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     

应用晶体结构数据进行化学反应途径研究 Ⅰ. 五配位钼化合物Mo(L)5的动态立体化学

The principle of structure correlation is applied to 28 crystal structures which contain 44 different five-coordinate molybdenum fragments. The data derived map the reaction pathway for a bimolecular ligand substitution reaction at tetrahedral molybdenum centers. The dihedral-angle method from Muetterties and Guggenberger is employed in order to describe the interconversion between the trigonal bipyramidal (TBP) and the square pyramidal (SQP) conformations via the Berry pseudorotation mechanism in the system of Mo(L)_5 complexes. This structure correlation method provides a convincing mapping of the Berry pathway in this paper.