超幂模型与超闭映射

众所周知,拓扑空间的紧性具有可乘性而弱于紧性的可数紧性却不具有可乘性。于是存在着这样的问题:是否存在着一种介于紧性与可数紧性之间的另一种紧性,使其具有司乘性?1971年A.Bernstein利用超幂模型。给出了这样的一种紧性,即D-紧性([1])。1984年我国数学家李邦河与冯汉桥对这种紧性作了进一步的研究,给出了空间的     

关于可数个空间的箱拓扑

讨论了可数个空间的箱拓扑为紧性，序列式紧性，第二可数性，第一可数性，分性及连通性的条件。     

一般端点条件下一类样条插值的唯一可解性与凸性或单调性

一般端点条件下3次样条插值的唯一可解性见[1]—[7]。在特殊类型端点条件下一些样条插直的凸性或单调性见[8]—[11]。本文则考虑一般端点条件下一类样条插值的唯一可解性与凸性或单调性。在唯一可解性方面把[1]—[7]中一些结果推广到其他类型样条插值,在凸性或单调性方面则把[8]—[11]中结果推广到一般端点条件。这类样条插值在一般端点条件下的唯一可解性与凸性或单调性归结为下列类型的线性方程组的唯一可解性与解的非负性:     

广义近似空间的拓扑分离性与紧性

本文对一般广义近似空间(U,R)进行了拓扑式研究,利用R-开集概念诱导了广义近似空间对应的拓扑空间,并利用诱导的拓扑空间定义了相应广义近似空间的T_0性与T_1性及拓扑紧性。证明了广义近似空间的T_0性强于T_0~a性,T_1性与T_1~a性等价;证明了广义近似空间的关系紧性强于拓扑紧性,并用反例说明了关于分离性和紧性其他不能蕴含的情形。     

随机环境中马氏链状态的各种常返性与暂留性

考虑到随机环境中马氏链的状态在受到环境因素各种条件的影响下,引入了随机环境中马氏链状态的各种常返性与暂留性概念,讨论了这些常返性与暂留性的相互关系,从而说明随机环境中马氏链状态的常返性与暂留性和经典马氏链状态的常返性与暂留性有着显著的区别.     

局部凸空间的正规性

本文建立局部凸拓扑向量空间的正规性、完全正规性和单调正规性的等价条件．作为这些结果的应用，研究了函数空间的单调正规性和可度量性．     

边值系统的能控性与能观测性问题

把抽象系统的能控性和能观测性推广到由强连续双半群描述的抽象边值系统,给出了相应的边值系统能控性的充要条件,并研究了能观测性与能控性之间的对偶关系.最后作为例子,研究了双曲系统能控性.文中所得的结果可用于讨论现代物理系统中出现一类边值系统的能控性与能观测性问题.     

经验似然的冗余性

提出经验似然的冗余性和偏冗余性的概念,讨论了相应的冗余性等价条件,将GMM的冗余性结果推广到经验似然估计,同时模拟实验结果也证实了经验似然的冗余性和偏冗余性对估计的影响.     

Musielak—Orlicz空间L^p（x）（Ω）的若干凸性

本文研究了一类特殊的Musielak-Orlicz空间Lp(x)(Ω)赋予Luxemburg范数时的严格凸性,局部一致凸性,弱局部一致凸性,中点局部一致凸性与一致凸性.利用Banach空间几何学中刻画凸性的一般方法,并结合一般Musielak-Orlicz空间凸性的判别准则,获得了用p(x)刻画空间Lp(x)(Ω)赋予Luxemburg范数时,上述几种凸性的充分必要条件.     

平均跟踪性与双曲线性同胚

本文研究了双曲线性自同胚的平均跟踪性,利用双曲线性映射的性质和压缩映射定理,得到了在有界的Banach空间上的双曲线性自同胚具有平均跟踪性.另外,证明了在一般的度量空间上的压缩映射也具有平均跟踪性.     

Spectral properties of sums of certain Kronecker products

We introduce two kinds of sums of Kronecker products, and their induced operators. We study the algebraic properties of these two kinds of matrices and their associated operators; the properties include their eigenvalues, their eigenvectors, and the relationships between their spectral radii or spectral abscissae. Furthermore, two projected matrices of these Kronecker products and their induced operators are also studied.     

河北省城镇居民收入现状与收入水平预测

通过对河北省城镇居民收入水平现状,历年收入结构变化,收入增长特征的实证分析,建立了城镇居民收入水平预测模型,为提高居民收入、合理调控收入差距提供科学的依据.     

