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Thermodynamic formalism, statistical properties and multifractal analysis of non-uniformly hyperbolic systemsWang, Tianyu 20 October 2021 (has links)
No description available.
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A study of beamforming and beamshaping techniques for uniformly and non-uniformly spaced arraysLemes, Daniel Lima 05 April 2018 (has links)
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Previous issue date: 2018-04-05 / The main goal of this work was to develop a MATLAB-based co de capable of finding the optimum values for amplitudes, phases and spacings of a non-uniformly spaced linear antenna array for a specified purpose. This tool allowed investigating the influence of the relative spacings between the elements of an antenna array in its radiation pattern. Two optimization methods were implemented: PSO (Particle swarm optimization), which is an evolutionary heuristic based on the social interaction and movement of swarms, and Taguchi’s method, which is based on orthogonal arrays to reduce the number of experiments needed to find the optimum value of a given variable. Different optimization goals were investigated, so that a comparison between these techniques has been done. The developed co de was applied to solve two practical problems. In the first one, a dual-band antenna array for base stations of mobile communication systems was modeled and its amplitudes, phases and spacings were optimized. By doing so, it was possible to mitigate the granting lobes that app eared in the pattern in the higher band, because the relative spacings between the elements could not be smaller than λ0. The pattern of this array was also shaped following a squared cosecant contour, in order to illuminate a pico-cell with uniform power. The results of the optimizations in both bands were validated using the commercial software Ansys HFSS and a study about the influence of the mutual coupling in the pattern was done. The second practical problem was to design an antenna array with beamshaping. By using the proposed code, it was possible to reduce the number of array elements from seven to four comparing to an uniformly spaced array. The optimization was split into two parts in order to mitigate the influence of the mutual coupling. A passive feeder for the optimized array was designed and a prototype was manufactured. The results were validated using HFSS and by measurements. The complete development of the array and of the feeder are detailed in this work. Finally, the design of a transmitter for adaptive beamshaping is described. The architecture nis capable to change the phase and power level of the signal, hence allowing to deliver the weights optimized by the proposed code to the antenna array. A modular concept was chosen in order to increase the flexibility of the transmitter. The device translates the input frequency from 500 MHz to 7 GHz, in order to deliver the weights to the antenna array. Eight transmitters were assembled and they were coupled to the antenna array in order to test their functionality. The patterns were measured in an anechoic chamber. All measured results of the transmitter are presented. / O principal objetivo deste trabalho foi desenvolver uma ferramenta computacional em MATLAB capaz de otimizar as fases, as amplitudes e os espaçamentos de uma rede de antenas, a fim de satisfazer um determinado objetivo. De posse dessa ferramenta, foi possível analisar a influência do espaçamento relativo entre os elementos de uma rede no diagrama da mesma. Dois métodos de otimização foram implementados: PSO (Particle Swarm Opmitization), baseado na interação social e no movimento de um enxame, e o método de Taguchi, que utiliza matrizes ortogonais para diminuir o número de testes necessários para otimizar uma variável. Diferentes cenários foram analisados de forma a permitir uma comparação entre os dois métodos. O código desenvolvido foi aplicado a dois problemas práticos. No primeiro deles, uma rede de antenas dupla-faixa para emprego em estações rádio base de sistemas de comunicações móveis foi modelada e suas amplitudes, fases e espaçamentos foram otimizados. Como na banda mais alta o espaçamento entre os elementos não podia ser menor que λ0., fez-se necessário otimizar os espaçamentos para controle dos grating lobes. O diagrama dessa rede foi também conformado seguindo um contorno em cossecante ao quadrado, para iluminar uma certa região com potência uniforme. Os resultados de todas as otimizações em ambas bandas foram validados usando o software Ansys HFSS e um estudo sobre a influência do acoplamento mútuo foi feito. O segundo caso consistiu na otimização de uma rede de antenas com conformação de feixe. Foi possível diminuir o número de elementos de sete para quatro em comparação a uma rede com elementos uniformemente espaçados. A otimização foi dividida em duas partes para compensar o efeito do acoplamento mútuo. Para a rede otimizada, um sistema alimentador passivo foi desenvolvido e um protótipo foi fabricado. Os resultados foram validados com simulações no software comercial Ansys HFSS e, também, por medições. Todo o projeto da rede e do alimentador é detalhado neste trabalho. Finalmente, o desenvolvimento de um circuito transmissor para beamshaping adaptativo ´e detalhado. Tal sistema é composto por um defasador e um amplificador de ganho variável, com os quais é possível inserir as amplitudes e fases, otimizadas pelo código proposto, em uma rede de antenas. Desenvolveu-se um transmissor modular, a fim de aumentar a flexibilidade do sistema. A frequência de entrada do transmissor é de 500 MHz, que é transladada para 7 GHz antes de ser entregue à rede de antenas. Foram fabricados oito transmissores, os quais foram acoplados a uma rede de antenas para testar suas funcionalidades. Os diagramas de irradiação foram medidos em câmera anecóica. Todo o desenvolvimento e medições de cada componente do transmissor são também mostrados neste trabalho.
