Orientadores: Adriano Adrega de Moura, Evgeny Mukhin / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T22:56:39Z (GMT). No. of bitstreams: 1 Brito_MatheusBatagini_D.pdf: 1928614 bytes, checksum: bd194d09898859744dc51e0bcccd7fa1 (MD5) Previous issue date: 2015 / Resumo: Estudamos representações de dimensão finita para uma álgebra afim quantizada a partir de dois pontos de vista distintos. Na primeira parte deste trabalho estudamos o limite graduado de uma certa subclasse de representações irredutíveis. Seja V uma representação de dimensão finita para uma álgebra do tipo A e suponha que V é isomorfa ao produto tensorial de uma afinização minimal por partes cujo peso máximo é a soma de distintos pesos fundamentais por módulos de Kirillov--Reshetikhin cujos pesos máximos são o dobro de um peso fundamental. Provamos que V admite limite graduado L e que L é isomorfo a um módulo de Demazure de nível dois bem como ao produto de fusão dos limites graduados de cada um dos supramencionados fatores tensoriais de V. Provamos ainda que, se a álgebra for do tipo clássica (resp. G), o limite graduado das afinizações minimais (regulares) (resp. módulos de Kirillov--Reshetikhin) são isomorfos ao módulos CV para alguma R^+ partição descrita explicitamente. Na segunda parte provamos que um módulo para a álgebra afim quantizada do tipo B e posto n é manso se, e somente se, ele é fino. Em outras palavras, os geradores da subálgebra de Cartan afim são diagonalizáveis se, e somente se, os autoespaços generalizados associados têm dimensão um. Classificamos tais módulos e descrevemos seus respectivos q-caracteres. Em alguns casos, o q-caracter é descrito por super standard Young tableaux do tipo (2n|1) / Abstract: We study finite--dimensional representations for a quantum affine algebra from two different points of view. In the first part of this work we study the graded limit of a certain subclass of irreducible representations. Let V be a finite--dimensional representation for a quantum affine algebra of type A and assume that V is isomorphic to the tensor product of a minimal affinization by parts whose highest weight is a sum of distinct fundamental weights by Kirillov-Reshetkhin modules whose highest weights are twice a fundamental weight. We prove that V admits a graded limit L and that L is isomorphic to a level-two Demazure module as well as to the fusion product of the graded limits of each of the aforementioned tensor factors of V. We also prove that if the quantum affine algebra is of classical type (resp. type G), the graded limit of (regular) minimal affinizations (resp. Kirillov--Reshetkin modules) are isomorphic to CV-modules for some R^+ partition explicitly described. In the second part we show that a module for the quantum affine algebra of type B and rank n is tame if and only if it is thin. In other words, the Cartan currents are diagonalizable if and only if all joint generalized eigenspaces have dimension one. We classify all such modules and describe their q-characters. In some cases, the q-characters are described by super standard Young tableaux of type (2n|1) / Doutorado / Matematica / Doutor em Matemática

Le théorème de Mordell-Weil affirme que, pour toute variété abélienne définie sur un corps de nombres, le groupe des points K-rationnels est de type fini. Plus exactement, ce groupe peut être vu comme le produit d’un groupe libre et d’un sous-groupe fini de points de torsion définis sur K. Il est naturel de se demander si l’on peut obtenir une borne uniforme pour le cardinal du sous-groupe fini des points de torsion définis sur une extension finie de K, dépendant uniquement du degré de cette extension, lorsque la variété abélienne varie. Pour ce qui est des courbes elliptiques définies sur un corps de nombres, Merel a prouvé en 1994 que l’on peut obtenir une borne uniforme en utilisant des méthodes développées par Mazur, Kenku-Momose et Kamienny. Cependant, il est aussi naturel de se demander si l’on peut obtenir une borne de ce cardinal, qui dépend uniquement du degré de cette extension,lorsque l’extension varie et la variété abélienne est fixée. Concernant cette dernière question Hindry et Ratazzi ont énoncé plusieurs résultats concernant certaines classes de variétés abéliennes. L’objectif de cette thèse, sera de présenter des nouveaux résultats dans cette direction. On se concentrera sur la classe de variétés abéliennes de type III pleinement de type Lefschetz, c’est-à-dire, telles que leur groupe de Mumford-Tate soit le groupe des similitudes orthogonales qui commutent avec les endomorphismes et telles qu’elles vérifient la conjecture de Mumford-Tate. On démontre des nouveaux résultats concernant la conjecture de Mumford-Tate. En particulier, on fournit une liste de variétés abéliennes dont on sait prouver qu’elles sont pleinement de type Lefschetz. / Mordell-Weil’s theorem states that, for an abelian variety defined over a number field K the group of K-rational points is finitely generated. More precisely, it can be seen as a product of a free group by a finite subgroup of torsion points over K. One can wonder if we can get an uniform bound for the order of the subgroup of torsion points over a finite extension L over K, depending on the degree of this extension and the dimension of the abelian variety, when the abelian variety varies in a certain class. For elliptic curves defined over a number field K, Merel proved in 1994 that we can get a uniform bound using methods developed by Mazur, Kenku-Momose and Kamienny. A complementary question would be to ask if we can get a bound for the order of the subgroup of torsion points over a finite extension L over K, depending on the degree of this extension and the dimension of the abelian variety, when L varies over all the finite extensions of K and the abelian variety is fixed. This question had been already answered by Hindry and Ratazzi for certain classes of abelian variety.This thesis will focus on this last question and will extend the previous results. We are going to present some new results concerning the class of abelian variety of type III in Albert’s classification and “fully of Lefschetz type” (i.e. whose Mumford-Tate group is the group of symplectic or orthogonal similitudes commuting with endomorphisms and which satisfy the Mumford-Tate conjecture). We also show some new results in the direction of the Mumford-Tate conjecture. Moreover, we present a list of abelian varieties which, we know, are fully of Lefschetz type.

