Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0,2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.Comment: 9 page

Dynamics of ligand substitution in labile cobalt complexes resolved by ultrafast T-jump

Ligand exchange of hydrated metal complexes is common in chemical and biological systems. Using the ultrafast T-jump, we examined this process, specifically the transformation of aqua cobalt (II) complexes to their fully halogenated species. The results reveal a stepwise mechanism with time scales varying from hundreds of picoseconds to nanoseconds. The dynamics are significantly faster when the structure is retained but becomes rate-limited when the octahedral-to-tetrahedral structural change bottlenecks the transformation. Evidence is presented, from bimolecular kinetics and energetics (enthalpic and entropic), for a reaction in which the ligand assists the displacement of water molecules, with the retention of the entering ligand in the activated state. The reaction time scale deviates by one to two orders of magnitude from that of ionic diffusion, suggesting the involvement of a collisional barrier between the ion and the much larger complex

A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments

Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating predation risk, and cooperative breeding and foraging. Individuals within these populations may differ in age, size, or geographic location and thereby structure these populations. Here, I study structured population models accounting for positive density-dependence and environmental stochasticity i.e. random fluctuations in the demographic rates of the population. Under an accessibility assumption (roughly, stochastic fluctuations can lead to populations getting small and large), these models are shown to exhibit a dynamical trichotomy: (i) for all initial conditions, the population goes asymptotically extinct with probability one, (ii) for all positive initial conditions, the population persists and asymptotically exhibits unbounded growth, and (iii) for all positive initial conditions, there is a positive probability of asymptotic extinction and a complementary positive probability of unbounded growth. The main results are illustrated with applications to spatially structured populations with an Allee effect and age-structured populations experiencing mate limitation

Domain structure-dielectric property relationship in lead-free (1−x)(Bi1/2Na1/2)TiO3xBaTiO3 ceramics

The domain morphology and crystal structure of (1−x)(Bi1/2Na1/2)TiO3xBaTiO3 lead-free piezoelectric ceramics were systematically studied with transmission electron microscopy for compositions x=0.04through 0.11. It was found that the ceramics with compositions x\u3c0.06 display a R3csymmetry with ferroelectric domains of ∼100 nm forming complex structures at room temperature. Only nanodomains with faint contrast were observed in the compositions of 0.07≤x≤0.09. The presence of weak 1/2 (ooe)superlattice diffraction spots and absence of 1/2 (ooo) ones (o stands for odd and e stands for even miller indices) seem to suggest a P4bm symmetry at room temperature. The morphotropic phase boundary composition x=0.06 showed mixed R3c and P4bm phases. Large lamellar ferroelectric domains with P4mm symmetry were found to dominate in the ceramic of x=0.11. The observed domain structure correlates extremely well with the frequency dispersion of dielectric constant at room temperature and a new concept “relaxor antiferroelectric” was proposed to describe the dielectric behavior of compositions 0.07≤x≤0.09. These results are summarized in a phase diagram for unpoled ceramics in the (1−x)(Bi1/2Na1/2)TiO3xBaTiO3binary solid solution system

The effect of mode and context on survey results: Analysis of data from the Health Survey for England 2006 and the Boost Survey for London

Background: Health-related data at local level could be provided by supplementing national health surveys with local boosts. Self-completion surveys are less costly than interviews, enabling larger samples to be achieved for a given cost. However, even when the same questions are asked with the same wording, responses to survey questions may vary by mode of data collection. These measurement differences need to be investigated further.Methods: The Health Survey for England in London ('Core') and a London Boost survey ('Boost') used identical sampling strategies but different modes of data collection. Some data were collected by face-to-face interview in the Core and by self-completion in the Boost; other data were collected by self-completion questionnaire in both, but the context differed.Results were compared by mode of data collection using two approaches. The first examined differences in results that remained after adjusting the samples for differences in response. The second compared results after using propensity score matching to reduce any differences in sample composition. Results: There were no significant differences between the two samples for prevalence of some variables including long-term illness, limiting long-term illness, current rates of smoking, whether participants drank alcohol, and how often they usually drank. However, there were a number of differences, some quite large, between some key measures including: general health, GHQ12 score, portions of fruit and vegetables consumed, levels of physical activity, and, to a lesser extent, smoking consumption, the number of alcohol units reported consumed on the heaviest day of drinking in the last week and perceived social support (among women only).Conclusion: Survey mode and context can both affect the responses given. The effect is largest for complex question modules but was also seen for identical self-completion questions. Some data collected by interview and self-completion can be safely combined

The effect of survey method on survey participation: Analysis of data from the Health Survey for England 2006 and the Boost Survey for London

