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].     

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.     

三硼酸锂晶体的生长形态

用自由生长系统研究了三硼酸锂ＬｉＢ_３Ｏ_５（ＬＢＯ）晶体的实际生长形态。实验表明，它的各晶面簇的重要性的顺序为：｛１１０｝＞｛０１１｝＞｛２０１｝＞｛１１１｝。讨论了ＬＢＯ晶体的生长习性与内部结构之间的关系并应用负离子配位多面体理论模型解释了ＬＢＯ晶体的生长形态。