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Continuous Markovian model for Lévy random walks with superdiffusive and superballistic regimes
The European Physical Journal B. 2010. Vol. 78. P. 207–216.
Lubashevsky I., Heuer A., Friedrich R., Usmanov R.
We consider a previously devised model describing Lévy random walks [I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 79, 011110 (2009); I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 80, 031148 (2009)]. It is demonstrated numerically that the given model describes Lévy random walks with superdiffusive, ballistic, as well as superballistic dynamics. Previously only the superdiffusive regime has been analyzed. In this model the walker velocity is governed by a nonlinear Langevin equation. Analyzing the crossover from small to large time scales we find the time scales on which the velocity correlations decay and the walker motion essentially exhibits Lévy statistics. Our analysis is based on the analysis of the geometric means of walker displacements and allows us to tackle probability density functions with power-law tails and, correspondingly, divergent moments.
Khrapai V., Tikhonov E., Nature Physics 2026 P. 1–2
Feng et al.1 presented transport measurements of three-terminal normal–superconductor–normal devices based on topological insulator nanowires. They measured the full differential conductance matrix, defined as Gij = ∂Ii /∂Vj , beyond the linear response regime as a function of various control parameters. Here i, j∈ [1, 2] denote normal terminals biased by the voltages V1 and ...
Added: August 5, 2026
Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...
Added: August 3, 2026
Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129
Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...
Added: August 3, 2026
Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...
Added: August 3, 2026
G. G. Bondarenk, Kristya V. I., Savichkin D. O. et al., Journal of Surface Investigation: X-Ray, Synchrotron and Neutron Techniques 2026 Vol. 20 No. 2 P. 417–423
A model of a glow gas discharge in a mixture of argon and mercury vapor is formulated in the presence
of a thin insulating film on the cathode surface. Dependences of the discharge characteristics on the
mixture temperature are calculated in the range of its variation, in which a noticeable contribution to ionization
of the working gas is ...
Added: August 1, 2026
Касимов Р. Х., Аржанов А. И., Седых К. О. et al., Оптический журнал 2026 Т. 93 № 1 С. 80–86
Предмет исследования. Использование метода капельного нанесения для изготовления источника одиночных фотонов. Цель работы. Разработка технологического процесса изготовления источника одиночных фотонов на коллоидных квантовых точках для использования их в фотон- ных интегральных схемах. Метод. На первом этапе в программе ANSYS Lumerical рассчитыва- ются период и фактор заполнения фокусирующих элементов связи на длинах волн 545 и 600 ...
Added: July 31, 2026
Nevzorov A., Golikov A., Gneushev D. et al., JETP Letters 2026 Vol. 147–151 No. 3 P. 147–151
This paper demonstrates a special stochastic operation mode of a photonic element with a thin GeTe film deposited at a silicon nitride waveguide. As opposed to traditional deterministic switching between stable states, it has been shown that identical pump laser pulses cause a stochastic change in the transmission coefficient. The discovered effect opens up new ...
Added: July 31, 2026
Radomskii A., Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Dual-mode infrared detection via photovoltaic and barrier pyroelectric effects in PbTe p–n junctions
Jarashneli A., Кобцев Д. М., Upcher A. et al., Journal of Applied Physics 2026 Vol. 140 No. 2 Article 024501
In the work, two effects appeared in PbTe p–n junctions under mid-wavelength infrared (2 − 5 μm) and long-wavelength infrared irradiation (≈10.6 μm). The first effect was created by the optical absorption of lR-photons in PbTe and caused by its photovoltage effect. The second novel effect is related to the heating process and the formation ...
Added: July 31, 2026
Nikolaev G. A., Orlov O. V., Andreeva S. et al., Physical Review Applied 2026 Vol. 26 Article 014099
We report the electrical detection of the spin resonance with temporal resolution in a two-dimensional electron system. Spin resonance was excited by pulses of subterahertz radiation characterized by relatively short rise and fall times on the order of 10 ns and was observed as a resonant peak in the high-frequency conductivity of the two-dimensional channel. The ...
Added: July 31, 2026
S. A. Andreeva, Orlov O. V., A. V. Shchepetilnikov et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 6 Article 065420
We investigate the temperature dependence of the pseudospin phase transition at filling factor 𝜈=2 in the quantum Hall regime. Experiments were performed on a high-quality, wide AlAs quantum well, where the pseudospin degree of freedom arises naturally from the near degeneracy and equivalence of the two conduction-band valleys. The anisotropic 𝑔-factor inherent to AlAs enabled independent measurement of ...
Added: July 31, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234
Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing
interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications.
Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and
reason about. Here we build analytical representation for such ...
Added: July 28, 2026
Menovshchikov A., Ukhlov A., Rendiconti del Circolo Matematico di Palermo 2026 Vol. 75 Article 91
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These embeddings give the solvability of the Neumann spectral problem in this setting and provide estimates for the corresponding weighted Neumann eigenvalues. ...
Added: July 27, 2026
Menovshchikov A., Journal of Mathematical Sciences 2026 Vol. 298 P. 608–618
We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains. ...
Added: July 27, 2026
Dmitry Vasilyev, Gorev V., Ikhsanov R. et al., Journal of Materials Science 2026 No. 61 P. 25452–25470
The orthorhombic phase of 𝛼-Mo2 C is a key component in electrocatalytic applications, as Mo2C-based catalysts can exhibit catalytic performance comparable to or exceeding that of noble metals. Despite its technological relevance, theoretical understanding of the anisotropy in the thermal expansion and related thermoelastic properties of 𝛼-Mo2 C remains limited. In this work, first-principles calculations ...
Added: July 23, 2026
Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026 Vol. 14 P. 2169–3536
This work presents a hierarchy of strictly local fault-tolerant routing algorithms for 3D mesh networks-on-chip, culminating in an algorithm that combines a live-neighbor selection rule with a bounded single-hop rollback mechanism. The proposed algorithms operate exclusively on immediate neighbor information, maintain O(1) per hop complexity, and require no global topology knowledge, additional virtual channels, or ...
Added: July 23, 2026
Morozova E., Panov V., Finance Research Letters 2025 Vol. 86 No. A Article 108301
This paper presents a new approach to modeling the Bitcoin prices using the Lévy processes - a class of stochastic processes that are able to realistically capture the jump-type dynamics of financial time series. Our method is inspired by recent research on Bitcoin, which suggests that the prices are closely connected to the media attention ...
Added: September 4, 2025
Morozova E., Panov V., / Series SSRN "ERN: Speculation in Economic Markets". 2025. No. 5222389.
This paper presents a new approach to modeling the Bitcoin prices using the Lévy processes - a class of stochastic processes that are able to realistically capture the jump-type dynamics of financial time series. Our method is inspired by the findings in recent research on Bitcoin, which suggest that the prices are closely connected to ...
Added: May 2, 2025
Morozova E., Panov V., Applied Stochastic Models in Business and Industry 2023 Vol. 39 No. 6 P. 772–788
In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the Levy processes and is able to realistically reproduce the jump-type dynamics of the considered time series. We focus on the lowfrequency setup, which ...
Added: June 29, 2023