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.

Identification of products formed by a fructan:fructan fructosyltransferase activity from Lolium rigidum

The products formed by a fructan:fructan fructosyltransferase (FFT) activity purified from Lolium rigidum Gaudin were identified after gas chromatography-mass spectrometry of partially methylated alditol acetates, electrospray ionization-mass spectrometry and reversed-phase high-performance liquid chromatography. The FFT activity synthesized oligofructans up to degree of polymerization (DP) 6, but did not synthesize fructans of DP > 6 even when assayed with (1,1,1)-kestopentaose for up to 10 h. The FFT activity when assayed with 1-kestose or 6(G)-kestose synthesized fructan with fructosyl residues almost exclusively linked by beta-2,1-glycosidic linkages. When assayed with 1-kestose, the FFT activity synthesized tetrasaccharides and pentasaccharides with an internal glucosyl residue. The predominant tetrasaccharide was (1&6(G))-kestotetraose and the predominant pentasaccharide was (1&6(G),1)-kestopentaose. By comparison, tetrasaccharides and pentasaccharides extracted from L. rigidum also contained predominantly beta-2,1-glycosidic linked fructans with an internal glucosyl residue. The only exception was that one of the pentasaccharides contained beta-2,1- and beta-2,6-glycosidic linked fructosyl residues. This pentasaccharide was not synthesized by the FFT activity. The role of this FFT activity in formation of oligofructans in L. rigidum is discussed.

Synthesis of fructans by partially purified fructosyltransferase activities from Lolium rigidum

Sucrose:sucrose fructosyltransferase (SST) activity was partially purified from whole shoots of Lolium rigidum by a combination of affinity chromatography, gel filtration and anion-exchange chromatography. The SST activity co-eluted with some fructan:fructan fructosyltransferase (FFT) and invertase activities and consequently the partially purified preparation was termed the fructosyltransferase (FT) preparation. The SST-like activity in the FT preparation was purified 214-fold and had an apparent molecular mass of 84 000. The FT preparation contained several peptides with an apparent pI of 4.6-4.7. When assayed with sucrose concentrations up to 600 mM, the FT preparation synthesized 1-kestose at all concentrations, and synthesized 6-kestose at concentrations of 150 mM and greater. The K-m of 1-kestose production was 0.2 M. When the FT preparation was assayed at a concentration of activity approximately half that measured in fresh tissue with 100 mM sucrose, 1-kestose, or 6(G)-kestose as substrates, fructans of degree of polymerization (DP) less than or equal to 5 were synthesized. A partially purified FFT activity, free of SST and invertase activities, which synthesized beta-2,1-glycosidic linked oligofructans of DP less than or equal to 6, was combined in vitro with the FT preparation (FFT-FT preparation) to give a ratio of SST:FFT activities similar to that measured in crude enzyme extracts from L. rigidum. The FFT-FT preparation synthesized oligofructans when assayed with 100 mM concentrations of sucrose, 1-kestose or 6(G)-kestose, but was not able to synthesize fructans of DP greater than or equal to 6 even after extended assays of up to 10 h. The FFT-FT preparation was also assayed with 100 mM sucrose with small amounts of concentrated sucrose added periodically during the assay to maintain the substrate concentration. In this assay, the FFT-FT preparation synthesized fructans up to an apparent DP of 17 or greater. The fructans of DP greater than or equal to 6 synthesized in the assay appeared to form two molecular series containing both beta-2,1- and beta-2,6-glycosidic linked fructosyl residues with terminal or internal glucosyl residues. The apparent rate of SST activity in the assay of the FFT-FT preparation was greater than that measured in a similar assay of the FT preparation alone which did not result in fructans with DP greater than or equal to 6. It was concluded that the FFT-FT preparation, when assayed with a continual supply of sucrose, contained a factor which promoted synthesis of fructans of DP greater than or equal to 6 and synthesis of beta-2,B-glycosidic linkages between fructosyl residues.

