This thesis explores the geometry at infinity for certain hermitian locally symmetric spaces. Let Gamma < SU(r + 1, r) be a maximal nonuniform arithmetic lattice determined by automorphisms of a hermitian form on k^{2 r + 1}, where k is an imaginary quadratic field. We give a formula for the number of cusps of X / Gamma, where X is the hermitian symmetric space on which SU(r + 1, r) acts. If r > 1 and 2 r + 1 is prime, this completely determines the number of cusps for minimal finite volume orbifolds with X-geometry, and there are only finitely many commensurability classes of noncompact finite volume quotients of X containing a one-cusped orbifold. In the case r = 1, which corresponds to the complex hyperbolic plane, we show that this holds for any N: there are only finitely many commensurability classes of arithmetic lattices in SU(2, 1) which contain an N-cusped orbifold. / text

Cette thèse s’inscrit dans la problématique générale de la caractérisation et de la classification des systèmes. Plus précisément, nos contributions s’orientent vers les applications robotiques et, plus particulièrement, vers la classification de manipulateurs. Les algorithmes et méthodologies proposés dans ce document s’appuient sur plusieurs théories mathématiques dont la théorie des singularités et l’Analyse par Intervalles, qui sont formalisés dans la première partie de cette Thèse.Classifier des systèmes induit deux objectifs que sont la formalisation des éléments communs aux systèmes dans la même classe ainsi que leur détection formelle et pratique. Ainsi, ce mémoire compile, pour chacun dans un chapitre dédié, nos contributions vis-à-vis de ces deux objectifs associés à la classification. Une méthodologie générale est proposée, afin de distinguer plusieurs sous ensembles singuliers caractéristiques et génériquement non vides. Cette méthodologie est illustrée pour des fonctions entre espaces de même dimension, allant de 1à 3. Chaque application met en lumière des propriétés différentes de la méthodologie générale proposée.Complémentairement, chacune de ces applications mène à la conception d’algorithmes, basé sur l’Analyse par Intervalles, mettant en œuvre cette méthodologie.Complémentairement à la détection de points d’intérêt,nous présentons une méthodologie générale pour définir un objet combinatoire codant le comportement d’une fonction. Cette méthodologie s’appuie sur la détection préalable d’ensembles d’intérêt dont les topologies sont invariantes pour l’équivalence choisie. Ces développements ouvrent vers de nombreuses perspectives futures qui concluent ce mémoire. / This thesis is within the scope of the general problematic of characterizing and classifying systems. More precisely, our contributions are aimed toward robotic applications and, more particularly, at the classification of manipulators. The algorithms and methodologies proposed in this document are based upon several mathematical theories including Singularity Theory and Interval Analysis, which are formalized in the first part of this Phd Thesis report. Classifying systems induces two objectives that are the formalization of the elements commons to systems in the same class as well as their formal and practical detection. Then, this report compiles, for each one in a dedicated chapter, our contributions regarding these two objectives associated with the classification. A general methodology is proposed, with the objective to distinguish several characteristic singular subsets that prove to be generically not empty. This methodology is illustrated for functions between spaces of the same dimension, ranging from 1 to 3. Each application highlights different properties that are admitted by the proposed general methodology. Furthermore, each of these applications leads to the conception of severalalgorithms, based on Interval Analysis, that enforce the proposed methodology. Complementarily to the detection of interest points, we introduce a general methodology to define a combinatorial object encoding the behavior of a function. This methodology is based on the preliminary detection of interest sets whose topologies are invariant for the chosen equivalence. These developments open up to numerous future perspectives that conclude this report.

The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.

Approved for public release, distribution is unlimited / Rip current spacings are compared with wave energetics and directional spreading in the Southern Monterey Bay. Southern Monterey Bay affords a unique environment to study rip currents owing to their prevalence created by near-normally incident waves on a sandy shoreline. It is hypothesized that rip current spacing is a function of wave directional spreading and energy flux, based on the morphodynamic modeling by Reniers et al. 2003. A gradient of wave energy flux exists due to headlands and refraction over Monterey Canyon. Rip currents are shown to occur between cusps in the shoreline, allowing cusp spacing to be a surrogate for rip spacing. Rip current spacing was inferred from beach morphology surveys, LIDAR imagery, and Argus cameras, and found to be O(150m) at Sand City and O(300m) at Marina, separated by 6km . Measured waves during a two month period using wave-rider buoys, show a gradient of across-shore energy flux between Sand City, 2 28000( / ) F Jm x . , and Marina, 2 33000( / ) F Jm x . . The two sites have the same peak directional spreading of energy value, 14 peak ̤= o , and slightly different bulk values for Sand City, 18 bulk ̤= o , and Marina, 20 bulk ̤= o . Therefore, the variations in rip current spacing could not be attributed to directional spreading but appear related to variations in energy flux. / Ensign, United States Naval Reserve

In the presented thesis we study analytical behavior of vibrational excitation cross sections and probability flux density in nonlocal resonance model. An analytical formula for determining the shape of Wigner cusps from three complex parameters is derived. The results of this formula are compared to numerical calculations with complex scaling method and interpreted within Feynman approach to quantum mechanics. Furthermore, we derive nonlocal continuity equation and show how it implies the multichannel optical theorem. Detail analysis of fluxes in the nonlocal resonance model is used to accelerate the convergence of formula for the dissociative attachment cross section and we present a simple model describing boomerang oscillations. A program in Fortran language is attached to this work. The program allows calculation of vibrational excitation and dissociative attachment cross sections, flux divergences and other quantities specified in this text.

