An investigation of information loss in black hole spacetimes is performed. We demon- strate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the ra- diation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schr ̈dinger picture. o We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric space- time with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a self- similarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.

An investigation of information loss in black hole spacetimes is performed. We demon- strate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the ra- diation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schr ̈dinger picture. o We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric space- time with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a self- similarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.

Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 222-230). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (M.A.)--Memorial University of Newfoundland, 1996. / Typescript. Bibliography: leaves 136-139. Also available online.

Thesis (Ph. D.)--University of California, Santa Cruz, 1992. / Typescript. Includes bibliographical references (leaves 236-258).

Made available in DSpace on 2014-06-11T19:30:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2013-01-28Bitstream added on 2014-06-13T19:40:05Z : No. of bitstreams: 1 nunes_rso_dr_sjrp_parcial.pdf: 159616 bytes, checksum: e530de9f87ecb29201522bba4142a965 (MD5) / Neste trabalho resolvemos o problema de controlabilidade exata na fronteira para a equação linear de Klein-Gordon em domínios limitadosΩ deR N , N≥2, com fronteira suave por partes e sem cuspides. Para dados iniciais emH 1 (Ω)×L 2 (Ω) obtemos controle do tipo Neuman, de quadrado integr´avel, atuando em toda a fronteira do domínio em tempo próximo ao diâmetro de Ω. Inicialmente provamos que a energia da solução do problema de Cauchy para a referida equação decai localmente numa taxa polinomial. Em seguida, estendendo a solução do problema de Cauchy para tempo complexo provamos que o operador solução associado ao problema de Cauchy é analítico num setor adequado do plano complexo. Utilizando o decaimento de energia, a analitidade do operador solução e argumentos introduzidos por D. L. Russell e J. Lagnese nos anos setenta do século passado obtemos o resultado desejado / In this work we solve the problem of exact controllability on the boundary for the linear Klein-Gordon equation in limited domains ΩofR N , N≥2, with piecewise smooth boundary without cusps. For initial data inH 1 (Ω)×L 2 (Ω)we get square integrable control of Neuman type, acting on the entire boundary, in a time near the diameter ofΩ. Initially we prove that the energy of the solution of the Cauchy problem for this equation locally decays at a polynomial rate. Then extending the solution of the Cauchy problem for complex time we prove that the solution operator associated with the Cauchy problem is analytic in a suitable sector of the complex plane. Using the local decay of energy, the analiticity of the solution operator and arguments introduced by D. L. Russell and J. Lagnese in the seventies we obtain the desired result

The main focus of my dissertation is the Modified Stochastic Sine-Gordon Equation: utt = 2uxx − ut − sin(|u|^(&gamma)) + b(u, du/dt)dW/dt where &gamma > 0 is the parameter of the power of non-linearity, &delta &ge 0 is the magnitude of non-linearity, &alpha> 0 be the damping parameter, and &sigma the diffusion intensity, on one dimensional domain. We analyze the properties of the solution of the SPDE by the eigenfunctions approach allowing us to truncate the infinite-dimensional stochastic system (i.e the SDEs of Fourier coefficients related to the SPDE), to control its energy, existence, uniqueness, continuity and stability. The analysis relies on the investigation of expected Lyapunov functional of the energy in terms of all system-parameters. We simulate the model with respect to all system-parameters to visualize our conclusions.

Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-23T20:38:51Z No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:35:27Z (GMT) No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:35:33Z (GMT) No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5) / Made available in DSpace on 2016-09-26T20:35:40Z (GMT). No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5) Previous issue date: 2016-02-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients. / Nesta tese estudamos as propriedades assintóticas para a solução do problema de Cauchy para a equação de Klein-Gordon com potencial não efetivo dependente do tempo. O principal objetivo foi definir uma energia adequada relacionada ao problema de Cauchy e derivar estimativas para tal energia. Estimativas de Strichartz e resultados de scatering e scatering modificados também foram estabelecidos. A teoria C m e a condição de estabilização foram aplicados para tratar o caso em que o coeficiente da massa oscila muito rápido. Além disso, consideramos um mod- elo de onda semi-linear scale-invariante com massa e dissipação dependentes do tempo, nesta etapa usamos as estimativas lineares de tal modelo para provar ex- istência global (no tempo) de solução de energia para dados iniciais suficientemente pequenos e demonstramos um resultado de blow-up para uma escolha adequada dos coeficientes.

This thesis presents extended program notes for a sixty–minute vocal graduate recital consisting of the following repertoire for soprano: the arias “Soffri, o cor” and “Dimmi qual prova mai” from Alessandro Scarlatti’s cantata Dal Bel Volto d’Irene; a role study of Zerlina from Wolfgang Amadeus Mozart’s opera Don Giovanni, including her arias “Batti, batti, o bel Masetto” and “Vedrai, carino;” Francis Poulenc’s song cycle Cocardes; selections from Arnold Schoenberg’s song cycle Das Buch der Hängenden Gärten; “Der Hirt auf dem Felsen” by Franz Schubert, a chamber work written for soprano, piano, and clarinet; and selections from American composer Ricky Ian Gordon’s song cycle Orpheus and Euridice, composed as a companion piece to the Schubert “Der Hirt auf dem Felsen.” These works span three centuries and cover four languages and multiple genres and musical styles. The content of this thesis contains detailed information on these works through historical study, musical analysis, and research in performance practice.

The first purpose of this study was to investigate whether different modeling conditions (Aural and Aural/Notated Transcription) produced significant differences for improvisation achievement. Another purpose was to investigate whether music learning theory-based improvisation instruction had an effect on students' self-efficacy for improvisation and for instrumental music. Participants (N = 76) from an accessible population of 6th through 8th grade instrumental music students were assigned to either an aural model group or an aural and notated transcription model group based on scores from Gordon's Harmonic and Rhythmic Readiness Records (1998). All students were administered two researcher-designed self-efficacy scales before and after a 10 treatment session music learning theory-based improvisation instruction. Following the treatment sessions, each participant was individually recorded and assessed by three experienced music educators. The posttest improvisation scores were subjected to an ANOVA, while the pretest to posttest scores of the students' self-efficacies for music improvisation and instrumental music were subjected to two repeated measures ANOVAs. The Bonferroni technique was used to adjust the alpha level from .05 to .017. The statistical analysis showed that there was no significant difference in improvisation achievement for the modeling conditions of aural and aural/notated transcription. Further statistical analyses showed there were significant increases in students' self-efficacy for improvising and for instrumental music following improvisation instruction. This study's results suggest that music educators should consider using either modeling technique for improvisation learning experiences. Results also suggest that music educators may wish to consider using a music learning theory-based improvisation approach to facilitate greater confidence in improvising. Additionally, results suggest that classroom music educators may wish to consider improvisation instruction as a means for achieving greater student confidence in instrumental music. This study concludes with issues for further study.