How to Exhibit Toroidal Maps in Space

Steinitz's theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of the embedded graph. Its faces are bounded by convex polygons whose points are coplanar. A map on the torus does not necessarily have such a geometric realization. In this paper we relax the condition that faces are the convex hull of coplanar points. We require instead that the convex hull of the points on a face can be projected onto a plane so that the boundary of the convex hull of the projected points is the image of the boundary of the face. We also require that the interiors of the convex hulls of different faces do not intersect. Call this an exhibition of the map. A map is polyhedral if the intersection of any two closed faces is simply connected. Our main result is that every polyhedral toroidal map can be exhibited. As a corollary, every toroidal triangulation has a geometric realization.     

Preparation of dye-loaded SiO2 nanoparticles

A room temperature method for the encapsulation of pyrene in SiO₂ nanoparticles is described. The relation between alkoxysilane surfactant chain length, reactant molar ratios and the uptake of dye, sample morphology, photophysical properties, and the ability of the silicate matrix to protect the encapsulated dye was examined. The synthesis can easily be adapted for the encapsulation of other hydrophobic and thermolabile substances, and used in the development of nanostructured optically active coatings, films and monoliths.     

CoNiZ系列合金的结构和马氏体相变性质

利用X射线衍射研究了CoNiZ(Z=Si,Sb,Sn,Ga等)合金在不同热处理条件下的相组成.当Z元素为Sn,Sb时,材料是完全的B2结构;但Z为Si时,材料变成面心立方的γ相.形成B2还是γ相由电子浓度和原子尺寸效应两种因素共同决定.而CoNiGa的研究结果表明,在合金中除了形成B2结构的同时还容易形成γ相,常表现出两相共存的特性.对材料进行不同方式的热处理可以使合金中两相的含量有所消长,γ相含量的多少对CoNiGa合金的马氏体相变有很大的影响.分析指出,两相共存及其所带来的物性变化是CoNiGa铁磁性形状记忆合金非常有利用价值的物理性质.     

La1-xPrxMnO3(x=0.1,0.2)薄膜庞磁电阻性质的研究

一种新的庞磁电阻氧化物薄膜La1-xPrxMnO3(x=0.1,0.2)薄膜用脉冲激光沉积(PLD)方法生长在(100)SrTiO3单晶基底上.XRD结果显示薄膜具有很好的外延单晶取向.电输运和磁性质的研究表明薄膜具有显著的庞磁电阻效应(CMR)效应,其中磁电阻比率达95%(在5T的磁场下).X射线光电子能谱(XPS)的结果表明薄膜体系中Pr离子的价态为+4价,因此该薄膜很可能是电子掺杂的庞磁电阻体系.     

A highly sensitive and rapid assay for protein determination in human urine and penicillin using a Rayleigh light-scattering technique with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt.

A simple and sensitive method was conducted for the determination of trace amounts of proteins with benzeneazo-8-acetylamino-1-naphthol-3,6-disulfonic acid sodium salt (azophloxine, AP) using a Rayleigh light-scattering (RLS) technique. At pH 2.60 and in the presence of an emulsifier OP microemulsion, the RLS of AP can be greatly enhanced by proteins, owing to the interaction between AP and protein. The enhanced intensity is proportional to the concentration of proteins. Four proteins, including bovine serum albumin (BSA), human serum albumin (HSA), lysozyme (Lys) and gamma globulin (gamma-G) have been tested. For example, the linear range of BSA was 0 - 0.06 microg mL(-1) with detection limits of 2.38 ng mL(-1). The method was applied to the analysis of protein in human urine and penicillin samples with satisfactory results. The relative standard deviation was in all instances less than 4.0%, and the recovery was in the range of 97.5 - 104%.     

Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications

This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.     

The newton filtration and d-determination of bifurcation problems related to C 0 contact equivalence

In this paper, from the Newton filtration’s point of view, we construct the singular Riemannian metric and use the method in singular theory to study the bifurcation problems, and give the sufficient condition of d-determination of bifurcation problems with respect to C ⁰ contact equivalence. The special cases of the main result in this paper are the results of Sun Weizhi and Zou Jiancheng.     

MnBiDy(Sm)永磁膜的结构和磁性

报道了采用真空蒸镀的方法制备的MnBiDy(Sm)永磁膜的结构和磁性.Mn:Bi:Dy(Sm)的投料比为2:1:0.10.薄膜经过退出处理(350—425℃,保温4h)后,具有NiAs型hcp结构,C轴垂直膜面,剩余磁感应强度B=3.4-6.5kG,内禀矫顽力_MH_c≈3-8kOe,最大磁能积(BH)_(max)=13.39MG·Oe.实验发现,薄膜厚度对MnBiDy(Sm)永磁膜的结构和磁性具有很大的影响. 关键词：     

Entropy of Bogoliubov automorphisms of the canonical anticommutation relations

We compute the entropyh _A ( _U ) in the sense of Connes, Narnhofer and Thirring of Bogoliubov automorphisms _U of the CAR-algebra with respect to invariant quasifree states _A with 0A1 having pure point spectrum.Supported in part by a grant from the National Science Foundation