Overgroups of SU(n,K, f) or Ω(n,K, Q) in GL(n,K)

All the overgroups of SU(n, K, f) or (n, K, Q) in GL(n, K) are determined, for arbitrary division rings K and arbitrary forms f or Q with positive Witt indices.     

High-precision Monte Carlo test of the conformai-invariance predictions for two-dimensional mutually avoiding walks

Let _l be the critical exponent associated with the probability thatl independentN-step ordinary random walks, starting at nearby points, are mutually avoiding. Using Monte Carlo methods combined with a maximum-likelihood data analysis, we find that in two dimensions ₂=0.6240±0.0005±0.0011 and ₃=1.4575±0.0030±0.0052, where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second error bar represents statistical error (classical 95% confidence limits). These results are in good agreement with the conformal-invariance predictions ₂=5/8 and ₃=35/24.     

Picosecond four-wave mixing reflectivity of GaAs at 1.06 μm

The picosecond degenerate four-wave mixing reflectivity of semi-insulating gallium arsenide at 1.06 m is calculated in this paper. The dependence of the reflectivity on the pump and signal fluences is measured. Reflectivities of more than one are possible. The Fourier components of the excited-carrier densities are calculated as a function of the pump fluence. The wavefront-correction property of this reflectivity is demonstrated with a lens group in the signal beam.     

Geometric optimization andD P -completeness

In this paper we show a number of natural geometric optimization problems in the plane to becomplete for a classD ^P . The classD ^p contains both NP and Co-NP and is contained in ₂ ^P =P ^NP. Completeness inD ^p is exhibited under many-one and positive reductions. Further anOptP(O(logn)) result is also obtained for some of these optimization problems.Work on this paper by the first author was supported in part by NSF Grant No. MIP 85-21356 and ARO Contract No. DAAG29-85-C-0018 under Cornell/MSI. Work by the second author was supported in part by NSF Grant No. DCR 86-06366 at Ohio State and ONR Grant No. N00014-k-0045 at Harvard.On leave from Ohio State University.