The degree of Q-Fano threefolds

We prove that the degree of Fano threefolds with terminal Q-factorial singularities and Picard number one is at most 125/2 and the bound is sharp.Comment: 23 pages, LATE

The first main theorem on complements: from global to local

The aim of this paper is to clarify and generalize techniques of works alg-geom/9711024 (see also math.AG/9810097 and math.AG/9901004). Roughly speaking, we prove that for local Fano contractions the existence of complements can be reduced to the existence of complements for lower dimensional projective Fano varieties.Comment: 27 pages, LaTeX2

On birational involutions of P3P^3

Let $X$ be a rationally connected three-dimensional algebraic variety and let $\tau$ be an element of order two in the group of its birational selfmaps. Suppose that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program we give a rough classification of such elements.Comment: 24 pages, late

Unruh effect in curved space-time and hydrodynamics

We consider an accelerated relativistic fluid in four-dimensional (anti-)de Sitter space-time. Analyzing only hydrodynamic equations, we construct the equilibrium stress-energy tensor. We confirm that (A)dS vacuum corresponds to a thermal bath in the accelerated frame with a temperature, depending on the acceleration in a flat higher-dimensional (namely, five-dimensional) space, in which curved space-times are embedded. We develop the duality between hydrodynamics and gravity finding a direct relationship between the transport coefficients in flat and curved space-times

Noise-induced topological transformations of vortex solitons in optical fibers filled with a cold atomic gas

We consider the influence of optical and temperature-dependent atomic fluctuations on the formation and propagation of optical vortex solitons in dense media realized as hollow-core optical fibers filled with a cold atomic gas in presence of optical pumping. We show different perturbation-induced scenaria of complete destruction and smooth transformations of the topological characteristics of localized optical structures in hollow-core fiber. The maximum levels of optical and atomic fluctuations at which the soliton regime can be maintained has been determined. The estimates for these levels show an opportunity to observe the optical vortex solitions in the core-filling gas of the fiber for temperatures smaller than the critical temperature for Bose-Einstein condensate.Comment: 12 pages, 10 EPS figures, submitted to Physical Review

The Features of Surface Plasmon-Polariton Pulses Generation Via Cooperative Effects in Waveguide Spaser

The problem of sub-picosecond plasmon-polariton pulse formation in metal/dielectric interface due to collective decay of excited quantum dots, placed in the dielectric layer near the metal surface, is considered. Theoretical approach to selection of semiconductor quantum dots and dielectric host medium to increase the energy transmission of quantum dot collective excitations into surface plasmon-polariton modes of waveguide spaser is developed