24,475 research outputs found
Estimates for multilinear commutators of generalized fractional integral operators on weighted Morrey spaces
Let be the infinitesimal generator of an analytic semigroup on
with Gaussian kernel bounds, and let be the
fractional integrals of for . Assume that
is a finite family of locally integrable
functions, then the multilinear commutators generated by and
is defined by \begin{equation*}
L_{\vec{b}}^{-\alpha/2}f=[b_m,\cdots,[b_2,[b_1,L^{-\alpha/2}]],\cdots,]f
\end{equation*} when , , the authors obtain the
boundedness of on weighted Morrey spaces.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1203.4407 by
other author
Iterative Grassmannian Optimization for Robust Image Alignment
Robust high-dimensional data processing has witnessed an exciting development
in recent years, as theoretical results have shown that it is possible using
convex programming to optimize data fit to a low-rank component plus a sparse
outlier component. This problem is also known as Robust PCA, and it has found
application in many areas of computer vision. In image and video processing and
face recognition, the opportunity to process massive image databases is
emerging as people upload photo and video data online in unprecedented volumes.
However, data quality and consistency is not controlled in any way, and the
massiveness of the data poses a serious computational challenge. In this paper
we present t-GRASTA, or "Transformed GRASTA (Grassmannian Robust Adaptive
Subspace Tracking Algorithm)". t-GRASTA iteratively performs incremental
gradient descent constrained to the Grassmann manifold of subspaces in order to
simultaneously estimate a decomposition of a collection of images into a
low-rank subspace, a sparse part of occlusions and foreground objects, and a
transformation such as rotation or translation of the image. We show that
t-GRASTA is 4 faster than state-of-the-art algorithms, has half the
memory requirement, and can achieve alignment for face images as well as
jittered camera surveillance images.Comment: Preprint submitted to the special issue of the Image and Vision
Computing Journal on the theme "The Best of Face and Gesture 2013
Multi-objective Differential Evolution with Helper Functions for Constrained Optimization
Solving constrained optimization problems by multi-objective evolutionary
algorithms has scored tremendous achievements in the last decade. Standard
multi-objective schemes usually aim at minimizing the objective function and
also the degree of constraint violation simultaneously. This paper proposes a
new multi-objective method for solving constrained optimization problems. The
new method keeps two standard objectives: the original objective function and
the sum of degrees of constraint violation. But besides them, four more
objectives are added. One is based on the feasible rule. The other three come
from the penalty functions. This paper conducts an initial experimental study
on thirteen benchmark functions. A simplified version of CMODE is applied to
solving multi-objective optimization problems. Our initial experimental results
confirm our expectation that adding more helper functions could be useful. The
performance of SMODE with more helper functions (four or six) is better than
that with only two helper functions.Comment: Accepted by The 15th UK Workshop on Computational Intelligence (UKCI
2015
Integrated Facility Location and Production Scheduling in Multi-Generation Energy Systems
In this paper, we investigate the energy system design problems with the
multi-generation technologies, i.e., simultaneous generation of multiple types
of energy. We propose a long-term planning model which integrates macro-level
strategic decisions such as facility location and multi-generation technology
investment, and micro-level operational decisions such as production planning
and energy transportation. Our results illustrate the economic value of
multi-generation technologies in lieu of the spatio-temporal demand uncertainty
for energy. In particular, we show that the multi-generation technologies can
reduce demand uncertainty by risk pooling both within and across different
facilities
The Multiparty Coherent Channel and its Implementation with Linear Optics
The continuous-variable coherent (conat) channel is a useful resource for
coherent communication, producing coherent teleportation and coherent
superdense coding. We extend the conat channel to multiparty conditions by
proposing definitions about multiparty position-quadrature conat channel and
multiparty momentum-quadrature conat channel. We additionally provide two
methods to implement this channel using linear optics. One method is the
multiparty version of coherent communication assisted by entanglement and
classical communication (CCAECC). The other is multiparty coherent superdense
coding.Comment: 13 pages, 4figure
Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential
QCD at finite isospin chemical potential possesses a
positively definite fermion determinant and the lattice simulation can be
successfully performed. While the two-flavor effective models may be sufficient
to describe the phenomenon of pion condensation, it is interesting to study the
roles of the strangeness degree of freedom and the U anomaly. In
this paper, we present a systematic study of the three-flavor
Nambu--Jona-Lasinio model with a Kobayashi-Maskawa-'t Hooft (KMT) term that
mimics the U anomaly at finite isospin chemical potential. In the
