Doeblin's and Harris' theory of Markov processes

Our notation and definitions are taken from (Chung, K. L.: The general theory of Markov processes according to Doeblin. Z. Wahrscheinlichkeitstheorie und verw. Gebiete 2, 230–254 (1964)). A closed set H is called recurrent in the sense of Harris if there exists a σ-finite measure ? such that for E=H, ?(E) >0 implies Q(x, E)=1 for all tx?H. Theorem 1. Let X be absolutely essential and indecomposable. Then there exists a closed set B?X. such that B contains no acountable disjoint collection of perpetuable sets if and only if X=H+1 where H is recurrent in the sense of Harris and I is either inessential or improperly essential. Theorem 2. If there exists no uncountable disjoint collection of closed sets, then there exists a countable disjoint collection {D_n} _n=1 ^∞ of absolutely essential and indecomposable closed sets such that \(I = X - \sum\nolimits_{n = 1}^\infty {D_n } \) . Under the additional assumption that Suslin's Conjecture holds, Theorem 2 was proved by Jamison (Jamison, B.: A Result in Doeblin's Theory of Markov Chains implied by Suslin's Conjecture. Z. Wahrscheinlichkeitstheorie verw. Gebiete 24, 287–293 (1972)).     

Anisotropic interface magnetoresistance in Pt/Co/Pt sandwiches

We report on an effect of reduced dimensionality on the magnetotransport in cobalt layers sandwiched by platinum. In a current in-plane geometry it is found that the resistivity depends on the magnetization orientation within the plane perpendicular to the current direction. The resistivity shows a symmetry adapted cos(2) dependence on the angle to the surface normal, with the maximum along the surface normal. The Co thickness dependence of the effect in Pt/Co/Pt sandwiches clearly points out that the mechanism behind this effect originates at the Co/Pt interfaces and is disparate to the texture induced geometrical size effect.     

Determination of241Pu by low level β-proportional counting. Application to Chernobyl fallout samples and comparison with the241Am build-up method

A chemical separation procedure is described which allows the direct determination of low²⁴¹Pu activities in environmental samples with a windowless gas-flow proportional counter. While current separation schemes based on anion exchange yield counting sources of sufficient purity for subsequent -spectrometry, for -counting of²⁴¹Pu additional purification steps are required. A combination of anion exchange from 9 mol/l HCl, LaF₃ precipitation and TTA extraction was found to be suitable even for the analysis of long-range Chernobyl fallout samples which contained interfering radionuclides with -activities at least 3 to 4 orders of magnitude higher than usually encountered. No difference is detectable between the results of the present, direct procedure and the results of the conventional indirect method based on the build-up of²⁴¹Am. Average²⁴¹Pu/^239+240Pu ratios in air and deposition samples taken at Neuherberg near Munich were 70±6 with the present procedure and 66±9 from²⁴¹Am build-up.