Neste trabalho tratamos o assunto de existência e unicidade de estados de equilíbrio para uma classe importante de fluxos e aplicações com singularidades. Mostramos a existência de estados de equilíbrio para potenciais contínuos no contexto de fluxos singular-hiperbólicos, em particular fluxos de Lorenz. Demonstramos um critério para unicidade de estados de equilíbrio para aplicações unidimensionais do tipo Lorenz. Utilizando o critério, provamos que potenciais Hölder por partes com único estado de equilíbrio formam um conjunto aberto na topologia \'C POT.0\' e que a unicidade ainda é garantida para potenciais próximos a uma constante \'K IND. 0\' \' pertence a\' R / In this work we deal with the existence and uniqueness of equilibrium states for an important class of flows and transformations with singularities. In the context of singular-hyperbolic flows, we show the existence of equilibrium states for continuous potentials. In particular, this shows the existence of equilibrium states for Lorenz-like flows. We prove a criterium for the uniqueness of the equilibrium states of one-dimensional Lorenz-like applications. Using such criterium, we prove that piecewise Hölder continuous potentials with unique equilibrium states form an open in the \'C POT. 0\' topology and that the uniqueness is still guaranteed to a potential close to a constant \'K IND.0\' \'it belongs\' R

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-07-03T19:23:35Z No. of bitstreams: 1 josecarlosvalerio.pdf: 982623 bytes, checksum: 72d4cd36b83464bfd6a83caee289315d (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-08-08T13:23:10Z (GMT) No. of bitstreams: 1 josecarlosvalerio.pdf: 982623 bytes, checksum: 72d4cd36b83464bfd6a83caee289315d (MD5) / Made available in DSpace on 2017-08-08T13:23:10Z (GMT). No. of bitstreams: 1 josecarlosvalerio.pdf: 982623 bytes, checksum: 72d4cd36b83464bfd6a83caee289315d (MD5) Previous issue date: 2017-05-04 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Na presente dissertação será introduzido o desenvolvimento histórico da Geometria Hiperbólica. Será apresentado o quinto postulado de Euclides, de acordo com o ponto de vista dos Axiomas de Hilbert, correlacionando-os com os resultados da Geometria Neutra. Serão apresentados e provados alguns resultados da Geometria Hiperbólica, no que diz respeito às propriedades das retas paralelas, dos triângulos generalizados e seus critérios de congruência. Por fim, serão discutidas as propriedades que são válidas tanto para a Geometria Euclidiana quanto Hiperbólica, enfatizando que a principal diferença entre elas é o postulado das paralelas. / In the present dissertation we will introduce the historical development of the hyperbolic geometry. We will present Euclid’s fifth postulate from the Hilbert’s axioms point of view and we will correlate them with results of the Neutral Geometry. We will present and prove some results of the Hyperbolic Geometry, regarding the properties of the parallel lines, and the generalized triangles and their congruence criteria. At last, we will discuss the proprieties which are valid in both Euclidean and Hyperbolic Geometry, and we will emphasize that the main difference between them is the parallel postulate.

Thermal Integrity Profiling (TIP) is a relatively new non-destructive test method for evaluating the post-construction quality of drilled shafts. Therein anomalies in a shaft are indicated by variations in its thermal profile when measured during the curing stages of the concrete. A considerable benefit with this method is in the ability to detect anomalies both inside and outside the reinforcement cage, as well as provide a measure of lateral cage alignment. Similarly remarkable, early developments showed that the shape of a temperature profile (with depth) matched closely with the shape of the shaft, thus allowing for a straightforward interpretation of data. As with any test method, however, the quality of the results depends largely on the level of analysis and the way in which test data is interpreted, which was the focus of this study. This dissertation presents the findings from both field data and computer models to address and improve TIP analysis methods, specifically focusing on: (1) the analysis of non-uniform temperature distributions caused by external boundary conditions, (2) proper selection of temperature-radius relationships, and (3) understanding the effects of time on analysis. Numerical modeling was performed to identify trends in the temperature distributions in drilled shafts during concrete hydration. Specifically, computer generated model data was used to identify the patterns of the non-linear temperature distributions that occur at the ends of a shaft caused by the added heat loss boundary in the longitudinal direction. Similar patterns are observed at locations in a shaft where drastic changes in external boundary conditions exist (e.g. shafts that transition from soil to water or air). Numerical modeling data was also generated to examine the relationship between measured temperatures and shaft size/shape which is a fundamental concept of traditional TIP analysis. A case study involving a shaft from which 24hrs of internal temperature data was investigated and compared to results from a computer generated model made to mimic the field conditions of the shaft. Analysis of field collected and model predicted data was performed to examine the treatment of non-linear temperature distributions at the ends of the shaft and where a mid-shaft change in boundary was encountered. Additionally, the analysis was repeated for data over a wide range of concrete ages to examine the effects of time on the results of analysis. Finally, data from over 200 field tested shafts was collected and analyzed to perform a statistical evaluation of the parameters used for interpretation of the non-linear distributions at the top and bottom of each shaft. This investigation incorporated an iterative algorithm which determined the parameters required to provide a best-fit solution for the top and bottom of each shaft. A collective statistical evaluation of the resulting parameters was then used to better define the proper methods for analyzing end effects. Findings revealed that the effects of non-uniform temperature distributions in drilled shaft thermal profiles can be offset with a curve-fitting algorithm defined by a hyperbolic tangent function that closely matches the observed thermal distribution. Numerical models and statistical evaluations provided a rationale for proper selection of the function defining parameters. Additionally, numerical modeling showed that the true temperature-to-radius relationship in drilled shafts is non-linear, but in most cases a linear approximation is well suited. Finally, analysis of both model and field data showed that concrete age has virtually no effect on the final results of thermal profile analysis, as long as temperature measurements are taken within the dominate stages of concrete hydration.

