O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de característica zero) e D é uma derivação localmente nilpotente sobre B, então seu núcleo A = ker D satisfaz A = B &cap: Frac(A). Assim encontramos o contraexemplo esperado, ao mostrar que A não é finitamente gerado sobre k. Além disso, no apêndice deste trabalho, é dada uma prova para o caso de dimensão 1 do Décimo Quarto Problema de Hilbert. / The main objective of this thesis is to study a counterexample to the Hilberts Fourteenth Problem in dimension n = 5, which was presented by Arno van den Essen ([6]) in 2006 and that is based on a counterexample of D. Daigle and G. Freudenburg ([4]). For these purpose, we study the fundamental concepts of the theory of derivations and the basic principles of locally nilpotent derivations and their corollaries. Among these principles, Principle 13 ensures that if B is a k-algebra polynomial, say B = k[x1; ..., xn], (where k is a field of characteristic zero) and D is a locally nilpotent derivation on B, then its kernel A = ker D satisfies A = B ∩ Frac(A). Once we have proved that A is not finitely generated over k, we find the expected counterexample. In addition, in the appendix of this work is given a proof for the Hilberts Fourteenth Problemin dimension n = 1.

Submitted by Almir Azevedo (barbio1313@gmail.com) on 2017-08-07T17:26:37Z No. of bitstreams: 1 FABIO DE LACERDA D.pdf: 4651972 bytes, checksum: 40eb0d71a79f39e524da9bb7fc917c63 (MD5) / Made available in DSpace on 2017-08-07T17:26:37Z (GMT). No. of bitstreams: 1 FABIO DE LACERDA D.pdf: 4651972 bytes, checksum: 40eb0d71a79f39e524da9bb7fc917c63 (MD5) Previous issue date: 2017-03 / Este trabalho trata da realização de um circuito integrado analógico para a conversão de sinais com modulação em amplitude de banda dupla (Double Sideband ou DSB) para modulação de banda simples (Single Sideband ou SSB). Implementado por circuitos de tempo discreto a capacitores chaveados, utiliza-se de um filtro com resposta infinita ao impulso (Infinite Input Response ou IIR) para compor um transformador de Hilbert como alternativa a implementações digitais, que se aproveitam da grande capacidade de processamento paralelo dos circuitos digitais para a obtenção do transformador de Hilbert por meio de filtros com resposta finita ao impulso (Finite Impulse Response ou FIR) de ordem elevada. Fabricado em tecnologia CMOS de 180 nm com capacitores do tipo metal-metal (MiM), a adoção de filtros estruturalmente passa-tudo reduz significativamente a sensibilidade do conversor ao descasamento de capacitores. Para alimentação de 1,8 V e sinais diferenciais de até 1 V, resultados experimentais mostram que o conversor atinge taxa de rejeição de imagem (Image Rejection Ratio ou IRR) maior que 39,5 dB para modulação Lower Sideband (LSB) e 38,0 dB para modulação Upper Sideband (USB) para sinais de entrada na faixa de 25% a 75% da frequência da portadora, valores estes superiores a propostas analógicas anteriores e comparáveis a propostas digitais do estado da arte em circuitos integrados. Com área de silício de 1,09 mm2, o conversor consome apenas 17,7 mW para frequência de amostragem de 1 MHz enquanto sua IRR apresentou desvio padrão de apenas 0,5 dB dentre 20 amostras avaliadas. / The realization of an analog integrated circuit for conversion of Double-Sideband (DSB) amplitude-modulated signals into Single-Sideband (SSB) is presented. Implemented by discrete-time switched-capacitor circuits, it adopts an Infinite Impulse Response (IIR) filter to realize a Hilbert transformer as alternative to digital implementations which take advantage of high processing capacity from parallel digital circuits to obtain the Hilbert transformer by means of high-order Finite Impulse Response (FIR) filters. Fabricated in a 180 nm CMOS technology with metal-metal (MiM) capacitors, the use of structurally all-pass filters greatly reduces the converter’s sensitivity to capacitor mismatch. For 1.8 V power supply and 1 V differential input/output signals, experimental results show the converter achieves Image Rejection Ratio (IRR) greater than 39.5 dB for Lower-Sideband (LSB) modulation and 38.0 dB for Upper-Sideband (USB) modulation for input signals ranging from 25% to 75% of the carrier frequency. These figures are higher than previous analog circuit proposals and comparable to digital implementations of state-of-the-art integrated circuits. Its silicon area is 1.09 mm2 and the converter consumes only 17.7 mW for 1 MHz sampling frequency while its IRR presents standard deviation of only 0.5 dB among 20 chip samples.

