OLIVEIRA FILHO, Itamar Sales de. Time-frequency analysis : the bilinear Hilbert transform and the Carleson theorem. 2016. 109 f. Dissertação (Mestrado em Matemática em Rede Nacional) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016. / Submitted by Rocilda Sales (rocilda@ufc.br) on 2016-08-03T13:04:26Z No. of bitstreams: 1 2016_dis_isoliveirafilho.pdf: 1052932 bytes, checksum: 65cea71bb69c14d263414a81de75c8d8 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-08-03T13:09:30Z (GMT) No. of bitstreams: 1 2016_dis_isoliveirafilho.pdf: 1052932 bytes, checksum: 65cea71bb69c14d263414a81de75c8d8 (MD5) / Made available in DSpace on 2016-08-03T13:09:30Z (GMT). No. of bitstreams: 1 2016_dis_isoliveirafilho.pdf: 1052932 bytes, checksum: 65cea71bb69c14d263414a81de75c8d8 (MD5) Previous issue date: 2016 / In 1966, Lennart Carleson proved that the Fourier series of a periodic function, square integrable over a fundamental domain of the real line converges to the same function almost everywhere. This result was revisited years later by Charles Fe erman (1973) and by Lacey and Thiele (2000). It is studied here Lacey and Thiele's work, where they approached the problem through time-frequency analysis. This proof was inspired in a previous work of theirs, where they establish boundedness for the bilinear Hilbert transform in Lebesgue spaces. The study of boundedness for this operator started with the attempts to establish boundedness for the first Calderon's commutator. Also through time-frequency analysis, it will be studied one of the works of Lacey and Thiele about the bilinear Hilbert transform. / Em 1966, Lennart Carleson provou que a série de Fourier de uma função periódica, quadrado-integrável em um domínio fundamental na reta converge para a prápria função em quase todo ponto. Esse resultado foi revisitado alguns anos depois por Charles Fefferman (1973) e por Lacey e Thiele (2000). É estudado aqui o trabalho desses ultimos, onde o problema é abordado através de análise de tempo e frequência. Essa demonstração foi inspirada em um trabalho anterior dos mesmos autores em que estabelecem limitação para a transformada de Hilbert bilinear em espaços de Lebesgue. O estudo da limitação desse operador começou com as tentativas de estabelecer limitação para o primeiro comutador de Calderón. Também sob o ponto de vista da análise de tempo e frequência, será estudado um dos trabalhos de Lacey e Thiele sobre a transformada de Hilbert bilinear.

Thesis (DTech (Electrical Engineering))--Cape Peninsula University of Technology, 2018. / Industrial processes tend to have very complex mathematical models that in most instances result in very model specific optimal estimation and designs of control strategies. Such models have many composition components, energy compartments and energy inventories that result in many process variables that are intertwined and too complex to separate from one another. Most of the derived mathematical process models, based on the application of first principles, are nonlinear and incorporate unknown parameters and unmeasurable states. This fact results in difficulties in design and implementation of controllers for a majority of industrial processes. There is a need for the existing parameter and state estimation methods to be further developed and for new methods to be developed in order to simplify the process of parameters or states calculation and be applicable for real-time implementation of various controllers for nonlinear systems. The thesis describes the research work done on developing new parameter and state estimation methods and algorithms for bilinear and nonlinear processes. Continuous countercurrent ion exchange (CCIX) process for desalination of water is considered as a case study of a process that can be modelled as a bilinear system with affine parameters or as purely nonlinear system. Many models of industrial processes can be presented in such a way. The ion exchange process model is developed based on the mass balance principle as a state space bilinear model according to the state and control variables. The developed model is restructured according to its parameters in order to formulate two types of parameter estimation problem – with process models linear and nonlinear according to the parameters. The two models developed are a bilinear model with affine and a nonlinear according to the parameters model. Four different methods are proposed for the first case: gradient-based optimization method that uses the process output measurements, optimization gradient based method that uses the full state vector measurements, direct solution using the state vector measurements, and Lagrange’s optimization technique. Two methods are proposed for the second case: direct solution of the model equation using MATLAB software and Lagrange’s optimisation techniques. / National Research Foundation (NRF)