Structural characterisation of galactoglucomannan secreted by suspension-cultured cells of Nicotiana plumbaginifolia

Galactoglucomannan (GGM) from cultures of Nicotiana plumbaginifolia has Man:Glc:Gal:Ara:Xyl in 1.0:1.1:1.0:0.1:0.04 ratio. Linkage analysis contained 4- and 4,6-Manp, 4-Glcp, terminal Galp and 2-Galp, small amounts and terminal Arap and terminal Xylp, and similar to 0.03 mol acetyl per mol of glucosyl residue. Treatment with alpha- and beta-D-galactosidases showed that the majority of the side-chains were either single Galp-alpha-(1 --> residues or the disaccharide Galp-beta-(1 --> 2)-Galp-alpha-(1 --> linked to O-6 of the 4-Manp residues of the glucomannan backbone. Analysis of the oligosaccharides generated by endo-(1 --> 4)-beta-mannanase digestion confirmed that the GGM comprises a backbone of predominantly alternating --> 4)-D-Manp-beta-(1 --> and --> Lt)-D-Glcp-beta-(1 --> branched at O-6 of 65% of the 4-Manp residues. The major oligosaccharide identified was D-Glcp-beta-(1 --> 4)-[D-Galp-beta-(1 --> 2)-D-Galp-alpha-(1 --> 6)]-D-Manp-beta-(1 --> 4)-D-Glcp-beta-(I --> 4)-[D-Galp-alpha-(1 --> 6)]-D-Manp-beta-(1 --> (27%), and most of the other oligosaccharides produced in significant quantities were based on this structure. (C) 1997 Elsevier Science Ltd.

Liquid distribution in wet granulation: dimensionless spray flux

This study investigates binder distribution in wet granulation and focuses on the nucleation zone, which is the area where the liquid binder and powder surface come into contact and form the initial nuclei. An equipment independent parameter, dimensionless spray flux Psi (a), is defined to characterise the most important process parameters in the nucleation process: solution flowrate, powder flux, and binder drop size. Ex-granulator experiments are used to study the relationship between dimensionless spray flux, process variables and the coverage of binder fluid on the powder surface. Lactose monohydrate powder on a variable speed riffler passed under a flat spray once only. Water and 7% HPC solution at two spray pressures were used as binders. Experiments with red dye and image analysis demonstrate that changes in dimensionless spray flux correlate with a measurable difference in powder surface coverage. Nucleation experiments show that spray flux controls the size and shape of the nuclei size distribution. At low Psi (a), the system operates in the drop controlled regime, where one drop forms one nucleus and the nuclei size distribution is narrow. At higher Psi (a), the powder surface cakes creating a broader size distribution. For controlled nucleation with the narrowest possible size distribution, it is recommended that the dimensionless spray flux be less than 0.1 to be in the drop-controlled regime. (C) 2001 Elsevier Science S.A. All rights reserved.

Scale-up of mixer granulators for effective liquid distribution

There is considerable anecdotal evidence from industry that poor wetting and liquid distribution can lead to broad granule size distributions in mixer granulators. Current scale-up scenarios lead to poor liquid distribution and a wider product size distribution. There are two issues to consider when scaling up: the size and nature of the spray zone and the powder flow patterns as a function of granulator scale. Short, nucleation-only experiments in a 25L PMA Fielder mixer using lactose powder with water and HPC solutions demonstrated the existence of different nucleation regimes depending on the spray flux Psi(a)-from drop-controlled nucleation to caking. In the drop-controlled regime at low Psi(a) values. each drop forms a single nucleus and the nuclei distribution is controlled by the spray droplet size distribution. As Psi(a) increases, the distribution broadens rapidly as the droplets overlap and coalesce in the spray zone. The results are in excellent agreement with previous experiments and confirm that for drop-controlled nucleation. Psi(a) should be less than 0.1. Granulator flow studies showed that there are two powder flow regimes-bumping and roping. The powder flow goes through a transition from bumping to roping as impeller speed is increased. The roping regime gives good bed turn over and stable flow patterns. This regime is recommended for good liquid distribution and nucleation. Powder surface velocities as a function of impeller speed were measured using high-speed video equipment and MetaMorph image analysis software, Powder surface velocities were 0.2 to 1 ms(-1)-an order of magnitude lower than the impeller tip speed. Assuming geometrically similar granulators, impeller speed should be set to maintain constant Froude number during scale-up rather than constant tip speed to ensure operation in the roping regime. (C) 2002 Published by Elsevier Science B.V.

Investigation of hip abductor activation in subject with clinical unilateral hip osteoarthritis

Objectives: (a) To compare the magnitude of gluteus medius and tensor fascia lata activation between a group of subjects with clinical unilateral hip osteoarthritis and a group of healthy older adults. (b) To compare the magnitude of activation of the gluteus medius and tensor fascia lata between sides in a group of subjects with clinical unilateral hip osteoarthritis and a group of healthy older adults. Methods: 19 subjects with clinical unilateral hip osteoarthritis and 19 healthy controls were investigated. The subjects performed a stepping task during which recordings were obtained using surface electromyograms from the hip abductors, and kinetic data were obtained from a dual force platform. Results: Subjects with clinical hip osteoarthritis had higher gluteus medius activation than the healthy older adults (p=0.037). In addition, there were no differences in the magnitude of gluteus medius activation between the sides (p=0.733). There was no difference in the force platform data between the groups (p=0.078). Conclusions: The increased magnitude of gluteus medius activation in the group with hip osteoarthritis is evidence of a muscular dysfunction associated with hip disease. This has implications for the progressive nature of the disease and for its conservative management.

