Cyclization and Isomerization Reactionsin Silylhydrazine Chemistry

Summary.  This review describes the synthesis and isomerization reactions of cyclic silylhydrazines. Topics of discussion are the ring expansion of the three-membered Si(SiN₂) to the four-membered (SiN)₂ ring by lithiation of the (SiN₂) ring and by thermal silyl group insertion into the N*N bond, the ring expansion of a three-membered (SiN₂) to a five-membered (CSi₂N₂) ring by SiCH₂ insertion into the Si*N bond, the formation of isomeric four- and six-membered (SiN₂)₂ rings, the synthesis of five- and six-membered silylhydrazine rings, and the expansion of a five-membered (N₂Si₂N)N ring to the isomeric six-membered (SiNN)₂ ring. The mechanisms of the isomerizations are explained by quantum chemical calculations, and the results are verified by crystal structure determinations. Received February 23, 2001. Accepted (revised) April 24, 2001     

Comment on “Minimal parabolic quantum groups in twist deformations" by M. Ilyin and V. Lyakhovsky On a “new" deformation of GL(2)

We refute a recent claim in the literature [Czech. J. Phys. 56, 1191 (2006)] of a “new" quantum deformation of GL(2).     

When Min(A)−1 is Hausdorff

For a commutative ring with identity, say A, its collection of minimal prime ideals is denoted by Min(A). The hull-kernel topology on Min(A) is a well-studied structure. For example, it is known that the hull-kernel topology on Min(A) has a base of clopen subsets, and classifications of when Min(A) is compact abound. Recently, a program of studying the inverse topology on Min(A) has begun. This article adds to the growing literature. In particular, we characterize when Min(A)^?1 is Hausdorff. In the final section, we consider rings of continuous functions and supply examples.     

Approximating call-scheduling makespan in all-optical networks

We study the problem of routing and scheduling requests of limited durations in all-optical networks with restrictions on the number of available wavelengths on each link. The task is servicing the requests, assigning each of them a route from source to destination, a starting time and a wavelength with the goal of minimizing the overall time needed to serve all requests. We study the relationship between this problem and minimum path coloring and we show how to exploit known results on path coloring to derive approximation scheduling algorithms for meshes, trees and nearly-Eulerian, uniformly high-diameter graphs. We also propose different approximation algorithms for stars, trees and in trees of rings.     

Le satellite Encelade source d'ions N dans la magnétosphère de Saturne

The first pass of the Cassini probe in the vicinity of Saturn, above the E-ring, demonstrated a plasma consisting of water group ions (H⁺, O⁺, OH⁺, H₂O⁺) with a small N⁺ ion component (3%). Using a simple model for the transport of magnetospheric ions, we show that the N⁺ ions can be traced back to the Enceladus satellite. Such a result can be explained by the existence in this icy satellite, supposed to be still geologically active, of volatile components such as ammonia NH₃, or by the previous implantation of N⁺ ions of external origin on its surface. To cite this article: M. Bouhram et al., C. R. Physique 6 (2005).     

Difference set constructions of DRADs and association schemes

Doubly Regular Asymmetric Digraphs (DRAD) with rank 4 automorphism groups were previously thought to be rare. We exhibit difference sets in Galois Rings that can be used to construct an infinite family of DRADs with rank 4 automorphism groups. In addition, we construct difference sets in groups for all r?2 that can be used to construct DRADs and nonsymmetric 3-class imprimitive association schemes. Finally, we prove a new product construction for difference sets so that the resulting difference sets can be used to build nonsymmetric 3-class imprimitive association schemes.     

A Class of Rings Satisfying S~m=S~(m+1) on Subrings

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