On symmetries of singular implicit ODEs

We study implicit ODEs, cubic in derivative, with infinitesimal symmetry at singular points. Cartan showed that even at regular points the existence of nontrivial symmetry imposes restrictions on the ODE. Namely, this algebra has the maximal possible dimension 3 iff the web of solutions is flat. For cubic ODEs with flat 3-web of solutions we establish sufficient conditions for the existence of nontrivial symmetries at singular points and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling is some coordinates. We use this symmetry to find first integrals of the ODE.

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Experimental measurements of the NOx and CO concentrations operating in oscillatory and non-oscillatory burning conditions

The effects of combustion driven acoustic oscillations in carbon monoxide and nitrogen oxides emission rates of a combustor operated with liquefied petroleum gas (LPG) were investigated. Because the fuel does not contain nitrogen, tests were also conducted with ammonia injected in the fuel, in order to study the formation of fuel NOx. The main conclusions were: (a) the pulsating combustion process is more efficient than the non-pulsating one and (b) the pulsating combustion process generates higher rates of NOx, with and without ammonia injection, as shown by CO and NO concentrations as function of the O-2 concentration. An increase in the LPG flow rate, keeping constant the air to fuel ratio, increased the acoustic pressure amplitude and the frequency of oscillation. The injection of ammonia had no influence on either pressure amplitude or frequency. (c) 2005 Elsevier Ltd. All rights reserved.

Attitude propagation using non-singular canonical variables

Three sets of non-singular canonical variables for the rotational motion are analyzed. These sets are useful when the angle between z-axis of a coordinate system fixed in artificial satellite ( here defined by the directions of principal moments of inertia of the satellite) and the rotational angular momentum vector is zero or when the angle between Z-inertial axis and rotational angular momentum vector is zero. The goal of this paper is to compare all these sets and to determine the benefits of their uses. With this objective, the dynamical equations of each set were derived, when mean hamiltonian associate with the gravity gradient torque is included. For the torque-free rotational motion, analytical solutions are computed for symmetrical satellite for each set of variables. When the gravity gradient torque is included, an analytical solution is shown for one of the sets and a numerical solution is obtained for one of the other sets. By this analysis we can conclude that: the dynamical equation for the first set is simple but it has neither clear geometrical nor physical meaning; the other sets have geometrical and physical meaning but their dynamical equations are more complex.

High-frequency oscillatory ventilation attenuates oxidative lung injury in a rabbit model of acute lung injury

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

High-Frequency Oscillatory Ventilation Associated With Inhaled Nitric Oxide Compared to Pressure-Controlled Assist/Control Ventilation and Inhaled Nitric Oxide in Children: Randomized, Non-Blinded, Crossover Study

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Electromyographic activity of shoulder muscles during exercises performed with oscillatory and non-oscillatory poles

CONTEXTUALIZAÇÃO: A dor e a disfunção no complexo articular do ombro é comumente encontrada na prática fisioterapêutica. Essas anormalidades musculoesqueléticas estão relacionadas à instabilidade e inadequado funcionamento cinemático, que dependem da integridade dos tecidos musculares. Assim, no sentido de prevenir e reabilitar esses sintomas, o uso da haste oscilatória vem sendo implantado para melhorar os resultados de técnicas cinesioterapêuticas. OBJETIVOS: Analisar a atividade eletromiográfica (EMG) dos músculos que estabilizam a articulação do ombro durante a realização de exercícios com haste oscilatória e haste não-oscilatória. MÉTODOS: Participaram do estudo 12 voluntárias com idade de 20,4±1,9 anos. Os dados EMG foram coletados nos músculos trapézio superior (TrS), trapézio inferior (TrI) e deltoide médio (DM) durante três diferentes exercícios realizados com haste oscilatória e haste não-oscilatória. O sinal EMG foi analisado no domínio do tempo pelo cálculo do Root Mean Square (RMS). Os valores de RMS foram normalizados pelo valor de pico obtido em todas as tentativas por cada músculo. A análise estatística foi feita com os testes ANOVA para medidas repetidas e post-hoc de Bonferroni. RESULTADOS: A atividade EMG dos músculos TrS, TrI e DM foi significativamente maior nos exercícios com haste oscilatória do que com haste não-oscilatória (todos p<0,001). Não foram significativas as diferenças na ativação desses músculos entre os exercícios. CONCLUSÃO: Os resultados do presente estudo indicaram que a haste oscilatória requisitou maior atividade EMG dos músculos do ombro e, assim, pode ser um instrumento útil no treinamento desses músculos.

Asymptotics of zeros of polynomials arising from rational integrals

We prove that the zeros of the polynomials P.. (a) of degree m, defined by Boros and Moll via[GRAPHICS]approach the lemmiscate {zeta epsilon C: \zeta(2) - 1\ = Hzeta < 0}, as m --> infinity. (C) 2004 Elsevier B.V. All rights reserved.

Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)