Entire functions with Julia sets of positive measure

Let f be a transcendental entire function for which the set of critical and asymptotic values is bounded. The Denjoy-Carleman-Ahlfors theorem implies that if the set of all z for which |f(z)|>R has N components for some R>0, then the order of f is at least N/2. More precisely, we have log log M(r,f) > (N/2) log r - O(1), where M(r,f) denotes the maximum modulus of f. We show that if f does not grow much faster than this, then the escaping set and the Julia set of f have positive Lebesgue measure. However, as soon as the order of f exceeds N/2, this need not be true. The proof requires a sharpened form of an estimate of Tsuji related to the Denjoy-Carleman-Ahlfors theorem.Comment: 17 page

Molecular genetic differentiation of native populations of Mediterranean blue mussels, Mytilus galloprovincialis Lamarck, 1819, and the relationship with environmental variables

publishedVersio

Radio-Continuum Study of the Nearby Sculptor Group Galaxies. Part 2: NGC 55 at {\lambda}=20, 13, 6 and 3 cm

A series of new radio-continuum ({\lambda}=20, 13, 6 and 3 cm) mosaic images focused on the NGC55 galactic system were produced using archived observational data from the Australia Telescope Compact Array. These new images are both very sensitive (down to rms=33 {\mu}Jy) and feature high angular resolution (down to <4"). Using these newly created images, 66 previously unidentified discrete sources are identified. Of these sources, 46 were classified as background sources, 11 as HII regions and 6 as supernova remnant candidates. This relatively low number of SNR candidates detected coupled with the low number of large HII regions is consistent with the estimated low star formation rate of the galaxy at 0.06 solar masses per year. Our spectral index map shows that the core of galaxy appears to have a shallow spectral index between {\alpha} = -0.2 and -0.4. This indicates that the core of the galaxy is a region of high thermal radiation output.Comment: 11 pages, 8 figures. Accepted for publication in Astrophysics and Space Scienc

Passport, a native Tc1 transposon from flatfish, is functionally active in vertebrate cells

The Tc1/mariner family of DNA transposons is widespread across fungal, plant and animal kingdoms, and thought to contribute to the evolution of their host genomes. To date, an active Tc1 transposon has not been identified within the native genome of a vertebrate. We demonstrate that Passport, a native transposon isolated from a fish (Pleuronectes platessa), is active in a variety of vertebrate cells. In transposition assays, we found that the Passport transposon system improved stable cellular transgenesis by 40-fold, has an apparent preference for insertion into genes, and is subject to overproduction inhibition like other Tc1 elements. Passport represents the first vertebrate Tc1 element described as both natively intact and functionally active, and given its restricted phylogenetic distribution, may be contemporaneously active. The Passport transposon system thus complements the available genetic tools for the manipulation of vertebrate genomes, and may provide a unique system for studying the infiltration of vertebrate genomes by Tc1 elements

The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result

We construct a self-affine sponge in R 3 whose dynamical dimension, i.e. the supremum of the Hausdorff dimensions of its invariant measures, is strictly less than its Hausdorff dimension. This resolves a long-standing open problem in the dimension theory of dynamical systems, namely whether every expanding repeller has an ergodic invariant measure of full Hausdorff dimension. More generally we compute the Hausdorff and dynamical dimensions of a large class of self-affine sponges, a problem that previous techniques could only solve in two dimensions. The Hausdorff and dynamical dimensions depend continuously on the iterated function system defining the sponge, implying that sponges with a dimension gap represent a nonempty open subset of the parameter space