Background: There is a need for local level health data for local government and health bodies, for health surveillance and planning and monitoring of policies and interventions. The Health Survey for England (HSE) is a nationally-representative survey of the English population living in private households, but sub-national analyses can be performed only at a regional level because of sample size. A boost of the HSE was commissioned to address the need for local level data in London but a different mode of data collection was used to maximise participant numbers for a given cost. This study examines the effects on survey and item response of the different survey modes.Methods: Household and individual level data are collected in HSE primarily through interviews plus individual measures through a nurse visit. For the London Boost, brief household level data were collected through interviews and individual level data through a longer self-completion questionnaire left by the interviewer and collected later. Sampling and recruitment methods were identical, and both surveys were conducted by the same organisation. There was no nurse visit in the London Boost. Data were analysed to assess the effects of differential response rates, item non-response, and characteristics of respondents.Results: Household response rates were higher in the 'Boost' (61%) than 'Core' (HSE participants in London) sample (58%), but the individual response rate was considerably higher in the Core (85%) than Boost (65%). There were few differences in participant characteristics between the Core and Boost samples, with the exception of ethnicity and educational qualifications. Item non-response was similar for both samples, except for educational level. Differences in ethnicity were corrected with non-response weights, but differences in educational qualifications persisted after non-response weights were applied. When item non-response was added to those reporting no qualification, participants' educational levels were similar in the two samples.Conclusion: Although household response rates were similar, individual response rates were lower using the London Boost method. This may be due to features of London that are particularly associated with lower response rates for the self-completion element of the Boost method, such as the multi-lingual population. Nevertheless, statistical adjustments can overcome most of the demographic differences for analysis. Care must be taken when designing self-completion questionnaires to minimise item non-response

Corrugated single layer templates for molecules: From h -BN nanomesh to graphene based quantum dot arrays

Functional nano-templates enable self-assembly of otherwise impossible arrangements of molecules. A particular class of such templates is that of sp 2 hybridized single layers of hexagonal boron nitride or carbon (graphene) on metal supports. If the substrate and the single layer have a lattice mismatch, superstructures are formed. On substrates like rhodium or ruthenium these superstructures have unit cells with ∼3-nm lattice constant. They are corrugated and contain sub-units, which behave like traps for molecules or quantum dots, which are small enough to become operational at room temperature. For graphene on Rh(111) we emphasize a new structural element of small extra hills within the corrugation landscape. For the case of molecules like water it is shown that new phases assemble on such templates, and that they can be used as "nano-laboratories” where many individual processes are studied in parallel. Furthermore, it is shown that the h-BN/Rh(111) nanomesh displays a strong scanning tunneling microscopy-induced luminescence contrast within the 3 nm unit cell which is a way to address trapped molecules and/or quantum dot

Explanatory factors for health inequalities across different ethnic and gender groups: data from a national survey in England

BACKGROUND: The objective of this study was to examine the relative contribution of factors explaining ethnic health inequalities (EHI) in poor self-reported health (pSRH) and limiting long-standing illness (LLI) between Health Survey for England (HSE) participants. METHOD: Using HSE 2003-2006 data, the odds of reporting pSRH or of LLI in 8573 Bangladeshi, Black African, Black Caribbean, Chinese, Indian, Irish and Pakistani participants was compared with 28,470 White British participants. The effects of demographics, socioeconomic position (SEP), psychosocial variables, community characteristics and health behaviours were assessed using separate regression models. RESULTS: Compared with White British men, age-adjusted odds (OR, 95% CI) of pSRH were higher among Bangladeshi (2.05, 1.34 to 3.14), Pakistani (1.77, 1.34 to 2.33) and Black Caribbean (1.60, 1.18 to 2.18) men, but these became non-significant following adjustment for SEP and health behaviours. Unlike Black Caribbean men, Black African men exhibited a lower risk of age-adjusted pSRH (0.66, 0.43 to 1.00 (p=0.048)) and LLI (0.45, 0.28 to 0.72), which were significant in every model. Likewise, Chinese men had a lower risk of age-adjusted pSRH (0.51, 0.26 to 1.00 (p=0.048)) and LLI (0.22, 0.10 to 0.48). Except in Black Caribbean women, adjustment for SEP rendered raised age-adjusted associations for pSRH among Pakistani (2.51, 1.99 to 3.17), Bangladeshi (1.85, 1.08 to 3.16), Black Caribbean (1.78, 1.44 to 2.21) and Indian women (1.37, 1.13 to 1.66) insignificant. Adjustment for health behaviours had the largest effect for South Asian women. By contrast, Irish women reported better age-adjusted SRH (0.70, 1.51 to 0.96). CONCLUSIONS: SEP and health behaviours were major contributors explaining EHI. Policies to improve health equity need to monitor these pathways and be informed by them