Convergence of path measures arising from a mean field or polaron type interaction

Summary We discuss the limiting path measures of Markov processes with either a mean field or a polaron type interaction of the paths. In the polaron type situation the strength is decaying at large distances on the time axis, and so the interaction is of short range in time. In contrast, in the mean field model, the interaction is weak, but of long range in time. Donsker and Varadhan proved that for the partition functions, there is a transition from the polaron type to the mean field interaction when passing to a limit by letting the strength tend to zero while increasing the range. The discussion of the path measures is more subtle. We treat the mean field case as an example of a differentiable interaction and discuss the transition from the polaron type to the mean field interaction for two instructive examples.Research supported by the Swiss National Foundation (21-29833.90)This article was processed by the authors using the Springer-Verlag T_EX ProbTh macro package 1991.     

On self-repellent one dimensional random walks

Summary We consider an ordinary one dimensional recurrent random walk on. A self-repellent random walk is defined by changing the ordinary law of the random walk in the following way: A path gets a new relative weight by multiplying the old one with a factor 1– for every self intersection of the path. 0<<1 is a parameter.It is shown that if the jump distribution of the random walk has an exponential moment and if is small enough then the displacement of the endpoint is asymptotically of the order of the length of the path.Partially supported by the Deutsche Forschungsgemeinschaft and the Akademie der Wissenschaften zu Berlin     

Solid-phase microextraction–capillary gas chromatography combined with microwave-induced plasma atomic-emission spectrometry for selenite determination

The use of solid-phase microextraction (SPME) with gas chromatography coupled to microwave-induced plasma atomic-emission detection (GC–MIP-AED) is described for selenite [Se(IV)] speciation. Aqueous standards were derivatised with sodium tetraethyl- or tetrapropylborate and extracted by SPME. Headspace extraction of the ethyl and propyl derivatives was studied. Relevant experimental conditions were optimised, including conditions for derivatisation and extraction and those of gas chromatographic analysis. The limits of detection achieved for headspace sampling of derivatised Se(IV) were in the low ng mL^–1 range for both ethylation and propylation. When the method was applied to analysis of selenite in selenised yeast reference material results were in good agreement with the indicated values.     

Distribution and valence of the cations in the spinel system Fe3O4-Fe2VO4

The Mössbauer spectra of the solid solution Fe[Fe_xV_2–x]O₄ within 1.0×2.0 consist of two sets of sextets corresponding to A- and B-sites. From the superimposed sextets of the B-site pattern result typical values of isomer shift and internal magnetic field strength due to different environments of the B-site iron. It is shown that V ions both enhance the conduction electron density at the neighbouring Fe ions and diminish the strength of the magnetic interactions.     

Total Synthesis of Cyclothialidine

A total synthesis of cyclothialidine ( 1 ), a new DNA gyrase inhibitor isolated from Streptomyces filipinensis, is described. The synthetic concept was tested by preparing the lactone 13 (Scheme 2) which contains the characteristic bicyclic core entity of 1 . Key features of the synthesis of 1 are: preparation of 3,5-dihydroxy-2,6-dimethylbenzoic acid ( 23 ) from 3,5-dihydroxybenzoic acid ( 19 ) by two consecutive Mannich aminomethylation/hydrogenation sequences; benzylic N-bromosuccinimide bromination of an ester derivative 25 thereof and its subsequent coupling with Boc-Ser-Cys-OMe ( 11 ); cyclization of the ω-hydroxy acid 29 29 to the 12-membered lactone 30 using preferably Mitsunobu conditions; completion of the peptidic side chains of 1 using Boc strategy (Scheme 4). Optically pure cis-N-(tert-butoxycarbonyl)-3-hydroxy-L -proline ((–)- 14 ) was obtained by resolution of the racemate via an efficient reaction sequence containing a lipase-catalyzed enantiospecific acetate hydrolysis (Scheme 3). The structure of natural 1 was confirmed by comparison with the synthetic material. The synthetic route described provides also easy access to analogues of 1 , e.g., via the intermediate 30 .