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

Effect of Dilution and Contaminants on Strength and Hydraulic Conductivity of Sand Grouted With Colloidal Silica Gel

Colloidal silica (CS) is a low-viscosity liquid that can be made to gel by addition of brine. This property allows it to be injected into, or mixed with, soil, so that after gelling the colloidal silica blocks the pore space in the soil and forms a barrier to the flow of contaminated groundwater or non-aqueous liquids (NAPLs). Gelled-in-place CS was first studied for the petroleum industry and later for protecting groundwater quality. Noll investigated the use of colloidal silica diluted so that its solids content was reduced from 30% (a typical nominal value for material as delivered) to values as low as 5%. The more dilute colloids could still be made to gel, although more slowly, and the resulting gel was weaker. Because the proposed application of colloidal silica grout involves emplacing it in the subsurface by permeation, jet grouting, or soil mixing where its role as a barrier will be to resist flow of contaminants, the effects of these contaminants on the properties of the grouted soil is also of interest. This work comprised four tasks. In Task 1, samples of grouted sand were prepared with a range of CS dilutions, for measurement of hydraulic conductivity and unconfined-compressive strength. In Task 2, these properties were measured on samples of grouted sand that incorporated 5% volumetric saturation of NAPLs. In Task 3, samples, prepared without any contaminants, were immersed in contaminant liquids and tested after 30 and 90 days. Task 4 was added because NAPL contamination in the samples of Tasks 2 and 3 impelled modifications in the test methods, and comparison of the results of Task 2 and Task 1 suggested that these modifications had introduced errors. In Task 4, samples were tested both ways, to confirm that in Tasks 2 and 3 strength was underestimated and hydraulic conductivity was overestimated. Despite the existence of these known systematic errors, the inclusion of control samples in Tasks 2 and 3 permits conclusions to be drawn from these data

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

Further functional determinants

Functional determinants for the scalar Laplacian on spherical caps and slices, flat balls, shells and generalised cylinders are evaluated in two, three and four dimensions using conformal techniques. Both Dirichlet and Robin boundary conditions are allowed for. Some effects of non-smooth boundaries are discussed; in particular the 3-hemiball and the 3-hemishell are considered. The edge and vertex contributions to the $C_{3/2}$ coefficient are examined.Comment: 25 p,JyTex,5 figs. on request

Characterization the Cool KOIs. II. The M Dwarf KOI-254 and its Hot Jupiter

We report the confirmation and characterization of a transiting gas giant planet orbiting the M dwarf KOI-254 every 2.455239 days, which was originally discovered by the Kepler mission. We use radial velocity measurements, adaptive optics imaging, and near-infrared spectroscopy to confirm the planetary nature of the transit events. KOI-254 b is the first hot Jupiter discovered around an M-type dwarf star. We also present a new model-independent method of using broadband photometry to estimate the mass and metallicity of an M dwarf without relying on a direct distance measurement. Included in this methodology is a new photometric metallicity calibration based on J – K colors. We use this technique to measure the physical properties of KOI-254 and its planet. We measure a planet mass of M_P = 0.505 M_(Jup), radius R_P = 0.96 R_(Jup), and semimajor axis a = 0.030 AU, based on our measured stellar mass M_* = 0.59 M_☉ and radius R_* = 0.55 R_☉. We also find that the host star is metal-rich, which is consistent with the sample of M-type stars known to harbor giant planets