12,009 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
Development of advanced control schemes for telerobot manipulators
To study space applications of telerobotics, Goddard Space Flight Center (NASA) has recently built a testbed composed mainly of a pair of redundant slave arms having seven degrees of freedom and a master hand controller system. The mathematical developments required for the computerized simulation study and motion control of the slave arms are presented. The slave arm forward kinematic transformation is presented which is derived using the D-H notation and is then reduced to its most simplified form suitable for real-time control applications. The vector cross product method is then applied to obtain the slave arm Jacobian matrix. Using the developed forward kinematic transformation and quaternions representation of the slave arm end-effector orientation, computer simulation is conducted to evaluate the efficiency of the Jacobian in converting joint velocities into Cartesian velocities and to investigate the accuracy of the Jacobian pseudo-inverse for various sampling times. In addition, the equivalence between Cartesian velocities and quaternion is also verified using computer simulation. The motion control of the slave arm is examined. Three control schemes, the joint-space adaptive control scheme, the Cartesian adaptive control scheme, and the hybrid position/force control scheme are proposed for controlling the motion of the slave arm end-effector. Development of the Cartesian adaptive control scheme is presented and some preliminary results of the remaining control schemes are presented and discussed
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