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.     

Anatomy of the shape Hessian via lie brackets

The goal of this paper is to study the anatomy of the shape Hessian for some classes of smooth shape functionals. A structure theorem gives a decomposition of the shape Hessian in three additive bilinear forms acting on the two fields: the first one acting on the normal components at the boundary, the second one being symmetrical and the third one involving a half of the Lie bracket of the pair of fields at which the shape Hessian is computed. Applications to the commutation of the mixed derivatives and the symmetry of the linear operator which appears in the structure theorem are given.     

A desingularization theorem of Néron type

Summary LetA→A′ be a regular morphism between two noetherian rings. Then for everyA-algebra of finite typeB, everyA-morphism fromB toA′ can be factorised through aB-algebra of finite typeB′ which is standard (smooth) overA and which is ?as smooth as possible? overB (i.e. except above the singular locus ofB overA). This result is a positive answer to one conjecture due to M. Artin.

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Riassunto SiaA→A′ un omomorfismo regolare di anelli noetheriani. Si dimostra che per ogniA-algebraB di tipo finito, ogniA-omomorfismoB→A′ si può fattorizzare mediante unaB-algebraB′ di tipo finito che è liscia suA ed è ?la più liscia posibile? suB (più precisamente liscia suB meno il luogo singolare diB suA). Questo risultato è una risposta affermativa a una congettura di M. Artin.

     

Kinetics of thiophene hydrodesulfurization over a supported Mo–Co–Ni catalyst

In this study, the kinetics of thiophene (TH) hydrodesulfurization (HDS) over the Mo–Co–Ni-supported catalyst was investigated. Trimetallic catalyst was synthesized by pore volume impregnation and the metal loadings were 11.5 wt % Mo, 2 wt % Co, and 2 wt % Ni. A large surface area of 243 m²/g and a relatively large pore volume of 0.34 cm³/g for the fresh Mo–Co–Ni-supported catalyst indicate a good accessibility to the catalytic centers for the HDS reaction. The acid strength distribution of the fresh and spent catalysts, as well as for the support, was determined by thermal desorption of diethylamine (DEA) with increase in temperature from 20 to 600 °C. The weak acid centers are obtained within a temperature range between 160 and 300 °C, followed by medium acid sites up to 440 °C. The strong acid centers are revealed above 440 °C. We found a higher content of weak acid centers for fresh and spent catalysts as well as alumina as compared to medium and strong acid sites. The catalyst stability in terms of conversion as a function of time on stream in a fixed bed flow reactor was examined and almost no loss in the catalyst activity was observed. Consequently, this fact demonstrated superior activity of the Mo–Co–Ni-based catalyst for TH HDS. The activity tests by varying the temperature from 200 to 275 °C and pressure from 30 to 60 bar with various space velocities of 1–4 h^?1 were investigated. A Langmuir–Hinshelwood model was used to analyze the kinetic data and to derive activation energy and adsorption parameters for TH HDS. The effect of temperature, pressure, and liquid hourly space velocity on the TH HDS activity was studied.     

General and Efficient Insertions of Carbons Carrying Aryl and Heteroaryl Groups: Synthesis of alpha-Aryl- and alpha-Heteroaryl-Substituted Ketones

Anions formed from the lithiation of a variety of 1-(arylmethyl)- and 1-(heteroarylmethyl)benzotriazoles 1 with n-BuLi underwent addition to aliphatic and aromatic aldehydes and cyclic and acyclic ketones. Subsequent in situ thermal rearrangements of the intermediates in the presence of zinc bromide provided one-carbon chain-extended or ring-expanded alpha-aryl- and alpha-heteroaryl-substituted ketones 2 in moderate to excellent yields in simple one-pot operations with excellent regioselectivity in most cases. Substituent effects on the relative migration rates were investigated in the insertion reactions of 1-(4-methoxybenzyl)benzotriazole (1e) with XC(6)H(4)COPh. The small and negative Hammett rho(+) value (-0.92) suggested that the rearrangements proceed via early, reagent-like, electron deficient transition states.