In this thesis superconducting correlations on both a one-dimensional chain and a two-dimensional honeycomb lattice are analyzed using the t-J model Hamiltonian. Both systems use periodic boundary conditions and different electron fillings, and both are solved numerically using the Lanczos algorithm. In order to search for superconducting correlations in the ground state the pair-pair correlation and susceptibility functions are defined. In one dimension the correlation function, at lower electronic fillings, displayed appreciable, non-zero values for all pair-pair separations. In general, the one-dimensional results were consistent with the literature. However, the honeycomb results did not show such strong superconducting correlations, as the correlation function remained close to zero for most separation distances. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2008-03-17 14:06:20.094

In this dissertation, we explore the approximate diagonalization of unital homomorphisms between C*-algebras. In particular, we prove that unital homomorphisms from commutative C*-algebras into simple separable unital C*-algebras with tracial rank at most one are approximately diagonalizable. This is equivalent to the approximate diagonalization of commuting sets of normal matrices. We also prove limited generalizations of this theorem. Namely, certain injective unital homomorphisms from commutative C*-algebras into simple separable unital C*-algebras with rational tracial rank at most one are shown to be approximately diagonalizable. Also unital injective homomorphisms from AH-algebras with unique tracial state into separable simple unital C*-algebras of tracial rank at most one are proved to be approximately diagonalizable. Counterexamples are provided showing that these results cannot be extended in general. Finally, we prove that for unital homomorphisms between AF-algebras, approximate diagonalization is equivalent to a combinatorial problem involving sections of lattice points in cones.

No description available.

Organic conductors are of considerable interest to the condensed matter community. In contrast to conventional metal conductors, these organic materials allow for large variability in their construction giving both quasi-one and two dimensional behavior. Organic superconductors also give useful insight into the properties of general superconductivity as well as insight into the properties of strongly correlated electronic materials. These materials exhibit interesting phenomena like spin-Peierls, antiferromagnetic, and superconducting phases. The aim of this thesis is not only to inform the reader of various studies into organic superconductors but also to advance research into these materials through massively parallel numerical methods. This thesis will cover two studies: a quantum Monte Carlo study on an infinite one-dimensional chain and an exact diagonalization study on a 16-site two-dimensional lattice. These studies will be used to better understand the charge and bond behavior of quasi-one dimensional 1/4illed organic superconductors.

[pt] Modulação Espacial com Pré-codificação Generalizada (Generalized Precoding Aided Spatial Modulation, GPSM) é uma estratégia de comunicação em sistemas MIMO em que o transmissor codifica a informação em duas entidades: a transmissão paralela de símbolos pertencentes à constelação de uma modulação digital, e os índices das posições do vetor de informação que transportam estes símbolos, denominada information bearing positions (IBP), enquanto as demais posições transportam zero. Além disto, o transmissor, previamente à transmissão dos dados pré-codifica o vetor de informação, possibilitando a redução da complexidade do nó receptor. Entre as vantagens desta estratégia destaca-se a concentração da energia transmitida apenas nas posições do vetor de informação que efetivamente contém símbolos, favorecendo o desempenho do sistema. Esta tese considera um sistema MIMO multiusuário (MU-MIMO) que emprega GPSM no enlace direto. O modelo de sinais desenvolvido para descrever este sistema evidencia a influência das matrizes que codificam as IBP no desempenho do sistema. Com base neste modelo, o sistema GPSM MU-MIMO é apresentado para três pré-codificadores lineares: Zero-Forcing, Block Diagonalization e Block Diagonalization de Duas Fases. Para cada um destes pré-codificadores são propostas estratégias de seleção das matrizes de codificação IBP, de acordo com a matriz que descreve o canal MU-MIMO corrente, a serem empregadas pelo transmissor visando melhorar o desempenho de detecção do sistema. As curvas de desempenho de detecção são comparadas a limitantes semianalíticos desenvolvidos. Por fim, considera-se o cenário em que existem mais antenas disponíveis na estação rádio-base e/ou nos usuários do que o número de cadeias de radiofrequência que os equipam. Esta tese apresenta estratégias ótimas e de complexidade reduzida de se explorar o uso das antenas mais favoráveis à transmissão e/ou recepção, em adição à escolha das matrizes de codificação IBP, com o objetivo de prover melhorias ao desempenho do sistema. / [en] Generalized Pre-coding Aided Spatial Modulation (GPSM) is a MIMO system communication strategy in which the transmitter encodes the information in two entities: the parallel transmission of symbols belonging to a digital modulation constellation, and the choice of the indices of the information vector elements that carries the informaiton symbols, denoted information bearing positions (IBP), while the remaing positions are set to zero. Besides, the transmitter precodes, prior to transmission, the information vector, which lets the receiver node benefit from complexity reduction. Among the advantages of this strategies, the concentration of the transmitted energy only on the information vector positions that transports modulated symbols, resulting in system performance improvement. This thesis considers a multiuser MIMO (MU-MIMO) that employs GPSM in the donwlink transmission. The presented signal model to describe this system evidences the influence of the IBP coding matrices on the system performance. Based on this model, GPSM MU-MIMO system is presented considering three linear precoders: Zero-Forcing, Block Diagonalization and Double-Stage Block Diagonalization. For each precoder, strategies to select the IBP encoding matrix, acording to the matrix that describes the current MU-MIMO channel, is proposed. These matrices are to be employed by the user, aiming at system detection performance improvement. Detection performance curves are compared to semianalytic lower bounds. Finally, a scenario in which that are a number of available antennas at the BS and/or at the users that exceed the number of radiofrequency chains. this thesis porposes optimal and reduced complexity strategies that exploit the use of the most favorable antennas for transmission and/or reception, in addition to the choice of the IBP enconding matrices, aiming at system performance improvement.

