Myers' type theorems and some related oscillation results

In this paper we study the behavior of solutions of a second order differential equation. The existence of a zero and its localization allow us to get some compactness results. In particular we obtain a Myers' type theorem even in the presence of an amount of negative curvature. The technique we use also applies to the study of spectral properties of Schroedinger operators on complete manifolds.Comment: 16 page

A within farm clinical trial to compare two treatments (parenteral antibacterials and hoof trimming) for sheep lame with footrot

From observational studies, farmers who use parenteral antibacterials to promptly treat all sheep with footrot (FR) or interdigital dermatitis (ID) have a prevalence of lameness of <2% compared with a prevalence of 9% lameness reported by farmers who treat lame sheep by trimming affected feet. We tested the hypothesis that prompt treatment of sheep lame with naturally developing FR or ID with parenteral and topical antibacterials reduces the prevalence and incidence of lameness with these conditions compared with less frequent treatment with trimming of hoof horn and applying topical antibacterials. A further hypothesis was that reduction of ID and FR would improve productivity. A lowland sheep flock with 700 ewes was used to test these hypotheses in an 18-month within farm clinical trial with four groups of ewes: two intervention and two control. The duration and severity of lameness was used to categorise sheep into three weighted scores of lameness (WLS): never lame (WLS0), mildly lame/lame for <6 days (WLS1) and severely or chronically lame (WLS2). The intervention reduced the prevalence of lameness due to FR and ID in ewes and lambs and the incidence of lameness in ewes. The WLS was also significantly lower in sheep in the intervention groups. Ewes with a higher WLS were subsequently significantly more likely to have a body condition score <2.5 and to have lame lambs. Significantly more ewes lambed and successfully reared more lambs that were ready for slaughter at a younger age in the intervention versus control groups. There was an increase in the gross margin of £630/100 ewes mated in the intervention group, including the cost of treatment of £150/100 ewes mated. We conclude that prompt parenteral and topical antibacterial treatment of sheep lame with ID and FR reduced the prevalence and incidence of these infectious conditions and led to improved health, welfare and productivity

Factors associated with changes of state of foot conformation and lameness in a flock of sheep

The aim of this research was to investigate transitions between foot conformation, lameness and footrot in sheep. Data came from one lowland flock of approximately 700 ewes studied for 18 months. Multilevel multistate analyses of transitions between good and poor foot conformation states in ewes, and lame and non-lame states in ewes and lambs were conducted. Key results were that the longer sheep had feet in good conformation, the more likely they were to stay in this state; similarly, the longer a ewe was not lame the more likely she was not to become lame. Ewes with poor foot conformation were more likely to become lame (OR: 1.83 (1.24-2.67)) and to be > 4 years (OR: 1.50(1.09-2.05)). Ewes with footrot were less likely to move to good foot conformation (OR: 0.48 (0.31-0.75)) and were more likely to become lame (OR: 3.81(2.60-5.59)). Ewes lame for > 4 days and not treated with parenteral antibacterials had a higher risk of developing (OR: 2.00 (1.08-3.61)), or remaining in (OR: 0.49 (0.29-0.95)) poor foot conformation compared with ewes never lame. Treatment of ewes lame with footrot with parenteral antibacterials increased the probability of transition from a lame to a non-lame state (OR: 1.46 (1.05-2.02)) and these ewes, even if lame for > 4 days, were not more likely to develop poor foot conformation. The risk of a ewe becoming lame increased when at least one of her offspring was lame (OR: 2.03 (1.42-2.92)) and when the prevalence of lameness in the group was ≥ 5% (OR: 1.42 (1.06-1.92)). Lambs were at increased risk of becoming lame when they were male (OR: 1.42 (1.01-2.01)), single (OR: 1.86 (1.34-2.59)) or had a lame dam or sibling (OR: 3.10 (1.81-5.32)). There were no explanatory variables associated with lambs recovering from lameness. We conclude that poor foot conformation in ewes increases the susceptibility of ewes to become lame and that this can arise from untreated footrot. Treatment of ewes lame with footrot with parenteral antibacterials leads to recovery from lameness and prevents or resolves poor foot conformation which then reduces the susceptibility to further lameness with footrot

Existence of the Abrikosov vortex state in two-dimensional type-II superconductors without pinning

Theory alternative to the vortex lattice melting theories is advertised. The vortex lattice melting theories are science fiction cond-mat/9811051 because the Abrikosov state is not the vortex lattice with crystalline long-range order. Since the fluctuation correction to the Abrikosov solution is infinite in the thermodynamic limit (K.Maki and H.Takayama, 1972) any fluctuation theory of the mixed state should consider a superconductor with finite sizes. Such nonperturbative theory for the easiest case of two-dimensional superconductor in the lowest Landau level approximation is presented in this work. The thermodynamic averages of the spatial average order parameter and of the Abrikosov parameter $\beta_{a}$ are calculated. It is shown that the position H_{c4} of the transition into the Abrikosov state (i.e. in the mixed state with long-range phase coherence) depends strongly on sizes of two-dimensional superconductor. Fluctuations eliminate the Abrikosov vortex state in a wide region of the mixed state of thin films with real sizes and without pinning disorders, i.e. H_{c4} << H_{c2}. The latter has experimental corroboration in Phys.Rev.Lett. 75, 2586 (1995).Comment: 4 pages, 0 figure

