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

BIODIESEL PRODUCTION FROM MICROWAVE IRRADIATED REACTOR USING HOMOGENEOUS AND HETEROGENEOUS CATALYSIS

Biodiesel was successful produced in a microwave irradiation reactor using homogeneous and heterogeneous catalysis. The biodiesel was production by the trasesterification reaction of soybean oil using metanol. Sodium methylate (30% solution in metanol) was used for the homogeneous catalyst and the heterogeneous catalyst was developed using wasted eggshells. The eggshells were calcined and tested pure and doped with potassium hydroxide in 10, 30 and 50% of weight. The power and temperature of the microwave were kept constant in every reaction being 800W and 200º Celsius, respectively. The reaction time was significantly reduced using microwave compared to the conventional process. In only one minute of reaction, the methyl ester (FAME) conversion obtained was 98.9% with the homogeneous catalyst and within 15 minutes, the heterogeneous catalysis accomplished 100%. For heterogeneous catalyst, the best results were acquired when the doped catalyst contained 50% of KOH. The results indicated that the eggshells treated with KOH has a great potential to be used for microwave-assisted transesterification reactions of oils with mild operations conditions: molar ratio oil/alcochol 1:6 and just 5% of catalyst. In addition, the heterogenous catalyst was recovered and reused in other reactions with a relatively satisfying results. The physico-chemical properties of the catalysts were characterized by X-ray diffraction and thermogravimectric analysis

Device-independent bounds for Hardy's experiment

In this Letter we compute an analogue of Tsirelson's bound for Hardy's test of nonlocality, that is, the maximum violation of locality constraints allowed by the quantum formalism, irrespective of the dimension of the system. The value is found to be the same as the one achievable already with two-qubit systems, and we show that only a very specific class of states can lead to such maximal value, thus highlighting Hardy's test as a device-independent self-test protocol for such states. By considering realistic constraints in Hardy's test, we also compute device-independent upper bounds on this violation and show that these bounds are saturated by two-qubit systems, thus showing that there is no advantage in using higher-dimensional systems in experimental implementations of such test.Comment: 4 pages, 2 figure

Nonlocality tests enhanced by a third observer

We consider Bell tests involving bipartite states shared between three parties. We show that the simple inclusion of a third part may greatly simplify the measurement scenario (in terms of the number of measurement settings per part) and allows the identification of previously unknown nonlocal resources.Comment: 4 pags, 4 figs. v2: fig 3 corrected. V3: refs corrected. Close to published versio

Avaliação de genótipos de arroz de terras altas sob preparo do solo convencional.

O arroz é uma excelente fonte de calorias e proteínas na dieta do brasileiro. Assim, este trabalho teve como objetivo avaliar o desempenho de genótipos de arroz sob Cerrado em plantio convencional

Avaliação de genótipos de arroz de terras altas sob cerrado em sistema plantio direto.

O arroz é um alimento básico na mesa do brasileiro. Assim, este trabalho teve como objetivo avaliar o desempenho de genótipos de arroz de terras altas sob Cerrado em Sistema Plantio Direto. O delineamento experimental foi em blocos ao acaso com 4 repetições