一类等式约束优化问题的改进牛顿算法

提出了牛顿方法与预优广义共轭梯度方法相结合的方法(简称为Newton-PGCG)求解库恩-塔克方程组。给出Newton-PGCG算法中预优广义共轭梯度法中预优阵的选取问题及其步数参数的确定原则，并在保证牛顿方法恰二阶收敛的条件下，证明了此算法也具有恰二阶收敛的优点。     

广义伴随Pell数列的平方类

设V是参数为t的广义伴随Pell数列．给出了V有平方类的充要条件．同时，本文证明了：V至多有1个平方类，而且该平方类仅含有2个元素．     

On modal energy in civil structural control

A new control strategy based on modal energy criterion is proposed to demonstrate the effectiveness of the control system in reducing structural earthquake responses. The modal control algorithm combining LQR （linear quadratic regulator） control algorithm is adopted in the discrete time-history analysis. The various modal energy forms are derived by definition of the generalized absolute displacement vector. A preliminary numerical study of the effectiveness of this control strategy is carried out on a 20-storey framed steel structural model. The controlled performance of the model is studied from the perspectives of both response and modal energy. Results show that the modal energy-based control strategy is very effective in reducing structural responses as well as in consuming a large amount of modal energy, while augmentation of additional generalized control force corresponding to the modes that contain little modal energy is unnecessary, as it does little help to improve the controlled structural performance.     

对称矩阵特征向量的神经网络求解

对已有的一种用于求解正定矩阵特征向量（特征值得数为１）的人工神经网络进行了研究。通过细致的数学分析，得出用这种网络同样能求出一般对称矩阵最大（最小）特征值对应的特征向量。     

Diversity as an opportunity or a challenge? A cross-national study of ethnic diversity and students’ generalized trust

In this study, we explore how ethnic diversity at the macro-level relates to students’ generalized trust by using cross-national data. Our analysis shows a positive relationship between ethnic diversity and generalized trust. This relationship is, however, inverted U-shaped curvilinear rather than linear, indicating that the positive relationship levels off and turns negative. While we also find that students’ educational experiences such as social relations at school are positively associated with generalized trust, ethnic diversity at the macro-level is still the most powerful factor in our analysis predicting students’ generalized trust. Theoretical and practical implications are discussed.     

关于无界函数广义积分integralfromn=atob(f(x)dx(a为奇点))的两个性质

由无穷限广义积分和无界函数的广义积分的关系,得出了无界函数的广义积分integral from n=a to b (f(x)dx(a为奇点))收敛的两个性质。     

泛化教育与边界教育——对现行教育理论的反思与改造导论

以对现行教育理论的取样为前提,揭示出现行教育观的“活动——传承”框架及其包括德育论、教学论和管理论在内的整个理论的泛化实质,从对历史变迁过程的叙述与抽象中对其根据与偏执进行反思,在“影响——传承与创新”框架内对其进行了基础性改造。     

关于广义带及正则广义簇的若干注记

定义了一类特殊广义簇──广义带的概念，并引进了两类特殊的广义簇：W＝UWn，V＝UVn，其中Wn＝〔xyzt＝xzyt，xyn＋1＝xn＋1y＝xy〕，Vn＝〔xyzt＝xzyt，zn＋1yn＋1＝xy〕，得出了这些广义簇的若干性质．     

根植"知识记忆":图书馆作为"人类永久记忆客观知识精华的社会机制"自立在世——图书馆广义本体论基本原理研究之一

从"广义本体论"视角出发,提出了一个关于图书馆"是何独特存在"、"为何独特存在"和"如何独特存在"的整体性解释框架,论证了为何"社会知识记忆"是解释图书馆存在及运动的统一视角,认为图书馆的独特本质是"人类永久记忆客观知识精华的社会机制".该社会机制有着由特定的主体、中介、客体和背景构成的基本结构.     

平方误差损失函数下广义Pareto分布参数的Bayes估计

本文在参数的先验分布为逆伽玛先验分布条件下研究广义Pareto分布参数的Bayes估计问题,并在平方误差损失函数下,导出了参数的Bayes估计。文末通过Monte Carlo数值模拟试验对极大似然估计和Bayes估计进行了比较。