11,682 research outputs found
On coherent systems of type (n,d,n+1) on Petri curves
We study coherent systems of type on a Petri curve of genus
. We describe the geometry of the moduli space of such coherent systems
for large values of the parameter . We determine the top critical value
of and show that the corresponding ``flip'' has positive codimension.
We investigate also the non-emptiness of the moduli space for smaller values of
, proving in many cases that the condition for non-emptiness is the
same as for large . We give some detailed results for and
applications to higher rank Brill-Noether theory and the stability of kernels
of evaluation maps, thus proving Butler's conjecture in some cases in which it
was not previously known.Comment: 33 page
A 300 GHz "Always-in-Focus" Focusing System for Target Detection
A focusing system for a 300 GHz radar with 5 m target distance and 10 mm diameter spot size resolution is proposed. The focusing system is based on a Gaussian telescope scheme and its main parameters have been de¬signed using Gaussian beam quasi-optical propagation theory with an in-house developed MATLAB® based analysis tool. Then, this approach has been applied to a real focusing system based on two elliptical mirrors in order to reduce the distortion and cross-polar level and a plane mirror to provide scanning capabilities. The over¬all system has been simulated with a full-wave electromag¬netic simulator and its behavior is presented. With this approach, the focusing system always works "in-focus" since the only mirror that is rotated when scanning is the output plane mirror, so the beam is almost not distorted. The design process, although based in the well-known Gaussian beam quasi-optical propagation theory, provides a fast and accurate method and minimizes the overall size of the mirrors. As a consequence, the size of the focusing system is also reduced
An Effective Field Theory Look at Deep Inelastic Scattering
This talk discusses the effective field theory view of deep inelastic
scattering. In such an approach, the standard factorization formula of a hard
coefficient multiplied by a parton distribution function arises from matching
of QCD onto an effective field theory. The DGLAP equations can then be viewed
as the standard renormalization group equations that determines the cut-off
dependence of the non-local operator whose forward matrix element is the parton
distribution function. As an example, the non-singlet quark splitting functions
is derived directly from the renormalization properties of the non-local
operator itself. This approach, although discussed in the literature, does not
appear to be well known to the larger high energy community. In this talk we
give a pedagogical introduction to this subject.Comment: 11 pages, 1 figure, To appear in Modern Physics Letters
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