Latin-American guitarist-composers Ernesto Cordero, Leo Brouwer, and Sergio Assad are three of the most influential figures in the contemporary world of classical guitar. In addition to their important compositions for solo guitar, their compositions for guitar ensemble represent significant contributions to the concert repertory. These three guitarist-composers share a knowledge of popular, folkloric and classical music and demonstrate a commitment to bridging these realms in their compositions in the classical tradition. This study reviews the history of the guitar quartet. It then examines the different cultural influences in selected compositions for classical guitar quartet by each composer, exploring the significance of these choices for the performer and for the medium. The document also offers a performer’s guide for accurate and stylistic performance. When performed well, these quartets represent the vitality of contemporary Latin American composition and confirm the stature of the guitar quartet as a compelling medium for the concert artist.

Neste trabalho demonstram-se os teoremas de ponto fixo de Brouwer e Kakutani com o objetivo de provar a existência do equilíbrio de Nash em jogos finitos em forma normal. No primeiro capítulo apresentam-se as definições de teoria dos jogos, começando com jogos finitos em forma normal e terminando com o conceito de equilíbrio de Nash. Na primeira seção do capítulo dois desenvolve-se a teoria de simplexes, em Rn, e se demonstra o teorema de Brouwer. Na seção seguinte, são relacionadas as propriedades de semi-continuidade superior e gráfico fechado em set functions, para então provar os teoremas de Celina e von Neumann que, em conjunto com o teorema de Brouwer, resultam no teorema de Kakutani no fim da seção. Como último resultado é demonstrado o teorema de existência do equilíbrio de Nash em jogos finitos em forma normal através do teorema de Kakutani, mostrando que o equilíbrio de Nash é um ponto fixo de uma set function. / In this work, the fixed-point theorems of Kakutani and Brouwer are proved with the intention of showing the existence of Nash equilibrium in finite normal-form games. In the first chapter the needed definitions of game theory are shown, starting with finite normal-form games and ending with the concept of Nash equilibrium. In the first section of chapter two, simplex theory in Rn is developed and then the Brouwer fixer point theorem is proved. In the next section, some relations of upper hemi-continuity and closed graph in set functions are shown, then proving the theorems of Celina and von Neumann that, along with Brouwer theorem, result in Kakutani fixed-point theorem in the end of the section. As the last result, the existence of Nash equilibrium in finite normal-form games is proved through Kakutani’s theorem, relating the Nash equilibrium to the fixed-point of a set function.

This study examines phrase and larger formal structures in the first movement of Leo Brouwer’s Elegio de la Danza (1964), a work that draws on tonal and post-tonal traditions. By adapting key features of the tonal motive, as described by Douglass Green, and the tonal period, as proposed by Green and William Caplin, the model seeks to provide a tool for the discussion of phrases and larger forms in Brouwer’s work. An analysis of primary parameters, such as melody, harmony, and rhythm, provides the means to discuss how the composer articulates beginnings and endings of statements and responses, which are then grouped into antecedent and consequent phrases. These periods articulate large-scale sections, which outline a ternary formal design. Secondary parameters (dynamics, tempo markings, instrumental markings) further contribute to the identification of formal structures in Brouwer’s work.

The Laplacian energy of a graph is the sum of the distances of the eigenvalues of the Laplacian matrix of the graph to the graph's average degree. The maximum Laplacian energy over all graphs on n nodes and m edges is conjectured to be attained for threshold graphs. We prove the conjecture to hold for graphs with the property that for each k there is a threshold graph on the same number of nodes and edges whose sum of the k largest Laplacian eigenvalues exceeds that of the k largest Laplacian eigenvalues of the graph. We call such graphs spectrally threshold dominated. These graphs include split graphs and cographs and spectral threshold dominance is preserved by disjoint unions and taking complements. We conjecture that all graphs are spectrally threshold dominated. This conjecture turns out to be equivalent to Brouwer's conjecture concerning a bound on the sum of the k largest Laplacian eigenvalues.