mean-field approximation, the model predicts a phase transition from the vacuum
to the pion superfluid phase, which takes place at equal to the
pion mass . Due to the U anomaly, the strangeness degree of
freedom couples to the light quark degrees of freedom and the strange quark
effective mass depends on the pion condensate. However, the strange quark
condensate and the strange quark effective mass change slightly in the pion
superfluid phase, which verifies the validity of the two-flavor models. The
effective four-fermion interaction of the Kobayashi-Maskawa-'t Hooft term in
the presence of the pion condensation is constructed. Due to the U
anomaly, the pion condensation generally induces scalar-pseudoscalar
interaction. The Bethe-Salpeter equation for the mesonic excitations is
established and the meson mass spectra are obtained at finite isospin chemical
potential and temperature. Finally, the general expression for the topological
susceptibility at finite isospin chemical potential is
derived. In contrast to the finite temperature effect which suppresses ,
the isospin density effect leads to an enhancement of .Comment: Version punlished in PR
Rotational Properties of the Odd- Transfermium Nucleus Lr by a Particle-number-conserving Method in the Cranked Shell Model
Experimentally observed ground state band based on the Nilsson
state and the first exited band based on the Nilsson state in
the odd- nucleus Lr are studied by the cranked shell model (CSM)
with the paring correlations treated by the particle-number-conserving (PNC)
method. This is the first time the detailed theoretical investigations being
performed on these rotational bands. Both the experimental kinematic and
dynamic moment of inertia ( and ) versus
rotational frequency are reproduced quite well by the PNC-CSM calculations. By
comparing the theoretical kinematic moment of inertia with
the experimental ones extracted from different spin assignments, the spin
is assigned to the lowest-lying keV
transition of the band, and to the
keV transition of the band, respectively. The proton
major shell is included in the calculations. The intruder of the high
low orbitals at the high spin leads to
the band-crossing at () MeV
for the () band, and at
MeV for the band,
respectively. Further investigations show that the band-crossing frequencies
are quadrupole deformation dependent.Comment: arXiv admin note: text overlap with arXiv:1208.1156 by other author
Post Newtonian Rigid Body
In this paper, it is the first time to construct a complete post-Newtonian
(PN) model of a rigid body by means of a new constraint on the mass current
density and mass density. In our PN rigid body model most of relations, such as
spin vector proportional to the angular velocity, the definition on the moment
of inertia tensor, the key relation between the mass quadrupole moment and the
moment of inertia tensor, rigid rotating formulae of mass quadrupole moment and
the moment of inertia tensor, are just the extension of the main relations in
Newtonian rigid body model. When all of terms are neglected, the PN
rigid body model and the corresponding formulae reduce to Newtonian version.
The key relation is obtained in this paper for the first time, which might be
very useful in the future application to problems in geodynamics and astronomy.Comment: Revtex4, 5 page
Amplification effects in optomechanics via weak measurement
We revisit the scheme of single-photon weak-coupling optomechanics using
post-selection, proposed by Pepper, Ghobadi, Jeffrey, Simon and Bouwmeester
[Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the
dynamical evolution. Positive and negative amplification effects of the
displacement of the mirror's position can be generated when the Kerr phase is
considered. This effect occurs when the post-selected state of the photon is
orthogonal to the initial state, which can not be explained by the usual weak
measurement results. The amplification effect can be further modulated by a
phase shifter, and the maximal displacement state can appear within a short
evolution time
Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
Conventional -dimensional topological superconductors (TSCs) have
protected gapless -dimensional boundary states. In contrast to this,
second-order TSCs are characterized by topologically protected gapless -dimensional states with usual gapped -boundaries. Here, we study a
second-order TSC with a two-dimensional (2D) magnetic topological insulator
(TI) proximity-coupled to a high-temperature superconductor, where Majorana
bound states (MBSs) are localized at the corners of a square sample with gapped
edge modes. Due to the mirror symmetry of the hybrid system considered here,
there are two MBSs at each corner for both cases: d-wave and -wave
superconducting pairing. We present the corresponding topological phase
diagrams related to the role of the magnetic exchange interaction and the
pairing amplitude. A detailed analysis, based on edge theory, reveals the
origin of the existence of MBSs at the corners of the 2D sample, which results
from the sign change of the Dirac mass emerging at the intersection of any two
adjacent edges due to pairing symmetry. Possible experimental realizations are
discussed. Our proposal offers a promising platform for realizing MBSs and
performing possible non-Abelian braiding in 2D systems.Comment: 11 pages, 9 figures. Published versio
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