Local Isometric immersions of pseudo-spherical surfaces and evolution equations

The class of differential equations describing pseudo-spherical surfaces, first introduced by Chern and Tenenblat [3], is characterized by the property that to each solution of a differential equation, within the class, there corresponds a 2-dimensional Riemannian metric of curvature equal to $-1$. The class of differential equations describing pseudo-spherical surfaces carries close ties to the property of complete integrability, as manifested by the existence of infinite hierarchies of conservation laws and associated linear problems. As such, it contains many important known examples of integrable equations, like the sine-Gordon, Liouville and KdV equations. It also gives rise to many new families of integrable equations. The question we address in this paper concerns the local isometric immersion of pseudo-spherical surfaces in ${\bf E}^{3}$ from the perspective of the differential equations that give rise to the metrics. Indeed, a classical theorem in the differential geometry of surfaces states that any pseudo-spherical surface can be locally isometrically immersed in ${\bf E}^{3}$. In the case of the sine-Gordon equation, one can derive an expression for the second fundamental form of the immersion that depends only on a jet of finite order of the solution of the pde. A natural question is to know if this remarkable property extends to equations other than the sine-Gordon equation within the class of differential equations describing pseudo-spherical surfaces. In an earlier paper [11], we have shown that this property fails to hold for all other second order equations, except for those belonging to a very special class of evolution equations. In the present paper, we consider a class of evolution equations for $u(x,t)$ of order $k\geq 3$ describing pseudo-spherical surfaces. We show that whenever an isometric immersion in ${\bf E}^3$ exists, depending on a jet of finite order of $u$, then the coefficients of the second fundamental forms are functions of the independent variables $x$ and $t$ only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and Applications, pp.N

Socioespacial correlation of student evasion in public schools of middle school of DF 2012/2016

Trabalho de Conclusão de Curso (especialização)—Universidade de Brasília, Instituto de Geociências, [2018].O presente estudo trata da análise da evasão escolar no ensino médio das escolas públicas do Distrito Federal (DF). O objetivo principal é avaliar a evasão escolar com o foco social, geograficamente posicionado nas Regiões Administrativas (RA) do DF. A metodologia foi estruturada para coletar dados socioeconômicos na base governamental e classificar os casos em escala, com pesos distribuídos por RA. O Resultado é um mapa temático das RA do DF, no qual se pode inferir as localidades prioritárias para implantação de políticas e ações públicas com o intuito de diminuir o quadro atual em que se encontra este sério problema educacional no DF.The present study deals with the analysis of school dropout in the high school of the public schools of the Federal District (DF). The main objective is to evaluate school dropout with the social focus, geographically positioned in the Administrative Regions (RA) of the DF. The methodology was structured to collect socioeconomic data in the governmental base and classify the cases in scale, with weights distributed by RA. The result is a thematic map of the DF of the DF, in which it is possible to infer the priority locations for the implementation of public policies and actions in order to reduce the current situation of this serious educational problem in the Federal District

Socioespacial correlation of student evasion in public schools of middle school of DF 2012/2016

Trabalho de Conclusão de Curso (especialização)—Universidade de Brasília, Instituto de Geociências, [2018].O presente estudo trata da análise da evasão escolar no ensino médio das escolas públicas do Distrito Federal (DF). O objetivo principal é avaliar a evasão escolar com o foco social, geograficamente posicionado nas Regiões Administrativas (RA) do DF. A metodologia foi estruturada para coletar dados socioeconômicos na base governamental e classificar os casos em escala, com pesos distribuídos por RA. O Resultado é um mapa temático das RA do DF, no qual se pode inferir as localidades prioritárias para implantação de políticas e ações públicas com o intuito de diminuir o quadro atual em que se encontra este sério problema educacional no DF.The present study deals with the analysis of school dropout in the high school of the public schools of the Federal District (DF). The main objective is to evaluate school dropout with the social focus, geographically positioned in the Administrative Regions (RA) of the DF. The methodology was structured to collect socioeconomic data in the governmental base and classify the cases in scale, with weights distributed by RA. The result is a thematic map of the DF of the DF, in which it is possible to infer the priority locations for the implementation of public policies and actions in order to reduce the current situation of this serious educational problem in the Federal District

Looking Behind the Scenes: An Assessment of the Interdependence of Brazilian Cultural Industries

