8,474 research outputs found
On spectral stability of solitary waves of nonlinear Dirac equation on a line
We study the spectral stability of solitary wave solutions to the nonlinear
Dirac equation in one dimension. We focus on the Dirac equation with cubic
nonlinearity, known as the Soler model in (1+1) dimensions and also as the
massive Gross-Neveu model. Presented numerical computations of the spectrum of
linearization at a solitary wave show that the solitary waves are spectrally
stable. We corroborate our results by finding explicit expressions for several
of the eigenfunctions. Some of the analytic results hold for the nonlinear
Dirac equation with generic nonlinearity.Comment: 20 pages with figure
On a Penrose Inequality with Charge
We construct a time-symmetric asymptotically flat initial data set to the
Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) <
0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost
horizon and Q is the total charge. This yields a counter-example to a natural
extension of the Penrose Inequality to charged black holes.Comment: Minor revision: some typos; author's address updated; bibliographical
reference added; journal information: to appear in Comm. Math. Phy
Instanton interpolating current for --tetraquark
We perform a QCD sum rule analysis for the light scalar meson
() with a tetraquark current related to the instanton picture for QCD
vacuum. We demonstrate that instanton current, including equal weights of
scalar and pseudoscalar diquark-antidiquarks, leads to a strong cancelation
between the contributions of high dimension operators in the operator product
expansion (OPE). Furthermore, in the case of this current direct instanton
contributions do not spoil the sum rules. Our calculation, obtained from the
OPE up to dimension 10 operators, gives the mass of --meson around
780MeV.Comment: 11 pages, 7 figures, final version to be appeared in Phys. Lett.
The Design of RFID Convey or Belt Gate Systems Using an Antenna Control Unit
This paper proposes an efficient management system utilizing a Radio Frequency Identification (RFID) antenna control unit which is moving along with the path of boxes of materials on the conveyor belt by manipulating a motor. The proposed antenna control unit, which is driven by a motor and is located on top of the gate, has an array structure of two antennas with parallel connection. The array structure helps improve the directivity of antenna beam pattern and the readable RFID distance due to its configuration. In the experiments, as the control unit follows moving materials, the reading time has been improved by almost three-fold compared to an RFID system employing conventional fixed antennas. The proposed system also has a recognition rate of over 99% without additional antennas for detecting the sides of a box of materials. The recognition rate meets the conditions recommended by the Electronic Product Code glbal network (EPC)global for commercializing the system, with three antennas at a 20 dBm power of reader and a conveyor belt speed of 3.17 m/s. This will enable a host of new RFID conveyor belt gate systems with increased performance
-Equivariant Dimensionality Reduction on Stiefel Manifolds
Many real-world datasets live on high-dimensional Stiefel and Grassmannian
manifolds, and respectively, and
benefit from projection onto lower-dimensional Stiefel (respectively,
Grassmannian) manifolds. In this work, we propose an algorithm called Principal
Stiefel Coordinates (PSC) to reduce data dimensionality from to in an -equivariant manner (). We begin by observing that each element defines an isometric embedding of into
. Next, we optimize for such an embedding map that minimizes
data fit error by warm-starting with the output of principal component analysis
(PCA) and applying gradient descent. Then, we define a continuous and
-equivariant map that acts as a ``closest point operator''
to project the data onto the image of in
under the embedding determined by , while
minimizing distortion. Because this dimensionality reduction is
-equivariant, these results extend to Grassmannian manifolds as well.
Lastly, we show that the PCA output globally minimizes projection error in a
noiseless setting, but that our algorithm achieves a meaningfully different and
improved outcome when the data does not lie exactly on the image of a linearly
embedded lower-dimensional Stiefel manifold as above. Multiple numerical
experiments using synthetic and real-world data are performed.Comment: 26 pages, 8 figures, comments welcome
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