The instability degree in the diemnsion of spaces of bivariate spline

In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.     

在几何和参数上表示同一条曲线的两条有理NURBS曲线的权与控制顶点之间的关系

The paper discusses the relationship between weights and control vertices of two rational NURBS curves of degree two or three with all weights larger than zero when they represent the same curve parametrically and geometrically, and gives sufficient and necessary conditions for coincidence of two rational NURBS curves in non-degeneracy case.     

ON A SET OF h-HARMONIC HOMOGENEOUS POLYNOMIALS

1　IntroductionLet Sd- 1 bethe unitsphere of Rd,Πdthe space of allpolynomialsofd variables,and x(i)= (x1 ,… ,xi) (i=1 ,… ,d) .In this paper,we are concerned with the homogeneous polyno-mials orthogonal with the weightfunction h(x(d) ) =x2 k11 …x2 kdd on Sd- 1 ,where ki≥ 0 (i=1 ,… ,d) .Connected with the weightfunction h(x(d) ) are the following differential-differenceoperators introduced by Charles F. Dunkl in [3 ] ,Dip(x(d) ) = p(x(d) ) xi+ di=1kip(x(d) ) -p(x1 ,… ,-xi,… ,xd)xi,Δ…     

薄荷醇酯香料的合成研究进展

许多薄荷醇酯类化合物是重要的香料成分,已广泛应用于食品、烟草、医药和化妆品等领域。近年来,人们对常见的乙酸薄荷醇酯、乳酸薄荷醇酯等单薄荷醇酯的合成,在催化剂、脱水剂筛选等条件优化方面进行了深入的研究,同时开发了氨基酸薄荷醇酯、水杨酸薄荷醇酯等单薄荷醇酯以及由丁烯二酸、苹果酸、酒石酸等合成双薄荷醇酯,并进行了包括多薄荷醇酯在内的潜香添加剂研究。本文根据薄荷醇酯类香料的不同结构类型,综述了其近年来的合成研究新进展。     

作为一元等距结点样条推广的多元样条

作者们在[4]中已经指出了给定剖分下多元B-样条存在的必要条件(1).它表明,并不是对所有的剖分都有多元B-样条存在的。人们也许以为,如同一元情况一样,只要多元B-样条存在,则它们一定组成多元样条空间的支集(即多元样条空间是所有多元B-样条所支架起来的空间)。本文以标准的三角剖分(2-单纯形)下,多元样条空间S²:=S₄²为例指出这种认识是错误的。事实上,本文定理2,3和4对这个问题已给出了明确的结论。 以上结论说明多元B-样条并不是基本的     

电导法研究树脂与游离酸的相互作用

利用电导实验技术跟踪树脂吸附游离酸的行为 ,讨论了外加盐和乙醇等因素对吸附的影响 ,利用固 -液相互作用方程求取吸附剂 -吸附质相互作用能。实验结果表明 ,树脂吸附游离酸 ,其表观吸附速率常数随着外加盐离子浓度的增大而减少 ;表观吸附速率常数与吸附剂 -吸附质相互作用能存在线性关系。     

THE INSTABILITY DEGREE IN THE DIEMNSION OF SPACES OF BIVARIATE SPLINE

In this paper ,the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is consdered.The concept of the instability degree in the dimension of spaces of bivariate spline is presented.The resulats in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.     

BIVARIATE CUBIC B-SPLINES RELATIVE TO CROSS-CUT TRIANGULATIONS

In this paper we prove that there are no locally supported bivariate G~(k-1)spline functionsof degree k on cross-cut grid partitioned regions with no more than three lines meeting at acommon vertex.We also give explicit expressions of bivariate C~1 cubic B-spline with smallestlocal support on cross-cut triangular grid partitioned regions where each vertex is theintersection of three lines.Properly normalized,these B-splines are proved to be uniquelydetermined and form a partition of unity.Furthermore,the corresponding waxationdiminishing bivariate spline operators are proved to preserve all linear polynomials of twovariables.These facts enable us to give error estimates for approximation by bivariate C~1cubic splines for functions of class C,C~1 and C~2.     

Preparation of LiNi0.5Mn1.5O4 cathode materials by using different-sized Mn3O4 nanocrystals as precursors

Journal of Solid State Electrochemistry - High-voltage LiNi0.5Mn1.5O4 with a spinel structure is considered as important cathode materials for high-energy density Li-ion batteries (LIBs). In this...     

多元弱样条空间和最小确定集

根据研究多元弱样条函数的B—网方法,给出了某些多元弱样条函数空间的最小确定集的构造方法,并从而求出了它们的维数．本文还讨论了对偶基的局部支集性质。