In Life Sciences Education, the use of educational external representations (ERs) such as diagrams, models and animations are increasingly appearing in learning and teaching resources. However, their effectiveness is limited if learners experience learning difficulties due to lack of visual literacy and spatial ability skills to work with ERs. The study explored the level of visual literacy of 225 Grade 10 Life Sciences learners in cytology across six secondary schools in Pretoria, Gauteng. It was theorised that ERs need to be integrated in the Life Sciences curricula to develop learners’ visual literacy and spatial ability skills. With this theory, the study aimed to explore the visual literacy of Grade 10 Life Sciences learners and the influence of gender and school location on the visual literacy and spatial ability skills of the learners. Through a quantitative research method a Life Sciences visual literacy questionnaire and a spatial ability test were used to collect data. Collected data was analysed descriptively and inferentially through Statistical Package Social Sciences Version 23. The results showed that most Grade 10 Life Sciences learners lack average visual literacy skills. Furthermore, the results showed that gender doesn’t play a role on the learners’ performance in visual literacy skills as both genders performed equally in both tests, On the other hand, the results showed that the location of the school (urban, rural or township) has an effect on the learners’ performance in visual literacy skills. Teachers need to incorporate different ERs that would stimulate different senses and which will also enhance learners’ visual literacy and spatial ability skills in their lessons. A conclusion and some recommendations for future research are given. / Dissertation (MEd)--University of Pretoria, 2017. / Science, Mathematics and Technology Education / MEd / Unrestricted

The poor learner outcomes in the TIMSS assessment, the SACMEQ assessment, and the Grade 9 ANAs led to this study being conducted. The purpose of the study was to explore whether Grade 9 mathematics teachers’ teaching can improve learner outcomes. This study therefore investigated the literature regarding mathematics teachers’ classroom practices with an emphasis on teachers’ Pedagogical Content Knowledge (PCK), Pedagogical Content Knowledge and Skills (PCK&S), and how these teachers used assessment outcomes to inform their teaching of mathematics. In developing learners’ conceptual understanding and higher-order thinking skills, mathematics teachers not only need subject matter knowledge, but also PCK and the skill to implement their planning efficiently during instruction. The conceptual framework for this study is based on Gess-Newsome’s (in Berry et al., 2015) Model of Teachers’ Professional Knowledge and Skills. Based on this, PCK was examined in the planning and executing of topic-specific instruction and as a skill when teaching this content to the learners for enhanced learner outcomes. The research approach was qualitative and the research design was a case study. Two Grade 9 mathematics teachers from one school were selected through purposive sampling. The data were collected using a baseline test, three classroom observations, one semi-structured interview and a formative test. Both teachers used Direct Instruction in all their lessons, but proficiently used various representations when explaining the work, and integrated the topic into other mathematical topics and real-life scenarios. The teachers admitted that they did not usually make use of baseline tests to inform their teaching due to time constraints, but found it valuable during this endeavour. The findings from the two tests showed many learners still have the same misconceptions regarding the concepts of surface area, volume and capacity; continued to make the same typical mistakes in finding formulae for surface area and volume; and still found it difficult to convert between the SI units. There was, however, significant improvement in learner outcomes, but the positive outcomes regarding all typical mistakes and learner difficulties were still below 46%. / Dissertation (MEd)--University of Pretoria, 2017. / Science, Mathematics and Technology Education / MEd / Unrestricted

