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

A hair-tube survey of small mammals from Serra di Ivrea (NW Italy)

Natura 2000 is the largest coordinated network of protected areas in the world and the main tool for biodiversity conservation within the European Union. Monitoring the protected habitats and species in all network sites by efficient survey methods is essential to plan effective conservation strategies. Small mammals, although including species of conservation interest and being major components of the food web, are often understudied. Through an intensive survey, we investigated the small mammal community of the Special Area of Conservation IT1110057 Serra di Ivrea (Piedmont, NW Italy). We overimposed a 1×1 km grid to the study area and selected a random linear transect in each cell. From mid-May to midJune 2016 we collected small mammal presence data along 55 transects, where we set 955 hair-tubes of 60 mm (n=369) and 30 mm (n=586) in diameter, in a number proportional to each transect length. The largest hair-tubes were positioned on trunks or horizontal branches of trees (ca. 160 cm above ground level) about 100 m from each other, whereas the smallest tubes were tied to shrubs (ca. 80 cm a.g.l.) with 30 m spacing. A bait (hazelnut cream) was used to attract animals and an adhesive strip was attached at each end of the tube to collect the hairs. We checked the hair-tubes twice, with an interval of 15 days. We examined the hairs using a microscope (20× and 40× magnifications) and species were identified by comparing the characteristics of the cuticle scale pattern, medulla and cross-section of the hairs. To collect information on ground-dwelling species, in September 2019 we carried out a four-nights capture session using Sherman traps (7.5×9×23 cm). We placed 10 traps at a distance of 10 m from each other along each of three selected transects. Hazelnut cream was spread at the entrance of each trap, while seeds, a slice of apple and cotton were put at the bottom. Traps were checked daily and trapped individuals were sexed and weighted before being released at the site of capture. In 28650 trap-days we found 185 positive hair-tubes. We detected a total of five to six species: Sciurus vulgaris, Eliomys quercinus, Moscardinus avellanarius, Glis glis and Apodemus sylvaticus/flavicollis, mice’s hairs being indistinguishable by hair morphology. Most occurrences were in the second check (n=156) when we found 126 Apodemus sp., 15 Sciurus vulgaris, 7 Eliomys quercinus, 6 Moscardinus avellanarius and 2 Glis glis. In the first check (n=29) only 19 Apodemus sp., 3 Sciurus vulgaris, 4 Eliomys quercinus and 3 Moscardinus avellanarius were detected. Overall, 168 presence data were collected: 132 Apodemus sp. (13.82%), 17 Sciurus vulgaris (1.78%), 10 Eliomys quercinus (1.05%), 7 Moscardinus avellanarius (0.73%) and 2 Glis glis (0.21%). Sherman trapping allowed detection of 41 small rodents belonging to two species: Apodemus sylvaticus (92.7%) and Myodes glareolus (7.3%). Hair-trapping allowed to record a species not included in the SAC Standard Data Form, namely Moscardinus avellanarius, included in Annex 4 of the Habitats Directive, and also an elusive and understudied species such as Eliomys quercinus. Hair-tubes are a non-invasive and cost-effective method to get information on small mammal distribution. Anyway, considering the number of hair-tubes deployed, capture success was low, also for a potentially common species such as Glis glis, suggesting that a large trapping effort is needed for assessing spatial niche overlap between ecologically similar species and their habitat preferences. The simultaneous use of multiple survey methods may provide a more complete assessment of the small mammal community and allow to collect more reliable data about the genus Apodemus and others ground-dwelling species such as Myodes glareolus

A Lower/Upper Solutions Result for Generalised Radial p-Laplacian Boundary Value Problems

We provide existence results to some planar nonlinear boundary value problems, in the presence of lower and upper solutions. Our results apply to a class of systems generalising radial elliptic equations driven by the p-Laplace operator, and to some problems involving the Laplace–Beltrami operator on the sphere. After extending the definition of lower and upper solutions to the planar system, we prove our results by a shooting method involving a careful analysis of the solutions in the phase plane

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