Finite nilpotent semigroups of small coclass

The parameter coclass has been used successfully in the study of nilpotent algebraic objects of different kinds. In this paper a definition of coclass for nilpotent semigroups is introduced and semigroups of coclass 0, 1, and 2 are classified. Presentations for all such semigroups and formulae for their numbers are obtained. The classification is provided up to isomorphism as well as up to isomorphism or anti-isomorphism. Commutative and self-dual semigroups are identified within the classification.Comment: 11 page

Success and limiting factors in health service innovation: a theory generating mixed-methods evaluation of UK projects

Objectives: To explore and explain success and limiting factors in UK health service innovation. Design: Mixed methods evaluation of a series of health service innovations involving a survey and interviews, with theory-generating analysis. Setting: The research explored innovations supported by one of the UK’s Academic Health Science Networks which provides small grants, awards and structural support to health service innovators including clinical academics, health and social care professionals and third-sector organisations. Participants: All recipients of funding or support 2014–2018 were invited to participate. We analysed survey responses relating to 56 innovation projects. Results: Responses were used to conceptualise success along two axes: value creation for the intended beneficiaries and expansion beyond its original pilot. An analysis of variance between categories of success indicated that participation, motivation and evaluation were critical to value generation; organisational, educational and administrative support were critical to expansion; and leadership and collaborative expertise were critical to both value creation and expansion. Additional limiting factors derived from qualitative responses included difficulties navigating the boundaries and intersections between organisations, professions, sectors and cultures; a lack of support for innovation beyond the start-up phase; a lack of protected time; and staff burn-out and turnover. Conclusions: A nested hierarchy of innovation needs has been derived via an analysis of these factors, providing targeted suggestions to enhance the success of future innovations. Data availability statement Data are available upon reasonable request. Due to the highly individual nature of healthcare innovations and the limited geographic area of this study, we are unable to provide our raw data. We undertake to provide a redacted data set upon reasonable request

Intra- and interprofessional practices through fresh eyes: a qualitative analysis of medical students’ early workplace experiences

Background Professional identities are influenced by experiences in the clinical workplace including socialisation processes that may be hidden from academic faculty and potentially divergent from formal curricula. With the current educational emphasis on complexity, preparedness for practice, patient safety and team-working it is necessary to evaluate and respond to what students are learning about collaborative practices during their clinical placements. Methods 394 second year medical students at a London medical school were invited to submit a short formative essay as part of their coursework describing, evaluating and reflecting on their experiences of how healthcare professionals work together. Their experiences were derived from having spent two days each week for 25 weeks in clinical contexts across primary and secondary care. We consented 311 participants and used a Consensual Qualitative Research approach to analyse these essays, creating a ‘students-eye view’ of intra- and interprofessional practices in the workplace. Results We identified four overarching themes in students’ essays: Theme 1: analyses of contextual factors driving team tensions including staff shortages, shifting teams, and infrastructural issues; Theme 2: observations of hierarchical and paternalistic attitudes and behaviours; Theme 3: respect for team members’ ability to manage and mitigate tensions and attitudes; and Theme 4: take-forward learning including enthusiasm for quality improvement and system change. Conclusions Students are being socialised into a complex, hierarchical, pressurised clinical workplace and experience wide variations in professional behaviours and practices. They articulate a need to find constructive ways forward in the interests of staff wellbeing and patient care. We present educational recommendations including providing safe reflective spaces, using students’ lived experience as raw material for systems thinking and quality improvement, and closing the feedback loop with placement sites on behalf of students

Increasing concentrations of dichloromethane, CH2Cl2, inferred from CARIBIC air samples collected 1998–2012

