Multilateral inversion of A_r, C_r and D_r basic hypergeometric series

In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series. This matrix inversion result was directly extracted from an instance of Bailey's very-well-poised 6-psi-6 summation theorem, and involves two infinite matrices which are not lower-triangular. The present paper features three different multivariable generalizations of the above result. These are extracted from Gustafson's A_r and C_r extensions and of the author's recent A_r extension of Bailey's 6-psi-6 summation formula. By combining these new multidimensional matrix inverses with A_r and D_r extensions of Jackson's 8-phi-7 summation theorem three balanced very-well-poised 8-psi-8 summation theorems associated with the root systems A_r and C_r are derived.Comment: 24 page

Summation and transformation formulas for elliptic hypergeometric series

Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.Comment: 21 pages, AMS-LaTe

Radio Emission from the Composite Supernova Remnant G326.3-1.8 (MSH15-56)

High resolution radio observations of the composite supernova remnant (SNR) G326.3-1.8 or MSH 15-56 with the Australia Telescope Compact Array show details of both the shell and the bright plerion which is offset about 1/3 of the distance from the center of the SNR to the shell. The shell appears to be composed of thin filaments, typical of older shell SNRs. The central part of the elongated plerion is composed of a bundle of parallel ridges which bulge out at the ends and form a distinct ring structure on the northwestern end. The magnetic field with a strength of order 45 microGauss, is directed along the axis of the ridges but circles around the northwestern ring. This plerion is large and bright in the radio but is not detected in x-ray or optical wavelengths. There is, however, a faint hard x-ray feature closer to the shell outside the plerion. Perhaps if the supernova explosion left a rapidly moving magnetar with large energy input but initially rapid decay of both relativistic particles and magnetic field, the observed differences with wavelength could be explained.Comment: 15 pages, 10 figures, accepted by Ap

Quantum steering ellipsoids, extremal physical states and monogamy

A Corrigendum for this article has been published in 2015 New J. Phys. 17 019501Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for steering that are strictly stronger than the Coffman-Kundu- Wootters (CKW) inequality for monogamy of concurrence. The CKW result is thus found to follow from the simple perspective of steering ellipsoid geometry. Remarkably, we can also use steering ellipsoids to derive non-trivial results in classical Euclidean geometry, extending Eulers inequality for the circumradius and inradius of a triangle.The EPSRC and the ARC Centre of Excellence grant no. CE110001027. DJ is funded by the Royal Society. TR would like to thank the Leverhulme Trust. SJ acknowledges EPSRC grant EP/ K022512/1

IC 4406: a radio-infrared view

IC 4406 is a large (about 100'' x 30'') southern bipolar planetary nebula, composed of two elongated lobes extending from a bright central region, where there is evidence for the presence of a large torus of gas and dust. We show new observations of this source performed with IRAC (Spitzer Space Telescope) and the Australia Telescope Compact Array. The radio maps show that the flux from the ionized gas is concentrated in the bright central region and originates in a clumpy structure previously observed in H_alpha, while in the infrared images filaments and clumps can be seen in the extended nebular envelope, the central region showing toroidal emission. Modeling of the infrared emission leads to the conclusion that several dust components are present in the nebula.Comment: 22 pages, 7 figures, accepted for publication in The Astrophysical Journal; v.2 has changes in both figures and content; preprint forma

A high-resolution radio survey of the Vela supernova remnant

This paper presents a high-resolution radio continuum (843 MHz) survey of the Vela supernova remnant. The contrast between the structures in the central pulsar-powered nebula of the remnant and the synchrotron radiation shell allows the remnant to be identified morphologically as a member of the composite class. The data are the first of a composite remnant at spatial scales comparable with those available for the Cygnus Loop and the Crab Nebula, and make possible a comparison of radio, optical and soft X-ray emission from the resolved shell filaments. The survey, made with the Molonglo Observatory Synthesis Telescope, covers an area of 50 square degrees at a resolution of 43'' x 60'', while imaging structures on scales up to 30'.Comment: 18 pages, 7 jpg figures (version with ps figures at http://astro.berkeley.edu/~dbock/papers/); AJ, in pres

Evidence of a Curved Synchrotron Spectrum in the Supernova Remnant SN 1006

A joint spectral analysis of some Chandra ACIS X-ray data and Molonglo Observatory Synthesis Telescope radio data was performed for 13 small regions along the bright northeastern rim of the supernova remnant SN 1006. These data were fitted with a synchrotron radiation model. The nonthermal electron spectrum used to compute the photon emission spectra is the traditional exponentially cut off power law, with one notable difference: The power-law index is not a constant. It is a linear function of the logarithm of the momentum. This functional form enables us to show, for the first time, that the synchrotron spectrum of SN 1006 seems to flatten with increasing energy. The effective power-law index of the electron spectrum is 2.2 at 1 GeV (i.e., radio synchrotron-emitting momenta) and 2.0 at about 10 TeV (i.e., X-ray synchrotron-emitting momenta). This amount of change in the index is qualitatively consistent with theoretical models of the amount of curvature in the proton spectrum of the remnant. The evidence of spectral curvature implies that cosmic rays are dynamically important instead of being "test" particles. The spectral analysis also provides a means of determining the critical frequency of the synchrotron spectrum associated with the highest-energy electrons. The critical frequency seems to vary along the northeastern rim, with a maximum value of 1.1e17 (0.6e17 - 2.1e17) Hz. This value implies that the electron diffusion coefficient can be no larger than a factor of ~4.5-21 times the Bohm diffusion coefficient if the velocity of the forward shock is in the range 2300-5000 km/s. Since the coefficient is close to the Bohm limit, electrons are accelerated nearly as fast as possible in the regions where the critical frequency is about 1.0e17 Hz.Comment: 41 pages, 8 figures, accepted by Ap

Toxoplasma gondii: An Underestimated Threat?

Traditionally, the protozoan parasite Toxoplasma gondii has been thought of as relevant to public health primarily within the context of congenital toxoplasmosis or postnatally acquired disease in immunocompromised patients. However, latent T. gondii infection has been increasingly associated with a wide variety of neuropsychiatric disorders and, more recently, causal frameworks for these epidemiological associations have been proposed. We present assimilated evidence on the associations between T. gondii and various human neuropsychiatric disorders and outline how these may be explained within a unifying causal framework. We argue that the occult effects of latent T. gondii infection likely outweigh the recognised overt morbidity caused by toxoplasmosis, substantially raising the public health importance of this parasite. [Abstract copyright: Copyright © 2020 Elsevier Ltd. All rights reserved.

Chabauty-Coleman experiments for genus 3 hyperelliptic curves

We describe a computation of rational points on genus 3 hyperelliptic curves $C$ defined over $\mathbb{Q}$ whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty and Coleman, we present and implement an algorithm in Sage to compute the zero locus of two Coleman integrals and analyze the finite set of points cut out by the vanishing of these integrals. We run the algorithm on approximately 17,000 curves from a forthcoming database of genus 3 hyperelliptic curves and discuss some interesting examples where the zero set includes global points not found in $C(\mathbb{Q})$.Comment: 18 page