Ashtekar's New Variables and Positive Energy

We discuss earlier unsuccessful attempts to formulate a positive gravitational energy proof in terms of the New Variables of Ashtekar. We also point out the difficulties of a Witten spinor type proof. We then use the special orthonormal frame gauge conditions to obtain a locally positive expression for the New Variables Hamiltonian and thereby a ``localization'' of gravitational energy as well as a positive energy proof.Comment: 12 pages Plain Te

Quasi-local Energy for Spherically Symmetric Spacetimes

We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime.Comment: 16 pages, no figure

The quadratic spinor Lagrangian is equivalent to the teleparallel theory

The quadratic spinor Lagrangian is shown to be equivalent to the teleparallel / tetrad representation of Einstein's theory. An important consequence is that the energy-momentum density obtained from this quadratic spinor Lagrangian is essentially the same as the ``tensor'' proposed by Moller in 1961.Comment: 10 pages, RevTe

Professional appraisal of online information about children’s footwear measurement and fit : readability, usability and quality

Parents increasingly use the internet to seek health information, share information and for purchasing textiles and footwear. This shift in footwear purchasing habits raises concern about how (and if) parents are getting their children's feet measured, and what support strategies are in place to support the fit of footwear. In response to this, some companies and healthcare organisations have developed resources to support home measurement of foot size, and link these measures to footwear selection, measurement and fitting. The aim of this research was to undertake an appraisal of web-based resources about measurement and fit of children's footwear, focussing specifically on readability, usability and quality. Search terms relating to children's foot measurement were compiled and online searching was undertaken. Search results were saved and screened for relevance. Existing resources were categorised based on their source e.g. a footwear company or a health website. The 15 most commonly identified resources were reviewed by a professional panel for readability, content, usability and validity. One researcher also assessed the accessibility and reading ease of the resources. Online resources were predominantly from commercial footwear companies (54%). Health information sources from professional bodies made up 4.2% of the resources identified. The top 15 resources had appropriate reading ease scores for parents (SMOG Index 4.3-8.2). Accessibility scores (the product of the number of times it appeared in search results and its ranking in the results) were highest for commercial footwear companies. The panel scores for readability ranged from 2.7 to 9 out of 10, with a similar range for content, usability and validity. Information for parents seeking to purchase footwear for their children is readily available online but this was largely dominated by commercial footwear companies. The quality and usability of this information is of a moderate standard; notable improvements could be made to the validity of the task the child is asked to undertake and the measures being taken. Improvements in these resources would improve the data input to the selection of footwear and therefore have a beneficial impact on footwear fit in children. [Abstract copyright: © The Author(s). 2020.

The effect of aging, obesity and diabetes on foot health and its association with current and future footwear technologies

Changes in foot health trends are beginning to demand significant changes to foot health provision globally, for which appropriate provision to retail and health services is key. With the right input to innovation and design, footwear can help keep us fit and active and contribute to our overall wellbeing, creating exciting opportunities for the footwear market. Likewise, the development of orthotic materials, designs and manufacturing processes is enabling more complex solutions to equally complex developing foot conditions. There are three key issues driving the demand for specific footcare; the global increase in the number of people with diabetes, those who are obese and the fact we are all living longer. The populations of diabetic, elderly and obese adults require specific footcare solutions to meet the specific characteristics of their foot health issues such as wider-fit footwear and pressure relieving orthotic materials. Characteristics of these populations' feet relating to their morphology, tissue characteristics, vascular supply and sensation impact on their requirements from footwear. Additional characteristics relating to their overall health such as excess mass and instability additionally impact on the wear on the loading of the footwear and design features which may be beneficial

Quasi-local energy for cosmological models

First we briefly review our covariant Hamiltonian approach to quasi-local energy, noting that the Hamiltonian-boundary-term quasi-local energy expressions depend on the chosen boundary conditions and reference configuration. Then we present the quasi-local energy values resulting from the formalism applied to homogeneous Bianchi cosmologies. Finally we consider the quasi-local energies of the FRW cosmologies. Our results do not agree with certain widely accepted quasi-local criteria.Comment: Contributed to International Symposium on Cosmology and Particle Astrophysics (CosPA 2006), Taipei, Taiwan, 15-17 Nov 200

Validity and repeatability of three in-shoe pressure measurement systems

In-shoe pressure measurement devices are used in research and clinic to quantify plantar foot pressures. Various devices are available, differing in size, sensor number and type; therefore accuracy and repeatability. Three devices (Medilogic, Tekscan and Pedar) were examined in a 2 day×3 trial design, quantifying insole response to regional and whole insole loading. The whole insole protocol applied an even pressure (50-600kPa) to the insole surface for 0-30s in the Novel TruBlue™ device. The regional protocol utilised cylinders with contact surfaces of 3.14 and 15.9cm(2) to apply pressures of 50 and 200kPa. The validity (% difference and Root Mean Square Error: RMSE) and repeatability (Intra-Class Correlation Coefficient: ICC) of the applied pressures (whole insole) and contact area (regional) were outcome variables. Validity of the Pedar system was highest (RMSE 2.6kPa; difference 3.9%), with the Medilogic (RMSE 27.0kPa; difference 13.4%) and Tekscan (RMSE 27.0kPa; difference 5.9%) systems displaying reduced validity. The average and peak pressures demonstrated high between-day repeatability for all three systems and each insole size (ICC≥0.859). The regional contact area % difference ranged from -97 to +249%, but the ICC demonstrated medium to high between-day repeatability (ICC≥0.797). Due to the varying responses of the systems, the choice of an appropriate pressure measurement device must be based on the loading characteristics and the outcome variables sought. Medilogic and Tekscan were most effective between 200 and 300kPa; Pedar performed well across all pressures. Contact area was less precise, but relatively repeatable for all systems

Variability in foot contact patterns in independent walking in infants

The purpose of this work was to quantify plantar pressures and contact areas (and variability thereof) in natural independent walking in infants