Norm formulas for finite groups and induction from elementary abelian subgroups

It is known that the norm map N_G for a finite group G acting on a ring R is surjective if and only if for every elementary abelian subgroup E of G the norm map N_E for E is surjective. Equivalently, there exists an element x_G in R with N_G(x_G) = 1 if and only for every elementary abelian subgroup E there exists an element x_E in R such that N_E(x_E) = 1. When the ring R is noncommutative, it is an open problem to find an explicit formula for x_G in terms of the elements x_E. In this paper we present a method to solve this problem for an arbitrary group G and an arbitrary group action on a ring.Using this method, we obtain a complete solution of the problem for the quaternion and the dihedral 2-groups,and for a group of order 27. We also show how to reduce the problem to the class of (almost) extraspecial p-groups.Comment: 31 pages. In Section 1 a universal ring and the proof of the existence of formulas for any finite group were adde

The Original Beat: An Electronic Music Production System and Its Design

The barrier to entry in electronic music production is high. It requires expensive, complicated software, extensive knowledge of music theory and experience with sound generation. Digital Audio Workstations (DAWs) are the main tools used to piece together digital sounds and produce a complete song. While these DAWs are great for music professionals, they have a steep learning curve for beginners and they must run native on a user’s computer. For a novice to begin creating music takes much more time, eort, and money than it should. We believe anyone who is interested in creating electronic music deserves a simple way to digitize their ideas and hear results. With this idea in mind, we created a web based, co-creative system to allow beginners and pros alike to easily create electronic digital music. We outline the requirements for such a system and detail the design and architecture. We go through the specifics of the system we implemented covering the front-end, back-end, server, and generation algorithms. Finally, we will review our development time-line, examine the challenges and risks that arose when building our system, and present future improvements

Multi-Dimensional Explorations in Supernova Theory

In this paper, we bring together various of our published and unpublished findings from our recent 2D multi-group, flux-limited radiation hydrodynamic simulations of the collapse and explosion of the cores of massive stars. Aided by 2D and 3D graphical renditions, we motivate the acoustic mechanism of core-collapse supernova explosions and explain, as best we currently can, the phases and phenomena that attend this mechanism. Two major foci of our presentation are the outer shock instability and the inner core g-mode oscillations. The former sets the stage for the latter, which damp by the generation of sound. This sound propagates outward to energize the explosion and is relevant only if the core has not exploded earlier by some other means. Hence, it is a more delayed mechanism than the traditional neutrino mechanism that has been studied for the last twenty years since it was championed by Bethe and Wilson. We discuss protoneutron star convection, accretion-induced-collapse, gravitational wave emissions, pulsar kicks, the angular anisotropy of the neutrino emissions, a subset of numerical issues, and a new code we are designing that should supercede our current supernova code VULCAN/2D. Whatever ideas last from this current generation of numerical results, and whatever the eventual mechanism(s), we conclude that the breaking of spherical symmetry will survive as one of the crucial keys to the supernova puzzle.Comment: To be published in the "Centennial Festschrift for Hans Bethe," Physics Reports (Elsevier: Holland), ed. G.E. Brown, E. van den Heuvel, and V. Kalogera, 200

Efficacy And Voting In The Obama Era

In the past 50 years political science and sociological scholarship has demonstrated a consistent white-minority gap in political attitudes and behaviors. However, recent developments in the national political scene have introduced a new element that likely impacts these well-established trends, and must be taken into account: Barak Obama, an individual identifying with a minority group, ran for the office of the president of the United States. To explore the impact of Obama’s presence on the political behavior of minorities, I performed a secondary data analysis of variables from both the pre-election and post-election modules of the ANES 2008 Time-Series study, and examined four hypotheses: (H1) Racial minorities will have lower perceptions of political efficacy than white respondents; (H2) Racial minorities will have lower rates of political participation than white respondents; (H3) Respondents’ lowered efficacy will result in similarly lowered political participation; (H4) Respondents who voted for Barak Obama in 2008 will have increased levels of political efficacy after the 2008 election. The results are compelling: literature states that many racial differences in efficacy and voting are due to moderating factors such as differences in SES, but I\u27ve found that black citizens were in fact far more likely to vote in 2008 regardless of whether or not SES was controlled for. I\u27ve also found statistical significance in each of the relationships highlighted in my hypotheses

