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, CPCP asymmetries and polarizations of B→ψ(2S)VB\rightarrow \psi(2S) V decays

We analyzed the nonleptonic decays $B/B_s\to \psi(2S) V$ with $V=(\rho, \omega, K^{*}, \phi)$ by employing the perturbative QCD (PQCD) factorization approach. Here the branching ratios, the $CP$ 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 $B_{(s)}\to \psi(2S)K^{*}, \psi(2S) \phi$ decays are consistent with the measured values within errors. As for $B\to \psi(2S) \rho, \psi(2S) \omega$ decays, the branching ratios can reach the order of $10^{-5}$ and could be measured in the LHCb and Belle-II experiments. The numerical results show that the direct $CP$ asymmetries of the considered decays are very small. Thus the observation of any large direct $CP$ asymmetry for these decays will be a signal for new physics. The mixing induced $CP$ asymmetries in the neutral modes are very close to $\sin 2\beta_{(s)}$, which suggests that these channels can give a cross-check on the measurement of the Cabbibo-Kobayashi-Maskawa (CKM) angle $\beta$ and $\beta_s$. We found that the longitudinal polarization fractions $f_0$ are suppressed to $\sim 50\%$ due to the large nonfactorizable contributions. The magnitudes and phases of the two transverse amplitudes $\mathcal {A}_{\parallel}$ and $\mathcal {A}_{\perp}$ are roughly equal, which is an indication for the approximate light quark helicity conservation in these decays. The overall polarization observables of $B\to \psi(2S) K^{*0}$ and $B_s\to \psi(2S) \phi$ 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