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.     

Ring Expansion Strategies for the Synthesis of Medium Sized Ring and Macrocyclic Sulfonamides

Two new ring expansion strategies are reported for the synthesis of medium sized ring and macrocyclic sulfonamides. Both methods can be performed without using classical protecting groups, with the key ring expansion step initiated by nitro reduction and amine conjugate addition respectively. Each method can be used to make diversely functionalised cyclic sulfonamides in good to excellent yields, in a range of ring sizes. The ring size dependency of the synthetic reactions is in good agreement with the outcomes modelled by Density Functional Theory calculations.     

On the Krull Dimension of Rings of Transfer Functions

In this article, we prove that the Krull dimension of several commonly used classes of transfer functions of infinite dimensional linear control systems is infinite. On the other hand, we also show that the weak Krull dimension of the Hardy algebra , the disk algebra and the Wiener algebra is equal to 1. A. Sasane is supported by the Nuffield Grant NAL/32420.     

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).     

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).     

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.     

Ideal-comparability over Regular Rings

We introduce the concept of ideal-comparability condition for regular rings. Let I be an ideal of a regular ring R. If R satisfies the I-comparability condition, then R is one-sided unit-regular if and only if so is R/I. Also, we show that a regular ring R satisfies the general comparability if and only if the following hold： （1） R/I satisfies the general comparability; （2） R satisfies the general I-comparability condition; （3） The natural map B（R） → B（R/I） is surjective.     

New ring of a class of Bessel integral operators

In this paper, we introduce a new ring of ponderation functions which allowed us to describe and classify a large class of ring of Bessel integral operators. The main result is to give an explicit form of some ideals of such a ring of operators.     

Reversible Isomerization Between Silacyclopropyl Cation and Cyclic (Alkyl)(Amino)Silylene

A phosphine-stabilized silacyclopropyl cation 2 has been synthesized and fully characterized. Of particular interest, 2 reversibly isomerizes into the corresponding seven-membered cyclic (alkyl)(amino)silylene 3 at room temperature via a formal migratory ethylene insertion into the Si−P bond. Although silylene 3 has not been spectroscopically detected, its transient formation has been evidenced by the isolation of the corresponding disilene dimer 5 as well as by trapping reactions.