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.