陈省身和华罗庚

陈省身说与他数学生涯关系密切的有6个朋友：华罗庚、吴文俊、胡国定、A．韦伊、格里菲斯和西蒙斯。其中前三位是中国朋友，后三位是外国朋友。我们先来叙述有关华罗庚的故事。     

A New Approach for Calculating Vacuum Susceptibility

Based on the Dyson-Schwinger approach, we propose a new method for calculating vacuum susceptibilities. As an example, the vector vacuum susceptibility is calculated. A comparison with the results of the previous approaches is presented.     

M进制双正交对称小波的频率优化设计

§ 1　IntroductionM-band wavelets are used in a lotof applications such asspeech coding,image analysisand image coding[1 ,2 ] .When applied to the low-rate subband image coding,the symmetricextension method[3] has been shown to outperform the circular convolution method andyield both objective and subjective quality improvementat image boundaries.The symmet-ric extension method requires linear-phase scaling filters and wavelet filters.Two-bandbiorthogonal symmetric waveletbases have been const…     

Nucleon—Nucleon Phase Shifts in the Extended Quark—Delocalization Colour—Screening Model

An alternative method is applied to the study of nocleon-nucleon scattering phase shifts within the framework of the extended quark delocalization colour-screening model,in which the one-pion exchange with short-range cutoff is included.     

Terahertz Conductivity of Single Walled Nanotube Films

The conductivity of single walled nanotube films is investigated with a combination of the Maxwell-Garnett (MG) model and the Drude-Lorentzian (DL) model in the Terahertz region. A theoretical fit for Jeon‘‘s experiment is given and a decrease of the real conductivity with increasing frequency is predicted. Meanwhile, the MG and DL models are also discussed for different samples.     

拉压性能不同材料厚壁圆筒与厚壁球壳的极限压力

本文就拉压屈服极限不同的理想弹塑性材料厚壁圆筒及厚壁球壳在内压力作用下进行了应力分析，得到了依赖于压拉比的弹性极限载荷与塑性极限载荷。由分析结果可见，拉压性能不同材料的弹性极限载荷与塑性极限载荷均有所提高，并且随着壁厚的增加提高量也有显著增加。     

两种缓冲材料的应力松驰实验分析

用逐次残余法分析了聚乙烯和聚苯忆乙烯缓冲材料的应力松也试验数据，结果表明可用有限个并联的Ｍａｘｗｅｌｌ模型来表示这两种材料的应务松驰试验曲线。     

无催化剂条件下经微波辐射一步合成9-芳基-3,4,5,6,7,9-六氢-1H-氧杂蒽-1,8(2H)-二酮

微波辐射下以芳醛、1,3-环己二酮为原料在无催化剂条件下合成了一系列9-芳基-3,4,5,6,7,9-六氢-1H-氧杂蒽-1,8(2H)-二酮, 该反应时间短、产率高、后处理方便、环境友好.     

多功能芯片对合成样本中肝癌细胞HepG2的测试研究

设计并制作了一种集多孔流分离(Multi-orifice flow fractionation,MOFF)技术与磁捕获技术于一体的用于特异性分离和捕获合成样本中肝癌细胞HepG2的多功能微流控细胞芯片.此芯片由玻璃基片和PDMS微通道盖片组成,PDMS盖片上含有3条进样通道、MOFF分离区和六边形腔体的细胞富集检测区.其中,MOFF分离区总长20 mm,由80组长度为0.18 mm、深度为50μm、收缩区域宽度为0.06 mm、扩张区域宽度为0.20 mm的半菱形收缩/扩张重复单元组成,每组收缩/扩张重复单元间的夹角为103.0°.实验以肝癌细胞HepG2-血细胞混悬液为样本;根据磁珠表面修饰c-Met抗体能与肝癌细胞HepG2特异性结合的原理,通过表面羧基化的磁珠、EDC(1 mg/mL)、NHS(1 mg/mL)和c-Met抗体制备了浓度为50μg/mL的免疫磁珠(Anti-MNCs)悬浮液.在样本流速为50μL/min条件下,利用外加磁场实现了血细胞合成样本中微量肝癌细胞HepG2的有效捕获;采用微波加热法以柠檬酸、硫脲为原料制备了用于荧光标记HepG2的碳量子点,在芯片上实现了血液中肝癌细胞HepG2的原位荧光可视化观测.对芯片检测区捕获到的HepG2进行了显微计数分析,对500μL血细胞(107 cell/mL)中含10个HepG2细胞的合成样本,捕获效率达到88.5%±6.7%(n=20).结果表明,所设计的多模式多功能的微流控芯片具有良好的肿瘤细胞分离和检测功能.     

不用计算器求tan22°30’与tan15°的值

在学习三角函数这一章时,老师引导我们大家通过构造特殊直角三角形,探究出了tan30°=√3/3,tan45°=1,tan60°=√3,一般的角度的正切值,书上给出了怎样用计算器来求,如果不用计算器能求出tan22°30’与tan15°的值吗？