Integrated Pb- and S-isotope investigation of sulphide minerals from the early Archaean of southwest Greenland

We present high-spatial resolution secondary ion mass spectrometry (SIMS) measurements of Pb and S isotopes in sulphides from early Archaean samples at two localities in southwest Greenland. Secondary pyrite from a 3.71 Ga sample of magnetite-quartz banded iron formation in the Isua Greenstone Belt, which has previously yielded unradiogenic Pb consistent with its ancient origin, contains sulphur with a mass independently fractionated (MIF) isotope signature (Delta(33)S =+3.3 parts per thousand). This reflects the secondary mineralization of remobilized sedimentary S carrying a component modified by photochemical reactions in the early Archaean atmosphere. It further represents one of the most extreme positive excursions so far known from the early Archaean rock record. Sulphides from a quartz-pyroxene rock and an ultramafic boudin from the island of Akilia, in the Godth (a) over circle bsfjord, have heterogeneous and generally radiogenic Pb isotopic compositions that we interpret to represent partial re-equilibration of Pb between the sulphides and whole rocks during tectonothermal events at 3.6, 2.7 and 1.6 Ga. Both these samples have Delta(33)S=0 (within analytical error) and therefore show no evidence for MIF sulphur. These data are consistent with previous interpretations that the rock cannot be proven to have a sedimentary origin. Our study illustrates that SIMS S-isotope measurements in ancient rocks can be used to elucidate early atmospheric parameters because of the ability to obtain combined S and Pb-isotope data, but caution must be applied when using such data to infer protolith. When information from geological context, petrography and chronology (i.e. by Pb isotopes) is combined and fully evaluated, Delta(33)S signatures from sulphides and their geological significance can be interpreted with a higher degree of confidence. (c) 2005 Elsevier B.V All rights reserved.

Encounter success of free-ranging marine predator movements across a dynamic prey landscape

Movements of wide-ranging top predators can now be studied effectively using satellite and archival telemetry. However, the motivations underlying movements remain difficult to determine because trajectories are seldom related to key biological gradients, such as changing prey distributions. Here, we use a dynamic prey landscape of zooplankton biomass in the north-east Atlantic Ocean to examine active habitat selection in the plankton-feeding basking shark Cetorhinus maximus. The relative success of shark searches across this landscape was examined by comparing prey biomass encountered by sharks with encounters by random-walk simulations of ‘model’ sharks. Movements of transmitter-tagged sharks monitored for 964 days (16754km estimated minimum distance) were concentrated on the European continental shelf in areas characterized by high seasonal productivity and complex prey distributions. We show movements by adult and sub-adult sharks yielded consistently higher prey encounter rates than 90% of random-walk simulations. Behavioural patterns were consistent with basking sharks using search tactics structured across multiple scales to exploit the richest prey areas available in preferred habitats. Simple behavioural rules based on learned responses to previously encountered prey distributions may explain the high performances. This study highlights how dynamic prey landscapes enable active habitat selection in large predators to be investigated from a trophic perspective, an approach that may inform conservation by identifying critical habitat of vulnerable species.

Using continuous plankton recorder data

The continuous plankton recorder (CPR) survey is the largest multi-decadal plankton monitoring programme in the world. It was initiated in 1931 and by the end of 2004 had counted 207,619 samples and identified 437 phyto- and zoo-plankton taxa throughout the North Atlantic. CPR data are used extensively by the research community and in recent years have been used increasingly to underpin marine management. Here, we take a critical look at how best to use CPR data. We first describe the CPR itself, CPR sampling, and plankton counting procedures. We discuss the spatial and temporal biases in the Survey, summarise environmental data that have not previously been available, and describe the new data access policy. We supply information essential to using CPR data, including descriptions of each CPR taxonomic entity., the idiosyncrasies associated with counting many of the taxa, the logic behind taxonomic changes in the Survey, the semi-quantitative nature of CPR sampling, and recommendations on choosing the spatial and temporal scale of study. This forms the basis for a broader discussion on how to use CPR data for deriving ecologically meaningful indices based on size, functional groups and biomass that can be used to support research and management. This contribution should be useful for plankton ecologists, modellers and policy makers that actively use CPR data. (c) 2005 Elsevier Ltd. All rights reserved.