Level-one highest weight representation of U-q[sl((N)over-cap vertical bar 1)] and Bosonization of the multicomponent Super t-J model

We study the level-one irreducible highest weight representations of the quantum affine superalgebra U-q[sl((N) over cap\1)], and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible U-q[sl((N) over cap\1)] modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multicomponent super t-J model by using the bosonized vertex operators. (C) 2000 American Institute of Physics. [S0022- 2488(00)00508-9].

Free field and parafermionic realizations of twisted su(3)(k)((2)) current algebra

Free field and twisted parafermionic representations of twisted su(3)(k)((2)) current algebra are obtained. The corresponding twisted Sugawara energy-momentum tensor is given in terms of three (beta, gamma) pairs and two scalar fields and also in terms of twisted parafermionic currents and one scalar field. Two screening currents of the first kind are presented in terms of the free fields.

Changing representations and practices in school mathematics: the case of Modern Math in Portugal

The curricular movement known as Modern Mathematics aimed at the transformation of representations and practices in school mathematics. Its study provides us with ways of understanding how these changes came about. The purpose of this paper is to contribute to the understanding of the ways in which representations of school mathematics gradually were influenced by ideas from the Modern Mathematics movement, how these new ideas merged into local educational traditions, and how they were transformed into meaningful practice. This work is centred on the Portuguese context from the middle 1950s to the middle 1960s, and builds on Chervel’s notion of school culture and Gruzinski’s discussion of connected histories.

Modularity of auditory spatial representations

Abstract : Auditory spatial functions are of crucial importance in everyday life. Determining the origin of sound sources in space plays a key role in a variety of tasks including orientation of attention, disentangling of complex acoustic patterns reaching our ears in noisy environments. Following brain damage, auditory spatial processing can be disrupted, resulting in severe handicaps. Complaints of patients with sound localization deficits include the inability to locate their crying child or being over-loaded by sounds in crowded public places. Yet, the brain bears a large capacity for reorganization following damage and/or learning. This phenomenon is referred as plasticity and is believed to underlie post-lesional functional recovery as well as learning-induced improvement. The aim of this thesis was to investigate the organization and plasticity of different aspects of auditory spatial functions. Overall, we report the outcomes of three studies: In the study entitled "Learning-induced plasticity in auditory spatial representations" (Spierer et al., 2007b), we focused on the neurophysiological and behavioral changes induced by auditory spatial training in healthy subjects. We found that relatively brief auditory spatial discrimination training improves performance and modifies the cortical representation of the trained sound locations, suggesting that cortical auditory representations of space are dynamic and subject to rapid reorganization. In the same study, we tested the generalization and persistence of training effects over time, as these are two determining factors in the development of neurorehabilitative intervention. In "The path to success in auditory spatial discrimination" (Spierer et al., 2007c), we investigated the neurophysiological correlates of successful spatial discrimination and contribute to the modeling of the anatomo-functional organization of auditory spatial processing in healthy subjects. We showed that discrimination accuracy depends on superior temporal plane (STP) activity in response to the first sound of a pair of stimuli. Our data support a model wherein refinement of spatial representations occurs within the STP and that interactions with parietal structures allow for transformations into coordinate frames that are required for higher-order computations including absolute localization of sound sources. In "Extinction of auditory stimuli in hemineglect: space versus ear" (Spierer et al., 2007a), we investigated auditory attentional deficits in brain-damaged patients. This work provides insight into the auditory neglect syndrome and its relation with neglect symptoms within the visual modality. Apart from contributing to a basic understanding of the cortical mechanisms underlying auditory spatial functions, the outcomes of the studies also contribute to develop neurorehabilitation strategies, which are currently being tested in clinical populations.

Impact of a Cleft Lip and/or Palate on Maternal Stress and Attachment Representations.