Counter-examples for refinement of conjectures and proofs in primary school mathematics

The purpose of this study is to explore how primary school students reexamine their conjectures and proofs when they confront counter-examples to the conjectures they have proved. In the case study, a pair of Japanese fifth graders thought that they had proved their primitive conjecture with manipulative objects (that is, they constructed an action proof), and then the author presented a counter-example to them. Confronting the counter-example functioned as a driving force for them to refine their conjectures and proofs. They understood the reason why their conjecture was false through their analysis of its proof and therefore could modify their primitive conjecture. They also identified the part of the proof which was applicable to the counter-example. This identification and their action proof were essential for their invention of a more comprehensive conjecture.     

影响用户换手机的关键因素及其效应研究——基于中国移动西安分公司的样本数据

影响用户换手机的因素有客观因素和主观因素,本研究基于中国移动西安分公司的用户信息数据,根据用户的实际消费和相关非线性多元回归理论,探索了影响用户换手机的客观因素及其效应。研究发现:较长的总通话次数、较大的平均流量和较小的手机屏幕(在用手机)等因素能促进用户换手机;换手机的主要驱动力不是经济能力的差异而是在用手机的屏幕大小;用户的年龄差异对是否换手机的影响可以忽略;城乡标识对是否换手机的影响显著,用户品牌的影响不显著。另外,手机捆绑销售方式的存在,本研究最后站在制造商和运营商的角度,根据以上影响效果给出了提高手机制造商和运营商竞争力的相关建议。     

Combinatorial Gelfand Models for Semisimple Diagram Algebras

We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebras, their partial analogues, walled Brauer algebras, their partial analogues, Temperley-Lieb algebras, their partial analogues, walled Temperley-Lieb algebras, their partial analogues, partition algebras and their Temperley-Lieb analogues.     

Pre-service science teachers’ perceptions of mathematics courses in a science teacher education programme1

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers’ opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were ‘difficult’ because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers’ lack of knowledge in terms of teaching mathematics.     

Adolescent girls’ construction of moral discourses and appropriation of primary identity in a mathematics classroom

This qualitative study examines the way three American young adolescent girls who come from different class and racial backgrounds construct their social and academic identities in the context of their traditional mathematics classroom. The overall analysis shows an interesting dynamic among each participant’s class and racial background, their social/academic identity and its collective foundation, the types of ideologies they repudiate and subscribe to, the implicit and explicit strategies they adopt in order to support the legitimacy of their own position, and the ways they manifest their position and identity in their use of language referring to their mathematics classroom. Detailed analysis of their use of particular terms, such as “I,” “we,” “they,” and “should/shouldn’t” elucidates that each participant has a unique view of her mathematics classroom, developing a different type of collective identity associated with a particular group of students. Most importantly, this study reveals that the girls actively construct a social and ideological web that helps them articulate their ethical and moral standpoint to support their positions. Throughout the complicated appropriation process of their own identity and ideological standpoint, the three girls made different choices of actions in mathematics learning, which in turn led them to a different math track the following year largely constraining their possibility of access to higher level mathematical knowledge in the subsequent schooling process.     

Writing as a Tool to Demonstrate Mathematical Understanding

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers' Workshop (WW) in a fourth‐grade mathematics class. On a biweekly basis, the data were reviewed and changes made to the model. The analysis of the students' writing revealed (a) their understandings and misunderstandings of the mathematical content, (b) their readiness for more challenging tasks, and (c) their connections to prior knowledge. Students used writing to demonstrate their understanding of mathematics and show their mathematical processes. In some cases, examining only the numerical work failed to illuminate the students' understanding, their writing provided deeper insight. Students recognized writing as a tool for learning; this was evident in interview responses.     

Volume, surface area and inward injectivity radius

We show some relations among the volumes of domains in Euclidean spaces, their surface areas and the inward injectivity radii from their boundaries. In particular, we give an estimate for the upper bound of the ratios of their surface areas and volumes by means of inward injectivity radii. The upper bound seems to depend on their topological structures.

     

Z16环上的二次剩余码

本文研究了整数环模16剩余类环Z16上的二次剩余码,讨论了它们的幂等生成元及其扩展码的自对偶性等代数性质,并研究了码长为7的Z16二次剩余码在两种已有的Gray映射下的有趣性质,尤其是确定了它们的Lee重量分布.