Isoperimetric phase transitions of two-dimensional droplets

We consider two-dimensional assemblies of particles governed by hamiltonians depending on the area and the perimeter of their convex hull. Provided the hamiltonian is quadratically homogeneous in the coordinates, we find an exact formula for the free energy. Phase transitions resulting from the competition between area and perimeter can easily be produced and explicitly dealt with. We illustrate those features by a simple example undergoing a second-order transition.     

Catégories de Möbius et fonctorialités: un cadre général pour l'inversion de Möbius

This paper proposes a general setting for Möbius inversion which includes the cases of locally finite partially ordered sets and monoids with the finite decomposition property (f.d.p.). The unifying concept is that of categories with the f.d.p., called Möbius categories, which we characterize in four different ways. The established theory of incidence algebras, Möbius functions, product formulas, reduced algebras, etc., is carried over. Furthermore, the study of functors between Möbius categories yields results in two directions: firstly, inspired from the substitution of formal power series is the construction of a homomorphism between incidence algebras which allows the transfer of Möbius inversions; secondly, surjective functors often give rise to a reduced incidence algebra, thus shedding new light on many important reduced algebras in combinatorial theory.     

Sur une voie d'acces potentiellement generale aux phosphines fonctionnelles a phosphore optiquement actif

Optically active methyl-phenyl-cyclohexylphosphine sulfide is metallated by BuLi and reacted with ethyl carbonate to yield carbethoxymethyl-phenyl-cyclohexylphosphine sulfide with retention of the optical activity at phosphorus ; this sulfide is converted into the corresponding optically active functional phosphine through a nickelocene reduction-complexation.     

A new synthesis of 3-fluoro phnylalanine esters

Isopropyl 2-Phenyl 3-aziridinecarboxylate (III) obtained from isopropyl 2,3-dibromo-2,3-dihydrocinnamate (I) or isopropyl 2-bromocinnamate (II) reacts in mild conditions with hydrogen fluoride to give the isopropyl ester of 3-fluorophenylalanine (IV) in good yield.     

Structural requirements of Na+-dependent antidopaminergic agents: Tropapride,Piquindone, Zetidoline,and Metoclopramide Comparison with Na+-independent ligands

Summary Molecular graphic design coupled with PCILO and crystallographic results have been used to investigate the three-dimensional structure of Tropapride, Piquindone, Zetidoline, and Metoclopramide, four dopamine D-2 receptor antagonists showing Na⁺-dependent binding. Three putative pharmacophoric elements, a nitrogen lone pair, a phenyl ring and a carbonyl moiety, are similarly oriented in all the Na⁺-dependent drugs. Conversely, for Na⁺-independent analogs, the two latter pharmacophoric elements play a subordinate role, but two -electron regions are systematically localized on the other side of the molecule: the first is a phenyl group while the second is a carbonyl function as in butyrophenones, a cyano group as in R48455, or a phenyl ring as in diphenylbutylpiperidines or tricyclics. The presence of a benzyl ring on this side in Tropapride might explain its weak extrapyramidal effects.     

Groupes d’homotopie des variétés de Stiefel complexes

Sans résumé L’auteur tient à remercier vivement MM. les professeursB. Eckmann etP. J. Hilton pour leurs suggestions enrichissantes au cours de la rédaction de ce travail.     

Analyticity of the pressure for Heisenberg and plane rotator models

We use complex rotations and convex completion to extend the analyticity region of the pressure for the Heisenberg and plane rotator models.