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Viana maps and limit distributions of sums of point measuresSchnellmann, Daniel January 2009 (has links)
No description available.
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Optimal Mechanisms for Selling Two Heterogeneous ItemsThirumulanathan, D January 2017 (has links) (PDF)
We consider the problem of designing revenue-optimal mechanisms for selling two heterogeneous items to a single buyer. Designing a revenue-optimal mechanism for selling a single item is simple: Set a threshold price based on the distribution, and sell the item only when the buyer’s valuation exceeds the threshold. However, designing a revenue-optimal mechanism to sell two heterogeneous items is a harder problem. Even the simplest setting with two items and one buyer remains unsolved as yet. The partial characterizations available in the literature have succeeded in solving the problem largely for distributions that are bordered by the coordinate axes. We consider distributions that do not contain (0; 0) in their support sets. Specifically, we consider the buyer’s valuations to be distributed uniformly over arbitrary rectangles in the positive quadrant. We anticipate that the special cases we solve could be a guideline to un-derstand the methods to solve the general problem. We explore two different methods – the duality method and the virtual valuation method – and apply them to solve the problem for distributions that are not bordered by the coordinate axes. The thesis consists of two parts.
In the first part, we consider the problem when the buyer has no demand constraints. We assume the buyer’s valuations to be uniformly distributed over an arbitrary rectangle [c1; c1 + b1] [c2; c2 + b2] in the positive quadrant. We first study the duality approach that solves the problem for the (c1; c2) = (0; 0) case. We then nontrivially extend this approach to provide an explicit solution for arbitrary nonnegative values of (c1; c2; b1; b2). We prove that the optimal mechanism is to sell the two items according to one of eight simple menus. The menus indicate that the items must be sold individually for certain values of (c1; c2), the items must be bundled for certain other values, and the auction is an interplay of individual sale and a bundled sale for the remaining values of (c1; c2). We conjecture that our method can be extended to a wider class of distributions. We provide some preliminary results to support the conjecture.
In the second part, we consider the problem when the buyer has a unit-demand constraint. We assume the buyer’s valuations (z1; z2) to be uniformly distributed over an arbitrary rectangle [c; c + b1] [c; c + b2] in the positive quadrant, having its south-west corner on the line z1 = z2. We first show that the structure of the dual measure shows significant variations for different values of (c; b1; b2) which makes it hard to discover the correct dual measure, and hence to compute the solution. We then nontrivially extend the virtual valuation method to provide a complete, explicit solution for the problem considered. In particular, we prove that the optimal mechanism is structured into five simple menus. We then conjecture, with promising preliminary results, that the optimal mechanism when the valuations are uniformly distributed in an arbitrary rectangle [c1; c1 + b1] [c2; c2 + b2] is also structured according to similar menus.
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Estados de equilíbrio / Equilibrium states.Silva, Márcio Henrique Batista da 08 December 2005 (has links)
We prove existence of Equilibrium states, including measures of maximal entropy, for a robust (open) class of expanding and non-uniformly expanding maps on compact and connect manifolds / Fundação de Amparo a Pesquisa do Estado de Alagoas / Provaremos a existência de Estados de equilíbrio, incluindo medidas de entropia máxima, para uma classe robusta (aberta) de transformações expansoras e nãouniformemente
expansoras sobre uma variedade compacta e conexa.
