44,680 research outputs found
Boundary smoothness of analytic functions
We consider the behaviour of holomorphic functions on a bounded open subset
of the plane, satisfying a Lipschitz condition with exponent , with
, in the vicinity of an exceptional boundary point where all such
functions exhibit some kind of smoothness. Specifically, we consider the
relation between the abstract idea of a bounded point derivation on the algebra
of such functions and the classical complex derivative evaluated as a limit of
difference quotients. We obtain a result which applies, for example, when the
open set admits an interior cone at the special boundary point.Comment: 14 pages. This revision corrects a misprint on p.12: In equation (3),
should have been . Also a misprint on page 14 in the
formula for . The validity of the argument is not affected and the
result stand
Nonperturbative QCD, gauge-fixing, Gribov copies, and the lattice
Perturbative QCD uses the Faddeev-Popov gauge-fixing procedure, which leads
to ghosts and the local BRST invariance of the gauge-fixed perturbative QCD
action. In the asymptotic regime, where perturbative QCD is relevant, Gribov
copies can be neglected. In the nonperturbative regime, one must adopt either a
nonlocal Gribov-copy free gauge (e.g., Laplacian gauge) or attempt to maintain
local BRST invariance at the expense of admitting Gribov copies. These issues
are explored. In addition, we discuss the relationship between recent
Dyson-Schwinger based model calculations of the infrared behavior of QCD
Green's functions and the lattice calculation of these quantities.Comment: 9 pages, 2 figures, to appear in Prog. Theor. Phys. Suppl. in the
proceedings of the Tokyo-Adelaide Joint Workshop on Quarks, Astrophysics and
Space Physic
ELSA and the frontiers of astrometry
ELSA stands for the ambitious goal of `European Leadership in Space
Astrometry'. In this closing contribution I will examine how the ELSA network
has advanced this goal. I also look ahead to the time when the Gaia data will
be published and consider what needs to be done to maintain European
leadership.Comment: Closing remarks at the ELSA conference "Gaia: at the frontiers of
astrometry". Proceedings editors: C. Turon, F. Arenou & F. Meynadie
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