Cantor集的性质及应用

文章总结归纳了Cantor集的一些重要性质，并举例说明如何利用Cantor集的性质来解决实变函数中的一些典型问题。     

Cantor K分集性质

将Cantor集的构造方法推广，得Cantor任意K（K≥3）分集；证明Cantor K分集也具有Cantor集的一般性质。     

三类重要的集合—数集、点集和空集

集合是高中数学中的一个重要内容 ,集合中元素的广泛性 ,决定了集合的形式是丰富多彩的 .而在高中数学的学习中 ,我们主要关心的是数集、点集和空集这三种集合 ,正确理解和掌握这三种集合 ,将有利于学好集合这一内容 .下面通过几例来说明这三种集合的特点和解题中应注意的事项 .例 1　集合Ｍ ={ ｙ｜ ｙ=ｘ2 ,ｘ∈Ｒ} ,Ｎ ={ (ｘ ,ｙ) ｜ｙ =ｘ2 ,ｘ∈Ｒ} ,Ｐ ={ｔ｜ｔ=ａ2 ,ａ∈Ｒ} ,则三者的关系是 (　　 )Ａ .Ｍ =Ｎ≠Ｐ　　　　　Ｂ .Ｍ =Ｎ =ＰＣ .Ｍ =Ｐ ,Ｍ ∩Ｎ = Ｄ .Ｍ、Ｎ、Ｐ互不相等 .分析　此题首先要了解这三个集合中的元素…     

关于Cantor集的教学注记

给出与Cantor集相关的两点注记 :对任何非负数α ,0 α 相似文献   

Cantor集、Cantor函数及其在构造反例中的应用

讨论了Cantor集的3种定义,根据Cantor集的特征,构造了Cantor函数的4种定义并证明了其等价性.例举了Cantor集及Cantor函数在构造反例中的应用.     

子群H、K的重陪集及其性质

设G是群,H≤G,K≤G,a∈G,称HaK是G的关于H、K的重陪集;证明了重陪集Ha-1K恰由重陪集KaH中每个元素的逆元组成,给出了两个重陪集相等的条件,证明了重陪集HaK构成子群的7个等价命题.     

Cantor集的性质及应用

系统地总结了Cantor集的性质,并利用这些性质证明了几个结论及构造了一些好的反例。     

紧集上的连续函数性质是闭区间上连续函数性质的拓广

紧集上的连续函数性质是泛函分析中的重要内容，而闭区间上连续函数性质是数学分析的重要内容。本文从紧集上连续函数的性质的论证出发，得出一个重要结论：紧集上的连续函数性质是闭区间上连续函数性质的拓广。     

关于一般的CANTOR集

给出了测度为 1-α(<α≤ 1)的一般的Cantor集的定义 ,并给出了一些在实分析中应用的例子。     

质数的一种判别法及应用

证明了下述质数判别法 :设不大于m的所有质数组成的集为Pm={ 2 ,3 ,5… pπ(m) } ,ri 为m2 关于模 pi(i =1,2…π(m) )的最小剩余。Bi={ pin -ri|n∈N∧ (pin -ri<2m 1) } ,则m2 x是质数的充分必要条件是x属于A与∪π(m )i =1Bi 的差集 ,其中A ={ 1,2 ,… 2m} ,0 相似文献   

Assessing the mess: challenges to assemblage theory and teacher education

This article examines the Deleuzian concept of ‘assemblage’ in educational research in the context of Teacher Education (TE) for the ‘continuing education’ or ‘Lifelong Learning’ sector. Drawing on Deleuze’s creative approach to analysis, it draws a portrait of practice which identifies problems and successes in specific cases of TE with wider applicability. I argue that the concept of assemblage recognises developmental practices in distinctive ways and that it challenges the centripetal views implied by other models’ elision of more specific types of convergence, each of which is analysed. This is followed by suggestions which could help provide scope for creativity in research and practice in TE, if a set of challenges can be met. I argue that a situated and dynamic epistemological model is offered by assemblage theory which recognises not just the spatial but also the temporal and political complexities of actual practice.     

