Maslov-type index and brake orbits in nonlinear Hamiltonian systems

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.     

激光标线的原理和实验

根据几何光学知识分析了激光标线原理.理论和实验表明:激光标线长度与激光光束形状、光学元件形状及材料折射率有关.并讨论了激光标线向两侧扩展的原因.     

Monotonic solutions of a quadratic integral equation of fractional order

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness.     

基于Copula的金融资产相关结构建模

分析了几种相关结构函数(Copula)表示的相关结构模型,给出了用相关结构函数对金融资产间的相关结构进行建模的方法.结果表明混合Gumbel(M-Gumbel)相关结构函数能较全面地描述上海深圳两证券指数的相关结构,模拟计算VaR的结果支持了实证分析的结论.     

Refraction of light in media

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dB _M/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the electron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work. Supported by Beijing Science and Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education and the Excellent Young Teachers Program of Ministry of Education of China     

多媒体教育资源库层次索引模型

依据多媒体教育资源各层次特征及其关系,通过定义资源媒体特征空间,构建了教育资源库层次索引模型,各层次特征间的映射规则将资源的高层语义特征映射到低层媒体特征,达到了扩充描述语义的目的,提高了查全率;结合学科本体,规范了资源标注内容和用户查询条件的描述,减少了人为因素对查询项和索引项匹配相似度计算的影响,提高了查准率.     

四阶微分方程奇异边值问题的正解

本文利用锥上的不动点指数理论,在更一般的边界条件下讨论了一类四阶奇异边值问题正解的存在性并给出了应用．     

负折射指数物质中金属线对电磁波的影响

构造两种结构负折射指数物质(NRM)，利用数值模拟计算两种结构的S参数.由于这种结构尺度比波长小，为精确利用有限积分技术(FIT)进行模拟.通过对这两种结构中金属线位置变化对金属谐振频率影响进行模拟，最后得出由于金属线与谐振环耦合，金属线对称破缺影响谐振环谐振频率和通带，并对等效负折射指数为负的频带产生影响. 关键词： 负折射率 左手物质 通带 金属线对称破缺     

SPR棱镜传感器测量液体折射率的原理

推导了消失波函数的表达式,介绍了衰减全反射现象及SPR传感器测量液体折射率的原理,并利用SPR传感器测量了牛奶样品的反射系数及折射率与脂肪等主要成分含量的关系曲线.     

短波通滤光片膜系设计

详细介绍用等效折射率概念设计短波通滤光片的原理和计算方法。根据原理和方法，选择二氧化钛（TiO2）作为高折射率材料、二氧化硅（SiO2）作为低折射率材料。首先从理论上计算出用这2种材料设计的波长λ=950～1150nm的短波通滤光片所需要的周期数，然后给出短波通滤光片的主膜系和光谱曲线。由于据此周期数设计出的膜系光谱曲线在750～810nm处的透过率不符合要求，因此对该膜系进行了改进。依照改进的设计进行多次制备，最终制备出了符合要求的短波通滤光片，找到了最佳制备工艺和方法。最后，对制备出来的短波通滤光片薄膜进行了各种环境实验。实验结果表明，膜层的各项指标符合设计要求。