赤道不是轨道弧的n次多项式向量场的Poincaré紧化场之拓扑结构

本文证明了赤道不是轨道弧的n次多项式向量场的Poincare紧化场之拓扑结构包含赤道是轨道弧的n-1次多项式向量场的Poincare紧化场之拓扑结构;当n=2时,这种包含关系是相等的,且其Poincare紧化场有五种不同的拓扑结构;当n=2k+1(k=1,2…)时,这种包含关系是真子集。     

具Hardy-Sobolev临界指数的奇异椭圆方程多解的存在性

运用变分方法研究了下面问题-Δpu=μupx(s)s-2u f(x,u),x∈Ω,u=0,x∈Ω,多重解的存在性,其中Ω是一个具有光滑边界的有界区域.     

图与补图全独立数间的关系

对图G(V,E),V∪E中既不相邻、又不相关联的最大元素个数,称为G的全独立数,并简记为α_T(G)。本文研究了图和补图全独立数之间的关系,得到α_T(G) α_T(G~C)≤「3y 1/2」。其中y=|V(G)|,G~C是G的补图,「x」为不大于x的最大整数,且界可达。     

4一致反超图的最小边数问题

混合超图是在超图的基础上添加一个反超边得到的图．超边和反超边的区别主要体现在着色要求上．在着色中,要求每一超边至少要有两个点着不同的颜色,而每一反超边至少有两个点着相同的颜色．最大最小颜色数分别称为混合超图的上色数和下色数。本文主要研究反超图,即只含反超边的超图。讨论了上色数为3的4一致超图的最小边数问题．给出了上色数为3的4一致反超图的最小边数的一个上界和一个下界．     

研究K4-同胚图K4(α,1,1,δ,ε,η)色性的一个引理

主要介绍了一个引理，这个引理奠定了K4－同胚图K4（α，1，1，δ，ε，η）色性研究的基础。     

Regular Balanced Cayley Maps for Cyclic, Dihedral and Generalized Quaternion Groups

A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and generalized quaternion groups are classified.     

Open Superstring Star as a Continuous Moyal Product with B Field

In this paper, we recast the matter part of the open superstring star in the present of a constant B field. By using a different coordinate representation the matter part of the open superstring star is identified with the continuous Moyal product of functions of anti-commuting variables. Fortunately we find it does not depend on the value of the B field.     

障碍拟阵图

Let G be a simple graph and T={S :S is extreme in G}. If M(V(G), T) is a matroid, then G is called an extreme matroid graph. In this paper, we study the properties of extreme matroid graph.     

Effects of External Electric Field on Ferroelectric Superlattice with Two Alternating Layers

The effects of the external electric field on the ferroelectric superlattice with two alternating layers have been studied using the transverse Ising model based on the effective-field theory with the differential technique. The hysteresis loops and susceptibility of the system have been given. The stronger the external electric field, the smaller the susceptibility, reflecting that the polarization is weaker.     

Nano-tribological study on a super-hydrophobic film formed on rough aluminium substrates

A novel super-hydrophobic stearic acid (STA) film with a water contact angle of 166^o was prepared by chemical adsorption on aluminum wafer coated with polyethyleneimine (PEI) film. The micro-tribological behavior of the super-hydrophobic STA monolayer was compared with that of the polished and PEI-coated Al surfaces. The effect of relative humidity on the adhesion and friction was investigated as well. It was found that the STA monolayer showed decreased friction, while the adhesive force was greatly decreased by increasing the surface roughness of the Al wafer to reduce the contact area between the atomic force microscope (AFM) tip and the sample surface to be tested. Thus the friction and adhesion of the Al wafer was effectively decreased by generating the STA monolayer, which indicated that it could be feasible and rational to prepare a surface with good adhesion resistance and lubricity by properly controlling the surface morphology and the chemical composition. Both the adhesion and friction decreased as the relative humidity was lowered from 65% to 10%, though the decrease extent became insignificant for the STA monolayer. The project supported by the National Natural Science Foundation of China (50375151, 50323007, 10225209) and the Chinese Academy of Sciences (KJCX-SW-L2)