再论一类二次系统的无界双中心周期环域的POincare分支

本文再一次讨论了具有双曲线与赤道弧为边界的双中心周期环域的二次系统的Poincare分支，并构造出了此系统出现极限环的(0，3)分布或出现一个三重极限环的具体例子．     

测度链上非线性微分方程的三正解

运用文[1]中的Leggett—Williams不动点定理，我们给出了测度链上的非线性微分方程-x^△△(t)=f(t,x(σ(t))),t∈[a,b,]关于两点边值条件ax(a)-βx^△(a)=0，γx(σ(b)) δx^△(σ(b))=0三正解存在性准则。     

关于复微分方程组的形式

本文的目的是研究一类复微分方程组存在允许解时它的形式．方法是利用亚纯函数Nevanlinna的值分布理论．该文得到了二个结果。是文[3]的进一步讨论．     

Additive formulae of theta functions and modular equations of degree five

Ramanujan recorded additive formulae of theta functions that are related to modular equations of degree five. We present elementary and simple proofs.     

李三系与Laurent多项式代数F[t,t~(-1)]

本文通过讨论Laurent多项式代数及其导子代数的对合自同构确定了一类具体的无限维单李三系, 并且提供了一种利用Novikov代数上自然的李代数结构来构造李三系的方法.     

Hydrogen bubbles and formation of nanoporous silicon during electrochemical etching

Many nanoporous Si structures, including those formed by common electrochemical etching procedures, produce a uniformly etched nanoporous surface. If the electrochemical etch rate is slowed down, details of the etch process can be explored and process parameters may be varied to test hypotheses and obtain controlled nanoporous and defect structures. For example, after electrochemical etching of heavily n‐doped (R = 0.05–0.5 Ω·cm) silicon 〈100〉 single crystals at a current density of 10 mA cm^?2 in buffer oxide etch (BOE) electrolyte solution, defect craters containing textured nanopores were observed to occur in ring‐shaped patterns. The defect craters apparently originate at the hydrogen/BOE bubble interface, which forms during hydrogen evolution in the reaction. The slower hydrogen evolution due to low current density and high BOE viscosity allows sufficient bubble residence time so that a high defect density appears at the bubble edges where local reaction rates are highest. Current‐carrying Si? OH species are most likely responsible for the widening of the craters. Reducing the defect/doping density in silicon lowers the defect concentration and thereby the density of nanopores. Measurements of photoluminescence lifetime and intensity show a distinct feature when the few nanopores formed at the ring edges are isolated from each other. Overall features observed in the photoluminescence intensity by XPS strongly emphasize the role of surface oxide that influences these properties. Copyright © 2005 John Wiley & Sons, Ltd.     

完全单半群上同余的两种刻画

给出了完全单半群的相容组和同余结的定义,并利用它们刻画了完全单半群上的同余.     

A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters

We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points lines, where three interfaces meet, and at the boundary points lines, where an interface meets a fixed planar boundary. We propose a parametric finite element method based on a suitable variational formulation. The constructed method is semi-implicit and can be shown to satisfy the volume conservation of each enclosed bubble and the unconditional energy-stability, thus preserving the two fundamental geometric structures of the flow. Besides, the method has very good properties with respect to the distribution of mesh points, thus no mesh smoothing or regularization technique is required. A generalization of the introduced scheme to the case of anisotropic surface energies and non-neutral external boundaries is also considered. Numerical results are presented for the evolution of two-dimensional curve networks and three-dimensional surface clusters in the cases of both isotropic and anisotropic surface energies.     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅱ)──PART 1

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李color三系的Frattini子系的性质

给出了李color三系的Frattini子系的定义,得到了李color三系的Frattini子系的一些性质·特别的,证明了李color三系T有分解T=T_1⊕T_2⊕…⊕T_m,则φ(T)有分解φ(T)=φ(T_1)⊕φ(T_2)⊕…⊕φ(T_m).