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.     

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.     

Self-energy of one electron in non-relativistic QED

We investigate the self-energy of one electron coupled to a quantized radiation field by extending the ideas developed in Hainzl (Ann. H. Poincaré, in press). We fix an arbitrary cut-off parameter Λ and recover the α²-term of the self-energy, where α is the coupling parameter representing the fine structure constant. Thereby we develop a method which allows to expand the self-energy up to any power of α. This implies that perturbation theory in α is correct if Λ is fix. As an immediate consequence we obtain enhanced binding for electrons.     

Error Bounds and Implicit Multifunction Theorem in Smooth Banach Spaces and Applications to Optimization

In this paper we provide an error bound estimate and an implicit multifunction theorem in terms of smooth subdifferentials and abstract subdifferentials. Then, we derive a subdifferential calculus and Fritz–John type necessary optimality conditions for constrained minimization problems.     

Near-infrared laser photoacoustic detection of methane: the impact of molecular relaxation

A photoacoustic sensor has been developed for trace-gas monitoring using a near-infrared semiconductor laser emitting in the 2ν₃ band of methane at 1.65 μm. The apparatus was designed for on-line process control in the manufacturing of the novel low-water-peak fibres developed for optical telecommunications. The importance of collisional relaxation processes in the generation of the photoacoustic signal is reported in the particular case of CH₄ detection in dry O₂ and O₂–N₂ mixtures. The negative influence of these effects results in a strongly reduced and phase-shifted photoacoustic signal, induced by a fast resonant coupling between the vibrational states of methane and oxygen, associated with the slow relaxation of the excited oxygen molecules. An unusual parabolic response of the sensor with respect to the methane concentration has been observed and is discussed. Finally, the beneficial effect of several species, including water vapour and helium, acting as a catalyst to hasten the relaxation of the CH₄–O₂ system, is demonstrated. PACS 42.62.Fi; 33.20.Ea; 34.50.Ez