Orientador: Alagacone Sri Ranga / Banca: Walter dos Santos Motta Junior / Banca: Eliana Xavier Linhares de Andrade / Resumo: O estudo da obtenção de fórmulas assintóticas para polinômios ortogonais clássicos foi amplamente desenvolvido por Szegö. Recentemente, a necessidade de obtenção de assintóticas para polinômios, ortogonais com respeito a funções peso variadas, foi renovada devido a novos estudos na teoria de matrizes randômicas. Nestes estudos, uma das principais ferramentas utilizadas é a teoria dos problemas de Riemann-Hilbert, caracterizada pelo método de máxima descida de autoria de Deft e Zhou. Essas novas técnicas também aprimoraram os resultados obtidos por Szegö e outros autores predecessores. O objetivo do presente trabalho é esclarecer a conexão entre as teorias de polinômios ortogonais e problemas de Riemann-Hilbert, demonstrando os passos que devem ser seguidos a fim de se obter assintóticas que valham em qualquer subconjunto compacto do plano complexo. Como aplicação, escolhemos os polinômios ortogonais em [¡1; 1] com respeito a uma função peso modificada de Jacobi. / Abstract: The study of obtaining asymptotics for Classical Orthogonal Polynomials was vas- tly developed by Szegö. Recently, the need for obtaining asymptotics for polynomials, orthogonal with respect to varied weight functions, was renewed due to new researches in the theory of Random Matrices. In these studies, one of the most important tools used lies in the theory of Riemann-Hilbert problems, enforced by the steepest descent method of Deft and Zhou. These new techniques also have improved the results obtained by Szegö and other previous authors. The main purpose of this work is to explain the connection between the theories of Orthogonal Polynomials and Riemann-Hilbert problems, showing the steps to be followed on the way of finding asymptotics which hold true for any compact subsets of the complex plane. As an application, we choose the polynomials orthogonal on [¡1; 1] with respect to a modified Jacobi weight. / Mestre

Orientador: Cleonice Fátima Bracciali / Banca: Alagacone Sri Ranga / Banca: Vanessa Avansini Botta Pirani / Resumo: Nesta dissertação estudamos sequências de polinômios ortogonais que surgem como auto-funções polinomiais do problema de Sturm-Liouville, sob a condição de que, nem todos os graus das auto-funções polinomiais estejam presentes na sequência de graus dos polinômios que formam o conjunto ortogonal completo. Estas sequências são chamadas de sequências de polinômios ortogonais excepcionais. Emparticular,realizamosumestudodospolinômiosortogonaisexcepcionais X1-Jacobi e X1-Laguerre / Abstract: In this dissertation we study sequences of orthogonal polynomials that arise as polynomial eigenfunctions of the Sturm-Liouville problem, with the condition that not all degrees of polynomial eigenfunctions are present in the sequence of degrees of the polynomials that form a complete orthogonal set. These sequences are called exceptional orthogonal polynomial sequences. In particular, we study the exceptional orthogonal polynomials X1-Jacobi and X1-Laguerre / Mestre

