Affine descents and the Steinberg torus

Let $W\ltimes L$ be an irreducible affine Weyl group with Coxeter complex $\Sigma$, where $W$ denotes the associated finite Weyl group and $L$ the translation subgroup. The Steinberg torus is the Boolean cell complex obtained by taking the quotient of $\Sigma$ by the lattice $L$. We show that the ordinary and flag $h$-polynomials of the Steinberg torus (with the empty face deleted) are generating functions over $W$ for a descent-like statistic first studied by Cellini. We also show that the ordinary $h$-polynomial has a nonnegative $\gamma$-vector, and hence, symmetric and unimodal coefficients. In the classical cases, we also provide expansions, identities, and generating functions for the $h$-polynomials of Steinberg tori.Comment: 24 pages, 2 figure

Real-time flight test analysis and display techniques for the X-29A aircraft

The X-29A advanced technology demonstrator flight envelope expansion program and the subsequent flight research phase gave impetus to the development of several innovative real-time analysis and display techniques. These new techniques produced significant improvements in flight test productivity, flight research capabilities, and flight safety. These techniques include real-time measurement and display of in-flight structural loads, dynamic structural mode frequency and damping, flight control system dynamic stability and control response, aeroperformance drag polars, and aircraft specific excess power. Several of these analysis techniques also provided for direct comparisons of flight-measured results with analytical predictions. The aeroperformance technique was made possible by the concurrent development of a new simplified in-flight net thrust computation method. To achieve these levels of on-line flight test analysis, integration of ground and airborne systems was required. The capability of NASA Ames Research Center, Dryden Flight Research Facility's Western Aeronautical Test Range was a key factor in enabling implementation of these methods

Demographics and the long-term outlook for housing investment

John Hill and D'Ann Petersen measure the importance of projected shifts in the size and age distribution of the U.S. population for domestic housing investment. Their analysis runs through the year 2010 and provides separate estimates for single-family and multifamily investment. ; Hill and Petersen find that the contractionary effects of the population slowdown are already being felt in the housing industry and probably have been since the latter part of the 1980s. In Hill and Petersen's simulations, demographic shifts lower net housing investment by 17 percent from the late 1980s through the first half of the 1990s. Population factors then reduce net investment an additional 22 percent through the year 2005 before turning favorable. ; Hill and Petersen discuss the implications of their findings for construction jobs and housing prices. They suggest that the population slowdown need not produce an absolute contraction in housing employment. It will, however, reduce housing's share of national employment by as much as one-third. According to the authors, the changing demographics do not provide a compelling reason for average home prices to suffer a deep decline. They do suggest, however, that significant relative price adjustments may need to take place between different types of homes.Demography ; Housing

Though This be Madness: Heritage Methods for Working in Culturally Diverse Communities

In 1998, the NSW Migration Heritage Centre was conceived by the NSW Government as a virtual heritage centre to help ageing former migrants tell their stories. Migration museums and other organisations interested in heritage are grappling with how to identify, record, preserve and interpret the heritage legacy of migration and settlement in their communities. The distinctions between museum and environmental heritage practices have diminished during the past decade in Australia. The Centre’s methodologies are based on historic method and thematic and typology studies, better known for their application to heritage place identification and archaeological artefact studies than for their more recent use by some Australian museum curators for the survey and documentation of collections and community participation in heritage. The ‘virtual museum’ has enabled the Centre to break away from the centralised museum concept, with the associated trappings of venue management, to pioneer a decentralised and dispersed museum model that works almost entirely in collaborative community history research partnerships to document culturally significant collections, and associated migration memories, held by communities and private individuals. The work is centralised on the Centre’s website as a virtual collection of objects, places and associated memories. They are presented in online exhibitions for student research and as a destination for the mass audiences of the worldwide web

Describing and understanding the enacted curriculum of selected Grade 10 Life Science teachers in the Western Cape, South Africa

This study was conducted in a school in the Western Cape, South Africa situated in a community where learners came from difficult social backgrounds. Previous research has alluded to the challenges faced by teachers equipped with inadequate skills and a lack of effective modelling or mentoring to implement a formal curriculum that is outcomes-based and learner centred. The focus of the study was to uncover the enacted curriculum (and the underlying reasons for the enactment) of four Grade 10 Life Sciences Teachers. This multiple case study is based on data collection strategies that included video and audio-transcripts of the lessons as well as the use of additional relevant documents such as, for example, notes from lesson observations, and learner notebooks. These data were coded using NUDIST and then further analysed using the Pedagogic Content Knowledge (PCK) evidence-reporting table (PCK ERT). Interviews were conducted before the teaching events to allow for content representations (CoRes) to be developed. Overall the teachers lacked planning and the habit of reflection in and of practice. Hence video-stimulated interviews conducted after the teaching events allowed for Pedagogical and Professional experience Repertoires (PaP-eRs) to be developed in order to describe (from a teachers' perspective) what teachers did and why they did what they did. Teachers had varying backgrounds and experience and displayed very individualised and different enactments of the curriculum but they all used a consistent didactic approach in their teaching. The absence of teacher efficacy and the lack of integration of the PCK components limited the transformation of the content in any meaningful way and hence resulted in weak PCK. The relevance of PCK ERT as a descriptive framework for PCK in the context of this research is questioned on epistemic grounds. Factors identified that constrained the enacted practices of teachers included teachers' belief, orientation, poor Subject Matter Knowledge (SMK), school context and their perceptions of learners