A generalization of the classical moment problem on *-algebras with applications to relativistic quantum theory. I.

A (non-commutative) generalization of the classical moment problem is formulated on arbitrary *-algebras with units. This is used to produce aC*-algebra associated with the space of test functions for quantum fields. ThisC*-algebra plays a role in theories of bounded localized observables in Hilbert space which is similar to that of the space of test functions in quantum field theories (namely it is represented in Hilbert space). The case of local quantum fields which satisfy a slight generalization of the growth condition is investigated. Laboratorie associé au Centre National de la Recherche Scientifique.     

Determination of the geometric structure of three substituted polyacetylenes: Polymethylacetylene,polypentylacetylene, and poly(tbutylacetylene)

The geometric structure of polymethylacetylene (PMA), polypentylacetylene (PPA), and poly(t-butylacetylene) (PTA) was investigated by ¹H NMR, ¹³C NMR, and IR spectroscopies. It was shown that both NMR techniques can be used to determine the trans isomer content of PPA and PTA, whereas the ¹H NMR and IR methods can be used for PMA. A calibration curve was constructed by using the 965- and 720-cm^?1 bands of the IR spectrum of PPA, and could be used in future work for the same purpose if the samples had molecular weights similar to that of the one used in this study. The isomerization kinetics of PTA was investigated and cis^→ trans activation energies of 88 and 121 kJ/mol were calculated in solution and in the solid state, respectively. Heat treatment of the PMA and PPA samples always leads to a cis^→ trans isomerization with a 100% trans content under extreme conditions. Moreover, a cis^→ trans isomerization of PTA was induced in CCl₄, CDCl₃, toluene, and benzene, but a trans^→ cis isomerization was induced in decalin. The reversible isomerization of PTA covered a trans isomer concentration ranging form 25 to 60%.     

A simple two-step para-diacetylation of benzene and p-xylene

Aromatic hydrocarbons (benzene, p-xylene) are conveniently p-diacetylated by the regiospecific reductive p-disilylation/diacetylation process, followed by oxidative aromatization. The reaction uses trimethylchlorosilane which is recovered during the course of reaction. It gives diacetyl cyclohexadiene intermediates, novel species which prove relatively stable in an inert atmosphere.     

Fermeture en probabilité de certains sous-espaces d'un espace L 2

Summary Let _i , iI be a family of equidistributed, independant random variables, defined on a probability space (, , P). Let {f _m , mN{ be a sequence of functions such that the f _m ( _i ) are, for every i, centered random variables in L ²(, , P) and in an L _p (, , P) (where p is an even integer at least equal to 4).In this paper the closed linear subspaces of L ² (, , P) generated by the variables of the form , where for fixed M, are studied. A uniform bound of the L ^p norm of elements of the unit ball of the above defined subspaces and also the closure in probability of these subspaces is thus obtained. These results are applied to Wiener's chaos of gaussian variables.

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Equipe de Recherche n⁰ 1 « Processus stochastiques et applications » dépendant de la Section n⁰ 2 «Théories Physiques et Probabilités », associée au C.N.R.S.     

Le théorème deBarden-Mazur-Stallings

Sans résumé L’auteur est titulaire d’uneAlfred P. Sloan Fellowship.