Nanostructured thermoset epoxy resin templated by an amphiphilic poly(ethylene oxide)‐block‐poly(dimethylsiloxane) diblock copolymer

An amphiphilic poly(ethylene oxide)‐block‐poly(dimethylsiloxane) (PEO–PDMS) diblock copolymer was used to template a bisphenol A type epoxy resin (ER); nanostructured thermoset blends of ER and PEO–PDMS were prepared with 4,4′‐methylenedianiline (MDA) as the curing agent. The phase behavior, crystallization, hydrogen‐bonding interactions, and nanoscale structures were investigated with differential scanning calorimetry, Fourier transform infrared spectroscopy, transmission electron microscopy, and small‐angle X‐ray scattering. The uncured ER was miscible with the poly(ethylene oxide) block of PEO–PDMS, and the uncured blends were not macroscopically phase‐separated. Macroscopic phase separation took place in the MDA‐cured ER/PEO–PDMS blends containing 60–80 wt % PEO–PDMS diblock copolymer. However, the composition‐dependent nanostructures were formed in the cured blends with 10–50 wt % PEO–PDMS, which did not show macroscopic phase separation. The poly(dimethylsiloxane) microdomains with sizes of 10–20 nm were dispersed in a continuous ER‐rich phase; the average distance between the neighboring microdomains was in the range of 20–50 nm. The miscibility between the cured ER and the poly(ethylene oxide) block of PEO–PDMS was ascribed to the favorable hydrogen‐bonding interaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3042–3052, 2006     

Photonic crystal beam splitters

In this work, the beam splitter with two input ports and two output ports in two-dimensional photonic crystals is studied through the finite-difference time-domain method. The beam splitter consists of two orthogonally cross line defects. The diameter of the two diagonal air holes at the intersection of the two line defects was modified. The input light can be identically divided into the two output ports. The beam splitters can be applied in the photonic crystal Mach-Zehnder interferometers or photonic crystal optical switches.     

数学与物理的导数

这是一篇关于数学和物理中以导数的推广为中心交流的非正式介绍文章。     

Rigidity and finiteness under Ricci curvature and volume controls

Consider the class of closed Riemannian manifolds M of dimension dim(M) \geqq 3 \dim(M) \geqq 3 , Ricci curvature Ric(M) \geqq -(n - 1) \textrm{Ric}(M) \geqq -(n - 1) , diameter diam(M) < D and almost maximal volume. We show that the isomorphism types of fundamental groups characterize the diffeomorphism types of manifolds in such a class. In particular, it can be viewed as a generalization of the well-known Mostow‘s rigidity theorem and a finiteness theorem.     

凸域内单叶函数的导数

设函数f（w）为凸区域D内的单叶解析函数,对于2≤n≤8和所有w∈D,本文得到估计式|f（n）（w）/f＇（w）|的精确上界.这个结果推广了一些已知的结论.     

On a class of new and practical performance indexes for approximation of fold bifurcations of nonlinear power flow equations

Efficient measurement of the performance index (the distance of a loading parameter from the voltage collapse point) is one of the key problems in power system operations and planning and such an index indicates the severity of a power system with regard to voltage collapse. There exist many interesting methods and ideas to compute this index. However, some successful methods are not yet mathematically justified while other mathematically sound methods are often proposed directly based on the bifurcation theory and they require the initial stationary state to be too close to the unknown turning point to make the underlying methods practical.This paper first gives a survey of several popular methods for estimating the fold bifurcation point including the continuation methods, bifurcation methods and the test function methods (Seydel's direct solution methods, the tangent vector methods and the reduced Jacobian method) and discuss their relative advantages and problems. Test functions are usually based on scaling of the determinant of the Jacobian matrix and it is generally not clear how to determine the behaviour of such functions. As the underlying nonlinear equations are of a particular type, this allows us to do a new analysis of the determinants of the Jacobian and its submatrices in this paper. Following the analysis, we demonstrate how to construct a class of test functions with a predictable analytical behaviour so that a suitable index can be produced. Finally, examples of two test functions from this class are proposed. For several standard IEEE test systems, promising numerical results have been achieved.     

溴酸钾-亚甲蓝催化光度法测定硝酸盐和亚硝酸盐

用镉柱将NO-3 还原为NO-2 ,利用在磷酸介质中NO-2 对溴酸钾氧化亚甲蓝这一褪色反应具有强烈的催化作用而建立了同时测定痕量硝酸盐和亚硝酸盐的新方法。本方法简便、快速、灵敏 ,对亚硝酸盐和硝酸盐测定的线性范围分别为 0～ 2 0 0 μg·L-1和 0 0 0 3～ 310 μg·L-1,用于测定各种水样中痕量NO-2 和NO-3 的含量均获得满意结果     

Formation of hydrogenated amorphous carbon films from polymer pyrolysis

Free-standing and supported hydrogenated amorphous carbon films (a:C–H) were prepared upon pyrolysis of the polymer formed by ethanolamine (EA) and citric acid (CA), under an ambient atmosphere at 300 °C. EA facilitates the formation of the macroscopic films, while CA is essential for obtaining the a:C–H microstructure, which comprises a mixture of sp² and sp³ carbon. Received: 29 May 2001 / Accepted: 17 August 2001 / Published online: 20 December 2001     

加肋圆柱壳在轴压作用下的屈曲和后屈曲

本文讨论完善和非完善的,纵向加肋和正交加肋圆柱壳在轴压作用下的屈曲和后屈曲性态.依据文[1]提供的圆柱薄壳屈曲的边界层理论及其分析方法,给出了加肋圆柱壳在轴压作用下的屈曲和后屈曲理论分析.本文同时讨论肋骨与壳板材料不同时对加肋圆柱壳屈曲和后屈曲性态的影响.     

Theoretical Research on a Kind of Quantum Left-handed Metamaterial

Recently, research on left-handed materials （LHMs） has attracted considerable attentions. The LHMs are a kind of metameterial which have negative permittivity and negative permeability, which lead to negative refractive index in a frequency range. The LHMs that have been available so far are in the microwave range and are usually composed of classical particles, such as split-ring resonators. Some quantum phenomena such as spontaneous emission of atoms in the LHMs which are considered to be ＇classical background＇ have also been investigated. Many potential applications of LHMs have been proposed, such as superlenses which, in principle, can achieve arbitrary subwavelength resolution.