Esse trabalho trata um pouco da teoria de A-loops comutativos finitos. No primeiro captulo estudamos propriedades básicas de loops em geral e exi- bimos exemplos de loops não associativos. No captulo 2 falamos de A-loops em geral e mesmo sem assumirmos comutatividade obtivemos resultados importantes, um exemplo é que A-loop associa potências. Também determinamos quando um isótopo e K -holomorfo de um A-loop é um A-loop. No captulo 3, nossos únicos objetos de estudo foram os A-loops comutativos finitos. Vimos que tais estruturas têm proriedades muito interessantes, por exemplo, para um A-loop comutativo finito valem os teoremas de Lagrange, Cauchy. Também, um A-loop comutativo finito, Q, tem ordem potência de um primo p se e somente se todo elemento de Q tem ordem potência de p. Mais ainda, todo A-loop comutativo finito de ordem mpar é solúvel. No último captulo, apresentamos algumas maneira de se construir um A-loop. / In the first chapter we studied basic properties of general loops and we showed some examples of nonassociative loops. In chapter 2, we talked about general A-loops (without commutativity) and even that we obtained important results, for instance, that any A-loop is power-associative. We also determined when an isotope and a K -holomorph of an A-loop is an A-loop. In chapter 3 we dealt only with finite commutative A-loops. We saw that such structures have very interesting properties, for example, for a finite commutative A- loop, Lagrange, Cauchys theorems apply. Also a finite commutative A-loop, Q, has order a power of a prime p if and only if every element of Q has order a power of p. Moreover, finite commutative A-loops of odd order are solvable. In the last chapter we introduce some ways to construct a commutative A-loop

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-22T16:24:35Z No. of bitstreams: 1 arquivototal.pdf: 1096557 bytes, checksum: 096bafe0cd5d1cf118a6fa1546070e5d (MD5) / Made available in DSpace on 2017-08-22T16:24:35Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1096557 bytes, checksum: 096bafe0cd5d1cf118a6fa1546070e5d (MD5) Previous issue date: 2016-03-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study a recent general version of the Extrapolation Theorem, due to Botelho, Pellegrino, Santos and Seoane-Sep ulveda [6] that improves and uni es a number of known Extrapolation-type theorems for classes of mappings that generalize the ideal of absolutely p-summing linear operators. / Neste trabalho, dissertamos sobre uma recente vers~ao geral do Teorema de Extrapola c~ao, devida a Botelho, Pellegrino, Santos e Seoane-Sep ulveda [6], que melhora e uni ca v arios teoremas do tipo Extrapola c~ao para certas classes de fun c~oes que generalizam o ideal dos operadores lineares absolutamente p-somantes.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The main purpose of this dissertation is the study of ideals of multilinear mappings and homogeneous polynomials between linear spaces. By an ideal we mean a class that is stable under the composition with linear operators. First we study multilinear mappings and spaces of multilinear mappings. We also show how to obtain, from a given multilinear mapping, other multilinear mappings with degrees of multilinearity greater than, equal to or smaller than the degree of the original multilinear mapping. Next we study homogeneous polynomials and spaces of homogeneous polynomials, and we also show how to obtain, from a given n-homogeneous polynomial, other polynomials with degrees of homogeneity greater than, equal to or smaller than the degree of the original polynomial. Next we study ideals of multilinear mappings, or multi-ideals, and ideals of homogeneous polynomial, or polynomial ideals, giving several examples and presenting methods to generated multi-ideals and polynomial ideals from a given operator ideal. Finally we dene and give several examples of coherent multi-ideals and coherent polynomial ideals. / O principal objetivo desta dissertação e estudar os ideais de aplicações multilineares e polinômios homogêneos entre espaços vetoriais. Por um ideal entendemos uma classe de aplicações que e estavel atraves da composição com operadores lineares. Primeiramente estudamos as aplicações multilineares e os espaços de aplicações multilineares. Mostramos