Fixed Point Polynomials of Permutation Groups

In this paper we study, given a group $G$ of permutations of a finite set, the so-called fixed point polynomial $\sum_{i=0}^{n}f_{i}x^{i}$, where $f_{i}$ is the number of permutations in $G$ which have exactly $i$ fixed points. In particular, we investigate how root location relates to properties of the permutation group. We show that for a large family of such groups most roots are close to the unit circle and roughly uniformly distributed round it. We prove that many families of such polynomials have few real roots. We show that many of these polynomials are irreducible when the group acts transitively. We close by indicating some future directions of this research. A corrigendum was appended to this paper on 10th October 2014. </jats:p

Environmental Justice & Human Rights in the United States

The following discussion of environmental justice and human rights in the United States provides case studies of: the successful legal advocacy by AEHR attorneys in support of organized African American communities struggling for environmental justice; an analysis of the human rights violations arising from the deep flaws in the U.S. environmental regulatory system; and community-led advocacy in the United States that brings together environmental justice and human rights

General Nonlinear 2-Fluid Hydrodynamics of Complex Fluids and Soft Matter

We discuss general 2-fluid hydrodynamic equations for complex fluids, where one kind is a simple Newtonian fluid, while the other is either liquid-crystalline or polymeric/elastomeric, thus being applicable to lyotropic liquid crystals, polymer solutions, and swollen elastomers. The procedure can easily be generalized to other complex fluid solutions. Special emphasis is laid on such nonlinearities that originate from the 2-fluid description, like the transport part of the total time derivatives. It is shown that the proper velocities, with which the hydrodynamic quantities are convected, cannot be chosen at will, since there are subtle relations among them. Within allowed combinations the convective velocities are generally material dependent. The so-called stress division problem, i.e. how the nematic or elastic stresses are distributed between the two fluids, is shown to depend partially on the choice of the convected velocities, but is otherwise also material dependent. A set of reasonably simplified equations is given as well as a linearized version of an effective concentration dynamics that may be used for comparison with experiments

Meteorological buoy observations from the central Iceland Sea

Author Posting. © American Geophysical Union, 2015. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Atmospheres 120 (2015): 3199–3208, doi:10.1002/2014JD022584.We present the first continuous in situ atmospheric observations from the central Iceland Sea collected from a meteorological buoy deployed for a 2 year period between 23 November 2007 and 21 August 2009. We use these observations to evaluate the ERA-Interim reanalysis product and demonstrate that it represented low-level meteorological fields and surface turbulent fluxes in this region very well. The buoy observations showed that moderate to strong winds were common from any direction, while wind speeds below 5 ms−1 were relatively rare. The observed low-level air temperature and surface heat fluxes were related to the wind direction with cold-air outbreaks most common from the northwest. Mean wintertime turbulent heat fluxes were modest (<60 Wm−2), but the range was substantial. High heat flux events, greater than 200 Wm−2, typically occurred every 1–2 weeks in the winter, with each event lasting on average 2.5 days with an average total turbulent heat flux of ∼200 Wm−2 out of the ocean. The most pronounced high heat flux events over the central Iceland Sea were associated with cold-air outbreaks from the north and west forced by a deep Lofoten Low over the Norwegian Sea.This work was funded in part by the Ocean and Climate Change Institute at the Woods Hole Oceanographic Institution and NSF grant OCE-1433958.2015-10-2

Vegetation and environmental patterns on soils derived from Hawkesbury Sandstone and Narrabeen substrata in Ku-ring-gai Chase National Park, New South Wales

[Abstract]: The vegetation patterns in the Central Coast region of New South Wales have been extensively studied with respect to single environmental variables, particularly soil nutrients. However, few data are available on the effects of multiple environmental variables. This study examines the relationships between vegetation and multiple environmental variables in natural vegetation on two underlying rock types, Hawkesbury sandstone and Narrabeen group shales and sandstones, in Ku-ring-gai Chase National Park, Sydney. Floristic composition and 17 environmental factors were characterized using duplicate 500 m2 quadrats from fifty sites representing a wide range of vegetation types. The patterns in vegetation and environmental factors were examined through multivariate analyses: indicator species analysis was used to provide an objective classification of plant community types, and the relationships between vegetation and environmental factors within the two soil types were examined through indirect and direct gradient analyses. Eleven plant communities were identified, which showed strong agreement with previous studies. The measured environmental factors showed strong correlations with vegetation patterns: within both soil types, the measured environmental variables explained approximately 32 - 35% of the variation in vegetation. No single measured environmental variable adequately described the observed gradients in vegetation; rather, vegetation gradients showed strong correlations with complex environmental gradients. These complex environmental gradients included nutrient, moisture and soil physical and site variables. These results suggest a simple 'nutrient' hypothesis regarding vegetation patterns in the Central Coast region is inadequate to explain variation in vegetation within soil types