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

Infinite partition monoids

Let $\mathcal P_X$ and $\mathcal S_X$ be the partition monoid and symmetric group on an infinite set $X$. We show that $\mathcal P_X$ may be generated by $\mathcal S_X$ together with two (but no fewer) additional partitions, and we classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal S_X\cup\{\alpha,\beta\}$. We also show that $\mathcal P_X$ may be generated by the set $\mathcal E_X$ of all idempotent partitions together with two (but no fewer) additional partitions. In fact, $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$ if and only if it is generated by $\mathcal E_X\cup\mathcal S_X\cup\{\alpha,\beta\}$. We also classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$. Among other results, we show that any countable subset of $\mathcal P_X$ is contained in a $4$-generated subsemigroup of $\mathcal P_X$, and that the length function on $\mathcal P_X$ is bounded with respect to any generating set

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

Patient enablement requires physician empathy: a cross-sectional study of general practice consultations in areas of high and low socioeconomic deprivation in Scotland

<b>Background</b> Patient 'enablement' is a term closely aligned with 'empowerment' and its measurement in a general practice consultation has been operationalised in the widely used patient enablement instrument (PEI), a patient-rated measure of consultation outcome. However, there is limited knowledge regarding the factors that influence enablement, particularly the effect of socio-economic deprivation. The aim of the study is to assess the factors influencing patient enablement in GP consultations in areas of high and low deprivation.<p></p> <b>Methods</b> A questionnaire study was carried out on 3,044 patients attending 26 GPs (16 in areas of high socio-economic deprivation and 10 in low deprivation areas, in the west of Scotland). Patient expectation (confidence that the doctor would be able to help) was recorded prior to the consultation. PEI, GP empathy (measured by the CARE Measure), and a range of other measures and variables were recorded after the consultation. Data analysis employed multi-level modelling and multivariate analyses with the PEI as the dependant variable.<p></p> <b>Results</b> Although numerous variables showed a univariate association with patient enablement, only four factors were independently predictive after multilevel multivariate analysis; patients with multimorbidity of 3 or more long-term conditions (reflecting poor chronic general health), and those consulting about a long-standing problem had reduced enablement scores in both affluent and deprived areas. In deprived areas, emotional distress (GHQ-caseness) had an additional negative effect on enablement. Perceived GP empathy had a positive effect on enablement in both affluent and deprived areas. Maximal patient enablement was never found with low empathy.<p></p> <b>Conclusions</b> Although other factors influence patient enablement, the patients' perceptions of the doctors' empathy is of key importance in patient enablement in general practice consultations in both high and low deprivation settings

Multi-color Optical and NIR Light Curves of 64 Stripped-Envelope Core-Collapse Supernovae

We present a densely-sampled, homogeneous set of light curves of 64 low redshift (z < 0.05) stripped-envelope supernovae (SN of type IIb, Ib, Ic and Ic-bl). These data were obtained between 2001 and 2009 at the Fred L. Whipple Observatory (FLWO) on Mt. Hopkins in Arizona, with the optical FLWO 1.2-m and the near-infrared PAIRITEL 1.3-m telescopes. Our dataset consists of 4543 optical photometric measurements on 61 SN, including a combination of UBVRI, UBVr'i', and u'BVr'i', and 2142 JHKs near-infrared measurements on 25 SN. This sample constitutes the most extensive multi-color data set of stripped-envelope SN to date. Our photometry is based on template-subtracted images to eliminate any potential host galaxy light contamination. This work presents these photometric data, compares them with data in the literature, and estimates basic statistical quantities: date of maximum, color, and photometric properties. We identify promising color trends that may permit the identification of stripped-envelope SN subtypes from their photometry alone. Many of these SN were observed spectroscopically by the CfA SN group, and the spectra are presented in a companion paper (Modjaz et al. 2014). A thorough exploration that combines the CfA photometry and spectroscopy of stripped-envelope core-collapse SN will be presented in a follow-up paper.Comment: 26 pages, 17 figures, 8 tables. Revised version resubmitted to ApJ Supplements after referee report. Additional online material is available through http://cosmo.nyu.edu/SNYU

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

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

Septic arthritis in an in vivo murine model induced by Staphylococcus aureus:a comparison between actions of the haemolysin toxin and the effects of the host immune response

AIMS: Staphylococcus aureus is a major cause of septic arthritis, and in vitro studies suggest α haemolysin (Hla) is responsible for chondrocyte death. We used an in vivo murine joint model to compare inoculation with wild type S. aureus 8325-4 with a Hla-deficient strain DU1090 on chondrocyte viability, tissue histology, and joint biomechanics. The aim was to compare the actions of S. aureus Hla alone with those of the animal’s immune response to infection. METHODS: Adult male C57Bl/6 mice (n = 75) were randomized into three groups to receive 1.0 to 1.4 × 10(7) colony-forming units (CFUs)/ml of 8325-4, DU1090, or saline into the right stifle joint. Chondrocyte death was assessed by confocal microscopy. Histological changes to inoculated joints were graded for inflammatory responses along with gait, weight changes, and limb swelling. RESULTS: Chondrocyte death was greater with 8325-4 (96.2% (SD 5.5%); p < 0.001) than DU1090 (28.9% (SD 16.0%); p = 0.009) and both were higher than controls (3.8% (SD 1.2%)). Histology revealed cartilage/bone damage with 8325-4 or DU1090 compared to controls (p = 0.010). Both infected groups lost weight (p = 0.006 for both) and experienced limb swelling (p = 0.043 and p = 0.018, respectively). Joints inoculated with bacteria showed significant alterations in gait cycle with a decreased stance phase, increased swing phase, and a corresponding decrease in swing speed. CONCLUSION: Murine joints inoculated with Hla-producing 8325-4 experienced significantly more chondrocyte death than those with DU1090, which lack the toxin. This was despite similar immune responses, indicating that Hla was the major cause of chondrocyte death. Hla-deficient DU1090 also elevated chondrocyte death compared to controls, suggesting a smaller additional deleterious role of the immune system on cartilage. Cite this article: Bone Joint Res 2022;11(9):669–678

Economical adjunction of square roots to groups

How large must an overgroup of a given group be in order to contain a square root of any element of the initial group? We give an almost exact answer to this question (the obtained estimate is at most twice worse than the best possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: minor correction