On the Structure of the Observable Algebra of QCD on the Lattice

The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic $C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$ (factorized by a certain ideal).Comment: 33 page

A Categorical Approach to Groupoid Frobenius Algebras

In this paper, we show that \C{G}-Frobenius algebras (for \C{G} a finite groupoid) correspond to a particular class of Frobenius objects in the representation category of D(k[\C{G}]), where D(k[\C{G}]) is the Drinfeld double of the quantum groupoid k[\C{G}].Comment: final version; to appear in Applied Categorical Structure

Expanding e-MERLIN with the Goonhilly Earth Station

A consortium of universities has recently been formed with the goal of using the decommissioned telecommunications infrastructure at the Goonhilly Earth Station in Cornwall, UK, for astronomical purposes. One particular goal is the introduction of one or more of the ~30-metre parabolic antennas into the existing e-MERLIN radio interferometer. This article introduces this scheme and presents some simulations which quantify the improvements that would be brought to the e-MERLIN system. These include an approximate doubling of the spatial resolution of the array, an increase in its N-S extent with strong implications for imaging the most well-studied equatorial fields, accessible to ESO facilities including ALMA. It also increases the overlap between the e-MERLIN array and the European VLBI Network. We also discuss briefly some niche science areas in which an e-MERLIN array which included a receptor at Goonhilly would be potentially world-leading, in addition to enhancing the existing potential of e-MERLIN in its role as a Square Kilometer Array pathfinder instrument.Comment: 7 pages, 3 figures, to appear in the proceedings of "Astronomy with megastructures: Joint science with the E-ELT and SKA", 10-14 May 2010, Crete, Greece (Eds: Isobel Hook, Dimitra Rigopoulou, Steve Rawlings and Aris Karastergiou

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

The Dynamics of the M87 Globular Cluster System

We present the results from a study of the dynamics of the system of globular clusters around M87. After eliminating foreground galactic stars and background galaxies, we end up with a sample of 205 bona fide M87 globular clusters for which we have radial velocities determined from multi-slit spectra taken with the LRIS on the Keck Telescope. We find that the mean radial velocity of the M87 globular clusters agrees well with that of M87 itself, and that the velocity histogram is well represented by a Gaussian distribution. We find evidence for rotation in the globular cluster system. We find that the observed velocity dispersion of the M87 globular cluster system increases with radius from 270 \kms~ at $r$ = 9 kpc to $\approx$400 \kms~ at $r$ = 40 kpc. The inferred mass-to-light ratio in solar units increases from 5 at $r$ = 9 kpc to $\approx$30 at $r$ = 40 kpc with $M(r) \sim r^{1.7}$. The long slit optical spectroscopy near the center of M87 and the recent analysis of the ROSAT X-ray data are in good agreement with this analysis near the nucleus and in the outer parts of M87 respectively.Comment: 29 pages, TeX, with 6 Figures. Accepted for publication in the Ap

Very Low Levels of 25-Hydroxyvitamin D Are Not Associated With Immunologic Changes or Clinical Outcome in South African Patients With HIV-Associated Cryptococcal Meningitis

Background. Vitamin D deficiency is associated with impaired immune responses and increased susceptibility to a number of intracellular pathogens in individuals infected with human immunodeficiency virus (HIV). It is not known whether such an association exists with Cryptococcus neoformans. Methods. Levels of 25-hydroxyvitamin D (25[OH]D) were measured in 150 patients with cryptococcal meningitis (CM) and 150 HIV-infected controls in Cape Town, South Africa, and associations between vitamin D deficiency and CM were examined. The 25-hydroxyvitamin D levels and cryptococcal notifications were analyzed for evidence of reciprocal seasonality. Associations between 25(OH)D levels and disease severity, immune responses, and microbiological clearance were investigated in the patients with CM. Results. Vitamin D deficiency (plasma 25[OH]D ≤50 nmol/L) was present in 74% of patients. Vitamin D deficiency was not associated with CM (adjusted odds ratio, 0.93 [95% confidence interval, .6–1.6]; P = .796). Levels of 25(OH)D showed marked seasonality, but no reciprocal seasonality was seen in CM notifications. No significant associations were found between 25(OH)D levels and fungal burden or levels of tumor necrosis factor α, interferon γ, interleukin 6, soluble CD14, or neopterin in cerebrospinal fluid. Rates of fungal clearance did not vary according to vitamin D status. Conclusions. Vitamin D deficiency does not predispose to the development of CM, or lead to impaired immune responses or microbiological clearance in HIV-infected patients with CM

