Counting subspaces of a finite vector space — 2

This is the second of a two-part article where we discuss the relation between the Gaussian binomial and multinomial coefficients and ordinary binomial and multinomial coefficients from a combinatorial viewpoint, based on expositions by Knuth, Stanley and Butler.     

Applying two channels to vector space secret sharing based multi-signature scheme

Secret sharing and digital signature is an important research area in information security and has wide applications in such fields as safeguarding and legal use of confidential information, secure multiparty computation and electronic commerce. But up to now, study of signature based on general vector space secret sharing is very weak. Aiming at this drawback, the authors did some research on vector space secret sharing against cheaters, and proposed an efficient but secure vector space se…     

Convergence Theorms of Ishikawa Iterative for Asymptotically Non—expansive Mapping in a Uniformly Convex Banach space

文[4]把文[3]的主要结果从Hilbert空间推广到一致凸Banach空间,证明了一致凸Banach空间中文上从有界闭凸集到自身的渐近非扩张映象的迭代序列收敛定理.本文将有界闭凸集的条件减弱为闭凸集,从而推广了文[4]的相应结果.     

Coffee——a Good Source of Antioxidants

If your hand is trembling over your third coffee of the morning, do not despair. You could be getting more healthy antioxidants(抗氧化剂) from your liquid fix than from the fruit or vegetables you eat, according to a study of US diets. Although dates(海枣), cranberries(酸果蔓) and red grapes were the richest source of antioxidants, researchers found these were not a common part of the average American's diet.     

"On generalized hypercenter of a finite group"一文的一点注记

在文"On generalized hypercenter of a finite group,Comm.Alg.,29(5),2 239-2 248(2001)"中,有如下结论G为超可解当且仅当G=genz∞(G).很自然地,人们猜想若F*(G)≤genz∞(G),则G为超可解群.给出一个反例说明此猜想的回答是否定的.     

A characteristic condition of finite nilpotent group

INTRODUCTION In this paper, all groups considered are finite;G means a finite group. We use conventional notions and notations, asin Huppert (1968). Recall that a minimal subgroupof a finite group is a subgroup of prime order. Forthe group of even order, it is helpful to also considerthe cyclic subgroup of order 4. Two subgroups Hand K of a group G are said to permute if HK=KH.It is easily seen that H and K permute if and only ifthe set of HK is a subgroup of G. We know…     

The reflexive adaptations of school principals in a ‘local’ South African space

This paper is an analysis of the work of three principals in an impoverished black township in post‐apartheid South Africa. Based on qualitative approaches, it discusses the principals’ entry into the township, and their navigation of their schools’ surrounding social dynamics. It combines the lenses of ‘space’ and ‘performance’ to analyse the reflexive basis on which they establish their principal roles. The paper suggests that their identities as principals were established in light of a range of engaged pedagogical performances. It is argued that these were enacted based on nuanced readings of their discursive environment and the enactment of strategic practices that provided them an authoritative platform for their principal roles.     

Two kinds of B-basis of the algebraic hyperbolic space

In this paper, two new kinds of B-basis functions called algebraic hyperbolic (AH) Bezier basis and AH B-Spline basis are presented in the space (?)k=span{1,t,...,tk-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bezier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms: AH B-Spline surface and AH T-Spline surface.     

The development of research supervision: “Turning the light on a private space”

Educational development for research supervisors is still a recent phenomenon. Early optional sessions on research supervision have now been replaced, particularly in the UK, continental Europe, and Australasia, by comprehensive and, in some cases, mandatory programs. Yet some of these programs focus solely on the administrative roles and responsibilities of supervisors, attempting to provide technical “fixes” that deny the genuine difficulties and complexities involved in supervision relationships. Some research supervisors resent the intrusion of educational developers into what many of them have regarded as a private pedagogical space. They interpret such programs as further instances of the quality assurance agendas of governments and university administrators, and are justifiably suspicious of what some describe as the colonial underpinnings of educational development. These reactions create tensions for educational developers. This article explores why educational development can be problematic for research supervisors. It then charts some current supervision educational development programs that seek to go beyond administrative interpretations of supervision. Finally, it examines whether the “Compassionate Rigour” supervision program, developed to address these difficulties, manages to respond respectfully and sensitively to supervisors’ educational development needs.

