270 research outputs found
De Branges spaces and Krein's theory of entire operators
This work presents a contemporary treatment of Krein's entire operators with
deficiency indices and de Branges' Hilbert spaces of entire functions.
Each of these theories played a central role in the research of both renown
mathematicians. Remarkably, entire operators and de Branges spaces are
intimately connected and the interplay between them has had an impact in both
spectral theory and the theory of functions. This work exhibits the
interrelation between Krein's and de Branges' theories by means of a functional
model and discusses recent developments, giving illustrations of the main
objects and applications to the spectral theory of difference and differential
operators.Comment: 37 pages, no figures. The abstract was extended. Typographical errors
were corrected. The bibliography style was change
Plasma wave instabilities induced by neutrinos
Quantum field theory is applied to study the interaction of an electron
plasma with an intense neutrino flux. A connection is established between the
field theory results and classical kinetic theory. The dispersion relation and
damping rate of the plasma longitudinal waves are derived in the presence of
neutrinos. It is shown that Supernova neutrinos are never collimated enough to
cause non-linear effects associated with a neutrino resonance. They only induce
neutrino Landau damping, linearly proportional to the neutrino flux and
.Comment: 18 pages, 3 figures, title and references correcte
The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case
We present a technique for reconstructing a semi-infinite Jacobi operator in
the limit circle case from the spectra of two different self-adjoint
extensions. Moreover, we give necessary and sufficient conditions for two real
sequences to be the spectra of two different self-adjoint extensions of a
Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result
Collective Modes in Neutrino `Beam' Electron-Positron Plasma Interactions
We derive semiclassical neutrino-electron transport equations in the
collisionless (Vlasov) limit from the coupled Dirac equations, incorporating
the charged and neutral weak current-current as well as electromagnetic
interactions. A corresponding linear response theory is derived. In particular,
we calculate the response functions for a variety of beam-plasma geometries,
which are of interest in a supernova scenario. We apply this to the study of
plasmons and to a new class of collective {\it pharon} resonance modes, which
are characterized by . We find that the growth rates of the
unstable modes correspond to a strongly temperature ()
and linearly momentum dependent e-folding length of about km under
typical conditions for Type II supernovae. This appears to rule out such
long-wavelength collective modes as an efficient means of depositing neutrino
energy into the plasma sphere.Comment: 27 pages; LaTex. Replaced by published version. - Appendix about
neutrino Wigner functions added and main text correspondingly revised.
Conclusions unchange
A hyperchaotic system without equilibrium
Abstract: This article introduces a new chaotic system of 4-D autonomous ordinary differential equations, which has no equilibrium. This system shows a hyper-chaotic attractor. There is no sink in this system as there is no equilibrium. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. There is little difference between this chaotic system and other chaotic systems with one or several equilibria shown by phase portraits, Lyapunov exponents and time series methods, but the Poincaré maps show this system is a chaotic system with more complicated dynamics. Moreover, the circuit realization is also presented
Electromagnetic properties of a neutrino stream
In a medium that contains a neutrino background in addition to the matter
particles, the neutrinos contribute to the photon self-energy as a result of
the effective electromagnetic vertex that they acquire in the presence of
matter. We calculate the contribution to the photon self-energy in a dense
plasma, due to the presence of a gas of charged particles, or neutrinos, that
moves as a whole relative to the plasma. General formulas for the transverse
and longitudinal components of the photon polarization tensor are obtained in
terms of the momentum distribution functions of the particles in the medium,
and explicit results are given for various limiting cases of practical
interest. The formulas are used to study the electromagnetic properties of a
plasma that contains a beam of neutrinos. The transverse and longitudinal
photon dispersion relations are studied in some detail. Our results do not
support the idea that neutrino streaming instabilities can develop in such a
system. We also indicate how the phenomenon of optical activity of the neutrino
gas is modified due to the velocity of the neutrino background relative to the
plasma. The general approach and results can be adapted to similar problems
involving relativistic plasmas and high-temperature gauge theories in other
environments.Comment: Revtex, 19 pages and 3 included ps file
Spontaneous abortion and ectopic pregnancy: Case definition & guidelines for data collection, analysis, and presentation of maternal immunization safety data
Modelo hierárquico bayesiano aplicado na avaliação genética de curvas de crescimento de bovinos de corte
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