Orientador: Philippe Remy Bernard Devloo / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo / Made available in DSpace on 2018-08-13T10:14:35Z (GMT). No. of bitstreams: 1 Lucci_PauloCesardeAlvarenga_M.pdf: 6661587 bytes, checksum: b77bb456093ce1f153056c6b2fa89626 (MD5) Previous issue date: 2009 / Resumo: Este trabalho é dedicado ao desenvolvimento de uma metodologia específica de mapeamento curvo aplicável a qualquer tipo de elemento geométrico regular. Trata-se de uma generalização do modelo matemático de representação geométrica apresentado em 1967 por Steven Anson Coons, denominado "Bilinearly Blended Coons Patches", o qual ajusta uma superfície retangular em um contorno delimitado por quatro curvas arbitrárias. A generalização proposta permitirá a utilização deste tipo de interpolação geométrica em elementos de qualquer topologia, através de uma sistemática única e consistente. / Abstract: In this work a methodology is developed for mathematical representation of curved domains, applicable to any type of finite element geometry. This methodology is a generalization of the mathematical model of a geometric representation presented in 1967 by Steven Anson Coons, called "Bilinearly Blended Coons Patches", which patch a rectangular surface in four arbitrary boundary curves. The proposed methodology is a kind of geometric transfinite interpolation applicable to elements of any topology, using a single and consistent systematic. / Mestrado / Estruturas / Mestre em Engenharia Civil

Le travail présenté dans cette thèse s’inscrit à la fois dans le domaine de l’informatique musicale et dans celui de la réalité virtuelle. Nous présentons tout d’abord les avantages des environnements virtuels immersifs et de l’interaction graphique 3D pour les instruments multi-processus et en particulier pour le live-looping hiérarchique, un nouveau modèle d’instrument que nous définissons. Nous proposons ensuite des solutions pour la visualisation et la manipulation des processus sonores dans ces environnements virtuels. Afin de représenter les processus sonores, nous introduisons les widgets réactifs 3D qui s’appuient sur des mappings audiovisuels que nous évaluons. Nous développons un nouveau dispositif d’interaction 3D adapté à l’interaction musicale, appelé Piivert, ainsi que des techniques associées, dont les tunnels, afin de manipuler les widgets réactifs 3D. Finalement, nous mettons en œuvre le live-looping hiérarchique avec l’instrument immersif Drile, en utilisant les techniques développées précédemment, et nous étudions plusieurs scènes pour les performances musicales immersives. / The work presented in this thesis belongs to the computer music field as well as to the virtual reality field. First, we describe the advantages of immersive virtual environments and of 3D graphical interaction for multiprocesses instruments and particularly for the hierarchical live-looping, a new instrument model that we define. We then suggest solutions to visualize and manipulate sound processes in these virtual environments. In order to display the sound processes, we introduce the 3D reactive widgets, which rely on audiovisual mappings that we study. We develop a novel 3D interaction device suitable for musical interaction, called Piivert, together with associated interaction techniques, among which the tunnels, in order to manipulate the 3D reactive widgets Finally, we implement the hierarchical live-looping with an immersive instrument called Drile, using the previously developped techniques, and we study different stages for immersive musical performances.

