Minimal lenght elements of Thompson's groups F(p)

We describe a method for determining the minimal length of elements in the generalized Thompson's groups F(p). We compute the length of an element by constructing a tree pair diagram for the element, classifying the nodes of the tree and summing associated weights from the pairs of node classifications. We use this method to effectively find minimal length representatives of an element.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Parabolic and quasiparabolic subgroups of free partially commutative groups

Let Γ be a finite graph and G be the corresponding free partially commutative group. In this paper we study subgroups generated by vertices of the graph Γ, which we call canonical parabolic subgroups. A natural extension of the definition leads to canonical quasiparabolic subgroups. It is shown that the centralisers of subsets of G are the conjugates of canonical quasiparabolic centralisers satisfying certain graph theoretic conditions.

Discriminating groups: a comprehensive overview

Discriminating groups were introduced by G.Baumslag, A.Myasnikov and V.Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. However they have taken on a life of their own and have been an object of a considerable amount of study. In this paper we survey the large array results concerning the class of discriminating groups that have been developed over the past decade.

The equation xpyq=zr and groups that act freely on Λ-trees

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Ecology of sandflies (Diptera: Psychodidae) in a restricted focus of cutaneous leishmaniasis en Northern Venezuela: I. Description of the study area, catching methods and species composition

A study on the ecology of phlebotomine sandfly fauna in a restricted focus of cutaneous leishmaniasis in northern Venezuela was undertaken in order to investigate the species responsible for the transmission. The study area and catching methods for phlebotomine sandflies are described. A total of 9,061 females and 1,662 males were collected during a year-term study. 12 species of Lutzomya and 1 species of Brumptomya sp. were identified. Absolute and relative abundance and ocurrence for each species were determined. The rel ative occurrence allowed to distinguish the common species, viz. L. panamensis, L. ovallesi, L. gomezi, L. tinidadensis, L. atroclavata, L. cayennensis, L. shannoni and L. olmeca bicolor from the rare species vis., L. punctigeniculata, L. rangeliana, L. evansi and L. dubitans. General comments on the species composition of the sandfly fauna in this locality are made.

Ecology of sandflies (Diptera: Psychodidae) in a restricted focus of cutaneous leishmaniasis in Northern Venezuela: II. Species composition in relation to habitat, catching method and hour of catching

The ecology of phlebotomine sandflies in an endemic focus of cutaneous leishmaniasis in Northern Venezuela (San Esteban, Carabobo State) was investigated through a year-term study. Three different habitats: viz. a house, a pridomestic area and a sylvatic area, were covered and the species composition, the abundance and occurrence of each species were analyzed in relation to the habitats, catching methods and hour of catching. L. panamensis, L. gomezi and L. ovallesi are the species which bite man, although almost exclusively at night. All of them hide by day and are common in the sylvatic area. Moreover, L. panamensis and L. gomezi successfully approach the house and seem to settle in the peridomestic area. L. shannoni and L. olmeca bicolor also approach and accidentally bite man. L. trinidadensis, L. atroclavata and L. cayennensis are the common non-antrhopophilic species in the area.

Resting metabolic rate and protein turnover in apparently healthy elderly Gambian men.

Body composition, resting energy expenditure (REE), and whole body protein metabolism were studied in 26 young and 28 elderly Gambian men matched for body mass index during the dry season in a rural village in The Gambia. REE was measured by indirect calorimetry (hood system) in the fasting state and after five successive meals. Rates of whole body nitrogen flux, protein synthesis, and protein breakdown were determined in the fed state from the level of isotopic enrichment of urinary ammonia over a period of 12 h after a single oral dose of [15N]glycine. Expressed in absolute value, REE was significantly lower in the elderly compared with the young group (3.21 +/- 0.07 vs. 4.04 +/- 0.07 kJ/min, P < 0.001) and when adjusted to body weight (3.29 +/- 0.05 vs. 3.96 +/- 0.05 kJ/min, P < 0.0001) and fat-free mass (FFM; 3.38 +/- 0.01 vs. 3.87 +/- 0.01 kJ/min, P < 0.0001). The rate of protein synthesis averaged 207 +/- 13 g protein/day in the elderly and 230 +/- 13 g protein/day in the young group, whereas protein breakdown averaged 184 +/- 13 g protein/day in the elderly and 203 +/- 13 g protein/day in the young group (nonsignificant). When values were adjusted for body weight or FFM, they did not reveal any difference between the two groups. It is concluded that the reduced REE adjusted for body composition observed in elderly Gambian men is not explained by a decrease in protein turnover.

Orbit decidability and the conjugacy problem for some extensions of groups

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High fat versus high carbohydrate nutritional supplementation: a one year trial in stunted rural Gambian children.

OBJECTIVE: The study tests the hypothesis that a low daily fat intake may induce a negative fat balance and impair catch-up growth in stunted children between 3 and 9y of age. DESIGN: Randomized case-control study. SETTING: Three rural villages of the West Kiang District, The Gambia. SUBJECTS: Three groups of 30 stunted but not wasted children (height for age z-score < or = -2.0, weight for height z-score > or = -2.0) 3-9 y of age were selected by anthropometric survey. Groups were matched for age, sex, village, degree of stunting and season. INTERVENTION: Two groups were randomly assigned to be supplemented five days a week for one year with either a high fat (n = 29) or a high carbohydrate biscuit (n = 30) each containing approximately 1600 kJ. The third group was a non supplemented control group (n = 29). Growth, nutritional status, dietary intake, resting energy expenditure and morbidity were compared. RESULTS: Neither the high fat nor the high carbohydrate supplement had an effect on weight or height gain. The high fat supplement did slightly increase adipose tissue mass. There was no effect of supplementation on resting energy expenditure or morbidity. In addition, the annual growth rate was not associated with a morbidity score. CONCLUSIONS: Results show that neither a high fat nor a high carbohydrate supplement given during 12 months to stunted Gambian children induced catch-up growth. The authors suggest that an adverse effect of the environment on catch-up growth persists despite the nutritional interventions.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Metric properties of the braided Thompson's groups

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On the intersection of free subgroups in free products of groups

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A classification, up to hyperbolicity, of groups given by 2 generators and one relator of length 8

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