Leibenzon's backward shift and composition operators

We apply Leibenzon's backward shift to show that the composition operator on the unit ball of always maps the weighted Hardy space into the Hardy class .

     

Highly syndiospecific polymerization of styrene catalyzed by allyl lanthanide complexes

Allylic complexes of lanthanides bearing a fluorenyl-based ligand are active single-component catalysts for the polymerization of styrene, giving highly syndiotactic polymers (rrrr > 99%) with low to high molecular weight (Mn = 8000-135 000) and narrow polydispersities (Mw/Mn = 1.25-2.1).     

Nonvariational time-dependent multiconfiguration self-consistent field equations for electronic dynamics in laser-driven molecules

A time-dependent multiconfiguration self-consistent field (TDMCSCF) scheme is developed to describe the time-resolved electron dynamics of a laser-driven many-electron atomic or molecular system, starting directly from the time-dependent Schrodinger equation for the system. This nonvariational formulation aims at the full exploitations of concepts, tools, and facilities of existing, well-developed quantum chemical MCSCF codes. The theory uses, in particular, a unitary representation of time-dependent configuration mixings and orbital transformations. Within a short-time, or adiabatic approximation, the TDMCSCF scheme amounts to a second-order split-operator algorithm involving generically the two noncommuting one-electron and two-electron parts of the time-dependent electronic Hamiltonian. We implement the scheme to calculate the laser-induced dynamics of the two-electron H2 molecule described within a minimal basis, and show how electron correlation is affected by the interaction of the molecule with a strong laser field.     

Design and performance of two-channel EUV multilayer mirrors with enhanced spectral selectivity

In this paper, we present a study on two-channel multilayer mirrors which can operate at two wavelengths in Extreme Ultraviolet (EUV) spectral range. We propose a new method to design two-channel EUV multilayer mirrors with enhanced spectral selectivity. The mirror structure is a stack of two periodic multilayers separated by a buffer layer. We have defined the main parameters which allow adjustment of the distance between different order Bragg’s peak and of wavelength positions of reflectivity minima. Two mirrors have been designed and deposited for solar EUV telescope applications by using this method. The first mirror reflects Fe IX–X line (17.1 nm) and Fe XVI (33.5 nm) lines with attenuation of the He II line (30.4 nm). The second mirror reflects Fe IX–X and He II lines with attenuation of Fe XV (28.4 nm) and Fe XVI lines. Measurements with synchrotron radiation source confirm that, in both cases, for these mirrors, we are able to adjust reflectivity maxima (Bragg peak position) and minima. Such multilayers offer new possibilities for compact design of multi-wavelength EUV telescopes and/or for high spectral selectivity.     

On pseudolinearity and generic pairs

We continue the study of the connection between the “geometric” properties of SU ‐rank 1 structures and the properties of “generic” pairs of such structures, started in [8]. In particular, we show that the SU‐rank of the (complete) theory of generic pairs of models of an SU ‐rank 1 theory T can only take values 1 (if and only if T is trivial), 2 (if and only if T is linear) or ω, generalizing the corresponding results for a strongly minimal T in [3]. We also use pairs to derive the implication from pseudolinearity to linearity for ω ‐categorical SU ‐rank 1 structures, established in [7], from the conjecture that an ω ‐categorical supersimple theory has finite SU ‐rank, and find a condition on generic pairs, equivalent to pseudolinearity in the general case (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A split-step finite difference method for nonparaxial nonlinear Schrödinger equation at critical dimension

The critical nonlinear Schrödinger equation (NLS) is the model equation for propagation of laser beam in bulk Kerr medium. One of the final stages in the derivation of NLS from the nonlinear Helmholtz equation (NLH) is to apply paraxial approximation. However, there is numerical evidence suggesting nonparaxiality prevents singularity formation in the solutions of NLS. Therefore, it is important to develop numerical methods for solving nonparaxial NLS. Split-step methods are widely used for finding numerical solutions of NLS equation. Nevertheless, these methods cannot be applied to nonparaxial NLS directly. In this study, we extend the applicability of split-step methods to nonparaxial NLS by using Padé approximant operators. In particular, split-step Crank-Nicolson (SSCN) method is used in conjunction with Padé approximants to provide examples of numerical solutions of nonparaxial NLS.     

Mode-locked 1.93 microm thulium fiber laser with a carbon nanotube absorber

We report a ring-cavity thulium fiber laser mode locked with a single-wall carbon nanotube absorber used in transmission. A carboxymethyl cellulose polymer film with incorporated carbon nanotubes synthesized by the arc discharge method has an absorption coinciding with in the amplification bandwidth of a Tm-doped fiber. This laser is pumped by an erbium fiber laser at 1.57 microm wavelength and produces a 37 MHz train of mode-locked 1.32 ps pulses at 1.93 microm wavelength with an average output power of 3.4 mW.     

In situ XPS investigation of Pt(Sn)/Mg(Al)O catalysts during ethane dehydrogenation experiments

Calcined hydrotalcite with or without added metal (Mg(Al)O, Pt/Mg(Al)O and Pt,Sn/Mg(Al)O) have been investigated with in situ X-ray photoelectron spectroscopy (XPS) during ethane dehydrogenation experiments. The temperature in the analysis chamber was 450 °C and the gas pressure was in the range 0.3-1 mbar. Depth profiling of calcined hydrotalcite and platinum catalysts under reaction, oxidation and in hydrogen-water mixture was performed by varying the photon energy, covering an analysis depth of 10-21 Å. It was observed that the Mg/Al ratio in the Mg(Al)O crystallites does not vary significantly in the analysis depth range studied. This result indicates that Mg and Al are homogeneously distributed in the Mg(Al)O crystallites. Catalytic tests have shown that the initial activity of a Pt,Sn/Mg(Al)O catalyst increases during an activation period consisting of several cycles of reduction-dehydrogenation-oxidation. The Sn/Mg ratio in a Pt,Sn/Mg(Al)O catalyst was followed during several such cycles, and was found to increase during the activation period, probably due to a process where tin spreads over the carrier material and covers an increasing fraction of the Mg(Al)O surface. The results further indicate that spreading of tin occurs under reduction conditions.A PtSn₂ alloy was studied separately. The surface of the alloy was enriched in Sn during reduction and reaction conditions at 450 °C. Binding energies were determined and indicated that Sn on the particle surface is predominantly in an oxidised state under reaction conditions, while Pt and a fraction of Sn is present as a reduced Pt-Sn alloy.     

The role of cloud-scale resolution on radiative properties of oceanic cumulus clouds

Both individual and combined effects of the horizontal and vertical variability of cumulus clouds on solar radiative transfer are investigated using a two-dimensional (x- and z-directions) cloud radar dataset. This high-resolution dataset of typical fair-weather marine cumulus is derived from ground-based cloud radar observations. The domain-averaged (along x-direction) radiative properties are computed by a Monte Carlo method. It is shown that (i) different cloud-scale resolutions can be used for accurate calculations of the mean absorption, upward and downward fluxes; (ii) the resolution effects can depend strongly on the solar zenith angle; and (iii) a few cloud statistics can be successfully applied for calculating the averaged radiative properties.