一道自主招生试题的简证与推广

2009年清华大学自主招生（理科）数学试题2（1）为： x,y为实数,且x＋y=1,求证：对Vn∈N＋,x^2n＋y^2n〉（2^-1）^2n-1。     

Some Results on Planar Graphs of Class 1

We consider only simple graphs in this paper unless otherwise stated,A plane gragh is a,particular drawing of a planar graph in the Euclidean plane. For a plane graph G, we denote its vertex set, edge set, face set, and maximum degree by V(G), E(G), F(G), and △(G) (or simply     

Characterization of regular periodic surface structure by multi-pulse laser irradiation of a Zinc target

The circular-like sidewall and trench around the periphery of the crater are obtained on Zinc metal surface subjected to fewer than 200 cumulative pulses laser ablation.These patterns can be attributed to the higher secondary heating by regular plasma spherical pressure.The 600 pulses laser ablation,however,results in the formation of undesirable bulk wrinkles of super-heated liquid at the side of the trench.These features may be applied in micro-manufacturing of high localizability and selectivity using laser zone texturing.     

Influence of Annealing Temperature on Structure, Optical Loss and Laser-Induced Damage Threshold of TiO2 Thin Films

TiO2 thin films are prepared on fused silica with conventional electron beam evaporation deposition. After annealed at different temperatures for 4h, the spectra and XRD patterns of the TiO2 thin film are obtained. Weak absorption of coatings is measured by the surface thermal lensing technique, and laser-induced damage threshold （LIDT） is determined. It is found that with the increasing annealing temperature, the transmittance of TiO2 films decreases. Especially when coatings are annealed at high temperature over 1173K, the optical loss is very serious. Weak absorption detection indicates that the absorption of coatings decreases firstly and then increases, and the absorption and defects play major roles in the LIDT of TiO2 thin films.     

共振拉曼光谱在体测量类胡萝卜素含量

类胡萝卜素是人体内重要的抗氧化剂,能够消除体内的自由基和其它有害氧分。研究表明类胡萝卜素含量与癌症、心血管疾病、老化等疾病发病率呈反比关系。目前检测方法为采用血清液相色谱检测方法,不能做到在体无损伤、实时测量。文章介绍了一种用于测量类胡萝卜素的新技术——共振拉曼光谱技术,具有在体无损伤、灵敏度高和实时检测等特点。该技术利用强度远小于美国ANSI Z136.1-2000标准的473 nm激光激发拇指中类胡萝卜素,产生强荧光和叠加在其上的弱共振拉曼光,通过测量拉曼散射光强度在体评估类胡萝卜素的含量。同时,利用组织通透技术,改善了测量信噪比。测量了不同饮食习惯志愿者的类胡萝卜素含量,说明其含量与其摄入量成正比。该技术在临床应用和科学研究等领域具有重要意义。     

Tunable Anisotropic Absorption of Ag-Embedded SiO2 Thin Films by Oblique Angle Deposition

Ag-embedded SiO2 thin films are prepared by oblique angle deposition. Through field emission scanning electron microscopy （SEM）, an orientated slanted columnar structure is observed. Energy-dispersive x-ray （EDX） analysis shows the Ag concentration is about 3% in the anisotropic SiO2 matrix. Anisotropic surface plasma resonance （SPR） absorption is observed in the Ag-embedded SiO2 thin films, which is dependent on polarization state and incidence angle of two orthogonal polarized lights and the deposition angle. This means that optical properties and anisotropic SPR absorption can be tunable in Ag-embedded SiO2 thin films. Broadband polarization splitting is also observed and the transmission ratio Tp/Ts between p- and s-polarized lights is up to 2.7 for thin films deposited at a = 70°, which means that Ag-embedded SiO2 thin films are a promising candidate for thin film polarizers.     

Imaging photothermal microscopy for absorption measurements of optical coatings

For absorption measurement of large-aperture optical coatings, a novel method of imaging photothermal microscopy based on image lock-in technique is presented. Detailed theoretical analysis and numerical calculation are made based on the image photothermal technique. The feasibility of this imaging method is proved through the coincidence between the theoretical results of single spot method and multi-channel method. The measuring speed of this imaging method can be increased hundreds of times compared with that of the raster scanning. This technique can expand the applications of photothermal technique.     

虚光场对光场与玻色-爱因斯坦凝聚体相互作用系统中光场压缩性质的影响

在压缩真空态光场和二能级原子玻色-爱因斯坦凝聚体相互作用系统中, 应用全量子理论, 采用非旋波近似, 研究了光场的压缩特性以及原子本征频率、原子-光场的耦合系数、光场初始压缩因子以及虚光场对系统光场压缩特性的影响. 研究表明, 光场的两个正交分量均被周期性压缩, 其压缩深度与光场初始压缩因子有关, 光场与原子的耦合系数决定了光场的量子崩塌-回复频率,虚光场效应使得光场的压缩深度增强.     

粒子区别性稀疏表征的小弱运动目标跟踪算法

评估每个粒子的重要性是确保粒子滤波法跟踪目标准确性的重要因素。针对背景杂波和噪声干扰形成的大量虚警导致小弱目标跟踪识别的随机性和不确定性问题, 提出了一种基于粒子区别性稀疏表征的小弱目标跟踪方法。该方法根据红外图像信号自适应构建分类超完备字典, 即反映目标信号特征的目标字典和表示背景杂波的背景字典, 有利于突出目标粒子和背景粒子在联合分类字典的稀疏表征差异程度;建立基于目标粒子和背景粒子稀疏重构残差差异性的粒子滤波观测模型, 采用随机估计法对字典子空间进行在线更新, 实现对目标状态估计与跟踪。理论分析和试验结果表明, 该方法增强了随机粒子的状态估计能力, 提升了粒子稀疏表征对小弱运动目标的适应能力和跟踪识别准确度。     

新高考背景下高中数学试题命制的思考

试题命制是一线教师探讨的永久话题,高质量的试题能够体现命题者的综合能力,能够考查学生对基本知识、技能、方法的理解与应用,以及素养的形成与发展.本文以高中数学试题的命制为探究载体,从“知识源头、关联结构、学生思维、模型分析、思维拓展”等角度进行思考,探讨新高考背景下高中数学试题命制的具体方法.