A Borsuk–Ulam Theorem for Maps from a Sphere to a Generalized Manifold

H. J. Munkholm obtained a generalization for topological manifolds of the famous Borsuk–Ulam type theorem proved by Conner and Floyd. The purpose of this paper is to prove a version of Conner and Floyd's theorem for generalized manifolds.     

Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

Positive value of information in games

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments à la Blackwell. AMS 2000 Subject Classification:Primary 91A35.The work of Bruno Bassan and Marco Scarsini was partially supported by MIUR-COFIN. The authors express their thanks to Sylvain Sorin for enlightening comments.     

Hermitian quadratic eigenvalue problems of restricted rank

We consider a quadratic eigenvalue problem such that the second order term is a Hermitian matrix of rank r, the linear term is the identity matrix, and the constant term is an arbitrary Hermitian matrix . Of the n+r solutions that this problem admits, we show at least n-r to be real and located in specific intervals defined by the eigenvalues of A, whence at most 2r are nonreal occuring in possibly repeated conjugate pairs.     

Supersymmetry and bosonization in three dimensions

We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermions where the bosonized theory is non-local.     

Gravitational collapse of a charged and radiating fluid ball in the diffusion limit

The collapse of a charged and radiating ball in the diffusion limit is studied using a method reported by Herrera and collaborators. The interior solution is matched with the exterior Reissner-Nordström-Vaidya metric to obtain a system of differential equations at the surface of the distribution, which can be integrated numerically for some set of initial data. For one model, the profiles of the physical variables are obtained at any piece of the material in terms of Schwarzschild-like coordinates.     

On possible spin injection at non-ideal Schottky contacts

The role of the tunneling mechanisms in metal-disordered layer-semiconductor structure under spin injection at the interface is investigated. The non-ideal metal-semiconductor structure as prepared by ionized cluster beam deposition is considered, and it is shown that the depletion region of the semiconductor can be tailored to include a suitably heavily doped region near the interface. The tunneling is described within a simplified model in which the expression for the interface resistance of the metal-disordered layer-semiconductor structure is obtained. It is argued that in the case of ionized cluster beam deposited non-ideal Schottky structure a significant spin injection is achieved.