27,713 research outputs found
A general product of tensors with applications
We define a general product of two -dimensional tensors and
with orders and , respectively. This product is
a generalization of the usual matrix product, and satisfies the associative
law. Using this product, many concepts and known results of tensors can be
simply expressed and/or proved, and a number of applications of this product
will be given. Using this tensor product and some properties on the resultant
of a system of homogeneous equations on variables, we define the similarity
and congruence of tensors (which are also the generalizations of the
corresponding relations for matrices), and prove that similar tensors have the
same characteristic polynomials. We study two special kinds of similarity:
permutational similarity and diagonal similarity, and their applications in the
study of the spectra of hypergraphs and nonnegative irreducible tensors. We
define the direct product of tensors (in matrix case it is also called the
Kronecker product), and give its applications in the study of the spectra of
two kinds of the products of hypergraphs. We also give applications of this
tensor product in the study of nonnegative tensors, including a
characterization of primitive tensors, the upper bounds of primitive degrees
and the cyclic indices of some nonnegative irreducible tensors.Comment: 17 page
Equidistribution theorems on strongly pseudoconvex domains
This work consists of two parts. In the first part, we consider a compact
connected strongly pseudoconvex CR manifold with a transversal CR
action. We establish an equidistribution theorem on zeros of CR functions. The
main techniques involve a uniform estimate of Szeg\H{o} kernel on . In the
second part, we consider a general complex manifold with a strongly
pseudoconvex boundary . By using classical result of Boutet de
Monvel-Sj\"ostrand about Bergman kernel asymptotics, we establish an
equidistribution theorem on zeros of holomorphic functions on .Comment: 26 page
A possible relation between flare activity in superluminous supernovae and gamma-ray bursts
Significant undulations appear in the light curve of a recently discovered
super-luminous supernova (SLSN) SN 2015bn after the first peak, while the
underlying profile of the light curve can be well explained by a continuous
energy supply from a central engine, possibly the spin-down of a millisecond
magnetar. We propose that these undulations are caused by an intermittent
pulsed energy supply, indicating an energetic flare activity of the central
engine of the SLSN. Many post-burst flares were discovered during X-ray
afterglow observations of Gamma-Ray Bursts (GRBs). We find that the SLSN flares
described here approximately obey the empirical correlation between the
luminosity and time scale of GRB flares, extrapolated to the relevant longer
time scales of SLSN flares. This confirms the possible connection between these
two different phenomena as previously suggested.Comment: 6 pages, 4 figures, accepted for publication in MNRA
Shock breakout driven by the remnant of a neutron star binary merger: An X-ray precursor of mergernova emission
A supra-massive neutron star (NS) spinning extremely rapidly could survive
from a merger of NS-NS binary. The spin-down of this remnant NS that is highly
magnetized would power the isotropic merger ejecta to produce a bright
mergernova emission in ultraviolet/optical bands. Before the mergernova, the
early interaction between the NS wind and the ejecta can drive a forward shock
propagating outwards into the ejecta. As a result, a remarkable amount of heat
can be accumulated behind the shock front and the final escaping of this heat
can produce a shock breakout emission. We describe the dynamics and thermal
emission of this shock with a semi-analytical model. It is found that sharp and
luminous breakout emission appears mainly in soft X-rays with a luminosity of
at a few hours after the merger, by leading the
mergernova emission as a precursor. Therefore, detection of such an X-ray
precursor would provide a smoking-gun evidence for identifying NS-powered
mergernovae and distinguishing them from the radioactive-powered ones (i.e.,
kilonovae or macronovae). The discovery of NS-powered mergernovae would finally
help to confirm the gravitational wave signals due to the mergers and the
existence of supra-massive NSs.Comment: 7 pages, 4 figures, accepted by Ap
Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space
The discovery of new four-dimensional black hole solutions presents a new
approach to understand the Gauss-Bonnet gravity in low dimensions. In this
paper, we test the Gauss-Bonnet gravity by studying the phase transition and
microstructures for the four-dimensional charged AdS black hole. In the
extended phase space, where the cosmological constant and the Gauss-Bonnet
coupling parameter are treated as thermodynamic variables, we find that the
thermodynamic first law and the corresponding Smarr formula are satisfied. Both
in the canonical ensemble and grand canonical ensemble, we observe the
small-large black hole phase transition, which is similar to the case of the
van der Walls fluid. This phase transition can also appear in the neutral black
hole system. Furthermore, we construct the Ruppeiner geometry, and find that
besides the attractive interaction, the repulsive interaction can also dominate
among the microstructures for the small black hole with high temperature in a
charged or neutral black hole system. This is quite different from the
five-dimensional neutral black hole, for which only dominant attractive
