Smallest eigenvalues of Hankel matrices for exponential weights

AbstractWe obtain the rate of decay of the smallest eigenvalue of the Hankel matrices ∫Itj+kW2(t)dtj,k=0n for a general class of even exponential weights W2=exp(−2Q) on an interval I. More precise asymptotics for more special weights have been obtained by many authors

Superradiant and Aharonov-Bohm effect for the quantum ring exciton

The Aharonov-Bohm and superradiant effect on the redaitive decay rate of an exciton in a quantum ring is studied. With the increasing of ring radius, the exciton decay rate is enhanced by superradiance, while the amplitude of AB oscillation is decreased. The competition between these two effects is shown explicitly and may be observable in time-resolved exeriments.Comment: 4 pages, 2 figures, to appear in Solid State Communications (2004

UAV Maneuvering Target Tracking in Uncertain Environments based on Deep Reinforcement Learning and Meta-learning

This paper combines Deep Reinforcement Learning (DRL) with Meta-learning and proposes a novel approach, named Meta Twin Delayed Deep Deterministic policy gradient (Meta-TD3), to realize the control of Unmanned Aerial Vehicle (UAV), allowing a UAV to quickly track a target in an environment where the motion of a target is uncertain. This approach can be applied to a variety of scenarios, such as wildlife protection, emergency aid, and remote sensing. We consider multi-tasks experience replay buffer to provide data for multi-tasks learning of DRL algorithm, and we combine Meta-learning to develop a multi-task reinforcement learning update method to ensure the generalization capability of reinforcement learning. Compared with the state-of-the-art algorithms, Deep Deterministic Policy Gradient (DDPG) and Twin Delayed Deep Deterministic policy gradient (TD3), experimental results show that the Meta-TD3 algorithm has achieved a great improvement in terms of both convergence value and convergence rate. In a UAV target tracking problem, Meta-TD3 only requires a few steps to train to enable a UAV to adapt quickly to a new target movement mode more and maintain a better tracking effectiveness

Impact of Subleading Corrections on Hadronic B Decays

We study the subleading corrections originating from the 3-parton (q\bar q g) Fock states of final-state mesons in B decays. The corrections could give significant contributions to decays involving an \omega or \eta^{(\prime)} in the final states. Our results indicate the similarity of \omega K and \omega \pi^- rates, of order 5\times 10^{-6}, consistent with the recent measurements. We obtain a_2(B\to J/\psi K)\approx 0.27+0.05i, in good agreement with data. Without resorting to the unknown singlet annihilation effects, 3-parton Fock state contributions can enhance the branching ratios of K\eta' to the level above 50\times 10^{-6}.Comment: 5 pages, 5 figures, revtex4; some typos corrected, a new figure and a reference added, more explanations for the calculation provided, to appear in Phys. Rev.

Orientations of two coupled molecules

Orientation states of two coupled polar molecules controlled by laser pulses are studied theoretically. By varying the period of a series of periodically applied laser pulse, transition from regular to chaotic behavior may occur. Schmidt decomposition is used to measure the degree of entanglement. It is found that the entanglement can be enhanced by increasing the strength of laser pulse.Comment: 4 pages, 4 figures, to appear in Chem. Phys. Lett.(2004

Dynamic Analysis of a Rotating Shaft Subject to the Double Cutting Force and Time-varying Mass Effects of the Rod

AbstractThis paper investigates the dynamic behaviors of a rotating shaft subjected to the double cutting force and time-varying mass effects. The Timoshenko beam theory is used to model the rotating shaft, and the general boundary condition is assumed as the clamped-hinged supports. This system is used to simulate the manufacture process of the double turret CNC lathes, and the mass of the rod which is reduced gradually in cutting process. The system equations of motion are derived based on the global assumed mode method, and the dynamic responses of the system are obtained by Runge-Kutta numerical method. The transformation matrix is derived to make the equation of motion completing the boundary geometric constraints. The numerical results compare the dynamic response in different moving speeds and skew angles of the cutting forces with/without the time-varying mass effects. Additionally, this paper compares the response with single cutting force and double force. The results show that the double moving force system can reduce not only the machining time but also the amplitude of shaft vibration