Orientador: Cleonice Fátima Bracciali / Banca: Jorge Alberto Borrego Morell / Banca: Vanessa Avansini Botta Pirani / Banca: Alagacone Sri Ranga / Banca: Jo˜ao Carlos Ferreira Costa / Resumo: A partir dos zeros dos polinômios que satisfazem uma relação de recorrência do tipo R_II especial, obtemos uma fórmula de quadratura na reta real com fórmulas simples para o cálculo de seus pesos. Alguns polinômios para-ortogonais no círculo unitário podem ser obtidos por uma relação de recorrência de três termos. As duas relações de recorrência mencionadas são conectadas por uma transformação que leva a reta real ao círculo unitário. Desta maneira, obtemos também fórmulas de quadratura no círculo unitário. Os nós e pesos das fórmulas de quadratura no círculo unitário são facilmente obtidos através dos nós e pesos da primeira fórmula. Foram feitas algumas adaptações em métodos numéricos muito bem conhecidos para obter os nós e pesos destas fórmulas de quadratura / Abstract: From polynomials that satisfy a special recurrence relation of type RII we derive a quadrature formula in the real line with simple formulas to obtain the respective weights. Some para-orthogonal polynomials in the unit circle can be expressed by a three terms recurrence relation. The two mencioned recurrence relations are connected by a transformation that takes the real line onto the unit circle. Hence, we obtain also quadrature formula on the unit circle. The nodes and the weights of the quadratura on the unit circle are obteined easily from the nodes and the weights of the first quadrature formula. We have also made some adaptions in well known numerical methods to obtain the nodes and weights of these quadrature formulas / Doutor

Architectures of matched filter in packet detector, CFO corrector, FFT output reorder buffer and phase tracking block are optimized for low complexity. Implemented in O.13-mum CMOS technology, the proposed baseband receiver system has the core area of 2.5 mm2 and the estimated power consumption is 170 mW, which is equivalent to the energy efficiency of 88 pJ/b at 480 Mbps data rate. The implementation results verify the robustness, low complexity and power efficiency of the proposed MB-OFDM UWB baseband receiver. / As an OFDM-based system, MB-OFDM UWB is vulnerable and sensitive to carrier frequency offset (CFO). We employ multipartite table method (MTM) to implement arctangent and sin/cos functions for frequency synchronization. Compared with traditional algorithms, MTM has the advantages of low cost, low power consumption and higher processing speed. Residual phase distortion is corrected by a highly simplified phase tracking method, which also has better performance compared with traditional phase tracking scheme. / Synchronization plays the key role for the performance of the whole baseband receiver system. In this dissertation, a dual-threshold (DT) packet detection scheme is proposed for timing synchronization. Compared with traditional cross-correlation algorithm, DT has much better detection performance, especially in high noise environment. / Ultra-wideband (UWB) technology, targeting at wireless personal area networks (WPANs),brings the convenience of high-speed and short-range wireless interconnects. As a novel communication technique, multi-band orthogonal frequency division multiplexing (MB-OFDM) UWB has the features of high spectrum efficiency, multiple access capability and robustness against narrow band interference. However, its inherent high complexity and the requirement of powerful processing for good performance are the obstacles for practical application. / Fan, Wen. / Adviser: Choy Chiu-Sing. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 105-112). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In this thesis we focus on two problems. First we propose a numerical method for generating optimized Wannier functions with desired properties. Second we perform the state of the art density functional plus dynamical mean-field calculations in pyrochlore iridates, to investigate the physics induced by the cooperation of spin-orbit coupling and electron correlation. We begin with the introduction for maximally localized Wannier functions and other related extensions. Then we describe the current research in the field of spin-orbit coupling and its interplay with correlation effects, followed by a brief introduction of the `hot' materials of iridates. Before the end of the introduction, we discuss the numerical methods employed in our work, including the density functional theory; dynamical mean-field theory and its combination with the exact diagonalization impurity solver. Then we propose our approach for constructing an optimized set of Wannier functions, which is a generalization of the functionality of the classic maximal localization method put forward by Marzari and Vanderbilt. Our work is motivated by the requirement of the effective description of the local subspace of the Hamiltonian by the beyond density functional theory methods. In extensions of density functional theory such as dynamical mean-field theory, one may want highly accurate description of particular local orbitals, including correct centers and symmetries; while the basis for the remaining degrees of freedom is unimportant. Therefore, we develop the selectively localized Wannier function approach which allows for a greater localization in the selected subset of Wannier functions and at the same time allows us to fix the centers and ensure the point symmetries. Applications in real materials are presented to demonstrate the power of our approach. Next we move to the investigation of pyrochlore iridates, focussing on the metal-insulator transition and material dependence in these compounds. We perform combined density functional plus dynamical mean-field calculations in Lu$_2$Ir$_2$O$_7$, Y$_2$Ir$_2$O$_7$, Eu$_2$Ir$_2$O$_7$, with spin-orbit coupling included and both single-site and cluster approximations appiled. A broad range of Weyl metal is predicted as the intervening phase in the metal-insulator transition. By comparing to experiments, we find that the single-site approximation fails to predict the gap values and substantial difference between the Y and Eu-compound, demonstrating the inadequacy of this approximation and indicating the key role played by the intersite effects. Finally, we provide a more accurate description of the vicinity of the metal-insulator and topological transitions implied by density functional plus cluster dynamical mean-field calculations of pyrochlore iridates. We find definitive evidence of the Weyl semimetal phase, the electronic structure of which can be approximately described as ``Weyl rings" with an extremely flat dispersion of one of the Weyl bands. This Weyl semimetal phase is further investigated by the $k\cdot p$ analysis fitting to the numerical results. We find that this unusual structure leads to interesting behavior in the optical conductivity including a Hall effect in the interband component, and to an enhanced susceptibility.

