戏说数学家

九头鸟茶楼今天有故事会,门外挂出了一副新联. 左联是:主题一个专家只因专注 右联是:故事三则笑话到底笑谁 横批是:人在戏中.     

与高一新生讲"映射"

"映射"并不玄,与我常相伴, 　　顾名可思义,对镜解疑难! 　　上四句,是高一新生小何在新课本"映射"概念旁边写的一段感悟.……     

基于螺旋相位调制的非相干全息点扩散函数研究

分析了菲涅耳非相干相关全息(Fresnel incoherent correlation holography,FINCH)系统中纯相位空间光调制器(spatial light modulator,SLM)加载螺旋相位掩模时的点扩散函数.以氙灯为照明光源搭建了FINCH系统,电荷耦合器记录的点源全息图与点扩散函数模拟结果一致.采用该系统分别在SLM上加载双透镜掩模和螺旋相位调制双透镜掩模两种情况下对分辨率板和非染色洋葱细胞成像,给出了成像对比结果.结果表明:采用螺旋相位调制的FINCH系统可以在几乎不牺牲分辨率的情况下提高图像的边缘对比度;同样,对相位物体也可以实现图像的边缘提取和识别.该方法在实时监测活细胞的分裂、形变等方面具有重要应用前景.     

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the \textit{$\Ga$-K} direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band (MSB) is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, $r/a$. It is obtained that the critical $r/a$ value determining the occurrence or disappearance of MSB is 0.36. When $r/a $ is larger than or equal to 0.36, the MSB occurs. However, when $r/a $ is smaller than 0.36, the MSB disappears.     

A ministop band in a single-defect photonic crystal waveguide based on silicon on insulator

This paper reports that a two-dimensional single-defect photonic crystal waveguide in the Г-K direction with triangular lattice on a silicon-on-insulator substrate is fabricated by the combination of electron beam lithography and inductively coupled plasma etching. A ministop band （MSB） is observed by the measurement of transmission characteristics. It results from the coupling between the two modes with the same symmetry, which is analysed from the stimulated band diagram by the effective index and the two-dimensional plane wave expansion methods. The parameter working on the MSB is the ratio of the radius of air holes to the lattice constant, fla. It is obtained that the critical τ/a value determining the occurrence or disappearance of MSB is 0.36. When τ/a is larger than or equal to 0.36, the MSB occurs. However, when τ/a is smaller than 0.36, the MSB disappears.     

医用NiTi形状记忆合金表面类金刚石薄膜的生物摩擦磨损性能研究

利用脉冲电弧离子镀在医用NiTi形状记忆合金基底上沉积无氢类金刚石（DLC）薄膜，采用Raman光谱分析薄膜的微观结构，在UMT-2MT型摩擦磨损试验机上考察了薄膜的体外生物摩擦磨损特性．结果表明：所制备的类金刚石碳薄膜为四面体非晶碳薄膜，具有典型的类金刚石结构特征；在干摩擦及0．9％NaCl溶液和Hank’s溶液润滑条件下，DLC薄膜显示出良好的抗磨减摩性能；在NiTi合金表面沉积DLC薄膜以提高其生物相容性是可行的。     

分子内C—H键胺化反应机理的DFT研究

采用密度泛函理论研究了溴化亚铁催化芳基叠氮化物C—H键胺化生成苯并咪唑的反应机理.研究结果表明,溴化亚铁催化剂使反应由协同机理转变为分步机理,反应活化能降低了大约167kJ/mol.催化反应由氮气消去、C—N形成和2H-苯并咪唑异构化3个基元步骤组成.其中金属亚胺/金属氮烯FeNR PhNCPh进攻C形成C—N键是无能垒过程,且与金属氮烯中氮的电荷密切相关.氮气消去与2H-苯并咪唑异构化反应的能垒均在41~54kJ/mol之间.     

硫代草酸异构体结构及异构化反应机理的理论研究

采用量子化学CBS-QB3组合方法对硫代草酸可能存在的异构体构型及异构体间相互转化机理进行了详细计算研究,分别得到11种稳定结构及12种异构化过渡态。其中硫代草酸异构体的相对稳定性顺序为M11M7M10M1M9M6M2M3=M4M5,不稳定异构体M5极易向稳定异构体转化。异构体M6向M11转化仅需越过1.92k J·mol-1的能垒,且放出49.04k J·mol-1能量,因此M6向M11的转化是H迁移异构化反应的主通道。     

基于一种柔性双咪唑和不同双羧基配体构筑的两例镉(Ⅱ)的配位聚合物

在水热条件下合成了2个新颖的镉(Ⅱ)配位聚合物:[Cd₂(μ2-H₂O)(1,5-Bip)(Tpa)₂]_n(1)和[Cd(1,5-Bip)(Oba)]_n(2)(H₂Oba=4,4''-二羧酸二苯甲醚,H₂Tpa=对苯二甲酸,1,5-Bip=1,5-二(咪唑基)戊烷)。并通过X射线单晶衍射,粉末XRD、红外光谱、元素分析以及热重分析对其结构进行表征。单晶解析结果表明:配位聚合物1是一个单节点5连接(4⁶.6⁴)拓扑三维空间网络结构,配位聚合物2是一个二维的(4,4)网格层状结构。另外,研究了2个配位聚合物在室温下的热稳定和荧光性能。     

二氧化硅与液体介质的亲和性表征

利用动态核磁脉冲(Dynamic NMR)技术对高浓度的二氧化硅浆料的亲和性进行研究,并建立表征束缚层厚度与亲和性的定量模型。结果表明,在纯丁酮溶剂中,二氧化硅的含量越高,分散时间越长,填料表面束缚层厚度越大;而在树脂溶液体系中,在30%二氧化硅含量附近,填料表面束缚层厚度最大。当处理剂用量约为0.5%(w/w)时,颗粒表面与介质的吸附作用最强。使用不同处理剂制备的二氧化硅浆料,其表面吸附效应也有所不同,并且当浆料静置16 h后,其厚度层发生不同的变化,在丁酮体系中,束缚层厚度部分增加,而甲苯体系中,束缚层厚度减小。