A Quotient of the Set [BG, BU(n)] for a Finite Group G of Small Rank

We construct a natural map from the set [BG,BU(n)] into a set of characters of the Sylow p-subgroups of G and prove that this natural map is a surjection for all finite groups G of rank two. We show, furthermore, that this same natural map is in fact a bijection for two types of finite groups G: those with periodic cohomology and those of rank two with odd order.Comment: 14 page

A Water Monetary Standard: An Economic Thesis

In emerging markets and economies with limited supplies of potable water, the current monetary policy governing water distribution has failed or will eventually fail. Problems are not limited to developing nations but are magnified by tenuous circumstances. Historically, weaker economies suffer short falls in revenue for operation and proper maintenance of their respective water systems; however, even well funded systems are operating under potentially tenuous circumstances. The goal of this thesis is to offer an alternative to current global policies, through a new paradigm, a water based monetary standard. The immediate benefit of this policy is the elimination of user fees for public water and to protect the ongoing operation through revenues created through recognized rules of sovereignty and fiscal policy. Elimination of fees or associated taxes will lower the daily cost of living, consumer price index (CPI), and the producer price index (PPI) within subject economies. Adoption of this new monetary standard will create an environment of encouraged growth in a more stable economy, thereby increasing tax revenues.Economic theory; emerging markets; sustainable development; wastewater; water

Geometric Analysis of Bifurcation and Symmetry Breaking in a Gross-Pitaevskii equation

Gross-Pitaevskii and nonlinear Hartree equations are equations of nonlinear Schroedinger type, which play an important role in the theory of Bose-Einstein condensation. Recent results of Aschenbacher et. al. [AFGST] demonstrate, for a class of 3- dimensional models, that for large boson number (squared L^2 norm), N, the ground state does not have the symmetry properties as the ground state at small N. We present a detailed global study of the symmetry breaking bifurcation for a 1-dimensional model Gross-Pitaevskii equation, in which the external potential (boson trap) is an attractive double-well, consisting of two attractive Dirac delta functions concentrated at distinct points. Using dynamical systems methods, we present a geometric analysis of the symmetry breaking bifurcation of an asymmetric ground state and the exchange of dynamical stability from the symmetric branch to the asymmetric branch at the bifurcation point.Comment: 22 pages, 7 figure

Modeling the Orbital Sampling Effect of Extrasolar Moons

The orbital sampling effect (OSE) appears in phase-folded transit light curves of extrasolar planets with moons. Analytical OSE models have hitherto neglected stellar limb darkening and non-zero transit impact parameters and assumed that the moon is on a circular, co-planar orbit around the planet. Here, we present an analytical OSE model for eccentric moon orbits, which we implement in a numerical simulator with stellar limb darkening that allows for arbitrary transit impact parameters. We also describe and publicly release a fully numerical OSE simulator (PyOSE) that can model arbitrary inclinations of the transiting moon orbit. Both our analytical solution for the OSE and PyOSE can be used to search for exomoons in long-term stellar light curves such as those by Kepler and the upcoming PLATO mission. Our updated OSE model offers an independent method for the verification of possible future exomoon claims via transit timing variations and transit duration variations. Photometrically quiet K and M dwarf stars are particularly promising targets for an exomoon discovery using the OSE.Comment: published in ApJ; 11 figures (8 b/w, 3 col); OSE simulator available at https://github.com/hippke/pyos

The distinctive challenges and opportunities for creating leadership within social enterprises

Purpose The purpose of this study is to present a systematic assessment of the distinctive challenges and opportunities associated with creating leadership within the realm of social enterprise. A modified and expanded form of Grint’s leadership lenses heuristic framework (i.e. person, position, process, performance, purpose and place) is used to examine and highlight what is particular about creating leadership in social enterprises by virtue of their distinctive missions, strategic contexts, legal forms and organisational structures and cultures. Based on this initial exploration, five research priorities are identified to better understand and then develop leadership practice in the social enterprise realm. Design/methodology/approach An enhanced heuristic framework for systematically examining leadership within the social enterprise research literature has been applied, drawing on the leadership practice literature. The application is illustrated through six instrumental case studies. Findings While there are a number of similarities between leading in the social enterprise realm and leading within the private, public and not-for-profit sectors, the levels of complexity, ambiguity and the lack of an established theoretical and practical knowledge base makes creating leadership in the social enterprise sector that much more challenging. On the positive side of the ledger, the fact that the purpose is at the core of social enterprise means that it is relatively easier to use the purpose to create a basis for common meaningful action, compared to leadership within the private and public sectors. Related to this, given the strongly local or “glocal” nature of social enterprise, a ready opportunity exists for leaders to draw upon a place as a strategic resource in mobilising followers and other stakeholders. The novel, uncertain and pioneering nature of a social enterprise is also arguably more tolerant and accommodating of a leadership mindset that focuses on posing questions regarding “wicked” problems compared to public, private for-profit and, indeed, traditional not-for-profit sector organisations. Originality/value As far as we can ascertain, this is the first systematic attempt to examine the distinctive challenges and opportunities associated with creating leadership within the social enterprise realm. The application of the heuristic framework leads to the identification of five key inter-related lines of empirical research into leadership practices within social enterprises. </jats:sec

Ecosystem Shock: The Devastating Impacts of Invasive Species on the Great Lakes Food Web

Gives an account of the changes to the Great Lakes ecosystem brought about by non-native aquatic species. Assesses the current and future impacts on fish communities and commercial fisheries. Provides policy and research recommendations