The age of information means too much information. Users want relief from information overload. They need the ability to navigate and explore large data sets without getting buried. The challenge for application developers is to provide both an overview of huge data sets and a useful interface for drilling down to access details of interest. The use of new techniques for graphical visualisation of large hierarchies of information provides a solution to these problems. These new techniques apply knowledge gained from cognitive psychology and put them into practice. All to improve usability and lucidity for the user. In this thesis a case study has been conducted in order to provide proof to the above statement. An application was developed using the Visual tree studio from inxight. The application explored the Hyperbolic tree. The case study was connected to the theoretical part of the thesis and the conclusion is that using the hyperbolic tree when visualising large hierarchies of information will improve lucidity and usability.

This paper describes the design, implementation and evaluation of HyperSALmon, a Java™ open source prototype for visualizing service models in telecommunication networks. For efficient browsing and graphical monitoring of service models using SALmon, a service modeling language and a monitoring engine (Leijon et al., 2008), some kind of interactive GUI that implements a visualization of the service model is desired. This is what HyperSALmon is intended to do. The prototype has been designed in accordance with suggestions derived from a current research report of visualization techniques (Sehlstedt, 2008) appropriate for displaying service model data. In addition to these suggestions domain experts at Data Ductus Nord AB has expressed an urge for implementation of further features, some of their suggestions are deduced from research documents (Leijon et al., 2008; Wallin and Leijon, 2007, 2006), while others have been stated orally in direct relation to the prototype implementation work. The main visualization proposal is to use tree structures. Thus, both traditional tree structures and hyperbolic tree structures have been utilized, where the main navigation is set to occur in the hyperbolic tree view. In order to contribute further to this report I provide a discussion addressing problems related to the context of implementing a prototype for service model visualization using open source frameworks that meets the requirements set by the service model network architecture, the domain experts and the suggestions in the research report (Sehlstedt, 2008,page 51-52). Finally, I will present drawn conclusions of the attempted prototype implementation, illustrating potential strengths and weaknesses and consequently introduce suggestions for possible improvement and further development.

