A Novel Method to Synthesize Polyorganozircosilazane

A new kind of polyorganozircosilazane as Si/Zr/C/N-based ceramic precursor was synthesized from the condensation reaction of hexamethyleyclotrisilazane lithium salts(D3^NLi）and zirconium tetrachloride(ZrCl4).In the presence of N,N,N’,N’-tetramethyl ethylene diamine(TMEDA),polyorganozircosilazane was obtained in high yield.     

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.