s

A space X is called s-point finite refinable (ds-point finite refinable) provided every open cover of X has an open refinement such that, for some (closed discrete) C⫅X

Tissue-specific expression of high-voltage-activated dihydropyridine-sensitive L-type calcium channels

The cloning of the cDNA for the α1 subunit of L-type calcium channels revealed that at least two genes (CaCh1 and CaCh2) exist which give rise to several splice variants. The expression of mRNA for these α1 subunits and the skeletal muscle α2/δ, β and γ subunits was studied in rabbit tissues and BC3H1 cells. Nucleic-acid-hybridization studies showed that the mRNA of all subunits are expressed in skeletal muscle, brain, heart and aorta. However, the α1-, β- and γ-specific transcripts had different sizes in these tissues. Smooth muscle and heart contain different splice variants of the CaCh2 gene. The α1, β and γ mRNA are expressed together in differentiated but not in proliferating BC3H1 cells. A probe specific for the skeletal muscle α2/δ subunit did not hybridize to poly(A)-rich RNA from BC3H1 cells. These results suggest that different splice variants of the genes for the α1, β and γ subunits exist in tissues containing L-type calcium channels, and that their expression is regulated in a coordinate manner

Towards a sensitive search for variation of the fine structure constant using radio-frequency E1 transitions in atomic dysprosium

It has been proposed that the radio-frequency electric-dipole (E1) transition between two nearly degenerate opposite-parity states in atomic dysprosium should be highly sensitive to possible temporal variation of the fine structure constant ($\alpha$) [V. A. Dzuba, V. V. Flambaum, and J. K. Webb, Phys. Rev. A {\bf 59}, 230 (1999)]. We analyze here an experimental realization of the proposed search in progress in our laboratory, which involves monitoring the E1 transition frequency over a period of time using direct frequency counting techniques. We estimate that a statistical sensitivity of |\adota| \sim 10^{-18}/yr may be achieved and discuss possible systematic effects that may limit such a measurement.Comment: 8 pages, 7 figure

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

Average distances on self-similar sets and higher order average distances of self-similar measures

The purpose of this paper is twofold: (1) we study different notions of the average distance between two points of a self-similar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of ℝ

Fortified Settlements of the 9th and 10th Centuries ad in Central Europe: structure, function and symbolism

Open access article. © Society for Medieval Archaeology 2012.The structure, function(s)and symbolism of early medieval (9th-10th centuries ad) fortified settlements from central Europe, in particular today's Austria, Hungary, Czech Republic and Slovakia, are examined in this paper. It offers an overview of the current state of research together with new insights based on analysis of the site of Gars-Thunau in Lower Austria. Special emphasis is given to the position of the fortified sites in the landscape, to the elements of the built environment and their spatial organisation, as well as to graves within the fortified area. The region under study was situated on the SE border of the Carolingian (and later the Ottonian) Empire, with some of the discussed sites lying in the territory of the 'Great Moravian Empire' in the 9th and 10th centuries. These sites can therefore provide important comparative data for researchers working in other parts of the Carolingian Empire and neighbouring regions.Alexander von Humboldt FoundationAustrian Science Fun