A Helly-type transversal theorem for n-dimensional unit balls

Let be a family of unit balls in with the property that the mutual distances of the centers are at least . If any n² members of have a common line transversal, then has a line transversal too. Received: 27 January 2005; revised: 17 October 2005     

Staudinger and retro-Staudinger reactions. The dichloro-β-lactam moiety as a useful handle for the synthesis of 4-aryl-2H-1,3-benzothiazine 1,1-dioxides

The dichloro-β-lactam ring, obtained via Staudinger reaction of 4-aryl-2H-1,3-benzothiazines, proved to be a useful protecting strategy for the synthesis of 4-aryl-2H-1,3-benzothiazine 1,1-dioxides. After oxidation of the 1,1-dichloroazeto[2,1-c][1,3]-benzothiazin-2-ones, the thiazine ring could be recovered selectively and in good yield by treatment with base. Thus, novel 4-aryl-2H-1,3-benzothiazine 1,1-dioxides were obtained efficiently.     

Solution-phase synthesis of a tricyclic pyrrole-2-carboxamide discovery library applying a stetter-Paal-Knorr reaction sequence

The solution-phase synthesis of a discovery library of 178 tricyclic pyrrole-2-carboxamides was accomplished in nine steps and seven purifications starting with three benzoyl-protected amino acid methyl esters. Further diversity was introduced by two glyoxaldehydes and 41 primary amines. The combination of Pauson-Khand, Stetter, and microwave-assisted Paal-Knorr reactions was applied as a key sequence. The discovery library was designed with the help of QikProp 2.1, and physicochemical data are presented for all pyrroles. Library members were synthesized and purified in parallel and analyzed by LC/MS. Selected compounds were fully characterized.     

Die Reversibilität der Säuregelatine bei der Dialyse

Ohne Zusammenfassung     

Die Auflösung der Silbermizellen durch Wasserstoffperoxyd

Ohne Zusammenfassung     

Heterogeneous attachment strategies optimize the topology of dynamic wireless networks

In optimizing the topology of wireless networks built of a dynamic set of spatially embedded agents, there are many trade-offs to be dealt with. The network should preferably be as small (in the sense that the average, or maximal, pathlength is short) as possible, it should be robust to failures, not consume too much power, and so on. In this paper, we investigate simple models of how agents can choose their neighbors in such an environment. In our model of attachment, we can tune from one situation where agents prefer to attach to others in closest proximity, to a situation where agents attach to random others regardless of distance (which thus are, on average, further away than the connections to the spatial neighbors). We evaluate this scenario with several performance measures and find that the optimal topologies, for most of the quantities, is obtained for strategies resulting in a mix of most local and a few random connections.     

Canonical gravity in the parametric manifold picture

Canonical structures in the parametric picture of gravitation in general relativity are investigated. One of the fields, the scalarf, emerges as a secondary entity that interacts with a system consisting of the threemetricg and the connection form. We are employing the (g,) system for developing a canonical approach. While a naïve attempt would appear to founder, we do find an extension of the phase-space of the system which is computationally viable.     

Fragmentation of enamides derived from 6,7-dimethoxy-4-methyl-2H-1,3-benzothiazin and 3,4-dihydro-6,7-dimethoxy-1-methylixopuinoline

The electron impact mass spectra of several enamides have been examined. The enamides were prepared by reaction of aroyl halides with 6,7-dimethoxy-4-methyl-1,3-benzothiazin, and with 3,4-dihydro-6,7-dimethoxy-l-methylisoquinoline. The fragmentation pathways that have been proposed are supported by ion composition determinations and by mass-analysed ion kinetic energy spectrometry experiments carried out on the molecular ions and major fragment ions. The spectra are characterized by a loss of carbon monoxide from the molecular ion of each compound, a process which is accompanied by migration of the aryl group.