PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A simplified Fermi Accelerator Model under quadratic frictional force

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

A class of reversible quadratic polynomial vector fields on S-2

We study a class of quadratic reversible polynomial vector fields on S-2. We classify all the centers of this class of vector fields and we characterize its global phase portrait. (C) 2010 Elsevier B.V. All rights reserved.

On the reversible quadratic polynomial vector fields on S-2

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

Consequences of quadratic frictional force on the one dimensional bouncing ball model

Some dynamical properties of the one dimensional Fermi accelerator model, under the presence of frictional force are studied. The frictional force is assumed as being proportional to the square particle's velocity. The problem is described by use of a two dimensional non linear mapping, therefore obtained via the solution of differential equations. We confirm that the model experiences contraction of the phase space area and in special, we characterized the behavior of the particle approaching an attracting fixed point. © 2007 American Institute of Physics.

Utilization of neuromuscular electrical stimulation in the acute phase of ankle immobilization at 90°: Study in rats

Objective: To evaluate the skeletal muscle glycogen content and plasmatic concentration of interleukin -6 (IL-6), interleukin-4 (IL-4), interleukin-10 (IL-10) and tumor necrosis factor-alpha (TNF-α) in rats submitted to electrical stimulation sessions during the first three days of ankle immobilization at the position of 90°. Methods: Albinomale Wistar rats(3-4 months) were maintained in vivarium. conditions with food and water ad libitum, Submitted to 12 h photoperiodic cycles of light/dark, and distributed into 7 experimental groups (n = 6): control(C), immobilized 1 day(I1) immobilized 1 day and electrically stimulated(IE1) immobilized 2 days(12), immobilized 2 days and electrically stimulated(IE2), immobilized 3 days(13) and immobilized 3 days and electrically stimulated(IE3). Groups I utilized an acrylic resin orthesis model and groups electrically stimulated (IE) utilized the orthesis and a session of electrotherapy by a Dualpex 961 (biphasic quadratic pulse, 10 Hz, 0.4 ms, 5.0 mA, one 20 min session a day). After the experimental period, the rats were anesthetized with pentobarbital sodium(40 mg/kg) and a blood sample was colleted to evaluate the plasmatic concentration of interleukins by means of the radioimmunoassay method. The soleus and the white portion of the gastrocnemius muscle were colleted for glycogen reserves analysis(GLY). Other groups of rats were used to apply the glucose tolerance test(GTT) and insulin tolerance test(ITT). For statistical analysis, the Kolmogorov-Smirnov normality test followed by ANOVA and the Tukey tests were utilized, with a critical level established at 5%. Results: In ITT test, groups IE enhanced the skeletal muscle glucose uptake, but no changes were observed in GTT after the therapy session, which indicates that electrical stimulation is a sensibilizing method to augment skeletal muscle glucose uptake. The GLY reserves were reduced in I groups, which indicate that disuse altered insulin sensitivity and compromised energetic homeostasis. However. the IE groups displayed an augment in GLY content, suggesting that electrical stimulation restores the enzymatic pathways altered by immobilization. The improvement in GLY was accompanied by an elevation of the plasmatic concentration of IL-6 and TNF-α, showing the participation of these interleukins in the control of metabolic profile. Plasmatic concentrations of IL-10 were elevated only after 3 days of IE while IL-4 did not display any modifications. Conclusion: The results suggest that neuromuscular electricaf stimulation is an important toot in the maintenance of energetic, conditions of musculature submitted to immobilization, and presents multifactor mechanisms linked to interleukins action that converge to maintain the energetic equilibrium of the tissue in disuse.