Hétérocycles contenant du phosphore. XXXII. Etude de l'action des phosphorhydrazides sur les orthoesters,l'anhydride acétique et l'acide formique

The reaction of phosphodi- or trihydrazides with orthoesters affords mainly 2,3,4,5-tetrahydro-1,2,4,5,3-tetrazaphosphorines and sometimes 4-amino-1,2,4,3-triazaphospholidines. These 1,2,4,5,3-tetrazaphosphorines present a prototropy which explains different pathways of the reaction of these derivatives with formaldehyde or acetone, The structure of all heterocycles which were obtained was established by nmr spectra.     

Theory of dressed-excitons

We show that the exciton optical Stark effect is basically a dressed-exciton effect: excitons are dressed by the electromagnetic field in a way similar to the way atoms are dressed. The situation appears, however, much richer in semiconductor than in atomic physics due to both the complexity of the band structure and the Coulomb interaction between excitons. We show that the dressed-exciton effect can appear as either a blue or a red shift of the exciton line as well as a splitting of exciton levels, with an interesting dimensional effect in the absorption strength. We also relate the dressed-exciton to the polariton effect.     

A characterisation of the embeddings of PG(m,q) into PG(n,qr).

Let S_m be an embedding of PG(m,q) into PG(n,q^r),with n < m, such that S_m generates PG(n,q^r). S_m can be obtained as a projection from a (m–n–1)-dimensional subspace V_m–n–1 into a non incident n-dimensional subspace V_n of some strong embedding S of PG(m,q) into PG(m,q^r).     

A Hybrid Bounding Procedure for the Workload Allocation Problem on Parallel Unrelated Machines with Setups

A nonpreemptive single stage manufacturing process with parallel, unrelated machines and multiple job types with setups (PUMS) is considered. We propose a hybrid approximation procedure where a Lagrangean relaxation dual and a Lagrangean decomposition dual are solved one after the other to generate a good lower bound on the optimal makespan value. Computational results are reported.     

Poly-α-methyleneglutaronitrile. Characteristic features of some anionic polymers

For (initiator)/(monomer) ratios exceeding 10^-3, the anionic polymerization of α-methyleneglutaronitrile in homogeneous solution in DMF (initiated by lithium-naphthalene at -35° or by diphenylmethyl-lithium at -70°) leads to fairly white polymers with yields higher than 75 per cent. Infra-red and u.v. spectrometric studies and flash pyrolysis experiments show that the nitrile functions are involved in the polymerization only to a very small extent. On the other hand, molecular weight and sedimentation measurements and hydrodynamic behaviour of the polymer in DMF solution suggest a broad polydispersity for the samples, and a very high branching density for their higher molecular weight fractions. These characteristic features are to be correlated with those of anionic polyacrylonitrile; they may be tentatively attributed to transfer to polymer at the acidic methylene group a to the nitrile function.     

Catalytic N-sulfonyliminium ion-mediated cyclizations to alpha-vinyl-substituted isoquinolines and beta-carbolines and applications in metathesis

[reaction: see text] Catalytic Sn(OTf)2-induced cyclization of linear, aryl-containing allylic N,O-acetals produced vinyl-substituted tetrahydroisoquinolines and tetrahydro-1H-beta-carbolines. The usefulness of the vinyl moiety in the resulting products was demonstrated via the synthesis of various key building blocks for alkaloid structures. The alpha-vinyl moiety was utilized in a [2,3] sigmatropic rearrangement, in ring-closing metathesis and a cross-metathesis-based synthesis of vincantril, an antianoxia agent, and a synthetic member of the vincamine type natural products.     

Asymptotics for the Low-Lying Eigenstates of the Schrödinger Operator with Magnetic Field near Corners

The Neumann realization for the Schr?dinger operator with magnetic field is considered in a bounded two-dimensional domain with corners. This operator is associated with a small semi-classical parameter h or, equivalently, with a large magnetic field.We investigate the behavior of its eigenpairs as h tends to zero, like in a semi-classical limit. We prove, in the situation where the domain is a polygon and the magnetic field is constant, that the lowest eigenvalues are exponentially close to those of model problems associated with the corners. We approximate the corresponding eigenvectors by linear combinations of functions concentrated in corners at the scale If the domain has curved sides and the magnetic field is smoothly varying, we exhibit a full asymptotics for eigenpairs in powers of Communicated by Christian Gérard Submitted: October 13, 2005 Accepted: December 19, 2005