Jacobi多项式零点为结点的Lagrange插值多项式之逼近

对于可微函数ｆ∈Ｃｑ［－１，１］，本文研究以Ｊａｃｏｂｉ多项式Ｊ（α，β）ｎ（ｘ）的零点为结点组之Ｌａｇｒａｎｇｅ插值多项式对ｆ及其导数的同时逼近，证明不等式Ｌ（ｓ）ｎ（ｆ，α，β，ｘ）－ｆ（ｓ）（ｘ）＝Ｏ（１）Δ－ｓｎ（ｘ）Δｑｎ（ｘ）ω（ｆ（ｑ），Δｎ（ｘ））ｌｏｇｎ｛＋（１－ｘ＋ｎ－１）－α－１２ｎ－ｑω（ｆ（ｑ），ｎ－１）｝，在［０，１］上对于ｓ＝０，１，２，…，ｑ一致成立，其中Δｎ（ｘ）＝ｎ－１１－ｘ２＋ｎ－２     

一类重尾风险因子的模拟及其投资高风险值和置信区间的估计

由于金融市场中的日周期或短周期对数回报率的样本数据多数呈现胖尾分布，于是现有的正态或对数正态分布模型都在不同程度上失效，为了准确模拟这种胖尾分布和提高投资风险估计及金融管理，本文引进了一种可根据实际金融市场数据作出调正的蒙特卡洛模拟方法．这个方法可以有效地复制金融产品价格的日周期对数回报率数据的胖尾分布．结合非参数估计方法，利用该模拟方法还得到投资高风险值以及高风险置信区间的准确估计。     

Conditionally Optimal Weights of Evidence

A weight of evidence is a calibrated statistic whose values in [0,1] indicate the degree of agreement between the data and either of two hypothesis, one being treated as the null (H_0) and the other as the alternative (H_1). A value of zero means perfect agreement with the null, whereas a value of one means perfect agreement with the alternative. The optimality we consider is minimal mean squared error (MSE) under the alternative while keeping the MSE under the null below a fixed bound. This paper studies such statistics from a conditional point of view, in particular for location and scale models.     

指数分布尺度参数的区间估计

本文在截尾样本情况下，讨论了指数分布尺度参数的区间估计及其改进     

示波极谱法同时测定痕量硒和砷

在盐酸-酒石酸锑钾介质中,Se(Ⅳ)在—0.59V(vs.SCE,下同)左右产生示波极谱峰,其二阶导数峰高IP″_(Se)与Se(Ⅳ)浓度在1.26×10~(-8)～1.26×10~(-4)mol·L~(-1)范围呈良好线性关系,Se(Ⅳ)检出下限为5.0×10~(-9)mol·L~(-1)。在相同底液中,当Se(Ⅳ)浓度大于2.5×10~(-6)mol·L~(-1)时,As(Ⅲ)在—0.79V左右也出现一良好极谱峰,其峰高IP″_(As)与As(Ⅲ)浓度在5.3×10~(-7)～2.6×10~(-4)mol·L~(-1)之间呈良好线性关系,As(Ⅲ)检出下限为2.7×10~(-7)mol·L~(-1)。Se(Ⅳ)、As(Ⅲ)两峰电位相差较大,可在同一底液中同时测定。曾用本法测定了煤飞灰标样(82201)中痕量硒和砷,结果与证书值相符。硒、砷加标回收率为95％～110％,还研究了Se(Ⅳ)、As(Ⅱ)极谱波性质。     

停流FIA─协同系数补偿动力学方法双组份的同时测定

用停流光度法研究了Ｈｇ（Ⅱ）和Ａｇ（Ⅰ）对以硫脲为活化剂的Ｆｅ（ＣＮ）－α，α’－联吡啶配体交换反应的协同催化效应，提出了协同系数的概念。在协同系数补偿动力学体系中由于双组份的协同催化效应而引起的对吸光度加合性的偏离，建立了一种新的双组份同时测定方法，此法使双组份同时测定的线性范围显著扩大，且降低了检测限。测定了环境样品中汞和银含量，获得满意结果。     

Bidirectional Mapping between a Biphoton Polarization State and a Single-Photon Two-Qubit State

How to manipulate （operate or measure） single photons efficiently and simply is the basic problem in optical quantum information processing. We first present an efficient scheme to transform a biphoton polarization state to a corresponding single-photon state encoded by its polarization and spatial modes. This single-photon state carries both the information of the controlled and target photons. It will make the realization of bipartite positive- operator-valued measurements efficiently and simply. Moreover, the inverse transformation from the single-photon state back to the corresponding biphoton polarization state is also proposed. Using both the transformations, the realization of the arbitrary two-qubit unitary operation is simple with an M-Z interferometer. All the schemes are feasible with the current experimental technology.     

分数填补下两非参数总体一般差异的经验似然置信区间

在一定的条件下证明了缺失数据情形基于分数填补方法得到的两非参数总体一般差异指标的经验似然比统计量的渐近分布为加权χ21,由此可构造差异指标的经验似然置信区间.     

Bernstein算子的点态同时逼近

借助光滑模ω_φ~2(f,t)(φ是一般步权函数),研究了Bernstein算子的点态同时逼近问题,给出了Bernstein算子同时逼近的等价定理,建立了其导数与光滑函数间的关系,对以前已有的结果予以补充和完善.