Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 332–350, July–September, 2006.

Thesis (doctoral)--Technische Hogeschool Eindhoven, 1983. / Text in English ; summary and vita in Dutch. Includes indexes. Vita. Includes bibliographical references (p. 190-193).

Made available in DSpace on 2014-06-11T19:35:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-11-29Bitstream added on 2014-06-13T20:07:23Z : No. of bitstreams: 1 nacbar_dr_dr_bauru.pdf: 2409511 bytes, checksum: d8b3b66a4b3545e4d5be6d90dfe9abd1 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / São calculadas e analisadas funções de Wannier de elétrons num potencial periódico com ênfase nas funções de Wannier generalizadas de máxima localização. A máxima localização das funções calculadas é a sua propriedade mais relevente para as aplicações em Ciência dos Materiais. Inicialmente, é apresentado um procedimento analítico para calcular funções de Wannier generalizadas de localização máxima de cristais unidimensionais com simetria de inversão. O método consiste em combinar linearmente as funções de Bloch de duas bandas consecutivas com o intuito de se obter quase funções de Bloch. As funções de Wannier generalizadas são obtidas através do valor médio das quase funções de Bloch sobre a primeira zona de Brillouin. São apresentados resultados analíticos e numéricos para um modelo diatômico do tipo Kroning-Penney. A fim de verificar os resultados analíticos, são apresentados também os resultados numéricos conseguidos através do operador de posição projetado nas bandas consideradas. Posteriormente, funções de Wannier de localização máxima de super-redes diatômicas com simetria de inversão são calculadas e analisadas e analisadas. As funções de Wannier de cada banda são obtidas mediante a classificação das bandas de energia segundo a simetria das funções de Bloch nos pontos de simetria do cristal. Investiga-se também como a largura de uma das camadas da super-rede na classificação das bandas de energia e na escolha apropriada da fase das funções de Bloch. As funções de Wannier de bandas simples são comparadas com as funções de Wannier generalizadas, e suas relações com orbitais moleculares e atômicos são discutidas. Finalmente, são apresentadas expressões concisas e gerais que permitem obter funções de Wannier de localização máxima de elétrons em sistemas com... / The Wannier functions of an electron in a periodic potential are investigated, with emphasis on the generalized Wannier functions of maximal localization. The maximal localization of the calculated functions is their most important property for applications in Materials Science. We first present and analytical procedure to calculate maximally localized generalized Wannier functions in one-dimensional crystals with inversion symmetry. The method consists in linearly combiniting of Bloch functions of two consecutive bands, in order to obtain quasi-Bloch functions. The generalized Wannier functions are obtained by the mean value of quasi-Bloch functions over the first brillouim zone. We present analytical and numerical results for the a diatomic Kroning-Penney model. In order to verify the analytical results, we also present numerical results obtained using the method of the band-projected position operator. Then, maximally localized Wannier functions of diatomic superlattices with inversion symmetry are calculated and analyzed. Wannier functions of each band are obtained by classifying the energy bands according to the symmetry of the Bloch functions at the symmetry points of the crystal. It is also investigated how the width of one of the layers of the superlattice influences the energy-band classification and the appropriate phase choise for the Bloch functions. We compare the Wannier functions of simple bands with generalized Wannier functions, and discuss their relations with molecular-like and atomic-like orbitals. Finally, we present concise and general expressions for the calculation of maximally localized Wannier functions in systems presenting different types of dimensionality and periodicity. For the cases... (Complete abstract click electronic access below)

Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-19Bitstream added on 2014-06-13T20:27:27Z : No. of bitstreams: 1 lima_maf_me_sjrp.pdf: 528569 bytes, checksum: 3cad2d8f7175d945b2ead7fb45a5c4e1 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O principal objetivo deste trabalho é estudar métodos para construir os numeradores e denominadores parciais da fração contínua que corresponde a duas expansões em série de potências de uma função analítica f(z); em z =0 e em z = 00. / The main purpose of this work is to two series expansions of an analytic function f(z); in z =0 and z =00 simultaneously. Furthermore we considered the case when there are zero coefficients in the series and also whwn there is symmetry in the coefficients of the two series. Some examples are given.

We study certain confluences of equations with two Fuchsian singularities which produce an irregular singularity of Poincaré rank one. We demonstrate a method to understand how to pass from solutions with power-like behavior which are analytic in neighbourhoods to solutions with exponential behavior which are analytic in sectors and have divergent asymptotic behavior. We explicitly calculate the Stokes' matrices of the confluent system in terms of the monodromy data, specifically the connection matrices, of the original system around the merging singularities. The confluence of Gauss' hypergeometric equation gives an excellent opportunity to show our approach with a concrete example. We explicitly show how the Stokes' data arise in the confluences of the isomonodromic deformation problems for the Painlevé equations PVI to PV and PV to PIII(D6).

