Groups of Fibonacci type revisited

This article concerns a class of groups of Fibonacci type introduced by Johnson and Mawdesley that includes Conway?s Fibonacci groups, the Sieradski groups, and the Gilbert-Howie groups. This class of groups provides an interesting focus for developing the theory of cyclically presented groups and, following questions by Bardakov and Vesnin and by Cavicchioli, Hegenbarth, and Repov?s, they have enjoyed renewed interest in recent years. We survey results concerning their algebraic properties, such as isomorphisms within the class, the classification of the finite groups, small cancellation properties, abelianizations, asphericity, connections with Labelled Oriented Graph groups, and the semigroups of Fibonacci type. Further, we present a new method of proving the classification of the finite groups that deals with all but three groups

Acute classroom exercise breaks improve on-task behavior in 4th and 5th grade students: A dose-response

This study was the first to directly compare the acute effects of 5, 10, and 20 min of classroom exercise breaks on on-task behavior. Methods: In this within-subject experiment, 96 4th and 5th grade students, in 5 classroom groups, participated in each of four conditions: 10 min of sedentary classroom activity and 5, 10, 20 min of classroom exercise breaks led by research staff. On-task behavior was directly and systematically observed from videotapes before and after each condition. The post-test time-on-task scores were compared using a repeated measures mixed ANCOVA, adjusted for age, classroom, and the time-varying pre-test time-on-task. Results: Time-on-task was significantly higher in students after 10 min of classroom exercise breaks compared to a sedentary attention control (87.6% vs 77.1%, d = .45, p = .004). Conclusions: Ten minutes of classroom exercise breaks improved on-task behavior in children

Largeness and SQ-universality of cyclically presented groups

Largeness, SQ-universality, and the existence of free subgroups of rank 2 are measures of the complexity of a finitely presented group. We obtain conditions under which a cyclically presented group possesses one or more of these properties. We apply our results to a class of groups introduced by Prishchepov which contains, amongst others, the various generalizations of Fibonacci groups introduced by Campbell and Robertson

The structure of one-relator relative presentations and their centres

Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G\cup\{x_1^{\pm1},...,x_n^{\pm1}\} such that the word w' obtained from w by erasing all letters belonging to G is not a proper power in the free group F(x_1,...,x_n). We show how to reduce the study of the relative presentation \^G= to the case n=1. It turns out that an "n-variable" group \^G can be constructed from similar "one-variable" groups using an explicit construction similar to wreath product. As an illustration, we prove that, for n>1, the centre of \^G is always trivial. For n=1, the centre of \^G is also almost always trivial; there are several exceptions, and all of them are known.Comment: 15 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm . V4: the intoduction is rewritten; Section 1 is extended; a short introduction to Secton 5 is added; some misprints are corrected and some cosmetic improvements are mad

Physical activity behaviours of highly active preschoolers

Background: Understanding the physical activity behaviour of young children who are highly active mayprovide important guidance for promoting physical activity in preschools.Objectives: The objective of this study was to describe the movement characteristics of high-active (HA)children during attendance at preschools.Methods: Children in 20 preschools (n = 231) wore accelerometers and were classified into tertiles ofmoderate-to-vigorous physical activity. Children's movement characteristics were observed using the Observational System for Recording Physical Activity in Children – Preschool Version. Mixed-model analyses compared movement types between HA children and lower-active (LA) children during the total school day.Results: HA (n = 77) children were observed to be more active than LA children (n = 154) indoors(P < 0.001), but no differences were observed outdoors. HA children were more frequently observed running, crawling, climbing, jumping, skipping, swinging and throwing across the total school day than LA children. Outdoors, HA children participated in more swinging and throwing and less jumping or skipping than LA children. Indoors, HA children spent more time pulling, pushing and running, and less time walking than LA children.Conclusions: HA children have unique activity patterns. Further interventions to increase physical activity of all preschoolers should increase the time spent outside and include varied activity types throughout the entire school day

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts

The Kervaire-Laudenbach conjecture and presentations of simple groups

The statement ``no nonabelian simple group can be obtained from a nonsimple group by adding one generator and one relator" 1) is equivalent to the Kervaire--Laudenbach conjecture; 2) becomes true under the additional assumption that the initial nonsimple group is either finite or torsion-free. Key words: Kervaire--Laudenbach conjecture, relative presentations, simple groups, car motion, cocar comotion. AMS MSC: 20E32, 20F05, 20F06.Comment: 20 pages, 13 figure

High-pressure behavior of superconducting boron-doped diamond

This work investigates the high-pressure structure of freestanding superconducting ($T_{c}$ = 4.3\,K) boron doped diamond (BDD) and how it affects the electronic and vibrational properties using Raman spectroscopy and x-ray diffraction in the 0-30\,GPa range. High-pressure Raman scattering experiments revealed an abrupt change in the linear pressure coefficients and the grain boundary components undergo an irreversible phase change at 14\,GPa. We show that the blue shift in the pressure-dependent vibrational modes correlates with the negative pressure coefficient of $T_{c}$ in BDD. The analysis of x-ray diffraction data determines the equation of state of the BDD film, revealing a high bulk modulus of $B_{0}$=510$\pm$28\,GPa. The comparative analysis of high-pressure data clarified that the sp$^{2}$ carbons in the grain boundaries transform into hexagonal diamond.Comment: 7 pages, 4 figure

Intra-individual movement variability during skill transitions: A useful marker?

Applied research suggests athletes and coaches need to be challenged in knowing when and how much a movement should be consciously attended to. This is exacerbated when the skill is in transition between two more stable states, such as when an already well learnt skill is being refined. Using existing theory and research, this paper highlights the potential application of movement variability as a tool to inform a coach’s decision-making process when implementing a systematic approach to technical refinement. Of particular interest is the structure of co-variability between mechanical degrees-of-freedom (e.g., joints) within the movement system’s entirety when undergoing a skill transition. Exemplar data from golf are presented, demonstrating the link between movement variability and mental effort as an important feature of automaticity, and thus intervention design throughout the different stages of refinement. Movement variability was shown to reduce when mental effort directed towards an individual aspect of the skill was high (target variable). The opposite pattern was apparent for variables unrelated to the technical refinement. Therefore, two related indicators, movement variability and mental effort, are offered as a basis through which the evaluation of automaticity during technical refinements may be made

Triclinic form of bis­{di-μ-hydroxidobis[fac-aqua­tribromido­tin(IV)]} hepta­hydrate

The asymmetric unit of the title hydrate, 2[Sn(H2O)2(OH)2Br6]·7H2O, comprises two [Br3(H2O)Sn(μ-OH)2SnBr3(OH2)] units, but three independent mol­ecules as two of these are disposed about inversion centres, and seven water mol­ecules. In common with the monoclinic polymorph [Howie et al. (2005 ▶). Inorg. Chim. Acta, 358, 3283–3286], each of the dinuclear species features a central Sn2O2 core, distorted octa­hedral Sn atom geometries defined by a Br3O3 donor set, and an anti-disposition of the coordinated water mol­ecules. In the crystal, Oh—H⋯Ow, Oa—H⋯Ow, Ow—H⋯Ow, and Ow—H⋯Br (h = hydroxyl, a = aqua, w = water) hydrogen-bonding inter­actions generate a three-dimensional network