Outils dominants de représentation du monde social, les statistiques publiques jouent en France un rôledéterminant dans la revendication actuelle de rationalisation de l’action de l’Etat. A partir de l’étude dumode de publicité des statistiques de la délinquance et de la criminalité, ce travail analyse la place de cesdonnées chiffrées dans les stratégies de communication publique. Il apparaît ainsi que cetteprééminence tient à la fois au régime sémiotique spécifique des chiffres, à l’importance du quantitatifdans l’imaginaire individuel et collectif, autant qu’à une combinaison de légitimations (historiques,éthiques, politiques, scientifiques). Mais les rapports de pouvoir en jeu se définissent également par lamanipulation des signes en vue d’imposer un système de valeurs. Ils se distinguent par la force d’uneesthétique qui parvient à concilier complexité du savoir et apparente évidence de l’information,objectivité et subjectivité, opacité des instances auctoriales et transparence revendiquée. / As the prevailing tools of the representation of the social world, official statistics in France play akey role in the current claim to rationalise government actions. Studying the communicationalchoices concerning criminal statistics in France, this work emphasizes the role of statistics in thestrategies of public communication: their importance lies in the semiotic nature of figures, theinfluence of quantitative matters in the individual and collective imagination, as well as acombination of legitimacy (historical, ethical, political, scientific). But the balance of powersinvolved is also defined by the manipulation of signs in order to establish a system of values. Theseare distinguished by the strength of an aesthetic, which strikes a balance between complexity ofknowledge and apparent evidence of information, objectivity and subjectivity, opacity of auctorialauthorities and claimed transparency.

Research shows that pupils experience difficulties with the word problems in their mathematical textbooks. The forms of representations are made visible through the word problems and are vital elements considering the pupils’ understanding of the basic idea of important concepts. The purpose of this study is to provide knowledge about how word problems in mathematical textbooks and their forms of representations can be used by pupils’ as a linguistic tool. Moreover, this research has used a quantitative content analysis where two different textbooks, their word problems and the forms of representations have been analyzed and quantified. The result shows that almost every word problem uses the representation of symbols. Furthermore, the majority of the word problems use the representation of real situations while the representation of picture is less evident. The result also shows that mathematical textbooks can be seen as a linguistic tool for the pupils since mathematical concepts often are expressed through different forms of representation. As a suggestion, teachers’ can complement their mathematical textbooks with external assignments based on the representations of picture situations to develop the pupils’ understanding. / Forskning visar på att elever har svårigheter med läroböckers textbaserade uppgifter. I textbaserade uppgifter synliggörs representationsformer som kan koppla samman med elevers förståelse för matematiska begrepp. Arbetet syftar till att bidra med kunskap kring hur tryckta läroböckers textbaserade uppgifter och deras representationsformer kan ses som ett språkligt stöd i elevernas lärande. Genom en kvantitativ innehållsanalys har två tryckta läroböckers textbaserade uppgifter och deras representationsformer analyserats och kvantifierats.Resultatet visar att nästintill alla de textbaserade uppgifterna använder sig av representationsformen symbol. Majoriteten av de textbaserade uppgifterna använder verkliga situationer. Medan färre textbaserade uppgifter använder sig av den bildliga representationsfomen. Läroböckerna kan ses som ett språkligt stöd för eleven där matematiska begrepp ofta uttrycks genom olika representationsformer. Förslagsvis kan lärare komplettera läroböckerna med egna bildliga representationsformer för att öka elevernas förståelse.

京都大学 / 0048 / 新制・課程博士 / 博士(人間・環境学) / 甲第19795号 / 人博第766号 / 新制||人||184(附属図書館) / 27||人博||766(吉田南総合図書館) / 32831 / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)教授 立木 秀樹, 准教授 櫻川 貴司, 教授 日置 尋久 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DFAM

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This research aimed to explore the social representation of a ‘risky identity’ with regard to HIV. 12 students participated in the research and these participants were required to take photographs regarding their perceptions of a ‘risky identity’. Each participant also took part in a semi-structured interview that prompted discussion of the photographs and the different factors perceived to influence the risk of HIV infection. These interviews were audiorecorded and transcribed. Discourse analysis was used to analyse the data and how the participants position the ‘other’ as more at risk of HIV infection than the self. The analysis also revealed that the most common factor perceived to influence the risk of HIV infection is substance use. Other factors include: gender, race, age, and socio-economic status. Interestingly, the participants found it easier to attribute risk to behavioural and environmental factors, whereas they were more reluctant to associate risk with factors such as race and gender. In fact, when doing so, many of the participants emphasised the impact of environmental and behavioural factors as a means to justify their perceptions. The risk of justifying social representations in such a manner is that prejudiced attitudes remain, just in a seemingly more socially acceptable form. Subsequently, it is recommended that HIV prevention programs go beyond education to critical discussions about issues of identity and the social representations and risk perceptions influencing sexual behaviour.

The purpose of this essay is to examine how racialized workers are represented in the magazine Kommunalarbetaren which is a part of the Swedish trade union Kommunal. The covers from twenty issues of this magazine published in 2017 were analyzed to study if the representation of these workers was affected by discourses of white normativity. The study is based on theories of intersectionality by Kimberlé Crenshaw and representations and stereotypification by Stuart Hall. My result shows how work is exposed as something white people do and with dichotomies where one is represented as either white, Swedish worker or as a refugee, the latter having vague subject position and as someone who recently arrived in Sweden. The presence, participation and labour of people of color seem to be missing and be a blind spot for the magazine.