Cette thèse propose des contributions sur la commande événementielle pour des réseaux modélisés par une classe des systèmes de dimension infinie. Premièrement nous nous focalisons sur la modélisation et contrôle frontière des réseaux qui sont décrits par des systèmes hyperboliques de lois de conservation. En nous inspirant de modèles macroscopiques dans le cadre des réseaux de communications, nous traitons des systèmes couplés EDP-EDO, dont les noeuds (les serveurs) sont modélisés par des EDO non-linéaires alors que des lignes de transmission sont décrites par des systèmes hyperboliques lorsque des retards peuvent être pris en compte. Pour le système linéarisé resultant, autour d'un point d'équilibre optimal, on effectue aussi bien une analyse de stabilité "Input-to-state stable" que de la synthèse du contrôle pour le gain asymptotique grâce à une analyse de fonction de Lyapunov et une formulation LMI.Ensuite, nous considérons des aspects théoriques de la commande évènementielle aux frontières pour les systèmes hyperboliques. D'un côté, avec cette stratégie de contrôle, nous ciblons la réduction de la consommation d' énergie en traitant les contraintes de communication et de calcul. D' autre part, nous utilisons cette stratégie comme une manière rigoureuse pour échantillonner temporellement lorsqu' on a besoin de mettre en oeuvre les contrôleurs continus sur une plateforme numérique. Une étude mathématique sur l'existence et l' unicité des solutions ainsi que sur les aspects de stabilité est réalisée. / This thesis provides contributions on event-based control of networks model by a class of infinite dimensional systems. We first focus on the modeling and boundary control of networks described by hyperbolic systems of conservation laws. Highly inspired by macroscopic models in communication networks, we deal with a coupled PDE-ODE, where the nodes (servers) are modeled by nonlinear ODEs whereas transmission lines are described by hyperbolic equations when communication delays may be taken into account. For the resulting linearized system around an optimal equilibrium point, Input-to state stability (ISS) analysis as well as asymptotic gain control synthesis are carried out by means of Lyapunov techniques and LMI formulation.We then address some theoretical aspects of event-based boundary control of hyperbolic systems. One one hand, with this computer control strategy, we intend to reduce energy consumption when dealing with communication and computational constraints. On the other hand, we use this strategy as a rigorous way of sampling in time when implementation of continuous time controllers on a digital platform is required. A mathematical study regarding well-posedness of the solutions as well as stability issues is conducted.

[pt] Grupos de Coxeter ou de reflexões são importantes no estudo de inúmeras áreas da matemática, incluindo grupos e álgebras de Lie. Nesta dissertação apresentaremos a teoria básica de grupos de reflexões e a classificação dos grupos hiperbólicos, i.e., daqueles que agem no espaço hiperbólico tendo como domínio fundamental um politopo compacto. / [en] Groups of Coxeter or of reflections they are important in the study of countless areas of the mathematics, including groups and algebras of Lie. In this dissertation we will present the basic theory of groups of reflections and the classification of the hyperbolic groups, this is of those that act in the hyperbolic space tends as fundamental domain a compact politopo.

It is very unlikely to see at Czech high school in mathematics classes teaching the hyperbolic functions and their inverses. It's a pity, this could be a great opportunity to review and refresh the polynomial, rational, trigonometric and exponential function methods and skills. These functions even set an implicit connection between the exponential and gonio- metric functions, too. The aim of this thesis is to offer an alternative to the usual practice at the ordinary high schools and it is adopted to a limited schooling time available. Our approach has been successfully tested with a group of students at a small high school in the Czech borderland. The thesis also indicates the potential to expand this approach if more schooling time should have been available or more talented students should have been involved.

Generating samples from generalized hyperbolic distributions and non-central chi-square distributions by inversion has become an important task for the simulation of recent models in finance in the framework of (quasi-) Monte Carlo. However, their distribution functions are quite expensive to evaluate and thus numerical methods like root finding algorithms are extremely slow. In this paper we demonstrate how our new method based on Newton interpolation and Gauss-Lobatto quadrature can be utilized for financial applications. Its fast marginal generation times make it competitive, even for situations where the parameters are not always constant. / Series: Research Report Series / Department of Statistics and Mathematics

The main objects of interest in this thesis are relatively hyperbolic groups. We will study some of their geometric properties, and we will be especially concerned with geometric properties of their boundaries, like linear connectedness, avoidability of parabolic points, etc. Exploiting such properties will allow us to construct, under suitable hypotheses, quasi-isometric embeddings of hyperbolic planes into relatively hyperbolic groups and quasi-isometric embeddings of relatively hyperbolic groups into products of trees. Both results have applications to fundamental groups of 3-manifolds. We will also study probabilistic properties of relatively hyperbolic groups and of groups containing ``hyperbolic directions'' despite not being relatively hyperbolic, like mapping class groups, Out(F<sub>n</sub>), CAT(0) groups and subgroups of the above. In particular, we will show that the elements that generate the ``hyperbolic directions'' (hyperbolic elements in relatively hyperbolic groups, pseudo-Anosovs in mapping class groups, fully irreducible elements in Out(F_n) and rank one elements in CAT(0) groups) are generic in the corresponding groups (provided at least one exists, in the case of CAT(0) groups, or of proper subgroups). We also study how far a random path can stray from a geodesic in the context of relatively hyperbolic groups and mapping class groups, but also of groups acting on a relatively hyperbolic space. We will apply this, for example, to show properties of random triangles.