81,623 research outputs found
Entropy of a semigroup of maps from a set-valued view
In this paper, we introduce a new entropy-like invariant, named Hausdorff
metric entropy, for finitely generated semigroups acting on compact metric
spaces from a set-valued view and study its properties. We establish the
relation between Hausdorff metric entropy and topological entropy of a
semigroup defined by Bi\'s. Some examples with positive or zero Hausdorff
metric entropy are given. Moreover, some notions of chaos are also well
generalized for finitely generated semigroups from a set-valued view.Comment: 13 pages, 0 figure
The Fundamental Plane Relation of Early-Type Galaxies: Environmental Dependence
Using a sample of 70,793 early-type galaxies from SDSS DR7, we study the
environmental dependence of the fundamental plane relation. With the help of
the galaxy group catalogue based on SDSS DR7, we calculate the fundamental
planes in different dark matter halo mass bins for central and satellite
galaxies respectively. We find the environmental dependence of the fundamental
plane coefficients are similar in , , and bands. The
environmental dependence for central and satellite galaxies is significantly
different. While the fundamental plane coefficients of centrals vary
systematically with the halo mass, those of satellites are similar in different
halo mass bins. The discrepancy between centrals and satellites are significant
in small halos, but negligible in the largest halo mass bins. These results
remain the same when we only keep red galaxies, or galaxies with , or
galaxies in a specific radius range in the sample. After the correction of the
sky background, results are still similar. We suggest that the different
environmental effects of the halo mass on centrals and satellites may arise
from the different quenching processes of them.Comment: 14 pages, 5 Figures, 3 Tables. Accepted by RA
Unicyclic signed graphs with maximal energy
Let be the eigenvalues of a signed graph of
order . The energy of is defined as
Let be obtained by
connecting a vertex of the negative circle with a
terminal vertex of the path . In this paper, we show that for
and has the maximal energy among all connected
unicyclic -vertex signed graphs, except the cycles $C_5^+, C_7^+.
Non-perturbative Theory of Pauli Spin Blockade
Pauli spin blockade (PSB) is a significant physical effect in double quantum
dot (DQD) systems. In this paper, we start from the fundamental quantum model
of the DQD with the electron-electron interaction being considered, and then
systematically study the PSB effect in DQD by using a recently developed
non-perturbative method, the hierarchical equations of motion (HEOM) approach.
The physical picture of the PSB is elucidated explicitly and the gate voltage
manipulation is described minutely, which are both qualitatively consistent
with the experimental measurements. When dotdot exchange interaction is
involved, the PSB effect may be lifted by the strong antiferromagnetic exchange
coupling.Comment: 10 pages, 8 figure
Design of a Low-cost Miniature Robot to Assist the COVID-19 Nasopharyngeal Swab Sampling
Nasopharyngeal (NP) swab sampling is an effective approach for the diagnosis
of coronavirus disease 2019 (COVID-19). Medical staffs carrying out the task of
collecting NP specimens are in close contact with the suspected patient,
thereby posing a high risk of cross-infection. We propose a low-cost miniature
robot that can be easily assembled and remotely controlled. The system includes
an active end-effector, a passive positioning arm, and a detachable swab
gripper with integrated force sensing capability. The cost of the materials for
building this robot is 55 USD and the total weight of the functional part is
0.23kg. The design of the force sensing swab gripper was justified using Finite
Element (FE) modeling and the performances of the robot were validated with a
simulation phantom and three pig noses. FE analysis indicated a 0.5mm magnitude
displacement of the gripper's sensing beam, which meets the ideal detecting
range of the optoelectronic sensor. Studies on both the phantom and the pig
nose demonstrated the successful operation of the robot during the collection
task. The average forces were found to be 0.35N and 0.85N, respectively. It is
concluded that the proposed robot is promising and could be further developed
to be used in vivo.Comment: 5 pages, 8 figure
Deep Ranking Model by Large Adaptive Margin Learning for Person Re-identification
Person re-identification aims to match images of the same person across
disjoint camera views, which is a challenging problem in video surveillance.