Submitted by Marcele Costal de Castro (costalcastro@gmail.com) on 2017-09-11T18:04:32Z No. of bitstreams: 1 FABIO DE LACERDA D.pdf: 4651972 bytes, checksum: 40eb0d71a79f39e524da9bb7fc917c63 (MD5) / Made available in DSpace on 2017-09-11T18:04:32Z (GMT). No. of bitstreams: 1 FABIO DE LACERDA D.pdf: 4651972 bytes, checksum: 40eb0d71a79f39e524da9bb7fc917c63 (MD5) Previous issue date: 2017-03 / Este trabalho trata da realização de um circuito integrado analógico para a conversão de sinais com modulação em amplitude de banda dupla (Double Sideband ou DSB) para modulação de banda simples (Single Sideband ou SSB). Implementado por circuitos de tempo discreto a capacitores chaveados, utiliza-se de um filtro com resposta infinita ao impulso (Infinite Input Response ou IIR) para compor um transformador de Hilbert como alternativa a implementações digitais, que se aproveitam da grande capacidade de processamento paralelo dos circuitos digitais para a obtenção do transformador de Hilbert por meio de filtros com resposta finita ao impulso (Finite Impulse Response ou FIR) de ordem elevada. Fabricado em tecnologia CMOS de 180 nm com capacitores do tipo metal-metal (MiM), a adoção de filtros estruturalmente passa-tudo reduz significativamente a sensibilidade do conversor ao descasamento de capacitores. Para alimentação de 1,8 V e sinais diferenciais de até 1 V, resultados experimentais mostram que o conversor atinge taxa de rejeição de imagem (Image Rejection Ratio ou IRR) maior que 39,5 dB para modulação Lower Sideband (LSB) e 38,0 dB para modulação Upper Sideband (USB) para sinais de entrada na faixa de 25% a 75% da frequência da portadora, valores estes superiores a propostas analógicas anteriores e comparáveis a propostas digitais do estado da arte em circuitos integrados. Com área de silício de 1,09 mm2, o conversor consome apenas 17,7 mW para frequência de amostragem de 1 MHz enquanto sua IRR apresentou desvio padrão de apenas 0,5 dB dentre 20 amostras avaliadas. / The realization of an analog integrated circuit for conversion of Double-Sideband (DSB) amplitude-modulated signals into Single-Sideband (SSB) is presented. Implemented by discrete-time switched-capacitor circuits, it adopts an Infinite Impulse Response (IIR) filter to realize a Hilbert transformer as alternative to digital implementations which take advantage of high processing capacity from parallel digital circuits to obtain the Hilbert transformer by means of high-order Finite Impulse Response (FIR) filters. Fabricated in a 180 nm CMOS technology with metal-metal (MiM) capacitors, the use of structurally all-pass filters greatly reduces the converter’s sensitivity to capacitor mismatch. For 1.8 V power supply and 1 V differential input/output signals, experimental results show the converter achieves Image Rejection Ratio (IRR) greater than 39.5 dB for Lower-Sideband (LSB) modulation and 38.0 dB for Upper-Sideband (USB) modulation for input signals ranging from 25% to 75% of the carrier frequency. These figures are higher than previous analog circuit proposals and comparable to digital implementations of state-of-the-art integrated circuits. Its silicon area is 1.09 mm2 and the converter consumes only 17.7 mW for 1 MHz sampling frequency while its IRR presents standard deviation of only 0.5 dB among 20 chip samples.

This thesis presents the ADT transverse instability detection system, the next generation of instability detection in the LHC at CERN, Geneva. The system is presented after a thorough study of underlying causes for instabilities in high energy particle accelerators, current parallel programming paradigms, the available hardware and software at CERN and possible instability detection techniques. The requirements for the system involve handling vast amounts of data which need to be analyzed in real-time and in this data detect rapid amplitude growth while limiting the computational resources required to a minimum. The result of this thesis was a system that could generate a trigger when an instability was detected, which was used to save data from observation instruments around the LHC. A fixed display in the CERN control centre was also created which allows scientists and operators at CERN to monitor the oscillation amplitude of all particle bunches. The conclusion is that the complete system will be a valuable asset at CERN to help further develop the LHC.

No description available.