Orientador: Alagacone Sri Ranga / Coorientador: Eliana Xavier Linhares de Andrade / Banca: Dimitar Kolev Dimitrov / Banca: Waldemar Donizete Bastos / Banca: Geraldo Márcio de Azevedo Botelho / Banca: Valdir Antonio Menegatto / Resumo: Neste trabalho são obtidos diversos resultados sobre duas classes distintas de po-linômios ortogonais de Laurent, uma delas definida na reta real, chamados de polinômios L-ortogonais, e a outra definida no círculo unitário. Primeiramente, analisamos a conexão existente entre duas sequências de polinômios L-ortogonais {Q (0) n } e {Q (1) n } associados a duas medidas positivas fortes dψ0 e dψ1 definidas em [a,b] e relacionadas por (t −κ)dψ1 = γdψ0 , onde (t −κ)/γ é positivo para t ∈(a,b). Nossos estudos podem ser aplicados à geração de novos exemplos de polinômios L-ortogonais. Dentre os resultados obtidos, temos também a monotonicidade dos zeros dos polinômios {Q (1) n }. Em seguida, consideramos a classe de polinômios ortogonais de Laurent no cír-culo unitário {2 Φ1 ( q−n ,qb+1 ; q−c + b− n ; q,q− c+ d −1 z)}∞ n=0 , definidos a partir de funções q-hip ergeométricas, onde 0 < q < 1 e os parâmetros complexos b,c e d são tais que b ̸= −1,−2 ,..., c −b + 1 ̸= −1,−2,..., Re( d) > 0 e Re(c −d + 2) > 0. Obtivemos várias propriedades desses polinômios, dentre elas expressões explícitas para os co eficien-tes da relação de recorrência, momentos e ortogonalidade, além de seu comportamento assintótico. Fazendo uma escolha... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Several results concerning two different classes of orthogonal Laurent polynomials are obtained, one defined on the real line, called L-orthogonal p olynomials, and another class defined on the unit circle. First, we lo ok at the connection b etween two sequences of L-orthogonal p olynomials {Q (0) n } and {Q (1) n } asso ciated with two strong p ositive measures dψ0 and dψ1 defined on [a,b] and related to each other by ( t −κ)dψ1 = γdψ0 , where ( t −κ)/γ is p ositive when t ∈(a,b). As applications of our study, numerical generation of new L-orthogonal p olynomials and monotonicity prop erties of the zeros of the p olynomials {Q (1) n }are lo oked at. Then, we consider the class of orthogonal Laurent p olynomials on the unit circle {2 Φ 1 (q− n ,qb+1 ; q− c +b− n ; q,q− c +d − 1 z)}∞ n=0 , defined from q-hyp ergeometric functions, where 0 < q < 1 and the complex parameters b,c and d are such that b ̸= −1,−2 ,..., c−b+ 1 ̸= −1,−2 ,..., Re( d) > 0 e Re(c−d+ 2) > 0. Several prop erties of these p olynomi-als are given, like explicit expressions for recurrence co efficients, moments, orthogonality and also asymptotics. By sp ecial choice of... (Complete abstract click electronic access below) / Doutor

Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2005 / With the growth of the personal computer industry, a number of households now contain two or more personal computers. The need to share resources such as printers, scanners and other PC peripherals has become evident. Communication between personal computers and other smart devices in the home is also required. This brings the emergence of home networking together with home automation. Home networking is the collection of elements to enable the connection and integration of multiple computing, control and communication devices. There are various options at this stage for home networking. One of the broadband options is indoor power line communication. The aim of the project was to evaluate a communication system capable of performing efficiently in South African Home Power line environment. In designing a communication system capable of performing in the harsh conditions which are presented in the home environment (noise, attenuation, phase distortion, etc.), a mathematical model that is representative of a typical suburban South African home power line is required. To aid the modeling process, an experimental network was constructed so measurements could be taken in a controlled environment. In conjunction with simulation, the model of the home power line network has aided the design of the data communication system. The project has involved: • Determining optimal specifications for the communication system. • Development of a home power line model representative of a typical South African suburban home environment. • Construction and measurement of an experimental power grid • Development of methods, algorithms and programs for the design of an OFDM PLC modem (in software) to optimal specifications. • Simulation development in MA1LAB of the OFDM Modem. • Comparison of different OFDM sub-modulation schemes for enhancing the communication system performance, In conclusion, the simulation model of the PLC modem correlates well with typical practical systems. Optimising throughput of the communication system and hardware development of the modem will form the basis for further research.

