Covariant Representations for Matrix-valued Transfer Operators

Motivated by the multivariate wavelet theory, and by the spectral theory of transfer operators, we construct an abstract affine structure and a multiresolution associated to a matrix-valued weight. We describe the one-to-one correspondence between the commutant of this structure and the fixed points of the transfer operator. We show how the covariant representation can be realized on if the weight satisfies some low-pass condition.      

Electron holography with a Cs-corrected transmission electron microscope.

Cs correctors have revolutionized transmission electron microscopy (TEM) in that they substantially improve point resolution and information limit. The object information is found sharply localized within 0.1 nm, and the intensity image can therefore be interpreted reliably on an atomic scale. However, for a conventional intensity image, the object exit wave can still not be detected completely in that the phase, and hence indispensable object information is missing. Therefore, for example, atomic electric-field distributions or magnetic domain structures cannot be accessed. Off-axis electron holography offers unique possibilities to recover completely the aberration-corrected object wave with uncorrected microscopes and hence we would not need a Cs-corrected microscope for improved lateral resolution. However, the performance of holography is affected by aberrations of the recording TEM in that the signal/noise properties ("phase detection limit") of the reconstructed wave are degraded. Therefore, we have realized off-axis electron holography with a Cs-corrected TEM. The phase detection limit improves by a factor of four. A further advantage is the possibility of fine-tuning the residual aberrations by a posteriori correction. Therefore, a combination of both methods, that is, Cs correction and off-axis electron holography, opens new perspectives for complete TEM analysis on an atomic scale.     

Synthesis and catalytic properties of microemulsion-derived cerium oxide nanoparticles

The synthesis of cerium dioxide nanoparticles using an inverse microemulsion technique and precipitation method was investigated. Cerium hydroxide nanoparticles were synthesized by adding diluted ammonia to n-heptane–surfactant–cerium nitrate system. The micelle and particle size in the range of 5–12 nm were controlled by varying the molar water to surfactant ratio and analyzed by dynamic light scattering (DLS), small angle X-ray scattering (SAXS) and high-resolution transmission electron microscopy (HRTEM). Cerium hydroxide nanoparticles were isolated and subsequently treated at 100–600 °C to obtain nanoscale ceria. Crystallite sizes of cerium dioxide in the range of 6–16 nm were estimated by Scherrer analysis by X-ray diffraction (XRD) and HRTEM. The catalytic activity of particles annealed at 400 and 600 °C in soot combustion reactions was characterized by temperature-programmed oxidation (TPO) indicating a size-dependant activity. Crystallite sizes and catalytic stability of elevated ceria systems were tested in second combustion cycles.     

The algebra of harmonic functions for a matrix-valued transfer operator

We analyze matrix-valued transfer operators. We prove that the fixed points of transfer operators form a finite-dimensional C^∗-algebra. For matrix weights satisfying a low-pass condition we identify the minimal projections in this algebra as correlations of scaling functions, i.e., limits of cascade algorithms.     

A TQFT Associated to the LMO Invariant of Three-Dimensional Manifolds

We construct a Topological Quantum Field Theory associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from a category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. This is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup of the Mapping Class Group that contains the Torelli group. The N = 1 truncation is a TQFT for the Casson-Walker-Lescop invariant. The results of this article were obtained when the authors were at the Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA.     

Electrochemical study and MO — modeling of the reduction behaviour of some arylidene substituted derivatives of dibenz [b,e]-thiepin-5,5-dioxide-11-one

The electrochemical reduction of four arylidene substituted derivatives of dibenz-[b,e]-thiepin-5,5-dioxide-11- one has been studied by cyclic voltammetry on platinum (Pt) electrode in aprotic media (DMSO), coupled with spectral EPR techniques. From the analysis of cyclic voltammetry experiments, aided by digital simulations using DigiSim software, the kinetic and thermodynamic parameters were evaluated for each system. The electrochemical behaviour is strongly directed by the nature of the arylidene substituents bound to the central heterocycle. The electrochemical investigation and solvent dependent semiempirical modeling using the PM3 hamiltonian in the frame of AMPAC program package allowed a rationalisation of experimental data regarding the electrochemical reduction and the reactivity of the intermediate species involved.      

An Extension of the Admissibility-Type Conditions for the Exponential Dichotomy of C 0-Semigroups

In the present paper we obtain a sufficient condition for the exponential dichotomy of a strongly continuous, one-parameter semigroup , in terms of the admissibility of the pair . It is already known the equivalence between the -admissibility condition and and the hyperbolicity of a C ₀-semigroup , when we assume a priori that the kernel of the dichotomic projector (denoted here by X ₂) is T(t)-invariant and is an invertible operator. We succeed to prove in this paper that the admissibility of the pair still implies the existence of an exponential dichotomy for a C ₀-semigroup even in the general case where the kernel of the dichotomic projector, X ₂, is not assumed to be T(t)-invariant.      

Laser prepared organic heterostructures based on star-shaped arylenevinylene compounds

This paper presents some studies about the preparation by matrix-assisted pulsed laser evaporation (MAPLE) technique of organic bulk heterojunctions made from the mixture of a star-shaped arylenevinylene compound, 4,4′,4″-tris[(4′-diphenylamino)styryl] triphenylamine as donor and fullerene derivative, [6, 6]-phenyl C61 butyric acid butyl ester, as acceptor, in the weight ratio 1:2. The mixed layer has been characterized by spectroscopic (UV–Vis, Fourier transform infrared) and microscopic (AFM) methods, and the effects of the deposition conditions (number of pulses) and of a buffer layer of poly(aniline-co-aniline propane sulfonic acid) or poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) have been analyzed. The study of the electrical properties has revealed a typical solar cell behavior for the heterostructure glass/ITO/poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate)/4,4′,4″-tris[(4′-diphenylamino)styryl] triphenylamine: [6, 6]-phenyl C61 butyric acid butyl ester/Al, confirming that MAPLE could be an adequate method for the preparation of active layer based on bulk heterojunction for solar cells.