Contracting on Average Random IFS with Repelling Fixed Point

We consider random iterated function systems which consist of strictly increasing and (not necessarily strictly) convex functions on a compact interval or on a half line. We assume that the system is contracting on average in a sense which is wide enough to permit the existence of a common fixpoint at which some functions of the system are expanding and perhaps none of them are contracting (see Fig. 1). We prove that the Hausdorff dimension of any of the possibly uncountably many invariant measures is smaller than or equal to the accumulated entropy divided by the Liapunov exponent. Mathematics Subject Classification. Primary 42A85 Secondary 11R06; 26A46; 26A30; 26A78; 28A80     

Organic electroluminescence using polymer networks from smectic liquid crystals

We report the synthesis of a red light-emitting and photopolymerizable smectic liquid crystal (reactive mesogen). We investigate the suitability of polymer networks formed from smectic reactive mesogens for use in organic light-emitting diodes (OLEDs). The use of mixtures of smectic reactive mesogens is shown to lower the processing temperature for the fabrication of OLEDs to room temperature. We also report efficient energy transfer from a nematic polymer network host to a smectic light-emitting dopant and polarized emission from a polymer network formed from an aligned smectic reactive mesogen.     

Spatially resolved micro-X-ray fluorescence and micro-X-ray absorption fine structure study of a fractured granite bore core following a radiotracer experiment

Spatially resolved X-ray absorption and fluorescence investigation with a micrometer-scale resolution on actinide-containing samples provide information necessary for safety assessment of nuclear waste disposal. In this paper one example of such an experiment is presented. This example entails neptunium speciation in a fractured granite bore core from the Swedish Äspö Hard Rock Laboratory following a radiotracer experiment using µ-XAFS and µ-XRF. In order to probe micro-volumes below the surface in the granite samples and thereby avoid potential changes in the Np speciation during cutting of the bore core, a confocal irradiation–detection geometry is employed. µ-XAFS results for a selected granite bore core cross section with ~ 3 nmol Np/g reveal that Np, originally introduced as Np(V) in the tracer cocktail, is present in the granite in its reduced Np(IV) form. The Np(IV) is often present as particles, tens of µm in size. Elemental distribution maps show the tracer Np to be located in fissures and permeable channels not larger than 100 µm. The Np distribution appears often correlated with Zn also present in some fissures. We observe small granite fissures containing Fe (presumably Fe(II)), where we do not detect any Np. It is feasible that inflowing Np(V) has a shorter residence time in large fractures, while in the smaller fissures migration is slower, leading to longer residence times, i.e., reaction times, where it is reduced to less soluble Np(IV) and becomes thereby immobilized.     

Parabolic conjugacy in general linear groups

Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL _n (q). We show that the number of P(q)-conjugacy classes in GL _n (q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of Alperin in (Commun. Algebra 34(3): 889–891, 2006)