Hyperbolic Unit Groups and Quaternion Algebras

We Classify the rational quadratic extensions K and the finite groups G for which the group ring R[G] of G over the ring R of integers of K has the property that the group of units of augmentation 1 of R[G] is hyperbolic. We also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author. The paper was accepted in Proceedings Mathematical Science

A Detection Method for Tropical Race 4 of the Banana Pathogen Fusarium oxysporum f. sp. cubense

Fusarium oxysporum f. sp. cubense (Foc) is the causal agent of Fusarium wilt, the devastating disease that ruined the ‘Gros Michel’ (AAA)-based banana production in the first half of the 20th century. The occurrence of a new variant in Southeast Asia that overcomes the resistance in Cavendish clones such as ‘Grand Naine’ (AAA) is a major concern to current banana production worldwide. The threat posed by this new variant, called tropical race 4 (TR4), may be overcome by the introduction of resistant cultivars. However, the identification of new resistant sources or breeding for resistance is a long-term effort. Currently, the only option to control the disease is to avoid or reduce the spread of the pathogen by eradication of infected plants and isolation of infested plantations. This requires sensitive and highly specific diagnostics that enable early detection of the pathogen. A two-locus database of DNA sequences, from over 800 different isolates from multiple formae speciales of F. oxysporum, was used to develop a molecular diagnostic tool that specifically detects isolates from the vegetative compatibility group (VCG) 01213, which encompasses the Foc TR4 genotype. This diagnostic tool was able to detect all Foc TR4 isolates tested, while none of the Foc isolates from 19 VCGs other than 01213 showed any reaction. In addition, the developed diagnostic tool was able to detect Foc TR4 when using DNA samples from different tissues of ‘Grand Naine’ plants inoculated with TR4 isolate

Near-barrier Fusion Induced by Stable Weakly Bound and Exotic Halo Light Nuclei

The effect of breakup is investigated for the medium weight $^{6}$Li+$^{59}$Co system in the vicinity of the Coulomb barrier. The strong coupling of breakup/transfer channels to fusion is discussed within a comparison of predictions of the Continuum Discretized Coupled-Channels model which is also applied to $^{6}$He+$^{59}$Co a reaction induced by the borromean halo nucleus $^{6}$He.Comment: 6 pages, 3 figures. A talk given at the FUSION06: International Conference on Reaction Mechanisms and Nuclear Structure at the Coulomb barrier, March 19-23, 2006, San Servolo, Venezia, Ital

The graphene sheet versus the 2DEG: a relativistic Fano spin-filter via STM and AFM tips

We explore theoretically the density of states (LDOS) probed by an STM tip of 2D systems hosting an adatom and a subsurface impurity,both capacitively coupled to AFM tips and traversed by antiparallel magnetic fields. Two kinds of setups are analyzed, a monolayer of graphene and a two-dimensional electron gas (2DEG). The AFM tips set the impurity levels at the Fermi energy, where two contrasting behaviors emerge: the Fano factor for the graphene diverges, while in the 2DEG it approaches zero. As result, the spin-degeneracy of the LDOS is lifted exclusively in the graphene system, in particular for the asymmetric regime of Fano interference. The aftermath of this limit is a counterintuitive phenomenon, which consists of a dominant Fano factor due to the subsurface impurity even with a stronger STM-adatom coupling. Thus we find a full polarized conductance, achievable just by displacing vertically the position of the STM tip. To the best knowledge, our work is the first to propose the Fano effect as the mechanism to filter spins in graphene. This feature arises from the massless Dirac electrons within the band structure and allows us to employ the graphene host as a relativistic Fano spin-filter

The silicon stable isotope distribution along the GEOVIDE section (GEOTRACES GA-01) of the North Atlantic Ocean

The stable isotope composition of dissolved silicon in seawater (δ30SiDSi) was examined at 10 stations along the GEOVIDE section (GEOTRACES GA-01), spanning the North Atlantic Ocean (40–60∘ N) and Labrador Sea. Variations in δ30SiDSi below 500 m were closely tied to the distribution of water masses. Higher δ30SiDSi values are associated with intermediate and deep water masses of northern Atlantic or Arctic Ocean origin, whilst lower δ30SiDSi values are associated with DSi-rich waters sourced ultimately from the Southern Ocean. Correspondingly, the lowest δ30SiDSi values were observed in the deep and abyssal eastern North Atlantic, where dense southern-sourced waters dominate. The extent to which the spreading of water masses influences the δ30SiDSi distribution is marked clearly by Labrador Sea Water (LSW), whose high δ30SiDSi signature is visible not only within its region of formation within the Labrador and Irminger seas, but also throughout the mid-depth western and eastern North Atlantic Ocean. Both δ30SiDSi and hydrographic parameters document the circulation of LSW into the eastern North Atlantic, where it overlies southern-sourced Lower Deep Water. The GEOVIDE δ30SiDSi distribution thus provides a clear view of the direct interaction between subpolar/polar water masses of northern and southern origin, and allow examination of the extent to which these far-field signals influence the local δ30SiDSi distribution