The aim of this dissertation is to give explicit descriptions of the set of proper holomorphic mappings between two complex manifolds with reasonable restrictions on the domain and target spaces. Without any restrictions, this problem is intractable even when posed for do-mains in . We give partial results for special classes of manifolds. We study, broadly, two types of structure results: Descriptive. The first result of this thesis is a structure theorem for finite proper holomorphic mappings between products of connected, hyperbolic open subsets of compact Riemann surfaces. A special case of our result follows from the techniques used in a classical result due to Remmert and Stein, adapted to the above setting. However, the presence of factors that have no boundary or boundaries that consist of a discrete set of points necessitates the use of techniques that are quite divergent from those used by Remmert and Stein. We make use of a finiteness theorem of Imayoshi to deal with these factors. Rigidity. A famous theorem of H. Alexander proves the non-existence of non-injective proper holomorphic self-maps of the unit ball in . ,n >1. Several extensions of this result for various classes of domains have been established since the appearance of Alexander’s result, and it is conjectured that the result is true for all bounded domains in . , n > 1, whose boundary is C2-smooth. This conjecture is still very far from being settled. Our first rigidity result establishes the non-existence of non-injective proper holomorphic self-maps of bounded, balanced pseudo convex domains of finite type (in the sense of D’Angelo) in ,n >1. This generalizes a result in 2, by Coupet, Pan and Sukhov, to higher dimensions. As in Coupet–Pan–Sukhov, the aforementioned domains need not have real-analytic boundaries. However, in higher dimensions, several aspects of their argument do not work. Instead, we exploit the circular symmetry and a recent result in complex dynamics by Opshtein. Our next rigidity result is for bounded symmetric domains. We prove that a proper holomorphic map between two non-planar bounded symmetric domains of the same dimension, one of them being irreducible, is a biholomorphism. Our methods allow us to give a single, all-encompassing argument that unifies the various special cases in which this result is known. Furthermore, our proof of this result does not rely on the fine structure (in the sense of Wolf et al.) of bounded symmetric domains. Thus, we are able to apply our techniques to more general classes of domains. We illustrate this by proving a rigidity result for certain convex balanced domains whose automorphism groups are assumed to only be non-compact. For bounded symmetric domains, our key tool is that of Jordan triple systems, which is used to describe the boundary geometry.

We use transcendental shift-like automorphisms of Ck, k > 2 to construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of Dixon-Esterle in C2. The second example shows the existence of a Fatou-Bieberbach domain in Ck,k > 2 that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and Rosay-Rudin. In the second part we compute the order and type of entire mappings that parametrize one dimensional unstable manifolds for shift-like polynomial automorphisms and show how they can be used to prove a Yoccoz type inequality for this class of automorphisms.

M.Ed. / This study is an investigation into cognitive mapping as strategy in the constructivistic approach to mathematics education to learners with a visual disability with the view to describe the change in pupils' thoughts on mathematical concepts, as well as their experiences during the process of cognitive mapping. The rationale for the investigation was derived from the shift in South African Mathematics teaching from traditional teaching to constructivistic (or problem-centered) teaching. As this implies a shift in paradigm, teachers will be in need of relevant constructivistic training to equip them with effective teaching strategies. The objective of this study is to examine cognitive mapping as a possible supportive strategy to constructivism . The study commences with a theoretical framework in which constructivism is clearly explicated. The principles of radical and social constructivism, the roots of which can be traced back to the epistemological theories of Piaget and Vygotsky, are explored. The constructivistic view of knowledge, with the relationship between public knowledge and the forming of personal knowledge, is discussed and extended to include the formation of mathematical knowledge. The focus then shifts to the concepts of instruction and learning and the role they play in the constructivistic paradigm. In the constructivistic view, learning implies cognitive restructuring, which is facilitated by assimilation and accommodation. The implications of this view of learning for instruction, and in particular mathematics instruction, is then discussed. This chapter concludes with the working definition the researcher has used to conduct the remainder of the study. The theoretical framework is structured furthermore to give background regarding cognitive mapping. According to the constructivistic approach, learning implies conceptual change. Cognitive maps externalise conceptual change by means of visual representations, and therefore it was decided to investigate them as a teaching strategy. Some definitions, as found in the literature, are given, and three types of maps are illustrated as examples. The different uses of cognitive maps, among which study strategy, lesson planning and means of evaluation, are discussed. A discussion on the different methods of constructing a map follows, with specific focus on how to include the whole class in the activity. The advantage of social interaction while constructing knowledge, is highlighted. Lastly, the advantages and disadvantages connected to cognitive mapping as teaching strategy, are discussed. The theoretical framework is complemented by a chapter on the design of the research, substantiating the choice of format and methods of data collection and analysis. The data is reported in the succeeding chapter, and examples of raw data from transcriptions, journals of the pupils and cognitive maps are presented. Finally, the consolidated data is interpreted. In the concluding chapter the findings of the study are discussed. The most significant findings of this study are: cognitive mapping, as mathematical teaching strategy, improved the understanding of grade nine learners, with a visual disability, of real numbers; the learners experienced the teaching strategy of cognitive mapping positively; the number of group members involved in the construction of a cognitive map, influenced.

