Excited states in the full QCD hadron spectrum on a 163×4016^3 \times 40 lattice

We report the hadron mass spectrum obtained on a $16^3 \times 40$ lattice at $\beta = 5.7$ using two flavors of staggered fermions with $m a = 0.01$. We calculate the masses of excited states that have the same quantum numbers as the $\pi$, $\rho$ and $N$. They are obtained by a combined analysis of the hadron correlators from sources of size $16^3$ and $8^3$. We also report on the hadron spectrum for a wide range of valence quark masses.Comment: Contribution to Lattice 95. 4 pages. Compressed, uuencoded postscript file. Send questions to [email protected]

Observer-Based Controller Design for Systems on Manifolds in Euclidean Space

A method of designing observers and observer-based tracking controllers is proposed for nonlinear systems on manifolds via embedding into Euclidean space and transversal stabilization. Given a system on a manifold, we first embed the manifold and the system into Euclidean space and extend the system dynamics to the ambient Euclidean space in such a way that the manifold becomes an invariant attractor of the extended system, thus securing the transversal stability of the manifold in the extended dynamics. After the embedding, we design state observers and observer-based controllers for the extended system in one single global coordinate system in the ambient Euclidean space, and then restrict them to the original state-space manifold to produce observers and observer-based controllers for the original system on the manifold. This procedure has the merit that any existing control method that has been developed in Euclidean space can be applied globally to systems defined on nonlinear manifolds, thus making nonlinear controller design on manifolds easier. The detail of the method is demonstrated on the fully actuated rigid body system.Comment: SICE Annual Conference, Nara, Japan, September, 201

Some sufficient conditions for infinite collisions of simple random walks on a wedge comb

In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile \{f(n), n\in \ZZ\}. One interesting result is that if $f(n)$ has a growth order as $n\log n$, then two independent simple random walks on the wedge comb will collide infinitely many times. Another is that if \{f(n); n\in \ZZ\} are given by i.i.d. non-negative random variables with finite mean, then for almost all wedge comb with such profile, three independent simple random walks on it will collide infinitely many times

Novel CFT Duals for Extreme Black Holes

In this paper, we study the CFT duals for extreme black holes in the stretched horizon formalism. We consider the extremal RN, Kerr-Newman-AdS-dS, as well as the higher dimensional Kerr-AdS-dS black holes. In all these cases, we reproduce the well-established CFT duals. Actually we show that for stationary extreme black holes, the stretched horizon formalism always gives rise to the same dual CFT pictures as the ones suggested by ASG of corresponding near horizon geometries. Furthermore, we propose new CFT duals for 4D Kerr-Newman-AdS-dS and higher dimensional Kerr-AdS-dS black holes. We find that every dual CFT is defined with respect to a rotation in certain angular direction, along which the translation defines a U(1) Killing symmetry. In the presence of two sets of U(1) symmetry, the novel CFT duals are generated by the modular group SL(2,\mb Z), and for $n$ sets of U(1) symmetry there are general CFT duals generated by T-duality group SL(n,\mb Z).Comment: 31 pages; Significantly revised, one loophole in the treatment was figured out, as a result, the novel CFT pictures are generated by the group SL(n,\mb Z) rather than an continuous family. Published versio