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Versões das propriedades A e B de Lindenstrauss para operadores compactosBrito, Leonardo da Silva, 92-99307-3945 23 March 2018 (has links)
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Previous issue date: 2018-03-23 / CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / The main goal in this dissertation is to study the versions for compact operators of
Lindenstrauss property A and B. In the course of our work, we present results concerning
weak-star topology, Schauder basis, approximation properties, Banach spaces that locally
depend upon finitely many coordinates, strictly convex spaces, uniformly convex spaces,
among others. In 2014 Miguel Martín answered positively the following question: Are
there compact operators between Banach spaces that can not be approximated by compact
operators that attain their norms? In order to do that, he introduced two properties called
properties Ak and Bk or versions for compact operators of Lindenstrauss properties. In
this dissertation we present some results regarding Lindenstrauss properties A and B, and
we also provide several results regarding properties Ak and Bk. / O objetivo desta dissertação é estudar as versões das propriedades A e B de Lindenstrauss
para operadores compactos. No decorrer do nosso trabalho, apresentamos resultados sobre
a topologia fraca-estrela, bases de Schauder, propriedades da aproximação, espaços de Banach
cuja norma depende localmente de finitas coordenados, espaço estritamente convexo,
espaço uniformemente convexo, dentre outros. Em 2014 Miguel Martín publicou um artigo
respondendo de maneira positiva a seguinte pergunta: Existem operadores compactos
entre espaços de Banach que não podem ser aproximados por operadores compactos que
atingem a norma? Ao fazer isso, introduziu, no mesmo trabalho, duas propriedades chamadas
de propriedades Ak e Bk ou versões para operadores compactos das propriedades
de Lindenstrauss. Nesta dissertação, são apresentados de maneira detalhada resultados
relacionados às propriedades A e B de Lindenstrauss e propriedades Ak e Bk.
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Lançamento oblíquo: uma abordagem matemática / Oblique launch: a mathematical approachAlmeida, Francisco Fabio Monteiro de 31 March 2016 (has links)
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Previous issue date: 2016-03-31 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The main goal of this work is to verify that we can assign the oblique launch a
mathematical approach. To reach this conclusion, we address important issues of
mathematics and physics, as linear functions and quadratic functions , and uniform and
uniformly varied movements. These concepts were presented to facilitate understanding
and implement an equation that allows to determine the moment of rise, the maximum
height and horizontal reach, knowing an shot's angle, the initial velocity and gravity's
acceleration. / O objetivo principal desse trabalho é veri car que podemos atribuir ao lançamento
oblíquo uma abordagem matemática. Para chegarmos a esta conclusão, abordamos
assuntos importantes da Matemática e da Física, como funções a m e quadrática, e
movimentos uniforme e uniformemente variado. Tais conceitos foram apresentados
para facilitar o entendimento e implementar uma equação que permita determinar o
instante de subida, a altura máxima e o alcance horizontal, conhecendo um ângulo de
tiro, a velocidade inicial e a aceleração da gravidade.
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Actions hyperboliques du groupe multiplicatif sur des variétés affines : espaces exotiques et structures locales / Hyperbolic actions of the multiplicative group on affine varieties : exotic spaces and local structuresPetitjean, Charlie 30 March 2015 (has links)
Cette thèse est consacré à l'étude des T-variétés affines à l'aide de la présentation due à Altmann et Hausen. On s'intéresse plus particulièrement au cas des actions hyperboliques du groupe multiplicatif Gm. Dans une première partie, on étudie les espaces affines exotiques, c'est-à-dire des variétés affines lisses et contractiles, en supposant de plus qu'elles sont munies d'une action de Gm. En particulier, dans le cas de dimension 3, on réinterprète la construction des variétésde Koras-Russell en terme de diviseurs polyédraux, et on donne des constructions de variétés affines lisses et contractiles en dimension supérieure à 3.Dans une deuxième partie, on introduit la propriété pour une G-variété d'être G-uniformément rationnelle, c'est-à-dire que tout point de cette variété admet un voisinage ouvert G-stable, qui est isomorphe de manière equivariante à un ouvert G-invariant de l'espace affine. En particulier, on exhibera des Gm-variétés qui sont lisses et rationnelles mais qui ne sont pas Gm-uniformément rationnelle. / This thesis is devoted to the study of affine T-varieties using the Altmann-Hausen presentation. We are especially interested in the case of hyperbolic actions of the multiplicative group Gm. In the first part, exotic affine spaces are studied, that is, smooth contractible affine varieties, assuming in addition that they are endowed with a Gm-action. In particular, in the case of dimension 3, we reinterpret the construction of Koras-Russell threefolds in terms of polyhedral divisors andwe give constructions of smooth contractible affine varieties and in dimensionslarger than 3.In the second part we consider the property of G-uniform rationality for a G-variety. This means that every point of this variety there exists an open G-stable neighborhood, which is equivariantly somorphic to a G-stable open subset of the affine space. In particular we will exhibit Gm-varieties which are smooth and rational but not Gm-uniformly rational.