One the key feature behind Linked Data is the use of vocabularies that allow datasets to share a common language to describe similar concepts and relationships and resolve ambiguities between them. The development of vocabularies is often driven by a consensus process among datasets implementers, in which the criterion of interoperability is considered to be sufficient. This can lead to misrepresentation of real-world entities in Linked Data vocabularies entities. Such drawbacks can be fixed by the use of a formal methodology for modelling Linked Data vocabularies entities and identifying ontological distinctions. One proven example is the OntoClean methodology for curing taxonomies. In this work, it is presented a software tool that implements the PURO approach to ontological distinction modelling. PURO models vocabularies as Ontological Foreground Models (OFM), and the structure of ontological distinctions as Ontological Background Models (OBM), constructed using meta-properties attached to vocabulary entities, in a process known as vocabulary annotation. The software tool, named Background Annotation plugin, written in Java and integrated in the Protégé ontology editor, enables a user to graphically annotate vocabulary entities through an annotation workflow, that implements, among other things, persistency of annotations and their retrieval. Two kinds of workflows are supported: generic and dataset-specific, in order to differentiate a vocabulary usage, in terms of a PURO OBM, with respect to a given Linked Data dataset. The workflow is enhanced by the use of dataset statistical indicators retrieved through the Sindice service, for a sample of chosen datasets, such as the number of entities present in a dataset, and the relative frequency of vocabulary entities in that dataset. A further enhancement is provided by dataset summaries that offer an overview of the most common entity-property paths found in a dataset. Foreseen utilisation of the Background Annotation plugin include: 1) the checking of mapping agreement between different datasets, as produced by the R2R framework and 2) annotation of dependent resources in Concise Boundaries Descriptions of entities, used in data sampling from Linked Data datasets for data mining purposes.

Dans cette thèse, nous présentons des approches d’adaptation d’un processus d’alignement aux caractéristiques des ontologies alignées, qu'il s'agisse de caractéristiques quantitatives telles que leur volume ou de caractéristiques particulières liées par exemple à la façon dont les labels des concepts sont construits. Concernant les caractéristiques quantitatives, nous proposons deux méthodes de partitionnement d'ontologies qui permettent l’alignement des ontologies très volumineuses. Ces deux méthodes génèrent, en entrée du processus d'alignement, des sous ensembles de taille raisonnable des deux ontologies à aligner en prenant en compte dès le départ l'objectif d'alignement dans le processus de partitionnement.Concernant les caractéristiques particulières des ontologies alignées, nous présentons l’environnement TaxoMap Framework qui permet la spécification de traitements de raffinement à partir de primitives prédéfinies. Nous proposons un langage de patrons MPL (the Mapping Pattern Language) que nous utilisons pour spécifier les traitements de raffinement.En plus des approches d’adaptation aux caractéristiques des ontologies alignées, nous présentons des approches de réutilisation des résultats d'alignement pour l'ingénierie ontologique. Nous nous focalisons plus particulièrement sur l'utilisation de l'alignement pour l'enrichissement d'ontologies. Nous étudions l'apport des techniques d'alignement pour l'enrichissement et l'impact des caractéristiques de la ressource externe utilisée comme source d'enrichissement. Enfin, nous présentons la façon dont l'environnement TaxoMap Framework a été implémenté et les expérimentations réalisées : des tests sur le module d'alignement TaxoMap, sur l'approche de raffinement de mappings, sur les méthodes de partitionnement d'ontologies de très grande taille et sur l'approche d'enrichissement d'ontologies. / In this thesis, we present approaches for adapting an alignment process to the characteristics of the aligned ontologies, whether in respect of the quantitative characteristics such as their volume or the particular characteristics related for example to the way in which the labels of the concepts are built.Concerning the quantitative characteristics, we propose two ontology partitioning methods that make the alignment of very large ontologies possible. Both methods generate in the input of the alignment process, subsets of reasonable size of the two ontologies to be aligned by taking into account, as soon as possible, the alignment objective in the partitioning process.Concerning the particular characteristics of the aligned ontologies, we present the TaxoMap Framework environment that allows the specification of refinement treatments from predefined primitives. We propose a pattern language MPL (the Mapping Pattern Language) that we use to specify the refinement treatments.In addition to the adaptation approaches to the characteristics of the aligned ontologies, we present approaches for re-using the alignment results for the ontological engineering. We focus specifically on the use of the alignment for the ontology enrichment. We study the contribution of the alignment techniques for the enrichment and the impact of the characteristics of the external resource used as a source of enrichment.Finally, we present how the TaxoMap Framework environment was implemented and the performed experiments: tests on the TaxoMap alignment module, on the mappings refinement approach, on the partitioning methods of very large ontologies and on the ontology enrichment approach.

