关于度量投影的一些结果

设X是(实或复)域K上的赋范线性空间,M是X的闭线性子空间,令P_M(x)={m∈M;、||x-m||=d(x,M)},则称PM为x到M上的度量投影,耳中d(x,M)=inf||x—y||是x到M的距离, M称为可最佳逼近(Chebyshev)的,若对x∈X,P_M(x)至少含且仅含一点,若M是可最佳逼近的,定义 P_M的范数为 ||P_M||=sup{||b||:b∈P_M(x),且||x||,且||x||≤1} 易知1≤||P_M||≤2,我们主要有下列结果: 命题1 设X是自反Banach空间,M是Chebyshev子空间,PM线性,则||P_M||<2。 命题2 设M是e_p(或L_p)的闭子空间,则当p≥2时,||P_M||≤1+1/2~(1/p);当1相似文献   

确立现代教育观念 改革机械制图课堂教学

培养学生的创新精神，是《机械制图》课程教学中的一个重要内容。在机械制图投影理论教学中，可根据职高生的知识结构、生理特征、心理状况、思维方式，采用分层次教学，让学生人人参与教学活动，动手操作，训练学生的发散、开放、创新性思维。     

圆柱螺旋线投影法的工程图示应用

本文以螺旋线投影法解决工程中的图示问题为例，阐述曲线投影法的实际应用。     

精化调和Arnoldi方法的一种变形

本文利用调和Arnoldi算法的一种变形和求解大规模矩阵特征问题的精化思想给出了一种求解大规模矩阵内部特征问题的精化调和Arnoldi算法,理论分析表明精化变形更有效,数值试验表明了新方法能够达到更快的收敛速度。     

投射与语体分析

本主要讨论小句复合体中投射现象与英语语体的关系。投射是指小句间一种逻辑语义关系。而语体是指语言在具体语境中的实现形式，是指语言的功能变体。投射在语篇中的出现并非偶然，而是与一定的语体相联系。不同的英语功能变体呈现出不同数量的投射句。因此，投射结构的选择受到语体类型的制约，同进，投射小句的数量或出现频率也呈现一定的语篇类型。     

圆锥与圆柱正交时求相贯线上的特殊点的讨论

用三种作图分析讨论圆锥与圆柱正交时相贯线上特殊点的正确求法,并用理论分析阐明特殊点的规律性。     

Hilbert空间上最小二乘解的等价条件及其应用

给出了Hilbert空间上最小二乘解的等价条件,对最小二乘法的应用作了初步探讨。     

Mini-research Experience in Simple Linear Regression

Within the undergraduate mathematics curriculum, the topic of simple least-squares linear regression is often first encountered in multi-variable calculus where the line of best fit is obtained by using partial derivatives to find the slope and y-intercept of the line that minimizes the residual sum of squares. A markedly different approach from linear algebra, which could also be introduced in multi-variable calculus, obtains the regression line by vector projection. The latter viewpoint offers elegant proof of the equation relating the total, explained and unexplained variations. Consideration of data with the same regression line and correlation opens the door for a “mini-research experience” (MRE). A sequel MRE gives rise to an open Research Experience for Undergraduates topic to analyze reflection sequences and a fundamental connection between complex analysis and regression analysis. A few general guidelines and basic goals for MREs are included for those whose main interest is in undergraduate research.     

Ethical Reasoning and the Craft of Moral Practice

Abstract

Non-indoctrinational moral education involves teaching children to engage in ethical inquiry. This means that, since ethical inquiry has the status of a craft, the students will be apprentices in that craft. The classroom becomes, for this purpose, a community of ethical inquiry — an ethical atelier where students learn the tools, methods, practices and procedures which craftsmen associated with that tradition customarily utilize. It is only when one is adept at the generic procedures of reasoning that one can be adept at specifically moral reasoning, but to make the transition possible, the generic procedures should be taught within the humanistic and critical context of philosophy, and within the setting of a community of ethical inquiry.     

两阶段相结合的广义投影类算法

讨论了非线性不等式约束最优化问题，利用一种新的广义投影技术建立问题的一类算法，该算法的初始点可任意选取，且能自动地将初始化和最优化两阶段统一起来。算法不但无需作任何转轴运算，而且只采用ε－约束集内函数梯度确定广义投影阵，方法结构简单，计算量小，具有普遍意义。