Socioeconomic status, mental wellbeing and transition to secondary school: analysis of the School Health Research Network/Health Behaviour in School-aged Children survey in Wales

Young people’s wellbeing is often lowest where they assume a relatively low position within their school’s socioeconomic hierarchy, for example, among poorer children attending more affluent schools. Transition to secondary school is a period during which young people typically enter an environment which is more socio-economically diverse than their primary school. Young people joining a school with a higher socioeconomic status intake relative to their primary school may assume a relatively lowered position within their schools’ socioeconomic hierarchy, experiencing a detriment to their wellbeing as a consequence. This paper draws on data from 45,055 pupils in Years 7 and 8, from 193 secondary schools in Wales, who completed the 2017 Student Health Research Network (SHRN) Student Health and Wellbeing (SHW) Survey. Pupils reported which primary school they previously attended, and survey data on wellbeing were linked to publicly available data on the Free School Meal entitlement of schools attended. In cross-classified linear mixed-effects models, with primary and secondary school as levels, mental wellbeing varied significantly according to both primary and secondary school attended. A higher school-level deprivation was associated with worse mental wellbeing in both cases. Mental wellbeing was significantly predicted by the relative affluence of a child’s primary and secondary school, with movement to a secondary school of higher overall socioeconomic status associated with lowered wellbeing. These findings highlight transition to secondary school as a key point in which socioeconomic inequality in wellbeing ma

Synchronous pumping of an optical parametric oscillator using an amplified quasi-cw pump envelope

Pulse-slicing from a cw laser output followed by high gain amplification can produce quasi-cw pulses at power levels well in excess of those available from large frame cw lasers. Mode-locked pulse trains with an envelope of 10µs duration and at 2kHz repetition rate are amplified by a factor of 20 to give 5 Watts of envelope average power. These power levels allow efficient single-pass frequency doubling and subsequent pumping of a lithium triborate optical parametric oscillator

Prevalence of gambling behaviours and their associations with socioemotional harm among 11 to 16 year olds in Wales: findings from the School Health Research Network survey

Background: Gambling opportunities are increasingly available and acceptable to many adolescents. Adolescent problem gambling has been associated with poor outcomes, such as lower reported physical and mental health. While much research has focussed on ‘problem’ gambling, analysing the distribution and determinants of experimentation with gambling is important in order to understand its normalization and population level consequences. This study describes the distribution of inequalities and socioemotional harms associated with adolescent gambling. Methods: Data were drawn from a subsample of students (N = 37 363) who completed gambling questions as part of the 2017 School Health Research Network Student Health and Wellbeing Survey, representing 193 secondary schools in Wales. Using imputations, we estimated a series of single-predictor and multi-predictor regressions for count of gambling behaviours, any gambling in the past 12 months and socioemotional harms of gambling. Results: Approximately two-fifths (41.0%) of respondents reported gambling in the past 12 months, of whom 16.2% reported feeling bad as a result of their own gambling. We found significant sex differences in gambling, with boys gambling more frequently than girls. Adolescents from more affluent families reported a higher count of gambling behaviours and socioemotional harms, although paradoxically, increasing affluence was also associated with lower prevalence of gambling in the last year. Non-White British ethnicities and students who felt less connected to school were more likely to engage in gambling and experience socioemotional harms. Conclusions: Our findings provide important new insights regarding risk factors in adolescence associated with gambling behaviours and socioemotional harms

The role of emotional resilience, childhood parentification, and attachment style on antisocial behaviour in adulthood: a comparison of an offender and normative population

Purpose: Despite a robust link between poor caregiver attachment and antisociality, few studies have examined the influence of parentification and emotional resilience on delinquency in later life, in groups at differing risk for antisocial conduct. Methodology: This pilot study compared the influence of parentification, attachment style (avoidant or anxious) and emotional resilience on adulthood antisocial behaviour in an offender and normative sample. Of the 137 participants in this study, 66 were supervised by the National Probation Service (age M = 36.90, SD = 13.91), and 71 were recruited from community-dwelling and student populations (age M = 31.83, SD = 13.25). Findings: In partial support of the predictions, participants in the offender group reported significantly greater levels of attachment anxiety compared to the normative group. However, emotional resilience was positively associated with antisociality in the normative sample. Research implications: This small-scale investigation indicates value in exploring these specific variables in a larger, matched samples study, to enable clearer comparisons to be made between offender and normative groups. Practical implications: The preliminary findings suggest that attachment anxiety is associated with antisociality in offender populations, which indicate a therapeutic focus on attachment anxiety as part of correctional care and offender rehabilitation. Originality: This study is novel in its aim to examine the influence of childhood parentification, attachment deficits and emotional resilience on adulthood antisociality in participants from a high-risk offender sample and non-high-risk normative sample

Higgs Bundles, Gauge Theories and Quantum Groups

The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional topological U(N) gauge theory reproduce quantum wave functions of the Nonlinear Schr\"{o}dinger equation in the $N$-particle sector. This implies the full equivalence between the above gauge theory and the $N$-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger equation. This also implies the explicit correspondence between the gauge theory and the representation theory of degenerate double affine Hecke algebra. We propose similar construction based on the $G/G$ gauged WZW model leading to the representation theory of the double affine Hecke algebra. The relation with the Nahm transform and the geometric Langlands correspondence is briefly discussed.Comment: 48 pages, typos corrected, one reference adde