Orientador: Marco Aurélio Amaral Henriques / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-26T04:02:15Z (GMT). No. of bitstreams: 1 Sangalli_LeandroAparecido1988-_M.pdf: 2889538 bytes, checksum: 474d1ae695fc20d0f0b214ac8ba4716f (MD5) Previous issue date: 2014 / Resumo: Emparelhamentos bilineares sobre curvas elípticas são funções matemáticas que podem viabilizar protocolos criptográficos promissores. Porém, um fato que enfraquece o desenvolvimento destes protocolos é o alto custo computacional para calcular estes emparelhamentos. Diversas técnicas de otimização foram propostas nos últimos anos para realizar este cálculo de forma mais eficiente. Dentre estas técnicas existem as que mudam o tipo de emparelhamentos, o tipo de curvas elípticas ou a forma de cálculo dos emparelhamentos. As curvas Barreto-Naehrig são conhecidas como curvas amigáveis para emparelhamentos, pois se destacam para aplicações que buscam eficiência no cálculo dos mesmos. Este trabalho avalia em detalhes o custo das operações presentes no cálculo de alguns dos emparelhamentos mais utilizados atualmente definidos sobre curvas Barreto-Naehrig. Por meio desta análise, foi possível realizar uma comparação destes emparelhamentos no nível de operações de adição, multiplicação, quadrado, inversão e redução modular sobre um corpo finito primo e sobre um processador genérico. Os resultados mostram que de acordo com os parâmetros adotados, um dos emparelhamentos mais utilizados (Optimal Ate) pode não apresentar o melhor desempenho entre os analisados. Além disso, foi possível avaliar como o cálculo dos emparelhamentos é afetado pela adoção de diferentes processadores, desde aqueles com palavras curtas até aqueles que no futuro poderão ter palavras muito longas / Abstract: Bilinear pairings over elliptic curves are functions that support promising cryptographic protocols. However, a fact that hinders the development of these protocols is their high computational cost. Many techniques seeking more efficiency in the calculation of pairings have been proposed in the last years. Among these techniques are those that change the pairing type, the curve type and/or the pairing calculation method. Barreto-Naehrig curves are known as pairing-friendly curves, because they perform well in applications that require more efficiency in the pairing calculation. This work evaluates the cost of operations present in the most used pairings that are based on Barreto-Naehrig curves. With this evaluation, it was possible to compare these pairings at the level of basic operations as addition, multiplication, square, inversion and modular reduction over a prime finite field in a generic processor. The results show that, for the security parameters adopted in this work, one of the most used pairing algorithms (Optimal Ate) is not the fastest among those evaluated. Moreover, this work estimates the impact caused in the pairing calculation by different processors, ranging from the current short-medium word processors to the future very long word ones / Mestrado / Engenharia de Computação / Mestre em Engenharia Elétrica

<p>In this thesis, we devise a new finite branch-and-bound algorithm for disjoint bilinear programs. In these problems, there are two vectors of variables, $\b{x}$ and $\b{y}$, and two polytopes $P_{\b{x}}$ and $P_{\b{y}}$ such that $\b{x}$ (resp. $\b{y}$) is chosen from $P_{\b{x}}$ (resp. $P_{\b{y}}$) so that a bilinear objective function is minimized. By a bilinear objective, we mean that the objective becomes linear when either one of $\b{x}$ or $\b{y}$ is fixed. </p> <p>  This branch-and-bound scheme uses a relaxation that is derived using the reformulation-linearization technique (RLT). The RLT relaxation is constructed by taking products of constraints and linearizing the bilinear terms using introduced variables. The quality of this relaxation improves as higher order products and the corresponding monomial terms are linearized. Although it is known that, as RLT relaxations are constructed with increasingly higher order linearizations, the relaxation eventually converges to the true optimal value. However, no finite convergence properties are known. In contrast, we show that the first level of the RLT hierarchy suffices to convexify the problem when one of the polytopes is a simplex. Then, using this insight we devise a new class of relaxations by combining RLT with a variant of the double description procedure, where the latter lifts a polytope into a simplex in a finite number of steps.  This leads us to a finite hierarchy of relaxations that converges to the optimal value. Although this hierarchy is finite, from a computational perspective, we find that the relaxations grow rapidly in size. However, we utilize the insight to derive a simplicial branch-and-bound scheme, that expresses each polytope as a union of simplices allowing us to converge finitely to the optimal solution for the problem. We perform preliminary numerical experiments to show that this approach holds promise and competes favorably with state-of-the-art methods on larger instances.</p>

