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Beurling densities of regular spectra of self-similar spectral measure with consecutive digit sets
Beurling density plays a key role in the study of frame-spectrality of
normalized Lebesgue measure restricted to a set. Accordingly, in this paper,
the authors study the -Beurling densities of regular maximal orthogonal sets
of a class of self-similar spectral measures, where is the Hausdorff
dimension of its support and obtain their exact upper bound of the densities
Constraints on primordial curvature power spectrum with pulsar timing arrays
The stochastic signal detected by NANOGrav, PPTA, EPTA, and CPTA can be
explained by the scalar-induced gravitational waves. In order to determine the
scalar-induced gravitational waves model that best fits the stochastic signal,
we employ both single- and double-peak parameterizations for the power spectrum
of the primordial curvature perturbations, where the single-peak scenarios
include the -function, box, lognormal, and broken power law model, and
the double-peak scenario is described by the double lognormal form. Using
Bayesian inference, we find that there is no significant evidence for or
against the single-peak scenario over the double-peak model, with (Bayes
factors) among these models . Therefore, we are not able
to distinguish the different shapes of the power spectrum of the primordial
curvature perturbation with the current sensitivity of pulsar timing arrays.Comment: 19 pages, 1 table, 7 figure
Is the late near-infrared bump in short-hard GRB 130603B due to the Li-Paczynski kilonova?
Short-hard gamma-ray bursts (GRBs) are widely believed to be produced by the
merger of two binary compact objects, specifically by two neutron stars or by a
neutron star orbiting a black hole. According to the Li-Paczynski kilonova
model, the merger would launch sub-relativistic ejecta and a
near-infrared/optical transient would then occur, lasting up to days, which is
powered by the radioactive decay of heavy elements synthesized in the ejecta.
The detection of a late bump using the {\em Hubble Space Telescope} ({\em HST})
in the near-infrared afterglow light curve of the short-hard GRB 130603B is
indeed consistent with such a model. However, as shown in this Letter, the
limited {\em HST} near-infrared lightcurve behavior can also be interpreted as
the synchrotron radiation of the external shock driven by a wide mildly
relativistic outflow. In such a scenario, the radio emission is expected to
peak with a flux of Jy, which is detectable for current radio
arrays. Hence, the radio afterglow data can provide complementary evidence on
the nature of the bump in GRB 130603B. It is worth noting that good
spectroscopy during the bump phase in short-hard bursts can test validity of
either model above, analogous to spectroscopy of broad-lined Type Ic supernova
in long-soft GRBs.Comment: 4 pages, 2 figures, published in ApJ Lette
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