Macrocyclic host cyclophosphazenes from aminolysis of N3P3CI6 by bis-(2-ortho-aminophenoxyethyl)ether

Aminolysis of N₃P₃CI₆ by an oxodiamine, bis-(2-ortho-aminophenoxyethyl) ether, has been carried out under various experimental conditions and new products with different architectures have been obtained. The reaction in diethyl ether when using a Na₂CO₃-water interface process gives the mono-BINO as major product. Reaction on Al₂O₃/KOH leads to the spirocyclic compound, while, when the reaction is carried out in toluene in the presence of NEt₃, a mixture of mono- and di-BINO products are obtained. These new products have been characterized by IR, ¹H and ³¹P NMR spectroscopy.      

Espaces homogènes d'Einstein non-compacts

In this text, we consider the solvmanifolds obtained by an abelian extension of two-step nilmanifolds and obtain Einstein metrics (with negative scalar curvature) near to the symmetric spaces.     

Moment expansion approach to the time dynamics of genetic evolution

We use moment expansion methods to analyze the time dynamics for genetic evolution under selection, mutation, and reproduction. We consider a N-allele diploid genotype reproducing randomly in a fitness landscape with either one or two maxima, and mutation is assumed to occur such that any allele can mutate into any other type. We find that the moment expansion works well, where a small number of moments can capture the general behavior toward equilibrium. Our methods allow a systematic way to capture the time dynamics of the evolutionary process efficiently using a small number of coupled equations.     

Ricci flat rotating black branes with a conformally invariant Maxwell source

We consider Einstein gravity coupled to an U(1) gauge field for which the density is given by a power of the Maxwell Lagrangian. In d-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as d/4. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking–Page phase transition in spite of conformally invariant Maxwell field.     

Three-Component Reaction Between Trivalent Phosphorus,Dimethyl Acetylenedicarboxylate,and Amide Derivatives

Stabilized phosphoranes were synthesized from the reaction between dimethyl acetylenedicarboxylate and amide derivatives in the presence of triphenylphosphine. Dimethylurea containing a phosphorus ylide underwent a smooth reaction in boiling toluene to produce hydantoin and oxo-oxazolidin containing stable phosphorus ylides in good yields. Phosphorus ylides derived from (PhO)₃P were not stable and converted to diastereoisomeric phosphonates and phosphorimidate. The nature of the amide derivatives and type of trivalent phosphorus compounds, as well as solvents, determined the distribution of products.     

Variétés homogènes d'Einstein de courbure scalaire négative: Construction à l'aide de certains modules de Clifford

Using certain Clifford modules, we give a method for constructing many examples of homogeneous Einstein spaces with negative scalar curvature.     

Rank,term rank and chromatic number of a graph

Let G be a graph with a nonempty edge set, we denote the rank of the adjacency matrix of G and the term rank of G, by $\mathrm{rk}(G)$ and $\mathrm{Rk}(G)$, respectively. It was conjectured [C. van Nuffelen, Amer. Math. Monthly 83 (1976) 265–266], for any graph G, $\chi (G)?\mathrm{rk}(G)$. The first counterexample to this conjecture was obtained by Alon and Seymour [J. Graph Theor. 13 (1989) 523–525]. Recently, Fishkind and Kotlov [Discrete Math. 250 (2002) 253–257] have proved that for any graph G, $\chi (G)?\mathrm{Rk}(G)$. In this Note we improve Fishkind–Kotlov upper bound and show that $\chi (G)?\frac{\mathrm{rk}(G)+\mathrm{Rk}(G)}{2}$. To cite this article: S. Akbari, H.-R. Fanaï, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Existence of partial transversals

We use the polynomial method to study the existence of partial transversals in the Cayley addition table of Abelian groups.     

Dynamic 1H NMR study of the barrier to rotation about the C-N bond in primary carbamates and its solvent dependence

The dynamic 1H NMR study of some primary carbamates in the solvents CDCl3 and CD3COCD3 between 183 and 298 K is reported. The free energies of activation, thus obtained (12.4 to 14.3 kcal mol-1), were attributed to the conformational isomerization about the N-C bond. These barriers to rotation show solvent dependence in contrast to the tertiary analogues and are lower in free energy by ca. 2-3 kcal mol-1.     

On Triangularizability of a Group of Operators

Let ${\mathcal{G}}$ be a group of invertible linear transformations on a finite-dimensional vector space over an algebraically closed field. We show that if ${\mathcal{G}=\mathcal{H}\vee\mathcal{K}}$ , where ${\mathcal{H}}$ is a normal subgroup consisting of singleton spectrum operators and ${\mathcal{K}}$ is a triangularizable subgroup, then ${\mathcal{G}}$ is triangularizable.