THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

Tracking 10-year competitive winning performance of judo athletes across age groups

Little information is available concerning early specialization and competitive success in judo across the early training years. Thus, the present objective was to verify the stability of individual competitive performance of a state-level championship for judo athletes who had been previously successful. For this, 406 athletes from six age groups (9 to 20+ years old) of each sex were followed for 10 years. Using recorded data from the Sao Paulo State Judo Federation beginning in 1999, the scores and standings for these judo players were analyzed. The proportion of medal winners during this period was not constant, differing from the grand mean in all groups of both 204 males and 202 females. At the end of this period, only 7% of the male and 5% of the female athletes had maintained their competitive levels. Successful competitive performance in early judo competition was not associated with success later in adulthood.

A new thrombospondin-related anonymous protein homologue in Neospora caninum (NcMIC2-like1)

Neospora caninum is an Apicomplexan protozoan that has the dog as a definitive host and cattle (among other animals) as intermediate hosts. It causes encephalopathy in dogs and abortion in cows, with significant loss in worldwide livestock. As any Apicomplexan, the parasite invades the cells using proteins contained in the phylum-specific organelles, like the micronemes, rhoptries and dense granules. The aim of this study was the characterization of a homologue (denominated NcMIC2-like1) of N. caninum thrombospondin-related anonymous protein (NcMIC2), a micronemal protein previously shown to be involved in the attachment and connection with the intracellular motor responsible for the active process of invasion. A polyclonal antiserum raised against the recombinant NcMIC2-like1 functional core (thrombospondin and integrin domains) recognized the native form of NcMIC2-like1, inhibited the in vitro invasion process and localized NcMIC2-like1 at the apical complex of the parasite by confocal immunofluorescence, indicating its micronemal localization. The new molecule, NcMIC2-like1, has features that differentiates it from NcMIC2 in a substantial way to be considered a homologue dagger.

Behavior and interactions of children in cooperative groups in lower and middle elementary grades

The study investigated the behaviors and interactions of children in structured and unstructured groups as they worked together on a 6-week social studies activity each term for 3 school terms. Two hundred and twelve children in Grade 1 and 184 children in Grade 3 participated in the study. Stratified random assignment occurred so that each gender-balanced group consisted of 1 high-, 2 medium-, and 1 low-ability student. The results show that the children in the structured groups were consistently more cooperative and they provided more elaborated and nonelaborated help than did their peers in the unstructured groups. The children in the structured groups in Grade 3 obtained higher reading and learning outcome scores than their peers in the unstructured groups.

Australian doctors' beliefs and practice regarding Helicobacter pylori

Objective: To determine beliefs and behaviours of Australian doctors regarding Helicobacter pylori. Design: Anonymous reply-paid postal survey mailed in December 1995 and again in March 1996. Subjects: All members on the mailing lists of the Gastroenterological Society of Australia Endoscopy Section (n = 397) and the Australian Society of Infectious Diseases (n = 264; those without medical qualifications were asked not to reply), and 400 general practitioners (GPs) randomly selected from the Royal Australian College of General Practitioners. Main outcome measures: Differences between specialist groups in belief in a causative association between H. pylori and peptic disease and in use of eradication therapy and pre- and post-treatment testing for H. pylori. Results: 92.6% of doctors believed H. pylori causes duodenal ulcer, with GPs significantly less likely to believe than gastroenterologists (odds ratio [OR], 0.22; 95% confidence interval [CI], 0.00-0.81). In duodenal ulcer, 93.4% of doctors believed H. pylori eradication therapy should be given, but fewer (83.4%) claimed to give it always or mostly, with GPs less likely to report giving it than gastroenterologists (OR, 0.06; 95% CI, 0.02-0.19). For non-ulcer dyspepsia, gastrointestinal surgeons were more likely than gastroenterologists to believe in a causative link with H. pylori (OR, 5.6; 95% CI, 3.0-10.7) and in a need for eradication therapy (OR, 3.6; 95% CI, 1.7-7.7). Most doctors (79.3%) believed in confirming the presence of H. pylori before eradication therapy in duodenal ulcer. Only 51.6% believed post-eradication testing necessary (45.5%), yet 79.1% reported performing it. Conclusions: Significant differences exist between specialist groups in beliefs and self-reported behaviours regarding H. pylori.

Groups with exponent six

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent sis using substantial computations which we explain.

Maintenance of cooperative and helping behaviors in reconstituted groups

The authors conducted a 1-year investigation of whether children, who had been trained in the previous school gear to cooperate, were able to use the skills they had been taught in reconstituted groups without additional training. Sixty-four 4th graders, who had participated in training in cooperative group behaviors in the previous gear, were assigned to the trained condition; 84 4th graders, who had not received any training, were assigned to the untrained condition. The children worked in mixed-ability (high, medium, low) gender-balanced groups (2 boys, 2 girls). Results indicate that the children in the trained groups were consistently more cooperative and helpful than their peers in the untrained groups, although they had not received refresher training in cooperative group behaviors.

