The combinatorial Mandelbrot set as the quotient of the space of geolaminations

We interpret the combinatorial Mandelbrot set in terms of \it{quadratic laminations} (equivalence relations $\sim$ on the unit circle invariant under $\sigma_2$). To each lamination we associate a particular {\em geolamination} (the collection $\mathcal{L}_\sim$ of points of the circle and edges of convex hulls of $\sim$-equivalence classes) so that the closure of the set of all of them is a compact metric space with the Hausdorff metric. Two such geolaminations are said to be {\em minor equivalent} if their {\em minors} (images of their longest chords) intersect. We show that the corresponding quotient space of this topological space is homeomorphic to the boundary of the combinatorial Mandelbrot set. To each equivalence class of these geolaminations we associate a unique lamination and its topological polynomial so that this interpretation can be viewed as a way to endow the space of all quadratic topological polynomials with a suitable topology.Comment: 28 pages; in the new version a few typos are corrected; to appear in Contemporary Mathematic

Properties of 1D two-barrier quantum pump with harmonically oscillating barriers

We study a one-dimensional quantum pump composed of two oscillating delta-functional barriers. The linear and non-linear regimes are considered. The harmonic signal applied to any or both barriers causes the stationary current. The direction and value of the current depend on the frequency, distance between barriers, value of stationary and oscillating parts of barrier potential and the phase shift between alternating voltages.Comment: 7 pages, 8 figure

Ground increase of cosmic ray intensity on February 16, 1984

The event of February 16, 1984 is one of the two largest ground increases of solar cosmic rays (CR) in the last two cycles of solar activity. This event happended at a decrease of the 21-st cycle against a quiet background. Although at the beginning of 1984 the observed indices of solar activity were higher than those at the end of 1983, the day of February 16 16 may be characterized as very quiet. On that day the geomagnetic perturbance (Sigma F sub p = 14, A sub p = 7) was the lowest in February. After a small Forbush decrease due to the magnetic storm of February 12-13, the CR intensity almost completely recovered by February 16. Thus, the solar particles that came to the Earth on February 16 got into a practically unperturbed magnetosphere, and the variations of secondary CR induced by these particles were not superimposed on any other substantial variations of extraterrestrial or magnetospheric origin

Theory of one-dimensional double-barrier quantum pump in two-frequency signal regime

A one-dimensional system with two $\delta$-like barriers or wells bi-chromaticaly oscillating at frequencies $\omega$ and $2\omega$ is considered. The alternating signal leads to the direct current across the structure (even in a symmetric system). The properties of this quantum pump are studied in a wide range of the system parameters.Comment: 4 pages, 5 figure

Thermal radiation of conducting nanoparticles

The thermal radiation of small conducting particles was investigated in the region where the Stephan-Boltzmann law is not valid and strongly overestimates radiation losses. The new criterion for the particle size, at which black body radiation law fails, was formulated. The approach is based on the magnetic particle polarization, which is valid until very small sizes (cluster size) where due to drop of particle conductivity the electric polarization prevails over the magnetic one. It was also shown that the radiation power of clusters, estimated on the basis of the experimental data, is lower than that given by the Stephan-Boltzmann law.Comment: 12 pages, 5 figures, 1 tabl

Ландшафтная реновация исторических парков Припятского Полесья

Проведен анализ дендрофлоры пяти памятников природы Припятского Полесья. Определена средневзвешенная категория состояния по каждому объекту. Выявлены основные цели ландшафтной реновации исторических парков. Представлен вариант поэтапного восстановления ботанического памятника природы местного значения – парка ”Дубое“

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Epidemiological Situation on Tick-Borne Spotted Fever Group Rickettsioses in the Russian Federation in 2012–2021, Prognosis for 2022–2026

The aim of the review was to characterize the epidemiological situation on rickettsiosis of the tick-borne spotted fever (TSF) group in the constituent entities of the Russian Federation in 2012–2021 and provide a long-term forecast for 2022–2026. In 2020–2021, indicators of registered incidence of tick-borne rickettsiosis in Russia on the whole decreased relative to the average long-term pre-pandemic level in 2012–2019 by 2 fold for all forms of the TSF group on average (Siberian tick-borne typhus – STT, Astrakhan spotted fever and Mediterranean fever). A comparative analysis of the territories revealed a correlation between the incidence of STT and the number of medical facility visits due to “tick bites” (r=0.67, p=0.015), which, against the background of an increase in the frequency of contacts of the population with vectors in 2020–2021 in most regions and a decrease in the incidence in the same regions indicates the credible nature of the changes. The ranking of territories according to average long-term incidence rates made it possible to classify the Republic of Altai and the Altai Territory as regions of extremely high epidemic hazard as regards STT; high hazard – the Republic of Tuva; above average – the Republic of Khakassia, Khabarovsk Territory and the Jewish Autonomous Region. The established downward trend in the incidence of tick-borne rickettsiosis among the population will be sustained in most entities of the Russian Federation within the next 5 years, excluding the Republic of Altai, the Altai Territory, the Republic of Crimea and the city of Sevastopol, where current incidence or an increase should be expected. The results of the analysis indicate the need to put more emphasis on natural-focal infections at the time of COVID-19 pandemic

Review of Epidemiological Situation on Rickettsioses in the Russian Federation in 2022 as Compared with 2013–2021, Forecast for 2023

The aim of the review was to characterize the epidemiological situation on tick-borne rickettsioses (TR) in the Russian Federation in 2022 in comparison with the pandemic years of 2020–2021 and the pre-pandemic period of 2013–2019, to give the forecast for 2023. During 2013–2022, a pattern was observed in the incidence of rickettsiosis of the tick-borne spotted fever group (with the exception of Astrakhan spotted fever – ASF), that is also characteristic of most other natural focal infections (NFIs): a sharp decrease in registered incidence rates in 2020–2021 with the subsequent increase in 2022 almost up to pre-pandemic levels or even exceedance in some regions. The absence of a defining influence of the frequency of contacts of the population with vectors on the decrease in the incidence in the period of 2020–2021 and the rise in the value in 2022 confirms the registration-related nature of the changes. Given due attention to the problem of effective detection and reporting of NFIs, we expect the incidence of tick-borne rickettsioses to remain within the confidence intervals of long-term average values in most endemic regions in 2023. Relaxed vigilance to the problem of NFIs may lead to a decline in the reported incidence of Siberian tick-borne typhus in the Krasnoyarsk and Zabaikalsky Territories, Republics of Tuva and Khakassia, Novosibirsk and Amur Regions; reduction in the incidence of ASF in Astrakhan Region. The main issue in detecting and registration of the tick-borne rickettsiosis incidence, objective assessment and forecasting of the epidemic situation as regards this group of infections is conditioned by the lack of domestic certified diagnostic test kits for laboratory verification of rickettsioses. Close cooperation between epidemiologists and clinicians is required to establish and register cases of TR based on clinical and epidemiological data