When are two Coxeter orbifolds diffeomorphic?

One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional faces are diffeomorphic. It follows that two simple convex polytopes are combinatorially equivalent if and only if they are diffeomorphic as manifolds with corners. On the other hand, by a result of Akbulut, for each n > 3, there are smooth, contractible n-manifolds with contractible faces which are combinatorially equivalent but not diffeomorphic. Applications are given to rigidity questions for reflection groups and smooth torus actions.Comment: 24 page

The Abundance Pattern in the Hot ISM of NGC 4472: Insights and Anomalies

Important clues to the chemical and dynamical history of elliptical galaxies are encoded in the abundances of heavy elements in the X-ray emitting plasma. We derive the hot ISM abundance pattern in inner and outer regions of NGC 4472 from analysis of Suzaku spectra, supported by analysis of co-spatial XMM-Newton spectra. The low background and relatively sharp spectral resolution of the Suzaku XIS detectors, combined with the high luminosity and temperature in NGC 4472, enable us to derive a particularly extensive abundance pattern that encompasses O, Ne, Mg, Al, Si, S, Ar, Ca, Fe, and Ni in both regions. We apply simple chemical evolution models to these data, and conclude that the abundances are best explained by a combination of alpha-element enhanced stellar mass loss and direct injection of Type Ia supernova (SNIa) ejecta. We thus confirm the inference, based on optical data, that the stars in elliptical galaxies have supersolar alpha/Fe ratios, but find that that the present-day SNIa rate is 4-6 times lower than the standard value. We find SNIa yield sets that reproduce Ca and Ar, or Ni, but not all three simultaneously. The low abundance of O relative to Ne and Mg implies that standard core collapse nucleosynthesis models overproduce O by a factor of 2.Comment: 37 pages, including 23 figures, uses aastex.cls; accepted for publication in Ap

Race and Policing: An Agenda for Action

This paper is organized into two parts -- Strategic Voice and Tactical Agency. Strategic Voice argues that problems of race in policing cannot be resolved by the police alone. Other people must help by understanding and ameliorating the social conditions that cause race to be associated with crime and hence become a dilemma for American policing. Rather than accepting these conditions as givens, police leaders with their powerful collective voice should actively call attention to what needs to be changed. Tactical Agency outlines what the police can do on their own initiative to deal with the operational dilemmas of race -- in the communities they serve and in their own organizations

Escaping the \u3cem\u3eSporhase\u3c/em\u3e Maze: Protecting State Waters within the Commerce Clause

Eastern states, though they have enjoyed a history of relatively abundant water, increasingly face the need to conserve water, particularly to protect water-dependent ecosystems. At the same time, growing water demands, climate change, and an emerging water-oriented economy have intensified pressure for interstate water transfers. Thus, even traditionally wet states are seeking to protect or secure their water supplies. However, restrictions on water sales and exports risk running afoul of the Dormant Commerce Clause. This Article offers guidance for states, partciularly eastern states concerned with maintaining and improving water-dependent ecosystems, in seeking to restrict water exports while staying within the confines of the Dormant Commerce Clause