Encoding the dynamics of deterministic systems

We present a model for the dynamics of discrete deterministic systems, based on an extension of the Petri nets framework. Our model relies on the definition of a priority relation between conflicting transitions, which is encoded by orienting the edges of a transition conflict graph. We provide a characterization in terms of a local consistency condition of those deterministic systems whose dynamic behavior can be encoded using our approach. Finally, we consider the problem of recognizing when an orientation of the transition conflict graph is valid for encoding the dynamic behavior of a system.     

A gradient structure for systems coupling reaction–diffusion effects in bulk and interfaces

We derive gradient-flow formulations for systems describing drift-diffusion processes of a finite number of species which undergo mass-action type reversible reactions. Our investigations cover heterostructures, where material parameter may depend in a nonsmooth way on the space variable. The main results concern a gradient-flow formulation for electro-reaction–diffusion systems with active interfaces permitting drift-diffusion processes and reactions of species living on the interface and transfer mechanisms allowing bulk species to jump into an interface or to pass through interfaces. The gradient flows are formulated in terms of two functionals: the free energy and the dissipation potential. Both functionals consist of a bulk and an interface integral. The interface integrals determine the interface dynamics as well as the self-consistent coupling to the model in the bulk. The advantage of the gradient structure is that it automatically generates thermodynamically consistent models.     

Design of a Heterogeneous Catalyst Based on Cellulose Nanocrystals for Cyclopropanation: Synthesis and Solid‐State NMR Characterization

Heterogeneous dirhodium(II) catalysts based on environmentally benign and biocompatible cellulose nanocrystals (CNC‐Rh₂) as support material were obtained by ligand exchange between carboxyl groups on the CNC surface and Rh₂(OOCCF₃)₄, as was confirmed by solid‐state ¹⁹F and ¹³C NMR spectroscopy. On average, two CF₃COO^? groups are replaced during ligand exchange, which is consistent with quantitative analysis by a combination of ¹⁹F NMR spectroscopy and thermogravimetry. CNC‐Rh₂ catalysts performed well in a model cyclopropanation reaction, in spite of the low dirhodium(II) content on the CNC surface (0.23 mmol g^?1). The immobilization through covalent bonding combined with the separate locations of binding positions and active sites of CNC‐Rh₂ guarantees a high stability against leaching and allows the recovery and reuse of the catalyst during the cyclopropanation reaction.     

On the analysis of an electronic model for solar cells including energy resolved defect densities

In this paper we study analytic properties of electronic models for solar cells, which take into account varying, energy resolved densities of defects. We establish energy estimates and the boundedness of weak solutions and give an existence and uniqueness result for weak solutions to the model equations in two space dimensions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

One-Dimensional Representations of U (p,q) and the Howe Correspondence

We explicitly determine the theta lifts of all one-dimensional representations of U (p,q) in terms of Langlands parameters, and determine exactly which lifts are unitary. Moreover, we show that such a lift is unitary if and only if it is a weakly fair derived functor module of the form A_q(λ). Finally, we show that the correspondence of unitary representations behaves well with respect to associated cycles.     

Palladium-catalyzed carbonylation of haloindoles: no need for protecting groups

[reaction: see text] For the first time, palladium-catalyzed carbonylations of unprotected bromoindoles have been performed successfully with different N- and O-nucleophiles. Various indole carboxylic acid derivatives are accessible in excellent yield. For example, aminocarbonylation of 4-, 5-, 6-, or 7-bromoindole with arylethylpiperazines provides a direct one-step synthesis for CNS active amphetamine derivatives.