How important is Brazil’s cultural industries to its economy? We provide an answer to this question by evaluating the interdependence of the cultural activities in the Brazilian production structure and its evolution over the last few years (2005 – 2009). To accomplish this, we disaggregate 13 cultural economic industries in the Brazilian input-output table and calculate several indexes, such as, the production multiplier, linkage indexes, fields of influence and extraction analysis. Results show that the only cultural sector with high links to other sectors in the production structure is Telecommunication, edition and news agencies and that this sector provides the greatest loss in output when removed from the economy. Moreover, the sectors Jewelry, music instruments and toys, and Manufacture of telecommunication equipment have output multipliers higher than the average of the economy

Implementação de filtros digitais para afinação de guias digitais de ondas

Monografia (graduação)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Ciência da Computação, 2014.Este trabalho trata da análise do processo de propagação de ondas transversais numa corda ideal e sua sintetização, através de técnicas de modelamento físico de instrumentos musicais, com o objetivo de produzir sons musicais afinados a uma altura arbitrária. Métodos simples de determinação de altura e afinação são propostos. São apresentadas as técnicas de Guias Digitais de Ondas e o algoritmo Karplus-Strong para a síntese de sons complexos de altura bem definida, com a utilização de filtros Interpoladores de Lagrange como soluções para sua afinação. A análise dos sons produzidos pelo protótipo implementado é apresentada ao final do trabalho.This paper concerns the analysis and synthesis of transversal wave propagation on an ideal string, using techniques for physical modeling of musical instruments, with the objective of producing sounds well tuned to an arbitrary pitch. Simple methods for pitch determination and tuning are proposed. Digital Waveguide and Karplus-Strong algorithm are presented as techniques for pitched sound synthesis, and Lagrange Interpolators as tuning solutions. The analysis of sounds produced by the implemented prototype is presented at the end of the paper

Padrão de distribuição de espécies de formigas (Hymenoptera: Formicidae) e o efeito de variáveis ambientais em um gradiente latitudinal na Amazônia

Understanding how the number of species varies along the environment at different scales is a challenge. Nowadays we have a reasonable idea of how the species are distributed specially at small and continental scales, but information at mesoscales are stills scarce. Here we investigated the role of regional variables (temperature, precipitation and vegetation type) and local edaphic factors (soil clay content and slope of terrain) on ants species richness at regional and local scale along a latitudinal gradient of approximately 1,350 km in the central Amazon forest. We collected ants in permanent plots using five litter samples and/or ten pitfall samples. In total, we sampled 139 plots and 1,270 samples. We collected 510 species/morphospecies representing 77 genera and 13 subfamilies. At regional scale, the linear model using annual mean temperature, annual mean precipitation, proportion of soil clay content, terrain slope and vegetation type explained 40% of the variation in species richness for pitfall data and 70% to Winkler data. At local scale, the number of ant species sampled with pitfalls and winkler sacks were not related with the predictors variables investigated. Our results, showed that several environmental variables normally associated with local species assembly process, can also operate in larger scales.Compreender como o número de espécies varia ao longo de um ambiente em diferentes escalas é um desafio. Atualmente, temos uma razoável ideia de como as espécies estão distribuídas, especialmente em escalas pequenas, no entanto, informações na mesoescala ainda são escassas. O objetivo deste trabalho foi investigar o papel das variáveis regionais (temperatura, precipitação e tipo vegetacional) e fatores edáficos locais (teor de argila do solo e inclinação do terreno) sobre a riqueza de formigas na escala local e regional ao longo de um gradiente latitudinal de aproximadamente 1.350 km na Amazônia Central. As coletas foram realizadas em parcelas permanentes utilizando cinco amostras de Winkler e/ou 10 pitfalls. No total foram amostrados 139 parcelas e 1.270 amostras. Foram coletadas 510 espécies/morfoespécies, representando 77 gêneros e 13 subfamilias. Na escala regional, o modelo linear usando a média anual de temperatura, media anual de precipitação, teor de argila, inclinação e tipo de vegetação explicou 40% da variação na riqueza de espécies para os dados de pitfall e 70% para os dados de Winkler. Na escala local, o número de espécies coletadas com pitfall e Winkler não foram relacionadas com as variáveis preditoras investigadas. Nossos resultados mostram que diferentes variáveis ambientais, normalmente associadas com processos de assembléias locais, também podem operar em escalas maiores