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

Complexity in complex analysis

We show that the classical kernel and domain functions associated to an n-connected domain in the plane are all given by rational combinations of three or fewer holomorphic functions of one complex variable. We characterize those domains for which the classical functions are given by rational combinations of only two or fewer functions of one complex variable. Such domains turn out to have the property that their classical domain functions all extend to be meromorphic functions on a compact Riemann surface, and this condition will be shown to be equivalent to the condition that an Ahlfors map and its derivative are algebraically dependent. We also show how many of these results can be generalized to finite Riemann surfaces.Comment: 30 pages, to appear in Advances in Mat

Particle acceleration by shocks in supernova remnants

Particle acceleration occurs on a range of scales from AU in the heliosphere to Mpc in clusters of galaxies and to energies ranging from MeV to EeV. A number of acceleration processes have been proposed, but diffusive shock acceleration (DSA) is widely invoked as the predominant mechanism. DSA operates on all these scales and probably to the highest energies. DSA is simple, robust and predicts a universal spectrum. However there are still many unknowns regarding particle acceleration. This paper focuses on the particular question of whether supernova remnants (SNR) can produce the Galactic CR spectrum up to the knee at a few PeV. The answer depends in large part on the detailed physics of diffusive shock acceleration.Comment: Invited talk at the 33rd International Cosmic Ray Conference, Rio de Janeiro, Brazil, 2-9 July 2013. Submitted for publication in a special issue of the Brazilian Journal of Physic

The Green's function and the Ahlfors map

The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected domain in the plane in terms of a single Ahlfors mapping of the domain, which is a proper holomorphic mapping of the domain onto the unit disc that is the analogue of the Riemann map in the multiply connected setting.Comment: 14 page

Cruise report 72-KB-21: Marine atlas survey

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Delayed-Type hypersensitivity to latex: Computational prediction of MHC class II epitopes on latex allergens

Delayed type hypersensitivity to natural rubber latex is rare compared to IgE mediated immediate reactions. Binding of allergens to MHC Class II is a crucial step in the presentation of antigens to CD4+ T Cells responsible for delayed reactions. Computational prediction of MHC class II epitopes on thirteen known latex allergens using SMM-align method revealed strong binding with several alleles. This shows that latex allergens are capable of initiating delayed type hypersensitivity in susceptible individuals.
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California commercial lobster fishery 1973-1974 season

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