Control aspects in nonlinear Hill's equation

The Hill's equations-even in the linear original version are a describer of phenomenon having chaotic flavor, giving sometimes very unusual situations. The theory of the so called intervals of instability in the equation provides the precise description for most of these phenomena. Considerations on nonlinearities into the Hill's equation is a quite recent task. The linearized version for almost of these systems it reduces to the Hill's classical linear one. In this paper, some indicative facts are pointed out on the possibility of having the linear system stabilizable and/or exactly controllable. As consequence of such an approach we get results having strong classical aspects, like the one talking about location of parameters in intervals of stability. A result for nonlinear proper periodic controls, is considered too. (C) 2010 Elsevier B.V. All rights reserved.

A Weak Maximum Principle for Optimal Control Problems with Nonsmooth Mixed Constraints

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Filippov's selection theorem and the existence of solutions for optimal control problems in time scales

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Risk factors for facial melasma in women: a case-control study

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

Effects of Water-Based and Callisthenic Exercise on Freezing of Gait, Postural Control, and Functional Independence in Patients With Mild to Moderate Parkinson Disease

Objective: This study aimed to analyze and compare the role of a water-based exercise program versus a combination of water and callisthenic exercises on postural control, functional independence, and freezing of gait (FOG) in patients with mild to moderate Parkinson disease.Methods: Twenty-five community-dwelling participants with idiopathic Parkinson disease were recruited. Of these, 9 participants took part in a water-based program of physical exercises and the other 16 participants took part in a combined program that consisted of callisthenic exercises plus an aquatic exercise session. Both programs were 16 weeks in duration. The clinical evaluation assessed the festination by means of the FOG score test; postural control was verified by means of the balance test of the short physical performance battery, and the Spanish validated version of the Unified Parkinson's Disease Rating Scale part 2 was used to assess functional independence. Participants were evaluated before and after 16 weeks of both proposed programs.Results: The results showed improvement in FOG for both groups, although a significant main effect was observed only in the patients who performed the callisthenic exercise plus an aquatic exercise program. Postural control did not show significant improvements after both proposed physical exercise programs as soon as functional autonomy. Our preliminary results suggest that training sessions with the combination of water plus callisthenic exercises may be a useful physical rehabilitation strategy for individuals with mild to moderate Parkinson disease who have FOG.