Atmospheric concentrations of dichloromethane, CH2Cl2, a regulated toxic air pollutant and minor contributor to stratospheric ozone depletion, were reported to have peaked around 1990 and to be declining in the early part of the 21st century. Recent observations suggest this trend has reversed and that CH2Cl2 is once again increasing in the atmosphere. Despite the importance of ongoing monitoring and reporting of atmospheric CH2Cl2, no time series has been discussed in detail since 2006. The CARIBIC project (Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container) has analysed the halocarbon content of whole-air samples collected at altitudes of between ~10–12 km via a custom-built container installed on commercial passenger aircraft since 1998, providing a long-term record of CH2Cl2 observations. In this paper we present this unique CH2Cl2 time series, discussing key flight routes which have been used at various times over the past 15 years. Between 1998 and 2012 increases were seen in all northern hemispheric regions and at different altitudes, ranging from ~7–10 ppt in background air to ~13–15 ppt in regions with stronger emissions (equating to a 38–69% increase). Of particular interest is the rising importance of India as a source of atmospheric CH2Cl2: based on CARIBIC data we provide regional emission estimates for the Indian subcontinent and show that regional emissions have increased from 3–14 Gg yr^-1 (1998–2000) to 16–25 Gg yr^-1 (2008). Potential causes of the increasing atmospheric burden of CH2Cl2 are discussed. One possible source is the increased use of CH2Cl2 as a feedstock for the production of HFC-32, a chemical used predominantly as a replacement for ozone-depleting substances in a variety of applications including air conditioners and refrigeration

Gradings of non-graded Hamiltonian Lie algebras

A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras H(2\colon\n;\omega_2) (of dimension one less than a power of $p$) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of H(2\colon\n;\omega_2) with a Block algebra. We also compute its second cohomology group and its derivation algebra (in arbitrary prime characteristic).Comment: 36 pages, to be published in J. Austral. Math. Soc. Ser.

‘I was exhausted trying to figure it out’: the experiences of females receiving an autism diagnosis in middle to late adulthood

Females often receive autism spectrum condition diagnoses later than males, leaving needs misunderstood. This study aimed to explore the lived experiences of female adults diagnosed with an autism spectrum condition in middle to late adulthood. Eleven autistic females diagnosed over the age of 40 years completed semi-structured interviews, analysed using Interpretative Phenomenological Analysis. Four superordinate themes emerged: A hidden condition (pretending to be normal and fitting in; mental health and mislabelling), The process of acceptance (initial reactions and search for understanding; re-living life through a new lens), The impact of others post-diagnosis (initial reactions; stereotyped assumptions), and A new identity on the autism spectrum (negotiating relationships, connections and community; changing well-being and views of the self; the meaning of diagnosis). Findings highlight several factors not previously identified that affect late diagnosis in females, including widespread limited understandings of others. Diagnosis was experienced by several participants as facilitating transition from being self-critical to self-compassionate, coupled with an increased sense of agency. Participants experienced a change in identity that enabled greater acceptance and understanding of the self. However, this was painful to adjust to at such a late stage

Intense connection and love: The experiences of autistic mothers

Knowledge of how parenthood is experienced by autistic women is currently poor. Nine autistic mothers to children aged 5–15 years completed semi-structured interviews, analysed using Interpretative Phenomenological Analysis. All mothers considered at least one of their children to also be autistic. Four superordinate themes emerged: 1. Autism fundamentally impacts parenting; 2. Battle for the right support; 3. Development and acceptance; and 4. The ups and downs of parenting. The themes demonstrate that while motherhood is largely a joyful experience for autistic mothers (Themes 1 and 4), it is associated with specific issues unlikely to be found in neurotypical motherhood (Theme 1), including negotiating misunderstandings from others (Theme 2). The need for self-care and self-acceptance was expressed (Theme 3) with parenting resulting in personal growth and adaptation (Theme 3). Feelings of intense connection and closeness were experienced (Theme 4), though managing children’s needs had a profound personal impact (Themes 2 and 4). The findings demonstrate that service-providers would benefit from training, ideally led by autistic individuals, on how autism presents in adulthood, masking, the potential for mismatching between emotional experience and facial expression, sensory needs (especially in pregnancy), and the double empathy problem (Theme 2). This study represents the first systematic in-depth analysis of the experiences of autistic mothers presented from their own perspectives

Constructing composition factors for a linear group in polynomial time

We present a Las Vegas polynomial-time algorithm that takes as input a subgroup of and, subject to the existence of certain oracles, determines its composition factors, provided that none of those factors is isomorphic to one of , , , or , for any k