The occurrence of the extinct shark genus Sphenodus in the Jurassic of Sicily

During the systematic revision of some historical collections containing Mesozoic ammonites, housed at the "G.G. Gemmellaro" Geological Museum of the Palermo University, a fossil shark’s tooth has been discovered. This specimen, indicated as Lamna in the original catalogue, can be attributed to the genus Sphenodus, an extinct cosmopolitan shark ranging from Lower Jurassic rocks to the Paleocene. The specimen is part of the Mariano Gemmellaro Collection which mainly consists of Middle-Upper Jurassic ammonites coming from Tardàra Mountain, between Menfi and Sambuca di Sicilia (Agrigento Province, Southwestern Sicily). Some of the ammonite specimens were listed, but not illustrated, by M. Gemmellaro in a note of 1919. The succession described in this area consists (from bottom to the top) of Lower Jurassic shallow-water carbonates followed by condensed ammonitic limestones of “Rosso ammonitico-type” (Middle-Late Jurassic in age), Calpionellid limestones (Upper Jurassic-Lower Cretaceous) and cherty calcilutites of Scaglia-type (Upper Cretaceous-Eocene). Since the exact stratigraphic level from which the shark tooth comes is not recorded, a thin section was made of the rock matrix surrounding the tooth. The sedimentological and paleontological analysis of the thin section has highlighted the presence of a microfacies characteristic of the Upper Jurassic condensed deposits of Rosso ammonitico-type, data that fits very well with the geology of the Tardàra area. The study of the Tardàra shark’s tooth has provided both the stimulus and opportunity to undertake a taxonomic review of the Jurassic specimens of Sphenodus collected from a range of Sicilian localities (Gemmellaro G.G., 1871; Seguenza G., 1887; Di Stefano & Cortese, 1891; Seguenza L., 1900; De Gregorio A., 1922) that, to date, have not been re-examined in the light of more recent scholarship. In particular, the specimens described and illustrated by G.G. Gemmellaro (1871), and stored in his eponymous museum, have been revised with the aim of providing a contribution to our knowledge of the genus Sphenodus in the Sicilian Mesozoic successions

Assessing Alternatives for Directional Detection of a WIMP Halo

The future of direct terrestrial WIMP detection lies on two fronts: new, much larger low background detectors sensitive to energy deposition, and detectors with directional sensitivity. The former can large range of WIMP parameter space using well tested technology while the latter may be necessary if one is to disentangle particle physics parameters from astrophysical halo parameters. Because directional detectors will be quite difficult to construct it is worthwhile exploring in advance generally which experimental features will yield the greatest benefits at the lowest costs. We examine the sensitivity of directional detectors with varying angular tracking resolution with and without the ability to distinguish forward versus backward recoils, and compare these to the sensitivity of a detector where the track is projected onto a two-dimensional plane. The latter detector regardless of where it is placed on the Earth, can be oriented to produce a significantly better discrimination signal than a 3D detector without this capability, and with sensitivity within a factor of 2 of a full 3D tracking detector. Required event rates to distinguish signals from backgrounds for a simple isothermal halo range from the low teens in the best case to many thousands in the worst.Comment: 4 pages, including 2 figues and 2 tables, submitted to PR

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

A note on dimer models and McKay quivers

We give one formulation of an algorithm of Hanany and Vegh which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng, He, Kennaway and Vafa.Comment: 25 pages, 35 figures. v3:completely rewritte

A discrete Laplace-Beltrami operator for simplicial surfaces

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace-Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay triangulations of piecewise flat surfaces revised and expanded. References added. Some minor changes, typos corrected. v3: fixed inaccuracies in discussion of flip algorithm, corrected attributions, added references, some minor revision to improve expositio

