The ℓ2\ell^2-homology of even Coxeter groups

Given a Coxeter system (W,S), there is an associated CW-complex, Sigma, on which W acts properly and cocompactly. We prove that when the nerve L of (W,S) is a flag triangulation of the 3-sphere, then the reduced $\ell^2$-homology of Sigma vanishes in all but the middle dimension.Comment: 15 pages, 1 figur

The Causal Map and Moral Psychology

Some philosophers hold that the neuroscience of action is, in practice or in principle, incapable of touching debates in action theory and moral psychology. The role of desires in action, the existence of basic actions, and the like are topics that (they hold) must be sorted out by philosophers alone: at least at present, and perhaps by the very nature of the questions. This paper examines both philosophical and empirical arguments against the relevance of neuroscience to such questions and argues that neither succeeds. In practice, there is already a stable body of findings from neuroanatomy and neurophysiology that warrants attention. And as a matter of principle, the ‘causal map’ of action production derivable from these findings requires the study of action theorists and moral psychologists because every such philosopher has commitments (sometimes, deeply implicit) to the shape of this causal map: commitments that might be in conflict with reality

Prediction of heat transfer for a film cooled flat plate using a computational fluid dynamics analysis

It has become common practice within the gas turbine industry to simulate the flow of the primary air stream and cooling gas by using the numerical method associated with Computational Fluid Dynamics (CFD). A variety of CFD programs exist in the commercial market today and within the proprietary industry environment. While most can predict the aerodynamics inside engine turbines, the ability to predict heat transfer for a film-cooled turbine stage remains elusive. The purpose of this project was to benchmark the current state of heat transfer prediction for commonly used CFD software. The commercially available code FINE/Turbo, developed by Numeca International, was tested in this research effort. FINE/Turbo was used because of its ability to provide time-accurate solutions, which will be utilized in future research efforts. The computational model utilized a conjugate heat-transfer model for solid-fluid interactions, as well as 113 individual cooling holes spaced consistent with the turbine blade hardware. Current heat-transfer solutions are in the expected range of theoretical values, although the measurement program is still in process. The addition of cooling flow to the mainstream flow associated with a high-pressure turbine stage is difficult to model, especially when one is attempting to predict the surface heat-transfer rate. Boundary layer conditions and solid-fluid interactions dominate the region, making accurate computational predictions very difficult. Results of this project have identified areas for which improvement in the current state-of-the-art are required, and have provided a benchmark for computational solutions. Lessons learned from the flat-plate measurement program will be applied to a full-scale rotating turbine stage in the near future, so understanding how to predict the local heat transfer using the CFD code is of significant interest.No embarg

Move-minimizing puzzles, diamond-colored modular and distributive lattices, and poset models for Weyl group symmetric functions

The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain way as diamond-colored modular and distributive lattices. Such lattices can also arise naturally as models for certain algebraic objects, namely Weyl group symmetric functions and their companion semisimple Lie algebra representations. The motivation for this paper is therefore both diversional and algebraic: To show how some recreational move-minimizing puzzles can be solved explicitly within an order-theoretic context and also to realize some such puzzles as combinatorial models for symmetric functions associated with certain fundamental representations of the symplectic and odd orthogonal Lie algebras

An In-Situation Review of Flourishing in Ministry by First Call Pastors

First Call pastors reflect on Matt Bloom's Book, Flourishing in Ministry and their first call