12,624 research outputs found
Smooth Solutions and Discrete Imaginary Mass of the Klein-Gordon Equation in the de Sitter Background
Using methods in the theory of semisimple Lie algebras, we can obtain all
smooth solutions of the Klein-Gordon equation on the 4-dimensional de Sitter
spacetime (dS^4). The mass of a Klein-Gordon scalar on dS^4 is related to an
eigenvalue of the Casimir operator of so(1,4). Thus it is discrete, or
quantized. Furthermore, the mass m of a Klein-Gordon scalar on dS^4 is
imaginary: m^2 being proportional to -N(N+3), with N >= 0 an integer.Comment: 23 pages, 4 figure
Remarks on the Blowup Criteria for Oldroyd Models
We provide a new method to prove and improve the Chemin-Masmoudi criterion
for viscoelastic systems of Oldroyd type in \cite{CM} in two space dimensions.
Our method is much easier than the one based on the well-known \textit{losing a
priori estimate} and is expected to be easily adopted to other problems
involving the losing \textit{a priori} estimate.Comment: to appear in JD
Branching ratios, asymmetries and polarizations of decays
We analyzed the nonleptonic decays with by employing the perturbative QCD (PQCD) factorization
approach. Here the branching ratios, the asymmetries and the complete set
of polarization observables are investigated systematically. Besides the
traditional contributions from the factorizable and nonfactorizable diagrams at
the leading order, the next-to-leading order (NLO) vertex corrections could
also provide considerable contributions. The PQCD predictions for the branching
ratios of the decays are consistent
with the measured values within errors. As for decays, the branching ratios can reach the order of and could
be measured in the LHCb and Belle-II experiments. The numerical results show
that the direct asymmetries of the considered decays are very small. Thus
the observation of any large direct asymmetry for these decays will be a
signal for new physics. The mixing induced asymmetries in the neutral
modes are very close to , which suggests that these channels
can give a cross-check on the measurement of the Cabbibo-Kobayashi-Maskawa
(CKM) angle and . We found that the longitudinal polarization
fractions are suppressed to due to the large nonfactorizable
contributions. The magnitudes and phases of the two transverse amplitudes
and are roughly equal, which
is an indication for the approximate light quark helicity conservation in these
decays. The overall polarization observables of and
channels are also in good agreement with the
experimental measurements as reported by LHCb and BaBar. Other results can also
be tested by the LHCb and Belle-II experiments.Comment: 14 pages, 1 figure, 6 table
Learning-based position control of a closed-kinematic chain robot end-effector
A trajectory control scheme whose design is based on learning theory, for a six-degree-of-freedom (DOF) robot end-effector built to study robotic assembly of NASA hardwares in space is presented. The control scheme consists of two control systems: the feedback control system and the learning control system. The feedback control system is designed using the concept of linearization about a selected operating point, and the method of pole placement so that the closed-loop linearized system is stabilized. The learning control scheme consisting of PD-type learning controllers, provides additional inputs to improve the end-effector performance after each trial. Experimental studies performed on a 2 DOF end-effector built at CUA, for three tracking cases show that actual trajectories approach desired trajectories as the number of trials increases. The tracking errors are substantially reduced after only five trials
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