12,435 research outputs found
Harnack Inequalities for Stochastic Equations Driven by L\'evy Noise
By using coupling argument and regularization approximations of the
underlying subordinator, dimension-free Harnack inequalities are established
for a class of stochastic equations driven by a L\'evy noise containing a
subordinate Brownian motion. The Harnack inequalities are new even for linear
equations driven by L\'evy noise, and the gradient estimate implied by our
log-Harnack inequality considerably generalizes some recent results on gradient
estimates and coupling properties derived for L\'evy processes or linear
equations driven by L\'evy noise. The main results are also extended to
semi-linear stochastic equations in Hilbert spaces.Comment: 15 page
Perturbations of Functional Inequalities for L\'evy Type Dirichlet Forms
Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy
type Dirichlet forms are studied. When the range of jumps is finite our results
are natural extensions to the corresponding ones derived earlier for diffusion
processes; and we show that the study for the situation with infinite range of
jumps is essentially different. Some examples are presented to illustrate the
optimality of our results
The focusing of electron flow in a bipolar Graphene ribbon with different chiralities
The focusing of electron flow in a symmetric p-n junction (PNJ) of graphene
ribbon with different chiralities is studied. Considering the PNJ with the
sharp interface, in a armchair ribbon, the electron flow emitting from
in n-region can always be focused perfectly at in p-region in the whole
Dirac fermion regime, i.e. in whole regime where is the distance
between Dirac-point energy and Fermi energy and is the nearest hopping
energy. For the bipolar ribbon with zigzag edge, however, the incoming electron
flow in n-region is perfectly converged in p-region only in a very low energy
regime with . Moreover, for a smooth PNJ, electrons are
backscattered near PNJ, which weakens the focusing effect. But the focusing
pattern still remains the same as that of the sharp PNJ. In addition, quantum
oscillation in charge density occurs due to the interference between forward
and backward scattering. Finally, in the presence of weak perpendicular
magnetic field, charge carriers are deflected in opposite directions in the
p-region and n-region. As a result, the focusing effect is smeared. The lower
energy , the easier the focusing effect is destroyed. For the high energy
(e.g. ), however, the focusing effect can still survive in a
moderate magnetic field on order of one Tesla.Comment: 29 pages, 16 figure
Symmetry and transport property of spin current induced spin-Hall effect
We study the spin current induced spin-Hall effect that a longitudinal spin
dependent chemical potential induces a transverse spin
conductances . A four terminal system with Rashba and Dresselhaus
spin-orbit interaction (SOI) in the scattering region is considered. By using
Landauer-Bttiker formula with the aid of the Green function, various
spin current induced spin-Hall conductances are calculated. With the
charge chemical potential or spin chemical potential ,
there are 16 elements for the transverse conductances where . Due to the symmetry of our
system these elements are not independent. For the system with symmetry
half of elements are zero, when the center region only exists the Rashba SOI or
Dresselhaus SOI. The numerical results show that of all the conductance
elements, the spin current induced spin-Hall conductances are usually
much greater (about one or two orders of magnitude) than the spin Hall
conductances and the reciprocal spin Hall conductances . So
the spin current induced spin-Hall effect is dominating in the present device.Comment: 7 pages, 6 figure
Fast and Provable Algorithms for Spectrally Sparse Signal Reconstruction via Low-Rank Hankel Matrix Completion
A spectrally sparse signal of order is a mixture of damped or
undamped complex sinusoids. This paper investigates the problem of
reconstructing spectrally sparse signals from a random subset of regular
time domain samples, which can be reformulated as a low rank Hankel matrix
completion problem. We introduce an iterative hard thresholding (IHT) algorithm
and a fast iterative hard thresholding (FIHT) algorithm for efficient
reconstruction of spectrally sparse signals via low rank Hankel matrix
completion. Theoretical recovery guarantees have been established for FIHT,
showing that number of samples are sufficient for exact
recovery with high probability. Empirical performance comparisons establish
significant computational advantages for IHT and FIHT. In particular, numerical
simulations on D arrays demonstrate the capability of FIHT on handling large
and high-dimensional real data
DJpsiFDC: an event generator for the process at LHC
DJpsiFDC is an event generator package for the process .
It generates events for primary leading-order processes. The package
could generate a LHE document and this document could easily be embedded into
detector simulation software frameworks. The package is produced in Fortran
codes.Comment: 10 pages, 3 figure
Matrix of Polynomials Model based Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling
We study the problem of dictionary learning for signals that can be
represented as polynomials or polynomial matrices, such as convolutive signals
with time delays or acoustic impulse responses. Recently, we developed a method
for polynomial dictionary learning based on the fact that a polynomial matrix
can be expressed as a polynomial with matrix coefficients, where the
coefficient of the polynomial at each time lag is a scalar matrix. However, a
polynomial matrix can be also equally represented as a matrix with polynomial
elements. In this paper, we develop an alternative method for learning a
polynomial dictionary and a sparse representation method for polynomial signal
reconstruction based on this model. The proposed methods can be used directly
to operate on the polynomial matrix without having to access its coefficients
matrices. We demonstrate the performance of the proposed method for acoustic
impulse response modeling.Comment: 5 pages, 2 figure
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