The context of the Local Volume: structures and motions in the nearby universe

The 6dF Galaxy Survey (6dFGS) and the 2MASS Redshift Survey (2MRS) provide the most complete maps of the large-scale structures and motions in the nearby universe. These maps have been used to reconstruct the density field in the local volume, and to predict the corresponding velocity field and the dipole of the Local Group motion.Comment: 4 pages, to appear in "Galaxies in the Local Volume", 2008, eds B. Koribalski and H. Jerjen, Springer Astrophysics and Space Science Series (proceedings of conference held in Sydney on 8-13 July 2007

Green Functions for the Wrong-Sign Quartic

It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric explicitly, by truncation of the equations. Such a calculation has recently been carried out for various $PT$-symmetric theories, in both quantum mechanics and quantum field theory, including the wrong-sign quartic oscillator. For this particular theory the metric is known in closed form, making possible an independent check of these approximate results. We do so by numerically evaluating the ground-state wave-function for the equivalent Hermitian Hamiltonian and using this wave-function, in conjunction with the metric operator, to calculate the one- and two-point Green functions. We find that the Green functions evaluated by lowest-order truncation of the Schwinger-Dyson equations are already accurate at the (6-8)% level. This provides a strong justification for the method and a motivation for its extension to higher order and to higher dimensions, where the calculation of the metric is extremely difficult

Operator equations and Moyal products -- metrics in quasi-hermitian quantum mechanics

The Moyal product is used to cast the equation for the metric of a non-hermitian Hamiltonian in the form of a differential equation. For Hamiltonians of the form $p^2+V(ix)$ with $V$ polynomial this is an exact equation. Solving this equation in perturbation theory recovers known results. Explicit criteria for the hermiticity and positive definiteness of the metric are formulated on the functional level.Comment: References adde

On spherical averages of radial basis functions

A radial basis function (RBF) has the general form $$s(x)=\sum_{k=1}^{n}a_{k}\phi(x-b_{k}),\quad x\in\mathbb{R}^{d},$$ where the coefficients a 1,…,a n are real numbers, the points, or centres, b 1,…,b n lie in ℝ d , and φ:ℝ d →ℝ is a radially symmetric function. Such approximants are highly useful and enjoy rich theoretical properties; see, for instance (Buhmann, Radial Basis Functions: Theory and Implementations, [2003]; Fasshauer, Meshfree Approximation Methods with Matlab, [2007]; Light and Cheney, A Course in Approximation Theory, [2000]; or Wendland, Scattered Data Approximation, [2004]). The important special case of polyharmonic splines results when φ is the fundamental solution of the iterated Laplacian operator, and this class includes the Euclidean norm φ(x)=‖x‖ when d is an odd positive integer, the thin plate spline φ(x)=‖x‖2log  ‖x‖ when d is an even positive integer, and univariate splines. Now B-splines generate a compactly supported basis for univariate spline spaces, but an analyticity argument implies that a nontrivial polyharmonic spline generated by (1.1) cannot be compactly supported when d>1. However, a pioneering paper of Jackson (Constr. Approx. 4:243–264, [1988]) established that the spherical average of a radial basis function generated by the Euclidean norm can be compactly supported when the centres and coefficients satisfy certain moment conditions; Jackson then used this compactly supported spherical average to construct approximate identities, with which he was then able to derive some of the earliest uniform convergence results for a class of radial basis functions. Our work extends this earlier analysis, but our technique is entirely novel, and applies to all polyharmonic splines. Furthermore, we observe that the technique provides yet another way to generate compactly supported, radially symmetric, positive definite functions. Specifically, we find that the spherical averaging operator commutes with the Fourier transform operator, and we are then able to identify Fourier transforms of compactly supported functions using the Paley–Wiener theorem. Furthermore, the use of Haar measure on compact Lie groups would not have occurred without frequent exposure to Iserles’s study of geometric integration

A prehistoric Egyptian mummy: Evidence for an ‘embalming recipe’ and the evolution of early formative funerary treatments

Interdisciplinary scientific investigations utilising chemical analysis, shotgun metagenomics, textile analysis and radiocarbon dating have been applied to the study of an intact prehistoric Egyptian mummy, allowing insights into when this individual lived and died, and the funerary treatments employed in the preparation of the body. Here we present the first evidence for an extant prehistoric mummy that has undergone treatment with notably similar formative complex ‘balms’ that would later constitute the classic embalming recipes employed at the height of pharaonic mummification some 2500 years later. Making the informed assumption that the provenance of the Turin body was Gebelein, Qena or Luxor (Thebes), the findings offer the first indication that this type of funerary recipe was likely to have been employed over a wider geographical area at a time when the concept of a pan-Egyptian identity was supposedly still developing

Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity

Emphasizing the physical constraints on the formulation of a quantum theory based on the standard measurement axiom and the Schroedinger equation, we comment on some conceptual issues arising in the formulation of PT-symmetric quantum mechanics. In particular, we elaborate on the requirements of the boundedness of the metric operator and the diagonalizability of the Hamiltonian. We also provide an accessible account of a Krein-space derivation of the CPT-inner product that was widely known to mathematicians since 1950's. We show how this derivation is linked with the pseudo-Hermitian formulation of PT-symmetric quantum mechanics.Comment: published version, 17 page

Identification of a new snake fossil from the Canary Islands using micro-CT techniques

Abstract and keywords in English and SpanishThere are no native snakes on the Canary Islands today. The recovery of a boid vertebra from Miocene deposits on Fuertaventura suggested snakes could have been present in the past, but this single small vertebra could have reached the island from the nearby African continent in the gut of a bird. Now, however, the articulated remains of a snake have been found in a volcanic cave on Fuerteventura. The specimen is covered by a calcitic matrix and is of uncertain age. Given the fragility of the remains and the difficulty of removing the matrix, we used micro-Ct scans to make three-dimensional digital models for study. These reveal that the bones belong to a 'colubrid' snake. = En el Mioceno de las Islas Canarias se ha citado la presencia de una vértebra de boido, que por su pequeño temaño pudo haber llegado a las islas desde el cercano continente africano en el tracto digestivo de un ave. Sin embargo, en un tubo volcánico de Fuerteventura se han encontrado restos de vértebras y costillas articuladas, cubiertas por una capa de calcita y de edad incierta, que pertenecen a una seriente de la familia 'Colubridae'. Para su estudio, dadas la fragilidad de los restos y la dificultad para eliminar la calcita, se utilizó un escáner micro CT para obtener modelos digitales tridimensionales.Evans, S.E., Martín-González, E., Jones, M.E.H., Sánchez-Pinto, L. & García-Talavera, F

Crypto-unitary forms of quantum evolution operators

For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\neq G^\dagger$. A tradeoff analysis is performed recommending the latter option. The physical unitarity requirement is shown fulfilled in a suitable ad hoc representation of Hilbert space.Comment: 15 p