Approximation on the Voronoi Cells of the A d Lattice

We study several approximation problems on the Voronoi cells of the A _d lattice. The study depends on discretization of the Voronoi cells induced by a zonotopal algebra and finite quotient groups. The latter provides a natural tool for doing discrete Fourier analysis on the Voronoi cells. The interactions between the groups and their dual groups yield interpolation and quadrature formulas on the Voronoi cells. The zonotope structure allows us to investigate the approximation property of several types of kernels (including the Dirichlet type and the Fejér type) on the Voronoi cells. The convolution operator given by the Fejér type kernel is positive, and consequently an approximate identity. The Fejér type kernel can also be realized as a summability method. As an interesting comparison to the classical (C,1) summability which assigns equal weight to the partial sums of a Fourier series, the Fejér type summability method on the Voronoi cells assigns equal weights to about half of the partial sums and algebraically decaying weights to the rest.     

非对称线性代数方程组的块向量算法

预条件广义共轭余量法并行和向量计算的关键是预条件计算是否可并行和向量计算，我们利用分而治之的原则，构造了一处块预条件矩阵Ｍ，这里的矩阵Ｍ是通过对线性代数方程组Ａｘ＝ｆ的矩阵Ａ进行块分解，在块分解中利用近似逆技术。这样分解形成的预条件矩阵Ｍ在迭代计算时，可向量或并行计算。     

The fundamentality of translates of a continuous function on spheres

In this paper we discuss the fundamentality of translates of a continuous function on the unit spheres of Euclidean spaces. Our result partially answers a question of Cheney and Xu [1].     

铁镓驱动弯曲圆盘换能器设计及振动特性研究

为了研究新型磁致伸缩材料——铁镓合金(Galfenol)在换能器中应用,本文设计了一种低频弯曲圆盘换能器。借助有限元软件仿真分析换能器振动模态,对换能器结构参数进行优化设计,并研制了换能器样品。利用激光测振仪测量了换能器空气中模态及不同电流驱动下振动位移,测得振动模态与仿真结果吻合,换能器空气中共振频率为913 Hz,辐射头能够产生的最大振动位移达到93μm,磁致伸缩材料达到饱和应变。结果表明:铁镓材料能够驱动弯曲圆盘换能器大振幅振动;铁镓作为磁致伸缩换能器驱动材料具有较好的应用前景。     

Synthesis of uniform anatase TiO2 nanoparticles by gel-sol method. 4. Shape control

Uniform anatase-type TiO(2) nanoparticles of different shapes have been formed by phase transformation of a Ti(OH)(4) gel matrix in the presence of shape controllers. For example, triethanolamine (TEOA) was found to change the morphology of TiO(2) particles from cuboidal to ellipsoidal at pH above 11. The shape control can be explained in terms of the specific adsorption of TEOA onto the crystal planes parallel to the c-axis of the tetragonal system in the alkaline range, as supported by the observation of preferential adsorption of TEOA onto the crystal planes parallel to the c-axis at pH 11.5 and by the pH dependence of the adsorption onto ellipsoidal particles. Diethylenetriamine (DETA) also modified the particle shape to ellipsoidal above pH 9.5 and the aspect ratio was much higher than with TEOA. The mechanism of the shape control could be explained in the same way as with TEOA, since analogous specific adsorption was observed with DETA as well. Similar shape control to yield ellipsoidal particles of a high aspect ratio was also achieved with other primary amines, such as ethylenediamine (ED), trimethylenediamine (TMD), and triethylenetetramine (TETA). However, secondary amines, such as diethylamine, and tertiary amines, such as trimethylamine and triethylamine, acted as a complexing agent of Ti(IV) ions to promote the growth of ellipsoidal particles of a low aspect ratio, rather than a shape controller to produce ellipsoids of a high aspect ratio. Sodium oleate and sodium stearate were found to modify the particle shape from round-cornered cubes to sharp-edged cubes. The mechanism was explained in terms of the reduction of the specific surface energies of the [001] and [100] planes of the tetragonal crystal system by the preferential adsorption of oleate or stearate ion onto these planes, based on the adsorption experiment using ellipsoidal and cubic particles.     

VISCOSITY BEHAVIOR OF LACQUER POLYSACCHARIDE IN AQUEOUS SOLUTION

The dependence of measured viscosity on NaCl concentration (0.1 to 3.0M), pH (range of 2—13) and cadoxen composition w_(cad) (from 2% to 100%) for the lacquer polysaccharide in NaCl/cadoxen/H_2O mixture containing HCl or without were obtained. All the viscosity exponents γin the Mark-Houwink equations under three different solvent condition arc close to 0.5. The w_(cad) dependence of reduced viscosity ηsp/c confirms the single strand chain of the polysaccharide. As the γvalues close to 0.5 and values of unperturbed dimension _θ/M and [η] much smaller than those for usual linear polymers, these facts suggest that the polysaccharide chains in the aqueous solutions should be dense random coil owing to the highly branched structure.     

均匀球形锆基色谱柱填料的制备方法研究

利用油乳液法（Oil Emulsion Method，OEM）、改进油乳液法（Modified oil emulsion methods，MOEM）和层层纳米自组装方法（layer-by-layer self-assembly，LbLSA）制备锫基HPLC填料。比较了3种制备方法对填料颗粒分布的影响：OEM法和MOEM法制备的ZrO2微米球粒径分别为2—30μm和6-15μm,粒径均匀性取决于搅拌速度和液珠的液膜强度；用LbLSA方法制备的核-壳形复合物ZrO2／SiO2粒径为3—5μm，颗粒的粒径分布取决于作为内核的SiO2微球的均匀性。实验结果表明：LbL SA方法制备的填料比用OEM法和MOEM法制备的氧化锫填料的粒径分布更均匀。     

草酸单乙酯三尖杉碱酯的合成及其在三尖杉酯类生物碱合成中的应用

用醇钠催化的酯交换方法合成了草酸单乙酯三尖杉碱酯(4),并用4和格氏试剂反应,得到合成三尖杉酯类生物碱的关键中间体α-酮酰基三尖杉碱(2),简化了已报道的一些三尖杉酯类生物碱的合成方法。