Theoretical studies on vibrational spectra of some halides of Group IIB elements

The vibrational spectra of Group IIB elements halides MX2 and their dimers M2X4 (M=Zn(II), Cd(II) and Hg(II); X=F, Cl, Br and I) have been systematically investigated by ab initio RHF and B3LYP methods with LanL2MB, LanL2DZ and SDD basis sets. The optimized geometries, calculated vibrational frequencies are evaluated via comparison with the experimental data. The vibrational frequencies, calculated by these methods with different basis sets, are compared to each other too. The best results can be obtained by RHF/SDD method, with this method, the deviations for MX2 and Hg2X4 are <7%. Some vibrational frequencies of M2X4 that have not been experimentally reported are also predicted.     

Multiplicative posets

A functionf from the posetP to the posetQ is a strict morphism if for allx, y P withx we havef(x). If there is such a strict morphism fromP toQ we writeP Q, otherwise we writeP Q. We say a posetM is multiplicative if for any posetsP, Q withP M andQ M we haveP ×Q M. (Here (p ₁,q ₁)<(p ₂,q ₂) if and only ifp ₁<p ₂ andq ₁<q ₂.) This paper proves that well-founded trees with height are multiplicative posets.This research was supported in part by NSERC Grant #69-1325.     

Improved results on the robustness of stochastic approximation algorithms

This paper is a continuation of the research carried out in [1]–[2], where the robustness analysis for stochastic approximation algorithms is given for two cases: 1. The regression function and the Liapunov function are not zero at the sought-forx ⁰; 2. lim sup _n a131_{n i=1} ⁿ _i+1 is not zero, where { _i } are the measurement errors and {a _n} are the weighting coefficients in the algorithm. Allowing these deviations from zero to occur simultaneously but to remain small, this paper shows that the estimation error is still small even for a class of measurement errors more general than that considered in [2].This project is supported by the National Natural Science Foundation of China.