interaction can be found. The critical behaviors of the normalized scalar
curvature are also examined. These results will shed new light into the
characteristic property of four-dimensional Gauss-Bonnet gravity.Comment: 17 pages, 9 figures, and 2 tables, references added. Accepted for
publication in PR
Noncommutative Theory in Light of Neutrino Oscillation
Solar neutrino problem and atmospheric neutrino anomaly which are both
long-standing issues studied intensively by physicists in the past several
decades, are reckoned to be able to be solved simultaneously in the framework
of the assumption of the neutrino oscillation. For the presence of the Lorentz
invariance in the Standard Model, the massless neutrino can't have flavor
mixing and oscillation. However, we exploit the q-deformed noncommutative
theory to derive a general modified dispersion relation, which implies some
violation of the Lorentz invariance. Then it is found that the application of
the q-deformed dispersion relation to the neutrino oscillation can provide a
sound explanation for the current data from the reactor and long baseline
experiments.Comment: 8 pages,1 figure,Latex Fil
Computational Soundness Results for Stateful Applied pi Calculus
In recent years, many researches have been done to establish symbolic models
of stateful protocols. Two works among them, the SAPIC tool and StatVerif tool,
provide a high-level specification language and an automated analysis. Their
language, the stateful applied \pi-calculus, is extended from the applied
\pi-calculus by defining explicit state constructs. Symbolic abstractions of
cryptography used in it make the analysis amenable to automation. However, this
might overlook the attacks based on the algebraic properties of the
cryptographic algorithms. In our paper, we establish the computational
soundness results for stateful applied \pi-calculus used in SAPIC tool and
StatVerif tool.
In our approach, we build our results on the CoSP framework. For SAPIC, we
embed the non-monotonic protocol states into the CoSP protocols, and prove that
the resulting CoSP protocols are efficient. Through the embedding, we provide
the computational soundness result for SAPIC (by Theorem 1). For StatVerif, we
encode the StatVerif process into a subset of SAPIC process, and obtain the
computational soundness result for StatVerif (by Theorem 2). Our encoding shows
the differences between the semantics of the two languages. Our work inherits
the modularity of CoSP, which allows for easily extending the proofs to
specific cryptographic primitives. Thus we establish a computationally sound
automated verification result for the input languages of SAPIC and StatVerif
that use public-key encryption and signatures (by Theorem 3).Comment: to appear in POST 201
Area Spectrum of the Large AdS Black Hole from Quasinormal Modes
Using the new physical interpretation of quasinormal modes proposed by
Maggiore, we calculate the area and entropy spectra for the 3-dimensioal and
5-dimensional large AdS black holes. The spectra are obtained by imposing the
Bohr-Sommerfeld quantization condition to the adiabatic invariant quantity.
With this semiclassical method, we find that the spacings of the area and
entropy spectra are equidistant and independent of the AdS radius of the black
hole for both the cases. However, the spacings of the spectra are not the same
for different dimension of space-time. The equidistant area spectra will be
broken when the black hole has other parameters (i.e., charge and angular
momentum) or in a non-Einstein's gravity theory.Comment: 10 pages, no figure
Establishing a universal relation between gravitational waves and black hole lensing
Black hole lensing and gravitational waves are, respectively, closely
dependent of the property of the lens and radiation source. In this letter, a
universal relation between them is established for a rotating black hole acting
simultaneously as a lens and a gravitational wave source, in an asymptotically
flat spacetime. The relation only relies on the lens geometry and observable,
while is independent of the specific nature of the black hole. Therefore, the
possible gravitational wave sources could be located with modern astronomical
instrument from the side of the lensing without knowing the specific nature of
the black hole lens. Moreover, the low bound of the frequency of the
gravitational waves can also be well determined.Comment: 6 pages, 3 figure
Insight into the Microscopic Structure of an AdS Black Hole from Thermodynamical Phase Transition
Comparing with an ordinary thermodynamic system, we investigate the possible
microscopic structure of a charged anti-de Sitter black hole completely from
the thermodynamic viewpoint. The number density of the black hole molecules is
introduced to measure the microscopic degrees of freedom of the black hole. We
found that the number density suffers a sudden change accompanied by a latent
heat when the black hole system crosses the small-large black hole coexistence
curve, while when the system passes the critical point, it encounters a
second-order phase transition with a vanishing latent heat due to the
continuous change of the number density. Moreover, the thermodynamic scalar
curvature suggests that there is a weak attractive interaction between two
black hole molecules. These phenomena might cast new insight into the
underlying microscopic structure of a charged anti-de Sitter black hole.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let
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