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

Avaliação de sorgo biomassa visando a produção de bioenergia.

O objetivo deste trabalho foi caracterizar o potencial agronômico de linhagens de sorgo biomassa visando à geração de energia. O ensaio foi implantado no ano agrícola de 2013/2014, em Sete Lagoas-MG, com semeadura realizada no final do mês de janeiro de 2014. O delineamento experimental foi em blocos casualizados, com 3 repetições e 10 genótipos de sorgo. As parcelas experimentais foram constituídas por 2 fileiras de cinco metros, espaçadas de 0,70m. As avaliações foram feitas em uma fileira central de cada parcela e as características avaliadas foram florescimento, altura de plantas (AP), produção de massa verde total (PMV), produção de massa seca total (PMS). Os dados de PMV e PMS foram convertidos para t.ha-1. Híbridos de sorgo biomassa, sensíveis ao fotoperíodo, apresentaram ciclo médio de seis meses e porte alto (superior a 4m) que refletiu em alto potencial produtivo de biomass

Physicochemical properties of Butter cheese from Marajó manufactured with buffalo milk and cow milk.

This study aimed to evaluate the physicochemical characteristics, texture and color parameters of the artisanal Butter cheese from Marajó, manufactured with partial substitution of buffalo milk for cow milk. Four formulations were elaborated: B100 (100% buffalo milk); B80 (80% buffalo milk + 20% cow milk); B70 (70% buffalo milk + 30% cow milk) and B60 (60% buffalo milk + 40% cow milk). Three replicates were performed. The partial substitution of 20%, 30% and 40% of buffalo milk caused the reduction of fat in 16.2%, 21.6% and 25.4%, and protein in 5.2%, 5.7%, and 6%, respectively, with decrease of elasticity, cohesiveness, gumminess and chewiness, but had no influence on the hardness. Moisture had significant and strongly negative correlation with elasticity, cohesiveness, gumminess and chewiness. Fat and protein had significant and strongly positive correlations with elasticity, cohesiveness, gumminess and chewiness. Significant differences were found for color variables L*, a*, b* and ho. The increase in cow milk concentration increased the yellowgreenish tonality, with an emphasis in yellow tones

Microkinetic analysis of ethanol to 1,3-butadiene reactions over MgO-SiO 2 catalysts based on characterization of experimental fluctuations

Microkinetic analysis of ethanol to 1,3-butadiene reactions over MgO-SiO2 catalysts was performed based on the detailed characterization of experimental fluctuations, taking into account the influence of the reaction temperature and catalyst properties on ethanol conversion and product selectivities. The obtained results show that both reaction temperature and catalysts properties affected experimental fluctuations significantly. The local microkinetic information contained in the covariance matrix of experimental fluctuations indicated the change of the rate-limiting step as reaction temperature increased: from 300 to 400 °C, the rate-limiting step was identified as the acetaldehyde condensation, while at 450 °C, ethanol dehydrogenation step limits the 1,3-butadiene production

Desempenho e avaliação de cultivares de sorgo sacarino em Sete Lagoas-MG.

O sorgo sacarino possui grande potencial para a produção de açúcares e etanol, e também se destaca pela disponibilidade de matéria-prima no período de entressafra da cana-de-açúcar, quando ocorre ociosidade nas usinas. Dessa forma, o objetivo do trabalho foi realizar avaliação do desempenho agronômico das cultivares: BRS 511, CV 198, V82393, V82392, CMSXS629, CMSXS647, CMSXS646, CMSXS644, CMSXS630, BRS509, CMSXS643, V82391, BRS 508, BRS 506, Sugargraze, CV 568, para a recomendação dessas quanto ao seu potencial para a produção de etanol. O experimento foi implantado em blocos casualizados com três repetições, e espaçamento entre linhas de 0.70 m, em que foram avaliadas as características de florescimento, altura de planta, produção de massa verde, extração de caldo e sólidos solúveis totais. As cultivares que mais se destacaram para produção de massa verde e teores de sólidos solúveis foram CMSXS629, CMSXS646, BRS508 e BRS511, semelhantes à cultura da cana-de-açúcar, possuindo muito potencial para a produção de etanol de 1ª geração

Evaluation of thermal and non-thermal processing effect on non-prebiotic and prebiotic acerola juices using 1HqNMR and GC - MS coupled to chemometrics.

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Realistic loophole-free Bell test with atom-photon entanglement

The establishment of nonlocal correlations, obtained through the violation of a Bell inequality, is not only important from a fundamental point of view, but constitutes the basis for device-independent quantum information technologies. Although several nonlocality tests have been performed so far, all of them suffered from either the locality or the detection loopholes. Recent studies have suggested that the use of atom-photon entanglement can lead to Bell inequality violations with moderate transmission and detection efficiencies. In this paper we propose an experimental setup realizing a simple atom-photon entangled state that, under realistic experimental parameters available to date, achieves a significant violation of the Clauser-Horn-Shimony-Holt inequality. Most importantly, the violation remains when considering typical detection efficiencies and losses due to required propagation distances.Comment: 21 pages, 5 figures, 3 table, to appear in Nature Com

Correlações genotípicas e análise de trilha em sorgo sacarino visando a produção de etanol.

Este trabalho teve o objetivo de avaliar as correlações genotípicas e a análise de trilha em cinco caracteres na cultura do sorgo sacarino (Sorghum bicolor L. Moench). Os caracteres estudados foram: altura média, em metro (ALT); produtividade de massa verde, em ton/ha (PROD); teor de sólidos solúveis totais, em graus brix (BRIX), teor de sacarose no caldo, em porcentagem (POL); produção de etanol, em l/ha (ET). O caracter (ET) foi considerado a variável independente. O experimento foi realizado em blocos casualizados em três repetições. Considerando a produção de etanol, em l/ha (ET), como componente independente, as variáveis Teor de sacarose (POL) e produtividade (PROD) mostraram valores condizentes de coeficientes de trilha aos apresentados nas correlações genotípicas. Os caracteres sólidos solúveis totais (BRIX) e altura (ALT) mostraram valores discordantes entre os coeficientes de trilha, considerando os efeitos diretos sobre ET com as correlações genotípicas, evidenciando assim a grande importância do estudo da análise de trilha para os caracteres utilizados em um programa de melhoramento genético de plantas