Contingent epiderivatives and set-valued optimization

In this paper we introduce the concept of the contingent epiderivative for a set-valued map which modifies a notion introduced by Aubin [2] as upper contingent derivative. It is shown that this kind of a derivative has important properties and is one possible generalization of directional derivatives in the single-valued convex case. For optimization problems with a set-valued objective function optimality conditions based on the concept of the contingent epiderivative are proved which are necessary and sufficient under suitable assumptions.     

Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in derL p -Theorie

Zusammenfassung Die Hörmander-Klassen _1, ⁰ (0<1) von Pseudodifferentialoperatoren sind -Algebren. Insbesondere ist die Inverse eines inL(L ^p ( ⁿ )) invertierbaren Pseudodifferentialoperators der Klasse _1, ⁰ selbst wieder ein Pseudodifferential-operator derselben Klasse.Der Beweis beruht auf den von R. Beals, R. R. Coifman, Y. Meyer und H. O. Cordes entwickelten Methoden zur Charakterisierung von Algebren von Pseudodifferentialoperatoren.     

Asymmetric Diels-Alder reactions with 5-menthyloxy-2-(5H)-furanone

A new class of chiral dienophiles, 5-alkoxy-2(5H)-furanones, has been developed. Both enantiomers of 5-menthyloxy-2(5H)-ftiranone are readily available in enantiomerically pure form, starting from furfural and d- or l-menthol. Excellent diastereoselectivities (d.e. β99%) are obtained in thermal Diels-Alder reactions with several cyclic and acyclic dienes. The use of silyl dienol ethers has resulted in new routes to enantiomerically pure cyclohexanones in a highly regioselective manner.     

Controlled vesicle self-assembly in microfluidic channels with hydrodynamic focusing

Traditional liposome preparation methods are based on mixing of bulk phases, leading to inhomogeneous chemical and/or mechanical conditions during formation; hence liposomes are often polydisperse in size and lamellarity. Here we show the formation of liposomes that encapsulate reagents in a continuous two-phase flow microfluidic network with precision control of size from 100 to 300 nm by manipulation of liquid flow rates. We demonstrate that by creating a solvent-aqueous interfacial region in a microfluidic format that is homogeneous and controllable on the length scale of a liposome, we can facilitate the fine control of liposome size and polydispersity.     

The "invisible" 13C NMR chemical shift of the central carbon atom in [(Ph3PAu)6C]2+: a theoretical investigation

The experimental 13C NMR chemical shift of the central carbon atom in the octahedral [(Ph3PAu)6C]2+ cluster was investigated on the basis of relativistic density functional calculations. In order to arrive at independent model conclusions regarding the value of the chemical shift, a systematic study of the dependence of the cluster structure on the phosphine ligands, the chosen density functionals, and the basis set size was conducted. The best structures obtained were then used in the NMR calculations. Because of the cage-like cluster structure a pronounced deshielding of the central carbon nucleus could have been expected. However, upon comparison with the 13C NMR properties of the related complex [C{Au[P(C6H5)2(p-C6H4NMe2)]}6]2+, Schmidbaur et al. have assigned a signal at delta=135.2 ppm to the interstitial carbon atom. Our calculations confirm this value in the region of the aromatic carbon atoms of the triphenylphosphine ligands. The close-lying signals of the 108 phenyl carbon atoms can explain the difficulties of assigning them experimentally.     

Kinetic versus thermodynamic control during the formation of [2]rotaxanes by a dynamic template-directed clipping process

A template-directed dynamic clipping procedure has generated a library of nine [2]rotaxanes that have been formed from three dialkylammonium salts-acting as the dumbbell-shaped components-and three dynamic, imino bond-containing, [24]crown-8-like macrocycles-acting as the ring-shaped components-which are themselves assembled from three dialdehydes and one diamine. The rates of formation of these [2]rotaxanes differ dramatically, from minutes to days depending on the choice of dialkylammonium ion and dialdehyde, as do their thermodynamic stabilities. Generally, [2]rotaxanes formed by using 2,6-diformylpyridine as the dialdehyde component, or bis(3,5-bis(trifluoromethyl)benzyl)ammonium hexafluorophosphate as the dumbbell-shaped component, assembled the most rapidly. Those rotaxanes containing this particular electron-deficient dumbbell-shaped unit, or 2,5-diformylfuran units in the macroring, were the most stable thermodynamically. The relative thermodynamic stabilities of all nine of the [2]rotaxanes were determined by competition experiments that were monitored by (1)H NMR spectroscopy.