Quantum ergodicity for restrictions to hypersurfaces

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple dynamical condition, the restrictions of eigenstates to N are also quantum ergodic.Comment: 22 pages, 1 figure; revised according to referee's comments. To appear in Nonlinearit

Fractal Weyl laws and wave decay for general trapping

We prove a Weyl upper bound on the number of scattering resonances in strips for manifolds with Euclidean infinite ends. In contrast with previous results, we do not make any strong structural assumptions on the geodesic flow on the trapped set (such as hyperbolicity) and instead use propagation statements up to the Ehrenfest time. By a similar method we prove a decay statement with high probability for linear waves with random initial data. The latter statement is related heuristically to the Weyl upper bound. For geodesic flows with positive escape rate, we obtain a power improvement over the trivial Weyl bound and exponential decay up to twice the Ehrenfest time

The sectional curvature remains positive when taking quotients by certain nonfree actions

We study some cases when the sectional curvature remains positive under the taking of quotients by certain nonfree isometric actions of Lie groups. We consider the actions of the groups $S^1$ and $S^3$ such that the quotient space can be endowed with a smooth structure using the fibrations $S^3/S^1{\simeq}S^2$ and $S^7/S^3\simeq S^4$. We prove that the quotient space carries a metric of positive sectional curvature, provided that the original metric has positive sectional curvature on all 2-planes orthogonal to the orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam

Tuning of tunneling current noise spectra singularities by localized states charging

We report the results of theoretical investigations of tunneling current noise spectra in a wide range of applied bias voltage. Localized states of individual impurity atoms play an important role in tunneling current noise formation. It was found that switching "on" and "off" of Coulomb interaction of conduction electrons with two charged localized states results in power law singularity of low-frequency tunneling current noise spectrum ($1/f^{\alpha}$) and also results on high frequency component of tunneling current spectra (singular peaks appear).Comment: 7 pages, 4 figure

Asymptomatic Lone Atrial Fibrillation in Pregnant Women

We examined 43 pregnant women with paroxysms of asymptomatic lone atrial fibrillation. It was revealed that the increasing of the gestational age leads to increase of number of single, paired and group supraventricular extrasystoles; single and paired ventricular extrasystoles; number and duration of paroxysms of atrial fibrillation. However, the number of extrasystoles and paroxysms of arrhythmia decreased to baseline values after delivery. Thus, it was proved that pregnancy contributes to the increase of paroxysms of lone atrial fibrillation due to the increased influence of modulating components on the triggering extrasystoles. The importance of the method of 24-hour ECG monitoring in the detection of arrhythmia in pregnant women is emphasized. Keywords: lone atrial fibrillation, extrasystole, pregnancy

Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes

We establish a Bohr-Sommerfeld type condition for quasi-normal modes of a slowly rotating Kerr-de Sitter black hole, providing their full asymptotic description in any strip of fixed width. In particular, we observe a Zeeman-like splitting of the high multiplicity modes at a=0 (Schwarzschild-de Sitter), once spherical symmetry is broken. The numerical results presented in Appendix B show that the asymptotics are in fact accurate at very low energies and agree with the numerical results established by other methods in the physics literature. We also prove that solutions of the wave equation can be asymptotically expanded in terms of quasi-normal modes; this confirms the validity of the interpretation of their real parts as frequencies of oscillations, and imaginary parts as decay rates of gravitational waves.Comment: 66 pages, 6 figures; journal version (to appear in Annales Henri Poincar\'e

Vein-isolating and dissecting device

A description of special device for subcutaneous isolating and dissecting of veins in varicose disease of low extremities is presented. The scheme of its use is shown with the due explanation

On the phenomenology of a Z' coupling only to third-family fermions

The phenomenology of an additional U(1) neutral gauge boson Z' coupled to the third family of fermions is discussed. One might expect such a particle to contribute to processes where taus, b and t quarks are produced. Precision data from LEP1 put severe constraints on the mixing and heavy-boson mass. We find that the effects of such a particle could not be observed at hadronic colliders, be it at the Tevatron or the LHC, because of the QCD background. At LEP2 and future e^+e^- linear colliders, one could instead hope to observe such effects, in particular for b\bar b final states.Comment: 36 pages, LaTeX, including 12 figure

Optimization of the Process of Cholera Chemical Pelleted Vaccine Production Using Ultrafiltration Technology

Technology of O-antigen obtaining from Vibrio cholerae M41production strain, using the hollow fiber ultrafiltration modules, is developed and introduced into cholera vaccine manufacturing. Application of ultrafiltration makes it possible to obtain native high-activity O-antigen preparations which comply with the current regulatory requirements. Besides, it provides for economy (10-15-fold) of ammonium sulphate, used for antigen precipitation, reduces the duration of technological cycle (2 times), and the labor inputs. The technology of protective antigen concentrating is tested on V. cholerae strains MO45 and KM137 of O139 serogroup. Three series of experimental V. cholerae O139 vaccine are obtained