Hu Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 77-81). / Abstracts in English and Chinese. / Acknowledgement --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Evolution of Mobile Communications --- p.1 / Chapter 1.2 --- Overview of Multicarrier Systems --- p.3 / Chapter 1.3 --- Outline of This Thesis --- p.5 / Chapter 2 --- Multicarrier Communication Systems --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Multicarrier Modulation (MCM) Scheme versus Single Carrier Modulation (SCM) Scheme --- p.8 / Chapter 2.3 --- Orthogonal Frequency Division Multiplexing (OFDM) Systems --- p.12 / Chapter 2.4 --- Multicarrier CDMA --- p.16 / Chapter 2.4.1 --- MC-CDMA --- p.17 / Chapter 2.4.2 --- MC-DS-CDMA --- p.18 / Chapter 2.4.3 --- MT-CDMA --- p.19 / Chapter 3 --- Optimization for MC-CDMA Systems --- p.22 / Chapter 3.1 --- System Model --- p.22 / Chapter 3.2 --- Optimization with Normalized Power --- p.27 / Chapter 3.2.1 --- Transmission Time Minimization --- p.27 / Chapter 3.2.2 --- Throughput Maximization --- p.32 / Chapter 3.2.3 --- Performance --- p.33 / Chapter 3.3 --- Mathematical Programming --- p.36 / Chapter 3.3.1 --- Nonlinear Programming --- p.37 / Chapter 3.3.2 --- Convex Programming --- p.39 / Chapter 3.4 --- Optimization with Power Allocation --- p.42 / Chapter 3.4.1 --- Transmission Time Minimization with Power Allocation --- p.42 / Chapter 3.4.2 --- Throughput Maximization with Power Allocation --- p.43 / Chapter 3.4.3 --- Power Minimization --- p.44 / Chapter 3.5 --- Long-range Optimization --- p.45 / Chapter 3.5.1 --- Long-range Transmission Time Minimization --- p.46 / Chapter 3.5.2 --- Long-range Throughput Maximization --- p.50 / Chapter 3.5.3 --- Long-range Power Minimization --- p.51 / Chapter 3.5.4 --- Performance --- p.53 / Chapter 4 --- Joint Scheduling and Resource Allocation --- p.58 / Chapter 4.1 --- Queueing Model --- p.58 / Chapter 4.2 --- Problem Formulation --- p.62 / Chapter 4.3 --- Suboptimal Algorithm --- p.64 / Chapter 4.4 --- Performance --- p.69 / Chapter A --- Convexity Proof of Problem (3.32) --- p.73 / Chapter B --- Convexity Proof of Problem (3.36) --- p.75 / Bibliography --- p.77

I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.

