161 research outputs found
Periods implying almost all periods, trees with snowflakes, and zero entropy maps
Let be a compact tree, be a continuous map from to itself,
be the number of endpoints and be the number of edges of .
We show that if has no prime divisors less than and has a
cycle of period , then has cycles of all periods greater than
and topological entropy ; so if is the least prime
number greater than and has cycles of all periods from 1 to
, then has cycles of all periods (this verifies a conjecture
of Misiurewicz for tree maps). Together with the spectral decomposition theorem
for graph maps it implies that iff there exists such that has
a cycle of period for any . We also define {\it snowflakes} for tree
maps and show that iff every cycle of is a snowflake or iff the
period of every cycle of is of form where is an odd
integer with prime divisors less than
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
Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
We describe the topological behavior of typical orbits of complex quadratic
polynomials P_alpha(z)=e^{2\pi i alpha} z+z^2, with alpha of high return type.
Here we prove that for such Brjuno values of alpha the closure of the critical
orbit, which is the measure theoretic attractor of the map, has zero area. Then
combining with Part I of this work, we show that the limit set of the orbit of
a typical point in the Julia set is equal to the closure of the critical orbit.Comment: 38 pages, 5 figures; fixed the issues with processing the figure
The multipliers of periodic points in one-dimensional dynamics
It will be shown that the smooth conjugacy class of an unimodal map which
does not have a periodic attractor neither a Cantor attractor is determined by
the multipliers of the periodic orbits. This generalizes a result by M.Shub and
D.Sullivan for smooth expanding maps of the circle
Complex bounds for multimodal maps: bounded combinatorics
We proved the so called complex bounds for multimodal, infinitely
renormalizable analytic maps with bounded combinatorics: deep renormalizations
have polynomial-like extensions with definite modulus. The complex bounds is
the first step to extend the renormalization theory of unimodal maps to
multimodal maps.Comment: 20 pages, 3 figure
Rotation sets of billiards with one obstacle
We investigate the rotation sets of billiards on the -dimensional torus
with one small convex obstacle and in the square with one small convex
obstacle. In the first case the displacement function, whose averages we
consider, measures the change of the position of a point in the universal
covering of the torus (that is, in the Euclidean space), in the second case it
measures the rotation around the obstacle. A substantial part of the rotation
set has usual strong properties of rotation sets
Composition law of cardinal order permutations
In this paper the theorems that determine composition laws for both cardinal
ordering permutations and their inverses are proven. So, the relative positions
of points in a hs-periodic orbit become completely known as well as in which
order those points are visited. No matter how a hs-periodic orbit emerges, be
it through a period doubling cascade (s=2^n) of the h-periodic orbit, or as a
primary window (like the saddle-node bifurcation cascade with h=2^n), or as a
secondary window (the birth of a periodic window inside the h-periodic
one). Certainly, period doubling cascade orbits are particular cases with h=2
and s=2^n. Both composition laws are also shown in algorithmic way for their
easy use
Energy Spectra, Altitude Profiles and Charge Ratios of Atmospheric Muons
We present a new measurement of air shower muons made during atmospheric
ascent of the High Energy Antimatter Telescope balloon experiment. The muon
charge ratio mu+ / mu- is presented as a function of atmospheric depth in the
momentum interval 0.3-0.9 GeV/c. The differential mu- momentum spectra are
presented between 0.3 and about 50 GeV/c at atmospheric depths between 13 and
960 g/cm^2. We compare our measurements with other recent data and with Monte
Carlo calculations of the same type as those used in predicting atmospheric
neutrino fluxes. We find that our measured mu- fluxes are smaller than the
predictions by as much as 70% at shallow atmospheric depths, by about 20% at
the depth of shower maximum, and are in good agreement with the predictions at
greater depths. We explore the consequences of this on the question of
atmospheric neutrino production.Comment: 11 pages, 8 figures, to appear in Phys. Rev. D (2000
On the Lebesgue measure of Li-Yorke pairs for interval maps
We investigate the prevalence of Li-Yorke pairs for and
multimodal maps 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 is topologically mixing and has no Cantor attractor, then typical
(w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally
admits an absolutely continuous invariant probability measure (acip), then
typical pairs have a dense orbit for . 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 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
Tuberculosis outcomes related to the Mycobacterium tuberculosis genotype
Mycobacterium tuberculosis strains of different phylogenetic lineages and genetic families differ in biological properties that determine, to some extent, epidemiological features and clinical manifestation in tuberculosis (TB) patients.The aim of the study was to assess the risk of an adverse outcome of the disease in TB patients caused by various M. tuberculosis genotypes.Materials and methods. A total of 425 patients with respiratory TB were enrolled in this study. They were registered at phthisiatric facilities in the Omsk region from March 2015 to June 2017 period and included: males — 73.1%, mean age 39.9 years, females — 26.9%, mean age 42.0 years. M. tuberculosis culture and drug susceptibility testing and DNA extraction were performed in accordance with standard methods. Strains were assigned to the M. tuberculosis Beijing genotype and its epidemiologically relevant clusters B0/W148 and 94-32 by PCR based detection of specific markers. Non-Beijing strains were subjected to spoligotyping.Results. We found that 66.5% isolates belonged to the Beijing genotype, 12.8% — to LAM, 10.1% — to T, and 4.7% — to the Ural genotype. Multi-drug resistance (MDR) to anti-TB drugs was observed in 195 M. tuberculosis strains (45.9%). Moreover, Beijing genotype was more often isolated from patients with MDR-TB infection (PR = 2.09 (95% CI 1.6–2.74) and TB infection associated with HIV infection (PR = 1.14 (95% CI 1.01–1.31). Lethal outcome was double higher in patients infected with Beijing vs. non-Beijing strains, 28.6% vs. 14.0% (PR = 2.03; 95% CI 1.3–3.17). The risk factors were identified as follows: young age 18–44 years (RR = 1.7; 95% CI 1.18–2.7), co-morbidity with HIV (RR = 5.0; 95% CI 3.39–7.45), multiple (RR = 1.7; 95% CI 1.14–2.55) and extensive drug resistance (RR = 2.57; 95% CI 1.35–4.92), and association with the Beijing genotype (RR = 2.0, 95% CI 1.3–3.17).Conclusion. M. tuberculosis spread in the Omsk region is characterised by significant prevalence of the Beijing genotype, associated with multiple and extensive drug resistance. A significant association of adverse clinical outcomes and various factors, including association with the Beijing genotype, requires development of new approaches in the fight against tuberculosis
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