Orientadores: Dimitar Kolev Dimitrov, Roberto Andreani / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T03:16:09Z (GMT). No. of bitstreams: 1 Paschoa_VanessaGoncalves_D.pdf: 5593991 bytes, checksum: 19d08bd15df6ca11bb499a3d2de6db5d (MD5) Previous issue date: 2012 / Resumo: Neste trabalho estudamos o comportamento de zeros de polinômios ortogonais clássicos de variável discreta. Provamos que certas funções que envolvem os zeros dos polinômios de Charlier, Meixner, Kravchuck e Hahn são funções monótonas dos parâmetros dos quais os correspondentes polinômios dependem. Com esse resultado obtemos novos limitantes extremamente precisos para os zeros dessas famílias de polinômios em função dos zeros dos polinômios ortogonais clássicos, que são mais estudados. Analisamos quais são os melhores limitantes explícitos para os zeros desses polinômios e aplicamos aos nossos resultados, obtendo assim limitantes explícitos para os zeros dos polinômios de Charlier, Meixner, Kravchuck e Hahn. São feitas comparações entre os nossos resultados e os melhores resultados encontrados na literatura para os zeros desses polinômios e verifica-se que nossos limitantes são, em uma grande parte, melhores. Devido à sua grande aplicabilidade, um estudo ainda mais minucioso foi feito para os zeros dos polinômios de Gram, um caso particular de Hahn, que resultou em limitantes para os zeros dos polinômios de Gram. Experimentos numéricos comprovam a qualidade dos resultados / Abstract: In this thesis we study the behavior of zeros of classical orthogonal polynomials of discrete variable. We prove that certain functions which involve the zeros of polynomials of Charlier, Meixner, Kravchuck and Hahn are monotonic with respect to the parameters on which the polynomials depend. As a consequence of these results we obtain new extremely precise limits for the zeros of the above polynomials in terms of zeros of classical orthogonal polynomials of continuous variable which have been studied thoroughly. We analyze the best bounds for the latter zeros and apply them to obtain explicit limits for the zeros of the polynomials of Charlier, Meixner, Kravchuck and Hahn. Comparisons with the best results known in the literature show that our results are better in most of the cases. Due to its applications, we perform a very detailed study of the zeros of Gram polynomials / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

As the wireless communications networks expand, the number of both unwanted directional interferences and strong nearby sources increase, which degrade system performance. The signal-tointerference ratio (SIR) can be improved by using multiple nulls in the directions of the interferences while maintaining omnidirectional coverage in the direction of the network users. For the communication system considered, the interferences are static and their spatial positions are known. A non-adaptive antenna array is needed to provide spatial filtering in a static wireless environment. Omnidirectional arrays, such as cylindrical arrays, are the most suitable to provide the omnidirectional coverage and are capable of suppressing interferences when nulls are inserted in the radiation pattern. In this thesis, a cylindrical microstrip patch antenna array is investigated as an antenna to provide an omnidirectional radiation pattern with nulls at specified angular locations to suppress interference from directional sources. Three null synthesis methods are described and used to provide the omnidirectional array pattern with nulls using the radiation characteristics of the cylindrical microstrip patch antenna elements. The orthogonal projection method is extended to incorporate the directive radiation patterns of the cylindrical microstrip patch elements. Using this method, an optimal pattern that minimises the squared pattern error with respect to the ideal pattern is obtained. Instead of only minimising the array pattern error, a multi-objective optimisation approach is also followed. The objective weighting method is applied in null pattern synthesis to improve the amplitude pattern characteristics of the cylindrical patch arrays. As a third null synthesis technique, a constraint optimisation method is applied to obtain a constrained pattern with the desired amplitude pattern characteristics. The influence of the array attributes on the characteristics of the amplitude patterns obtained from the null synthesis methods, is also studied. In addition, the implementation of the cylindrical microstrip patch array is investigated. The influence of the mutual coupling on the characteristics of the null patterns of the cylindrical patch arrays is investigated utilising simulations and measurements. A mutual coupling compensation technique is used to provide matched and equal driving impedances for all the patch antenna elements given a required set of excitations. Test cases in which this technique is used, are discussed and the consequent improvements in the bandwidth and reflection coefficient of a linear patch arrays are shown. The characteristics of the resulting null pattern for the cylindrical microstrip patch array is also improved using the compensation technique. / Thesis (PhD (Electronic Engineering))--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / unrestricted

