I. Exact solution of some nonlinear evolution equations. II. The similarity solution for the Korteweg-De Vries equation and the related Painleve Transcendent

In Part I, a method for finding solutions of certain diffusive dispersive nonlinear evolution equations is introduced. The method consists of a straightforward iteration procedure, applied to the equation as it stands (in most cases), which can be carried out to all terms, followed by a summation of the resulting infinite series, sometimes directly and other times in terms of traces of inverses of operators in an appropriate space.

We first illustrate our method with Burgers' and Thomas' equations, and show how it quickly leads to the Cole-Hopft transformation, which is known to linearize these equations.

We also apply this method to the Korteweg and de Vries, nonlinear (cubic) Schrödinger, Sine-Gordon, modified KdV and Boussinesq equations. In all these cases the multisoliton solutions are easily obtained and new expressions for some of them follow. More generally we show that the Marcenko integral equations, together with the inverse problem that originates them, follow naturally from our expressions.

Only solutions that are small in some sense (i.e., they tend to zero as the independent variable goes to ∞) are covered by our methods. However, by the study of the effect of writing the initial iterate u_1 = u_(1)(x,t) as a sum u_1 = ^∼/u_1 + ^≈/u_1 when we know the solution which results if u_1 = ^∼/u_1, we are led to expressions that describe the interaction of two arbitrary solutions, only one of which is small. This should not be confused with Backlund transformations and is more in the direction of performing the inverse scattering over an arbitrary “base” solution. Thus we are able to write expressions for the interaction of a cnoidal wave with a multisoliton in the case of the KdV equation; these expressions are somewhat different from the ones obtained by Wahlquist (1976). Similarly, we find multi-dark-pulse solutions and solutions describing the interaction of envelope-solitons with a uniform wave train in the case of the Schrodinger equation.

Other equations tractable by our method are presented. These include the following equations: Self-induced transparency, reduced Maxwell-Bloch, and a two-dimensional nonlinear Schrodinger. Higher order and matrix-valued equations with nonscalar dispersion functions are also presented.

In Part II, the second Painleve transcendent is treated in conjunction with the similarity solutions of the Korteweg-de Vries equat ion and the modified Korteweg-de Vries equation.

Da impossibilidade da lucidez: a dissolução do Século XX em O arco-íris da gravidade, de Thomas Pynchon

Esta tese analisa a relação entre a ficcionalização da História Moderna e o desenvolvimento de uma ética da vida cotidiana no romance O arco-íris da gravidade, do norte-americano Thomas Pynchon. Para a sua análise e interpretação, será desenvolvido, no primeiro capítulo, um aporte teórico-metodológico que coteje a complexidade formal da narrativa (que dificulta a sua síntese temática) para se estabelecer, a partir daí, as condições de possibilidade de detecção de núcleos temáticos recorrentes que, numa rede de interconexões não-concêntrica ou dispersiva , perspectivizam no romance uma totalização fraturada do sistema-mundo moderno e contemporâneo. No segundo capítulo a ficcionalização do século XX é apresentada em suas configurações metafísica e intra-mundana, e no capítulo final são analisadas as condições que ela impõe para a formação, dentro do real ficcional, de rotinas e modos de vida eticamente positivos

O laboratório da Doutrina dos Nervos: autoria e autoridade em Thomas Willis

A presente pesquisa trata da análise da fundação da Neurologia. A maioria das obras que abordam o assunto a partir de uma perspectiva histórica, sobretudo, aquelas que privilegiam uma visão positivista, para a qual a investigação caminharia em direção a um ponto estático, tendem a alcançar o médico inglês seiscentista, Thomas Willis, como o inconteste precursor dessa já estabelecida especialidade médica. Nossa proposta é a de desconstruir essa ideia. A nosso ver, a historicidade do discurso científico estaria sempre em constante expansão e também em uma contínua transformação, pois diferentemente do ideal positivista, o instaurador do que Foucault designava como cientificidade não seria o descobridor de um objeto dado desde sempre, na medida em que seria enganoso supor uma história natural de um objeto cultural o objeto da história das ciências. Resta-nos, portanto, tentar compreender o sentido em que Willis funda o que ele mesmo denominava Doutrina dos Nervos. Entendemos que Willis instituiu um novo arquivo audiovisual, ou seja, uma nova articulação entre o visível e o enunciável, no que tange aos nervos. Propomos, enfim, que no horizonte da fundação a nova imbricação entre forma de representação e forma de vida emerge no mesmo processo em que Willis se consagra como um autor médico e cientista dos nervos.

