Cartan Invariants of Symmetric Groups and Iwahori-Hecke Algebras

K\"{u}lshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the $\ell$-Cartan matrix for $S_n$ (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra $\mathcal{H}_n(q)$, where $q$ is a primitive $\ell$th root of unity). We call these invariant factors Cartan invariants. In a previous paper, the second author calculated these Cartan invariants when $\ell=p^r$, $p$ prime, and $r\leq p$ and went on to conjecture that the formulae should hold for all $r$. Another result was obtained, which is surprising and counterintuitive from a block theoretic point of view. Namely, given the prime decomposition $\ell=p_1^{r_1}... p_k^{r_k}$, the Cartan matrix of an $\ell$-block of $S_n$ is a product of Cartan matrices associated to $p_i^{r_i}$-blocks of $S_n$. In particular, the invariant factors of the Cartan matrix associated to an $\ell$-block of $S_n$ can be recovered from the Cartan matrices associated to the $p_i^{r_i}$-blocks. In this paper, we formulate an explicit combinatorial determination of the Cartan invariants of $S_n$--not only for the full Cartan matrix, \emph{but for an individual block}. We collect evidence for this conjecture, by showing that the formulae predict the correct determinant of the $\ell$-Cartan matrix. We then go on to show that Hill's conjecture implies the conjecture of KOR

Portfolio Strategies, Relinquishment, The Urban School System of the Future, and Smart Districts

Today, there are many new proposals about governance of K-12 Education: The portfolio strategy emphasizes a system of continuous improvement for diverse, autonomous schools governed by performance contracts; devolution models include efforts to expand the role of charter management organizations and other nonprofit providers (Andy Smarick's "Urban School System of the Future," Neerav Kingslad's "Relinquishment"); and school transformation models emphasize the role of third-party support organizations that create K-12 feeder patterns of allied schools (Bill Guenther and Justin Cohen's Mass Insight "Smart Districts" proposal).Are these really rival proposals as the authors of some are claiming? This idea is misguided; these are complemetns not alternatives

Economic analysis of landholder water management under Cap & Pipe the Bores program: case studies in the NSW Great Artesian Basin

The NSW Cap & Pipe the Bores Program is a jointly funded Commonwealth and State initiative that operates within the Australian Government’s Great Artesian Basin Sustainability Initiative (GABSI) framework. The third five-year period of GABSI was due to commence on 1st July 2009. This economic study of changes in landholder water management under the Cap & Pipe the Bores program was undertaken to inform the development of GABSI phase 3 policy in NSW. The study consisted of a small number of case studies of farming enterprises across the Great Artesian Basin Groundwater Management Zones of Surat South, Surat East, Surat West, Warrego and Central in NSW. The apparent landholder economic feasibility of the program was dependent on individual farm characteristics as much as location to the bore and geographic location within the GAB.Resource /Energy Economics and Policy,

NSW Great Artesian Basin water market assessment pre and post auction

The NSW Cap & Pipe the Bores Program is a jointly funded Commonwealth and State initiative that operates within the Australian Government's Great Artesian Basin Sustainability Initiative framework. Under the Water Sharing Plan for the NSW Great Artesian Basin Groundwater Sources 2008, 70 per cent of the water savings made since 1999 shall be retained in the aquifers of the Basin to improve pressures and provide for groundwater dependent ecosystems. The remaining 30 per cent of the water savings may be released to extractive users over the term of the Water Sharing Plan to facilitate the continued economic and social welfare of regional western NSW. As the first step in this water release, part of the water savings from the Cap & Pipe the Bores program were auctioned in July 2009 in the western NSW town of Walgett. All lots offered at auction were sold. The study reviews the pre auction analysis of demand, and outlines the auction process and outcomes as well as the implications for future water sales. The outcomes of the auction will inform ongoing water allocation policy.water auction, economics, Great Artesian Basin, groundwater, Cap & Pipe the Bores, Water Sharing Plan., Resource /Energy Economics and Policy,