Results From Core-Collapse Simulations with Multi-Dimensional, Multi-Angle Neutrino Transport

We present new results from the only 2D multi-group, multi-angle calculations of core-collapse supernova evolution. The first set of results from these calculations was published in Ott et al. (2008). We have followed a nonrotating and a rapidly rotating 20 solar mass model for ~400 ms after bounce. We show that the radiation fields vary much less with angle than the matter quantities in the region of net neutrino heating. This obtains because most neutrinos are emitted from inner radiative regions and because the specific intensity is an integral over sources from many angles at depth. The latter effect can only be captured by multi-angle transport. We then compute the phase relationship between dipolar oscillations in the shock radius and in matter and radiation quantities throughout the postshock region. We demonstrate a connection between variations in neutrino flux and the hydrodynamical shock oscillations, and use a variant of the Rayleigh test to estimate the detectability of these neutrino fluctuations in IceCube and Super-K. Neglecting flavor oscillations, fluctuations in our nonrotating model would be detectable to ~10 kpc in IceCube, and a detailed power spectrum could be measured out to ~5 kpc. These distances are considerably lower in our rapidly rotating model or with significant flavor oscillations. Finally, we measure the impact of rapid rotation on detectable neutrino signals. Our rapidly rotating model has strong, species-dependent asymmetries in both its peak neutrino flux and its light curves. The peak flux and decline rate show pole-equator ratios of up to ~3 and ~2, respectively.Comment: 13 pages, 9 figures, ApJ accepted. Replaced with accepted versio

Living the dream – but not without hardship: stories about self-directed weight transformation from severe obesity

The objective of this narrative study was to explore experiences and assigned meanings in stories about self-directed weight loss (WL) maintenance after severe obesity (SO). Design In-depth interviews were conducted with eight women and two men, aged 27 to 59 years, who had carried out self-directed WL from SO for 5 years or more. Two themes ran across the stories: Fear of weight-regain, and food and emotion. We performed a case-based narrative analysis of especially rich interviews that illustrate these. Results pointed to persistently cultivating new competencies, establishing new eating habits, re-establishing old physical-training habits, and forming new relational bonds. Participants reinvented themselves and their lives. However, the stories are not all about transformation, but also about new and old health problems. Conclusion The study directs attention to ‘different obesities’, not only to initial weight from which WL takes place, but also linked to the experiential horizons that the persons embody from childhood on. Furthermore, there was no way back in the present stories, always haunted in the wake of the lost weight. A double burden imposed on the person with obesity related to meta-stories in society deepens the understanding of this imperative: being vulnerable health-wise and exposed to stigmatization.publishedVersio

Economic geography and business networks: creating a dialogue between disciplines An introduction to the special issue

This introductory article presents an outline of the papers accepted for this special issue. The Guest Editors provide an overview of the work within industrial marketing where synthesis between economic geography and industrial marketing literature has occurred. A discussion of the most synthesised areas of economic geography is advanced and each article is then discussed, compared and contrasted with other articles in the special issue and with articles within industrial marketing that have previously synthesized concepts drawn from economic geography. Within this narrative, the Guest Editor’s propose an agenda for future interdisciplinary research at what they refer to as the ‘nexus of interest’ between the disciplines

Percolation and connection times in multi-scale dynamic networks

We study the effects of mobility on two crucial characteristics in multi-scale dynamic networks: percolation and connection times. Our analysis provides insights into the question, to what extent long-time averages are well-approximated by the expected values of the corresponding quantities, i.e., the percolation and connection probabilities. In particular, we show that in multi-scale models, strong random effects may persist in the limit. Depending on the precise model choice, these may take the form of a spatial birth-death process or a Brownian motion. Despite the variety of structures that appear in the limit, we show that they can be tackled in a common framework with the potential to be applicable more generally in order to identify limits in dynamic spatial network models going beyond the examples considered in the present work