A propos de l'existence et de la régularité des solutions de certaines inéquations quasi-variationnelles

We prove existence and regularity results for a general inequality including fixed point problems, variational and quasi variational inequalities. Examples of such problems are considered.     

Convergence of convex integrals in Lp spaces

We consider functionals of the form: I_f(u) = ∝_Tf[t, u(t)]μ(dt), which are defined on spaces L^p(T, R^k), and we study for these functionals the properties of a convergence for which the conjugacy $\text{I}{}_{\mathrm{f}}\text{→ I}{}_{\mathrm{f1}}$ is a continuous operator.     

Implementation canonique pour les co-actions d'un groupe localement compact et les systèmes dynamiques généralisés

Sans résumé     

A threshold property for intersections in a finite set

Let F be any family of subsets of a finite set E and let n be an integer, n<|F|. Under what condition does the knowledge of cardinals of m-intersections in F, for all m≤n, univocally determine the cardinal of any intersection in F, and what is the minimal condition? We give a complete answer to that. For any n, this determination property is satisfied by n if and only if |E|<2ⁿ, without further condition on F.     

Diastereoselective addition of 2H-2-oxo-1,4,2-oxazaphosphinanes to aldehydes and imines

[reaction: see text] Diastereoselective additions of 2-hydrogeno-2-oxo-1,4,2-oxazaphosphinanes to aldehydes and imines are described. alpha,alpha'-Diaminophosphinic and alpha-amino-alpha'-hydroxyphosphinic derivatives were obtained with de's ranging from 24 to 90%.     

First syntheses of 2-hydrogeno-2-oxo-1,4,2-oxazaphosphinanes via intramolecular esterification

Synthesis of 2-hydrogeno-2-oxo-1,4,2-oxazaphosphinanes via either intramolecular transesterification, using potassium tert-butylate as catalytic agent, or phosphinic acid esterification, is described for the first time.     

Asymmetric sulfur ylide mediated aziridination: application in the synthesis of the side chain of taxol

[reaction: see text] Sulfur ylide methodology has been used to construct the Taxol side chain with a high degree of enantioselectivity via a trans-aziridine followed by stereospecific rearrangement of the trans-benzoylaziridine into a trans-oxazoline.     

Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb Systems. I. Low Fugacity Expansion

We present an exact field theoretical representation of the statistical mechanics of classical hard-core Coulomb systems. This approach generalizes the usual sine-Gordon theory valid for point-like charges or lattice systems to continuous Coulomb fluids with additional short-range interactions. This formalism is applied to derive the equation of state of the restricted primitive model of electrolytes in the low fugacity regime up to order ρ^5/2 (ρ number density). We recover the results obtained by Haga by means of Mayer graphs expansions.     

Synthesis of unnatural 2- and 3-deoxyfuranose analogues

This Letter describes the synthesis of two racemic analogues of unnatural 3′-deoxy and 2′-deoxy sugars, where a phosphorus atom replaces the carbon atom in the 2′- or 3′-position. Two methods of four- and 5-steps were developed affording these new unnatural sugar analogues.     

Topological Entropy and Secondary Folding

A convenient measure of a map or flow’s chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is exactly equal to the growth induced by the map on the fundamental group of the torus. However, in many situations the numerically computed topological entropy is greater than the bound implied by this action. We associate this gap between the bound and the true entropy with ‘secondary folding’: material lines undergo folding which is not homologically forced. We examine this phenomenon both for physical rod stirring devices and toral linked twist maps, and show rigorously that for the latter secondary folds occur.