Characterization of isolated homogeneous hypersurface singularities in ℂ4

Let V be a hypersurface with an isolated singularity at the origin in ? ⁿ⁺¹. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface signularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau’s theorem remains true for singularities with geometric genus equal to zero.     

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR NONLINEAR HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for nonlinear higher order ordinary differential equation involving two small parameters has been considered. Under appropriate assumptions, for the three cases:ε/μ2→0(μ→0),μ2/ε→0 (ε→0) andε=μ2, the uniformly valid asymptotic solution is obtained by using the expansion method of two small parameters and the theory of differential inequality.     

A warehouse-based design model for reverse logistics

In this paper, an MILP formulation is proposed for the design of a reverse logistics network based on a warehouse location–allocation model, which optimizes, simultaneously, the forward and reverse networks. A single product model with unlimited capacity is first defined. Subsequently, the model is extended to a multi-product capacitated recovery network model, where capacity limitations and a multi-product system can be considered. The proposed model is compared to published work in the field, where different model assumptions have been proposed. Two cases are described so as to gain a better insight into the model and allow a comparative analysis.     

k-树的补图的最小填充和树宽

一个图的最小填充问题是寻求边数最少的弦母图,一个图的树宽问题是寻求团数最小的弦母图,这两个问题分别在稀疏矩阵计算及图的算法设计中有非常重要的作用．一个k-树G的补图G称为k-补树．本文给出了k-补树G的最小填充数f(G) 及树宽TW(G)．     

Electroactive conducting polymers for corrosion control

There is an intensive effort underway to develop new corrosion control coatings for structural metals. In part, this effort has been motivated by the desire to replace chromium(VI)-containing coatings currently used for corrosion control of iron and aluminum alloys. Cr(VI) has been shown to be hazardous to the environmental and to human health, and its use in many countries will be sharply curtailed in the coming years. Electroactive conducting polymers (ECPs) represent a class of interesting materials currently being explored for use in corrosion control coating systems, possibly as a replacement for Cr(VI)-based coatings. The electroactivity and the electronic conductivity (or semiconductivity) of ECPs set them apart from traditional organic coatings. As with chromate, interesting and potentially beneficial interactions of ECPs with active metal alloys such as steel and aluminum are anticipated, with concomitant alteration of their corrosion behavior. A review of this active research area will be presented in two parts. Here in Part 1, a general introduction to the topic of corrosion control by ECPs will be presented, including an overview of corrosion and its control by traditional methods, an introduction to ECPs and their properties, and a discussion of the processing issues surrounding the use of ECPs as coatings. Part 1 also includes a review of the literature on the use of ECPs as coatings (or components of coatings) on non-ferrous active metals, principally aluminum and aluminum alloys, although some work on zinc, copper, silver, titanium and silicon will also be described. In Part 2 of this review (to be published in the next issue of this journal), the rather extensive literature on the use of ECPs for the corrosion control of ferrous alloys (steels) will be reviewed. Electronic Publication     

Quadratic data envelopment analysis

Data Envelopment Analysis (DEA) offers a piece-wise linear approximation of the production frontier. The approximation tends to be poor if the true frontier is not concave, eg in case of economies of scale or of specialisation. To improve the flexibility of the DEA frontier and to gain in empirical fit, we propose to extend DEA towards a more general piece-wise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). We show that QDEA gives statistically consistent estimates for all production frontiers with bounded Hessian eigenvalues. Our Monte-Carlo simulations suggest that QDEA can substantially improve efficiency estimation in finite samples relative to standard DEA models.     

Effective dimensionality approach to the RKKY interaction in multilayer systems

We consider RKKY interaction in a quasi 2D system with nonparabolic dispersion. In our paper we calculate the RKKY range function assuming the in-layer confinement via effective dimensionality approach. We show, that indirect magnetic exchange in our system can be modelled by the effective spectral dimension which equals one.     

原子力显微镜在生物物理领域的新应用

介绍了原子力显微镜在生物物理领域的最新应用:蛋白质去折叠、DNA拉伸、生物膜受力,通过分析实验得到的力谱,可以获取关于蛋白质、DNA、生物膜结构信息.原子力显微镜不仅能反映测量体系的力学性质,由于其具有独特的时间、空间分辨及实时成像,因而能提供更多信息.     

关于左手性介质几何光学的研究（一）

根据几何光学中的费马原理和完善成像原理研究了光线经过正负折射率界面时的传播特性，推导了单负折射率完善成像的曲面方程，讨论了单块负折射率透镜成像特性的一些缺陷及改进方案，依此指出了最短时间原理的适用范围的局限性和利用左手性介质制作光学器件的优越性，为进一步研究左手性介质的光学特性和相关光学器件设计提供了理论基础.     

合肥光源高亮度模式Lattice设计

介绍了一组合肥光源新高亮度模式的Lattice. 新的设计维持了储存环上所有元件和光束线位置不变,也没有加入新的元件. 取得了较低发射度. 所有直线节处的垂直方向β函数值都很小，适合插入件的运行. 跟踪计算表明新Lattice具有足够大的动力学孔径用于注入和储存粒子.