Friedmanniella spumicola sp nov and Friedmanniella capsulata sp nov from activated sludge foam: Gram-positive cocci that grow in aggregates of repeating groups of cocci

Two Gram-positive, non-motile, non-spore-forming, strictly aerobic, pigmented cocci, strains Ben 107(T) and Ben 108(T), growing in aggregates were isolated from activated sludge samples by micromanipulation. Both possessed the rare type A3 gamma' peptidoglycan. Major menaquinones of strain Ben 107(T) were MK-9(H-4) and MK-7(H-2), and the main cellular fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). In strain Ben 108(T), MK-9(H-4), MK-9(H-2) and MK-7(H-4) were the menaquinones and again the main fatty acid was 12-methyltetradecanoic acid (ai-C-15:0). Polar lipids in both strains consisted of phosphatidyl inositol, phosphatidyl glycerol and diphosphatidyl glycerol with two other unidentified glycolipids and phospholipids also present in both. These data, together with the 16S rDNA sequence data, suggest that strain Ben 107(T) belongs to the genus Friedmanniella which presently includes a single recently described species, Friedmanniella antarctica. Although the taxonomic status of strain Ben 108(T) is far less certain, on the basis of its 16S rRNA sequence it is also adjudged to be best placed in the genus Friedmanniella, The chemotaxonomic characteristics and DNA-DNA hybridization data support the view that Ben 107(T) and Ben 108(T) are novel species of the genus Friedmanniella. Hence, it is proposed that strain Ben 107(T) (=ACM 5121(T)) is named as Friedmanniella spumicola sp. nov. and strain Ben 108(T) (=ACM 5120(T)) as Friedmanniella capsulata sp. nov.

Metal-directed synthesis routes to a 16-membered tetraazamacrocycle with two pendant primary amine groups

The reaction of the bis(propane-1,3-diamine)copper(II) ion with paraformaldehyde and nitroethane in dry methanol under basic conditions produces a macrocyclic product, (cis-3,11-dimethyl-3,11-dinitro-1,5,9,13-tetraazacyclohexadecane)copper(II) perchlorate, in low yield, compared with the good yield obtained in the parallel chemistry possible even under aqueous conditions using palladium(II) as a template. The palladium complex was reduced with zinc amalgam in dilute aqueous acid to yield the metal-free 16-membered macrocyclic hexaamine, in this case re-complexed and characterised by an X-ray crystal structure as the (cis-3,11-dimethyl-1,5,9,13-tetraazacyclohexadecane-3,11-diamine)copper(II) perchlorate. The copper ion is found in a tetragonally elongated and trigonally-distorted octahedral environment, with all six of the ligand nitrogens coordinated, the two primary amine pendant groups occupying cis sites. (C) 2000 Elsevier Science S.A. All rights reserved.

Naltrexone in the treatment of male alcoholics - an effectiveness study in Singapore

Naltrexone has been demonstrated in western studies to be a useful pharmacological adjunct within treatment programmes for alcoholic patients. We report the first study of its efficacy and usefulness in an Asian region. This project was designed to allow naltrexone's performance to be assessed under routine clinical conditions but with patients selected on the basis of their being likely to comply. Following in-patient detoxification, 53 male alcohol-dependent patients admitted to the Alcohol Treatment Centre at Woodbridge Hospital, Singapore, were enrolled in a 12-week, placebo-controlled trial of naltrexone hydrochloride (50 mg/day). Subjects were randomized on a 2:1 basis, with 35 receiving naltrexone and 18 receiving placebo. Analyses identified that a higher percentage of naltrexone patients completed the study (40% vs. 22%). In the study non-completers, the dropout rate due to drinking relapse was also lower in the naltrexone group (9% vs. 43%). Of the 39 patients for whom drinking status over the trial could be ascertained, fewer naltrexone-treated patients drank (33% vs. 53%). Alcohol craving scores also showed a selective and distinct reduction in the naltrexone-treated group. Results suggest that naltrexone may be an effective and safe aid to treatment of alcohol dependent patients in Asian patients, for whom the aims are to reduce alcohol craving and drinking reinstatement, but where compliance is likely to be low.

Participation in recreational physical activity: Why do socioeconomic groups differ?

This qualitative study explored how influences on recreational physical activity (RPA) were patterned by socioeconomic position. Face-to-face interviews were conducted with 10 males and 10 females in three socioeconomic groups (N = 60). Influences salient across all groups included previous opportunities, physical health, social assistance, safety, environmental aesthetics and urban design, physical and health benefits, and barriers of self-consciousness, low skill, and weather/time of year. Influences more salient to the high socioeconomic group included social benefits, achieving a balanced lifestyle, and the barrier of an unpredictable lifestyle. Influences more salient to the high and mid socioeconomic groups included efficacy, perceived need, activity demands, affiliation, emotional benefits, and the barrier of competing demands. Influences more salient to the low socioeconomic group included poor health and barriers of inconvenient access and low personal functioning. Data suggest that efforts to increase RPA in the population should include both general and socioeconomically targeted strategies.