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

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

Acoustic analysis of cement composites with lignocellulosic residues

Received: January 19th, 2021 ; Accepted: May 20th, 2021 ; Published: October 5th, 2021 ; Correspondence: [email protected] concept of environmental sustainability has been seeking a way to develop projects that reduce the impacts provided by agricultural development and the excessive consumption of natural resources. However, there is still little knowledge about the acoustic insulation/absorption behaviour of lignocellulosic materials. Hence, this study aimed to evaluate the acoustic properties of five cement panels reinforced with the following lignocellulosic materials: eucalyptus, sugarcane bagasse, coconut shell, coffee husk, and banana pseudostem, which ones have as a reference a commercial plaster used as sealing in civil constructions. The proposed panels were produced with each lignocellulosic material residue. It was produced three replicates for each type including plaster (being 18 panels in total). The sound insertion loss (SIL) measurement of the above-mentioned panels have been performed using an acoustical treated inexpensive facility developed based on the literature. The characterization of the acoustic behaviour of the studied materials were analysed according to the IEC (61260-1). The acoustic measurements have been done in the range of 20 Hz to 20 kHz and the analysis in octave bands have been performed. To make the analysis easier, the overall range of frequencies mentioned above was divided as ‘low’, ‘middle’ and ‘high’ ranges. Additionally, the measurement of thickness, density and porosity structure parameters of the lignocellulosic samples have been performed. According to the results and doing a trade-off analysis, the eucalyptus presented the overall best performance considering the overall range of analysis, being the banana pseudostem and sugarcane bagasse materials as good competitors