Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

Emergy-based sustainability assessment of different energy options for green buildings

It is necessary to minimize the environmental impact and utilize natural resources in a sustainable and efficient manner in the early design stage of developing an environmentally-conscious design for a heating, ventilating and air-conditioning system. Energy supply options play a significant role in the total environmental load of heating, ventilating and air-conditioning systems. To assess the environmental impact of different energy options, a new method based on Emergy Analysis is proposed. Emergy Accounting, was first developed and widely used in the area of ecological engineering, but this is the first time it has been used in building service engineering. The environmental impacts due to the energy options are divided into four categories under the Emergy Framework: the depletion of natural resources, the greenhouse effect (carbon dioxide equivalents), the chemical rain effect (sulphur dioxide equivalents), and anthropogenic heat release. The depletion of non-renewable natural resources is indicated by the Environmental Load Ratio, and the environmental carrying capacity is developed to represent the environmental service to dilute the pollutants and anthropogenic heat released. This Emergy evaluation method provides a new way to integrate different environmental impacts under the same framework and thus facilitates better system choices. A case study of six different kinds of energy options consisting of renewable and non-renewable energy was performed by using Emergy Theory, and thus their relative environmental impacts were compared. The results show that the method of electricity generation in energy sources, especially for electricity-powered systems, is the most important factor to determine their overall environmental performance. The direct-fired lithium-bromide absorption type consumes more non-renewable energy, and contributes more to the urban heat island effect compared with other options having the same electricity supply. Using Emergy Analysis, designers and clients can make better-informed, environmentally-conscious selections of heating, ventilating and air-conditioning systems.

On aposteriori error analysis of dG schemes approximating hyperbolic conservation laws

This contribution is concerned with aposteriori error analysis of discontinuous Galerkin (dG) schemes approximating hyperbolic conservation laws. In the scalar case the aposteriori analysis is based on the L1 contraction property and the doubling of variables technique. In the system case the appropriate stability framework is in L2, based on relative entropies. It is only applicable if one of the solutions, which are compared to each other, is Lipschitz. For dG schemes approximating hyperbolic conservation laws neither the entropy solution nor the numerical solution need to be Lipschitz. We explain how this obstacle can be overcome using a reconstruction approach which leads to an aposteriori error estimate.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.

Solar Collectors for Historic Homes : Linking consumption to perceptions of space

Reduction of household energy consumption is one of the top issues in contemporary discussions on sustainable consumption. This chapter concerns one way through which consumption of purchased energy for house heating can be reduced; by having a solar thermal system added to one's house. However, the fact that one of the components - the solar collector - usually is situated on the roof or the facade of a building, is a recurrent impediment to such installations. In certain contexts, these attributes may melt into the building, while in others, they may be perceived as problematic. The latter may particularly be the case when the appearance of the building is of major imiportance, as with houses deemed worthy of preservation for coming generations. This chapter draws upon a study carried out in Visby Town, a walled Hanseatic town and a World Heritage site on the island of Gotland, Sweden.

Carl Maria von Weber’s Overture to Oberon: A History of Recorded Performance

My research examines the recorded performance history of the Overture to Weber’s Oberon in light of these aesthetic goals. I have charted changes in performance practice trends, including in timing, tempo fluctuation, rhythmic accuracy and ensemble, and the use of portamento. The twenty recordings studied that I surveyed span nearly seventy-five years, and include many of the 20th century’s most prominent conductors and orchestras, including groups from Communist Russia, both pre-World War II and post-World War II continental Europe, the British Isles, and the United States.8 Though by no means comprehensive, my selections encompass a diverse sampling of surviving recordings, ensuring a large enough sample size to reflect general trends in the performance of Weber’s masterpiece. My research and analysis confirms the conventional view of a move toward more accurate—but also more cautious, uniform, and inexpressive— performances. Surprisingly, however, this analysis also suggests that we are on the cusp of a new era in orchestra performance practice, one that shares many of the values of the earlier recorded performances. While maintaining today’s high standards of execution, modern performances now look to regain many of the past’s expressive qualities, doing so in sometimes surprising ways.

Verdi's Settings of Shakespeare : from Play to Liberetto to Opera

As a Senior Scholar pursuing the topic, Verdi's Settings of Shakespeare: From Play to Libretto to Opera, I have endeavoured to study a project relevant to my majors, Music and English. During first semester, I carefully analysed Shakespeare's plays, Macbeth, Othello and Falstaff. The highlight of my project was in January when I travelled to New York City and spent the day working with the Metropolitan Opera Guild. I was also able to see a performance of Verdi's Othello with Jon Vickers in the lead role. During the second semester, I studied the musical aspects of the compositions. I spent time analysing musical passages and relating them to the plays and the operas. I was also able to continue my study of Italian, which I find extremely beneficial while studying Verdi's libretti. On Monday, 13th May, 1974, I gave a lecture presentation of my project. At this time, I showed slides of Metropolitan productions of the operas, presented my own rendition of five arias (in costume) and talked about comparisions between the plays and the operas. I applied for a Rotary Fellowship to take my project to Europe and am presently waiting to hear the results. If I do receive the fellowship, I am planning to spend a year studying the plays and operas in England and Italy. Afterwards, I hope to publish a paper explaining my findings. The paper is divided into six sections. The first section is an introduction which explains the period of Romanticism and its relationship to Shakespeare and Verdi. The second section is devoted to discussing the librettist for Macbeth, Francesco Piave. Following this section the opera Macbeth is discussed. Arrigo Boito, the librettist for Otello and Falstaff is discussed in the fourth section. The last two sections deal with Otello and Falstaff. I have also included a number of musical selections to better explain certain passages. My project has been invaluable to me. My Senior Scholar project has allowed me the freedom of independent study as well as a means of tying my majors together.

