环sum u~iF_2 from i=0 to s-1上的α和β类型单形码

介绍了环sum uⁱF_2 from i=0 to s-1(us=0)上Typeα和β线性单形码,确定了它们的性质.     

一类$L^2(\mathbb{R}^n)$的紧支撑不可分正交小波

本篇文章给出一类$L^{2}(\mathbb{R}^{n})$, $n\geq2$的紧支撑不可分正交小波基的具体构造算法,其中正交小波的伸缩矩阵为$\alpha I_{n}~(\alpha\geq2,\ \alpha \in \mathbb{Z})$, $I_{n}$是$n$阶单位矩阵.最后给出两个不可分正交小波基的构造算例.     

二氧化铅修饰玻碳电极的镀膜/循环伏安法制备及电催化性能

采用镀膜/循环伏安法制备了PbO2修饰玻碳电极.在Pb(NO3)2溶液中,在-0.7 V 将Pb膜沉积在玻碳电极表面,然后在5 mol/L NaOH溶液中以100 mV/s速度在-1.0～1.0 V循环伏安扫描20次,PbO2膜均匀沉积在玻碳电极表面.采用交流阻抗法监控电极修饰每一过程,环境扫描电镜表征电极表面形貌.探讨了PbO2膜的沉积机理及其电化学行为,表面活性位点覆盖量为7.5×10-10 mol/cm2.PbO2修饰电极对H2O2电氧化表现出较高催化活性,起始氧化电位低至0.1 V,考察了影响催化活性的因素.计时电流法测定H2O2 (工作电位0.40 V),响应时间小于2 s; 线性范围为5.0 ×10-6 ～ 5.5×10-4 mol/L;检出限1.1×10-6 mol/L (信噪比为3).在实际水样中H2O2测定结果满意.电极在室温环境下储存30 d,其催化活性基本不变.该修饰电极制备工艺简单、重现性良好、稳定性高.     

水杨醛缩苯乙酰腙对阴离子的识别研究

设计合成了用于识别阴离子的荧光传感分子水杨醛缩苯乙酰腙(1),通过红外光谱、核磁共振谱和质谱表征其结构;利用其光谱性质研究了该物质对几种阴离子的识别性质,初步探讨了其结合模式。实验表明:在乙腈介质中,受体分子1表现出对F-良好的选择性,F-的加入导致1在478 nm处荧光增强44倍,而其它阴离子只引起1的荧光略微增强,Job法实验得出1与F-的结合比为1∶1。     

Atomic-Scale Study of Ge-Induced Incommensurate Phases on Si（111）

Two Ge-induced incommensurate phases, γ and β, on Si（111） are observed and studied by {／it in situ} scanning tunneling microscopy. The γ phase consists of aligned triangular domains whose stacking sequence is faulted with respect to the Si（111）-1×1 surface. The β phase consists of two kinds of triangular domains whose stacking sequences are faulted and unfaulted with respect to the Si（111）-1×1 surface, respectively. In the β phase, two types of domain walls, zigzag＇＇ and face-to-face＇＇, form to release the strain. The triangular domains all exhibit a quasi-1×1 hexagonal close-packed structure. By studying the structural evolution from magic clusters to incommensurate structures, the structure models for γ and β phases are proposed.     

纵向数据下部分线性EV模型的渐近性质

研究了纵向数据下部分线性EV函数关系模型.应用一般非参数权函数法和广义最小二乘法给出了未知参数β,误差方差σ2以及未知函数g(·)的估计.在一般的条件下,证明了β,σ2估计的渐近正态性,同时也给出了未知函数g(·)估计的收敛速度,其结果是独立数据情形下相应结果的推广.     

一种求解混合约束优化问题的半可行序列线性方程组滤子算法的局部收敛性

作者在[10]中提出了一种半可行序列线性规划滤子方法.它将QP-free方法推广至混合约束优化问题上,并且保持对不等式约束的可行性,对等式约束部分用滤子方法处理,从而避免了罚参数的选取.该算法只需求解四个具有相同系数矩阵的线性方程组以得到搜索方向.在一定程度上克服了序列二次规划方法的缺点.[10]中仅给出了全局收敛性.本文主要给出了该算法的局部超线性收敛性证明以及数值结果.     

分数跳-扩散环境下欧式期权定价的Ornstein-Uhlenbeck模型

假设股票价格遵循分数布朗运动和复合泊松过程驱动的随机微分方程,建立分数跳-扩散Ornstein-Uhlenbeck模型,利用价格过程的实际概率测度和公平保费原理,得到欧式看涨期权定价的解析表达式。推广了关于欧式期权定价的结论。     

中美一些《线性代数》教材分析与思考

通过中美有代表性的几本《线性代数》教材在内容、知识、应用、习题、现代化教学手段等方面的比较,分析国内外教材的特点,从数学观、教育理念、文化影响等方面提出了一些值得思考的问题,给我国代数教材建设提供一些启示.     

Streamlined synthesis of phosphatidylinositol (PI), PI3P, PI3,5P2, and deoxygenated analogues as potential biological probes

Highly direct total syntheses of phosphatidylinositol (PI), phosphatidylinositol-3-phosphate (PI3P), phosphatidylinositol-3,5-bisphosphate (PI3,5P2), and a range of deoxygenated versions are reported. Each synthesis is carried out to deliver the target in optically pure form. The key step for each synthesis is a catalytic asymmetric phosphorylation reaction that affects desymmetrization of an appropriate myo-inositol precursor. Elaboration to each target compound is then carried out employing a diversity-oriented strategy from the common precursors. In addition to three natural products, several additional streamlined total syntheses of deoxygenated PI analogues are reported. These syntheses set the stage for high-precision biological investigations of polar headgroup/biological target interactions of these membrane-associated signaling molecules.