tambem como obter, a partir de uma aplicação multilinear dada, outras aplicações com graus de multilinearidade maiores, iguais ou menores que o da aplicação original. Em seguida estudamos os polinômios homogêneos e os espacos de polinômios homogêneos, e mostramos que, a partir de um polinômio n-homogêneo, tambem podemos construir novos polinômios homogêneos com graus de homogeneidade maiores, iguais ou menores que n. Posteriormente estudamos os ideais de aplicações multilineares, ou multi-ideais, e os ideais de polinômios homogêneos, exibindo varios exemplos e apresentando metodos para se obter um multi-ideais, ou ideais de polinômios, a partir de ideais de operadores lineares dados. Por m, denimos e exibimos varios exemplos de multi-ideais coerentes e de ideais coerentes de polinômios. / Mestre em Matemática

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The rst aim of this dissertation is to construct the tensor product of nitely many linear spaces from elementary tensors and to show that this is the space through which multilinear mappings can be linearized. Next continuous multilinear mappings between Banach spaces are studied. The projective norm is introduced in the tensor product in order to perform the linearization of continuous multilinear mappings. The last chapter is devoted to the study of operator ideals and their generalization to the multilinear setting. The interplay between the theory of multi-ideals and the projective tensor product is established by the theory of composition multi-ideals. / O primeiro objetivo desta dissertação é construir o produto tensorial de um número finito de espaços vetoriais a partir dos tensores elementares e mostrar que e atraves desse espaco que aplicações multilineares podem ser linearizadas. Em seguida são estudadas as aplicações multilineares contnuas entre espacos de Banach. A norma projetiva e introduzida no produto tensorial para realizar a linearização das aplicações multilineares contnuas. No ultimo captulo os ideais de operadores lineares são estudados e generalizados para o contexto de ideais de aplicações multilineares. A conexão da teoria de multi-ideais com o produto tensorial projetivo e feita atraves dos multi-ideais de composição. / Mestre em Matemática

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-06-29T13:52:59Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) tese_final.pdf: 5635071 bytes, checksum: b300efb627e9ece412ad5936ab67e8e2 (MD5) / Made available in DSpace on 2016-06-29T13:52:59Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) tese_final.pdf: 5635071 bytes, checksum: b300efb627e9ece412ad5936ab67e8e2 (MD5) Previous issue date: 2013-08-26 / CNPq / No presente trabalho duas classes de problemas são abordadas. Primeiramente, são apresentados estudos computacionais sobre o modelo O(n) de spins na rede quadrada, e em seguida apresentamos novas soluções exatas para a dinâmica de bolhas na célula de Hele-Shaw. O estudo do modelo O(n) é feito utilizando sua representação em laços (cadeias fechadas), a qual é obtida a partir de uma expansão para altas temperaturas. Nesse representação, a função de partição do modelo possui uma expansão diagramática em que cada termo depende do número e comprimento total de laços e do número de (auto)interseções entre esses laços. Propriedades críticas do modelo de laços O(n) são obtidas através de conceitos oriundos da teoria de percolação. Para executar as simulações Monte Carlo, usamos o eficiente algoritmo WORM, o qual realiza atualizações locais através do movimento da extremidade de uma cadeia aberta denominada de verme e não sofre com o problema de "critical slowing down". Para implementar esse algoritmo de forma eficiente para o modelo O(n) na rede quadrada, fazemos uso de um nova estrutura de dados conhecida como listas satélites. Apresentamos estimativas para o ponto crítico do modelo para vários valores de n no intervalo de 0 < n ≤ 2. Usamos as estatísticas de laços e vermes para extrair, respectivamente, os expoentes críticos térmicos e magnéticos do modelo. No estudo de dinâmica de interfaces, apresentamos uma solução exata bastante geral para um arranjo periódico de bolhas movendo-se com velocidade constante ao longo de uma célula de Hele-Shaw. Usando a periodicidade da solução, o domínio relevante do