Solvability of subprincipal type operators

In this paper we consider the solvability of pseudodifferential operators in the case when the principal symbol vanishes of order $k \ge 2$ at a nonradial involutive manifold $\Sigma_2$. We shall assume that the operator is of subprincipal type, which means that the $k$:th inhomogeneous blowup at $\Sigma_2$ of the refined principal symbol is of principal type with Hamilton vector field parallel to the base $\Sigma_2$, but transversal to the symplectic leaves of $\Sigma_2$ at the characteristics. When $k = \infty$ this blowup reduces to the subprincipal symbol. We also assume that the blowup is essentially constant on the leaves of $\Sigma_2$, and does not satisfying the Nirenberg-Treves condition (${\Psi}$). We also have conditions on the vanishing of the normal gradient and the Hessian of the blowup at the characteristics. Under these conditions, we show that $P$ is not solvable.Comment: Changed the formulation of Theorem 2.15, added an assuption. Corrected errors and clarified the arguments. Added reference

Risks associated with obesity in pregnancy, for the mother and baby: a systematic review of reviews

Maternal obesity is linked with adverse outcomes for mothers and babies. To get an overview of risks related to obesity in pregnant women, a systematic review of reviews was conducted. For inclusion, reviews had to compare pregnant women of healthy weight with women with obesity, and measure a health outcome for mother and/or baby. Authors conducted full-text screening, quality assurance using the AMSTAR tool and data extraction steps in pairs. Narrative analysis of the 22 reviews included show gestational diabetes, pre-eclampsia, gestational hypertension, depression, instrumental and caesarean birth, and surgical site infection to be more likely to occur in pregnant women with obesity compared with women with a healthy weight. Maternal obesity is also linked to greater risk of preterm birth, large-for-gestational-age babies, foetal defects, congenital anomalies and perinatal death. Furthermore, breastfeeding initiation rates are lower and there is greater risk of early breastfeeding cessation in women with obesity compared with healthy weight women. These adverse outcomes may result in longer duration of hospital stay, with concomitant resource implications. It is crucial to reduce the burden of adverse maternal and foetal/child outcomes caused by maternal obesity. Women with obesity need support to lose weight before they conceive, and to minimize their weight gain in pregnancy

The Egorov theorem for transverse Dirac type operators on foliated manifolds

Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a first order transversally elliptic operator with the (classical) evolution of its symbols determined by the parallel transport along the orbits of the associated transverse bicharacteristic flow. For a particular case of a transverse Dirac operator, the transverse bicharacteristic flow is shown to be given by the transverse geodesic flow and the parallel transport by the parallel transport determined by the transverse Levi-Civita connection. These results allow us to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.Comment: 27 pages, to appear in Journal of Geometry and Physic

Probabilistic Weyl laws for quantized tori

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.Comment: 33 pages, 3 figures, v2 corrected listed titl

Cardiorespiratory fitness is associated with hard and light intensity physical activity but not time spent sedentary in 10–14 year old schoolchildren: the HAPPY study

Sedentary behaviour is a major risk factor for developing chronic diseases and is associated with low cardiorespiratory fitness in adults. It remains unclear how sedentary behaviour and different physical activity subcomponents are related to cardiorespiratory fitness in children. The purpose of this study was to assess how sedentary behaviour and different physical activity subcomponents are associated with 10–14 year-old schoolchildren's cardiorespiratory fitness

Associations of sedentary behaviour, physical activity, blood pressure and anthropometric measures with cardiorespiratory fitness in children with cerebral palsy

Background - Children with cerebral palsy (CP) have poor cardiorespiratory fitness in comparison to their peers with typical development, which may be due to low levels of physical activity. Poor cardiorespiratory fitness may contribute to increased cardiometabolic risk. Purpose - The aim of this study was to determine the association between sedentary behaviour, physical activity and cardiorespiratory fitness in children with CP. An objective was to determine the association between cardiorespiratory fitness, anthropometric measures and blood pressure in children with CP. Methods- This study included 55 ambulatory children with CP [mean (SD) age 11.3 (0.2) yr, range 6-17 yr; Gross Motor Function Classification System (GMFCS) levels I and II]. Anthropometric measures (BMI, waist circumference and waist-height ratio) and blood pressure were taken. Cardiorespiratory fitness was measured using a 10 m shuttle run test. Children were classified as low, middle and high fitness according to level achieved on the test using reference curves. Physical activity was measured by accelerometry over 7 days. In addition to total activity, time in sedentary behaviour and light, moderate, vigorous, and sustained moderate-to-vigorous activity (≥10 min bouts) were calculated. Results - Multiple regression analyses revealed that vigorous activity (β = 0.339, p<0.01), sustained moderate-to-vigorous activity (β = 0.250, p<0.05) and total activity (β = 0.238, p<0.05) were associated with level achieved on the shuttle run test after adjustment for age, sex and GMFCS level. Children with high fitness spent more time in vigorous activity than children with middle fitness (p<0.05). Shuttle run test level was negatively associated with BMI (r2 = -0.451, p<0.01), waist circumference (r2 = -0.560, p<0.001), waist-height ratio (r2 = -0.560, p<0.001) and systolic blood pressure (r2 = -0.306, p<0.05) after adjustment for age, sex and GMFCS level. Conclusions - Participation in physical activity, particularly at a vigorous intensity, is associated with high cardiorespiratory fitness in children with CP. Low cardiorespiratory fitness is associated with increased cardiometabolic risk

