Analysis of hidden-bottom bb\bar{b}\bar{b} states

Motivated by the searching for $bb\bar{b}\bar{b}$ states at LHC recently, we calculate the ground-state energies of $bb\bar{b}\bar{b}$ states with quantum numbers $IJ^P=00^+,01^+,02^+$ in a nonrelativistic chiral quark model using the Gaussian expansion method. In our calculations, two structures, meson-meson and diquark-antidiquark, and their coupling, along with all possible color configurations are considered. It is expected that the studies shall be helpful for the experimental searching of fully-heavy exotic tetraquark states.Comment: 7 pages, 1 figur

Is the exotic X(5568)X(5568) a bound state?

Stimulated by the recent observation of the exotic $X(5568)$ state by D0 Collaboration, we study the four-quark system $us\bar{b}\bar{d}$ with quantum numbers $J^P=0^+$ in the framework of chiral quark model. Two structures, diquark-antidiquark and meson-meson, with all possible color configurations are investigated by using Gaussian expansion method. The results show that energies of the tetraquark states with diquark-antiquark structure are too high to the candidate of $X(5568)$, and no molecular structure can be formed in our calculations. The calculation is also extended to the four-quark system $us\bar{c}\bar{d}$ and the same results as that of $us\bar{b}\bar{d}$ are obtained.Comment: 5 pages, 1 figur

The Caltech helicopter control experiment

This report describes the Caltech helicopter control experiment. The experiment consists of an electric model helicopter interfaced to and controlled by a PC. We describe the hardware and software. A state-space model for the angular position is identified from experimental data near hover, using the prediction error method. An LQR controller with integrators for set point tracking is designed for the system. We also undertake a separate identification and loop shaping control for the yaw dynamics

Star-factors of tournaments

Let S_m denote the m-vertex simple digraph formed by m-1 edges with a common tail. Let f(m) denote the minimum n such that every n-vertex tournament has a spanning subgraph consisting of n/m disjoint copies of S_m. We prove that m lg m - m lg lg m <= f(m) <= 4m^2 - 6m for sufficiently large m.Comment: 5 pages, 1 figur

Distributed Optimal Rate-Reliability-Lifetime Tradeoff in Wireless Sensor Networks

The transmission rate, delivery reliability and network lifetime are three fundamental but conflicting design objectives in energy-constrained wireless sensor networks. In this paper, we address the optimal rate-reliability-lifetime tradeoff with link capacity constraint, reliability constraint and energy constraint. By introducing the weight parameters, we combine the objectives at rate, reliability, and lifetime into a single objective to characterize the tradeoff among them. However, the optimization formulation of the rate-reliability-reliability tradeoff is neither separable nor convex. Through a series of transformations, a separable and convex problem is derived, and an efficient distributed Subgradient Dual Decomposition algorithm (SDD) is proposed. Numerical examples confirm its convergence. Also, numerical examples investigate the impact of weight parameters on the rate utility, reliability utility and network lifetime, which provide a guidance to properly set the value of weight parameters for a desired performance of WSNs according to the realistic application's requirements.Comment: 27 pages, 10 figure