On the topological degree of planar maps avoiding normal cones

The classical Poincar\ue9\u2013Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than 1

Multiplicity of periodic solutions for systems of weakly coupled parametrized second order differential equations

We prove a multiplicity result of periodic solutions for a system of second order differential equations having asymmetric nonlinearities. The proof is based on a recent generalization of the Poincar\ue9\u2013Birkhoff fixed point theorem provided by Fonda and Ure\uf1a

Optical and electrical recording of neural activity evoked by graded contrast visual stimulus

BackgroundBrain activity has been investigated by several methods with different principles, notably optical ones. Each method may offer information on distinct physiological or pathological aspects of brain function. The ideal instrument to measure brain activity should include complementary techniques and integrate the resultant information. As a "low cost" approach towards this objective, we combined the well-grounded electroencephalography technique with the newer near infrared spectroscopy methods to investigate human visual function.MethodsThe article describes an embedded instrumentation combining a continuous-wave near-infrared spectroscopy system and an electroencephalography system to simultaneously monitor functional hemodynamics and electrical activity. Near infrared spectroscopy (NIRS) signal depends on the light absorption spectra of haemoglobin and measures the blood volume and blood oxygenation regulation supporting the neural activity. The NIRS and visual evoked potential (VEP) are concurrently acquired during steady state visual stimulation, at 8 Hz, with a b/w "windmill" pattern, in nine human subjects. The pattern contrast is varied (1%, 10%, 100%) according to a stimulation protocol.ResultsIn this study, we present the measuring system; the results consist in concurrent recordings of hemodynamic changes and evoked potential responses emerging from different contrast levels of a patterned stimulus.The concentration of [HbO2] increases and [HHb] decreases after the onset of the stimulus. Their variation shows a clear relationship with the contrast value: large contrast produce huge difference in concentration, while low contrast provokes small concentration difference. This behaviour is similar to the already known relationship between VEP response amplitude and contrast.ConclusionThe simultaneous recording and analysis of NIRS and VEP signals in humans during visual stimulation with a b/w pattern at variable contrast, demonstrates a strong linear correlation between hemodynamic changes and evoked potential amplitude. Furthermore both responses present a logarithmic profile with stimulus contrast

Suppression of Zeno effect for distant detectors

We describe the influence of continuous measurement in a decaying system and the role of the distance from the detector to the initial location of the system. The detector is modeled first by a step absorbing potential. For a close and strong detector, the decay rate of the system is reduced; weaker detectors do not modify the exponential decay rate but suppress the long-time deviations above a coupling threshold. Nevertheless, these perturbing effects of measurement disappear by increasing the distance between the initial state and the detector, as well as by improving the efficiency of the detector.Comment: 4 pages, 4 figure

No classical limit of quantum decay for broad states

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances

Exponential behavior of a quantum system in a macroscopic medium

An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation.Comment: 8 pages, report BA-TH/94-17

Complex Scaled Spectrum Completeness for Coupled Channels

The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case of inelastic scattering with many channels, the existence of such a resolution under complex scaling is still debated. Taking advantage of results obtained earlier for the two channel case, this paper proposes a representation in which the convergence of a resolution of the identity can be more easily tested. The representation is valid for any finite number of coupled channels for inelastic scattering without rearrangement.Comment: Latex file, 13 pages, 4 eps-figure

The role of initial state reconstruction in short and long time deviations from exponential decay

We consider the role of the reconstruction of the initial state in the deviation from exponential decay at short and long times. The long time decay can be attributed to a wave that was, in a classical-like, probabilistic sense, fully outside the initial state or the inner region at intermediate times, i.e., to a completely reconstructed state, whereas the decay during the exponential regime is due instead to a non-reconstructed wave. At short times quantum interference between regenerated and non-regenerated paths is responsible for the deviation from the exponential decay. We may thus conclude that state reconstruction is a ``consistent history'' for long time deviations but not for short ones.Comment: 4 pages, 6 figure