Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

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

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

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket

Point sets on the sphere S2\mathbb{S}^2 with small spherical cap discrepancy

In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges with order $N^{-1/2}$. Such point sets are therefore useful for numerical integration and other computational simulations. The proof uses an area-preserving Lambert map. A detailed analysis of the level curves and sets of the pre-images of spherical caps under this map is given

The plants, rituals and spells that 'cured' helminthiasis in Sicily

<p>Abstract</p> <p>Background</p> <p>The author reports on the plants, rituals and spells used against worms and the so-called <it>scantu </it>(fright) in some areas of Sicily. The work is based on ethnobotanical research carried out, prevalently, between 2002-2006, in some areas of Eastern, South-Eastern, North-Central and South-Central Sicily.</p> <p>Methods</p> <p>This research is based on dialogue. Senior 'healers' were contacted; furthermore, doctors, teachers, farmers and in general 'experts' with herbs and 'magic' rituals. Information was collected about the way the plants of folk medicine are prepared. The interviewees were also invited to recite prayers and spells against helminthiasis.</p> <p>Results</p> <p>The author has highlighted the importance of how, in some parts of Sicily, some ailments like helminthiasis and other correlated pathologies like <it>scantu </it>are 'treated' and, especially within the rural social classes, by folk medicine remedies, herbal practises, particular prayers, rituals and spells.</p> <p>Conclusion</p> <p>As regards health/illness, it should be noted that in the last ten years conventional medicine has provided very satisfactory results even resolving potentially mortal pathologies. However, in certain social classes, there is no real collaboration between conventional and folk medicine; so for some senior citizens, the 'healer' with his rituals and empirical and magical herbs is still the person to turn to for the 'cure' of particular ailments. Interest in these practises from ancestral heritage in an advanced country like Italy, is only relevant if the aim is to recoup a cultural identity which is already in decline.</p> <p>It is significant to report a piece: on 14 October 2007 the news on a well-known national Italian TV channel reported an interview with a 94 year-old man from Arbatax (Sardinia) referred to as a 'healer' because both his townspeople and others from all over the world go to him for his cures. He is not paid except in kind and has been known to cure St. Anthony's fire, burns, scalding and marine fungal infections, by smearing his saliva over the infected part and reciting 'special words'.</p

Spatio‐temporal patterns of tree growth as related to carbon isotope fractionation in European forests under changing climate

Aim To decipher Europe-wide spatiotemporal patterns of forest growth dynamics and their associations with carbon isotope fractionation processes inferred from tree rings as modulated by climate warming. Location Europe and North Africa (30‒70°N, 10°W‒35°E). Time period 1901‒2003. Major taxa studied Temperate and Euro-Siberian trees. Methods We characterize changes in the relationship between tree growth and carbon isotope fractionation over the 20th century using a European network consisting of 20 site chronologies. Using indexed tree-ring widths (TRWi), we assess shifts in the temporal coherence of radial growth across sites (synchrony) for five forest ecosystems (Atlantic, Boreal, cold continental, Mediterranean and temperate). We also examine whether TRWi shows variable coupling with leaf-level gas exchange, inferred from indexed carbon isotope discrimination of tree-ring cellulose (Δ13Ci). Results We find spatial autocorrelation for TRWi and Δ13Ci extending over up to 1,000 km among forest stands. However, growth synchrony is not uniform across Europe, but increases along a latitudinal gradient concurrent with decreasing temperature and evapotranspiration. Latitudinal relationships between TRWi and Δ13Ci (changing from negative to positive southwards) point to drought impairing carbon uptake via stomatal regulation for water saving occurring at forests below 60°N in continental Europe. A rise in forest growth synchrony over the 20th century together with increasingly positive relationships between TRWi and Δ13Ci indicate intensifying drought impacts on tree performance. These effects are noticeable in drought-prone biomes (Mediterranean, temperate and cold continental). Main conclusions At the turn of this century, convergence in growth synchrony across European forest ecosystems is coupled with coordinated warming-induced drought effects on leaf physiology and tree growth spreading northwards. Such a tendency towards exacerbated moisture-sensitive growth and physiology could override positive effects of enhanced leaf intercellular CO2 concentrations, possibly resulting in Europe-wide declines of forest carbon gain in the coming decades