The symmetry of intersection numbers in group theory

For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.Comment: 19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol2/paper2.abs.html . Includes erratum added to the original, published 19 Mar 199

Perma/Culture: Imagining Alternatives in an Age of Crisis by Molly Wallace and David Carruthers

Review of Molly Wallace and David Carruthers\u27 Perma/Culture: Imagining Alternatives in an Age of Crisis

Shortjaw kokopu (Galaxias postvectis Clarke) distribution, habitat selection and seasonal activity in the northern Tararua Ranges : a thesis presented in partial fulfillment of the requirements for the degree of a Masters of Science in Ecology at Massey University, Palmerston North, New Zealand

Freshwater fish communities were surveyed at 59 sites in the Mangatainoka, Makakahi and Ruamahanga catchments of the northeastern Tararua Ranges during 2000/01. At each site, habitat characteristics were recorded and fish identified by spotlighting over a 100 m reach. Benthic invertebrate samples were also collected from 50 of these sites. Shortjaw kokopu (Galaxias postvectis Clarke) occurred at 16 sites, located in the Mangatainoka and Makakahi catchments only. Ninty-five shortjaw kokopu were caught in total, ranging from juveniles (120 mm), with adults comprising approximately 75% of the population. Six other fish species were also recorded. Koaro (G. brevipinnis GÜnther), longfin eel (Anguilla dieffenbachii Gray), Cran's bully (Gobiomorphus basalis Gray), torrentfish (Cheimarrichthys fosteri Haast) and brown trout (Salrmo trutta Linnaeus) all co-occurred with shortjaw kokopu; and a single banded kokopu (G. fasciatus Gray) was found in the Ruamahanga catchment. Discriminant analysis found six habitat factors defined shortjaw kokopu presence. These were low percentages of debris jams, pasture and backwaters; high percentages of shrubs and riffles; and high conductivity. The invertebrate community also proved effective at predicting shortjaw kokopu presence. However, it appears that shortjaw kokopu are limited in distribution by recruitment rather than habitat. Different age classes of shortjaw kokopu were also found to use distinct microhabitats. Sand substrate, pool length, width at the top of the pool, velocity, gradient below the pool, and cobble in the habitat above the pool were found to discriminate between the age class microhabitats. At three sites in the Mangatainoka River, surveys were undertaken monthly, for 16 months. Number of shortjaw kokopu observed was greatly reduced at all three sites during winter and at a maximum in autumn. This showed that shortjaw kokopu exhibited reduced activity rather than seasonal movements within the catchment. Three methods for surveying fish communities were tested on shortjaw kokopu. Gee-minnow traps failed to catch any shortjaw kokopu, but electrofishing and spotlighting both proved effective. While spotlighting caught more shortjaw kokopu at more sites, no significant difference in performance was found between the two methods

Saying NO To the Mega Prison

This activist contribution draws upon the issues emphasised by abolitionist activists in their struggles throughout 2017 (and before) to challenge government plans to build six new mega prisons in England and Wales by 2020. This activist contribution focuses specifically on the arguments utilised by campaigners in one of the proposed sites for a new mega prison: Bickershaw, Wigan, Greater Manchester

Wind power compensation is not for the birds : an opinion from an environmental economist

This article advocates for better implementation of the Environmental Impact Assessment (EIA) framework as applied to wind power development, with a particular focus on improving compensatory restoration scaling. If properly enforced, the environmental impacts hierarchy "avoid - minimize - compensate" provides the regulated community with incentives to prevent wildlife and habitat impacts in sensitive areas and, if necessary, compensate for residual impacts through restoration or conservation projects. Given the increase in legislation requiring resource-based environmental compensation, methods for scaling an appropriate quantity and quality of resources is of increasing relevance. I argue that Equivalency Analysis (EA) represents a transparent and quantitative approach for scaling compensation in the case of wind power development. Herein, I identify the economic underpinnings of environmental compensation legislation and identify weaknesses in current scaling approaches within wind power development. I demonstrate how the recently-completed REMEDE Toolkit, which provides guidance on EA, can inform an improved scaling approach and summarize a case study involving raptor collisions with turbines that illustrates the EA approach. Finally, I stress the need for further contributions from the field of restoration ecology. The success of ex ante compensation in internalizing the environmental costs of wind development depends on the effective implementation of the environmental impacts hierarchy, which must effectively encourage avoidance and minimization over environmental restoration and repair