In this thesis, an antenna reduction technique in Multiple Input Multiple Output (MIMO) systems, which is called Code Shift Keying (CSK) Modulation, is introduced. With the use of Walsh Hadamard orthogonal spreading codes, we overcome the biggest drawback of conventional Spatial Modulation (SM) which is the antenna index estimation errors due to channel correlation. Also SM fails to perform in non normalised channel conditions. The combination of orthogonal spreading codes and antenna devices, as a means to convey information at the receiver, results in a remarkable performance improvement at the receiver.Moreover, an improved scheme that uses half the amount of spreading codes so as to represent the total number of information bits has been introduced leading to an important reduction in bandwidth usage. By maintaining the net spreading levels of the system we attain remarkable performance improvements.A technique called Polarisation Assisted Space Shift Keying Modulation (PASSK) has also been proposed which manages to exploit the polarisation domain and it is able to outperform the conventional SM technique as well as the Maximal Ratio Receiver Combine (MRRC) and Vertical-Bell Laboratories Layered Space-Time (V-BLAST) schemes. A new precoding scheme that manages to either eliminate or exploit the cross polarisation effects has also been proposed as a complementary study of the PASSK scheme.As modern and future communications show a rising demand for higher data transmission rates, network coding is increasingly incorporated in wireless communication standards. In harmonisation with this trend, this thesis discusses the main state-of-art network coding schemes. The contribution here includes a number of innovative schemes that are able to further increase throughput. Finally, the employment of network coding is discussed in conjunction with CSK Modulation resulting to further improvement in terms of throughput as well as Bit Error Rate (BER) performance at the cost of increased bandwidth usage.

Orientador: Alagacone Sri Ranga / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:37:15Z (GMT). No. of bitstreams: 1 Felix_HeronMartins_D.pdf: 783541 bytes, checksum: cea4459f391a5da7e61d9cff02244ec0 (MD5) Previous issue date: 2015 / Resumo: O objetivo do presente trabalho se divide em duas partes: na primeira, estudaremos uma regra de quadratura interpolatória sobre os zeros de polinômios núcleo obtidos a partir de uma sequência de polinômios L-ortogonais, oferecendo técnicas numéricas para a obtenção dos nós e pesos dessa regra de quadratura. Na segunda parte, forneceremos uma caracterização dos polinômios de Szegö em termos de duas sequências reais, dentre as quais uma é sequência encadeada. Tal caracterização afeta a relação entre os polinômios núcleo e os polinômios ortogonais no círculo unitário aos quais estes estão associados / Abstract: The main goal of the present work falls under two parts: firstly, we'll study a quadrature rule over the zeros of the kernel polynomials obtained from a sequence of L-orthogonal polynomials, offering numerical techniques for evaluating the nodes and weights of such quadrature rule. Secondly, we'll give a characterization for Szegö polynomials in terms of two real sequences, in which one is a chained sequence. Such characterization influences the connection between the kernel polynomials and the related orthogonal polynomials over the unit circle / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

In this thesis, we classify up to conjugacy the maximal elliptic toral subgroups of all special orthogonal groups SO(V), where (q,V) is a 4-dimensional quadratic space over a non-archimedean local field of odd residual characteristic. Our parameterization blends the abstract theory of Morris with a generalization of the practical work performed by Kim and Yu for Sp(4). Moreover, we compute an explicit Witt basis for each such torus, thereby enabling its concrete realization as a set of matrices embedded into the group. This work can be used explicitly to construct supercuspidal representations of SO(V).

In recent years, mentoring has emerged as a research domain, however, the preponderance of mentoring research has been situated first, in the business or organizational settings and second, in the K-12 educational setting, focusing on protégé experiences, using quantitative survey instruments to collect data. Thus, mentoring research literature includes a paucity of formal studies in the arena of graduate education. Situated in the higher education setting, this study investigated the perspectives of faculty-mentors who provided mentoring to doctoral students who completed the doctoral degree, employing the qualitative research methodology known as phenomenology, as an orthogonal but complimentary epistemology to previous quantitative studies. Located specifically in the College of Education of a large research university, the study asked 262 College of Education doctoral graduates to nominate College of Education faculty who provided mentoring to them during their degree pursuit. A total of 59 faculty were nominated as mentors. Six of the most frequently nominated mentors participated in two semi-structured interviews (Berg, 2004). The interviews addressed the mentor's experience of the mentoring endeavor, seeking to gather a description of their lived experience (Creswell, 1998) of mentoring and the meanings (Cohen & Omery, 1994) they garnered from it. The interviews yielded several shared perspectives on mentoring, including: a Gratifying Perspective, an Intentional Perspective, an Idiographic Perspective, a Teleological Perspective, and a Dynamic Perspective. Other noteworthy concepts that emerged from the mentors' data were: values, motivations, symbiotic relationship, and contextual negotiation. Implications for mentoring theory and practice as well as mentor development were described. The study contributed to development of a fuller phenomenological understanding of the perspectives of faculty-mentors in a mentoring relationship with doctoral students.