Geometric Characterizations for Subgroups of PU（1, n; C）

In this paper, we discuss non-elementary subgroups and discontinuous subgroups of PU(1,n; C), and give their geometric characterizations.     

球体内部三模型

高考中有关球体的考查年年推陈出新,涉及球面上两点,三点,四点的问题考得可谓“淋漓尽致”.这类问题往往围绕球体部分的主要知识点:截面,球面距离,地球经纬度展开.但在一般考生眼中,有关球体的此类问题由于图形的难画而变的抽象难解,往往遇之绕道而行.本文拟将此类问题抽象为三种具体的几何模型,从而使问题简单化,避免解题过程中,由于画不出图而造成的思维受阻.     

Rapid Fabrication of Hollow SiO2 Spheres with Novel Morphology

The hydrolysis of tetraethoxysilane (TEOS) occurred on the surface of poly(methyl methacrylate) (PMMA) microshperes immediately after these microshperes were prepared in TEOS. Micron-sized hollow SiO2 spheres were obtained by calcination of the coated PMMA microshperes. It was found that the final hollow spheres were constituted by small SiO2 particles.     

STUDY ON SYNTHESIS OF SELF CORSS LINKED POLYSTYRENE LATEX MICROSPHERES

Emulsifier-free emulsion polymerization of styrene in the presence of β-hydroxy propyl acrylate was studied.The emulsifier-free self cross linked polystyrene latex microspheres was obtained.Monomer conversion is higher than 90% when [St],[β-HPA],[KPS] is 2.66,0.228,and 5.8×10^-3mol/L respectively under 80℃ for 5h.The mono-dispersed latex particle diameter and colloidal particle concentration were given as D=0.23um,N=3.13×10^13/cm^3 by TEM analyse,The factors of influencing latex stability were discussed.Thecopolymer was characterized by IR and dissolution experiment.The apparent activation energy of polymerization and polymerization rate constant were obtained to be 78.7KJ/mol and 514.4/mol.s respectively.     

NARROW-DISPERSED CROSSLINKED CORE-SHELL POLYMER MICROSPHERES PREPARED BY SURFACE-INITIATED ATOM TRANSFER RADICAL POLYMERIZATION＊

Grafting of polystyrene with narrowly dispersed polymer microspheres through surface-initiated atom transfer radical polymerization (ATRP) was investigated. Polydivinylbenzene (PDVB) microspheres were prepared by dispersion polymerization with poly(N-vinyl pyrrolidone) (PVP) as stabilizer. The surfaces of PDVB microspheres were chloromethylated by chloromethyl methyl ether in the presence of zinc chloride as catalyst to form chloromethylbenzene initiating core sites for subsequent ATRP grafting of styrene using CuCl/bpy as catalytic system. Polystyrene was found to be grafted not only from the particle surfaces but also from within a thin shell layer, resulting in the formation of particles size increased from 2.38-2.58μm, which can further grow to 2.93μm during secondary grafting polymerization of styrene. This demonstrates that grafting polymerization proceeds through a typical ATRP procedure with living nature. All of the prepared microspheres have narrow particle size distribution with coefficient of variation around 10%.     

PREPARATION OF POLYMER MICROSPHERES WITH PYRIDYL GROUP AND THEIR STABILIZED GOLD METALLIC COLLOIDS

Narrow disperse poly(ethyleneglycol dimethacrylate-co-4-vinylpyridine)(poly(EGDMA-co-4-VPy))microspheres were prepared by distillation-precipitation copolymerization of ethyleneglycol dimethacrylate(EGDMA)and 4-vinylpyridine (4-VPy)with 2,2'-azobisisobutyronitrile(AIBN)as initiator in neat acetonitrile.The polymer microspheres containing pyridyl group were then utilized as stabilizer for gold metallic colloids with the diameter around 7 nm,which were prepared by the in situ reduction of gold chloride trihydrate with sodium borohydride through the coordination of the pyridyl group on the gel layer and surface of the microsphere with the gold metallic nano-particles.The catalytic properties of the pyridyl- functionalized microsphere-stabilized gold metallic colloids and the behavior of the stabilized-catalyst for the recycling were investigated with reduction of 4-nitrophenol to 4-aminophenol as a model reaction.     

学一点数学史(续)——谈谈中学数学教师的数学史素养

这就是希尔伯特第 3 问题.希尔伯特第3问题,正是指向了数千年来数学家们一直努力求解的体积理论基础的谜团.     

均匀球体转动惯量的多种求法

用不同的方法计算了均匀球体的转动惯量,以开拓学生的思路,提高学生的学习兴趣.     

对球体的合理想象

对球体的考查是高考的一个热点和难点。由于在多考一点想，少考一点算的指导思想下，对球体的空间想象能力的考查，有时会比较难，只有进行合理想象，才能算出需要的量，如体积、面积和球面距离等等。下面通过具体例子来说明。     

EFFECT OF POLYETHYLENEIMINE ON THE PROPERTIES OF CONCENTRATED SUSPENSIONS OF TITANIUM DIOXIDE MICROBEADS

The effect of polyethyleneimine (PEI) concentration on the properties of titanium dioxide (TiO2) suspensions is studied with or without the addition of an electrolyte (barium acetate). Measurements of the apparent viscosity and the stability of TiO2 suspensions showed that PEI is an effective dispersant for TiO2 particles in suspension in the absence of an electrolyte, not only reducing the viscosity of the suspension but also increasing its stability. In the presence of an electrolyte, however, small quantities of polyethyleneimine could neither disperse the TiO2 particles nor de-crease the viscosity of the TiO2 suspensions; only PEI concentrations beyond saturation adsorption could perceptively improve the stabilitv of TiO2 suspensions.