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.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

Investigation of organic impurities adsorbed on and incorporated into electroplated copper layers

At room temperature electroplated copper layers exhibit changes in resistivity, residual stress, and microstructure. This process, known as self-annealing, is intimately linked to the release of organic impurities, which stem from the incorporation of organic additives into the Cu layer in the course of the electroplating process. The behavior of these impurities during self-annealing, represented by the carbon content, could be detected by analytical radio frequency glow discharge optical emission spectrometry (GD-OES) and carrier gas hot extraction (CGHE). The precondition of a quantitative determination is a surface cleaning procedure to remove adsorbed organics from the copper surface. It was observed that at first almost all impurities have to leave the Cu metallization before an accelerated abnormal grain growth can start. The small amount of remaining organic species after self-annealing could be quantified by both examination techniques, GD-OES and CGHE.     

Uran im Quellengebiete von Franzensbad

Ohne Zusammenfassung