Objective : The announcement, prenatally or at birth, of a cleft lip and/or palate represents a challenge for the parents. The purpose of this study is to identify parental working internal models of the child (parental representations of the child and relationship in the context of attachment theory) and posttraumatic stress disorder symptoms in mothers of infants born with a cleft. Method : The study compares mothers with a child born with a cleft (n  =  22) and mothers with a healthy infant (n  =  36). Results : The study shows that mothers of infants with a cleft more often experience insecure parental working internal models of the child and more posttraumatic stress symptoms than mothers of the control group. It is interesting that the severity or complexity of the cleft is not related to parental representations and posttraumatic stress disorder symptoms. The maternal emotional involvement, as expressed in maternal attachment representations, is higher in mothers of children with a cleft who had especially high posttraumatic stress disorder symptoms, as compared with mothers of children with a cleft having fewer posttraumatic stress disorder symptoms. Discussion : Mothers of children with a cleft may benefit from supportive therapy regarding parent-child attachment, even when they express low posttraumatic stress disorder symptoms.

The Island of Drive. Representations, somatic states and the origin of drive

Freud defined the drive as "a concept on the frontier between the mental and the somatic". Today this view that was based on clinical observations interpreted within the psychoanalytical framework, can be revisited in light of the current neuroscientific notions of neuronal plasticity and somatic states. Indeed, through the mechanisms of plasticity experience leaves a trace that forms the neural basis of a representation of the experience. Such a representation R is associated with a somatic state S in the sense taken from the "somatic marker" model of Damasio. Thus, the internal reality of the subject, particularly the unconscious one, is constituted by such connected R's and S's. In the model that we discuss, the posterior insula represents the primary interoceptive cortex where information about somatic states S converges, while in the anterior insula the connection between R and S can take place and establish a neurobiological correlate for the notion of drive. We posit that the re-representations of S associated with R in the anterior insula may correspond to the Vorstellungsrepräsentanz postulated by Freud. We further propose that the tension between R and S established in the anterior insula is discharged according to the notion of drive through the motor arm of the limbic system, namely the anterior cingulate cortex which is heavily connected with the anterior insula.

The emergence of parental and paternity leaves in Switzerland : a challenge to gendered representations and practices of parenthood?

The thesis addresses the issue of parenthood and gender equality in Switzerland through the emergence of parental leave policies. This is an original and relevant research topic, as Switzerland is one of the few industrialized countries that have not yet implemented a parental or paternity leave. I first describe the emergence of parental leave policies in the last ten to fifteen years in the political, media, and labor-market spheres. Secondly, adopting a gender and discursive theoretical approach, I analyze whether and to what extent this emergence challenged gendered representations and practices of parenthood. The multilevel and mixed-methods research design implies analyzing various data sets such as parliamentary interventions (N=23J and newspaper articles (N=579) on parental leave policies. A case study of a public administration which implemented a one-month paid paternity leave draws on register data of leave recipients (N=95) and in-depth interviews with fathers and managers (n=30). Results show that parental leave policies, especially in recent years, have been increasingly problematized in the three social spheres considered, as a result of political and institutional events. While there is a struggle over the definition of the legitimate leave type to implement [parental or paternity leave) in the political sphere, paternity leave has precedence in the media and labor-market spheres. Overall, this emergence contributes to making fatherhood visible in the public sphere, challenging albeit in a limited way gendered representations and practices of parenthood. Along with representations of involved fatherhood and change in gender relations, different roles and responsibilities are attributed to mothers and fathers, the latter being often defined as secondary, temporary and optional parents. Finally, I identify a common trend, namely the increasing importance of the economic aspects of parental leave policies with the consequence of sidelining their gender-equality potential. The dissertation contributes to the literature which analyzes the interconnections between the macro-, the meso- and the micro-levels of society in the constitution of gender relations and parenthood. It also provides useful tools for the analysis of the politics of parental leave policies in Switzerland and their effects for gender equality. - Cette thèse traite de la parentalité et de l'égalité de genre en Suisse à travers l'émergence des congés parentaux. Ce sujet de recherche est original et pertinent puisque la Suisse est à ce jour un des seuls pays industrialisés à ne pas avoir adopté de droit au congé parental ou paternité. Cette recherche décrit l'émergence des congés parentaux au cours des 10 à 15 dernières années dans les sphères politique, médiatique et du marché de l'emploi en Suisse. En combinant perspective de genre et analyse de discours, elle examine dans quelle mesure cette émergence remet en question les représentations et pratiques genrées de parentalité. Des méthodes de recherche mixtes sont employées pour analyser des interventions parlementaires (N=23) et des articles de presse (N=579) sur les congés parentaux. L'étude de cas d une entreprise publique qui a adopté un congé paternité payé d'un mois s'appuie sur des données de registre (N=95) et des entretiens semi-structurés avec des pères et des cadres (n=30). Les résultats indiquent que dans les trois sphères considérées, les congés parentaux ont reçu une attention croissante au cours de ces dernières années, en lien avec des événements politiques et institutionnels. Alors que dans la sphère politique il n'y a pas de consensus quant au type de congé considéré comme légitime (congé parental ou paternité), dans les sphères médiatique et du marché de l'emploi le congé paternité semble l'emporter. Dans l'ensemble, l'émergence des congés parentaux contribue à rendre la paternité plus visible dans l'espace public, remettant en question-bien que d'une manière limitée-les représentations genrées de la parentalité. En effet, d'une part l'image de pères impliqués et de rapports de genre plus égalitaires au sein de la famille est diffusée. D'autre part, mères et pères continuent à être associés à des rôles différents, les pères étant définis comme des parents secondaires et temporaires. Finalement, l'analyse révèle une tendance générale, soit l'importance croissante accordée aux aspects économiques des congés parentaux, avec pour conséquence la mise à l'écart de leur potentiel pour l'égalité de genre. Cette thèse contribue à la recherche sur les liens entre les niveaux macro- meso- et microsociaux dans la constitution des rapports de genre et de la parentalité. Elle propose également des outils pour analyser les politiques de congés parentaux en Suisse et leurs implications pour l'égalité de genre.

