The economics of defence in France and the UK

France and the UK face similar geostrategic circumstances: both were once Great Powers and still retain their positions among the five permanent members of the UN Security Council. During the Cold War both were dwarfed by the super-powers and were thus extremely sensitive about their status: what the French called their grandeur and the British called their seat at the top table. Despite their strategic similarities, they have differed in many of their defence policy choices and in particular how they balanced their strategic aspirations with their limited financial resources. Thus a comparison of British and French defence policies provides a revealing case study of military choices

A Hubble Space Telescope Survey of X-ray Luminous Galaxy Clusters: Gravitationally Lensed Arcs and EROs

We are conducting a systematic lensing survey of X-ray luminous galaxy clusters at z~0.2 using the Hubble Space Telescope and large ground-based telescopes. We summarize initial results from our survey, including a measurement of the inner slope of the mass profile of A383, and a search for gravitationally lensed Extremely Red Objects.Comment: 4 pages, 2 figures. To appear in "A New Era in Cosmology" (ASP Conference Proceedings), eds. T. Shanks and N. Metcalf

On the M\"obius Function of Permutations With One Descent

The set of all permutations, ordered by pattern containment, is a poset. We give a formula for the M\"obius function of intervals $[1,\pi]$ in this poset, for any permutation $\pi$ with at most one descent. We compute the M\"obius function as a function of the number and positions of pairs of consecutive letters in $\pi$ that are consecutive in value. As a result of this we show that the M\"obius function is unbounded on the poset of all permutations. We show that the M\"obius function is zero on any interval $[1,\pi]$ where $\pi$ has a triple of consecutive letters whose values are consecutive and monotone. We also conjecture values of the M\"obius function on some other intervals of permutations with at most one descent

Hubble, chandra and keck constraints on massive galaxy clusters at z=0.2 and z=0.5

I present recent observations from two Hubble Space Telescope(HST)/ACS programs that target the most X–ray luminous and thus (presumably) most massive galaxy clusters at z=0.5 – the highest redshift at which complete, well–defined samples of such rare systems are available. The first program (GO:9836, PI: R.S. Ellis) exploits a huge mosaic of 41 ACS pointings spanning a 10 Mpc region centered on MS0451-03. This is the largest contiguous space–based image of a cluster to date. I describe a preliminary weak–lensing analysis and a new Keck/DEIMOS redshift catalog of 1000 galaxies in this field. The second program (GO:9722, PI: H. Ebeling) studies the core regions of the twelve most luminous clusters at z≥0.5 from the MAssive Cluster Survey (MACS; Ebeling et al. 2001). Multi–color ACS observations in combination with recent Keck/LRIS spectroscopy of gravitational arcs constrain the distribution of mass in the cluster cores, thus laying the foundation for detailed multi–diagnostic (lensing, X–ray, near–infrared, SZE) investigation of this sample. For example, it is of particular interest to explore how the structure and state of relaxation of massive clusters evolved between this sample at z≥0.5 that measured by Smith et al. (2004, astro–ph/0403588) at z=0.2