Topological decoupling, linearization and perturbation on inhomogeneous time scales

We derive a linearization theorem in the framework of dynamic equations on time scales. This extends a recent result from [Y. Xia, J. Cao, M. Han, A new analytical method for the linearization of dynamic equation on measure chains, J. Differential Equations 235 (2007) 527-543] in various directions: Firstly, in our setting the linear part need not to be hyperbolic and due to the existence of a center manifold this leads to a generalized global Hartman-Grobman theorem for nonautonomous problems. Secondly, we investigate the behavior of the topological conjugacy under parameter variation.These perturbation results are tailor-made for future applications in analytical discretization theory, i.e., to study the relationship between ODEs and numerical schemes applied to them.     

Structural investigation of icosahedral Pd58.8U20.6Si20.6

The structure factors of the amorphous, icosahedral and crystalline Pd_58.8U_20.6Si_20.6 were measured with X-rays and neutrons. By comparing the radial distribution functions of the three phases, we find a similar short range order in the amorphous and icosahedral phase, but a different atomic arrangement in the crystalline phase. A magnetic long range order observed in the crystalline material is absent in the icosahedral phase.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

On variational approximations in quantum molecular dynamics

The Dirac-Frenkel-McLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate time-dependent wave function on an approximation manifold of reduced dimension. This paper gives a near-optimality result for variational approximations. It bounds the error in terms of the distance of the exact wave function to the approximation manifold and identifies the parameters that control the deviation of the variational approximation from the best approximation on the manifold.

     

Dependence of CO oxidation on Pt nanoparticle shape: a shape‐selective approach to the synthesis of PEMFC catalysts

In real catalyst systems, it is difficult to establish a correlation between catalytic properties and the shape (crystal planes, corners and steps) of the active catalytic particles. In this paper we present a clear shape dependence of the catalytic properties of a Vulcan‐supported fuel cell catalyst having 4 nm cubo‐octahedral platinum(0) nanocrystallites with (111) and (100) surfaces stabilized by sodium polyacrylate. The electrode materials were characterized by CO‐stripping cyclic voltammetry and transmission electron microscopy (TEM), showing that no agglomeration had occurred among the nanoparticles on the catalyst surfaces. Copyright © 2007 John Wiley & Sons, Ltd.     

Asymmetric total synthesis of the indole alkaloid cyclopiazonic acid and first structure-activity data

The indole alkaloid α-cyclopiazonic acid (CPA) is one of the few known inhibitors of sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) besides the terpenoids thapsigargin and artemisinin. We report here the first asymmetric total synthesis of cyclopiazonic acid by a modification of the Knight synthesis, currently the most efficient route to CPA. First structure-activity data of CPA derivatives and stereoisomers are presented and will be discussed in connection with the published crystal structures of CPA-SERCA complexes.     

4‐Benzoyl‐3,4‐dihydro‐2H‐1,4‐benzoxazine‐2‐carbonitrile: refinement using a multipolar atom model

The structural model for the title compound, C₁₆H₁₂N₂O₂, was refined using a multipolar atom model transferred from an experimental electron‐density database. The refinement showed some improvements of crystallographic statistical indices when compared with a conventional spherical neutral‐atom refinement. The title compound adopts a half‐chair conformation. The amide N atom lies almost in the plane defined by the three neighbouring C atoms. In the crystal structure, molecules are linked by weak intermolecular C—H...O and C—H...π hydrogen bonds.     

On quantitative aspects of the unit sum number problem

We investigate the function u _K,S (n; q) which counts the number of representations of algebraic integers α with |N_{K/\mathbb Q}(a)| ￡ q{|N_{K/{\mathbb Q}}(\alpha)| \leq q} for some real positive q that can be written as sums of exactly n S-units of the number field K.