We address stability of receding horizon control for stochastic linear systems with additive noise and bounded control authority. We construct tractable and recursively feasible receding horizon control policies that ensure a mean-square bounded system in closed-loop if the noise has bounded forthorder moment, the unexcited system is stabilizable, the system matrix A is Lyapunov stable, and the...

I attempt to answer the question of the title by giving an annotated list of the major results achieved, over the last six years, in the program to construct quantum general relativity using the Ashtekar variables and the loop representation. A summary of the key open problems is also included.

We construct the Hamiltonian operator of the string field theory for c = 0 string theory. It describes how strings evolve in the coordinate frame, which is defined by using the geodesic distance on the worldsheet. The Hamiltonian consists of three-string interaction terms and a tadpole term. We show that one can derive the loop amplitudes of c = 0 string theory from this Hamiltonian.

We construct boundary states for the AdS2 D-branes in AdS3. We show that, in the semiclassical limit, the boundary states correctly reproduce geometric configurations of these branes. We use the boundary states to compute the one loop free energy of open string stretched between the branes. The result agrees precisely with the open string computation in hep-th/0106129.

We propose a method to analyze infrared contributions to non-inclusive processes in QCD. We use the one-loop Sudakov form factor as a working example. Borrowing techniques from renormalization theory, we construct coun-terterms for the contributions from the soft and collinear regions, and we relate them to eikonal Wilson lines taken along non-lightlike directions.

Two hepatitis B core proteins bearing the immunodominant region of the hepatitis E virus (HEV) capsid protein, one at the C terminus of hepatitis B virus core antigen (HBcAg) and the other within the HBcAg immunodominant loop, were constructed. Both chimeric proteins exhibited HEV reactivity, but only the first construct retained HBcAg reactivity. The second construct was used to develop an ant...

We construct a natural co-Riemannian structure on the manifold of smooth loops in a Riemannian manifold. We show that the smooth loop space of a stringmanifold is a per-Hilbert–Schmidt locally equivalent co-spin manifold and thus admits a Dirac operator.

We consider the Super Yang–Mills/spin system map to construct the SU(2) spin bit model at the level of two loops in Yang–Mills perturbation theory. The model describes a spin system with chaining interaction. In the large N limit the model is shown to be reduced to the two loop planar integrable spin chain.

We construct a string field theory for c = 1 noncritical strings using the loop variables as the string field. We show how one can express the nonrelativistic free fermions which describes the theory, in terms of these string fields. [email protected] [email protected]