Dominated, diagonal polynomials on ℓ p spaces

We show that the r-dominated polynomials on _p(2 p ) are integral on ₁, and give examples proving that the converse is not true. We characterize when the 2-homogeneous, diagonal polynomials on _p(1 < p ) are r-dominated. We prove that, unlike the linear case, there are nuclear polynomials which are not 1-dominated.Received: 6 June 2004; revised: 28 September 2004     

Arithmétique fonctorielle des topologies de Grothendieck

Riassunto Il punto di partenza di questo lavoro è l'interpretazione delle topologie di Grothendieck nel linguaggio dei sistemi relazionali (cfr. [5]); ciò permette uno studio aritmetico di tali topologie. Attraverso nuove tecniche, qui introdotte, si ottengono risultati non privi di interesse, tra i quali una caratterizzazione degli spazi topologici noetheriani, ed ulteriori strutture topologiche di tipo locale (siti tangenti), per le quali vengono dimostrate numerose proprietà. Vengono, infine, date alcune applicazioni alla teoria degli schemi, utilizzando il funtore inviluppo affine.

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Summary The starting point of this paper is the interpretation of Grothendieck's topologies in the language of relational systems (cfr. [5]); this permits an arithmetical study of these topologies. By applying new techniques introduced here, we have achieved interesting results. These include a new characterization of Noetherian topological spaces, and further topological structures of local type (tangent sites) for which we have shown numerous properties. Finally, we have used the affine-envelope functor to illustrate some applications to the theory of schemes.

     

Diffusional and vibrational dynamics of ZnCl2 aqueous solutions by inelastic neutron scattering

We have studied saturated solutions of ZnCl₂ (and NiCl₂) in D₂O by time-of-flight quasi-elastic and inelastic neutron scattering spectroscopy. Spectra were taken at room temperature as a function of transferred momentum. We find that ionic diffusion in these solutions is best described by a crystal vacancy diffusion model. We also find evidence of collective excitations in the region of ～ 20 meV.     

Evidence for the production of slow antiprotonic hydrogen in vacuum

We present evidence showing how antiprotonic hydrogen, the quasistable antiproton (p)-proton bound system, has been synthesized following the interaction of antiprotons with the molecular ion H2+ in a nested Penning trap environment. From a careful analysis of the spatial distributions of antiproton annihilation events, evidence is presented for antiprotonic hydrogen production with sub-eV kinetic energies in states around n=70, and with low angular momenta. The slow antiprotonic hydrogen may be studied using laser spectroscopic techniques.     

Diffusion dynamics during the nucleation and growth of Ge/Si nanostructures on Si(111)

We report a low energy electron microscopy study of the relation between self-organized Ge/Si(111)nanostructures and their local environment. By comparison with Monte Carlo simulations, three-dimensional islands are shown to display a substantial tendency towards self-ordering. This tendency may result from the diffusive nature of the nucleation processes. The size of individual nanostructures does not significantly correlate with the distance between neighboring islands. Thus energetic factors are thought to govern the competition among coexisting nanostructures to capture the deposited mass.     

A Diffusive Strategic Dynamics for Social Systems

We propose a model for the dynamics of a social system, which includes diffusive effects and a biased rule for spin-flips, reproducing the effect of strategic choices. This model is able to mimic some phenomena taking place during marketing or political campaigns. Using a cost function based on the Ising model defined on the typical quenched interaction environments for social systems (Erdös-Renyi graph, small-world and scale-free networks), we find, by numerical simulations, that a stable stationary state is reached, and we compare the final state to the one obtained with standard dynamics, by means of total magnetization and magnetic susceptibility. Our results show that the diffusive strategic dynamics features a critical interaction parameter strictly lower than the standard one. We discuss the relevance of our findings in social systems.     

Properties of chains of prime ideals in an amalgamated algebra along an ideal

Let f:A→B be a ring homomorphism and let J be an ideal of B. In this paper, we study the amalgamation of A with B along J with respect to f (denoted by A?^fJ), a construction that provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D’Anna and Fontana in 2007, and other classical constructions (such as the A+XB[X], the A+XB?X? and the D+M constructions). In particular, we completely describe the prime spectrum of the amalgamated duplication and we give bounds for its Krull dimension.