Neste trabalho demonstram-se os teoremas de ponto fixo de Brouwer e Kakutani com o objetivo de provar a existência do equilíbrio de Nash em jogos finitos em forma normal. No primeiro capítulo apresentam-se as definições de teoria dos jogos, começando com jogos finitos em forma normal e terminando com o conceito de equilíbrio de Nash. Na primeira seção do capítulo dois desenvolve-se a teoria de simplexes, em Rn, e se demonstra o teorema de Brouwer. Na seção seguinte, são relacionadas as propriedades de semi-continuidade superior e gráfico fechado em set functions, para então provar os teoremas de Celina e von Neumann que, em conjunto com o teorema de Brouwer, resultam no teorema de Kakutani no fim da seção. Como último resultado é demonstrado o teorema de existência do equilíbrio de Nash em jogos finitos em forma normal através do teorema de Kakutani, mostrando que o equilíbrio de Nash é um ponto fixo de uma set function. / In this work, the fixed-point theorems of Kakutani and Brouwer are proved with the intention of showing the existence of Nash equilibrium in finite normal-form games. In the first chapter the needed definitions of game theory are shown, starting with finite normal-form games and ending with the concept of Nash equilibrium. In the first section of chapter two, simplex theory in Rn is developed and then the Brouwer fixer point theorem is proved. In the next section, some relations of upper hemi-continuity and closed graph in set functions are shown, then proving the theorems of Celina and von Neumann that, along with Brouwer theorem, result in Kakutani fixed-point theorem in the end of the section. As the last result, the existence of Nash equilibrium in finite normal-form games is proved through Kakutani’s theorem, relating the Nash equilibrium to the fixed-point of a set function.

Submitted by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-10-17T15:52:46Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação Valdenildo Alves de Araújo.PDF: 2285927 bytes, checksum: d9b15f3d010205d5d0cac3514733f5d8 (MD5) / Approved for entry into archive by Divisão de Documentação/BC Biblioteca Central (ddbc@ufam.edu.br) on 2018-10-17T15:53:00Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação Valdenildo Alves de Araújo.PDF: 2285927 bytes, checksum: d9b15f3d010205d5d0cac3514733f5d8 (MD5) / Made available in DSpace on 2018-10-17T15:53:00Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação Valdenildo Alves de Araújo.PDF: 2285927 bytes, checksum: d9b15f3d010205d5d0cac3514733f5d8 (MD5) Previous issue date: 2012-12-04 / This work has as aim to demosntrate two classical results from the Fixed Point Theory, namely the theorems of Brouwer and Schauder-Tychonoff, to present some recent progress in this reseach line, as well as to explore some of its applications. / Este trabalho tem por objetivos demonstrar dois resultados da Teoria dos Pontos Fixos, a saber os teoremas de Brouwer e Schauder-Tychonoff, apresentar alguns recentes progressos na linha de pesquisa bem como explorar algumas de suas aplicações

