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.     

Arc erosion reduction on electrical contacts using transversecurrent injection

Electrical contact lifetime is often directly determined by arc erosion. A method for reducing are erosion was developed consisting of injecting from an external current source an additional electrical current flowing parallel to the contact surface. This method was examined in three are environments using the additional transverse electrical current with a density less than 1 A/mm²: 1) automobile ignition contacts; 2) pulsed air arc; and 3) low pressure (P=100 mTorr) arc in nitrogen, SEM and X-ray examination showed that application of a transverse current in a contact during arcing changed the phase composition and microstructure of the contact surface. Under optimal conditions, the microstructure which is formed is significantly more erosion resistant than without the transverse current injection     

The unitary irreducible representations of the quantum heisenberg algebra

The goal of this work is to describe the irreducible representations of the quantum Heisenberg algebra and the unitary irreducible representation of one of its real forms. The solution of this problem is obtained through the investigation of theleft spectrum of the quantum Heisenberg algebra using the result about spectra of generic algebras of skew differential operators (cf. [R]).     

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.