Construction process for simple Lie algebras

We give here a construction process for the complex simple Lie algebras and the non-Hermitian type real forms which intersect the minimal nilpotent complex adjoint orbit, using a finite dimensional irreducible representation of the conformal group, or of some two-fold covering of it, with highest weight vector a semi-invariant of degree four. This process leads to a five-graded simple complex Lie algebra and the underlying semi-invariant is intimately related to the structure of the minimal nilpotent orbit. We also describe a similar construction process for the simple real Lie algebras of Hermitian type.     

Synthesis of 3-amino-1,2,4-benzothiadi- azine 1,1-dioxides via a tandem aza-Wittig/heterocumulene annulation

[reaction: see text] Reaction of o-azidobenzenesulfonamides with polymer-supported triphenylphosphine affords the corresponding iminophosphoranes. Subsequent reaction with isocyanates gives 3-amino-1,2,4-benzothiadiazine 1,1-dioxides in high yields and purities. The reaction has been successfully applied to the synthesis of derivatives with various substituents at the 2- and 3-positions and in the benzenoid ring.     

Properties of silver nanoparticle-polypyrrole composite film grown on cellulosic paper

Cellulose - In this work, a cellulosic paper substrate (Pap) coated by in situ polymerization of polypyrrole (PPY) was designed. This paper was subsequently coated with silver nanoparticles...     

A construction of new exact periodic wave and solitary wave solutions for the 2D Ginzburg–Landau equation

Using a uniform algebraic method, new exact solitary wave solutions and periodic wave solutions for 2D Ginzburg–Landau equation are obtained. Moreover, three-dimensional and two-dimensional graphics of some solutions have been plotted.     

Unsaturated Sugars : An Alternative Route to 3, 5, 6-Trideoxy-1, 2-O-Isopropylidene-α-D-Glycero-Hex-3, 5-Dienofuranose

Unsaturated sugars are among the most important and useful compounds in carbohydrate chemistry. They assume key roles in the synthesis of modified sugars and complex natural products. The title compound 5, an unsaturated sugar containing a conjugated diene system, has been reported¹ recently and its potential synthetic value for Diels-Alder reaction giving access to functionalized annulated furanoses has been pointed out.² For a different synthetic purpose we prepared this compound by an alternative route albeit from the same starting material used by the previous authors. Our synthetic sequence is outlined in the following scheme.     

Espace de Hardy pour les quotients \Gamma \backslash G

Résumé. Soit G un groupe linéaire réel simple hermitien, un sous-groupe arithmétique de covolume fini. Soit C un c?ne régulier Ad(G)-invariant dans l'algèbre de Lie de G, l'intérieur de C, et S(C)=Gexp(iC) le semi-groupe complexe d'Olshanski. L'espace de Hardy associéà ces données est l'espace des fonctions holomorphes sur , -invariantes à gauche telles qu'une certaine norme soit finie. C'est un espace de Hilbert, qui se plonge de manière isométrique dans l'espace . On donne une décomposition de l'espace de Hardy en représentations unitaires irréductibles avec des multiplicités égales à des dimensions d'espaces de formes automorphes. Les résultats les plus importants sont obtenus dans le cas de et , où l'on démontre que l'espace des vecteurs distributions des représentations de la série discrète, qui sont -invariants et qui vérifient une condition de carré intégrabilité, s'identifie à l'espace des formes modulaires paraboliques correspondant, ce qui nous permet de décrire explicitement la décomposition de l'espace de Hardy cuspidal en représentations irréductibles et d'en calculer le noyau reproduisant (appelé noyau de Cauchy-Szeg?) à l'aide des noyaux reproduisants des espaces de cusp forms. L'espace de Hardy cuspidal s'identifie au “morceau holomorphe” du spectre cuspidal .

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Received April 30, 1997; in final form September 18, 1997     

Highly enantioselective oxidation of sulfides to sulfoxides by a new oxaziridinium salt

The new oxaziridinium salt 5 (R2 = TBDPS) is an effective reagent for the highly enantioselective oxidation of sulfides to sulfoxides with up to >99% ee and good yields. As such, it represents a new valuable nonmetallic alternative to the existing methods for asymmetric sulfoxidation.