28,462 research outputs found
A generalization of Bohr's Equivalence Theorem
Based on a generalization of Bohr's equivalence relation for general
Dirichlet series, in this paper we study the sets of values taken by certain
classes of equivalent almost periodic functions in their strips of almost
periodicity. In fact, the main result of this paper consists of a result like
Bohr's equivalence theorem extended to the case of these functions.Comment: Because of a mistake detected in one of the references, the previous
version of this paper has been modified by the authors to restrict the scope
of its application to the case of existence of an integral basi
Bohr's equivalence relation in the space of Besicovitch almost periodic functions
Based on Bohr's equivalence relation which was established for general
Dirichlet series, in this paper we introduce a new equivalence relation on the
space of almost periodic functions in the sense of Besicovitch,
, defined in terms of polynomial approximations. From
this, we show that in an important subspace , where Parseval's equality and Riesz-Fischer theorem
holds, its equivalence classes are sequentially compact and the family of
translates of a function belonging to this subspace is dense in its own class.Comment: Because of a mistake detected in one of the references, the
equivalence relation which is inspired by that of Bohr is revised to adapt
correctly the situation in the general case. arXiv admin note: text overlap
with arXiv:1801.0803
Optical absorption and energy-loss spectra of aligned carbon nanotubes
Optical-absorption cross-sections and energy-loss spectra of aligned
multishell carbon nanotubes are investigated, on the basis of photonic
band-structure calculations. A local graphite-like dielectric tensor is
assigned to every point of the tubules, and the effective transverse dielectric
function of the composite is computed by solving Maxwell's equations in media
with tensor-like dielectric functions. A Maxwell-Garnett-like approach
appropriate to the case of infinitely long anisotropic tubules is also
developed. Our full calculations indicate that the experimentally measured
macroscopic dielectric function of carbon nanotube materials is the result of a
strong electromagnetic coupling between the tubes. An analysis of the
electric-field pattern associated with this coupling is presented, showing that
in the close-packed regime the incident radiation excites a very localized
tangential surface plasmon.Comment: 7 pages, 12 figures, to appear in Eur. Phys. J.
Comment on "High Field Studies of Superconducting Fluctuations in High-Tc Cuprates. Evidence for a Small Gap distinct from the Large Pseudogap"
By using high magnetic field data to estimate the background conductivity,
Rullier-Albenque and coworkers have recently published [Phys.Rev.B 84, 014522
(2011)] experimental evidence that the in-plane paraconductivity in cuprates is
almost independent of doping. In this Comment we also show that, in contrast
with their claims, these useful data may be explained at a quantitative level
in terms of the Gaussian-Ginzburg-Landau approach for layered superconductors,
extended by Carballeira and coworkers to high reduced-temperatures by
introducing a total-energy cutoff [Phys.Rev.B 63, 144515 (2001)]. When
combined, these two conclusions further suggest that the paraconductivity in
cuprates is conventional, i.e., associated with fluctuating superconducting
pairs above the mean-field critical temperature.Comment: 9 pages, 1 figur
Limit to the radio emission from a putative central compact source in SN1993J
SN1993J in M81 is the best studied young radio-luminous supernova in the
Northern Hemisphere. We recently reported results from the analysis of a
complete set of VLBI observations of this supernova at 1.7, 2.3, 5.0, and 8.4
GHz, covering a time baseline of more than one decade. Those reported results
were focused on the kinematics of the expanding shock, the particulars of its
evolving non-thermal emission, the density profile of the circumstellar medium,
and the evolving free-free opacity by the supernova ejecta. In the present
paper, we complete our analysis by performing a search for any possible signal
from a compact source (i.e., a stellar-mass black hole or a young pulsar
nebula) at the center of the expanding shell. We have performed a stacking of
all our VLBI images at each frequency, after subtraction of our best-fit shell
model at each epoch, and measured the peak intensity in the stacked residual
image. Given the large amount of available global VLBI observations, the
stacking of all the residual images allows us to put upper limits to the
eventual emission of a putative compact central source at the level of
Jy at 5 GHz (or, more conservatively, Jy, if we
make a further correction for the ejecta opacity) and somewhat larger at other
wavelengths.Comment: 4 pages, 3 figures. Accepted for publication in A&
Quantum phase transitions in fully connected spin models: an entanglement perspective
We consider a set of fully connected spins models that display first- or
second-order transitions and for which we compute the ground-state entanglement
in the thermodynamical limit. We analyze several entanglement measures
(concurrence, R\'enyi entropy, and negativity), and show that, in general,
discontinuous transitions lead to a jump of these quantities at the transition
point. Interestingly, we also find examples where this is not the case.Comment: 9 pages, 7 figures, published versio
Atmospheric turbulence in phase-referenced and wide-field interferometric images: Application to the SKA
Phase referencing is a standard calibration procedure in radio
interferometry. It allows to detect weak sources by using quasi-simultaneous
observations of closeby sources acting as calibrators. Therefore, it is assumed
that, for each antenna, the optical paths of the signals from both sources are
similar. However, atmospheric turbulence may introduce strong differences in
the optical paths of the signals and affect, or even waste, phase referencing
for cases of relatively large calibrator-to-target separations and/or bad
weather. The situation is similar in wide-field observations, since the random
deformations of the images, mostly caused by atmospheric turbulence, have
essentially the same origin as the random astrometric variations of
phase-referenced sources with respect to the phase center of their calibrators.
In this paper, we present the results of a Monte Carlo study of the astrometric
precision and sensitivity of an interferometric array (a realization of the
Square Kilometre Array, SKA) in phase-referenced and wide-field observations.
These simulations can be extrapolated to other arrays by applying the
corresponding corrections. We consider several effects from the turbulent
atmosphere (i.e., ionosphere and wet component of the troposphere) and also
from the antenna receivers. We study the changes in dynamic range and
astrometric precision as a function of observing frequency, source separation,
and strength of the turbulence. We find that, for frequencies between 1 and 10
GHz, it is possible to obtain images with high fidelity, although the
atmosphere strongly limits the sensitivity of the instrument compared to the
case with no atmosphere. Outside this frequency window, the dynamic range of
the images and the accuracy of the source positions decrease. [...] (Incomplete
abstract. Please read manuscript.)Comment: 9 pages, 11 figures. Accepted for publication in A&A
Modified Whittle Estimation of Multilateral Models on a Lattice
In the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d >= 2, the achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the "edge effect", which worsens with increasing d. The other is the possible difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, due mainly to the Jacobian term. This is especially a problem in "multilateral" models, which are naturally expressed in terms of lagged values in both directions for one or more of the d dimensions. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the computational problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. The asymptotic regime allows increase in both directions of all d dimensions, with the central limit theorem established after re-ordering as a triangular array. However our work offers something new for "unilateral" models also. When the data are non-Gaussian, asymptotic variances of all parameter estimates may be affected, and we propose consistent, non-negative definite estimates of the asymptotic variance matrix.spatial data, multilateral modelling, Whittle estimation, edge effect, consistent variance estimation
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