Thinking with Deleuze and Guattari: An exploration of writing as assemblage

We need to keep experimenting with writing to meet the challenges of Deleuze and Guattari’s flattened ontology in the humanities. The paper reports on a small, experimental research project at a university in the north-west of England. The findings are written in an experimental mode, inspired by the Deleuze and Guattarian concept, ‘assemblage’. The experiment is theorised and assessed in a non-reductive way that offers future creative possibilities to other researchers. First, the paper presents a context for the subsequent experimental writing. Some current innovative writerly practice and some theoretical and methodological standpoints are reviewed. Next, this paper presents its theorisation of ‘assemblage’ with particular reference to Deleuze and Guattari’s use of the idea, ‘double articulation’. This approach supports and justifies the author’s schematisation of the textual assemblage into four areas: identity, work, territory and dissolving territory. The author explains how these ideas function within an experimental discursive text and illustrates their possible usage in the experimental text itself. Thus, this paper offers a theoretical justification, an explanation of and an assessment of experimental writing, in addition to the experimental text itself, all of which are of potential interest to researchers in the fields of education and philosophy.     

Cantor尘的Hausdorff测度的初等证明

该文从自相似集的几何性质出发，用初等的方法得到了Cantor尘的Hausdorff测度。     

Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge

Traditionally measured skills with arithmetic are not related to later algebra success at levels that would be expected given the close conceptual relation between arithmetic and algebra. However, adaptivity with arithmetic may be one aspect of arithmetic competences that can account for additional variation in algebra attainment. With this in mind, the present study aims to present evidence for the existence and relevance of a newly acknowledged component of adaptivity with arithmetic, namely, adaptive number knowledge. In particular, we aim to examine whether there are substantial individual differences in adaptive number knowledge and to what extent these differences are related to arithmetic and pre-algebra skills and knowledge. Adaptive number knowledge is defined as the well-connected knowledge of numerical characteristics and relations. A large sample of 1065 Finnish late primary school students completed measures of adaptive number knowledge, arithmetic conceptual knowledge, and arithmetic fluency. Three months later they completed a measure of pre-algebra skills. Substantial individual differences in adaptive number knowledge were identified using latent profile analysis. The identified profiles were related to concurrent arithmetic skills and knowledge. As well, adaptive number knowledge was found to predict later pre-algebra skills, even after taking into account arithmetic conceptual knowledge and arithmetic fluency. These results suggest that adaptive number knowledge is a relevant component of mathematical development, and may help account for disparities in algebra development.     

论劳伦斯笔下的女性形象

劳伦斯是英国20世纪著名的作家。他的笔下塑造了大量的女性形象。她们因与环境的不和谐而使感情受到压抑，人格发生分裂。她们的生活充满了痛苦、迷惘和无奈。     

素数的排列规律和鉴别方法

素数的排列规律和鉴别方法一直是数论中研究的重要问题之一。本文在潘树明研究素数成果的基础上,给出了素数的排列规律和鉴别方法,从而改进了潘树明的结果。     

Action research and the assemblage: engaging Deleuzian pedagogy and inquiry beyond the constraints of the individual and the group in education settings

Drawing upon the author’s previous attempts to engage the work of Deleuze and Deleuze and Guattari with contemporary pedagogic practices and research, this paper offers a conceptually tentative reworking of the theory and practice of action research, both as a means of challenging antecedent positions and as a way of proposing a volatile and incisive approach that, it will be argued, can help in generating a more plural, reflexive and methodologically relevant pedagogy/research praxis. In this, it is hoped that the mobilisation of a Deleuzian conceptualisation of assemblage as a form of inquiry will open up the animation of revitalisation as event.     

Translocal assemblage and the practice of alternative media toward racial justice: a pedagogical perspective

There is a growing cultural and social movement among youth who draw on spoken word poetry and documentary style videos to participate in the new media landscape. Many multimedia poems have appeared on social media sites such as YouTube and Vimeo as a form of participatory politics. In this article, the author takes up a discussion of translocal practices and ‘translocal assemblage’ wherein individuals and groups engage in the exchange of ideas across space and time. One example is a multimedia poem about the underrepresentation and invisibility of racialized minority students at a major American university. This viral multimedia poem remixed elsewhere based on students’ experiences at another university demonstrates not only the potential of translocal assemblage in participatory politics but also the practice of alternative media in the movement toward racial justice. That is, young people are finding civic resources and building on each other’s work to challenge the social order. Pedagogically, the author built on the theoretical underpinning of translocal assemblage to shape work with students in the college classroom who, in turn, produced other genres of alternative media. The resultant video documentaries about locally unjust social arrangements make evident the subtle nature of cultural flows that have direct consequences for critical studies in education.