Retracts of vertex sets of trees and the almost stability theorem

Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V' of VT such that no G-tree has vertex set V'.Comment: 15 pages, 0 figures. Formerly titled "Some refinements of the almost stability theorem". Version

Nanofibers Offer Alternative Ways to the Treatment of Skin Infections

Injury to the skin causes a breach in the protective layer surrounding the body. Many pathogens are resistant to antibiotics, rendering conventional treatment less effective. This led to the use of alternative antimicrobial compounds, such as silver ions, in skin treatment. In this review nanofibers, and the incorporation of natural antimicrobial compounds in these scaffolds, are discussed as an alternative way to control skin infections. Electrospinning as a technique to prepare nanofibers is discussed. The possibility of using these structures as drug delivery systems is investigated

Neurophysiological studies may provide a misleading picture of how perceptual-motor interactions are coordinated

Neurophysiological measurement techniques like fMRI and TMS are increasingly being used to examine the perceptual-motor processes underpinning the ability to anticipate the actions of others. Crucially, these techniques invariably restrict the experimental task that can be used and consequently limit the degree to which the findings can be generalised. These limitations are discussed based on a recent paper by Tomeo et al. (2012) who sought to examine responses to fooling actions by using TMS on participants who passively observed spliced video clips where bodily information was, and was not, linked to the action outcome. We outline two particular concerns with this approach. First, spliced video clips that show physically impossible actions are unlikely to simulate a "fooling" action. Second, it is difficult to make meaningful inferences about perceptual-motor expertise from experiments where participants cannot move. Taken together, we argue that wider generalisations based on these findings may provide a misunderstanding of the phenomenon such a study is designed to explore. © 2013 D Mann, M Dicks, R Cañal-Bruland, J van der Kamp

Nanocomposite Polymer Electrolyte Membranes: Methanol Crossover and Conductivity

Commercial Nafion® 117 membranes were successfully modified by in-situ reactions (sol-gel of TEOS and/or polymerization of aniline) within Nafion structures. Water-methanol permeability and proton conductivity were investigated in order to determine the potential performance of these membranes for DMFC systems. Silica-polyaniline modification resulted in 84% methanol crossover reduction, from 2.45x10^-5 cm2.s^-1 for conventional Nafion membranes to 3.71x10^-6 cm2.s^-1 for the modified silica-polyaniline composite membrane at 75 degrees C. In addition, conductivity was not hindered, as the polyaniline-Nafion membrane increased from 12.2 to 15 mS.cm^-1 as compared to Nafion, while a reduction of 11% was observed for silica-polyaniline-Nafion composite membrane. The results in this work strongly suggest the potential of polyaniline nanocomposites to enhance the performance of DMFCs

Retracts of vertex sets of trees and the almost stability theorem

Abstract Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let V T denote the vertex set of T . We show that, for each G-retract V of the G-set V T , there exists a G-tree whose edge stabilizers are finite and whose vertex set is V . This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V of V T such that no G-tree has vertex set V

Advantages and challenges of microalgae as a source of oil for biodiesel

Microalgal oil is currently being considered as a promising alternative feedstock for biodiesel. The present demand for oil for biofuel production greatly exceeds the supply, hence alternative sources of biomass are required. Microalgae have several advantages over land-based crops in terms of oil production. Their simple unicellular structure and high photosynthetic efficiency allow for a potentially higher oil yield per area than that of the best oilseed crops. Algae can be grown on marginal land using brackish or salt water and hence do not compete for resources with conventional agriculture. They do not require herbicides or pesticides and their cultivation could be coupled with the uptake of CO2 from industrial waste streams, and the removal of excess nutrients from wastewater (Hodaifa et al., 2008; An et al., 2003). In addition to oil production, potentially valuable co-products such as pigments, antioxidants, nutraceuticals, fertilizer or feeds could be produced (Mata et al., 2010; Rodolfi et al., 2009)

Are prices of new dwellings different? A spectral analysis of UK property vintages

The work makes two contributions to Hui’s (2011) dynamic house price classification. First, a house price ripple in cycles from Modern to Older dwellings is revealed and, second, as New housing is shown to have lower volatility than the other two. Using spectral analysis, it is argued that there is a 7½-year repeat buyer-second-hand cycle and a five year, first time buyer-New housing cycle, common to three house price vintages. These cycles reinforce each other every fifteen years, which corresponds with a Minsky super-cycle in housing finance. The equity of the owner-occupier is fortified by higher house prices whereas new builds extract embedded equity from the market. Government should support builders and facilitate access to market to first time buyers and through programmes like Help-to-Buy 1. However, to address the greater price instability that should follow, Government should impose a capital gains tax on the house seller

Peak reduction technique in commutative algebra

The "peak reduction" method is a powerful combinatorial technique with applications in many different areas of mathematics as well as theoretical computer science. It was introduced by Whitehead, a famous topologist and group theorist, who used it to solve an important algorithmic problem concerning automorphisms of a free group. Since then, this method was used to solve numerous problems in group theory, topology, combinatorics, and probably in some other areas as well. In this paper, we give a survey of what seems to be the first applications of the peak reduction technique in commutative algebra and affine algebraic geometry.Comment: survey; 10 page