A representação de música brasileira nos livros didáticos de música

O presente trabalho de pesquisa teve como objetivo analisar de que forma a música brasileira é representada nos livros didáticos de música direcionados para a escola do Ensino Básico e produzidos no Brasil nas décadas de 60 e 70. A escolha desse período é justificada por ser nessas décadas que a música brasileira é apresentada como conteúdo nos livros didáticos de forma mais acentuada do que em outros períodos. Tendo como referencial teórico-metodológico o conceito de representação de R. Chartier, o estudo procurou abarcar as concepções explícitas e implícitas, relativo a idéias, valores e intenções que perpassam nos textos e imagens, permitindo compreender o porquê de certas escolhas referentes a determinados conteúdos, em detrimento de outros, da forma como são abordados nos livros didáticos, bem como identificar os cânones eleitos para representar estilos, gêneros musicais, compositores, obras e épocas da música brasileira.

Resiliência - um estudo exploratório da percepção de gestores sobre o constructo, nas dimensões humana e organizacional

Afinal, o que os gestores entendem por resiliência? É o questionamento que pautou este estudo e para respondê-lo desenvolvemos uma pesquisa empírica com 17 gestores de empresas de diversos portes, aqui no Rio de Janeiro, por meio de entrevista semi-estruturada, realizada durante os meses de janeiro a junho de 2015. As respostas colhidas foram submetidas à Análise do Discurso posibilitando identificar na prática discursiva, figuras de linguagem, ethos do entrevistado, seleção lexical predominante, intertextualidade e temas de fundo, e relacioná-los aos elementos do corpus discursivo acadêmico, o que permitiu a constituição das categorias analíticas sobre: resiliência humana e resiliência organizacional. A análise concluiu que, para os gestores, embora o conceito de resiliência humana ainda seja influenciado pelos conceitos de elasticidade e invulnerabilidade, que informaram a construção do conceito de resiliência nos estudos iniciais no campo da Psicologia, a resiliência é um processo dinâmico cujo resultado é a adaptação bem sucedida e a transformação do indivíduo. A resiliência organizacional é personificada na resiliência dos indivíduos, especificamente, na dos gestores cujos comportamentos, individuais e coletivos, contribuem ou impedem a resiliência organizacional, com destaque para a revelação a respeito de como a resiliência influencia o processo de tomada de decisão, tanto por sua presença como por sua ausência. Este estudo é relevante na medida que suas revelações consubstanciam implicações para a academia e para as empresas. Para a academia a influência da resiliência no processo decisório sinaliza um denominador comum diante do qual as pesquisas acadêmicas podem partir, viabilizando a elaboração de proposições epistemológicas, metodológicas e praxiólogicas que ampliem, de forma realista, as possibilidades de acesso, por indivíduos e organizações, de um repertório de respostas produtivas às adversidades. Para as empresas as revelações deste estudo implicam em maior foco das iniciativas de desenvolvimento, tanto organizacional quanto de pessoas, no alinhamento de estrutura, processos e gestão de ativos intangíveis relacionados ao exercício da liderança, que resultem no delineamento de uma cultura organizacional favorável e compatível com um contexto viabilizador da resiliência organizacional.

Propagação de três genótipos de abieiro (Pouteria caimito) por estaquia de ramos herbáceos

Foram selecionadas três plantas de um pomar comercial, com características agronômicas desejáveis, proveniente de propagação seminífera, que forneceram estacas herbáceas, contando com cerca de 15 cm de comprimento, um par de folhas no nó superior, corte em bisel na base e foram tratadas com 4 doses de IBA (0, 1.000, 3.000 e 5.000 mg.l-1) e, posteriormente, plantadas em caixas plásticas perfuradas contendo como substrato, vermiculita textura média. A condução do experimento foi em ambiente de 50 % de sombreamento, sob nebulização intermitente. A análise estatística foi em esquema fatorial 3X4, (genótipos X doses de IBA), com 4 repetições de 10 estacas cada. Após 90 dias foram avaliados a percentagem de enraizamento e sobrevivência, o comprimento e número médio de raízes por estaca. O IBA não influenciou as variáveis analisadas. O genótipo somente induziu mais raízes na seleção 3 e maiores raízes nas seleções 1 e 3.

Fenologia e produção de gemas em cultivares e seleções de pessegueiro na região de Jaboticabal-SP

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Qualidade pós-colheita de pêssegos de cultivares e seleções produzidos na microrregião de Jaboticabal-SP

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Genetic characterization of fig tree mutants with molecular markers

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Digital radiography using digital detector arrays fulfills critical applications for offshore pipelines

Digital radiography in the inspection of welded pipes to be installed under deep water offshore gas and oil pipelines, like a presalt in Brazil, in the paper has been investigated. The aim is to use digital radiography for nondestructive testing of welds as it is already in use in the medical, aerospace, security, automotive, and petrochemical sectors. Among the current options, the DDA (Digital Detector Array) is considered as one of the best solutions to replace industrial films, as well as to increase the sensitivity to reduce the inspection cycle time. This paper shows the results of this new technique, comparing it to radiography with industrial films systems. In this paper, 20 test specimens of longitudinal welded pipe joints, specially prepared with artificial defects like cracks, lack of fusion, lack of penetration, and porosities and slag inclusions with varying dimensions and in 06 different base metal wall thicknesses, were tested and a comparison of the techniques was made. These experiments verified the purposed rules for parameter definitions and selections to control the required digital radiographic image quality as described in the draft international standard ISO/DIS 10893-7. This draft is first standard establishing the parameters for digital radiography on weld seam of welded steel pipes for pressure purposes to be used on gas and oil pipelines.