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

Estudo comparativo entre técnicas de extração de DNA para o futuro diagnóstico do endossimbionte Wolbachia em Haematobia irritans.

Editores técnicos: João de Mendonça Naime, Caue Ribeiro, Maria Alice Martins, Elaine Cristina Paris, Paulino Ribeiro Villas Boas, Ladislau Marcelino Rabello

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

MOLYBDENUM CATALYZED ACID PEROXIDE BLEACHING OF EUCALYPTUS KRAFT PULP

Molybdenum catalyzed peroxide bleaching (PMo Stage) consists of pulp treatment with hydrogen peroxide under acidic conditions in the presence of a molybdenum catalyst. Molybdenum is applied in catalytic doses (50-200 mg/kg pulp) and may originate from various sources, including (NH4)6Mo7O24.4H2O, Na2MoO4.2H2O, siliconmolybdate, etc. This work is aimed at optimizing the PMo stage and evaluating its industrial application in the OAZDP sequence. Optimum PMo stage conditions for bleaching eucalyptus pulp were 90 ºC, pH 3.5, 2 h, 0.1 kg/adt Mo and 5 kg/adt H2O2. The PMo stage was more efficient to remove pulp hexenuronic acids than lignin. Its efficiency decreased with increasing pH in the range of 1.5-5.5, while it increased with increasing temperature and peroxide and molybdenum doses. The application of the PMo stage as replacement for the A-stage of the AZDP sequence significantly decreased chlorine dioxide demand. The PMo stage caused a decrease of 20-30% in the generation of organically bound chlorine. The quality parameters of the pulp produced during the PMo stage mill trial were comparable to those obtained with the reference A-stage

Study of infection by Babesia bovis and Anaplasma marginale in dairy water buffaloes in the state of São Paulo.

The aim of this study was to evaluate the prevalence of infection by Babesia bovis and Anaplasma margina/e in dairy water buffaloes infested by ticks on farms, either in exclusive buffalo herds or in in mixed herds along with cattle

Efeito da adição de leite bovino ao leite de búfala nas diferentes características do queijo artesanal do Marajó, tipo creme.

O objetivo do estudo foi comparar os efeitos da substituição parcial do leite bubalino por leite de vaca, nas características físico-químicas, de textura, cor e nos parâmetros sensoriais do queijo artesanal do Marajó tipo Creme, tradicionalmente elaborado com leite de búfala. Quatro queijos foram elaborados com as seguintes formulações: C100 (100% leite de búfala); C80 (80% leite de búfala + 20% leite de vaca); C70 (70% leite de búfala + 30% leite de vaca) e C60 (60% leite de búfala + 40% leite de vaca). Três repetições foram realizadas. Os resultados analíticos da composição (umidade, proteína, gordura, minerais e acidez); dos parâmetros de textura (dureza, elasticidade, coesividade, mastigabilidade) e dos atributos de cor (L*, a*, b*, C*, ho) foram significativamente diferentes entre as formulações. Por outro lado, a presença do leite de vaca não ocasionou alterações nos atributos sensoriais. Com base nos resultados desse estudo, concluiu-se que a adição de até 40% de leite bovino na elaboração do queijo tipo Creme não afeta a sua aceitação pelo consumidor, permitindo um abastecimento do mercado em períodos de entressafra, quando a produção do leite bubalino diminui

Implantação do curso pós-técnico florestal na Amazônia.

1 CD-ROM. Autoria bilíngue: CONGRESSO E EXPOSICAO INTERNACIONAL SOBRE FLORESTAS, 5., 1999, Curitiba