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Dôsledky porušenia predpokladov použitia vybraných štatistických metód / Consequences of assumption violations of selected statistical methodsMarcinko, Tomáš January 2010 (has links)
Classical parametric methods of statistical inference and hypothesis testing are derived under fundamental theoretical assumptions, which may or may not be met in real world applications. However, these methods are usually used despite the violation of their underlying assumptions, while it is argued, that these methods are quite insensitive to the violation of relevant assumptions. Moreover, alternative nonparametric or rank tests are often overlooked, mostly because these methods may be deemed to be less powerful then parametric methods. The aim of the dissertation is therefore a description of the consequences of assumption violations concerning classical one-sample and two-sample statistical methods and a consistent and comprehensive comparison of parametric, nonparametric and robust statistical techniques, which is based on extensive simulation study and focused mostly on a normality and heteroscedasticity assumption violation. The results of the simulation study confirmed that the classical parametric methods are relatively robust, with some reservations in case of outlying observations, when traditional methods may fail. On the other hand, the empirical study clearly proved that the classical parametric methods are losing their optimal properties, when the underlying assumptions are violated. For example, in many cases of non-normality the appropriate nonparametric and rank-based methods are more powerful, and therefore a statement, that these methods are unproductive due to their lack of power may be considered a crucial mistake. However, the choice of the most appropriate distribution-free method generally depends on the particular form of the underlying distribution.
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Synthèse d'observateurs pour les systèmes non linéaires, non uniformément observables / Synthesis observers for non uniformly observable nonlinear systemsLtaief, Ali 19 May 2017 (has links)
Les résultats présentés dans cette thèse s’articulent autour de la synthèse d’observateurs de type grand gain pour des classes de systèmes non linéaires multi-entrées, multi-sorties non uniformément observables. Dans un premier temps, la classe de systèmes considérées est telle que la dynamique des variables d’état est décrite par la somme de deux termes. Le premier correspond à une partie affine en l’état décrite par le produit d’une matrice, dont les entrées (fonctions non linéaires de l’état) ont une structure triangulaire, par le vecteur d’état. Le deuxième terme est composé par les non linéarités du système qui ont aussi une structure triangulaire. Le gain de l’observateur proposé est issu de la résolution d’une équation différentielle ordinaire de type Lyapunov.La convergence exponentielle de l’erreur d’observation sous-jacente est établie sous une une certaine condition d’excitation persistante dépendant de l’entrée du système et de l’état de l’observateur.Dans un deuxième temps, la synthèse de cet observateur est étendue à une classe plus large de systèmes non linéaires où des états peuvent intervenir de manière non triangulaire.La notion d’indices caractéristiques associés à ces états est alors introduite et elle a permis de définir une structure triangulaire étendue pour la quelle la synthèse de l’observateur a aussi été effectuée.Enfin, il a été établi que les observateurs proposés peuvent être utiliséscomme observateurs adaptatifs pour l’estimation simultanée de l’état et de certains paramètres et une forme adaptative de ces observateurs a été générée.Les performances des différents observateurs proposés ont été illustrées à travers des exemples en simulation / The results given in this thesis deal with the design of high gain observers for some classes on Multi Input Multi Output non uniformly observable nonlinear systems. In a first step, the class of considered systems is such that the dynamics of the state variables is the sum of two terms. The first term is affine in the state and is composed by the product of a matrix, whose entries are nonlinear functions of the state with a triangular structure, by the state vector. The second term describes the system nonlinearities which also assume a triangular structure. The gain of the proposed observer is issued from the resolution of a Lyapunov ordinary differential equation. The exponential convergence of the underlying observation error is established under a persistent excitation condition involving the system inputs and the state of the observer. In a second step, the observer design has been extended to a larger class of nonlinear systems where some state variables may intervene in a non triangular way. The notion of the characteristic indices associated to these state variables is then introduced and it allowed to define an extended triangular structure for which a high gain observer has been designed. Finally, it has been established that the proposed observers can be used as adaptive ones to jointly estimate the system state together with some unknown parameters and an adaptive form of these observers has been derived. The performance and main properties of the proposed observers have been illustrated in simulation by considering many examples throughout this thesis.
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