A note on model diagnostics in longitudinal data analysis

Longitudinal study has become one of the most commonly adopted designs in medical research. The generalized estimating equations (GEE) method and/or mixed effects models are employed very often in causal inferences. The related model diagnostic procedures are not yet fully formalized, and perhaps never will be. The potential causes of major problems are the high variety of the dependence within subjects and/or the number of repeated measurements. A single testing procedure, e.g., run test, is not possible to resolve all model diagnostics problems in longitudinal data analysis. Multiple quantitative indexes for model diagnostics are needed to take into account this variety. We propose eight testing procedures for randomness accompanied with some conventional and/or non-conventional plots to remedy model diagnostics in longitudinal data analysis. The proposed issue in this paper is well illustrated with four clinical studies in Taiwan.     

单壁碳纳米管的SERS研究

本文通过改进实验方法,将单壁碳纳米管的乙醇溶液与金胶混合并制作成固体薄膜,使单壁碳纳米管夹裹在金纳米粒子之间,保证了吸附的紧密性,获得了高质量的单壁碳纳米管SERS光谱。不但观测到文献中报道的径向呼吸振动模(RBM)和C-C正切拉伸模(GM)的增强,还在1100-1500cm-1区域观测到一组新峰,其峰形完整并有相当的强度。这些峰在现有的文献中几乎没有报导。文章对这组新峰的出现进行了初步的分析。     

溃坝问题的间断有限元方法

本文研究90年代初提出的Runge-Kutta间断Galerkin有限元方法，给出该方法的精度分析，通过经典算例验证该方法处理间断问题、捕捉锐利波形的能力，并将其推广到求解浅水问题．针对坝底无摩擦，无坡度的理想情形进行讨论，给出方溃坝和圆溃坝问题的数值模拟结果．     

藻类植物中钙、镁、铁、锰、铜和锌含量分析

本文采用火焰原子吸收光谱法测定了七种藻类植物中钙 ,镁 ,铁 ,锰 ,铜 ,锌六种元素的含量。结果表明 ,藻类植物中含有较丰富的钙 ,镁 ,铁 ,锰 ,锌元素 ,其含量由大到小顺序为Ca >Mg >Fe >Zn >Mn >Cu ,尤以钙的含量最为丰富 ,铜含量较少。本实验结果为探讨藻类植物作为资源开发利用提供了有用数据。     

免疫珠技术快速检测腹泻性大肠杆菌

采用表面光滑玻璃珠作为载体材料，用1：40的腹泻性大肠杆菌诊断血清进行包被。可制成免疫珠。这种免疫珠能与腹泻性大肠杆菌发生特异性结合。经乳糖蛋白胨培养液培养，然后根据其产酸产气进行判断。能在18h内完成腹泻性大肠杆菌的检测。其灵敏度为样液中含有腹泻性大肠杆菌数必须大于10CFu／mL．该法简单、快速、易操作、灵敏度高。     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME

The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

OnM-ideals and best approximation

In this paper we will prove some theorems on theM-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].This work is supported in part by the National Natural Science Foundation of China.     

不等式约束优化问题的一个势函数

基于Carroll(1961)建立的罚函数，本文给出了不等式约束优化问题的一个势函数，并且讨论了该函数的性质．最后证明了在此基础上建立的对偶算法具有Q-线性收敛性．