Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati

A new approach to multi-frequency synthesis in radio interferometry

We present a new approach to multi-frequency synthesis in radio astronomy. Using Bayesian inference techniques, the new technique estimates the sky brightness and the spectral index simultaneously. In principle, the bandwidth of a wide-band observation can be fully exploited for sensitivity and resolution, currently only limited by higher order effects like spectral curvature. Employing this new approach, we further present a multi-frequency extension to the imaging algorithm RESOLVE. In simulations, this new algorithm outperforms current multi-frequency imaging techniques like MS-MF-CLEAN.Comment: 13 pages, 5 fugures, submitted to Astronomy and Astrophysic

Further Evidence that the Redshifts of AGN Galaxies May Contain Intrinsic Components

In the decreasing intrinsic redshift (DIR) model galaxies are assumed to be born as compact objects that have been ejected with large intrinsic redshift components, z_(i), out of the nuclei of mature AGN galaxies. As young AGN (quasars) they are initially several magnitudes sub-luminous to mature galaxies but their luminosity gradually increases over 10^8 yrs, as z_(i) decreases and they evolve into mature AGN (Seyferts and radio galaxies). Evidence presented here that low- and intermediate-redshift AGN are unquestionably sub-luminous to radio galaxies is then strong support for this model and makes it likely that the high-redshift AGN (quasars) are also sub-luminous, having simply been pushed above the radio galaxies on a logz-m_(v) plot by the presence of a large intrinsic component in their redshifts. An increase in luminosity below z = 0.06 is also seen. It is associated in the DIR model with an increase in luminosity as the sources mature but, if real, is difficult to interpret in the cosmological redshift (CR) model since at this low redshift it is unlikely to be associated with a higher star formation rate or an increase in the material used to build galaxies. Whether it might be possible in the CR model to explain these results by selection effects is also examined.Comment: 12 pages, 2 figures. Contains response to referees suggestions. (Accepted for ApJL

Fermi surface and superconductivity in low-density high-mobility {\delta}-doped SrTiO3

The electronic structure of low-density n-type SrTiO3 delta-doped heterostructures is investigated by angular dependent Shubnikov-de Haas oscillations. In addition to a controllable crossover from a three- to two-dimensional Fermi surface, clear beating patterns for decreasing dopant layer thicknesses are found. These indicate the lifting of the degeneracy of the conduction band due to subband quantization in the two-dimensional limit. Analysis of the temperature-dependent oscillations shows that similar effective masses are found for all components, associated with the splitting of the light electron pocket. The dimensionality crossover in the superconducting state is found to be distinct from the normal state, resulting in a rich phase diagram as a function of dopant layer thickness.Comment: 4 pages, 5 figures, submitted for publicatio

Leavitt path algebras satisfying a polynomial identity

Leavitt path algebras L of an arbitrary graph E over a field K satisfying a polynomial identity are completely characterized both in graph-theoretic and algebraic terms. When E is a finite graph, L satisfying a polynomial identity is shown to be equivalent to the Gelfand-Kirillov dimension of L being at most one, though this is no longer true for infinite graphs. It is shown that, for an arbitrary graph E, the Leavitt path algebra L has Gelfand-Kirillov dimension zero if and only if E has no cycles. Likewise, L has Gelfand-Kirillov dimension one if and only if E contains at least one cycle, but no cycle in E has an exit.Comment: 12 page

Unified criteria for multipartite quantum nonlocality

Wiseman and co-workers (Phys. Rev. Lett. 98, 140402, 2007) proposed a distinction between the nonlocality classes of Bell's nonlocality, steering and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.Comment: V2: corrected image display; V3: substantial changes including new proofs, arguments, and result

Testing non-local realism with entangled coherent states

We investigate the violation of non-local realism using entangled coherent states (ECS) under nonlinear operations and homodyne measurements. We address recently proposed Leggett-type inequalities, including a class of optimized incompatibility ones and thoroughly assess the effects of detection inefficiency.Comment: 7 pages, 6 figures, RevTeX4, accepted for publication in Phys. Rev.

Light Element Abundance Inhomogeneities in Globular Clusters: Probing Star Formation and Evolution in the Early Milky Way

Abundance patterns of the elements C, N, and O are sensitive probes of stellar nucleosynthesis processes and, in addition, O abundances are an important input for stellar age determinations. Understanding the nature of the observed distribution of these elements is key to constraining protogalactic star formation history. Patterns deduced from low-resolution spectroscopy of the CN, CH, NH, and CO molecules for low-mass stars in their core-hydrogen or first shell-hydrogen burning phases in the oldest ensembles known, the Galactic globular star clusters, are reviewed. New results for faint stars in NGC 104 (47 Tuc, C0021-723) reveal that the bimodal, anticorrelated pattern of CN and CH strengths found among luminous evolved stars is also present in stars nearing the end of their main-sequence lifetimes. In the absence of known mechanisms to mix newly synthesized elements from the interior to the observable surface layers of such unevolved stars, those particular inhomogeneities imply that the original material from which the stars formed some 15 billion years ago was chemically inhomogeneous in the C and N elements. However, in other clusters, observations of abundance ratios and C isotope ratios suggest that alterations to surface chemical compositions are produced as stars evolve from the main sequence through the red giant branch. Thus, the current observed distributions of C, N, and O among the brightest stars (those also observed most often) may not reflect the true distribution from which the protocluster cloud formed. The picture which is emerging of the C, N and O abundance patterns within globular clusters may be one whichComment: 12 pages in uuencoded compressed postscript (including figures), to appear in the Canadian Journal of Physics (Special Issue in Honor of G. Herzberg

Dominant mobility modulation by the electric field effect at the LaAlO_3 / SrTiO_3 interface

Caviglia et al. [Nature (London) 456, 624 (2008)] have found that the superconducting LaAlO_3 / SrTiO_3 interface can be gate modulated. A central issue is to determine the principal effect of the applied electric field. Using magnetotransport studies of a gated structure, we find that the mobility variation is almost five times as large as the sheet carrier density. Furthermore, superconductivity can be suppressed at both positive and negative gate bias. These results indicate that the relative disorder strength strongly increases across the superconductor-insulator transition.Comment: 4 pages, 4 figure