Orientador: Alexys Bruno Alfonso / Banca: Ricardo Wagner Nunes / Banca: Jeverson Teodoro Arantes Junior / Banca: Julio Ricardo Sambrano / Banca: Andre Luiz Malvezzi / Resumo: São calculadas e analisadas funções de Wannier de elétrons num potencial periódico com ênfase nas funções de Wannier generalizadas de máxima localização. A máxima localização das funções calculadas é a sua propriedade mais relevente para as aplicações em Ciência dos Materiais. Inicialmente, é apresentado um procedimento analítico para calcular funções de Wannier generalizadas de localização máxima de cristais unidimensionais com simetria de inversão. O método consiste em combinar linearmente as funções de Bloch de duas bandas consecutivas com o intuito de se obter quase funções de Bloch. As funções de Wannier generalizadas são obtidas através do valor médio das quase funções de Bloch sobre a primeira zona de Brillouin. São apresentados resultados analíticos e numéricos para um modelo diatômico do tipo Kroning-Penney. A fim de verificar os resultados analíticos, são apresentados também os resultados numéricos conseguidos através do operador de posição projetado nas bandas consideradas. Posteriormente, funções de Wannier de localização máxima de super-redes diatômicas com simetria de inversão são calculadas e analisadas e analisadas. As funções de Wannier de cada banda são obtidas mediante a classificação das bandas de energia segundo a simetria das funções de Bloch nos pontos de simetria do cristal. Investiga-se também como a largura de uma das camadas da super-rede na classificação das bandas de energia e na escolha apropriada da fase das funções de Bloch. As funções de Wannier de bandas simples são comparadas com as funções de Wannier generalizadas, e suas relações com orbitais moleculares e atômicos são discutidas. Finalmente, são apresentadas expressões concisas e gerais que permitem obter funções de Wannier de localização máxima de elétrons em sistemas com... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The Wannier functions of an electron in a periodic potential are investigated, with emphasis on the generalized Wannier functions of maximal localization. The maximal localization of the calculated functions is their most important property for applications in Materials Science. We first present and analytical procedure to calculate maximally localized generalized Wannier functions in one-dimensional crystals with inversion symmetry. The method consists in linearly combiniting of Bloch functions of two consecutive bands, in order to obtain quasi-Bloch functions. The generalized Wannier functions are obtained by the mean value of quasi-Bloch functions over the first brillouim zone. We present analytical and numerical results for the a diatomic Kroning-Penney model. In order to verify the analytical results, we also present numerical results obtained using the method of the band-projected position operator. Then, maximally localized Wannier functions of diatomic superlattices with inversion symmetry are calculated and analyzed. Wannier functions of each band are obtained by classifying the energy bands according to the symmetry of the Bloch functions at the symmetry points of the crystal. It is also investigated how the width of one of the layers of the superlattice influences the energy-band classification and the appropriate phase choise for the Bloch functions. We compare the Wannier functions of simple bands with generalized Wannier functions, and discuss their relations with molecular-like and atomic-like orbitals. Finally, we present concise and general expressions for the calculation of maximally localized Wannier functions in systems presenting different types of dimensionality and periodicity. For the cases... (Complete abstract click electronic access below) / Doutor

Orientador: Jorge Tulio Mujica Ascui / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação / Made available in DSpace on 2018-08-04T04:15:50Z (GMT). No. of bitstreams: 1 Bertoloto_FabioJose_M.pdf: 1324259 bytes, checksum: f7fd3d37bfe8d06ad156b30761402bfe (MD5) Previous issue date: 2005 / Resumo: O principal objetivo deste trabalho é o estudo de certos espaços de Banach de funções analíticas no disco aberto unitário, conhecidos como espaços de Hardy. Um outro objetivo é o estudo das propriedades básicas de álgebras de Banach, com especial ênfase na álgebra do disco e na álgebra das funções analíticas e limitadas no disco aberto unitário / Abstract: The main objective of this work is the study of certain Banach spaces of analytic functions on the open unit disc, known as Hardy spaces. Another objective is the study of the basic properties of Banach algebras, with special emphasis in the disc algebra and the algebra of bounded analytic functions in the open unit disc / Mestrado / Matematica / Mestre em Matemática

We wish to study those domains in Cn,for n ≥ 2, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study is radically different from that of domains in C by discussing some examples of special types of domains in Cn , n ≥2, such that every function holomorphic on them extends to strictly larger domains. Given a domain in Cn , n ≥ 2, we wish to construct the maximal domain of existence for the holomorphic functions defined on the given domain. This leads to Thullen’s construction of a domain (not necessarily in Cn)spread overCn, the so-called envelope of holomorphy, which fulfills our criteria. Unfortunately this turns out to beavery abstract space, far from giving us sense in general howa domain sitting in Cn can be constructed which is strictly larger than the given domain and such that all the holomorphic functions defined on the given domain extend to it. But with the help of this abstract approach we can give a characterization of the domains of holomorphyin Cn , n ≥ 2. The aforementioned characterization is as follows: adomain in Cn is a domain of holomorphy if and only if it is holomorphically convex. However, holomorphic convexity is a very difficult property to check. This calls for other (equivalent) criteria for a domain in Cn , n ≥ 2, to be a domain of holomorphy. We survey these criteria. The proof of the equivalence of several of these criteria are very technical – requiring methods coming from partial differential equations. We provide those proofs that rely on the first part of our survey: namely, on analytic continuation theorems. If a domain Ω Cn , n ≥ 2, is not a domain of holomorphy, we would still like to explicitly describe a domain strictly larger than Ω to which all functions holomorphic on Ω continue analytically. Aspects of Thullen’s approach are also useful in the quest to construct an explicit strictly larger domain in Cn with the property stated above. The tool used most often in such constructions s called “Kontinuitatssatz”. It has been invoked, without a clear statement, in many works on analytic continuation. The basic (unstated) principle that seems to be in use in these works appears to be a folk theorem. We provide a precise statement of this folk Kontinuitatssatz and give a proof of it.

In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.

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