Rigidity of graph products of abelian groups

We show that if $G$ is a group and $G$ has a graph-product decomposition with finitely-generated abelian vertex groups, then $G$ has two canonical decompositions as a graph product of groups: a unique decomposition in which each vertex group is a directly-indecomposable cyclic group, and a unique decomposition in which each vertex group is a finitely-generated abelian group and the graph satisfies the $T_0$ property. Our results build on results by Droms, Laurence and Radcliffe.Comment: 11 pages, 1 figur

The Open Society and coach education: a philosophical agenda for policy reform and future sociological research

Background: The realisation of the strategic importance of high quality coaching to the achievement of national sport policy objectives is resulting in extensive movements to professionalise the coaching industry. Interest in coach education is therefore growing among academics and policy-makers alike. A recent review of literature in this field, however, reveals a troubling problem situation: formal coach education is important for coach learning but tends to be expensive, inflexible and overly technical and therefore has little real impact on coaching practice. The solutions offered by many academics are, unfortunately, vague and often philosophically flawed. This is particularly so when the descriptive model of communities of practice (CoP) is suggested as a prescriptive model for coach education. The first part of the paper, therefore, ends with an extended critique of the use of CoP as a model for coach education. Purpose: To provide a clear philosophical argument for the direction of reform for coach education, drawing on a normative theory of the ideal conditions for the growth of knowledge. Discussion: Starting with the argument that any descriptive (or ‘evidence-based’) model is inherently conservative, the second part of the paper offers an alternative solution to the problem of coach education that is openly prescriptive (or normative). It is the Popperian ideal type of an Open Society (OS). It is argued that the concept of an OS is a better prescriptive model for coach learning for a number of reasons. First, it is based on a logically sound epistemological theory of the ideal social conditions for the growth of knowledge. Second, it is simple and easy for lay people to understand. Third, as an ideal type, it offers a target or goal against which progress towards a better method of coach education can be measured. In this final sense, it also offers a clear agenda for policy reform and future sociological research. Conclusions: The paper makes a series of practical recommendations for reforming coach education and its institutions based on the model of the OS. Foremost among these are making learning resources free at the point of use and using Web 2.0 technologies to democratise educational episodes and widen participation in coach education programmes of all kinds

On the automorphisms of a graph product of abelian groups

We study the automorphisms of a graph product of finitely-generated abelian groups W. More precisely, we study a natural subgroup Aut* W of Aut W, with Aut* W = Aut W whenever vertex groups are finite and in a number of other cases. We prove a number of structure results, including a semi-direct product decomposition of Aut* W in which one of the factors is Inn W. We also give a number of applications, some of which are geometric in nature.Comment: 38 pages, 4 figure

Indexing pensions

Pension indexation should anchor the parameters of the pension system to one or more economic and demographic variables to ensure that the system is implemented in a sustainable way, while minimizing distortions affecting important economic choices. Arguing that financial sustainability, incentive compatibility and consistency across multiple government programs are critical, the author examine the many linkages between the various parameters of pension schemes. Finally, the author turn to the cost of the insurance dimension of indexation, and suggest that option pricing techniques could be used to price indexation guarantees, and that this approach may suggest refinements to indexation practice not thus far implemented.Emerging Markets,Debt Markets,Pensions&Retirement Systems,Economic Theory&Research,Markets and Market Access

REPRODUCTIVE SUCCESS IN HATCHERY-PRODUCED EASTERN OYSTER, CRASSOSTREA VIRGINICA (GMELIN)

The eastern oyster (Crassostrea virginica Gmelin 1791) has great ecological and economic importance but populations have declined, especially in Chesapeake Bay, to historically low numbers. Hatcheries strive to produce oysters with beneficial characteristics for supplementation and commercial purposes, both natural and stimulated mass spawning. Unequal contribution of parents in mass spawnings potentially can lead to high levels of inbreeding and a loss of beneficial characteristics in offspring. In this study, we determined microsatellite genotypes for parents (n^parents =24, 49, and 77 parents) and progeny (n=96 each) of three hatchery-produced families and used the data for parental assignment. We observed the presence of more than two alleles per locus for some offspring, yet because genetic analysis software only allows for a maximum of two alleles per locus, we chose the two alleles with the strongest signals. For the three parent “populations,” 71% of alleles had frequencies of \u3c0.05 and observed heterozygosities were lower than expected by an average factor of 0.27. Inbreeding within the various parent populations was similar across the three families ranging from F^IS 0.26–0.43. In all three families, the offspring exhibited greater levels of genetic diversity and lower inbreeding levels than the parents (F^IS 0.14–0.21), and in some cases offspring exhibited alleles that were not present in the parents. Variance in the number of offspring produced per parent was observed for all families and in general, \u3c10% of potential parents (generally 2-5 females and 1-3 males) produced \u3e10% of the offspring. Reproductive success for spawning parents, N^b, determined by three methods, ranged from 0.07 to 0.27. As the number of parents per family increased, a higher proportion of parents failed to produce offspring. Across all three families, the average effective number of breeders was N^b = 7.1 and the level of reproductive success was inversely proportional to the number of potential parents. This finding implies that to maintain high levels of diversity and beneficial characteristics in the offspring (and to avoid the chance of unintentional inbreeding), hatcheries should perform more spawnings with fewer parents

Widening Participation in Golf: Barriers to Participation and GolfMark

This research was commissioned by the EGU and R&A in 2010. The aims of the research project were threefold: 1) To review the academic literature on barriers to participation in sport, especially golf; 2) To survey clubs, members and nomadic golfers to describe their perceptions of GolfMark and the issues it intends to address; 3) To gather in-depth data from a range of golf clubs to help understand how different club cultures may lead to the exclusion of underrepresented demographic groups

The automorphism group of the free group of rank two is a CAT(0) group

We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.Comment: 7 pages, 2 figures. The manuscript has been modified in minor ways in accordance with a referee's recommendations, and a misattribution of the result "Aut F_2 is biautomatic" has been correcte

Investigation of an R134A Refrigerant/Iso 32 Polyol Ester Oil Mixture in Condensation

Air Conditioning and Refrigeration Project 12