Experimental study of quantum chaos with cold atoms

We investigate experimentally the quantum behavior of laser-cooled atoms in a pulsed standing wave, a system that is an atomic analog of the quantum kicked rotor. In particular, it may display the well-known phenomenon of “dynamical localization”, when the standing wave is driven periodically. Furthermore, we study some interesting properties of a quasi-periodically driven kicked rotor, which presents resonances that are shown to be sharper than the inverse of the driven–excitation duration, thus presenting a sub-Fourier character.     

Preparation of α,α-Dibromocyclobutanones from Olefins: A simple procedure for the regioselective functionalization of olefins

Dibromoketene is prepared by in-situ Zn dehalogenation of tribromoacetyl bromide in the presence of POCl₃. Under these conditions, the cycloaddition of dibromoketene with olefins 5 yields α,α-dibromocyclobutanones 2 , which are cleaved with alkoxides to yield β-dibromomethyl esters 4 . Several examples are given. For monosubstituted olefins, the functionalization is regioselective, the methoxycarbonyl group being introduced at the terminal C-atom.     

Conditions d'application et de convergence de procédés d'extrapolation

Some extrapolation algorithms for convergent sequences are studied herein. Application theorems and convergence theorems dealing with the construction law of the terms of the sequence are proved for these algorithms. The second part is concerned with two generalizations of the -algorithm. They are studied in detail and various numerical examples are given.     

Influence of butadiene-1,3 on ethanal pyrolysis at 495°C

At 495°C and a low extent of reaction, ethanal pyrolysis is slightly inhibited by the addition of small quantities of butadiene-1,3, whereas it is accelerated by more important quantities. The inhibiting effect is interpreted in terms of a free-radical chain mechanism in which the main chain carriers of ethanal pyrolysis (CH₃.free radicals) reversibly add to butadiene-1,3 and yield penten-2-yl (R.) free radicals. These free radicals either react in a metathetical step: or in terminating steps. But butadiene-1,3 also gives rise to new initiation steps: which account for the accelerating effect. Process (i₃) seems to be more important than process (i₂) in the experimental conditions, but its nature could not be identified. The results are consistent with literature data and the following value of k₆: (4.57T in cal/mol).     

Long-time averaging for integrable Hamiltonian dynamics

Summary. Given a Hamiltonian dynamical system, we address the question of computing the limit of the time-average of an observable. For a completely integrable system, it is known that ergodicity can be characterized by a diophantine condition on its frequencies and that this limit coincides with the space-average over an invariant manifold. In this paper, we show that we can improve the rate of convergence upon using a filter function in the time-averages. We then show that this convergence persists when a symplectic numerical scheme is applied to the system, up to the order of the integrator.     

Use of polymeric nucleophiles for the selective binding and removal of α-methylene-γ-butyrolactone allergens from complex mixtures.

An insoluble polymer containing primary amines selectively removed α-methylene-γ-butyrolactone allergens from solutions.     

Etude en RMN du 13C des Effets de Substituant sur les Déplacements Chimiques du Carbone dans les Méthyl Tétrahydrofurannes

Carbon-13 nuclear magnetic resonance spectra have been recorded and interpreted for some methyltetrahydrofurans. The effects of a methyl substituent on the ring carbon atoms are discussed in terms of steric hindrance and conformational equilibrium.     

Probabilistic analysis of the subset-sum problem

Two linear time algorithms are shown to solve the n-object SUBSET-SUM problem with probability approaching 1 as n gets large, for a uniform instance distribution. Precise evaluations of the probabilities involved are given.