Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts

We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class $\mathcal B$), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is greater than 1.Comment: 7 pages, 1 figur

Genetic differentiation of brackish water populations of cod Gadus morhua in the southern Baltic, inferred from genotyping using SNP-arrays

The Baltic is a semi-enclosed sea characterised by decreasing salinity in the eastern and northern direction with only the deeper parts of the southern Baltic suitable as spawning grounds for marine species like cod. Baltic cod exhibits various adaptations to brackish water conditions, yet the inflow of salty North Sea water near the bottom remains an influence on the spawning success of the Baltic cod. The eastern Baltic population has been very weakly studied in comparison with the western population. The aim of this study is to demonstrate for the first time genetic differentiation by the use of a large number of SNPs between eastern and western Baltic populations existing in differentiated salinity conditions. Two cod samples were collected from the Bay of Gdańsk, Poland and one from the Kiel Bight, Germany. Samples were genotyped using a cod derived SNP-array (Illumina) with 10 913 SNPs. A selection of diagnostic SNPs was performed. A set of 7944 validated SNPs were analysed to assess the differentiation of three samples of cod. Results indicated a clear distinctness of the Kiel Bight from the populations of the eastern Baltic. FST comparison between both eastern samples was non-significant. Clustering analysis, principal coordinates analysis and assignment test clearly indicated that the eastern samples should be considered as one subpopulation, well differentiated from the western subpopulation. With the SNP approach, no differentiation between groups containing ‘healthy’ and ‘non-healthy’ cod individuals was observed

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

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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