Aubry-Mather Theory and Hamilton-Jacobi Equations

 We review and extend some results of Jauslin, Kreiss, Moser and Weinan E on the smooth approximation of Mather sets. Received: 20 November 2000 / Accepted: 4 November 2002 Published online: 24 January 2003 Communicated by G. Gallavotti     

The site-selectivity of cycloadditions of nitrile oxides to β-aminocinnamonitriles. A remarkable solvent dependence

Cycloadditions of nitrile oxides to N-mono and unsubstituted β-aminocinnamonitriles are remarkably affected by the hydrogen acceptor ability of the solvent. Addition to C ? N bond predominates in non and weak hydrogen bond acceptor solvents because of the assistance of favourable hydrogen bonding effects. In strong hydrogen bond acceptor solvents the assistance is fully relieved and the regular addition to C ? C bond becomes prevalent.     

Variational characterization of torsionless connections on Riemannian manifolds

We state a variational principle which allows the variational characterization of the class of torsionless affine connections on a Riemannian manifold, as well as of any subclass of it determined by a suitable set of constraints on the metricity of the connection.Work performed under the auspices of the Italian Group for Mathematical Physics (GNFM) of the Italian Research Council (CNR).     

Homogeneous catalytic hydrogenation of free carboxylic acids in the presence of cluster ruthenium carbonyl hydrides

Saturated monocarboxylic acids up to C₆, several bicarboxylic acids and some of the corresponding anhydrides are hydrogenated in the homogeneous phase with H₄Ru₄(CO)₈(PBu₃)₄ as catalyst to give the corresponding alcohols (present among the reaction products as esters) or lactones at 100–200°C under a pressure of 100–200 atm of hydrogen. Anhydrides react at temperatures lower than those needed for acids. Esters are not reduced. Only δ-valerolactone is hydrogenated to 1,5-pentanediol. Ruthenium carbonyl carboxylates have been recovered at the end of the reaction and appear to be catalytically active intermediates.     

Preferential protonation and methylation at the nitrogen atoms of N,N-dimethylamino derivatives of pyridine

The relative reactivity toward protonation and methylation of the two nitrogen atoms in N,N-dimethylaminopyridines has been examined by ¹H NMR. The ring position of the dimethylamino group has no influence on protonation, which occurs in all the derivatives at the heterocyclic nitrogen. The N-methylation reaction does not follow a homogeneous behaviour, occurring at the exocyclic nitrogen in the 2-substituted dimethylamino derivative. The electronic characteristics of the molecules, determined by MO calculations at a semi-empirical level, indicate that both protonation and methylation should occur at the heterocyclic nitrogen; the calculated relative stabilites, however, of the N-protonated and N-methylated forms are in full agreement with the experimental results, and it appears that the anomalous behaviour of 2-dimethylaminopyridine in the N-methylation reaction is caused by steric factors.     

A study of the 75As(n,n'γ)75As reaction

The de-excitation gammas following the inelastic scattering of neutrons from ⁷⁵As have been studied for incident neutron energies from 1300 to 2800 keV in steps of 100 keV. The energy levels and the branching ratios of their decays have been deduced from excitation function measurements: 58 energy levels have been found in the excitation energy region below 2.8 MeV, twelve of which are reported for the first time in this work. The experimental excitation functions and angular distributions have been compared with the theoretical predictions based on the statistical theory of the compound nucleus. Spin and parity assignments for the levels and multipolarities for the decays are proposed for excitation energies of levels up to 2300 keV.     

Incentives and individual motivation in supervised work groups

This paper introduces and analyzes a model of supervised work group where subordinates decide how to exert their effort in complementary tasks while the supervisors decide incentives. Incentives may be a combination of individual and group-based ones. The optimality of incentives is analyzed when considering two different cost functions for subordinates. The two cost functions describe different individual motivations; comparing the resulting effort allocations and production optimality, we can relate them to different organizational theories. Our results provide a measure of how motivation among subordinates may affect production and incentives. Furthermore, the optimal incentives schemes are examined in terms of Adams’ equity theory.     

Particle Decays and Stability on the de Sitter Universe

We study particle decay in de Sitter space–time as given by first-order perturbation theory in a Lagrangian interacting quantum field theory. We study in detail the adiabatic limit of the perturbative amplitude and compute the “phase space” coefficient exactly in the case of two equal particles produced in the disintegration. We show that for fields with masses above a critical mass m _c there is no such thing as particle stability, so that decays forbidden in flat space–time do occur here. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with mass lower than critical have a completely different behavior: the masses of their decay products must obey quantification rules, and their lifetime is zero.