图的直径与Betti亏数

对于任意的正数Ｍ以及正整数ｄ≥４,存在直径为ｄ的ｉ－边连通无环图Ｇ使得ζ（Ｇ）≥Ｍ,其中ζ（Ｇ）是Ｇ的Ｂｅｔｔｉ亏数,ｉ＝１,２,３。     

新型塑料导线直径在线测量系统

本文提出了一种用线阵ＣＣＤ非接触实时测量塑料导线直径的仪器，它有如下特点：（１）采用了对被测目标所发出的烟雾不敏感的光学系统，提高了测量精度；（２）采用工作于脉冲方式的大功率近红外ＬＥＤ做照明光源，其寿命比采用白炽灯作为光源大为增长，同时缩小了体积并有利于抑制可见光的干扰；（３）对电信号采用了两级滤波、直流恢复、自适应阈值二值化等处理技术；（４）采用定标的方法来消除目标位置移动的影响，提高了测量精度，降低了加工装配精度要求。现场使用证明，它能长期可靠地工作，总的测量误差小于±０．０２ｍｍ。     

Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models

Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the nean square errors criterion,where the model matrix need not have full rank and the dispersion matrix can be singular.Our results show that any one of both estimates cannot be always superior to the other.Some sufficient criteria for any one of them to be better than the other are established.Some interesting relations between these two estimates are also given.     

小世界网络与无标度网络的社区结构研究

模块性(modularity)是度量网络社区结构(community structure)的主要参数.探讨了Watts和Strogatz的小世界网络(简称W-S模型)以及Barabàsi 等的B-A无标度网络(简称B-A模型)两类典型复杂网络模块性特点.结果显示，网络模块性受到网络连接稀疏的影响，W-S模型具有显著的社区结构，而B-A模型的社区结构特征不明显.因此，应用中应该分别讨论网络的小世界现象和无标度特性.社区结构不同于小世界现象和无标度特性，并可以利用模块性区别网络类型，因此网络复杂性指标应该包括 关键词： 模块性 社区结构 小世界网络 无标度网络     

亚微米直径光纤的非线性特性研究

用电磁场的严格解分析了亚微米直径光纤的非线性系数，发现光纤直径在700 nm左右（亚微米量级）非线性系数较大，喇曼阈值较小，喇曼增益谱线较多；受激喇曼散射特性的分析表明，由于直径小，光纤在较小的泵浦光功率作用下能量密度就很大，因此很容易观察到受激喇曼散射.实验结果表明，理论分析与实验结果吻合得很好.     

GaN发光二极管表观电容极值分析

利用正向交流(ac)小信号方法对GaN发光二极管的电容-电压特性进行测量,可以观察到GaN发光二极管中的负电容现象。正向偏压越大,测试频率越低,负电容现象越明显。测量到的负电容现象是表象,不存在负电容;提出GaN发光二极管p-n结的结电容在特定的正向电压范围内等效于可变电容。分析可变电容对正向交流小信号响应得到:特定参数的可变电容使结电容电流相位落后于交流小信号电压相位π/2,使得在测量中表现为负电容。发现表观电容-正向电压曲线的极值点与理论模型相吻合,证明了该理论模型的正确性。     

Light Irradiation through Small Particles and Its Applications for Surface Nanostructuring in Near Field

We investigate the light scattering through small particles and its applications in nanostructuring, such as nanobumping, nanopatterning and dry laser cleaning. The theoretical calculation based on Mie theory provides an exact solution for sphere cavity resonance and plasmon resonance, which are two mechanisms for dielectric and metallic particles assisted surface nanostructuring in near field. The experimental results indicate that nanobumps on glass surface and subwavelength holes array on silicon surface can be formed without cracks with the self-assembly of 1 μm silica particle mask under laser irradiation. It is also found that the scattering wave by 40 nm gold particles can propagate 200 times away in terms of particle radius as recorded by photoresist under the UV light irradiation. Meanwhile, dry laser cleaning of 40nm gold particle on silicon wafer is demonstrated at plasmonic resonance frequency. The total cleaning efficiency is estimated to be 80%.     

共振小实验

共振现象非常有趣，下面提供3个简单易行的小实验，不妨做一做，亲自感悟一下共振吧．     

Ultralite系列DPSS激光器

镭宝光电技术有限公司的Ultralite系列DPSS激光器，具有高性能、小体积、长寿命的特点，它按照输出波长的不同分为6种机型，有1064nm，1053nm，1319nm，660nm，527nm，355nm等输出波长，适用于各种科研、精细工业加工领域的应用。     

An optical fiber methane gas sensing film sensor based on core diameter mismatch

<正>An optical fiber evanescent wave methane gas sensor based on core diameter mismatch is reported.The sensor consists of a multimode fiber in which a short section of standard single-mode fiber,coated with the inclusion of cryptophane molecules E in a transparent polysiloxane film,is inserted.The sensing principle is analyzed by optical waveguide theory.For different sensing film thicknesses and interaction lengths,the sensor signal is investigated within the methane concentration range of 0-14.5%(v/v).It is shown that the sensor signal with the thickness of 5μm and the interaction length of 3 mm strengthens linearly with the increasing concentration of methane,with a slope of 0.0186.The best detection limit of the sensor for methane is 2.2%(v/v) with a response time of 90 s.This sensor is suitable for the detection of methane concentration below the critical value of 5%.