A weak*-topological dichotomy with applications in operator theory

Denote by $[0,\omega_1)$ the locally compact Hausdorff space consisting of all countable ordinals, equipped with the order topology, and let $C_0[0,\omega_1)$ be the Banach space of scalar-valued, continuous functions which are defined on $[0,\omega_1)$ and vanish eventually. We show that a weakly$^*$ compact subset of the dual space of $C_0[0,\omega_1)$ is either uniformly Eberlein compact, or it contains a homeomorphic copy of the ordinal interval $[0,\omega_1]$. Using this result, we deduce that a Banach space which is a quotient of $C_0[0,\omega_1)$ can either be embedded in a Hilbert-generated Banach space, or it is isomorphic to the direct sum of $C_0[0,\omega_1)$ and a subspace of a Hilbert-generated Banach space. Moreover, we obtain a list of eight equivalent conditions describing the Loy-Willis ideal, which is the unique maximal ideal of the Banach algebra of bounded, linear operators on $C_0[0,\omega_1)$. As a consequence, we find that this ideal has a bounded left approximate identity, thus resolving a problem left open by Loy and Willis, and we give new proofs, in some cases of stronger versions, of several known results about the Banach space $C_0[0,\omega_1)$ and the operators acting on it.Comment: accepted to Transactions of the London Mathematical Societ

Do functional traits improve prediction of predation rates for a disparate group of aphid predators?

Aphid predators are a systematically disparate group of arthropods united on the basis that they consume aphids as part of their diet. In Europe, this group includes Araneae, Opiliones, Heteroptera, chrysopids, Forficulina, syrphid larvae, carabids, staphylinids, cantharids and coccinellids. This functional group has no phylogenetic meaning but was created by ecologists as a way of understanding predation, particularly for conservation biological control. We investigated whether trait-based approaches could bring some cohesion and structure to this predator group. A taxonomic hierarchy-based null model was created from taxonomic distances in which a simple multiplicative relationship described the Linnaean hierarchies (species, genera, etc.) of fifty common aphid predators. Using the same fifty species, a functional groups model was developed using ten behavioural traits (e.g. polyphagy, dispersal, activity, etc.) to describe the way in which aphids were predated in the field. The interrelationships between species were then expressed as dissimilarities within each model and separately analysed using PROXSCAL, a multidimensional scaling (MDS) program. When ordinated using PROXSCAL and then statistically compared using Procrustes analysis, we found that only 17% of information was shared between the two configurations. Polyphagy across kingdoms (i.e. predatory behaviour across animal, plant and fungi kingdoms) and the ability to withstand starvation over days, weeks and months were particularly divisive within the functional groups model. Confirmatory MDS indicated poor prediction of aphid predation rates by the configurations derived from either model. The counterintuitive conclusion was that the inclusion of functional traits, pertinent to the way in which predators fed on aphids, did not lead to a large improvement in the prediction of predation rate when compared to the standard taxonomic approach

Angled decompositions of arborescent link complements

This paper describes a way to subdivide a 3-manifold into angled blocks, namely polyhedral pieces that need not be simply connected. When the individual blocks carry dihedral angles that fit together in a consistent fashion, we prove that a manifold constructed from these blocks must be hyperbolic. The main application is a new proof of a classical, unpublished theorem of Bonahon and Siebenmann: that all arborescent links, except for three simple families of exceptions, have hyperbolic complements.Comment: 42 pages, 23 figures. Slightly expanded exposition and reference

Observations of pre-stellar cores

Our understanding of the physical and chemical structure of pre-stellar cores, the simplest star-forming sites, has significantly improved since the last IAU Symposium on Astrochemistry (South Korea, 1999). Research done over these years has revealed that major molecular species like CO and CS systematically deplete onto dust grains at the interior of pre-stellar cores, while species like N2H+ and NH3 survive in the gas phase and can usually be detected towards the core centers. Such a selective behaviour of molecular species gives rise to a differentiated (onion-like) chemical composition, and manifests itself in molecular maps as a dichotomy between centrally peaked and ring-shaped distributions. From the point of view of star-formation studies, the identification of molecular inhomogeneities in cores helps to resolve past discrepancies between observations made using different tracers, and brings the possibility of self-consistent modelling of the core internal structure. Here I present recent work on determining the physical and chemical structure of two pre-stellar cores, L1498 and L1517B, using observations in a large number of molecules and Monte Carlo radiative transfer analysis. These two cores are typical examples of the pre-stellar core population, and their chemical composition is characterized by the presence of large freeze out holes in most molecular species. In contrast with these chemically processed objects, a new population of chemically young cores has started to emerge. The characteristics of its most extreme representative, L1521E, are briefly reviewed.Comment: 10 pages, 5 figures. To appear in IAU 231 conf. proc. "Astrochemistry: Recent Successes and Current Challenges," eds. D.C. Lis, G.A. Blake, and E. Herbs

Rational homotopy theory: a brief introduction

These notes contain a brief introduction to rational homotopy theory: its model category foundations, the Sullivan model and interactions with the theory of local commutative rings.Comment: A slight revision (some minor errors corrected) of lecture notes from a minicourse given in the summer school "Interactions between Homotopy Theory and Algebra," August 2004. (28 pages

The Evolution of Radio Loud Active Galactic Nuclei as a Function of Black Hole Spin

Recent work on the engines of active galactic nuclei jets suggests their power depends strongly and perhaps counter-intuitively on black hole spin. We explore the consequences of this on the radio-loud population of active galactic nuclei and find that the time evolution of the most powerful radio galaxies and radio-loud quasars fits into a picture in which black hole spin varies from retrograde to prograde with respect to the accreting material. Unlike the current view, according to which jet powers decrease in tandem with a global downsizing effect, we argue for a drop in jet power resulting directly from the paucity of retrograde accretion systems at lower redshift $z$ caused by a continuous history of accretion dating back to higher $z$. In addition, the model provides simple interpretations for the basic spectral features differentiating radio-loud and radio-quiet objects, such as the presence or absence of disk reflection, broadened iron lines and signatures of disk winds. We also briefly describe our models' interpretation of microquasar state transitions. We highlight our result that the most radio-loud and most radio-quiet objects both harbor highly spinning black holes but in retrograde and prograde configurations, respectively.Comment: MNRAS accepte

The extreme flare in III Zw 2: Evolution of a radio jet in a Seyfert galaxy

A very detailed monitoring of a radio flare in the Seyfert I galaxy III Zw 2 with the VLA and the VLBA is presented. The relative astrometry in the VLBA observations was precise on a level of a few microarcseconds. Spectral and spatial evolution of the source are closely linked and these observations allowed us to study in great detail a textbook example of a synchrotron self-absorbed jet. We observe a phase where the jet gets frustrated, without expansion and no spectral evolution. Then the jet breaks free and starts to expand with apparent superluminal motion. This expansion is accompanied by a strong spectral evolution. The results are a good confirmation of synchrotron theory and equipartition for jets.Comment: Astronomy & Astrophysics, accepted, 11 pages, 14 Figures, also available at http://www.jive.nl/~brunthal/pub.shtm