Lipschitz Kernel of a Closed Set-Valued Map

This paper deals with Lipschitz selections of set-valued maps with closed graphs. First, we characterize Lipschitzianity of a closed set-valued map in the differential games framework in terms of a discriminating property of its graph. This allows us to consider the -Lipschitz kernel of a given set-valued map as the largest -Lipschitz closed set-valued map contained in the initial one, to derive an algorithm to compute the collection of Lipschitz selections, and to extend the Pasch–Hausdorff envelope to set-valued maps.     

New families of hypohamiltonian graphs

We construct three new infinite families of hypohamiltonian graphs having respectively 3k+1 vertices (k?3), 3k vertices (k?5) and 5k vertices (k?4); in particular, we exhibit a hypohamiltonian graph of order 19 and a cubic hypohamiltonian graph of order 20, the existence of which was still in doubt. Using these families, we get a lower bound for the number of non-isomorphic hypohamiltonian graphs of order 3k and 5k. We also give an example of an infinite graph G having no two-way infinite hamiltonian path, but in which every vertex-deleted subgraph G - x has such a path.     

Theory of carbon monoxide chemisorption on transition metals

An Anderson formalism including overlap is used to treat the chemisorption of carbon monoxide on the transition metals Cu, Ni and Pd. According to the generally accepted scheme only coupling of the 2π¹- and 5σ-orbitals of CO to the metallic d-states is regarded. The wave functions of the metal surface are approximated by a linear combination of atomic d-orbitals, which are oriented in such a manner that maximum overlap with the 2π¹-orbital of CO is achieved. The error involved in this procedure is absorbed into the only adjustable parameter B. Predictions are made for the electronic structure, i.e. the chemisorption levels and occupation numbers. Comparison with results of photoelectron spectroscopy, energy loss spectroscopy and infrared experiments is encouraging. The variation of adsorption energy with geometric location, crystallographic orientation and nature of the substrate metal is extensively treated and compared with experiment. It was possible for example to predict correctly the structure models derived from LEED data and the changes in adsorption energy associated with structural modifications due to varying coverage.     

Theory of decoherence at solid surfaces

Decoherence processes at solid surfaces are observed at all time scales. The most common surface processes are classified according to the presently common view on decoherence theory. Prominent examples of decoherent surface processes are electronic relaxation and deexcitation, vibrational relaxation, diffusion, inelastic scattering, sticking, STM-induced chemical reactions and desorption, localization of adsorbates. Various mechanisms, suggested at the present state of the art of decoherence theory, are investigated for their ability of providing the understanding of decoherence at solid surfaces. In some cases environmental decoherence by coupling to phonons and electron-hole pairs in the surface is a viable mechanism. Some new ideas are introduced, which have not been discussed in the framework of decoherence theory so far.     

Scale of Viability and Minimal Time of Crisis

In this paper, we introduce and study the minimal time of a crisis map which measures the minimal time spent outside a given closed domain of constraints by trajectory solutions of a differential inclusion. The interest of such a notion is basically to tackle simultaneously viability and target issues. The main mathematical result characterizes the epigraph of the crisis map in terms of a viability kernel of an augmented problem. This allows the obtaining of the numerical schemes we specify and to derive an equivalent Hamilton–Jacobi formulation. A simple economic example illustrates the results.