关于非均匀剖分下多元样条空间S_2~1(△_(mn)~(2))的拟插值算子

１引言随着计算机科学技术的发展,多元样条在力学和计算机辅助几何设计（ＣＡＧＤ）中的应用越来越引起人们极大兴趣．然而,由于一般剖分下样条空间的研究有相当的难度,迄今为止只对于一些特殊剖分的样条空间取得了一定的进展,如：矩形剖分,均匀的１－型,２－型三角剖分等．王仁宏和崔锦泰讨论了均匀２－型三角剖下的拟插值算子以及其逼近性质,鉴于在工程和实际应用中均匀剖分具有一定局限性,作者在文献（［１］,［３］）的基础上,对于非均匀２－型三角剖分,给出了一类拟插值算子,并研究了它的逼近性质．同时,利用其构造了一类…     

任意剖分下的多元样条分析

本文采用代数几何的方法,研究了在任意剖分下多元样条函数的各种性质.定理2—4给出了一个函数S(υ,ν)是多元参数型样条的充分必要条件.定理1指出了多元样条函数具有“解析延拓”的特征性质.文中得到在任意剖分下多元样条的一般表达形式(定理9和10)和多元样条插值的一般理论.文中也讨论了多元有理样条函数.     

拟贯穿剖分上分片代数曲线的Nother型定理

代数曲线的Nother定理是代数几何中经典并且十分重要的结论.作为二元样条的零点集,分片代数曲线是经典代数曲线的推广.分片代数曲线的Nother型定理对研究二元样条空间的Lagrange插值有至关重要的作用.利用拟贯穿剖分的特点、二元样条的性质与代数几何的相关知识,给出了拟贯穿剖分上分片代数曲线的Nother型定理.     

三角剖分上分片代数曲线的Nöther型定理

分片代数曲线是经典代数曲线的推广. 贯穿剖分上的分片代数曲线的Nöther型定理对构造二元样条空间的Lagrange插值适定结点组有非常重要的作用. 文中利用二元样条的性质, 给出了任意三角剖分上分片代数曲线的Nöther型定理.     

三角剖分上分片代数曲线的N(o)ther型定理

分片代数曲线是经典代数曲线的推广.贯穿剖分上的分片代数曲线的N(o)ther型定理对构造二元样条空间的Lagrange插值适定结点组有非常重要的作用.文中利用二元样条的性质,给出了任意三角剖分上分片代数曲线的N(o)ther型定理.     

三角剖分上分片代数曲线的Nther型定理

分片代数曲线是经典代数曲线的推广．贯穿剖分上的分片代数曲线的Nther型定理对构造二元样条空间的Lagrange插值适定结点组有非常重要的作用．文中利用二元样条的性质,给出了任意三角剖分上分片代数曲线的N(?)ther型定理．     

构造非均匀剖分上局部支集样条函数的积分方法

１　引　　言 给定递增数列｛ｘｉ｝,｛ｙｉ｝,｛ｚｋ｝．对于Ｒ２,由直线｛ｘ＝ｘｉ）和｛ｙ＝ｙｊ｝形成的剖分称为非均匀矩形剖分;再连接每个矩形［ｘｉ,ｘｉ＋１］×［ｙｊ,ｙｊ＋１］的正斜率对角线形成的剖分称为非均匀Ｉ－型三角剖分,记为　１;若连接每个矩形的两条对角线,则所得剖分为非均匀Ⅱ－型三角剖分,记为　２．对于Ｒ３,由平面｛ｘ＝ｘｉ｝,｛ｙ＝ｙｊ｝,｛ｚ＝ｚｋ｝形成的剖分称为非均匀长方体剖分;若再连接每个小长方体［ｘｉ,ｘｉ＋１］×［ｙｊ,ｙｊ＋１］×［ｚｋ,ｚｋ＋１］的过点（ｘｉ,ｙｊ,ｚ…     

Ⅱ型三角剖分上一类C2-连续的三次样条插值与逼近

本文研究矩形区域在Ⅱ-型三角剖分下二元三次样条的C2-连续的插值问题.首先给出了一类具有C2-连续的二元三次样条插值格式,然后证明了分片样条的存在性与唯-性,并给出了它的表达式和逼近度.     

作为一元等距结点样条推广的多元样条

作者们在[4]中已经指出了给定剖分下多元B-样条存在的必要条件(1).它表明,并不是对所有的剖分都有多元B-样条存在的。人们也许以为,如同一元情况一样,只要多元B-样条存在,则它们一定组成多元样条空间的支集(即多元样条空间是所有多元B-样条所支架起来的空间)。本文以标准的三角剖分(2-单纯形)下,多元样条空间S²:=S₄²为例指出这种认识是错误的。事实上,本文定理2,3和4对这个问题已给出了明确的结论。 以上结论说明多元B-样条并不是基本的     

一类具有C^2-拼接的二元三次样条的插值分析

研究了矩形区域在Ⅱ型三角剖分下具有C2-拼接的二元三次样条插值与逼近问题.给出了一类具有C2-拼接的二元三次样条的插值条件,存在性,唯一性,逼近度估计及其凸性分析.     

