Centers on center manifolds in the Lu system

We confirm a conjecture of Mello and Coelho [Phys. Lett. A 373 (2009) 1116] concerning the existence of centers on local center manifolds at equilibria of the Lu system of differential equations on R(3). Our proof shows that the local center manifolds are algebraic ruled surfaces, and are unique. (C) 2011 Elsevier B.V. All rights reserved.

On the appearance of a Hopf bifurcation in a non-ideal mechanical problem

In this paper we studied a non-ideal system with two degrees of freedom consisting of a dumped nonlinear oscillator coupled to a rotatory part. We investigated the stability of the equilibrium point of the system and we obtain, in the critical case, sufficient conditions in order to obtain an appropriate Normal Form. From this, we get conditions for the appearance of Hopf Bifurcation when the difference between the driving torque and the resisting torque is small. It was necessary to use the Bezout Theorem, a classical result of Algebraic Geometry, in the obtaining of the foregoing results. (C) 2003 Elsevier Ltd. All rights reserved.

Multidisciplinary approach to chronic pain from myofascial pain dysfunction syndrome: A four-year experience at a Brazilian center

Chronic pain is the major complaint of myofascial pain dysfunction syndrome (MPDS) and is a complex problem which involves physical, psychological and social aspects, the etiology of MPDS is multifactorial and the multidisciplinary approach is essential for differential diagnosis and for comprehensive treatment planning, In 1993, the Dental School of Piracicaba-UNICAMP, Brazil, opened a Center for Pain Studies (CPS), staffed by health care providers including, dentists, psychologists, physicians, physiotherapists and phonoaudiologists. The major aims of the CPS are to provide clinical care and to develop basic and applied research, Sixty-two MPDS patients had been admitted to the CPS by 1997, There were 60 females and 2 males, mean age -32.5 years, the mean duration of chronic pain was 48 months. Pain intensity and unpleasantness were measured employing the Visual Analogue Scale, the tendency to develop stress-related diseases was assessed by the Social Readjustment de Scale, There was a mean reduction of chronic pain of 69.89% and 71.78% relative to intensity and unpleasantness, respectively, the experience of clinical attendance at a multidisciplinary center showed the relevance of a team consisting of health care providers from different specialties with well-established aims, completely integrated and sensitive enough to understand the painful complaints of MPDS patients.

Closed-orbit dependence on the field direction in the anisotropic diamagnetic Kepler problem

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