problema pode ser reduzido a uma célula unitária que contém uma única bolha. Nenhuma imposição de simetria sobre forma da bolha é feita, de modo que a solução é capaz de produzir bolhas completamente assimétricas. Nossa solução é obtida por métodos de transformações conformes entre domínios duplamente conexos, onde utilizamos a transformação de Schwarz-Christoffel generalizada para essa classe de domínios. / In this thesis two classes of problems are discussed. First, we present computational studies of the O(n) spin model on the square lattice and determine its critical properties, whereas in the second part of the thesis we present new exact solutions for bubble dynamics in a Hele-Shaw cell. The O(n) model is investigated by using its loop representation which is obtained from a high-temperature expansion of the original model. In this representation, the partition function admits an diagrammatic expansion in which each term depends on the number and total length of loops (closed graphs) as well as on the number of intersections between these loops. Critical properties of the O(n) model are obtained by employing concepts from percolation theory. To perform Monte Carlo simulations of the model, we use the WORM algorithm, which is an efficient algorithm that performs local updates through the motion of one of the ends (called head) of an open chain (called worm) and hence does not suffer from “critical slowing down”. To implement this algorithm efficiently for the O(n) model on the square lattice, we make use of a new data structure known as a satellite list. We present estimates for the critical point of the model for various values of n in the range 0 < n ≤ 2. We use the statistics about the loops and the worm to extract the thermal and magnetic critical exponents of the model, respectively. In our study about interface dynamics, we present a rather general exact solution for a periodic array of bubbles moving with constant velocity in a Hele-Shaw cell. Using the periodicity of the solution, the relevant domain of the problem can be reduced to a unit cell containing a single bubble. No symmetry requirement is imposed on the bubble shape, so that the solution is capable of generating completely asymmetrical bubbles. Our solution is obtained by using conformal mappings between doubly-connected domains and employing the generalized Schwarz-Christoffel formula for this class of domains.

Indiana University-Purdue University Indianapolis (IUPUI) / This paper is a study of the dynamics of a new family of maps from the complex plane to itself, which we call twisted tent maps. A twisted tent map is a complex generalization of a real tent map. The action of this map can be visualized as the complex scaling of the plane followed by folding the plane once. Most of the time, scaling by a complex number will \twist" the plane, hence the name. The "folding" both breaks analyticity (and even smoothness) and leads to interesting dynamics ranging from easily understood and highly geometric behavior to chaotic behavior and fractals.

No description available.

Abstract The dissertation considers a degree theory and the index of a critical point of demi-continuous, everywhere defined mappings of the monotone type. A topological degree is derived for mappings from a Banach space to its dual space. The mappings satisfy the condition (S+), and it is shown that the derived degree has the classical properties of a degree function. A formula for the calculation of the index of a critical point of a mapping A : X→X* satisfying the condition (S+) is derived without the separability of X and the boundedness of A. For the calculation of the index, we need an everywhere defined linear mapping A' : X→X* that approximates A in a certain set. As in the earlier results, A' is quasi-monotone, but our situation differs from the earlier results because A' does not have to be the Frechet or Gateaux derivative of A at the critical point. The theorem for the calculation of the index requires a construction of a compact operator T = (A' + Γ)-1Γ with the aid of linear mappings Γ : X→X and A'. In earlier results, Γ is compact, but here it need only be quasi-monotone. Two counter-examples show that certain assumptions are essential for the calculation of the index of a critical point.

