Improved conditioning of the Floater--Hormann interpolants

The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of rounding errors increases with approximation order, and can make balancing the interpolation error and rounding error difficult. This article proposes to modify the Floater--Hormann interpolants by including additional local polynomial interpolants at the ends of the interval. This appears to improve the conditioning of the interpolants and allow higher approximation orders to be used in practice.Comment: 13 pages, 4 figures, 1 tabl

Fuller geographies and the care-ful co-production of transgressive pedagogies, or 'Who Cares?'

No abstract available

QSym over Sym has a stable basis

We prove that the subset of quasisymmetric polynomials conjectured by Bergeron and Reutenauer to be a basis for the coinvariant space of quasisymmetric polynomials is indeed a basis. This provides the first constructive proof of the Garsia-Wallach result stating that quasisymmetric polynomials form a free module over symmetric polynomials and that the dimension of this module is n!.Comment: 12 page

Yoga practice in the UK: a cross- sectional survey of motivation, health benefits and behaviours

Objectives Despite the popularity of yoga and evidence of its positive effects on physical and mental health, little is known about yoga practice in the UK. This study investigated the characteristics of people who practise yoga, reasons for initiating and maintaining practice, and perceived impact of yoga on health and well-being. Design, setting and participants A cross-sectional online anonymous survey distributed through UK-based yoga organisations, studios and events, through email invites and flyers. 2434 yoga practitioners completed the survey, including 903 yoga teachers: 87% were women, 91% white and 71% degree educated; mean age was 48.7 years. Main outcome measures Perceived impact of yoga on health conditions, health outcomes and injuries. Relationships between yoga practice and measures of health, lifestyle, stress and well-being. Results In comparison with national population norms, participants reported significantly higher well-being but also higher anxiety; lower perceived stress, body mass index and incidence of obesity, and higher rates of positive health behaviours. 47% reported changing their motivations to practise yoga, with general wellness and fitness key to initial uptake, and stress management and spirituality important to current practice. 16% of participants reported starting yoga to manage a physical or mental health condition. Respondents reported the value of yoga for a wide range of health conditions, most notably for musculoskeletal and mental health conditions. 20.7% reported at least one yoga-related injury over their lifetime. Controlling for demographic factors, frequency of yoga practice accounted for small but significant variance in health-related regression models (p<0.001). Conclusion The findings of this first detailed UK survey were consistent with surveys in other Western countries. Yoga was perceived to have a positive impact on physical and mental health conditions and was linked to positive health behaviours. Further investigation of yoga’s role in self-care could inform health-related challenges faced by many countries

Oculometer for remote tracking of eye movement

Prototype oculometer which tracks lateral eye position and measures the direction of the eyes optical axis, pupil size, and blink occurrence performs measurements on the subject on a real-time basis from a remote location

Experimental investigation of two nonaxisymmetric wedge nozzles at free stream Mach numbers up to 1.20

Forces and pressures on two nonaxisymmetric wedge nozzles were measured in a 16 foot transonic tunnel. Tests were conducted at static conditions and at free stream Mach numbers of 0.60, 0.80, 0.90, 0.94, and 1.20. The range of nozzle pressure ratios varied with configuration and Mach number. The internal and external geometry of the nozzles and the test model are defined in detail. Nozzle performance data are presented as discharge coefficients, internal thrust ratios, thrust minus nozzle drag ratios, and ideal thrust coefficients. Extensive internal and external pressure measurements are presented

Modelling electron interactions: a semi-rigorous method

We report total electron scattering cross sections (TCS) for SF6, SF5 CF3, and CF3I, molecules of interest to the plasma industry over the energy range from threshold to 2000 eV. We also report the total scattering cross sections for e-formaldehyde for which there are currently no theoretical or experimental results reported. The ionization cross sections for these targets are also estimated using the Deustch and Maerk formalism and are compared with Binary Encounter Bethe (BEB) data of Kim