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

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets

Evolutionary and Biochemical Aspects of Chemical Stress Resistance in Saccharomyces cerevisiae

Large-scale chemical genetics screens (chemogenomics) in yeast have been widely used to find drug targets, understand the mechanism-of-action of compounds, and unravel the biochemistry of drug resistance. Chemogenomics is based on the comparison of growth of gene deletants in the presence and absence of a chemical substance. Such studies showed that more than 90% of the yeast genes are required for growth in the presence of at least one chemical. Analysis of these data, using computational approaches, has revealed non-trivial features of the natural chemical tolerance systems. As a result two non-overlapping sets of genes are seen to respectively impart robustness and evolvability in the context of natural chemical resistance. The former is composed of multidrug-resistance genes, whereas the latter comprises genes sharing chemical genetic profiles with many others. Recent publications showing the potential applications chemogenomics in studying the pharmacological basis of various drugs are discussed, as well as the expansion of chemogenomics to other organisms. Finally, integration of chemogenomics with sensitive sequence analysis and ubiquitination/phosphorylation data led to the discovery of a new conserved domain and important post-translational modification pathways involved in stress resistance

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

Por uma genealogia em que a Educação Ambiental é potência na formação dos membros de comitês de bacias hidrográficas

Cabe aos comitês de bacias hidrográficas, conforme disposto nas Políticas Nacional e Estadual de Recursos Hídricos, a gestão dos recursos hídricos na área de abrangência da bacia. Para tanto, a Lei definiu também os principais instrumentos necessários à materialização dessa gestão, a saber: os planos de recursos hídricos, o enquadramento, a cobrança, a outorga e o sistema de informações. Formado por igual número de representantes dos segmentos da sociedade civil organizada, poder executivo e usuários, o comitê é eleito para um mandato que pode variar de dois a quatro anos no estado do Espírito Santo, e atua num ambiente de grande complexidade, uma vez que os instrumentos não estão consolidados. O comitê, enquanto uma comunidade necessita de que saberes para dar conta dessa gestão? Que saberes seus membros trazem para esse espaço de gestão compartilhada e participativa? A pesquisa realizada com o Comitê da Bacia Hidrográfica do Rio Guandu, por meio da participação na dinâmica do comitê, de uma conversa com seus membros e da análise documental, procurou a composição de um mapa, em que a cartografia considera o devir e o tempo presente, num platô de pura imanência. A partir de uma compreensão do conhecimento como genealogia, conforme proposto por Foucault, se sugere o acoplamento dos conhecimentos eruditos e das memórias locais, acoplamento que permite a constituição de um saber de lutas e a utilização desse saber nas táticas atuais. Desta forma, a Educação Ambiental é potência para a formação desse parlamento das águas, uma vez que defende a valorização dos saberes locais, descontínuos, desqualificados, não legitimados, como saberes tão legítimos e em construção quanto o saber científico, conforme aponta Tristão

Elaboração de uma dieta artificial protéica para Melipona fasciculata.

bitstream/item/27972/1/Doc363.pdfDisponível também on-line

Efect of bovine milk addition to buffalo's milk on different characteristics of artisanal Marajó "cream cheese" type.

1 CD-ROM

Dynamic modeling and stability analysis of a nonlinear system with primary resonance

In recent years, there has been growing interest in the study of nonlinear phenomena. This is due to the modernization of structures related to the need of using lighter, more resistant and flexible materials. Thus, this work aims to study the behavior of a mechanical system with two degrees of freedom with nonlinear characteristics in primary resonance. The structure consists of the main system connected to a secondary system to act as a Nonlinear Dynamic Vibration Absorber, which partially or fully absorbs the vibrational energy of the system. The numerical solutions of the problem are obtained using the Runge-Kutta methods of the 4th order and approximate analytical solutions are obtained using the Multiple Scales Method. Then, the approximation error between the two solutions is analyzed. Using the aforementioned perturbation method, the responses for the ordinary differential equations of the first order can be determined, which describe the modulation amplitudes and phases. Thus, the solution in steady state and the stability are studied using the frequency response. Furthermore, the behavior of the main system and the absorber are investigated through numerical simulations, such as responses in the time domain, phase planes and Poincaré map; which shows that the system displays periodic, quasi-periodic and chaotic movements. The dynamic behavior of the system is analyzed using the Lyapunov exponent and the bifurcation diagram is presented to better summarize all the possible behaviors as the force amplitude varies. In general, the main characteristics of a dynamic system that experiences the chaotic response will be identified