To gain an appreciation or understanding for the title of this study we must first understand what the phrases "non-orthogonal" and "error structure" mean. With an understanding of these terms the title of this study will become clear. To obtain an understanding of the term non-orthogonal, consider an experiment where differing treatments are applied to groups of experi­mental units in order to observe the differential treatment responses. If an equal number of experimental units are in each group, then we say we have an orthogonal situation. This means that when equal numbers exist among the experimental units, that the variability associated with the individual sources of variation can be orthogonally partitioned, such that the sources of variability add to the total source of variation. However, if unequal numbers exist among the experimental units, then we say we have a non-orthogonal situation. This implies that we can no longer obtain a completely orthogonal partition, and that the sources of variability associated with the individual sources of variation do not add to the total source of variation. The phrase, error structure, can best be described with reference to the statistical technique known as the analysis of variance. For any typical analysis of variance, there exists a one to one correspondence between the mean squares and the recognized sources of variation in the underlying model.

No description available.

<p>To let many users benefit from the high speed communication in an optical fiber, a way to share the channel is needed. One way to share the channel between the users is the multiple access technique of Code Division Multiple Access, CDMA. This technique is based on coding. By assigning the users different codewords, the receiver is able to distinguish the information sent from each user. One family of codes suitable to use in a fiber optic network is the constant weight Optical Orthogonal Codes, OOC.</p><p>To influence the users interference tolerability it is possible to assign the users codewords of the same length but with different weights. By letting the users have codewords of different length it is possible to have different data rates in the system. These two versions of optical orthogonal codes, with variable length and weight, are investigated in this thesis for their cardinality. The variable weight and variable length codes were created by combining optical orthogonal codes with different parameters.</p><p>I have found that for variable length OOC:s of weight 2 it seems to be possible to increase the cardinality of a code, but for codes with higer weights than that, it is better that all users are assigned codewords of the same length. But since an upper bound for the cardinality of these types of codes has not been found, it is not possible to verify if this conclusion is correct. For variable weight OOC:s it is found that it is only possible to increase the cardinality of small, not optimal, codes. For codes including many codewords it is rarely possible to include more codewords without breaking the conditions on cross correlation between the codewords.</p>

<p>In this thesis, we present algorithms for local and global minimization of some <i>Procrustes</i> type problems. Typically, these problems are about rotating and scaling a known set of data to fit another set with applications related to determination of rigid body movements, factor analysis and multidimensional scaling. The known sets of data are usually represented as matrices, and the rotation to be determined is commonly a matrix <i>Q</i> with orthonormal columns.</p><p>The algorithms presented use Newton and Gauss-Newton search directions with optimal step lengths, which in most cases result in a fast computation of a solution.</p><p>Some of these problems are known to have several minima, e.g., the weighted orthogonal Procrustes problem (WOPP). A study on the maximal amount of minima has been done for this problem. Theoretical results and empirical observations gives strong indications that there are not more than 2ⁿ minimizers, where <i>n</i> is the number of columns in <i>Q</i>. A global optimization method to compute all 2ⁿ minima is presented.</p><p>Also considered in this thesis is a cubically convergent iteration method for solving nonlinear equations. The iteration method presented uses second order information (derivatives) when computing a search direction. Normally this is a computational heavy task, but if the second order derivatives are constant, which is the case for quadratic equations, a performance gain can be obtained. This is confirmed by a small numerical study.</p><p>Finally, regularization of ill-posed nonlinear least squares problems is considered. The quite well known L-curve for linear least squares problems is put in context for nonlinear problems.</p>

The proper orthogonal decomposition (POD) has been widely used in fluid dynamic applications for extracting dominant flow features. The “gappy” POD is an extension to this method that allows the consideration of incomplete data sets. In this paper, the gappy POD is extended to handle unsteady flow reconstruction problems, such as those encountered when limited flow measurement data is available. In addition, a systematic approach for effective sensor placement is formulated within the gappy framework. Two applications are considered. The first aims to reconstruct the unsteady flow field using a small number of surface pressure measurements for a subsonic airfoil undergoing plunging motion. The second considers estimation of POD modal content of a cylinder wake flow for active control purposes. In both cases, using the dominant POD basis vectors and a small number of sensor signals, the gappy approach is found to yield accurate flow reconstruction results. / Singapore-MIT Alliance (SMA)