<p> Two-dimensional C-H chemical shift correlation spectroscopy provides a large amount of information in a two dimensional matrix. Many variations of these experiments have been in an effort to enhance the information content of these experiments. Decoupling of multiplet signals is one method used to increase the sensitivity of an NMR experiment. Simple broadband decoupling in ω2 is done by irradiating the correlated channel during acquisition. Decoupling in ω1 must be done using less direct methods, one of which is to use bilinear rotation decoupling. The traditional description of the effect that a BIRD pulse has on the spin systems is based on a simple AX system which is at equilibrium at the beginning of the pulse, which does not apply in many real systems.</p> <p> This study uses the Superspin formalism to show in more detail the behaviour of more complex spin systems during the BIRD sequence, and the effect of varying parameters within the BIRD sequence. This treatment involved the derivation of complete spherical tensor descriptions of AX, AX2, and AX3 spin systems. This allowed the derivation of a mathematical description of an INEPT style pulse sequence, where the refocussing pulse in INEPT was replaced with the BIRD sequence. The derivation of the general evolution transformations of the spherical tensors in Liouville space also allowed the theoretical treatment to be done in a single basis, where earlier implementations of the Superspin formalism converted between a spherical tensor basis for the treatment of pulses and a Hamiltonian basis for the treatment of delays. This theoretical treatment allows the derivation of a functional form for the dependence of the carbon signal intensity on the variation of the interpulse delay in the BIRD sequence.</p> <p> This formalism was also used to analyze the occurrence of artifacts in two dimensional heteronuclear shift correlation spectra, due to strong coupling between methylene protons. These artifacts were studied in experiments that attempt broadband homonuclear decoupling in ω1 through the use of constant evolution time between the initial excitation pulse and polarization transfer. Two experiments were analyzed, the COLOC experiment and the HETRES experiment. The superspin formalism was used to deduce a functional form for the intensity of the artifact as a function of the strength of the coupling between the methylene protons.</p> / Thesis / Master of Science (MSc)

Abstract Not Provided. / Thesis / Master of Science (MSc)

No description available.

Power converters are electronic circuits for conversion, control and regulation of electric power for various applications, such as from tablet computers in milliwatts to electric power systems at megawatts range. There are three basic types of power converters: buck (output voltage less than the input voltage), boost (output voltage higher than the input voltage) and buck-boost converters. The reliability of the power converters has become an essential focus of industrial applications. This research presents modeling and control of DC/DC boost converter using several control methods, such as Proportional-Integral (PI), Linear Quadratic Regulator (LQR) control, and nonlinear control concepts. Based on standard circuit laws, a mathematical model of the boost converter is derived which is expressed as a bilinear system. First a small signal model of the converter is derived to analyze the small deviations around the steady-state operating point which is used to develop closed loop control using the PI and the LQR methods. Simulation results show that the performance of the converter is good for operation around the operating state, however is unacceptable if there are large variations in the load or the reference input. To improve the performance of the closed loop system, the nonlinear control concept is used which shows excellent closed loop performance under large variations of load or setpoint. Comparative simulation results are presented for closed loop performance under various types of disturbances including random variations in load. / Electrical and Computer Engineering

Yes / In this technical note, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.

