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

Monotone Volume Formulas for Geometric Flows

We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a backwards reduced volume quantity, the former being non-increasing, the latter being non-decreasing along the flow. In the case where S=Ric is the Ricci curvature of M, the result corresponds to Perelman's well-known reduced volume monotonicity for the Ricci flow. Some other examples are given in the second section of this article, the main examples and motivation for this work being List's extended Ricci flow system, the Ricci flow coupled with harmonic map heat flow and the mean curvature flow in Lorentzian manifolds with nonnegative sectional curvatures. With our approach, we find new monotonicity formulas for these flows.Comment: v2: final version (as published

Mass of the black hole in the Seyfert 1.5 galaxy H 0507+164 from reverberation mapping

We present the results of our optical monitoring campaign of the X-ray source H 0507+164, a low luminosity Seyfert 1.5 galaxy at a redshift z = 0.018. Spectroscopic observations were carried out during 22 nights in 2007, from the 21 of November to the 26 of December. Photometric observations in the R-band for 13 nights were also obtained during the same period. The continuum and broad line fluxes of the galaxy were found to vary during our monitoring period. The R-band differential light curve with respect to a companion star also shows a similar variability. Using cross correlation analysis, we estimated a time delay of 3.01 days (in the rest frame), of the response of the broad H-beta line fluxes to the variations in the optical continuum at 5100 angstroms. Using this time delay and the width of the H-beta line, we estimated the radius for the Broad Line Region (BLR) of 2.53 x 10^{-3} parsec, and a black hole mass of 9.62 x 10^{6} solar mass.Comment: 7 pages, 8 figures, Accepted for publication in MNRA

Long-term EXOTIME photometry and follow-up spectroscopy of the sdB pulsator HS 0702+6043

Pulsating subdwarf B (sdB) stars oscillate in short-period p-modes or long-period g-modes. HS0702+6043 (DW Lyn) is one of a few objects to show characteristics of both types and is hence classified as hybrid pulsator. It is one of our targets in the EXOTIME program to search for planetary companions around extreme horizontal branch objects. In addition to the standard exercise in asteroseismology to probe the instantaneous inner structure of a star, measured changes in the pulsation frequencies as derived from an O-C diagram can be compared to theoretical evolutionary timescales. Based on the photometric data available so far, we are able to derive a high-resolution frequency spectrum and to report on our efforts to construct a multi-season O-C diagram. Additionally, we have gathered time-resolved spectroscopic data in order to constrain stellar parameters and to derive mode parameters as well as radial and rotational velocities.Comment: 2 pages, JENAM 2008 proceedings, to be published in 'Communications in Asteroseismology', 15

A Variable-Flavour Number Scheme for NNLO

At NNLO it is particularly important to have a Variable-Flavour Number Scheme (VFNS) to deal with heavy quarks because there are major problems with both the zero mass variable-flavour number scheme and the fixed-flavour number scheme. I illustrate these problems and present a general formulation of a Variable-Flavour Number Scheme (VFNS)for heavy quarks that is explicitly implemented up to NNLO in the strong coupling constant alpha_S, and may be used in NNLO global fits for parton distributions. The procedure combines elements of the ACOT(chi) scheme and the Thorne-Roberts scheme. Despite the fact that at NNLO the parton distributions are discontinuous as one changes the number of active quark flavours, all physical quantities are continuous at flavour transitions and the comparison with data is successful.Comment: 17 pages, 5 figures included as .ps files, uses axodraw. One additional explanatory sentence after eq. (25). Correction of typos and updated references. To be published in Phys. Rev.

Comment on ``Stripes and the t-J Model''

This is a comment being submitted to Physical Review Letters on a recent letter by Hellberg and Manousakis on stripes in the t-J model.Comment: One reference correcte

Reporting participation rates in studies of non-pharmacological interventions for patients with chronic obstructive pulmonary disease: a systematic review

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