The experimental localization of Aubry-Mather sets using regularization techniques inspired by viscosity theory

We provide a new method for the localization of Aubry-Mather sets in quasi-integrable two-dimensional twist maps. Inspired by viscosity theories, we introduce regularization techniques based on the new concept of "relative viscosity and friction," which allows one to obtain regularized parametrizations of invariant sets with irrational rotation number. Such regularized parametrizations allow one to compute a curve in the phase-space that passes near the Aubry-Mather set, and an invariant measure whose density allows one to locate the gaps on the curve. We show applications to the "golden" cantorus of the standard map as well as to a more general case.     

When is a Multiplicative Derivation Additive in Alternative Rings?

In this article, we generalize a result about multiplicative derivations due to Daif to alternative rings.     

The reactive bargaining set of some flow games and of superadditive simple games

We prove that the reactive bargaining set coincides with the core of simple flow games, and it essentially coincides with the kernel of simple superadditive games.     

MHD fluctuations and low energy solar neutrinos

We analyze here how future solar neutrino experiments could detect neutrino flux fluctuations due to magnetohydrodynamics (MHD) perturbations on the solar plasma. We state that if such time fluctuations are detected, this would provide a unique signature of the resonant spin-flavor precession (RSFP) mechanism as a solution to the solar neutrino problem. Received: 2 July 2001 / Revised version: 4 April 2002 / Published online: 20 August 2002     

RADIATIONLESS DEACTIVATION AND FLUORESCENCE OF SELECTED PYRIDONES

Abstract— Numerous 3-position derivatives of 2-hydroxy pyridine, also known as 2-pyridone, were synthesized and their optical absorption and fluorescence spectra examined. The quantum yield of emission varied from near zero to near unity depending on the kind of substitution made and the solvent. Data are presented that argue for the π-π* nature of the first excited state in all cases. It was concluded that intramolecular hydrogen bonding controls the extent of internal conversion and hence the amount of fluorescence. It is proposed that this hydrogen bonding suppresses the low energy out of plane vibrations necessary for internal conversion as required by the proximity effect. From studies of the temperature dependence of the emissions, it appeared that the energy separation of the first two excited states, in all cases ˜12.6 ± 2 kJ/mol (3000 ± 500 cal/mol), is not correlated to the extent of relaxation     

C-22 ketals related to the sapogenins

Reduction of 5,6-dihydrokryptogenin diacetate with Raney nickel in ethanol reduced the 16-ketone group and gave a mixture of a 22-ethyl ketal with a hemiketal. Both undergo elimination reactions very readily to yield the Δ²²-bond isomer of pseudotigogenin diacetate. The conversions are reversible and are catalyzed by acetic acid and in neutral solution by calcium sulfate and other surfaces. Alkaline hydrolysis followed by cyclization with acetic acid converted both the ketal and the Δ²²-olefin to tigogenin. The relative stabilities of ketal epimers at C-22 are discussed and related to the stereo-chemistry of the sapogenins and the cyclopseudosapogenins.     

The Nekhoroshev theorem and the observation of long-term diffusion in Hamiltonian systems

The long-term diffusion properties of the action variables in real analytic quasiintegrable Hamiltonian systems is a largely open problem. The Nekhoroshev theorem provides bounds to such a diffusion as well as a set of techniques, constituting its proof, which have been used to inspect also the instability of the action variables on times longer than the Nekhoroshev stability time. In particular, the separation of the motions in a superposition of a fast drift oscillation and an extremely slow diffusion along the resonances has been observed in several numerical experiments. Global diffusion, which occurs when the range of the slow diffusion largely exceeds the range of fast drift oscillations, needs times larger than the Nekhoroshev stability times to be observed, and despite the power of modern computers, it has been detected only in a small interval of the perturbation parameter, just below the critical threshold of application of the theorem. In this paper we show through an example how sharp this phenomenon is.