7,371 research outputs found
Riesz Transform Characterizations of Musielak-Orlicz-Hardy Spaces
Let be a Musielak-Orlicz function satisfying that, for any
, belongs to the
Muckenhoupt weight class with the critical weight
exponent and is an Orlicz
function with which are, respectively, its
critical lower type and upper type. In this article, the authors establish the
Riesz transform characterizations of the Musielak-Orlicz-Hardy spaces
which are generalizations of weighted Hardy spaces
and Orlicz-Hardy spaces. Precisely, the authors characterize via all the first order Riesz transforms when
, and via all the Riesz transforms
with the order not more than when
. Moreover, the authors also
establish the Riesz transform characterizations of ,
respectively, by means of the higher order Riesz transforms defined via the
homogenous harmonic polynomials or the odd order Riesz transforms. Even if when
for all and , these
results also widen the range of weights in the known Riesz characterization of
the classical weighted Hardy space obtained by R. L.
Wheeden from into with
the sharp range , where denotes the critical
index of the weight .Comment: 38 pages, Trans. Amer. Math. Soc. (to appear
Stronger uncertainty relations with improvable upper and lower bounds
We utilize quantum superposition principle to establish the improvable upper
and lower bounds on the stronger uncertainty relation, i.e., the
"weighted-like" sum of the variances of observables. Our bounds include some
free parameters which not only guarantee the nontrivial bounds but also can
effectively control the bounds as tightly as one expects. Especially, these
parameters don't obviously depend on the state and observables. It also implies
one advantage of our method that any nontrivial bound can always be more
improvable. In addition, we generalize both bounds to the uncertainty relation
with multiple observables, but the perfect tightness is not changed. Examples
are given to illustrate the improvability of our bounds in each case.Comment: 11 pages, and 2 figure
Photon statistics on the extreme entanglement
The effects of photon bunching and antibunching correspond to the classical
and quantum features of the electromagnetic field, respectively. No direct
evidence suggests whether these effects can be potentially related to quantum
entanglement. Here we design a cavity quantum electrodynamics model with two
atoms trapped in to demonstrate the connections between the steady-state photon
statistics and the two-atom entanglement . It is found that within the weak
dissipations and to some good approximation, the local maximal two-atom
entanglements perfectly correspond to not only the quantum feature of the
electromagnetic field---the optimal photon antibunching, but also the classical
feature---the optimal photon bunching. We also analyze the influence of strong
dissipations and pure dephasing. An intuitive physical understanding is also
given finally.Comment: 12 pages, 4 figure
Optimal Photon blockade on the maximal atomic coherence
There is generally no obvious evidence in any direct relation between photon
blockade and atomic coherence. Here instead of only illustrating the photon
statistics, we show an interesting relation between the steady-state photon
blockade and the atomic coherence by designing a weakly driven cavity QED
system with a two-level atom trapped. It is shown for the first time that the
maximal atomic coherence has a perfect correspondence with the optimal photon
blockade. The negative effects of the strong dissipations on photon statistics,
atomic coherence and their correspondence are also addressed. The numerical
simulation is also given to support all of our results.Comment: 7 pages, 4 figure
Entropic Uncertainty Principle and Information Exclusion Principle for multiple measurements in the presence of quantum memory
The Heisenberg uncertainty principle shows that no one can specify the values
of the non-commuting canonically conjugated variables simultaneously. However,
the uncertainty relation is usually applied to two incompatible measurements.