Approximation of conformal mappings by circle patterns

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles intersect with an intersection angle in $(0,\pi)$. Two sequences of circle patterns are employed to approximate a given conformal map $g$ and its first derivative. For the domain of $g$ we use embedded circle patterns where all circles have the same radius decreasing to 0 and which have uniformly bounded intersection angles. The image circle patterns have the same combinatorics and intersection angles and are determined from boundary conditions (radii or angles) according to the values of $g'$ ($|g'|$ or $\arg g'$). For quasicrystallic circle patterns the convergence result is strengthened to $C^\infty$-convergence on compact subsets.Comment: 36 pages, 7 figure

Barremian and Aptian (Cretaceous) sharks and rays from Speeton, Yorkshire, north-east England

Bulk sampling of a number of horizons within the upper part of the Speeton Clay Type section has produced teeth and other remains of sharks and rays from several poorly studied horizons. At least 10 shark and two ray species were recorded, with two sharks, Pteroscyllium speetonensis and Palaeobrachaelurus mitchelli, being described as new. The oldest occurrences of the family Anacoracadae and the genus Pteroscyllium, as well as the youngest occurrence of the genus Palaeobrachaelurus, were recorded. The palaeoenvironmental significance of the faunas is briefly discussed

A kinetic and theoretical study of the borate catalysed reactions of hydrogen peroxide: the role of dioxaborirane as the catalytic intermediate for a wide range of substrates

Our recent work has provided new insights into the equilibria and species that exist in aqueous solution at different pHs for the boric acid – hydrogen peroxide system, and the role of these species in oxidation reactions. Most recently, (M. C. Durrant, D. M. Davies and M. E. Deary, Org. Biomol. Chem., 2011, 9,7249–7254), we have produced strong theoretical and experimental evidence for the existence of a previously unreported monocyclic three membered peroxide species, dioxaborirane, that is the likely catalytic species in borate mediated electrophilic reactions of hydrogen peroxide in alkaline solution. In the present paper, we extend our study of the borate–peroxide system to look at a wide range of substrates that include substituted dimethyl anilines, methyl-p-tolyl sulfoxide, halides, hydrogen sulfide anion, thiosulfate ,thiocyanate, and hydrazine. The unusual selectivity–reactivity pattern of borate catalysed reactions compared with hydrogen peroxide and inorganic or organic peracids previously observed for theorganic sulfides (D. M. Davies, M. E. Deary, K. Quill and R. A. Smith, Chem.–Eur. J., 2005, 11, 3552–3558) is also seen with substituted dimethyl aniline nucleophiles. This provides evidence that the pattern is not due to any latent electrophilic tendency of the organic sulfides and further supports dioxaborirane being the likely reactive intermediate, thus broadening the applicability of this catalytic system. Moreover, density functional theory calculations on our proposed mechanism involving dioxaborirane are consistent with the experimental results for these substrates. Results obtained at high concentrations of both borate and hydrogen peroxide require the inclusion the diperoxodiborate dianion in the kinetic analysis .A scheme detailing our current understanding of the borate–peroxide system is presented

Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization

We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller

Performance of the ARIANNA Hexagonal Radio Array

Installation of the ARIANNA Hexagonal Radio Array (HRA) on the Ross Ice Shelf of Antarctica has been completed. This detector serves as a pilot program to the ARIANNA neutrino telescope, which aims to measure the diffuse flux of very high energy neutrinos by observing the radio pulse generated by neutrino-induced charged particle showers in the ice. All HRA stations ran reliably and took data during the entire 2014-2015 austral summer season. A new radio signal direction reconstruction procedure is described, and is observed to have a resolution better than a degree. The reconstruction is used in a preliminary search for potential neutrino candidate events in the data from one of the newly installed detector stations. Three cuts are used to separate radio backgrounds from neutrino signals. The cuts are found to filter out all data recorded by the station during the season while preserving 85.4% of simulated neutrino events that trigger the station. This efficiency is similar to that found in analyses of previous HRA data taking seasons.Comment: Proceedings from the 34th ICRC2015, http://icrc2015.nl/ . 8 pages, 6 figure