44,535 research outputs found
On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations
Considered herein are the generalized Camassa-Holm and Degasperis-Procesi
equations in the spatially periodic setting. The precise blow-up scenarios of
strong solutions are derived for both of equations. Several conditions on the
initial data guaranteeing the development of singularities in finite time for
strong solutions of these two equations are established. The exact blow-up
rates are also determined. Finally, geometric descriptions of these two
integrable equations from non-stretching invariant curve flows in
centro-equiaffine geometries, pseudo-spherical surfaces and affine surfaces are
given.Comment: 26 page
Quantum secure direct communication based on supervised teleportation
We present a quantum secure direct communication(QSDC) scheme as an extension
for a proposed supervised secure entanglement sharing protocol. Starting with a
quick review on the supervised entanglement sharing protocol -- the "Wuhan"
protocol [Y. Li and Y. Liu, arXiv:0709.1449v2], we primarily focus on its
further extend using for a QSDC task, in which the communication attendant
Alice encodes the secret message directly onto a sequence of 2-level particles
which then can be faithfully teleported to Bob using the shared maximal
entanglement states obtained by the previous "Wuhan" protocol. We also evaluate
the security of the QSDC scheme, where an individual self-attack performed by
Alice and Bob -- the out of control attack(OCA) is introduced and the
robustness of our scheme on the OCA is documented.Comment: 5 pages, 1 table, oral contribution in the Conference on Quantum
Optics and Applications in Computing and Communications, Photonics Asia 2007,
Proc. of SPI
Light speed variation from gamma ray bursts: criteria for low energy photons
We examine a method to detect the light speed variation from gamma ray burst
data observed by the Fermi Gamma-ray Space Telescope (FGST). We suggest new
criteria to determine the characteristic time for low energy photons by the
energy curve and the average energy curve, and obtain similar results compared
with those from the light curve. We offer a new criterion with both the light
curve and the average energy curve to determine the characteristic time for low
energy photons. We then apply the new criteria to the GBM NaI data, the GBM BGO
data, and the LAT LLE data, and obtain consistent results for three different
sets of low energy photons from different FERMI detectors.Comment: 26 latex pages, 23 figures, final version for publicatio
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