Le développement pédagogique des superviseurs de recherches demeure un phénomène récent. Les séances optionnelles portant sur la supervision de recherches de jadis ont été remplacées, particulièrement au Royaume‐Uni et en Australasie, par des programmes approfondis et, parfois, obligatoires. Pourtant, certains de ces programmes se concentrent seulement sur les rôles et les responsabilité des superviseurs au plan administratif, cherchant de la sorte à fournir des ‘trucs’ qui ne tiennent pas compte des difficultés et complexités réelles sous‐jacentes aux relations de supervision. Certains superviseurs de recherches n’apprécient guère l’intrusion des conseillers pédagogiques au sein de ce que d’aucuns considèrent être un espace pédagogique privé. Ils interprètent de tels programmes comme des composantes additionnelles des programmes de maintien de la qualité mis en place par les gouvernements et les administrations universitaires. Ces superviseurs redoutent, à juste titre, ce que d’aucuns décrivent comme les bases coloniales du développement pédagogique. De telles réactions instaurent créent des tensions pour les conseillers pédagogiques. Cet article explore pourquoi le développement pédagogique peut apparaître problématique aux yeux des superviseurs de recherches. Ensuite, il décrit certains programmes actuels de développement pédagogique reliés à la supervision qui cherchent à dépasser les interprétations strictement administratives de la supervision. Finalement, il examine le programme de supervision ‘Compassionate Rigour’, développé dans le but de palier à ces difficultés, pour voir si celui‐ci répond à la fois respectueusement et sensiblement aux besoins des superviseurs en matière de développement pédagogique.     

The Black Women’s Gathering Place: reconceptualising a curriculum of place/space

ABSTRACT

This article de-centres imperialist, capitalist, patriarchal traditions of critical approaches in Curriculum Studies via an examination of experiences shared at The Black Women’s Gathering Place (BWGP), a non-traditional space where a diverse, intergenerational group of Black women engage with each other through the sharing of stories. In the BWGP, we enact components of Pinar’s [2004. What is Curriculum Theory? Mahwah, NJ: Lawrence Erlbaum] concept of currere, simultaneously re-entering our collective and individual pasts and re-imagining our futures in an effort to reconcile our public and private selves. Taking up tenets of Black feminist theory, theoretical framings of hidden curriculum, and components of Ng-A-Fook’s [2007. An Indigenous Curriculum of Place: The United Houma Nation’s Contentious Relationship with Louisiana’s Educational Institutions. New York, NY: Peter Lang] ‘Curriculum of Place,’ we reconceptualise a curriculum of place/space that negotiates dominant norms expressed in social environments. In this space, we validate traditional knowledges upheld in communities of Black women across the Diaspora. The BWGP allows us to argue for a re-presentation of extant knowledge by and about Black women.     

Governing by inspection? European inspectorates and the creation of a European education policy space

This paper draws on the first, completed phase of a research project on inspection as governing in three European inspection systems. The data presented here draw attention to the rather under-researched associational activities of European inspectorates and their developing practices of policy learning and exchange, and highlight their significance as contributing to an emergent European Education Policy Space (EEPS). The paper is framed by original approaches to inspection that locate it as a set of governing practices, connected to changing governing forms and the growth of networks of relationships and flows of data across Europe. Comparisons are drawn between the relationships with Europe of inspectorates in Scotland, Sweden and England, drawing on Jacobsson's conceptualisation of regulative, inquisitive and meditative governance as a framing device.     

Translation of Movie Titles——from a functional perspective

This article intends to approach the translation of movie - titles from a different perspective - - - a functional perspective. Different titles may have different functions. In the process of translation, sometimes a certain function is maintained, sometimes changed. More often, a new function is added.     

Axisymmetric fundamental solutions for a finite layer with impeded boundaries

INTRODUCTIONBiot’sconsolidationtheorywasproposedin1 941fromcontinuousmediumfundamentalequations.Thetheorytakingintoaccountthecouplingbetweenthesolidstrainsandporepres suredissipationiscalled“coupledconsolidationtheory” .Thesolutionofgoverningequationso…     

Mathematics education in a time of crisis—a viral pandemic

Educational Studies in Mathematics -     

Language and content ‘integration’: the affordances of additional languages as a tool within a single curriculum space

‘Language across the curriculum’ has been pivotal in establishing a knowledge base on the role of language for accessing opportunities afforded by the curriculum. Yet, the ubiquity of language within all facets of human activity – not least of all the more abstract domains of thinking and relating with others – can easily obscure its perceptibility as an object for research relative to other priorities; especially when the curriculum focus is directed towards content-oriented areas, such as mathematics or the humanities. This paper uses an ecological framework to consider the place of language when the teacher’s focus is not solely on language, or content, but is equally attentive to both through a relatively new approach to theorizing learners’ non-native language within the curriculum: content and language integrated learning. In particular, it critically examines the notion of ‘integration’ as a pedagogical assumption for working with language in curriculum domains by focusing on teachers’ perceptions of the affordances of language as a meditational tool within the classroom space. Findings raise new implications for understanding the role of language(s) within the curriculum, and are significant for addressing the needs of a changing, globalized student demographic where the presence of multiple languages will increasingly shape learners’ engagement with the curriculum.