Spectral synthesis and topologies on ideal spaces for Banach *-algebras

This paper continues the study of spectral synthesis and the topologies τ∞ and τr on the ideal space of a Banach algebra, concentrating on the class of Banach *-algebras, and in particular on L1-group algebras. It is shown that if a group G is a finite extension of an abelian group then τr is Hausdorff on the ideal space of L1(G) if and only if L1(G) has spectral synthesis, which in turn is equivalent to G being compact. The result is applied to nilpotent groups, [FD]−-groups, and Moore groups. An example is given of a non-compact, non-abelian group G for which L1(G) has spectral synthesis. It is also shown that if G is a non-discrete group then τr is not Hausdorff on the ideal lattice of the Fourier algebra A(G).

The Development of an On-line Submission and Peer Review System

Online submission and peer review is emerging as the next step forward for many journal publishers in an ever increasing drive to take advantage of technological improvements in transferring data electronically over the internet. The Electronic Submission and PEer REview (ESPERE) project was initiated in 1996 as an electronic Libraries (eLib) initiative of the Higher Education Funding Council for England (HEFCE). Subsequently the project continued as a self-funding group composed of a consortium of learned society and commercial journal publishers intent on utilising the changes in technology to improve the services they provide to their authors as well as cutting their costs and increasing efficiencies.

Threshold behaviour and final outcome of an epidemic on a random network with household structure

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.