Charles Henry Gilbert (1859-1928), Naturalist-in-Charge, and Chauncey Thomas, Jr. (1850-1919), Commanding: Conflict Aboard the U. S. Fish Commission Steamer Albatross in 1902

Charles Henry Gilbert (1859-1928) was a pioneering ichthyologist who made major contributions to the study of fishes of the American West. As chairman of the Department ofZoology at Leland Stanford Junior University in Palo Alto, Calif., during 1891-1925, Gilbert was extremely devoted to his work and showed little patience with those ofa different mindset. While serving as Naturalist-in-Charge of the U.S. Fish Commission Steamer Albatross during her exploratory expedition to the Hawaiian Islands in 1902, Gilbert engaged in an acrimonious feud with the ship's captain, Chauncey Thomas, Jr. (1850-1919), U.S.N., over what Gilbert perceived to be an inadequate effort by the captain. This essay focuses on the conflict between two strong figures, each operatingf rom different world views, and each vying for authority. Despite the difficulties these two men faced, the voyage of the Albatross in 1902 must be considered a success, as reflected by the extensive biological samples collected, the many new species of animals discovered, and the resulting publication of important scientific papers.

A vida do artista e a crise da modernidade: uma leitura de Morte em Veneza, de Thomas Mann

Este trabalho busca compreender os problemas enfrentados pelo artista burguês para o cultivo de sua alma sem diante do problema da crise da modernidade. Entre os séculos XIX e XX a autonomização do mundo e a fragmentação da cultura em duas esferas distintas objetiva e subjetiva tornaram a vida cotidiana uma perspectiva problemática para aqueles que desejavam atingir um nível elevado de suas almas. Nesse sentido, a obra Morte em Veneza (1912) de Thomas Mann conta a história de um artista Gustav Aschenbach que rejeita o mundo e seus sentimentos no intuito de explorar um ideal estético clássico e impossível de se articular com a realidade. A história narra a trajetória desse artista do momento em que decide deixar a Alemanha, seu país natal, rumo à Veneza, no intuito de recuperar-se da exaustão que o exercício do trabalho vocacionado lhe impõe. Mostraremos que Veneza assume, sob tal perspectiva, um papel de grande relevância, pois se relaciona de maneira direta ao ideal de vida do artista. E será em Veneza que Aschenbach encontrará na figura de um garoto a manifestação real de seus anseios idealísticos do belo. Tal encontro produzirá, no artista, um descontrole e uma anarquia de sentimentos que o levará diretamente ao abismo.

Survey and impact assessment of derelict fish traps in St. Thomas and St. John, U.S. Virgin Islands

Since 2001, NOAA National Centers for Coastal Ocean Science (NCCOS), Center for Coastal Monitoring and Assessment’s (CCMA) Biogeography Branch (BB) has been working with federal and territorial partners to characterize, monitor, and assess the status of the marine environment across the U.S. Virgin Islands (USVI). At the request of the St. Thomas Fisherman’s Association (STFA) and NOAA Marine Debris Program, CCMA BB developed new partnerships and novel technologies to scientifically assess the threat from derelict fish traps (DFTs). Traps are the predominant gear used for finfish and lobster harvesting in St. Thomas and St. John. Natural phenomena (ground swells, hurricanes) and increasing competition for space by numerous user groups have generated concern about increasing trap loss and the possible ecological, as well as economic, ramifications. Prior to this study, there was a general lack of knowledge regarding derelict fish traps in the Caribbean. No spatially explicit information existed regarding fishing effort, abundance and distribution of derelict traps, the rate at which active traps become derelict, or areas that are prone to dereliction. Furthermore, there was only limited information regarding the impacts of derelict traps on natural resources including ghost fishing. This research identified two groups of fishing communities in the region: commercial fishing that is most active in deeper waters (30 m and greater) and an unknown number of unlicensed subsistence and or commercial fishers that fish closer to shore in shallower waters (30 m and less). In the commercial fishery there are an estimated 6,500 active traps (fish and lobster combined). Of those traps, nearly 8% (514) were reported lost during the 2008-2010 period. Causes of loss/dereliction include: movement of the traps or loss of trap markers due to entanglement of lines by passing vessels; theft; severe weather events (storms, large ground swells); intentional disposal by fishermen; traps becoming caught on various bottom structures (natural substrates, wrecks, etc.); and human error.