We present tighter bounds on both entropic uncertainty relation and information
exclusion principle for multiple measurements in the presence of quantum
memory. As applications, three incompatible measurements on Werner state and
Horodecki's bound entangled state are investigated in details.Comment: 17 pages, 4 figure
The Measurement-Disturbance Relation and the Disturbance Trade-off Relation in Terms of Relative Entropy
We employ quantum relative entropy to establish the relation between the
measurement uncertainty and its disturbance on a state in the presence (and
absence) of quantum memory. For two incompatible observables, we present the
measurement-disturbance relation and the disturbance trade-off relation. We
find that without quantum memory the disturbance induced by the measurement is
never less than the measurement uncertainty and with quantum memory they depend
on the conditional entropy of the measured state. We also generalize these
relations to the case with multiple measurements. These relations are
demonstrated by two examples.Comment: 6 pages, 4 figure
The classical correlation limits the ability of the measurement-induced average coherence
Coherence is the most fundamental quantum feature in quantum mechanics. For a
bipartite quantum state, if a measurement is performed on one party, the other
party, based on the measurement outcomes, will collapse to a corresponding
state with some probability and hence gain the average coherence. It is shown
that the average coherence is not less than the coherence of its reduced
density matrix. In particular, it is very surprising that the extra average
coherence (and the maximal extra average coherence with all the possible
measurements taken into account) is upper bounded by the classical correlation
of the bipartite state instead of the quantum correlation. We also find the
sufficient and necessary condition for the null maximal extra average
coherence. Some examples demonstrate the relation and, moreover, show that
quantum correlation is neither sufficient nor necessary for the nonzero extra
average coherence within a given measurement. In addition, the similar
conclusions are drawn for both the basis-dependent and the basis-free coherence
measure.Comment: 10 pages,2 figures,Accept by Sci.Re
Littlewood-Paley Characterizations of Haj{\l}asz-Sobolev and Triebel-Lizorkin Spaces via Averages on Balls
Let and . In this article, the authors
characterize the Triebel-Lizorkin space with
smoothness order via the Lusin-area function and the
-function in terms of difference between and its average
over a ball centered
at with radius . As an application, the authors
obtain a series of characterizations of via
pointwise inequalities, involving ball averages, in spirit close to Haj{\l}asz
gradients, here an interesting phenomena naturally appears that, in the
end-point case when , these pointwise inequalities characterize the
Triebel-Lizorkin spaces , while not
. In particular, some new pointwise
characterizations of Haj{\l}asz-Sobolev spaces via ball averages are obtained.
Since these new characterizations only use ball averages, they can be used as
starting points for developing a theory of Triebel-Lizorkin spaces with
smoothness orders not less than on spaces of homogeneous type.Comment: 28 pages; Submitted for its publication on September 28, 201
Optomechanically induced transparency in multi-cavity optomechanical system with and without one two-level atom
We analytically study the optomechanically induced transparency (OMIT) in the
-cavity system with the \textit{N}th cavity driven by pump, probing laser
fields and the \textit{1}st cavity coupled to mechanical oscillator. We also
consider that one atom could be trapped in the \textit{i}th cavity. Instead of
only illustrating the OMIT in such a system, we are interested in how the
number of OMIT windows is influenced by the cavities and the atom and what
roles the atom could play in different cavities. In the resolved sideband
regime, we find that, the number of cavities precisely determines the maximal
number of OMIT windows. It is interesting that, when the two-level atom is
trapped in the even-labeled cavity, the central absorptive peak (odd ) or
dip (even ) is split and forms an extra OMIT window, but if the atom is
trapped in the odd-labeled cavity, the central absorptive peak (odd ) or dip
(even ) is only broadened and thus changes the width of the OMIT windows
rather than induces an extra window.Comment: 10 pages, 4 figure
Building Fast and Compact Convolutional Neural Networks for Offline Handwritten Chinese Character Recognition
Like other problems in computer vision, offline handwritten Chinese character
recognition (HCCR) has achieved impressive results using convolutional neural
network (CNN)-based methods. However, larger and deeper networks are needed to
deliver state-of-the-art results in this domain. Such networks intuitively
appear to incur high computational cost, and require the storage of a large
number of parameters, which renders them unfeasible for deployment in portable
devices. To solve this problem, we propose a Global Supervised Low-rank
Expansion (GSLRE) method and an Adaptive Drop-weight (ADW) technique to solve
the problems of speed and storage capacity. We design a nine-layer CNN for HCCR
consisting of 3,755 classes, and devise an algorithm that can reduce the
networks computational cost by nine times and compress the network to 1/18 of
the original size of the baseline model, with only a 0.21% drop in accuracy. In
tests, the proposed algorithm surpassed the best single-network performance
reported thus far in the literature while requiring only 2.3 MB for storage.
Furthermore, when integrated with our effective forward implementation, the
recognition of an offline character image took only 9.7 ms on a CPU. Compared
with the state-of-the-art CNN model for HCCR, our approach is approximately 30
times faster, yet 10 times more cost efficient.Comment: 15 pages, 7 figures, 5 table
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