Childbirth experience questionnaire: validating its use in the United Kingdom

BACKGROUND: The Childbirth Experience Questionnaire (CEQ) was developed in Sweden in 2010 and validated in 920 primiparous women. It has not been validated in the United Kingdom (UK). Measuring the impact of an intervention on a woman's childbirth experience is arguably as important as measuring its impact on outcomes such as caesarean delivery and perinatal morbidity or mortality and yet surprisingly it is rarely done. The lack of a robust validated tool for evaluating labour experience in the UK is a topical issue in the UK at present. Indeed NICE say 'A standardised method to measure and quantify women's psychological and emotional wellbeing and their birth experiences is urgently required to support any study investigating the effectiveness of interventions, techniques or strategies during birth.' METHODS: The Childbirth Experience Questionnaire and part of the Care Quality Commission Maternity Survey (2010) was sent to 350 women at one month postnatal. The CEQ was sent again two weeks later. The CEQ was tested for face validity among 25 postnatal mothers. Demographic data and delivery data was used to establish construct validity of the CEQ using the method of known-groups validation. The results of the scored CEQ sent out twice were used to measure test-retest reliability of the CEQ by calculating the quadratic weighted index of agreement between the two scores. Criterion validity was measured by calculating the Pearson correlation coefficient for the CEQ and Maternity Survey scores. RESULTS: Face validity of the CEQ in a UK population was demonstrated with all respondents stating it was easy to understand and complete. A statistically significantly higher CEQ score for subgroups of women known to report a better birth outcome demonstrated construct validity of the CEQ. A weighted kappa of 0.68 demonstrated test-retest reliability of the CEQ. A Pearson correlation co-efficient of 0.73 demonstrated a strong correlation between the results of the CEQ and the results of the 'gold standard' assessment of childbirth experience in the UK: the Maternity Survey and hence criterion validity of the CEQ. CONCLUSIONS: The Childbirth Experience Questionnaire is a valid and reliable measure of childbirth experience in the UK population

A new electrochemical method for the determination of chondroitin sulfate based on its supramolecular interaction with cupferron-lead(II) complex

In this paper, the interaction of cupferron (Cup) and lead (II) complex [Cup-Pb (II)] with chondroitin sulfate (CS) was investigated by linear sweep voltammetric method. In the selected medium of pH 5.5 (acetic acid-hexamine buffer solution), Cup can interact with Pb (II) to form a stable complex of [Cup-Pb(II)], which has a sensitive second order derivative polarographic reductive peak at -0.64V (vs.SCE). After the addition of CS into Cup-Pb (II) complex solution, the reductive peak current decreased without any shift of the peak potential and no new peak appeared, which indicated that an unelectroactive supramolecular complex of CS with [Cup-Pb(II)] was formed. The binding reaction conditions were carefully investigated. Under the optimal conditions, the interaction mechanism was discussed. The decrease of reductive peak current was directly proportional to the CS concentration, thus a new quantitative determination method for CS was established with the linear regression equation as ΔIp″(nA)=36.97 C/mg L-1+12.45 (n=10, γ=0.995). The effects of other substances on the determination were carefully investigated and three synthetic samples were determined with satisfactory results. The binding constant (βs) and the binding number (m) of CS with [Cup-Pb(II)] complex were calculated from the voltammetric data with the results as βs=1.89×1010 and m≈2.5

Gupta–Bleuler Quantization of the Maxwell Field in Globally Hyperbolic Space-Times

We give a complete framework for the Gupta–Bleuler quantization of the free electromagnetic field on globally hyperbolic space-times. We describe one-particle structures that give rise to states satisfying the microlocal spectrum condition. The field algebras in the so-called Gupta–Bleuler representations satisfy the time-slice axiom, and the corresponding vacuum states satisfy the microlocal spectrum condition. We also give an explicit construction of ground states on ultrastatic space-times. Unlike previous constructions, our method does not require a spectral gap or the absence of zero modes. The only requirement, the absence of zero-resonance states, is shown to be stable under compact perturbations of topology and metric. Usual deformation arguments based on the time-slice axiom then lead to a construction of Gupta–Bleuler representations on a large class of globally hyperbolic space-times. As usual, the field algebra is represented on an indefinite inner product space, in which the physical states form a positive semi-definite subspace. Gauge transformations are incorporated in such a way that the field can be coupled perturbatively to a Dirac field. Our approach does not require any topological restrictions on the underlying space-time

Predicting new venture survival and growth: does the fog lift?

This paper investigates whether new venture performance becomes easier to predict as the venture ages: does the fog lift? To address this question we primarily draw upon a theoretical framework, initially formulated in a managerial context by Levinthal (Adm Sci Q 36(3):397–420, 1991) that sees new venture sales as a random walk but survival being determined by the stock of available resources (proxied by size). We derive theoretical predictions that are tested with a 10-year cohort of 6579 UK new ventures in the UK. We observe that our ability to predict firm growth deteriorates in the years after entry—in terms of the selection environment, the ‘fog’ seems to thicken. However, our survival predictions improve with time—implying that the ‘fog’ does lift