<p>Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points.</p> <p><br></p> <p>We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.</p>

No description available.

Na análise global e local de sistemas dinâmicos assumimos, em geral, que as equações estão numa forma normal. Em presença de simetrias, as equações e o domínio do problema são invariantes pelo grupo formado por estas simetrias; neste caso, o campo de vetores é equivariante pela ação deste grupo. Quando, além das simetrias, temos também ocorrência de anti-simetrias - ou reversibilidades - as equações e o domínio do problema são ainda invariantes pelo grupo formado pelo conjunto de todas as simetrias e anti-simetrias; neste caso, o campo de vetores é reversível-equivariante. Existem muitos modelos físicos onde simetrias e anti-simetrias aparecem naturalmente e cujo efeito pode ser estudado de uma forma sistemática através de teoria de representação de grupos de Lie. O primeiro passo deste processo é colocar a aplicação que modela tal sistema numa forma normal e isto é feito com a dedução a priori da forma geral dos campos de vetores. Esta forma geral depende de dois componentes: da base de Hilbert do anel das funções invariantes e dos geradores do módulo das aplicações reversíveis-equivariantes. Neste projeto, nos concentramos principalmente na aplicação de resultados recentes da literatura para a construção de uma lista de formas gerais de aplicações reversíveisequivariantes sob a ação de diferentes grupos. Além disso, adaptamos ferramentas algébricas da literatura existentes no contexto equivariante para o estudo sistemático de acoplamento de células idênticas no contexto reversível-equivariante / In the global and local analysis of dynamical systems, we assume, in general, that the equations are in a normal form. In presence of symmetries, the equations and the problem domain are invariant under the group formed by these symmetries; in that case, the vector field is equivariant by the action of this group. When, in addition to the symmetries, we have the occurrence of anti-symmetries - or reversibility - the equations and the problem domain are still invariant by the group formed by the set of all symmetries and anti-symmetries; in this case, the vector field is reversible-equivariant. There are many physical models where both symmetries and anti-symmetries occur naturally and whose effect can be studied in a systematic way through group representation theory. The first step of this process is to put the mapping that model the system in a normal form, and this is done with the deduction of the general form of the vector field. This general form depends on two components: the Hilbert basis of the invariant function ring and also the generators of the module of the revesible-equivariants. In this work, we mainly focus on the applications of recent results of the literature to build a list of general forms of reversible-equivariant mappings under the action of different groups. We also adapt algebraic tools of the existing literature in the equivariant context to the systematic study of coupling of identical cells in the reversible-equivariant context