On the local-indicability cohen–lyndon theorem

For a group H and a subset X of H, we let HX denote the set {hxh?1 | h ? H, x ? X}, and when X is a free-generating set of H, we say that the set HX is a Whitehead subset of H. For a group F and an element r of F, we say that r is Cohen–Lyndon aspherical in F if F{r} is a Whitehead subset of the subgroup of F that is generated by F{r}. In 1963, Cohen and Lyndon (D. E. Cohen and R. C. Lyndon, Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc. 108 (1963), 526–537) independently showed that in each free group each non-trivial element is Cohen–Lyndon aspherical. Their proof used the celebrated induction method devised by Magnus in 1930 to study one-relator groups. In 1987, Edjvet and Howie (M. Edjvet and J. Howie, A Cohen–Lyndon theorem for free products of locally indicable groups, J. Pure Appl. Algebra 45 (1987), 41–44) showed that if A and B are locally indicable groups, then each cyclically reduced element of A*B that does not lie in A ? B is Cohen–Lyndon aspherical in A*B. Their proof used the original Cohen–Lyndon theorem. Using Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem, one can deduce the local-indicability Cohen–Lyndon theorem: if F is a locally indicable group and T is an F-tree with trivial edge stabilisers, then each element of F that fixes no vertex of T is Cohen–Lyndon aspherical in F. Conversely, by Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem are immediate consequences of the local-indicability Cohen–Lyndon theorem. In this paper we give a detailed review of a Bass–Serre theoretical form of Howie induction and arrange the arguments of Edjvet and Howie into a Howie-inductive proof of the local-indicability Cohen–Lyndon theorem that uses neither Magnus induction nor the original Cohen–Lyndon theorem. We conclude with a review of some standard applications of Cohen–Lyndon asphericit

Non-orientable surface-plus-one-relation groups

Recently Dicks–Linnell determined the L2-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the L2-Betti numbers of the non-orientable surface-plus-one-relation group

Portfolio Composition and Pension Wealth: An Econometric Study

There has been very little study of the consequences of pension wealth for the composition of household portfolios. Using individual data for 10,118 Canadian households we estimate the portfolio effect of pension wealth. Because most households do not own all of the assets which we are able to distinguish, we model asset demands as a mixed discrete-continuous portfolio choice problem. We find that whereas there is an identifiable effect of pension wealth on total private savings, the effect on portfolio choice is less significant. Moreover, within the area of portfolio composition the main effect is in terms of the particular number and combination of assets held rather than the amount of any given asset as a proportion of total wealth.

Changes in the Spatial Allocation of Cropland in the Ft. Cobb Watershed as a Result of Environmental Restrictions

Pollution runoff estimates from SWAT are used in a mathematical programming model to optimally model site-specific crop and conservation practices for pollution abatement in the Ft. Cobb watershed in Southwestern Oklahoma. Results indicate the tradeoffs between producer income, sediment and nutrient runoff and the spatial allocation of crops in the watershed.Environmental Economics and Policy,

Taxonomic Status of Lactic Acid Bacteria in Wine and Key Characteristics to Differentiate Species

Oenococcus oeni is the best malolactic bacterium adapted to low pH and the high SO2 and ethanol concentrations inwine. Leuconostoc mesenteroides and Leuconostoc paramesenteroides (now classified as Weissella paramesenteroides)have also been isolated from wine. Pediococcus damnosus is not often found in wine and is considered a contaminantof high pH wines. Pediococcus inopinatus, Pediococcus parvulus and Pediococcus pentosaceus have occasionallybeen isolated from wines. Lactobacillus brevis, Lactobacillus plantarum, Lactobacillus buchneri, Lactobacillushilgardii (previously Lactobacillus vermiforme), Lactobacillus fructivorans (previously Lactobacillus trichoidesand Lactobacillus heterohiochii) and Lactobacillus fermentum have been isolated from most wines. Lactobacillushilgardii and L. fructivorans are resistant to high acid and alcohol and have been isolated from spoiled fortifiedwines. Lactobacillus vini, Lactobacillus lindneri, Lactobacillus nagelii and Lactobacillus kunkeei have been describedmore recently. The latter two species are known to cause sluggish or stuck alcoholic fermentations in wine.Although Lactobacillus collinoides and Lactobacillus mali (previously Lactobacillus yamanashiensis) decarboxylateL-malic acid, they are more often found in cider and fruit juices. Lactobacillus curvatus, Lactobacillus delbrueckii,Lactobacillus diolivorans, Lactobacillus jensenii and Lactobacillus paracasei are seldomly isolated from wines. Somestrains of Lactobacillus casei may be closer related to Lactobacillus paracasei or a distant relative, Lactobacilluszeae. Oenococcus kitaharae, isolated from compost is genetically closely related to Oenococcus oeni, but does notdecarboxylate malate, prefers higher growth pH and is phenotypically well distinguished from O. oeni. This reviewsummarises the current taxonomic status of malolactic bacteria and lists key phenotypic characteristics that maybe used to identify the species

Clinical vampirism: a review and illustrative case report

This paper aims to review the phenomenology of vampirism and the various forms of its expression including its presentation in the psychopathology of psychotic disorders. We will explore in detail the case of an African vampire in a psychiatric clinical setting. Vampirism does not have roots in traditional African culture or folklore and thus this case is worth examining due to the unusual nature of the patient's clinical presentation. After a review of the literature, both lay and professional, a clinical case will be described. The discussion will suggest a biopsychosocial and contemporary psychoanalytic understanding of vampirism, and more specifically, of this patient. We also propose an additional type of vampirism be considered for inclusion in the classification of clinical vampirism. South African Psychiatry Review Vol. 9(3) 2006: 163-16

Non-orientable surface-plus-one-relation groups

Recently Dicks-Linnell determined the $L^2$-Betti numbers of the orientable surface-plus-one-relation groups, and their arguments involved some results that were obtained topologically by Hempel and Howie. Using algebraic arguments, we now extend all these results of Hempel and Howie to a larger class of two-relator groups, and we then apply the extended results to determine the $L^2$-Betti numbers of the non-orientable surface-plus-one-relation groups.Comment: Version 1. 37 pages. 0 figures. Dedicated to the memory of Karl Gruenber