On nonlinear preconditioners in Newton–Krylov methods for unsteady flows

The application of nonlinear schemes like dual time stepping as preconditioners in matrix‐free Newton–Krylov‐solvers is considered and analyzed, with a special emphasis on unsteady viscous flows. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix‐free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes, which is demonstrated through numerical results. Copyright © 2009 John Wiley & Sons, Ltd.     

Eine Bemerkung über indefinite Variationsprobleme

Ohne Zusammenfassung     

Zur Bestimmung der St?rke als Traubenzucker

Ohne Zusammenfassung     

Fetts?uren

Ohne Zusammenfassung     

Twist-2 Compton Operator and Its Hidden Structure: WW-, CG- and Other Relations

We show that the group-theoretic structure of the Compton operator at leading geometric twist-2 allows, among other relations, to derive, without any approximation and using no dynamical input, operator versions of the Wandzura-Wilczek and the (power corrected) Callan-Gross relations. Their functional form is exactly the same as for deep inelastic scattering.     

Click chemistry in materials synthesis. 1. Adhesive polymers from copper‐catalyzed azide‐alkyne cycloaddition

The copper(I)‐catalyzed cycloaddition reaction between azides and alkynes has been employed to make metal‐adhesive materials. Copper and brass surfaces supply the necessary catalytic Cu ions, and thus the polymerization process occurs selectively on these metals in the absence of added catalysts. Alternatively, copper compounds can be added to monomer mixtures and then introduced to reducing metal surfaces such as zinc to initiate polymerization. The resulting materials were found to possess comparable or superior adhesive strength to standard commercial glues, and structure‐activity correlations have identified several important properties of the monomers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4392–4403, 2004     

Hydrogen-bond-induced selectivity of a head-to-head photo-dimerisation of dialkynylanthracene – access to tetradentate Lewis acids

Using 2-hydroxypropyl-protecting groups, 1,8-dialkynylanthracene photo-dimers were prepared in head-to-head-configuration by UV irradiation on a multi-gram scale. In non-polar solvents, the combination of non-covalent hydrogen bonds and π–π-interactions induces the formation of the syn-isomer in up to 85% yield. Instead, more polar solvents or irradiation of unprotected 1,8-diethynylanthracene led to formation of the corresponding anti-isomer in large excess. Cleavage of the protecting groups under basic conditions affords a rigid hydrocarbon skeleton with four directional functions. This was used as a building block for a tetradentate boron Lewis acid. Its applicability as a host for Lewis-base substrates was demonstrated by the formation of adducts with various nitrogen bases. Adduct formation with hydrazine leads to impressive networks between the tetraboron host and the substrate molecules.

Preorganised by hydrogen bonds and π-stacking, 2-hydroxypropylalkyne-protected 1,8-alkynylanthracene photo-dimerises preferably in head-to-head configuration; the resulting rigid organic frameworks can be converted into tetradentate boron Lewis acids.     

Investigating Three Qubit Entanglement with Local Measurements

In this paper we describe how three qubit entanglement can be analyzed with local measurements. For this purpose we decompose entanglement witnesses into operators that can be measured locally. Our decompositions are optimized in the number of measurement settings needed for the measurement of one witness. Our method allows to detect true threepartite entanglement and especially GHZ-states with only four measurement settings.