Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems

We study the Clarke–Rockafellar directional derivatives of the regularized gap functions (and of some modified ones) for the variational inequality problem (VIP) defined by a locally Lipschitz but not necessarily differentiable function on a closed convex set in an Euclidean space. As applications we show that, under the strong monotonicity assumption, the regularized gap functions have fractional exponent error bounds and consequently that the sequences provided by an algorithm of Armijo type converge to the solution of the (VIP). The research of this author was supported by an Earmarked Grant from the Research Council of Hong Kong.     

微波传输路由的数学模型

在微波通讯中，电波射束和障碍物之间应留有足够的余隙，以保证能量的有效传输．本文考虑地球表面自然凸特征，建立在此意义下的余隙的数学模型，从而获得微波传输路由的数学模型．利用此模型的解与海拔制高点的余隙进行比较，便可获得工程建设中的最佳余隙值及相联系的有效的经济的路由设计．     

Gap functions and error bounds for nonsmooth convex vector optimization problem

Abstract

In this article, our main aim is to develop gap functions and error bounds for a (non-smooth) convex vector optimization problem. We show that by focusing on convexity we are able to quite efficiently compute the gap functions and try to gain insight about the structure of set of weak Pareto minimizers by viewing its graph. We will discuss several properties of gap functions and develop error bounds when the data are strongly convex. We also compare our results with some recent results on weak vector variational inequalities with set-valued maps, and also argue as to why we focus on the convex case.     

产业结构变动与城乡收入差距关系的协整分析

根据中国1952-2008年的数据,运用协整理论和Granger因果检验分析了中国产业结构变动与城乡收入差距的关系.协整检验及误差修正模型结果表明,二者之间在所研究期间内存在长期稳定的正向均衡关系,并且短期动态校正作用明显.同时,Granger因果关系检验结果说明中国的产业结构变动与城乡收入差距扩大之间存在双向因果关系.     

A note on the integrality gap of an ILP formulation for the periodic maintenance problem

We address the integrality gap of the integer linear program introduced by Grigoriev et al. (2006) [3] for the periodic maintenance problem. We prove that the integrality gap of this program is bounded by a constant.     

Reflection and transmission of plane acoustic waves in an infinite annular duct with a finite gap on the inner wall

The diffraction of acoustic waves by an infinitely long annular duct having a finite gap on the inner wall is investigated rigorously. The related boundary‐value problem is formulated into a modified Wiener–Hopf equation, which is then reduced to a pair of simultaneous Fredholm integral equations of the second kind. At the end of the analysis, numerical results illustrating the effects of the width of the coaxial cylindrical waveguide and the gap length on the diffraction phenomenon are presented. Copyright © 2010 John Wiley & Sons, Ltd.     

Electronic structure modeling of InAs/GaSb superlattices with hybrid density functional theory

The application of first-principles calculations holds promise for greatly improving our understanding of semiconductor superlattices. Developing a procedure to accurately predict band gaps using hybrid density functional theory lays the groundwork for future studies investigating more nuanced properties of these structures. Our approach allows a priori prediction of the properties of SLS structures using only the band gaps of the constituent materials. Furthermore, it should enable direct investigation of the effects of interface structure, e.g., intermixing or ordering at the interface, on SLS properties. In this paper, we present band gap data for various InAs/GaSb type-II superlattice structures calculated using the generalized Kohn-Sham formulation of density functional theory. A PBE0-type hybrid functional was used, and the portion of the exact exchange was tuned to fit the band gaps of the binary compounds InAs and GaSb with the best agreement to bulk experimental values obtained with 18% of the exact exchange. The heterostructures considered in this study are 6 monolayer (ML) InAs/6 ML GaSb, 8 ML InAs/8 ML GaSb and 10 ML InAs/10 ML GaSb with deviations from the experimental band gaps ranging from 3% to 11%.     

Band structure characteristics of T-square fractal phononic crystals

The T-square fractal two-dimensional phononic crystal model is presented in this article.A comprehensive study is performed for the Bragg scattering and locally resonant fractal phononic crystal.We find that the band structures of the fractal and non-fractal phononic crystals at the same filling ratio are quite different through using the finite element method.The fractal design has an important impact on the band structures of the two-dimensional phononic crystals.     

Spectroscopic investigations and electrical properties of PVA/PVP blend filled with different concentrations of nickel chloride

Films of PVA/PVP blend (50/50) filled with different concentrations of NiCl₂ were prepared by casting method. The prepared films were investigated by different techniques. XRD scans demonstrated that the peak intensity at 2θ≈20° decreased and the band width increased with increase in the concentrations of NiCl₂ content, which implied decrease in the degree of crystallization and hence causes increase in the amorphous region. UV-vis analysis revealed that the values of the optical band gap are affected with increase in NiCl₂ content. This indicates the formation of charge transfer complexes between the polymer blend and the filler. The rise of conductivity is significant with increased concentration of NiCl₂ filler; this reveals an increase in degree of amorphosity. AC conductivity (σ_ac) behavior of all the prepared films was investigated over the frequency range 42 Hz-5 MHz and under different isothermal stabilization in the temperature range 313-393 K. It suggests that the hopping mechanism might be playing an important role in the conduction process in high frequency region. The dielectric behavior was analyzed using dielectric permittivity (ε´, ε″) dielectric loss tangent (tan δ) and electric modulus (M″). The decrease in dielectric permittivity was observed with increase in the concentration of NiCl₂ filler. This suggests the role of NiCl₂ as filler to improve the electrical conductivity of PVA/PVP blend.     

大气压尖板电极结构重复频率纳秒脉冲放电中X射线辐射特性研究

文章通过碘化钠晶体和光电倍增管构成的X射线探测系统,研究了上升沿15ns,脉宽30-40ns量级,电压90kV的大气压重频纳秒脉冲气体放电中X射线的辐射特性,X射线有效探测能量范围为10-130keV.结果表明放电产生的X射线主要集中在20-90keV能量范围,而能量在十几keV的软X射线和超过90keV的高能X射线数量很少.X射线辐射计数随脉冲重复频率的增加而增加,随着气隙距离的改变存在峰值,且峰值出现在弥散放电模式.