Goonhilly: a new site for e-MERLIN and the EVN

The benefits for the e-MERLIN and EVN arrays of using antennae at the satellite communication station at Goonhilly in Cornwall are discussed. The location of this site - new to astronomy - will provide an almost equal distribution of long baselines in the east-west- and north-south directions, and opens up the possibility to get significantly improved observations of equatorial fields with e-MERLIN. These additional baselines will improve the sensitivity on a set of critical spatial scales and will increase the angular resolution of e-MERLIN by a factor of two. e-MERLIN observations, including many allocated under the e-MERLIN Legacy programme, will benefit from the enhanced angular resolution and imaging capability especially for sources close to or below the celestial equator (where ESO facilities such as ALMA will operate) of including the Goonhilly telescopes. Furthermore, the baselines formed between Goonhilly and the existing stations will close the gap between the baselines of e-MERLIN and those of the European VLBI Network (EVN) and therefore enhance the legacy value of e-MERLIN datasets.Comment: 10 pages, 2 figue

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60

The environments of z~1 Active Galactic Nuclei at 3.6um

We present an analysis of a large sample of AGN environments at z~1 using stacked Spitzer data at 3.6um. The sample contains type-1 and type-2 AGN in the form of quasars and radio galaxies, and spans a large range in both optical and radio luminosity. We find, on average, that 2 to 3 massive galaxies containing a substantial evolved stellar population lie within a 200-300 kpc radius of the AGN, constituting a >8-sigma excess relative to the field. Secondly, we find evidence for the environmental source density to increase with the radio luminosity of AGN, but not with black-hole mass. This is shown first by dividing the AGN into their classical AGN types, where we see more significant over-densities in the fields of the radio-loud AGN. If instead we dispense with the classical AGN definitions, we find that the source over-density as a function of radio luminosity for all our AGN exhibits a positive correlation. One interpretation of this result is that the Mpc-scale environment is in some way influencing the radio emission that we observe from AGN. This could be explained by the confinement of radio jets in dense environments leading to enhanced radio emission or, alternatively, may be linked to more rapid black-hole spin brought on by galaxy mergers.Comment: 13 pages, 12 figures, accepted by MNRA

Economic analysis of hybrid renewable model for subtropical climate

Current power systems create environmental impacts due to utilization of fossil fuels, especially coal, as carbon dioxide is emitted into the atmosphere. In contrast to fossil fuels, renewable energy offers alternative sources of energy which are in general pollution free, technologically effective and environmentally sustainable. There is an increased interest in renewable energy, particularly solar and wind energy, which provides electricity without giving rise to carbon dioxide emissions. This paper presents economic analysis of a renewable hybrid system for a subtropical climate and also investigated the impact of renewable energy sources to the existing and future smart power system. The daily mean global solar irradiance and three hourly mean wind speed have been collected from the Rockhampton Aero Weather Station, Queensland (RAWS), Australia for this study. Hybrid Optimization Model for Electric Renewable (HOMER), a computer model developed by National Renewable Energy Laboratory (NREL) has been used to perform comparative analysis of solar and wind energy with diesel and hybrid systems. Initially total net present cost (NPC), cost of energy (COE) and the renewable fraction (RF) have been measured as performances metrics to compare the performances of different systems. For better optimization, the model has been refined with sensitivity analysis which explores performance variations due to wind speed, solar irradiation and diesel fuel prices. From the simulation, it is shown that there are a number of factors that impact the integration and performance of renewable energy sources to the power systems