O presente trabalho tem por objetivo relacionar a ação das ondas incidentes no arco praial de Massaguaçú com a presença e o comportamento de feições morfológicas como as cúspides praiais. O conjunto de dados utilizados consiste em uma série de imagens provenientes do sistema Argus. Esse sistema utiliza cinco câmeras de alta resolução resultando em uma cobertura de 180° da zona costeira. A partir destas imagens realizou-se a digitalização das cúspides praiais encontrando-se duas linhas de cúspides, uma na face praial superior (CFS) e a outra na face praial inferior (CFI). Em conjunto com os dados de imagem foi analisado o clima de ondas atuantes durante o período. A presença de feições rítmicas foi alta no arco praial de Massaguaçú, sendo praticamente predominante na face praial superior. O espaçamento médio da CFS foi superior ao espaçamento da CFI e a alternância das condições atuantes foi determinante na redução do espaçamento assim como condições energéticas baixas. O aumento do espaçamento das cúspides ocorreu sob condições energéticas médias à altas e sob condições extremas observou tanto a destruição como o aumento das feições rítmicas. A interação entre o espraiamento e a morfologia existente, modulado pela variação do nível d\'água, foi um dos motores para a formação de cúspides em níveis inferiores enquanto que as condições extremas causaram sua destruição. / This study aims to relate the action of incident waves on Massaguaçú\'s beach with the presence and the behavior of morphological features such as beach cusps. The set of data used consists in a series of images from the Argus system. This system uses five high-resolution cameras resulting in a 180 ° coverage of the coastal zone. From these images, realize the presence of beach cusps lying in two rows on the beach face, one in the upper beach face (CFS) and the other in the lower beach face (CFI). At the same time with the image data the wave regime acting at Massaguaçú\'s beach was analyzed during the period. The presence of rhythmic features was almost constant Massaguaçú\'s beach face, nearly predominant on the upper beach face. The average spacing of CFS was greater than the spacing of the CFI and the interchange in active conditions was crucial in reducing the spacing as well as low energy conditions. The increased spacing of the cusps occurred under medium to high energy conditions and under extreme conditions both as increased and destruction of the rhythmic features were observed. The interaction between the swash motions and the existing morphology, modulated by varying the water level, was important for the formation of cusps at lower levels while the extreme conditions caused its destruction.

O presente trabalho tem por objetivo relacionar a ação das ondas incidentes no arco praial de Massaguaçú com a presença e o comportamento de feições morfológicas como as cúspides praiais. O conjunto de dados utilizados consiste em uma série de imagens provenientes do sistema Argus. Esse sistema utiliza cinco câmeras de alta resolução resultando em uma cobertura de 180° da zona costeira. A partir destas imagens realizou-se a digitalização das cúspides praiais encontrando-se duas linhas de cúspides, uma na face praial superior (CFS) e a outra na face praial inferior (CFI). Em conjunto com os dados de imagem foi analisado o clima de ondas atuantes durante o período. A presença de feições rítmicas foi alta no arco praial de Massaguaçú, sendo praticamente predominante na face praial superior. O espaçamento médio da CFS foi superior ao espaçamento da CFI e a alternância das condições atuantes foi determinante na redução do espaçamento assim como condições energéticas baixas. O aumento do espaçamento das cúspides ocorreu sob condições energéticas médias à altas e sob condições extremas observou tanto a destruição como o aumento das feições rítmicas. A interação entre o espraiamento e a morfologia existente, modulado pela variação do nível d\'água, foi um dos motores para a formação de cúspides em níveis inferiores enquanto que as condições extremas causaram sua destruição. / This study aims to relate the action of incident waves on Massaguaçú\'s beach with the presence and the behavior of morphological features such as beach cusps. The set of data used consists in a series of images from the Argus system. This system uses five high-resolution cameras resulting in a 180 ° coverage of the coastal zone. From these images, realize the presence of beach cusps lying in two rows on the beach face, one in the upper beach face (CFS) and the other in the lower beach face (CFI). At the same time with the image data the wave regime acting at Massaguaçú\'s beach was analyzed during the period. The presence of rhythmic features was almost constant Massaguaçú\'s beach face, nearly predominant on the upper beach face. The average spacing of CFS was greater than the spacing of the CFI and the interchange in active conditions was crucial in reducing the spacing as well as low energy conditions. The increased spacing of the cusps occurred under medium to high energy conditions and under extreme conditions both as increased and destruction of the rhythmic features were observed. The interaction between the swash motions and the existing morphology, modulated by varying the water level, was important for the formation of cusps at lower levels while the extreme conditions caused its destruction.