Im Bereich der Lebenswissenschaften steht eine große und wachsende Menge heterogener Datenquellen zur Verfügung, welche häufig in quellübergreifenden Analysen und Auswertungen miteinander kombiniert werden. Um eine einheitliche und strukturierte Erfassung von Wissen sowie einen formalen Austausch zwischen verschiedenen Applikationen zu erleichtern, kommen Ontologien und andere strukturierte Vokabulare zum Einsatz. Sie finden Anwendung in verschiedenen Domänen wie der Molekularbiologie oder Chemie und dienen zumeist der Annotation realer Objekte wie z.B. Gene oder Literaturquellen. Unterschiedliche Ontologien enthalten jedoch teilweise überlappendes Wissen, so dass die Bestimmung einer Abbildung (Ontologiemapping) zwischen ihnen notwendig ist. Oft ist eine manuelle Mappingerstellung zwischen großen Ontologien kaum möglich, weshalb typischerweise automatische Verfahren zu deren Abgleich (Matching) eingesetzt werden. Aufgrund neuer Forschungserkenntnisse und Nutzeranforderungen verändern sich die Ontologien kontinuierlich weiter. Die Evolution der Ontologien hat wiederum Auswirkungen auf abhängige Daten wie beispielsweise Annotations- und Ontologiemappings, welche entsprechend aktualisiert werden müssen. Im Rahmen dieser Arbeit werden neue Methoden und Algorithmen zum Umgang mit der Evolution ontologie-basierter Mappings entwickelt. Dabei wird die generische Infrastruktur GOMMA zur Verwaltung und Analyse der Evolution von Ontologien und Mappings genutzt und erweitert. Zunächst wurde eine vergleichende Analyse der Evolution von Ontologiemappings für drei Subdomänen der Lebenswissenschaften durchgeführt. Ontologien sowie Mappings unterliegen teilweise starken Änderungen, wobei die Evolutionsintensität von der untersuchten Domäne abhängt. Insgesamt zeigt sich ein deutlicher Einfluss von Ontologieänderungen auf Ontologiemappings. Dementsprechend können bestehende Mappings infolge der Weiterentwicklung von Ontologien ungültig werden, so dass sie auf aktuelle Ontologieversionen migriert werden müssen. Dabei sollte eine aufwendige Neubestimmung der Mappings vermieden werden. In dieser Arbeit werden zwei generische Algorithmen zur (semi-) automatischen Adaptierung von Ontologiemappings eingeführt. Ein Ansatz basiert auf der Komposition von Ontologiemappings, wohingegen der andere Ansatz eine individuelle Behandlung von Ontologieänderungen zur Adaptierung der Mappings erlaubt. Beide Verfahren ermöglichen die Wiederverwendung unbeeinflusster, bereits bestätigter Mappingteile und adaptieren nur die von Änderungen betroffenen Bereiche der Mappings. Eine Evaluierung für sehr große, biomedizinische Ontologien und Mappings zeigt, dass beide Verfahren qualitativ hochwertige Ergebnisse produzieren. Ähnlich zu Ontologiemappings werden auch ontologiebasierte Annotationsmappings durch Ontologieänderungen beeinflusst. Die Arbeit stellt einen generischen Ansatz zur Bewertung der Qualität von Annotationsmappings auf Basis ihrer Evolution vor. Verschiedene Qualitätsmaße erlauben die Identifikation glaubwürdiger Annotationen beispielsweise anhand ihrer Stabilität oder Herkunftsinformationen. Eine umfassende Analyse großer Annotationsdatenquellen zeigt zahlreiche Instabilitäten z.B. aufgrund temporärer Annotationslöschungen. Dementsprechend stellt sich die Frage, inwieweit die Datenevolution zu einer Veränderung von abhängigen Analyseergebnissen führen kann. Dazu werden die Auswirkungen der Ontologie- und Annotationsevolution auf sogenannte funktionale Analysen großer biologischer Datensätze untersucht. Eine Evaluierung anhand verschiedener Stabilitätsmaße erlaubt die Bewertung der Änderungsintensität der Ergebnisse und gibt Aufschluss, inwieweit Nutzer mit einer signifikanten Veränderung ihrer Ergebnisse rechnen müssen. Darüber hinaus wird GOMMA um effiziente Verfahren für das Matching sehr großer Ontologien erweitert. Diese werden u.a. für den Abgleich neuer Konzepte während der Adaptierung von Ontologiemappings benötigt. Viele der existierenden Match-Systeme skalieren nicht für das Matching besonders großer Ontologien wie sie im Bereich der Lebenswissenschaften auftreten. Ein effizienter, kompositionsbasierter Ansatz gleicht Ontologien indirekt ab, indem existierende Mappings zu Mediatorontologien wiederverwendet und miteinander kombiniert werden. Mediatorontologien enthalten wertvolles Hintergrundwissen, so dass sich die Mappingqualität im Vergleich zu einem direkten Matching verbessern kann. Zudem werden generelle Strategien für das parallele Ontologie-Matching unter Verwendung mehrerer Rechenknoten vorgestellt. Eine größenbasierte Partitionierung der Eingabeontologien verspricht eine gute Lastbalancierung und Skalierbarkeit, da kleinere Teilaufgaben des Matchings