MODELS AND SUPER-MODELS: WAYS OF THINKING ABOUT PROFESSIONAL KNOWLEDGE IN MATHEMATICS TEACHING[1]

Teaching about teaching is a complex process requiring knowledge about teaching as well as knowledge about teaching about teaching. We have published findings on research carried out over the last few years about teachers’ subject knowledge. This research led to the proposal of a model for thinking about subject knowledge which distinguishes between knowledge needed to pass an examination and knowledge needed to help someone else to come to know that knowledge. The first is necessary but not sufficient for the latter. This model for thinking about subject knowledge has led to proposals for similar models for thinking about other aspects of teacher knowledge and has more recently developed into a parallel model for thinking about teacher education.     

关于模糊数贴近度问题的研究

利用模糊集和区间数的贴近度理论,讨论了模糊数的贴近度问题.通过区间数与模糊数之间的关系,根据区间数贴近度的一般表示形式,给出了构造一些模糊数贴近度的具体计算公式的方法;并通过实例说明了所得到的贴近度公式的有效性和实用性,解决了常用贴近度公式所不能解决的问题.     

多因素指派模型全局优化问题研究

基于多因素资源优化分配问题的不确定性,建立基于区间数型下的不确定多因素指派模型,给出模型建立的理论依据与全局优化算法,拓展区间数型多因素指派模型,解决了不确定条件下多因素资源优化分配问题.考虑多因素影响,基于任务完成效率,以5类任务多因素分配问题为例,获得了指派模型全局优化的解.为不确定条件下资源优化分配问题的研究拓宽了决策途径.     

单形极集的两个几何不等式及其应用

本文给出关于单形极集的两个几何不等式，作为其应用，获得单形的一个构造定理和关于单形中硕的一个几何不等式。     

Mathematics teachers’ conceptions about modelling activities and its reflection on their beliefs about mathematics

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.     

泊松分布高阶原点矩的两种计算方法

考虑到直接用定义计算泊松分布高阶原点矩的复杂性,将组合数学中的第二类Stirling数和二项式定理应用到泊松分布高阶原点矩的计算中,得到了泊松分布高阶原点矩的简单和式与递推表达式,并利用结论计算了泊松分布的前九阶原点矩.     

The Mystery of Gabor Frames

This is a survey about the theory of Gabor frames. We review the structural results about Gabor frames over a lattice and then discuss the few known results about the fine structure of Gabor frames. We add a new result about the relation between properties of the window and properties of the frame set and conclude with a vision of how a more complete theory of the fine structure might look like.     

圆柱壳小开孔理论解在工程实践中的应用

完全从一个新的角度,重新研究圆柱壳小开孔的理论解,指出了它与圆柱壳大开孔理论解之间的某一种特殊的内在联系。利用这种联系,重新估计了小开孔理论解在工程实践中的应用范围,为如何利用圆柱壳小开孔理论,提供了一种设想。对圆柱壳小开孔理论在工程实践中的应用重新做出了一个评价。     

关于正矩阵的最大特征值的包含定理及其应用

1　引　　言由于矩阵特征值问题在弹性动力学和自动控制等领域均已获得广泛的应用,所以关于矩阵特征值的计算方法及其上、下界的估计均为人们所关注.随着计算机的发展,有关矩阵特征值的各种有效算法应运而生[1].至于特征值的上、下界的估计问题,虽然也有很多成果[2-4],且它们在数学上都有一定的理论意义和应用价值,但常因其界限太宽而缺少工程价值.鉴于此,笔者利用文[3]引入的同步向量这一概念,讨论了正矩阵的最大特征值的上、下界的确定问题,获得了这类矩阵最大特征值的较为精确的包含定理,又与幂法[1]相结合,给出了非亏损正矩阵的最大特征…     

Backward Transfer: An Investigation of the Influence of Quadratic Functions Instruction on Students’ Prior Ways of Reasoning About Linear Functions

The transfer of learning has been the subject of much scientific inquiry in the social sciences. However, mathematics education research has given little attention to a subclass called backward transfer, which is when learning about new concepts influences learners’ ways of reasoning about previously encountered concepts. This study examined when and in what ways a quadratic functions instructional unit productively influenced middle school students’ ways of reasoning about linear functions. Results showed that students’ ways of reasoning about essential properties of linear functions were productively influenced. Furthermore, conceptual connections were identified linking changes in students’ ways of reasoning about linear functions to what they learned during the quadratics unit. These findings suggest that it is possible to productively influence learners’ ways of reasoning about previously learned-about concepts in significant respects while teaching them new material and that backward transfer offers promise as a new focus for mathematics education research.