13,534 research outputs found
Relativistic k-fields with Massless Soliton Solutions in 3+1 Dimensions
In this work, the relativistic non-standard Lagrangian densities (k-fields)
with massless solutions are generally introduced. Such solutions are not
necessarily energetically stable. However, in 3+1 dimensions, we introduce a
new k-field model that results in a single non-topological massless solitary
wave solution. This special solution is energetically stable; that is, any
arbitrary deformation above its background leads to an increase in the total
energy. In other words, its energy is zero which is the least energy in all
solutions. Hence, it can be called a massless soliton solution
Noncommutative QED+QCD and -function for QED
QED based on -unexpanded noncomutative space-time in contrast with
the noncommutative QED based on -expanded U(1) gauge theory via the
Seiberg-Witten map, is one-loop renormalizable. Meanwhile it suffers from
asymptotic freedom that is not in agreement with the experiment. We show that
QED part of gauge group as an appropriate gauge
group for the noncommutative QED+QCD, is not only one-loop renormalizable but
also has a function that can be positive, negative and even zero. In
fact the function depends on the mixing parameter as a
free parameter and it will be equal to its counterpart in the ordinary QED for
.Comment: 33 pages, 30 figures, to appear in PR
A Class of Nonconvex Penalties Preserving Overall Convexity in Optimization-Based Mean Filtering
mean filtering is a conventional, optimization-based method to
estimate the positions of jumps in a piecewise constant signal perturbed by
additive noise. In this method, the norm penalizes sparsity of the
first-order derivative of the signal. Theoretical results, however, show that
in some situations, which can occur frequently in practice, even when the jump
amplitudes tend to , the conventional method identifies false change
points. This issue is referred to as stair-casing problem and restricts
practical importance of mean filtering. In this paper, sparsity is
penalized more tightly than the norm by exploiting a certain class of
nonconvex functions, while the strict convexity of the consequent optimization
problem is preserved. This results in a higher performance in detecting change
points. To theoretically justify the performance improvements over
mean filtering, deterministic and stochastic sufficient conditions for exact
change point recovery are derived. In particular, theoretical results show that
in the stair-casing problem, our approach might be able to exclude the false
change points, while mean filtering may fail. A number of numerical
simulations assist to show superiority of our method over mean
filtering and another state-of-the-art algorithm that promotes sparsity tighter
than the norm. Specifically, it is shown that our approach can
consistently detect change points when the jump amplitudes become sufficiently
large, while the two other competitors cannot.Comment: Submitted to IEEE Transactions on Signal Processin
Nucleon-Nucleon Scattering in a Strong External Magnetic Field and the Neutrino Emissivity
The nucleon-nucleon scattering in a large magnetic background is considered
to find its potential to change the neutrino emissivity of the neutron stars.
For this purpose we consider the one-pion-exchange approximation to find the NN
cross-section in a background field as large as
. We show that the NN cross-section in
neutron stars with temperatures in the range 0.1-5 \texttt{MeV} can be changed
up to the one order of magnitude with respect to the one in the absence of the
magnetic field. In the limit of the soft neutrino emission the neutrino
emissivity can be written in terms of the NN scattering amplitude therefore the
large magnetic fields can dramatically change the neutrino emissivity of the
neutron stars as well.Comment: 21 pages, 5 figures, to appear in PR
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