Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Some Results on Fixed and Best Proximity Points of Precyclic Self-Mappings

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A new solution for the roommate problem: The Q-stable matchings

The aim of this paper is to propose a new solution for the roommate problem with strict preferences. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2])and maximum stable matchings (Ta [30] [32]). We find that almost stable matchings are incompatible with the other two solutions. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an effi cient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set.

Surface plasmons and effects of losses in propagating modes in a chain of silver nanoparticles

In this work a chain of 4000 silver nanoparticles embedded in a glass medium is considered, and its leftmost particle is excited by an electric field pulse of Gaussian shape. Considering Drude’s model, losses of the system are taken into account by γ factor, which stands for the Ohmic losses, and different quantities, such as frequencies of excited modes and group velocities are calculated. Besides, these results are compared to those obtained from the dispersion relation of an infinite chain. The increase of losses affects the lifetime and propagation length of the plasmon; besides, although the response dispersion relation for an infinite chain seems to remain invariable, this is not the case for a finite chain. The mismatches are bigger for higher losses. Furthermore, plasmon propagation velocities are analysed, and an explanation for the mismatch of longitudinal modes close to the intersection point with the dispersion of light is suggested. Finally, some concepts to treat this problem from the energy transport point of view are introduced.