Beach cusps, formed during a storm are observed. The storm acted for three hours together with high water conditions. These beach cusps exhibited a quasiuniform wavelength of 8 m. The measured topography after the storm, the calculated drift velocity of the incident wave and the synchronous edge wave are similar in scale and shape. The over one wavelength measured grain size is also correlated to the topography. A nonlinear hydro-numerical model is used to investigate the reaction of edge waves on alongshore change in bottom topography. Edge waves are greatly amplified over beach cusps. The relative amplification of edge waves on beach cusps is more than 17 times that without a change in longshore topography. Amplification is slightly greater for edge waves travelling in the same direction as the longshore current during the storm. An almost random positioning of sediment starts a feedback loop, which allows edge waves to grow and build short periodic cusps.

When we consider the nature of the scientific community in conjunction with a sense of typical economic circumstances we find that there are two distinct paths for development. One path involves hypothesis testing and evolution of strategies that are linked with iterations in equipment advances. A second, more complicated scenario, can involve external influences whether economic, political, or otherwise, such as the government closure of NASA's space program in 2011 which will no doubt influence research in associated fields. The following chapters are an account of examples of two statistical techniques and the importance of both on the two relatively unrelated geological fields of coastal geomorphology and ground water hydrology. The first technique applies a multi-dimensional approach to defining groundwater water table response based on precipitation in areas where it can reasonably be assumed to be the only recharge. The second technique applies a high resolution multi-scalar approach to a geologic setting most often restricted to either high resolution locally, or low resolution regionally. This technique uses time-frequency analysis to characterize cuspate patterns in LIDAR data are introduced using examples from the Atlantic coast of Florida, United States. These techniques permit the efficient study of beachface landforms over many kilometers of coastline at multiple spatial scales. From a LIDAR image, a beach-parallel spatial series is generated. Here, this series is the shore-normal position of a specific elevation (contour line). Well-established time-frequency analysis techniques, wavelet transforms, and S-Transforms, are then applied to the spatial series. These methods yield results compatible with traditional methods and show that it is useful for capturing transitions in cuspate shapes. To apply this new method, a land-based LIDAR study allowing for rapid high-resolution surveying is conducted on Melbourne Beach, Florida and Tairua Beach, New Zealand. Comparisons and testing of two different terrestrial scanning stations are evaluated during the course of the field investigation. Significant cusp activity is observed at Melbourne Beach. Morphological observations and sediment analysis are used to study beach cusp morphodynamics at the site. Surveys at Melbourne were run ~500 m alongshore and sediment samples were collected intertidally over a five-day period. Beach cusp location within larger scale beach morphology is shown to directly influence cusp growth as either predominantly erosional or accretional. Sediment characteristics within the beach cusp morphology are reported coincident with cusp evolution. Variations in pthesis size distribution kurtosis are exhibited as the cusps evolve; however, no significant correlation is seen between grain size and position between horn and embayment. During the end of the study, a storm resulted in beach cusp destruction and increased sediment sorting. In the former technique using multi-dimensional studies, a test of a new method for improving forecasting of surficial aquifer system water level changes with rainfall is conducted. The results provide a more rigorous analysis of common predictive techniques and compare them with the results of the tested model. These results show that linear interpretations of response-to-rainfall data require a clarification of how large events distort prediction and how the binning of data can change the interpretation. Analyses show that the binning ground water recharge data as is typically done in daily format may be useful for quick interpretation but only describes how fast the system responds to an event, not the frequency of return of such a response. Without a secure grasp on the nonlinear nature of water table and rainfall data alike, any binning or isolation of specific data carries the potential for aliasing that must be accounted for in an interpretation. The new model is proven capable of supplanting any current linear regression analysis as a more accurate means of prediction through the application of a multivariate technique. Furthermore, results show that in the Florida surficial aquifer system response-to-rainfall ratios exhibit a maxima most often linked with modal stage.

[pt] Uma reta bissetora divide uma região convexa do plano em duas partes com áreas iguais. É natural estudar as envoltórias destas linhas bissetoras, que em geral apresentam singularidades. O caso de polígonos é particularmente interessante, pois existem diversas noções distintas de envoltórias discretas. Nesta dissertação, nós estudamos três tipos diferentes de envoltórias discretas de retas bissetoras e as conexões entre elas. / [en] A bisection line divide a convex planar region into two parts with equal areas. It is natural to study the envelope of these lines, which in general present singularities. The polygonal case is particularly interesting, since there are several different notions of a discrete envelope. In this dissertation, we study three different notions of discrete envelopes of bisection lines and the connections between them.