The work is concerned with the band-limited signal extrapolation using truncated series of prolate spheroidal wave function. Our aim is to investigate the extent to which it is possible to extrapolate signal from its samples taken in a finite interval. It is often believed that this extrapolation method depends on computing definite integrals. We show an alternative approach by using the least squares method and we compare it with the methods of numerical integration. We also consider their performance in the presence of noise and the possibility of using these algorithms for real-time data processing. Finally all proposed algorithms are tested using real data from a microphone array, so that their performance can be compared.

In this paper, a new concept for ultrasonic indoor positioning based on instantaneous frequency of ultrasonic signals is presented. Nonlinear phase characteristics of ultrasonic transducers introduce a frequency deviation in ultrasonic signals. By sweeping at very fast rates, a large spike in the deviation is introduced. The artefacts observable in instantaneous frequency estimations are highly localized and present an opportunity for accurate frequency detection. In order to be useful, the artefacts need to take place within the pulse and have sufficient magnitude for accurate processing. The system consists of a transducer transmitter and receiver pair, which have a center frequency of 40kHz and a bandwidth of 460Hz. In order to incorporate more transmitters, a time-division multiple access (TDMA) scheme is applied to ensure orthogonality of signals. The concept includes four ultrasonic transmitters and a single receiver, which can uniquely identify each transmitter by a distinct signal sweep. Linear chirp signals are used to form narrow pulses and ensure no interference in the TDMA scheme. The received signal is amplified and passed through a phase-locked loop (PLL) to detect the chirp signals. Accurate instantaneous frequency detection can be done on the voltage-controlled oscillator (VCO) of the PLL, which has a narrower bandwidth than the overall signal sweep. The instantaneous frequency estimation methods are largely explored in this work and consider two methods: the Hilbert transform and a zero-crossings method. This work highlights some of the advantages and disadvantages of both methods. Time of flight (ToF) in this system can ultimately be obtained by considering the instantaneous frequency estimations and the time for one particular frequency to be transmitted and received.

We consider orthogonal polynomials P_n satisfying orthogonality relations where the measure of orthogonality is, in general, a complex-valued Borel measure supported on subsets of the complex plane. In our consideration we will focus on measures of the form d\mu(z) = \rho(z) dz where the function \rho may depend on other auxiliary parameters. Much of the asymptotic analysis is done via the Riemann-Hilbert problem and the Deift-Zhou nonlinear steepest descent method, and relies heavily on notions from logarithmic potential theory.

Estudia la ecuación de onda no lineal que modela la actividad neuronal del cerebro. Busca estudiar la existencia de la solución débil global del sistema dado utilizando el método de Faedo - Galerkin y además establecer la unicidad y estabilidad de la soluci´on utilizando criterios de desigualdades integrales e inmersiones de Sobolev. Los términos a(u, p)ut y b(u, p, pt) son términos no lineales que caracterizan la actividad neuronal del modelo. El estudio del sistema es planteado por Mauhamad y Maitine, quienes prueban que el sistema tiene una única solución estable, bajo supuestos datos reales. De hecho, estos supuestos están motivados por el modelo de la actividad cerebral física subyacente, que conduce a una ecuación que es un caso particular de la ecuación que se va a desenvolver. / Tesis

Riemann-Hilbert-Probleme sind Randwertaufgaben für im Einheitskreis $\mathbb D$ holomorphe Funktionen $w$, deren Randwerte $w(t)$ auf gewissen Kurven $M_t$ liegen sollen. Ein Teil der Untersuchungen ist dem Fall explizit gegebener Kurven gewidmet. Dabei werden bekannte Resultate über glatte Kurven auf stetige Restriktionskurven erweitert, und die Existenz von Lösungen in gewissen Hardy-Räumen gezeigt. Die Eindeutigkeitsfrage führt auf ein Gegenbeispiel, das zugleich eine Vermutung aus einer Dissertation von Belch widerlegt. Der andere Teil der Untersuchungen ist dem klassischen Fall geschlossener Restriktionskurven gewidmet. Hier steht statt der Abschwächung von Glattheitsvoraussetzungen die Formulierung geeigneter Nebenbedingungen im Mittelpunkt. Die Abhängigkeit der Lösung von Zusatzbedingungen erweist sich als Verallgemeinerung des Verhaltens von Blaschkeprodukten. Für drei Interpolationpunkte kann charakterisiert werden, wann durch sie eine Lösung mit Windungszahl 1 verläuft, durch $k$ Interpolationspunkte wird die Existenz einer Lösung mit Windungszahl $k-1$ gezeigt.