Die Kubaanse komponis Leo Brouwer (1939- ) het ʼn unieke idiomatiek vir die kitaar ontwikkel wat met die eerste oogopslag ingewikkeld lyk (en klink), maar steeds logies is en gemaklik onder die vingers lê. In hierdie mini-verhandeling word Brouwer in konteks geplaas met ontwikkelings in Kuba. Biografiese agtergrond van sy lewe word verskaf, en sy werke word in drie komposisiefases verdeel. Elke komposisiefase word afsonderlik bespreek met fokus op die volgende solo kitaarwerke: <ul> <li>Danza Caracteristica (1972)</li> <li>Elogio de la Danza (1964)</li> <li>10 Etudes Simples (1973)</li> <li>Canticuum (1968)</li> <li>La Espiral Eterna (1971)</li> <li>El Decameron Negro (1982)</li> <li>Paisaje Cubano con Campañas (1987)</li> <li>Sonata (1990)</li></ul> Hierdie werke word bespreek meestal in terme van komposisietegnieke en notasie. Aspekte wat Brouwer se idiomatiek verduidelik word uitgelig en die toeganklikheid van die werke word krities geëvalueer. Brouwer se groei en ontwikkeling as komponis word uitgewys, en sy invloed op hedendaagse komponiste en kitaarspelers word bespreek. Daar word bevind dat die idiomatiek in Brouwer se geselekteerde solo kitaarwerke ʼn dominante rol speel in sy benadering tot kitaarkomposisie. Die studie is veral vir kitaarkomponiste van waarde om sinvolle komposisie-besluite te kan maak. ENGLISH : The Cuban composer Leo Brouwer (1939- ) developed an idiomatic writing style for the classical guitar which is an important factor when the difficult technical requirements of the guitar are taken into consideration. This idiomatic writing style might seem (and sound) complex at first glance, but is in fact logical and easily accessible on the instrument. In this mini-dissertation Brouwer is placed in context with political and artistic development in Cuba. Biographical background of his life is given, and his works are divided into three compositional periods. Each period is discussed separately with the focus on the following solo guitar works: <ul> <li>Danza Caracteristica (1972)</li> <li>Elogio de la Danza (1964)</li> <li>10 Etudes Simples (1973)</li> <li>Canticuum (1968)</li> <li>La Espiral Eterna (1971)</li> <li>El Decameron Negro (1982)</li> <li>Paisaje Cubano con Campañas (1987)</li> <li>Sonata (1990)</li> </ul> These solo guitar works is discussed mostly in terms of compositional techniques and notation. Aspects that describe Brouwer’s idiomatic writing style are emphasised, and the accessibility of the works is critically evaluated. Brouwer’s development as a composer is highlighted, and his influence on guitar composers and guitarists is discussed. As a conclusion it is shown that the idiomatic writing style of Brouwer plays a leading role in his approach to solo guitar composition. The study is of value to guitar composers when sensible compositional decisions have to be made. / Dissertation (MMus)--University of Pretoria, 2012. / Music / unrestricted

This thesis presents extended program notes for a recorded graduate classical guitar recital consisting of the following works for solo guitar with string quartet and chamber orchestra: Mario Castelnuovo-Tedesco: Quintet for Guitar and Strings, Op. 143; Leo Brouwer: Concerto No. 3 (“Elegiaco”). Both works are pioneering and invaluable contributions to guitar literature. Tedesco’s Quintet for Guitar and Strings, Op. 143 is the first quintet ever composed to properly showcase the virtuosity of the guitar within a chamber setting. Concerto “Elegiaco” demonstrates the refinement of Leo Brouwer’s use of post-modern tonality and minimalism within classical form, and showcases his unique compositional style.

This study examines phrase and larger formal structures in the first movement of Leo Brouwer’s Elegio de la Danza (1964), a work that draws on tonal and post-tonal traditions. By adapting key features of the tonal motive, as described by Douglass Green, and the tonal period, as proposed by Green and William Caplin, the model seeks to provide a tool for the discussion of phrases and larger forms in Brouwer’s work. An analysis of primary parameters, such as melody, harmony, and rhythm, provides the means to discuss how the composer articulates beginnings and endings of statements and responses, which are then grouped into antecedent and consequent phrases. These periods articulate large-scale sections, which outline a ternary formal design. Secondary parameters (dynamics, tempo markings, instrumental markings) further contribute to the identification of formal structures in Brouwer’s work.

The Laplacian energy of a graph is the sum of the distances of the eigenvalues of the Laplacian matrix of the graph to the graph's average degree. The maximum Laplacian energy over all graphs on n nodes and m edges is conjectured to be attained for threshold graphs. We prove the conjecture to hold for graphs with the property that for each k there is a threshold graph on the same number of nodes and edges whose sum of the k largest Laplacian eigenvalues exceeds that of the k largest Laplacian eigenvalues of the graph. We call such graphs spectrally threshold dominated. These graphs include split graphs and cographs and spectral threshold dominance is preserved by disjoint unions and taking complements. We conjecture that all graphs are spectrally threshold dominated. This conjecture turns out to be equivalent to Brouwer's conjecture concerning a bound on the sum of the k largest Laplacian eigenvalues.