A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator

In [1,2] we have developed a method (we call it the S-function method) that is successful in treating certain classes of rational second order ordinary differential equations (rational 2ODEs) that are particularly `resistant' to canonical Lie methods and to Darbouxian approaches. In this present paper, we generalize the S-function method making it capable of dealing with a class of elementary 2ODEs presenting elementary functions. Then, we apply this method to a Duffing-Van der Pol forced oscillator, obtaining an entire class of first integrals

Solving 1ODEs with functions

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs. In this present paper, we will apply these results in order to produce a method that is more efficient in a great number of cases. Directly, the solving of 1ODEs is applicable to any problem presenting parameters to which the rate of change is related to the parameter itself. Apart from that, the solving of 1ODEs can be a part of larger mathematical processes vital to dealing with many problems.Comment: 31 page

Finding nonlocal Lie symmetries algorithmically

Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries) algorithmically. The procedure is based on an idea arising from the formal equivalence between the total derivative operator and the vector field associated with the 2ODE over its solutions (Cartan vector field). Basically, from the formal representation of a Lie symmetry it is possible to extract information that allows to use this symmetry practically (in the 2ODE integration process) even in cases where the formal operation cannot be performed, i.e., in cases where the symmetry is nonlocal. Furthermore, when the 2ODE in question depends on parameters, the procedure allows an analysis that determines the regions of the parameter space in which the integrable cases are located

Caracterização das classes de solo ocorrentes e aptidão agrícola de uma área destinada a um sistema de agrovila em Ouro Preto d'Oeste-RO.

A presente pesquisa teve por objetivo caracterizar as classes de solos ocorrentes e seus respectivos niveis de fertilidade, bem como, definião e um sistema de aptidão agrícola em uma área destinada a um projeto de Agrovila no Município de Ouro Preto d'Oeste no estado de Rondônia. Foram abertas 7 trincheiras em toda a área, nas dimensões de 1,00 m x 1,80 m utilizando-se retroescavadeira. Fez-se descrições pedológicas e coletas de amostras de solo para caracterização física e química, nas profundidades de 0-20 cm e 20 cm-40 cm. Constatou-se a ocorrência das classes de solo: LAd, PVAd, PVAe, Ce, PVEe, PVAe, PVAd com aptidões agrícolas 2bc, 3 (a)bc, 2 aBC, 2 ABc, 3 AB9c), 2 abc e 3 (a)bc, respectivamente.bitstream/item/70941/1/0000003287-Doc52-solos.pd