The C_2 heat-kernel coefficient in the presence of boundary discontinuities

We consider the heat-kernel on a manifold whose boundary is piecewise smooth. The set of independent geometrical quantities required to construct an expression for the contribution of the boundary discontinuities to the C_{2} heat-kernel coefficient is derived in the case of a scalar field with Dirichlet and Robin boundary conditions. The coefficient is then determined using conformal symmetry and evaluation on some specific manifolds. For the Robin case a perturbation technique is also developed and employed. The contributions to the smeared heat-kernel coefficient and cocycle function are calculated. Some incomplete results for spinor fields with mixed conditions are also presented.Comment: 25 pages, LaTe

Effectiveness of a social support intervention on infant feeding practices : randomised controlled trial

Background: To assess whether monthly home visits from trained volunteers could improve infant feeding practices at age 12 months, a randomised controlled trial was carried out in two disadvantaged inner city London boroughs. Methods: Women attending baby clinics with their infants (312) were randomised to receive monthly home visits from trained volunteers over a 9-month period (intervention group) or standard professional care only (control group). The primary outcome was vitamin C intakes from fruit. Secondary outcomes included selected macro and micro-nutrients, infant feeding habits, supine length and weight. Data were collected at baseline when infants were aged approximately 10 weeks, and subsequently when the child was 12 and 18 months old. Results: Two-hundred and twelve women (68%) completed the trial. At both follow-up points no significant differences were found between the groups for vitamin C intakes from fruit or other nutrients. At first follow-up, however, infants in the intervention group were significantly less likely to be given goats’ or soya milks, and were more likely to have three solid meals per day. At the second follow-up, intervention group children were significantly less likely to be still using a bottle. At both follow-up points, intervention group children also consumed significantly more specific fruit and vegetables. Conclusions: Home visits from trained volunteers had no significant effect on nutrient intakes but did promote some other recommended infant feeding practices

The California Planet Survey II. A Saturn-Mass Planet Orbiting the M Dwarf Gl649

We report precise Doppler measurements of the nearby (d = 10.34 pc) M dwarf Gl649 that reveal the presence of a planet with a minimum mass Msini = 0.328 Mjup in an eccentric (e = 0.30), 598.3 day orbit. Our photometric monitoring reveals Gl649 to be a new variable star with brightness changes on both rotational and decadal timescales. However, neither of these timescales are consistent with the 600-day Doppler signal and so provide strong support for planetary reflex motion as the best interpretation of the observed radial velocity variations. Gl649b is only the seventh Doppler-detected giant planet around an M dwarf. The properties of the planet and host-star therefore contribute significant information to our knowledge of planet formation around low-mass stars. We revise and refine the occurrence rate of giant planets around M dwarfs based on the California Planet Survey sample of low-mass stars (M* < 0.6 Msun). We find that f = 3.4^{+2.2}_{-0.9}% of stars with M* < 0.6 Msun harbor planets with Msini > 0.3$ Mjup and a < 2.5 AU. When we restrict our analysis to metal-rich stars with [Fe/H] > +0.2 we find the occurrence rate is 10.7^{+5.9}_{-4.2}%.Comment: 8 pages, 4 figures, 3 tables, PASP accepte

Heat Kernel Expansion for Semitransparent Boundaries

We study the heat kernel for an operator of Laplace type with a $\delta$-function potential concentrated on a closed surface. We derive the general form of the small $t$ asymptotics and calculate explicitly several first heat kernel coefficients.Comment: 16 page

Grip socks improve slalom course performance and reduce in-shoe foot displacement of the forefoot in male and female sports players

This study assessed whether grip socks reduce in-shoe foot motion and improve change of direction performance in team sports players and compared the effects between males and females. A sledge and pulley system confirmed the static coefficient of friction was increased in the grip socks (1.17) compared to the regular socks (0.60). Performance during a slalom course was faster in the grip socks compared to regular socks (p = .001). Yet, there was no difference in the utilised coefficient of friction between the shoe-floor interface during a side-cut and turn change of direction manoeuvre. Three-dimensional motion capture revealed the grip socks reduced in-shoe foot displacement during the braking phase, with greater effect during the sharper turn manoeuvre. The magnitude of natural foot spreading within the shoe was greater in the calcaneus region than the metatarsals which suggests in-shoe sliding may only occur at the forefoot. Males tended to have increased in-shoe displacement, which is associated with larger foot spreading due to their increased mass. Findings provide guidance for product developers to enhance the support inside the shoe at the forefoot, and change of direction performance