The major challenge of this task lies in how to preserve the similarity of the
same person against large variations caused by complex backgrounds, mutual
occlusions and different illuminations, while discriminating the different
individuals. In this paper, we present a novel deep ranking model with feature
learning and fusion by learning a large adaptive margin between the intra-class
distance and inter-class distance to solve the person re-identification
problem. Specifically, we organize the training images into a batch of pairwise
samples. Treating these pairwise samples as inputs, we build a novel part-based
deep convolutional neural network (CNN) to learn the layered feature
representations by preserving a large adaptive margin. As a result, the final
learned model can effectively find out the matched target to the anchor image
among a number of candidates in the gallery image set by learning
discriminative and stable feature representations. Overcoming the weaknesses of
conventional fixed-margin loss functions, our adaptive margin loss function is
more appropriate for the dynamic feature space. On four benchmark datasets,
PRID2011, Market1501, CUHK01 and 3DPeS, we extensively conduct comparative
evaluations to demonstrate the advantages of the proposed method over the
state-of-the-art approaches in person re-identification.Comment: Accepted to Pattern Recognitio
Rotating Black Hole Shadow in Perfect Fluid Dark Matter
We study analytically the shadow cast by the rotating black hole in the
perfect fluid dark matter. The apparent shape of the shadow depends upon the
black hole spin and the perfect fluid dark matter intensity parameter
(). In general, the shadow is a perfect circle in the non-rotating case
() and a deformed one in the rotating case (). The deformation
gets more and more significant with the increasing , similar to the
Schwarzschild and Kerr black holes. In addition, there exists a reflection
point . When , the size of the shadow decreases with the increasing
and the distortion increases with the increasing . When , the
size of the shadow increases with the increasing and the distortion
decreases with the increasing . Furthermore, the energy emission rate of the
black hole in the perfect fluid dark matter increases with the increasing
and the peak of the emission shifts to higher frequencies. Finally, we propose
that to observe the effect of the black hole spin and the perfect fluid
dark matter intensity on the shadow of the black hole Sgr A at the
center of the Milky Way, highly improved techniques would be necessary for the
development of future astronomical instruments.Comment: 9 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1806.09415, arXiv:1804.0811
The Mutual Inclusion in a Nonlocal Competitive Lotka Volterra System
We investigate the traveling front solutions of a nonlocal Lotka Volterra
system to illustrate the outcome of the competition between two species. The
existence of the front solution is obtained through a new monotone iteration
scheme, the uniqueness of the front solution corresponding to each propagation
speed is proved by sliding domain method adapted to nonlocal systems, and the
asymptotic decay rate of the fronts with critical and noncritical wave speeds
is derived by a new method, which is different from the single equation case.
The results demonstrate that in the long run, two weakly competing species can
co-exist.Comment: Need further update
Kerr-Anti-De-Sitter/De-Sitter Black Hole In Perfect Fluid Dark Matter Background
We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS)
black hole (BH) solutions to the Einstein field equation in the perfect fluid
dark matter background using the Newman-Janis method and Mathematica package.
We discuss in detail the black hole properties and obtain the following main
results: (i) From the horizon equation , we derive the relation
between the perfect fluid dark matter parameter and the cosmological
constant when the cosmological horizon exists. For
, we find that is in the range
and for . For positive cosmological constant
(Kerr-AdS BH), decreases if , and
increases if . For negative cosmological constant
(Kerr-dS BH), increases if and
decreases if ; (ii) An ergosphere exists between the
event horizon and the outer static limit surface. The size of the ergosphere
evolves oppositely for and , while decreasing with the
increasing . When there is sufficient dark matter around the
black hole, the black hole spacetime changes remarkably; (iii) The singularity
of these black holes is the same as that of rotational black holes. In
addition, we study the geodesic motion using the Hamilton-Jacobi formalism and
find that when is in the above ranges for , stable orbits
exist. Furthermore, the rotational velocity of the black hole in the equatorial
plane has different behaviour for different and the black hole spin
. It is asymptotically flat and independent of if while
is asymptotically flat only when is close to zero if .Comment: 22 pages, 4 figure
n-point functions at finite temperature
We study -point functions at finite temperature in the closed time path
formalism. With the help of two basic column vectors and their dual partners we
derive a compact decomposition of the time-ordered -point functions with
components in terms of independent retarded/advanced
-point functions. This representation greatly simplifies calculations in the
real-time formalism.Comment: Revtex, 14pages, no figur
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