Rearrangement invariance of Rademacher multiplicator spaces

Let X be a rearrangement invariant function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of all measurable functions x such that x⋅h∈X for every a.e. converging series h=∑anrn∈X, where (rn) are the Rademacher functions. We study the situation when Λ(R,X) is a rearrangement invariant space different from L^∞. Particular attention is given to the case when X is an interpolation space between the Lorentz space Λ(φ) and the Marcinkiewicz space M(φ). Consequences are derived regarding the behaviour of partial sums and tails of Rademacher series in function spaces.     

Nonself-adjoint operators with almost Hermitian spectrum: Cayley identity and some questions of spectral structure

Nonself-adjoint, non-dissipative perturbations of possibly unbounded self-adjoint operators with real purely singular spectrum are considered under an additional assumption that the characteristic function of the operator possesses a scalar multiple. Using a functional model of a nonself-adjoint operator (a generalization of a Sz.-Nagy–Foiaş model for dissipative operators) as a principle tool, spectral properties of such operators are investigated. A class of operators with almost Hermitian spectrum (the latter being a part of the real singular spectrum) is characterized in terms of existence of the so-called weak outer annihilator which generalizes the classical Cayley identity to the case of nonself-adjoint operators in Hilbert space. A similar result is proved in the self-adjoint case, characterizing the condition of absence of the absolutely continuous spectral subspace in terms of the existence of weak outer annihilation. An application to the rank-one nonself-adjoint Friedrichs model is given.     

Knudsen Gas in a Finite Random Tube: Transport Diffusion and First Passage Properties

We consider transport diffusion in a stochastic billiard in a random tube which is elongated in the direction of the first coordinate (the tube axis). Inside the random tube, which is stationary and ergodic, non-interacting particles move straight with constant speed. Upon hitting the tube walls, they are reflected randomly, according to the cosine law: the density of the outgoing direction is proportional to the cosine of the angle between this direction and the normal vector. Steady state transport is studied by introducing an open tube segment as follows: We cut out a large finite segment of the tube with segment boundaries perpendicular to the tube axis. Particles which leave this piece through the segment boundaries disappear from the system. Through stationary injection of particles at one boundary of the segment a steady state with non-vanishing stationary particle current is maintained. We prove (i) that in the thermodynamic limit of an infinite open piece the coarse-grained density profile inside the segment is linear, and (ii) that the transport diffusion coefficient obtained from the ratio of stationary current and effective boundary density gradient equals the diffusion coefficient of a tagged particle in an infinite tube. Thus we prove Fick’s law and equality of transport diffusion and self-diffusion coefficients for quite generic rough (random) tubes. We also study some properties of the crossing time and compute the Milne extrapolation length in dependence on the shape of the random tube.     

The Number of Open Paths in an Oriented <Emphasis Type="Italic">ρ</Emphasis>-Percolation Model

We study the asymptotic properties of the number of open paths of length n in an oriented ρ-percolation model. We show that this number is e ^{n α(ρ)(1+o(1))} as n→∞. The exponent α is deterministic, it can be expressed in terms of the free energy of a polymer model, and it can be explicitly computed in some range of the parameters. Moreover, in a restricted range of the parameters, we even show that the number of such paths is n ^−1/2 We ^{n α(ρ)}(1+o(1)) for some nondegenerate random variable W. We build on connections with the model of directed polymers in random environment, and we use techniques and results developed in this context.     

On slowdown and speedup of transient random walks in random environment

We consider one-dimensional random walks in random environment which are transient to the right. Our main interest is in the study of the sub-ballistic regime, where at time n the particle is typically at a distance of order O(n ^κ ) from the origin, ${\kappa \in (0, 1)}$ . We investigate the probabilities of moderate deviations from this behaviour. Specifically, we are interested in quenched and annealed probabilities of slowdown (at time n, the particle is at a distance of order ${O(n^{\nu_0})}$ from the origin, ${\nu_0 \in (0, \kappa)}$ ), and speedup (at time n, the particle is at a distance of order ${n^{\nu_1}}$ from the origin, ${\nu_1 \in (\kappa, 1)}$ ), for the current location of the particle and for the hitting times. Also, we study probabilities of backtracking: at time n, the particle is located around (?n ^ν ), thus making an unusual excursion to the left. For the slowdown, our results are valid in the ballistic case as well.     

