sample corresponds to an integrated luminosity of 365 fb^-1 collected at the ...

Added: October 2, 2026

Search for e+ e- -> gamma chi_bJ (J = 0, 1, 2) near sqrt(s) = 10.746 GeV at Belle II

Pakhlova G., Bodrov D., Aushev Т. et al., Physical Review Letters 2026 Vol. D No. 113 Article 052009

We search for the e+ e- -> gamma chi_bJ (J = 0, 1, 2) processes at center-of-mass energies sqrt(s) = 10.653, 10.701, 10.746, and 10.804 GeV. These data were collected with the Belle II detector at the SuperKEKB collider and correspond to 3.5, 1.6, 9.8, and 4.7 fb^-1 of integrated luminosity, respectively. We set upper ...

Added: October 2, 2026

Measurement of inclusive B -> Xu l nu partial branching fractions and |Vub| at Belle II

Bodrov D., Pakhlova G., Aushev Т. et al., Physical Review Letters 2026 Vol. D No. 113 Article 032004

A sample of 365 fb^-1 of e+ e- -> Upsilon(4S) -> B Bbar data collected by the Belle II experiment is used to measure the partial branching fractions of charmless semileptonic B meson decays and determine the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V_ub. Events containing a signal electron or muon l and a ...

Added: October 2, 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

Singularities of integrable Hamiltonian systems with the same boundary foliation. An infinite series

Tuzhilin M., Moscow University Mathematics Bulletin 2016 Vol. 71 No. 5 P. 185–190

Four-dimensional momentum mapping singularities of integrable Hamiltonian systems with two degrees of freedom are considered. An infinite series of pairs of 4-dimensional saddle–saddle singularities is constructed so that 4-singularities from each pair are not Liouville equivalent, but 2-foliations on their 3-boundaries are Liouville equivalent. ...

Added: September 12, 2025

Invariants of four- and three-dimensional singularities of integrable systems

Tuzhilin M., Doklady Mathematics 2016 Vol. 93 No. 2 P. 186–189

A relationship between invariants of four-dimensional singularities of integrable Hamiltonian systems (with two degrees of freedom) and invariants of two-dimensional foliations on three-dimensional manifolds being the “boundaries” of these four-dimensional singularities is discovered. Nonequivalent singularities which, nevertheless, have equal three-dimensional invariants are found. ...

Added: September 12, 2025

Estimating the Probability of Falling Share Price Below the Minimum Level

Sergei L. Semakov, , in: 2023 9th International Conference on Control, Decision and Information Technologies (CoDIT) (Italy, Rome, July 03–06, 2023).: IEEE, 2023. P. 142–144.

A technology is proposed for estimating the probability that a share price will fall below the minimum level. The exact expression is obtained for the required probability under the assumption that the behavior of the share price is described by the well-known model of Samuelson, according to which the relative change in price is the ...

Added: August 8, 2025

2023 9th International Conference on Control, Decision and Information Technologies (CoDIT) (Italy, Rome, July 03–06, 2023)

IEEE, 2023.

It is with great pleasure that we welcome all the participants of the 9th Conference on Control, Decision and Information Technologies (CoDIT 2023) at the University of Rome La Sapienza, Facolta di lngegneria Civile e lndustriale, July 3-6, 2023. CoDIT, at its 9t h edit bn, is now an affirmed conference in t t-e field ...

Added: August 8, 2025

Probability of the share price going beyond the established corridor

Sergei L. Semakov, , in: 2024 10th International Conference on Control, Decision and Information Technologies (CoDIT) (Malta, Valletta, July 01–04, 2024).: IEEE, 2024. P. 697–699.

A technology is proposed for estimating the probability that the share price will leave the established corridor by a given point in time. The exact expression is obtained for the required probability under the assumption that the behavior of the share price is described by the well-known model of Samuelson, according to which the relative ...

Added: August 4, 2025

Elementary Solution to the Fair Division Problem

M. L. Blank, Polyakov M. O., Problems of Information Transmission 2024 Vol. 60 No. 1 P. 53–70

A new and relatively elementary approach is proposed for solving the problem of fair division of a continuous resource (measurable space, pie, etc.) between several participants, the selection criteria of which are described by charges (signed measures). The setting of the problem with charges is considered for the first time. The problem comes down to analyzing the properties of the trajectories ...

Added: January 16, 2025

Upper bound on saturation time of metric graphs by intervals moving on them

Eliseev A., Chernyshev V. L., Journal of Mathematical Analysis and Applications 2024 Vol. 531 No. 2, Part 2 Article 127873

In this paper we study a dynamical system of intervals moving on a metric graph with incommensurable edge lengths. This system can be generally viewed as a collection of congruent intervals moving around the network at unit speed, propagating along all respective incident edges whenever they pass through a vertex. In particular, we analyse the ...

Added: November 22, 2023