Convex decomposition of games and axiomatizations of the core and the D-core

This paper provides an axiomatic framework to compare the D-core (the set of undominated imputations) and the core of a cooperative game with transferable utility. Theorem 1 states that the D-core is the only solution satisfying projection consistency, reasonableness (from above), (*)-antimonotonicity, and modularity. Theorem 2 characterizes the core replacing (*)-antimonotonicity by antimonotonicity. Moreover, these axioms also characterize the core on the domain of convex games, totally balanced games, balanced games, and superadditive games.      

Minimal large sets for cooperative games

We analyze the concept of large set for a coalitional game v introduced by Martínez-de-Albéniz and Rafels (Int. J. Game Theory 33(1):107–114, 2004). We give some examples and identify some of these sets. The existence of such sets for any game is proved, and several properties of largeness are provided. We focus on the minimality of such sets and prove its existence using Zorn’s lemma. Institutional support from research grants (Generalitat de Catalunya) 2005SGR00984 and (Spanish Government and FEDER) SEJ2005-02443/ECON is gratefully acknowledged, and the support of the Barcelona Economics Program of CREA.     

WKB Analysis for Nonlinear Schrödinger Equations with Potential

We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity.     

Polyoxometalates in solution: Molecular dynamics simulations on the alpha-PW12O40(3-) Keggin anion in aqueous media

The Keggin anion, PW12O40(3-), is one of the most representative polyoxometalates (POMs). In recent years increasing theoretical work focused on this family of compounds has explained or even predicted some of their properties using quantum mechanics methods. In this report we applied for the first time molecular dynamics (MD) to the title compound to analyze its interactions with water. We used three atomic charge definitions (Mulliken, ChelpG, and formal charges) to carry out MD simulations. The results show that the terminal oxygens of the cluster are invariably most effectively solvated by water because of their prominent position within the framework. On the other hand, bridging oxygens, which are confined in more internal positions, concentrate a smaller portion of the whole solvation. We investigated the hydrogen bonds existing between water and the cluster, confirming that the terminal positions form more contacts with H2O than any other site of the cluster. In the end, the lifetime of such contacts is longer with bridging oxygens, presumably due to their higher atomic charge.     

A new experimental method for the determination of the one phonon density of states in GaAs

The one phonon density of states in GaAs is obtained from the measured disorder-activated-first-order Raman-scattering in Ga_1?xAl_xAs_x alloys. The agreement with several theoretical determinations is excellent. We discuss the requirements that, both the isoelectronic substitution and the experimental conditions must fullfil in order to apply this method to other III–V compounds.     

Disorder activated Raman scattering in Ga1−xAlxAs alloys

We report Raman scattering experiments in mixed crystals Ga_1?xAl_xAs in the spectral range 20 – 400 cm^?1. We performed the measurements for several incident and scattered light polarizations. Besides the D.A.L.A. already observed¹ we find a new band at lower energy. We interpret this structure as due to disorder activated transverse acoustical phonons and label it D.A.T.A. Several weaker bands corresponding to disorder activated optical processes are also seen. Our results are compared with recent calculations of Talwar et al².     

Search for exotic mesons produced by baryon exchange in the reaction π+p → Λ + x++ at 12 GeV/c

A search for exotic mesons has been carried out at the CERN Omega spectrometer. The baryon-exchange reaction π⁺p → Λ + x⁺⁺ was studied at 12 GeV/c incident beam momentum. No evidence was found for the existence of doubly-charged strange mesons. The upper limit (95% confidence level) for this reaction is 60 nb for exotic mesons with squared masses from 1 to 7 (GeV/c²)² and 150 nb for 7 to 13 (GeV/c²)². These limits are of the same order of magnitude as the exotic cross-sections expected from two-component duality arguments.     

Insights into CO/styrene copolymerization by using Pd(II) catalysts containing modular pyridine-imidazoline ligands

Continuing our studies into the effect that N-N' ligands have on CO/styrene copolymerization, we prepared new C(1)-symmetrical pyridine-imidazoline ligands with 4',5'-cis stereochemistry in the imidazoline ring (5) and 4',5'-trans stereochemistry (6-10) and compared them with our previously reported ligands (1-4). Their coordination to neutral methylpalladium(II) (5 a-10 a) and cationic complexes (5 b-10 b), investigated in solution by NMR spectroscopy, indicates that both the electronic and steric properties of the imidazolines determine the stereochemistry of the palladium complexes. The crystal structures of two neutral palladium precursors [Pd(Me)(2-n)Cl(n)(N-N')] (n=1 for 8 a; n=2 for 9 a') show that the Pd-N coordination distances and the geometrical distortions in the imidazoline ring depend on the electronic nature of the substituents in the imidazoline fragment. Density functional calculations performed on selected neutral and cationic palladium complexes compare well with NMR and X-ray data. The calculations also account for the formation of only one or two stereoisomers of the cationic complexes. The performance of the cationic complexes as catalyst precursors in CO/4-tert-butylstyrene copolymerization under mild pressures and temperatures was analyzed in terms of the productivity and degree of stereoregularity of the polyketones obtained. Insertion of CO into the Pd-Me bond, which was monitored by multinuclear NMR spectroscopy, shows that the N ligand influences the stereochemistry of the acyl species formed.