Symmetric kernel of Rademacher multiplicator spaces

Let X be a rearrangement invariant (r.i.) function space on [0,1]. We consider the Rademacher multiplicator space Λ(R,X) of measurable functions x such that xh∈X for every a.e. converging series h=∑a_nr_n∈X, where (r_n) are the Rademacher functions. We show that for a broad class of r.i. spaces X, the space Λ(R,X) is not r.i. In this case, we identify the symmetric kernel of the Rademacher multiplicator space and study when reduces to L^∞. In the opposite direction, we find new examples of r.i. spaces for which Λ(R,X) is r.i. We consider in detail the case when X is a Marcinkiewicz or an exponential Orlicz space.     

Observation of spatial migration of excitation in Er-doped optical fibers by means of a population grating technique

The influence of spatial migration of excitation among neighboring Er3+ ions on the dynamics of population grating formation in Er-doped optical fibers is reported. The effect manifests itself in an additional increment in the grating formation rate compared with the fluorescence growth rate observed for the same spatially uniform average light power. The experiments, performed at lambda=1549 nm in the configuration of transient two-wave mixing with two similar single-mode Er-doped fibers with significantly different erbium concentrations (approximately 640 and approximately 5600 parts in 10(6)), demonstrated the essential contribution of this effect to the grating formation rate in the latter fiber. The evaluated diffusion coefficient proved to be approximately 2.3 x 10(-9) cm2/s, which ensures effective migration of the excitation by approximately 48 nm, i.e., by approximately 18 average inter-ion distances in this fiber.     

Ab initio study of a biradical radiationless decay channel of the lowest excited electronic state of cytosine and its derivatives

A theoretical model for the ultrafast S1-->S0 internal conversion of cytosine is presented, in which a state switch from the initially prepared 1pipi* state to the out-of-plane deformed excited state of biradical character controls the rate of the S1(1pipi*) decay. This mechanism successfully accounts for the dramatically longer S1 lifetimes of 5-fluorocytosine and N-acetylcytosine relative to cytosine. The replacement of the C5 hydrogen atom by a methyl group is predicted to lead to a substantial, but not dramatic, increase in the S1 lifetime, also consistent with experiment. It is this ability to correctly predict the substituent effects that distinguishes the present model from the previously proposed mechanisms.     

Lysine-enediyne conjugates as photochemically triggered DNA double-strand cleavage agents

Statistical analysis of DNA-photocleavage by two types of lysine-enediyne conjugates confirms that more double-strand breaks are produced than can be accounted for by coincident single-strand breaks.     

Electronic structure of diamagnetic and paramagnetic hexanuclear chalcohalide clusters of rhenium

Hexanuclear chalcohalide clusters of rhenium(III) of general formula [Re(6)S(4+x)Cl(10-x)](x-) with x = 1-4 have been studied using quantum chemical DFT calculations. The optimized structures reproduce the geometrical features found from X-ray data for the members of the series. The relative stability of different stereoisomers for the mono- and dianions has been estimated. The analysis of the tetraanion series [Re(6)Q(8)X(6)](4-) with Q = S, Se and X = Cl, Br, I, and CN demonstrates the influence of the mu(1)- and mu( 3)-ligands on the strength of Re-apical ligand bond. It is shown that the tetragonal distortion found for the stable oxidized paramagnetic species [Re(6)S(8)Cl(6)]*(3-) results from the Jahn-Teller effect for a doubly degenerate electronic state.