Submitted by Daniel Felipe Silva Santos null (danielfssantos@yahoo.com.br) on 2017-08-29T19:56:20Z No. of bitstreams: 1 ReconhecedorDeVeiculos2D-DBM.pdf: 3800862 bytes, checksum: 46f12ff55f4e0680833b9b1b184ad505 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-08-29T20:19:13Z (GMT) No. of bitstreams: 1 santos_dfs_me_sjrp.pdf: 3800862 bytes, checksum: 46f12ff55f4e0680833b9b1b184ad505 (MD5) / Made available in DSpace on 2017-08-29T20:19:13Z (GMT). No. of bitstreams: 1 santos_dfs_me_sjrp.pdf: 3800862 bytes, checksum: 46f12ff55f4e0680833b9b1b184ad505 (MD5) Previous issue date: 2017-08-14 / Neste trabalho é proposto um método para reconhecer veículos em imagens coloridas baseado em uma rede neural Perceptron Multicamadas pré-treinada por meio de técnicas de aprendizado em profundidade, sendo uma das técnicas composta por Máquinas de Boltzmann Profundas e projeção bilinear e a outra composta por Máquinas de Boltzmann Profundas Multinomiais e projeção bilinear. A proposição deste método justifica-se pela demanda cada vez maior da área de Sistemas de Transporte Inteligentes. Para se obter um reconhecedor de veículos robusto, a proposta é utilizar o método de treinamento inferencial não-supervisionado Divergência por Contraste em conjunto com o método inferencial Campos Intermediários, para treinar múltiplas instâncias das redes profundas. Na fase de pré-treinamento local do método proposto são utilizadas projeções bilineares para reduzir o número de nós nas camadas da rede. A junção das estruturas em redes profundas treinadas separadamente forma a arquitetura final da rede neural, que passa por uma etapa de pré- treinamento global por Campos Intermediários. Na última etapa de treinamentos a rede neural Perceptron Multicamadas (MLP) é inicializada com os parâmetros pré-treinados globalmente e a partir deste ponto, inicia-se um processo de treinamento supervisionado utilizando gradiente conjugado de segunda ordem. O método proposto foi avaliado sobre a base BIT-Vehicle de imagens frontais de veículos coletadas de um ambiente de tráfego real. Os melhores resultados obtidos pelo método proposto utilizando rede profunda multinomial foram de 81, 83% de acurácia média na versão aumentada da base original e 91, 10% na versão aumentada da base combinada (Carros, Caminhões e Ônibus). Para a abordagem de redes profundas não multinomiais os melhores resultados foram de 81, 42% na versão aumentada da base original e 91, 13% na versão aumentada da base combinada. Com a aplicação da projeção bilinear, houve um decréscimo considerável nos tempos de treinamento das redes profundas multinomial e não multinomial, sendo que no melhor caso o tempo de execução do método proposto foi 5, 5 vezes menor em comparação com os tempos das redes profundas sem aplicação de projeção bilinear. / In this work it is proposed a vehicle recognition method for color images based on a Multilayer Perceptron neural network pre-trained through deep learning techniques (one technique composed by Deep Boltzmann Machines and bilinear projections and the other composed by Multinomial Deep Boltzmann Machines and bilinear projections). This proposition is justified by the increasing demand in Traffic Engineering area for the class of Intelligent Transportation Systems. In order to create a robust vehicle recognizer, the proposal is to use the inferential unsupervised training method of Contrastive Divergence together with the Mean Field inferential method, for training multiple instances of deep models. In the local pre-training phase of the proposed method, bilinear projections are used to reduce the number of nodes of the neural network. The combination of the separated trained deep models constitutes the final recognizer’s architecture, that yet will be global pre-trained through Mean Field. In the last phase of training the Multilayer Perceptron neural network is initialized with globally pre-trained parameters and from this point, a process of supervised training starts using second order conjugate gradient. The proposed method was evaluated over the BIT-Vehicle database of frontal images of vehicles collected from a real road traffic environment. The best results obtained by the proposed method that used multinomial deep models were 81.83% of mean accuracy in the augmented original database version and 91.10% in the augmented combined database version (Cars, Trucks and Buses). For the non-multinomial deep models approach, the best results were 81.42% in the augmented version of the original database and 91.13% in the augmented version of the combined database. It was also observed a significant decreasing in the training times of the multinomial deep models and non-multinomial deep models with bilinear projection application, where in the best case scenario the execution time of the proposed method was 5.5 times lower than the deep models that did not use bilinear projection.