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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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