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.     

Effective dissipation and turbulence in spectrally truncated euler flows

A new transient regime in the relaxation towards absolute equilibrium of the conservative and time-reversible 3D Euler equation with a high-wave-number spectral truncation is characterized. Large-scale dissipative effects, caused by the thermalized modes that spontaneously appear between a transition wave number and the maximum wave number, are calculated using fluctuation dissipation relations. The large-scale dynamics is found to be similar to that of high-Reynolds number Navier-Stokes equations and thus obeys (at least approximately) Kolmogorov scaling.     

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.     

Production and distribution function of fast ions in laser produced plasma

Fast ions theoretical distribution functions deduced from ponderomotive force mechanism are computed and compared to those obtained in laser plasma experiments. Within the limit of validity of the calculations, experimental and theoretical results are in good agreement.