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.     

Non-destructive analysis of archeological samples by energy-dispersive X-ray fluorescence

Summary A non-destructive method is described for the determination of major and minor constituents in archeological specimens by energy-dispersive X-ray fluorescence. Homogeneity tests are made by measuring at various sites of the specimen. In the same way, mean values are obtained for inhomogeneous specimen without taking samples. For calibration, powder standards are used. In case of the determination of elements with numbers up to 14 (Si) a vacuum chamber is used and the dimensions of the specimens are limited by the dimensions of that vacuum chamber, whereas for the determination of elements from K up to U specimens of any size, form or weight are suitable.

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Zerstörungsfreie Analyse von archäologischen Proben mit Hilfe der Energie-dispersiven Röntgenfluorescenzanalyse

Zusammenfassung Eine zerstörungsfreie Methode für die Bestimmung von Haupt- und Nebenbestandteilen in archäologischen Proben mit Hilfe der Energie-dispersiven Röntgenfluorescenzanalyse wird beschrieben. Für Homogenitätstests wird an mehreren Stellen der Probe gemessen. In der gleichen Weise werden für inhomogene Proben Mittelwerte erhalten ohne Probenahme. Für die Eichung werden Pulverstandards verwendet. Im Falle der Bestimmung von Elementen mit Ordnungszahlen bis 14 (Si) wird eine Vakuumkammer eingesetzt, und die Dimensionen der Proben sind durch die Dimensionen dieser Vakuumkammer begrenzt, während für die Bestimmung der Elemente K bis U Proben jeder Größe, jeder Form oder jeden Gewichts verwendbar sind.

     

Helicoid Shiftamers for the Transport of π‐Clumps and Charges

Hypothetical helical organic polymers with localized electrons, charges, and/or atoms are described, in which these localized substructures can move along the backbones of the polymers via sigmatropic H shifts.