Near integral domains II

A direct product decomposition is given for the multiplicative semigroup of a finite near integral domain in terms of the subsemigroup of left identities and a group of automorphisms on the additive group of the domain. Conditions are given which insure that every element will have a uniquen-th root. If there existsx≠0 such that (?x)y=?(xy), for eachy, then the additive group of the near integral domain is abelian. Other conditions sufficient for the commutativity of the additive group are given. An example illustrates that non-isomorphic finite near integral domains can have a left ideal decomposition into Sylow subgroups which are isomorphic as near-rings. Another example shows that an infinite near integral domain need not have a nilpotent additive group, even in the d. g. case. It is conjectured that for each natural numbern there is a near integral domain whose additive group is of nilpotent classn.     

II. Anorganisch Substanzen

Ohne Zusammenfassung     

A fully vectorial technique for scattering and propagation in three-dimensional stratified photonic structures

We present a three-dimensional (3D) technique for computing light scattering and propagation in complex structures formed by scatterers embedded in a stratified background. This approach relies on the Green's tensor associated with the background and requires only the discretization of the scatterers, the entire stratified background being accounted for in the Green's tensor. Further, the boundary conditions at the edges of the computation window and at the different material interfaces in the stratified background are automatically fulfilled. Different examples illustrate the application of the technique to the modeling of photonic integrated circuits: waveguides with protrusions (single element grating) and notches. Subtle effects, like polarization crosstalks in an integrated optics device are also investigated.     

Second-order nonlinear optical coefficient of polyphosphazene-based materials: a theoretical study

The second-order nonlinear optical coefficient of polyphosphazene oligomers of increasing size has been determined by using ab initio methods taking into account electron correlation and frequency dispersion effects. The calculated first hyperpolarizability per unit cell converges rapidly with respect to chain length. It attains an amplitude of about one-third of the one of classical push-pull systems. This amplitude can be strongly increased by replacing the nitrogen of the backbone by silicon. The effects of the side groups (H, CH3, F, Cl, Br, and OH) on the first hyperpolarizability have been investigated as well. The different results have been rationalized in terms of alternations of bond lengths and atomic charges.     

First lanthanide dipolar complexes for second-order nonlinear optics

New push-pull NLO-phores based on lanthanide complexes (Ln = La, Gd, Dy, Yb) featuring an annelated dibutylaminophenyl functionalised terpyridyl ligand have been synthesised and shown to exhibit large first-order hyperpolarizability.     

Intramolecularly hydrogen-bonded versus copper(II) coordinated mono- and bis-phenoxyl radicals

Ligands bearing two salicylidene imine moieties substituted in ortho and para positions by tert-butyl groups have been electrochemically oxidized into mono- and bis-phenoxyl radicals. The process involves an intramolecular proton coupled to electron transfer and affords a radical in which the oxygen atom is hydrogen-bonded to a protonated ammonium or iminium group. A weak intramolecular dipolar interaction exists between the two phenoxyl moieties in the bis-radical species. The copper(II) complexes of these ligands have been characterized and electrochemically oxidized. The mono-phenoxyl radical species are X-band EPR silent. The bis-phenoxyl radical species exhibits a (S= 3/2) ground state: it arises from a ferromagnetic exchange coupling between the two spins of the radicals and that of the copper(II) when the spacer is rigid enough; a flexible spacer such as ethylidene induces decomplexation of at least one phenoxyl group. Metal coordination is more efficient than hydrogen-bonding to enhance the chemical stability of the mono-phenoxyl radicals.     

Enhanced two-photon absorption with novel octupolar propeller-shaped fluorophores derived from triphenylamine

[structure: see text] Novel octupolar fluorophores derived from the symmetrical functionalization of a triphenylamine core with strong acceptor peripheral groups via phenylene-ethynylene linkers have been synthesized and shown to exhibit high fluorescence quantum yields, very large TPA cross-sections in the red-NIR region, and suitable photostability.     

Groupes plongés quasi isométriquement dans un groupe de Lie

Soit un sous-groupe discret de type fini dun groupe de Lie semi-simple G. On donne ici une condition suffisante pour que linjection de dans le groupe G admet un voisinage de représentations fidèles et discrètes.     

Sur les caractères du groupe de Suzuki

Let σ be the automorphism of $\mathrm{Sp}(4\text{,}{2}^{2n+1})$ so that the set of fixed points is the Suzuki group. We propose in this Note to calculate the irreductible characters of $\mathrm{Sp}(4\text{,}{2}^{2n+1})?〈\sigma 〉$, extension of degree two of the symplectic group, and describe two consequences: first, the principal block of the Suzuki group and of this extension are perfectly isometric, and secondly we determine the eigenvalues of Frobenius of the unipotent characters of the Suzuki group. To cite this article: O. Brunat, C. R. Acad. Sci. Paris, Ser. I 339 (2004).