36,472 research outputs found
S-Lemma with Equality and Its Applications
Let and be two quadratic functions
having symmetric matrices and . The S-lemma with equality asks when the
unsolvability of the system implies the existence of a real
number such that . The
problem is much harder than the inequality version which asserts that, under
Slater condition, is unsolvable if and only if for some . In this paper, we
show that the S-lemma with equality does not hold only when the matrix has
exactly one negative eigenvalue and is a non-constant linear function
(). As an application, we can globally solve as well as the two-sided generalized trust region subproblem
without any condition. Moreover, the
convexity of the joint numerical range where is a (possibly non-convex) quadratic
function and are affine functions can be characterized
using the newly developed S-lemma with equality.Comment: 34 page
Spectroscopy of reflection-asymmetric nuclei with relativistic energy density functionals
Quadrupole and octupole deformation energy surfaces, low-energy excitation
spectra and transition rates in fourteen isotopic chains: Xe, Ba, Ce, Nd, Sm,
Gd, Rn, Ra, Th, U, Pu, Cm, Cf, and Fm, are systematically analyzed using a
theoretical framework based on a quadrupole-octupole collective Hamiltonian
(QOCH), with parameters determined by constrained reflection-asymmetric and
axially-symmetric relativistic mean-field calculations. The microscopic QOCH
model based on the PC-PK1 energy density functional and -interaction
pairing is shown to accurately describe the empirical trend of low-energy
quadrupole and octupole collective states, and predicted spectroscopic
properties are consistent with recent microscopic calculations based on both
relativistic and non-relativistic energy density functionals. Low-energy
negative-parity bands, average octupole deformations, and transition rates show
evidence for octupole collectivity in both mass regions, for which a
microscopic mechanism is discussed in terms of evolution of single-nucleon
orbitals with deformation.Comment: 36 pages, 21 figures, Accepted for Publication in Physical Review
Radiance and Doppler shift distributions across the network of the quiet Sun
The radiance and Doppler-shift distributions across the solar network provide
observational constraints of two-dimensional modeling of transition-region
emission and flows in coronal funnels. Two different methods, dispersion plots
and average-profile studies, were applied to investigate these distributions.
In the dispersion plots, we divided the entire scanned region into a bright and
a dark part according to an image of Fe xii; we plotted intensities and Doppler
shifts in each bin as determined according to a filtered intensity of Si ii. We
also studied the difference in height variations of the magnetic field as
extrapolated from the MDI magnetogram, in and outside network. For the
average-profile study, we selected 74 individual cases and derived the average
profiles of intensities and Doppler shifts across the network. The dispersion
plots reveal that the intensities of Si ii and C iv increase from network
boundary to network center in both parts. However, the intensity of Ne viii
shows different trends, namely increasing in the bright part and decreasing in
the dark part. In both parts, the Doppler shift of C iv increases steadily from
internetwork to network center. The average-profile study reveals that the
intensities of the three lines all decline from the network center to
internetwork region. The binned intensities of Si ii and Ne viii have a good
correlation. We also find that the large blue shift of Ne viii does not
coincide with large red shift of C iv. Our results suggest that the network
structure is still prominent at the layer where Ne viii is formed in the quiet
Sun, and that the magnetic structures expand more strongly in the dark part
than in the bright part of this quiet Sun region.Comment: 10 pages,9 figure
Space-like hypersurfaces with vanishing conformal forms in the conformal space
We study the space-like hypersurfaces with vanishing conformal form in the conformal geometry, and classify the the Einstein space-like hypersurfaces in the conformal spac
Photometric properties and luminosity function of nearby massive early-type galaxies
We perform photometric analyses for a bright early-type galaxy (ETG) sample
with 2949 galaxies ( mag) in the redshift range of 0.05 to
0.15, drawn from the SDSS DR7 with morphological classification from Galaxy Zoo
1. We measure the Petrosian and isophotal magnitudes, as well as the
corresponding half-light radius for each galaxy. We find that for brightest
galaxies ( mag), our Petrosian magnitudes, and isophotal
magnitudes to 25 and 1\% of the sky brightness are on
average 0.16 mag, 0.20 mag, and 0.26 mag brighter than the SDSS Petrosian
values, respectively. In the first case the underestimations are caused by
overestimations in the sky background by the SDSS PHOTO algorithm, while the
latter two are also due to deeper photometry. Similarly, the typical half-light
radii () measured by the SDSS algorithm are smaller than our
measurements. As a result, the bright-end of the -band luminosity function
is found to decline more slowly than previous works. Our measured luminosity
densities at the bright end are more than one order of magnitude higher than
those of Blanton et al. (2003), and the stellar mass densities at and are a few tenths
and a factor of few higher than those of Bernardi et al. (2010). These results
may significantly alleviate the tension in the assembly of massive galaxies
between observations and predictions of the hierarchical structure formation
model.Comment: 43 pages, 14 figures, version accepted for publication in the
Astrophysical Journa
Semantic Object Parsing with Graph LSTM
By taking the semantic object parsing task as an exemplar application
scenario, we propose the Graph Long Short-Term Memory (Graph LSTM) network,
which is the generalization of LSTM from sequential data or multi-dimensional
data to general graph-structured data. Particularly, instead of evenly and
fixedly dividing an image to pixels or patches in existing multi-dimensional
LSTM structures (e.g., Row, Grid and Diagonal LSTMs), we take each
arbitrary-shaped superpixel as a semantically consistent node, and adaptively
construct an undirected graph for each image, where the spatial relations of
the superpixels are naturally used as edges. Constructed on such an adaptive
graph topology, the Graph LSTM is more naturally aligned with the visual
patterns in the image (e.g., object boundaries or appearance similarities) and
provides a more economical information propagation route. Furthermore, for each
optimization step over Graph LSTM, we propose to use a confidence-driven scheme
to update the hidden and memory states of nodes progressively till all nodes
are updated. In addition, for each node, the forgets gates are adaptively
learned to capture different degrees of semantic correlation with neighboring
nodes. Comprehensive evaluations on four diverse semantic object parsing
datasets well demonstrate the significant superiority of our Graph LSTM over
other state-of-the-art solutions.Comment: 18 page
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