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].     

合成丙交酯中微量水分分析

合成丙交酯中微量水分分析徐溢，柳胜春（重庆大学化工学院分析教研室６３００４４）关键词丙交酯，微量水，定量分析丙交酯是人工合成骨材料聚乳酸的合成中间体，其性能决定着合成产品的品质，要获得高质量的合成材料，对中间体的分析和监测十分重要。一般要求丙交酯中间...