齐型空间上Herz空间中的分数次积分算子

本定义了一类齐型空间上的Herz空间，并研究了定义在这些空间的分数次积分算子的性质。     

幂线性空间的商空间

讨论类比商群、商空间的概念,提出了幂线性空间的商空间的概念.首先,给出幂线性空间和幂子空间的定义,并在此基础上构造了幂线性空间上一个等价关系,对幂线性空间进行分类,从而构造出幂线性空间的商空间.最后研究了商空间上基、维数及同态的性质.     

再谈物空间、象空间

本文重新定义了物空间、象空间，由此解决了物、象以及光程的虚、实的问题。     

概率赋范空间的乘积空间及拓扑

本定义了有限个概率线赋范空间的乘积空间，它仍是一个概率线性赋范空间。并证明了乘积空间中由概率范数导出的拓扑与乘积拓扑的等价性。本将概率线性赋范空间简称PN空间。     

双点空间及其一些拓扑性质

本文定义了双点空间并得出了一系列有意义的结果。     

模糊闭包空间的连通性

本定义了模糊闭包空间的概念，并将模糊拓扑空间连通性的一系列有关结果推广到模糊闭包空间中。     

Banach空间中的Banach框架

作者从另一个角度定义了Banach空间中的Xd框架,并在Banach空间中的Xd框架基础上定义Banach空间的Banach框架,并讨论它的一些性质.     

Banach空间上凸函数的一致可微性

1987年J.M.Borvein和D.Preiss对凸函数的Frechet可微性和Gsteaux可微性的定义给予了推广。本文在以上工作基础上定义了β—可微空间和弱β—可微空间,并主要讨论了弱β—可微空间。对β—可微空间的讨论参看(3).     

无关子空间

在高等代数线性子空间概念的基础上,给出了无关子空间的定义,并探究了无关子空间的一些充分必要条件,得出几个有趣的结论.     

闭包系统空间的连通性

文章定义了闭包系统空间的连通性并给出了等价刻画,讨论了连通性的一些性质,证明了闭包系统空间的连通性是连续不变的.文章还定义了连通分支,并研究了其性质.     

度规空间上非扩张型映射的不动点定理

在度规空间中建立了非扩张型映射不动点定理并利用它们，得到了度量空间、某类Menger概率度量空间以及局部凸Hausdorff拓扑向量空间中相应的不动点定理．     

关于可数空间

本文定义了几乎第二可数,几乎第一可数,几乎可分和几乎Lindelof空间,它们分别是第二可数,第一可数,可分和Lindelof空间的一般化,同时还讨论了这四类空间的性质。     

度量空间中的Orlicz—Sobolev容量

本文给出了度量空间中的Orlicz-Sobolev空间及Orlicz-Sobelev容量的概念，并研究了它们的一些基本性质．     

序拓扑空间上的择一不等式

首先在序拓扑空间上得到了KKM定理,然后应用这一定理推出了择一不等式的结果。     

L-拓扑空间超F连通性的樊畿定理

连通性是拓扑空间的重要概念,利用邻域给出L-拓扑空间超F连通性的樊畿定理的定理型刻画.     

Reconstruction algorithm in lattice-invariant signal spaces

In this paper, we mainly pay attention to the weighted sampling and reconstruction algorithm in lattice-invariant signal spaces. We give the reconstruction formula in lattice-invariant signal spaces, which is a generalization of former results in shift-invariant signal spaces. That is, we generalize and improve Aldroubi, Grochenig and Chen's results, respectively. So we obtain a general reconstruction algorithm in lattice-invariant signal spaces, which the signal spaces is sufficiently large to accommodate a large number of possible models. They are maybe useful for signal processing and communication theory.     

Shedding light on and with example spaces

Building on the papers in this special issue as well as on our own experience and research, we try to shed light on the construct of example spaces and on how it can inform research and practice in the teaching and learning of mathematical concepts. Consistent with our way of working, we delay definition until after appropriate reader experience has been brought to the surface and several ‘examples’ have been discussed. Of special interest is the notion of accessibility of examples: an individual’s access to example spaces depends on conditions and is a valuable window on a deep, personal, situated structure. Through the notions of dimensions of possible variation and range of permissible change, we consider ways in which examples exemplify and how attention needs to be directed so as to emphasise examplehood (generality) rather than particularity of mathematical objects. The paper ends with some remarks about example spaces in mathematics education itself.     

Teacher adaptation to personalized learning spaces

Personalized learning spaces are emerging in schools as a critical reaction to ‘industrial-era’ school models. As the form and function of schools and pedagogy change, this places pressure on teachers to adapt their conventional practice. This paper addresses the question of how teachers can adapt their classroom practice to create personalized learning spaces. Personalized learning spaces draw conceptually from several decades of attempts to personalize learning and open up classrooms, both physically and virtually. They are characterized by deliberate and active interactions between the context, teacher and students. Two case studies are presented of teachers in Australian regional schools reacting to new open plan school buildings by adapting their practice. Key findings discussed are the influence of context on teacher reasoning, and teacher agency when establishing alternative learning environments.     

A critical examination of informal learning spaces

ABSTRACT

Globally, the future of the higher education sector is under increasing scrutiny, and questions are being asked about the relevance of universities as traditional sites of teaching and learning. In an effort to adapt to the complexities that beset the higher education environment, universities are exploring the utility and benefits offered through informal learning spaces. However, the emergence of informal learning spaces raises important questions regarding student behaviours and ‘learning’, including the dichotomous positioning of the categories ‘formal’ and ‘informal’. This article highlights a tendency in the literature to treat informal learning spaces in a romanticised and overdetermined way. It challenges some of the popular imaginaries of these spaces as free, open and democratising in terms of students’ use, technological affordances, and a largely unchallenged emphasis on forms of community and collaboration as if they are unproblematic. Indeed, a persistently undefined ‘social’ quality attributed to informal learning settings, coupled with a focus on design and technology elements, elides the possibility of negative social practices such as exclusion and marginalisation. Moreover, empirical treatments of these spaces are dominated by quantitative methods that rely on deterministic cause and effect models, including normative understandings of academic success, as a measure of effectiveness. If universities are to proceed in better understanding these learning sites and the meanings and practices students bring to them, new perspectives incorporating more critical, interpretive qualitative approaches that give primacy to understanding the ways in which these spaces might reproduce marginalising or exclusionary social practices are required.     

Affinity spaces,literacies and classrooms: tensions and opportunities

Building communicative competence in textual and multimodal literacies has become a linchpin of learning, of engagement with the world, and of participation in online and blended spaces. Young creators now compose online and with digital tools, often in what we call “user‐generated content affinity spaces” – interest‐based spaces that focus on creating and sharing self‐made content. Such spaces focus on processes of developing users' creations and sharing the products with an audience. These spaces have been inspirations for teachers to reinvigorate classroom practices and expose students to learning opportunities for creation and critique. But questions remain about models of participation in such spaces, especially those that idealise youth who are the most highly engaged while ignoring those whose participation is less visible. Here, we share three experiences of bringing user‐generated content affinity spaces into more formal learning environments and reflect on the tensions emerging from these efforts. We end by outlining steps to develop theory and interventions to navigate tensions and propel the field forward.