1,896 research outputs found
On Symplectic Coverings of the Projective Plane
We prove that a resolution of singularities of any finite covering of the
projective plane branched along a Hurwitz curve and, maybe, along a
line "at infinity" can be embedded as a symplectic submanifold into some
projective algebraic manifold equipped with an integer K\"{a}hler symplectic
form (assuming that if has negative nodes, then the covering is
non-singular over them). For cyclic coverings we can realize this embeddings
into a rational algebraic 3--fold. Properties of the Alexander polynomial of
are investigated and applied to the calculation of the first Betti
number of a resolution of singularities of
-sheeted cyclic coverings of branched along
and, maybe, along a line "at infinity". We prove that is even
if is an irreducible Hurwitz curve but, in contrast to the algebraic
case, that it can take any non-negative value in the case when
consists of several irreducible components.Comment: 42 page
Cosmic Rays from Gamma Ray Bursts in the Galaxy
The rate of terrestrial irradiation events by galactic gamma-ray bursts
(GRBs) is estimated using recent standard-energy results. We assume that GRBs
accelerate high-energy cosmic rays, and present results of three-dimensional
simulations of cosmic rays moving in the Galactic magnetic field and diffusing
through pitch-angle scattering. An on-axis GRB extinction event begins with a
powerful prompt gamma-ray and neutron pulse, followed by a longer-lived phase
from cosmic-ray protons and neutron-decay protons that diffuse towards Earth.
Our results force a reinterpretation of reported ~ 10^{18} eV cosmic-ray
anisotropies and offer a rigorous test of the model where high-energy cosmic
rays originate from GRBs, which will soon be tested with the Auger Observatory.Comment: 9 pages, 4 figures, ApJ Letters, in press. Clarified limit of
test-particle approximation, prediction that Auger will not confirm SUGAR
source. (Data may not appear onscreen at low magnification.) Simulations at
http://heseweb.nrl.navy.mil/gamma/~dermer/invest/sim/index.ht
High energy cosmic-ray interactions with particles from the Sun
Cosmic-ray protons with energies above eV passing near the Sun may
interact with photons emitted by the Sun and be excited to a
resonance. When the decays, it produces pions which further decay to
muons and photons which may be detected with terrestrial detectors. A flux of
muons, photon pairs (from decay), or individual high-energy photons
coming from near the Sun would be a rather striking signature, and the flux of
these particles is a fairly direct measure of the flux of cosmic-ray nucleons,
independent of the cosmic-ray composition. In a solid angle within
around the Sun the flux of photon pairs is about \SI{1.3e-3}{}
particles/(kmyr), while the flux of muons is about \SI{0.33e-3}{}
particles/(kmyr). This is beyond the reach of current detectors like
the Telescope Array, Auger, KASCADE-Grande or IceCube. However, the muon flux
might be detectable by next-generation air shower arrays or neutrino detectors
such as ARIANNA or ARA. We discuss the experimental prospects in some detail.
Other cosmic-ray interactions occuring close to the Sun are also briefly
discussed.Comment: 8 pages, 11 figure
A MULTILAYERED PLATE ELEMENTS ACCOUNTING NODE-DEPENDENT KINEMATICS FOR STATIC ANALYSIS OF PIEZOELECTRIC STRUCTURES
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