Alkylation de la dimethyl-5 5′ isoxazolidinone-3 en catalyse par transfert de phase

Alkylation by phase transfert catalysis of ambidents anions of the N-C-0 type, leads to a mixture of N and O substitution. Isomers per cent are 20% for O alkylation and 80% for N alkylation when primary halides are used. With secondary halides, these figures are 35% and 65%. In both cases the overall yield ranges around 60%.     

Etude de la racemisation induite par la dmap dans les reactions de couplage peptidique

The scope and limitation for the use of 4-dimethylamino pyridine (DMAP) as additive to carbodiimides in peptide synthesis are studied and compared with the results obtained with H-hydroxybenzotriazole (HOBt). The activation of N-acylated aminoacids by the means of DMAP leads to a complete racemization. On the other hand, for the aminoacids protected under their urethans derivatives, DMAP gives better yields than HOBt with racemization extent generally equal to or slightly higer to that observed with HOBt.     

Relations de dépendance entre les équations fonctionnelles de Cauchy

Résumé Afin d'examiner les relations entre les différentes équations de Cauchy, nous résolvons, sans aucune hypothèse de régularité, l'équation fonctionnellea f(xy) + b f(x)f(y) + c f(x + y) + d (f(x) + f(y)) = 0, pour des fonctionsf, définies sur un anneau unifère divisible par deux et prenant leurs valeurs dans un corps, Les coefficientsa, b, c, etd appartiennent au centre de ce corps. Entre autres applications, nous en déduisons qu'une seule équation, à savoirf(xy) + f(x + y) = f(x)f(y) + f(x) + f(y), caractérise les endomorphismes des corps dont la caractéristique est différente de 2. En introduisant la notion d'équations fonctionnelles étrangères et d'équations fonctionnelles fortement étrangères, nous concluons à l'indépendance, au sens de cette notion, des équations classiques de Cauchy.

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Summary In order to study the inter-relations between the four Cauchy functional equations, we solve the functional equationa f(xy) + b f(x) f(y) + c f(x + y) + d(f(x) + f(y)) = 0. The functionf is defined over a ring which is divisible by 2 and which possesses a unit, while the values off are in a(skew)-field. The constantsa, b, c andd belong to this field and commute with all elements of thes-field. No regularity assumption is made onf. Among other applications, we show that the single equationf(xy) + f(x + y) = f(x)f(y) + f(x) + f(y), is enough to characterize field endormophisms in fields of characteristic different from 2. We introduce the notion of alien functional equations and that of strongly alien functional equations, to conclude that for such notions, Cauchy equations are indeed largely independent.

Dédié avec nos meilleurs voeux à Monsieur le Professeur Otto Haupt à l'occasion de son centenaire     

A short large scale synthesis of (±) sarkomycin esters

(±) Sarkomycin ethyl ester has been prepared in four steps from ethyl acrylate.     

Analytic extension of non quasi-analytic Whitney jets of Roumieu type

Let (M_r)_{r∈? 0} be a logarithmically convex sequence of positive numbers which verifies M₀ = 1 as well as M_r ≥ 1 for every r ∈ ? and defines a non quasi-analytic class. Let moreover F be a closed proper subset of ?ⁿ. Then for every function ? on ?ⁿ belonging to the non quasi-analytic (M_r)-class of Roumieu type, there is an element g of the same class which is analytic on ?ⁿ F and such that D^α ?(x) = D^αg(x) for every σ ∈ ?₀ ⁿ SBAP and x ∈ F.