Some global results for eigenvalue problems governed by a variational inequality

In this paper, we use the Leray-Schauder degree theory to obtain some information about the structure of the solution set of a large class of eigenvalue problems governed by a variational inequality. Applications are given to the unilateral postbuckling of a thin elastic plate.     

On nearly parallel G2-structures

A nearly parallel G₂-structure on a seven-dimensional Riemannian manifold is equivalent to a spin structure with a Killing spinor. We prove general results about the automorphism group of such structures and we construct new examples. We classify all nearly parallel G₂-manifolds with large symmetry group and in particular all homogeneous nearly parallel G₂-structures.     

Day-side auroral signatures based on simultaneous, coordinatedobservations at Svalbard and Greenland

The height distribution of the dayside cusp aurora and the relation between optical emissions and net downward electron energy flux are discussed. These two important characteristics of day-side cusp aurora are still unknown. It is instructive to compare particle flux and optical luminosity because these two quantities should be proportional if the cusp aurora is caused by electron impact, as has been found for nighttime aurora in the oval. Furthermore, there should then be a direct relation between auroral altitudes and particle energy. Based on coordinated auroral observations at Svalbard and Greenland, together with simultaneous, overhead F-9 satellite measurements, these quantities have been evaluated     

Nonlinear and bistable properties of doped PMMA lightguides

Polymer lightguides of PMMA doped with the azo dyes methyl-red and N, N-dihexyl-4-amino-4'-nitro-azobenzene (DHANA) are investigated with respect to their opto-optical properties. The trans-cis photoisomerisation of the dyes leads to reversible polarization-dependent optically induced refractive index changes. The index changes are anisotropic. Birefringence is measured using index matched lightguides. The changes with respect to each polarization are determined by leaky mode spectroscopy and by using a half-integrated interferometer. These changes are intensity dependent and, with a suitable geometry, bistability at low intensities (3 mW/mm³) can be obtained.     

A Note about the Appearance of Non-Hyperbolic Solutions in a Mechanical Pendulum System

The investigation of the behavior of a nonlinear system consists in theanalysis of different stages of its motion, where the complexity varieswith the proximity of a resonance region. Near this region the stabilitydomain of the system undergoes sudden changes due basically tocompetition and interaction between periodic and saddle solutions insidethe phase portrait, leading to the occurrence of the most differentphenomena. Depending of the domain of the chosen control parameter,these events can reveal interesting geometric features of the system sothat the phase portrait is not capable to express all them, since theprojection of these solutions on the two-dimensional surface can hidesome aspects of these events. In this work we will investigate thenumerical solutions of a particular pendulum system close to a secondaryresonance region, where we vary the control parameter in a restrictdomain in order to draw a preliminary identification about what happenswith this system. This domain includes the appearance of non-hyperbolicsolutions where the basin of attraction in the center of the phaseportrait diminishes considerably, almost disappearing, and afterwardsits size increases with the direction of motion inverted. Thisphenomenon delimits a boundary between low and high frequency of theexternal excitation.