Families of orthogonal functions defined by the Weyl groups of compact Lie groups

Plusieurs familles de fonctions spéciales de plusieurs variables, appelées fonctions d'orbites, sont définies dans le contexte des groupes de Weyl de groupes de Lie simples compacts/d'algèbres de Lie simples. Ces fonctions sont étudiées depuis près d'un siècle en raison de leur lien avec les caractères des représentations irréductibles des algèbres de Lie simples, mais également de par leurs symétries et orthogonalités. Nous sommes principalement intéressés par la description des relations d'orthogonalité discrète et des transformations discrètes correspondantes, transformations qui permettent l'utilisation des fonctions d'orbites dans le traitement de données multidimensionnelles. Cette description est donnée pour les groupes de Weyl dont les racines ont deux longueurs différentes, en particulier pour les groupes de rang $2$ dans le cas des fonctions d'orbites du type $E$ et pour les groupes de rang $3$ dans le cas de toutes les autres fonctions d'orbites.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Simple derivation of general Fierz-type identities

General Fierz-type identities are examined and their well-known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex 4 X 4 matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning. (c) 2005 American Association of Physics Teachers.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Symplectic bosons, Fermi fields and super Jordan algebras

A construction relating the structures of super Lie and super Jordan algebras is proposed. This may clarify the role played by field theoretical realizations of super Jordan algebras in constructing representations of super Kač-Moody algebras. The case of OSP(m, n) and super Clifford algebras involving independent Fermi fields and symplectic bosons is discussed in detail.

Egocentric speech in the works of Vygotsky and Piaget: educational implications and representations by teachers

This paper presents an applied qualitative and quantitative study and seeks to understand egocentric speech according to Vygotsky and Piaget and, through a literature review, the educational implications of Vygotsky and Piaget’s ideas. Additionally, the representations of these ideas by fifteen teachers of basic education are investigated. It is important to understand egocentric speech in Vygotsky and Piaget. Despite the differences in how they conceive its nature, functions and implications, for both, egocentric speech is intrinsically linked to and facilitates our understanding of child development. Regarding the representation of teachers who criticized children who used egocentric language, when teachers established any negative consequences of such language, they attributed it to the affective and moral aspects as well as to cognition. However, their approach was more practically oriented than those found in the psychological theories addressed. Therefore, this study aids in understanding the limits and scope of teacher-training courses.

Orthogonality relations and supercharacter formulas of U(m vertical bar n) representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. © 1997 American Institute of Physics.