Le sujet visé par cette dissertation est la logique ordinale de Turing. Nous nous référons au texte original de Turing «Systems of logic based on ordinals» (Turing [1939]), la thèse que Turing rédigea à Princeton sous la direction du professeur Alonzo Church. Le principe d’une logique ordinale consiste à surmonter localement l’incomplétude gödelienne pour l’arithmétique par le biais de progressions d’axiomes récursivement consistantes. Étant donné son importance considérable pour la théorie de la calculabilité et les fondements des mathématiques, cette recherche méconnue de Turing mérite une attention particulière. Nous retraçons ici le projet d’une logique ordinale, de ses origines dans le théorème d’incomplétude de Gödel jusqu'à ses avancées dans les développements de la théorie de la calculabilité. Nous concluons par une discussion philosophique sur les fondements des mathématiques en fonction d’un point de vue finitiste. / The main subject of this dissertation is Turing’s ordinal logic, i.e. Turing’s attempt to locally overcome Gödel’s incompleteness by means of transfinite recursive progressions. We shall refer to the original 1939 text «Systems of logic based on ordinals» which is, in fact, Turing’s Ph.D thesis at Princeton University under the direction of Professor Alonzo Church. Considering its importance for the theory of computability and the foundations of mathematics, Turing’s paper certainly didn’t get enough attention in the literature. Therefore, we want to retrace Turing’s project of an ordinal logic from its very foundation in Gödel’s incompleteness theorem to its further development in calculability theory. A discussion on the foundations of mathematics from a computational point of view will conclude this memoir.

Cette thèse traite de l'étude de méthodes de diagonalisation conjointe de matrices complexes, en vue de la séparation de sources, que ce soit dans le domaine des télécommunications numériques ou de la radioastronomie. Après avoir présenté les motivations qui ont poussé cette étude, nous faisons un bref état de l'art dans le domaine. Le problème de la diagonalisation conjointe, ainsi que celui de la séparation de source sont rappelés, et un lien entre ces deux sujets est établi. Par la suite, plusieurs algorithmes itératifs sont développés. Dans un premier temps, des méthodes utilisant une mise à jour de la matrice de séparation, de type gradient, sont présentées. Elles sont basées sur des approximations judicieuses du critère considéré. Afin d'améliorer la vitesse de convergence, une méthode utilisant un calcul du pas optimal est présentée, et plusieurs variantes de ce calcul, basées sur les approximations faites précédemment, sont développées. Deux autres approches sont ensuite introduites. La première détermine la matrice de séparation de manière analytique, en calculant algébriquement les termes composant la matrice de mise à jour par paire à partir d'un système d'équations linéaire. La deuxième estime récursivement la matrice de mélange, en se basant sur une méthode de moindres carrés alternés. Afin d'améliorer la vitesse de convergence, une recherche de pas d'adaptation linéaire est proposée. Ces méthodes sont alors validées sur un problème de diagonalisation conjointe classique. Puis les algorithmes sont appliqués à la séparation de sources de signaux de télécommunication numérique, en utilisant des statistiques d'ordre deux ou supérieur. Des comparaisons sont également effectuées avec des méthodes standards. La deuxième application concerne l'élimination des interférences terrestres à partir de l'estimation de l'espace associé, afin d'observer au mieux des sources cosmiques, issues de données de station LOFAR. / This thesis deals with the study of joint diagonalization of complex matrices methods for source separation, wether in the field of numerical telecommunications and radioastronomy. After having introduced the motivations that drove this study, we present a brief state-of-the-art in the field. The joint diagonalization and source separation problems are reminded, and a link between these two themes is established. Thereafter, several iterative algorithms are developed. First, methods using a gradient-like update of the separation matrix are introduced. They are based on wise approximations of the considered criterion. In order to improve the convergence speed, a method using a computation of an optimal step size is presented, and variations around this computation, based on the previously introduced approximations are done. Two other approaches are then introduced. The first one analytically determines the separation matrix, by algebraically computing the terms composing the update matrix pairwise from a linear equation system. The second one recursively estimates the mixing matrix, based on an alternating least squares method. In order to enhance the convergence speed, a seek of an enhanced line search algorithm is proposed. These methods are then validated on a classical joint diagonalization problem. Aterwards, these algorithms are applied to the source separation of numerical communication signals, while using second or higher order statistics. Comparisons are also made with well-known methods. The second application relates to elimination of rterrestrial interferences from the estimation of the associated space in order to observe at best cosmic sources from LOFAR station data.

Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-02-04T18:11:54Z No. of bitstreams: 2 Dissertacao - Berto Rodrigo Marinho da Luz.pdf: 651792 bytes, checksum: fc6bc3999eef4a5a3eab227ec82638b0 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Rejected by Erika Demachki (erikademachki@gmail.com), reason: on 2015-02-04T18:25:04Z (GMT) / Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-02-04T18:26:14Z No. of bitstreams: 2 Dissertacao - Berto Rodrigo Marinho da Luz.pdf: 651792 bytes, checksum: fc6bc3999eef4a5a3eab227ec82638b0 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-02-05T09:58:43Z (GMT) No. of bitstreams: 2 Dissertacao - Berto Rodrigo Marinho da Luz.pdf: 651792 bytes, checksum: fc6bc3999eef4a5a3eab227ec82638b0 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-02-05T09:58:43Z (GMT). No. of bitstreams: 2 Dissertacao - Berto Rodrigo Marinho da Luz.pdf: 651792 bytes, checksum: fc6bc3999eef4a5a3eab227ec82638b0 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-03-07 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Mathematics is an essential subject today, with the most varied applications. However, certain mathematical de nitions depends on the prerequisites. Thinking about it, this work deals on a method of calculating square root matrices of order 2. As presented de nitions are organized in a gradual way. For this we will use some de nitions known as multiplication of matrices, determinants and matrix diagonalization. / A matemática é uma disciplina essencial nos dias atuais, com as mais variadas aplicações. Porém, certas defi nições matemáticas dependem de pré-requisistos. Pensando nisso, este trabalho trata sobre um método de calcular raiz quadrada de matrizes de ordem 2. As de nições apresentadas estão organizados de forma gradativa. Para isso usaremos algumas de nições conhecidas como multiplicação de matrizes, determinantes e diagonalização de matrizes.

The use of multiple antennas to improve the reliability and capacity of wireless communication has been around for a while, leading to the concept of multiple-input multiple-output (MIMO) communications. To enable full MIMO potentials, the precoding design has been recognized as a crucial component. This thesis aims to design multiuser MIMO precoders of practical interest to achieve high reliability and capacity performance under various real-world constraints like inaccuracy of channel information acquired at the transmitter, hardware complexity, etc. Three prominent cases are considered which constitute the mainstream evolving directions of the current cellular communication standards and future 5G cellular communications. First, in a relay-assisted multiuser MIMO system, heavily quantized channel information obtained through limited feedback contributes to noticeable rate loss compared to when perfect channel information is available. This thesis derives an upper bound to characterize the system throughput loss caused by channel quantization error, and then develops a feedback quality control strategy to maintain the rate loss within a bounded range. Second, in a massive multiuser MIMO channel, due to the large array size, it is difficult to support each antenna with a dedicated radio frequency chain, thus making high-dimensional baseband precoding infeasible. To address this challenge, a low-complexity hybrid precoding scheme is designed to divide the precoding into two cascaded stages, namely, the low-dimensional baseband precoding and the high-dimensional phase-only processing at the radio frequency domain. Its performance is characterized in a closed form and demonstrated through computer simulations. Third, in a mmWave multiuser MIMO scenario, smaller wavelengths make it possible to incorporate excessive amounts of antenna elements into a compact form. However, we are faced with even worse hardware challenges as mixed signal processing at mmWave frequencies is more complex and power consuming. The channel sparsity is taken advantage of in this thesis to enable a simplified precoding scheme to steer the beam for each user towards its dominant propagation paths at the radio frequency domain only. The proposed scheme comes at significantly reduced complexity and is shown to be capable of achieving highly desirable performance based on asymptotic rate analysis. / Graduate

A non-linear edge-preserving solution to the least-squares migration problem with sparseness & illumination constraints is proposed. The applied formalism explores Curvelets as basis functions. By virtue of their sparseness and locality, Curvelets not only reduce the dimensionality of the imaging problem but they also naturally lead to a dense preconditioning that almost diagonalizes the normal/Hessian operator. This almost diagonalization allows us to recast the imaging problem into a ’simple’ denoising problem. As such, we are in the position to use non-linear estimators based on thresholding. These estimators exploit the sparseness and locality of Curvelets and allow us to compute a first estimate for the reflectivity, which approximates the least-squares solution of the seismic inverse scattering problem. Given this estimate, we impose sparseness and additional amplitude corrections by solving a constrained optimization problem. This optimization problem is initialized and constrained by the thresholded image and is designed to remove remaining imaging artifacts and imperfections in the estimation and reconstruction.