Complex homogeneous splines on the torus

We construct functions M_α which are piecewise homogeneous polynomials on the (d+1)-dimensional torus U^d+1. These functions possess complete symmetry with respect to the independent variables. The symmetry and homogeneous relations for these functions are exploited to obtain a recurrence relation and explicit representations. Furthermore, we show that , where ω=e^12x/k, 0≤j_t≤k−1, are linearly independent. By restricting M_α to U^d, we obtain the complex analogue of polynomial box splines on a (d+1)-direction mesh on U^d, which is a multivariate analogue of B-splines on the circle studied by I.J. Schoenberg^[8].     

4,4’-二苯甲酰基联苯构象的分子力学研究

4,4’—二苯甲酰基联苯有两个三岔点,属于二元三岔共轭体系。从结构式上看,卽可把它作为二苯甲酮骨架的取代产物,又可看作是在联苯骨架上的取代。作为系统研究三岔共轭体系结构效应的部分工作,我们用QCFF/PI+MCA(Quantum Mechanical Extension of the Consistent Force Field to PI Electron System+Molecular Crystal Analysis)程序研究了其晶态和孤立态(气态)构象。研究结果表明,在孤立态中,联苯基的二个苯环的最小二乘