Career Transitions Caused by Chronic Illness: A Career Construction Perspective

People living with chronic illness face significant challenges when it comes to finding and maintaining employment. There is ample research available that discussed the challenges and barriers to employment for this population. However, there is a lack of research devoted to interventions dedicated to assisting people with chronic illness in career exploration and development. This study attempted to address one possible intervention to assist people with chronic illness identify and pursue possible careers. The purpose of this research study was to explore the impact of participating in the Career Construction Interview on the career exploration of individuals facing a forced career transition due to the onset or exacerbation of a chronic illness. A qualitative instrumental multiple case study design was used, specifically a collective case study with an explanatory design. Three females with chronic illness participated in this study and completed four interviews. In answering the research questions, eight open codes fitting into two categories were discovered and five axial codes, also known as themes, were determined. Results from this study found that the Career Construction Interview was helpful to the participants in assisting them with making decisions about potential careers and options for employment

Exploring natural resource management tradeoffs in an agricultural landscape - an application of the MOSAIC model.

We describe a landscape scale non-linear discrete choice spatial optimisation model for identifying cost-effective strategies for achieving environmental goals. Spatial heterogeneity and configuration issues such as fencing costs, patch sizes and network linkages are explicitly accounted for and quasi-optimal allocations are determined using simulated annealing. Applications of the model being developed with New South Wales Catchment Management Authorities are discussed. These focus on targeting investments in revegetation to control dryland salinity and erosion and provide biodiversity benefits whilst minimising direct and opportunity costs. We compare our approach with alternate investment approaches.natural resource management, cost effectiveness, land use change, multicriteria, spatial optimisation, Resource /Energy Economics and Policy,

A Decade of Home Schooling in Saskatchewan, Canada (1984-1994): A Case Study

The efficacy of alternative education has had a significant impact on public education. The diversity of cultures, lifestyles, and needs of home-schooling families compelled the public educational sector to make available educational alternatives. The purpose of this study was to build upon previous research (Hill, 1988) by interviewing a sample of the same families and their children to investigate the longitudinal experiences for a follow-up study. The representative sample participated in a study entitled An Investigation of Home Schooling in Saskatchewan (Hill, 1988). Twenty families (18 parents and 25 children) were interviewed; 10 were selected as case studies. Home schoolers ranged from 16 to 26 years and presently are involved in various professions and vocations. In-depth interviews and open-ended questions elicited rich and detailed accounts of how home schooling had influenced each participant\u27s life. A large majority of participants were transformed through the recognition of choice, networking, and reflection. The follow-up interviews validated their experiences and allowed them to reflect on their respective roles, feelings of success and failure. To exercise choice was the dominant founding principle, and commitment to personal and communal needs were the keys to successful home-schooling practice. Evaluation and assessment were the acquisition of either a Christian or a liberal education, which could be achieved within the context of the home and community. Course content supported a basic core curriculum best described as a liberal education. Elective areas of study were principled by two schools of thought: families who prescribed to the free schools movement and those whose programs were based on evangelical Christianity. The definition of home schooling was expanded to focus on multidirectional teaching and learning. Each participant\u27s self-esteem, ambition, and self-confidence in transferring the skills, knowledge, and values to their networks validated their experiences and enhanced their personal growth. The globalization of education, integration of world resources, and rapid changes in lifestyles required an examination of the evolution of home schooling, its founding principles, and curriculum assessments

Issues of scale and scope in bio-physical modelling for natural resource management decision making in New South Wales

Natural resource management decision making by Catchment Management Authorities in NSW is being aided by a project involving bio-physical modelling and the development of an alternative decision-making framework. The objective of the bio-physical modelling process is to generate predictions of environmental or natural resource outcomes rather than project outputs. These outcomes can then be used in an investment framework to help priority setting and project decision making. Questions that arise in bio-physical modelling include those relating to scale and scope. Scale issues include how to address the landscape impacts of particular (or a series of local) on-ground works proposals. Scope issues include assessment of multiple-attribute responses to particular changes. In a multi-disciplinary context the challenge is then to translate this information into units that can be adapted to a decision-support framework. Existing Catchment Management Authorities decisions are often based on scoring and weighting of environmental improvements using an environmental benefits index, however other economic frameworks are possible. We discuss the important context for these questions in the decision making framework.environmental benefits, bio-physical models, scale, scope, investment decisions, Resource /Energy Economics and Policy,