parallel verarbeitet werden können. Die Evaluierung im Rahmen der Ontology Alignment Evaluation Initiative (OAEI) vergleicht GOMMA und andere Systeme für das Matching von Ontologien in verschiedenen Domänen. GOMMA kann u.a. durch Anwendung des parallelen und kompositionsbasierten Matchings sehr gute Ergebnisse bezüglich der Effektivität und Effizienz des Matchings, insbesondere für Ontologien aus dem Bereich der Lebenswissenschaften, erreichen. / In the life sciences, there is an increasing number of heterogeneous data sources that need to be integrated and combined in comprehensive analysis tasks. Often ontologies and other structured vocabularies are used to provide a formal representation of knowledge and to facilitate data exchange between different applications. Ontologies are used in different domains like molecular biology or chemistry. One of their most important applications is the annotation of real-world objects like genes or publications. Since different ontologies can contain overlapping knowledge it is necessary to determine mappings between them (ontology mappings). A manual mapping creation can be very time-consuming or even infeasible such that (semi-) automatic ontology matching methods are typically applied. Ontologies are not static but underlie continuous modifications due to new research insights and changing user requirements. The evolution of ontologies can have impact on dependent data like annotation or ontology mappings. This thesis presents novel methods and algorithms to deal with the evolution of ontology-based mappings. Thereby the generic infrastructure GOMMA is used and extended to manage and analyze the evolution of ontologies and mappings. First, a comparative evolution analysis for ontologies and mappings from three life science domains shows heavy changes in ontologies and mappings as well as an impact of ontology changes on the mappings. Hence, existing ontology mappings can become invalid and need to be migrated to current ontology versions. Thereby an expensive redetermination of the mappings should be avoided. This thesis introduces two generic algorithms to (semi-) automatically adapt ontology mappings: (1) a composition-based adaptation relies on the principle of mapping composition, and (2) a diff-based adaptation algorithm allows for individually handling change operations to update mappings. Both approaches reuse unaffected mapping parts, and adapt only affected parts of the mappings. An evaluation for very large biomedical ontologies and mappings shows that both approaches produce ontology mappings of high quality. Similarly, ontology changes may also affect ontology-based annotation mappings. The thesis introduces a generic evaluation approach to assess the quality of annotation mappings based on their evolution. Different quality measures allow for the identification of reliable annotations, e.g., based on their stability or provenance information. A comprehensive analysis of large annotation data sources shows numerous instabilities, e.g., due to the temporary absence of annotations. Such modifications may influence results of dependent applications such as functional enrichment analyses that describe experimental data in terms of ontological groupings. The question arises to what degree ontology and annotation changes may affect such analyses. Based on different stability measures the evaluation assesses change intensities of application results and gives insights whether users need to expect significant changes of their analysis results. Moreover, GOMMA is extended by large-scale ontology matching techniques. Such techniques are useful, a.o., to match new concepts during ontology mapping adaptation. Many existing match systems do not scale for aligning very large ontologies, e.g., from the life science domain. One efficient composition-based approach indirectly computes ontology mappings by reusing and combining existing mappings to intermediate ontologies. Intermediate ontologies can contain useful background knowledge such that the mapping quality can be improved compared to a direct match approach. Moreover, the thesis introduces general strategies for matching ontologies in parallel using several computing nodes. A size-based partitioning of the input ontologies enables good load balancing and scalability since smaller match tasks can be processed in parallel. The evaluation of the Ontology Alignment Evaluation Initiative (OAEI) compares GOMMA and other systems in terms of matching ontologies from different domains. Using the parallel and composition-based matching, GOMMA can achieve very good results w.r.t. efficiency and effectiveness, especially for ontologies from the life science domain.