Gravitational instantons, extra dimensions and form fields

A broad class of higher dimensional instanton solutions are found for a theory which contains gravity, a scalar field and antisymmetric tensor fields of arbitrary rank. The metric used, a warp product of an arbitrary number of any compact Einstein manifolds, includes many of great interest in particle physics and cosmology. For example 4D FRW universes with additional dimensions compactified on a Calabi-Yau three fold, a torus, a compact hyperbolic manifold or a sphere are all included. It is shown that the solution of this form which dominates the Hartle Hawking path integral is always a higher dimensional generalisation of a Hawking Turok instanton when the potential of the scalar field is such that these instantons can exist. On continuation to Lorentzian signature such instantons give rise to a spacetime in which all of the spatial dimensions are of equal size and where the spatial topology is that of a sphere. The extra dimensions are thus not hidden. In the case where the potential for the scalar field is generated solely by a dilatonic coupling to the form fields we find no integrable instantons at all. In particular we find no integrable solutions of the type under consideration for the supergravity theories which are the low energy effective field theories of superstrings.Comment: 11 pages, 4 figure

Gravitational instantons and internal dimensions

We Study instanton solutions in general relativity with a scalar field. The metric ansatz we use is composed of a particular warp product of general Einstein metrics, such as those found in a number of cosmological settings, including string cosmology, supergravity compactifications and general Kaluza Klein reductions. Using the Hartle-Hawking prescription the instantons we obtain determine whether metrics involving extra compact dimensions of this type are favoured as initial conditions for the universe. Specifically, we find that these product metric instantons, viewed as constrained instantons, do have a local minima in the action. These minima are then compared with the higher dimensional version of the Hawking-Turok instantons, and we argue that the latter always have lower action than those associated with these product metrics.Comment: 10 pages, 5 figure

Prediction of span loading of straight-wing/propeller combinations up to stall

A method is presented for calculating the spanwise lift distribution on straight-wing/propeller combinations. The method combines a modified form of the Prandtl wing theory with a realistic representation of the propeller slipstream distribution. The slipstream analysis permits calculations of the nonuniform axial and rotational slipstream velocity field of propeller/nacelle combinations. This nonuniform field was then used to calculate the wing lift distribution by means of the modified Prandtl wing theory. The theory was developed for any number of nonoverlapping propellers, on a wing with partial or full-span flaps, and is applicable throughout an aspect ratio range from 2.0 and higher. A computer program was used to calculate slipstream characteristics and wing span load distributions for a number of configurations for which experimental data are available, and favorable comparisons are demonstrated between the theoretical predictions and the existing data

The crystal and molecular structure of Hydridotetrakis(diethyl phenylphosphonite)cobalt(I)

An X-ray structure determination of the title compound shows that the co-ordination about the cobalt atom is approximately trigonal bipyramidal; n.m.r. data indicate that the complex is non-rigid in solution

The prevalence of metabolic syndrome amongst patients with severe mental illness in the community in Hong Kong--a cross sectional study

Background: Patients with severe mental illness are at increased risk of developing metabolic disorders. The risk of metabolic syndrome in the Hong Kong general population is lower than that observed in western countries; however the prevalence of metabolic syndrome in patients with severe mental illness in Hong Kong is unknown. Method: This cross-sectional study aimed to estimate the prevalence of metabolic syndrome in patients with severe mental illness in Hong Kong and to identify the relationships between metabolic syndrome and socio-demographic, clinical and lifestyle factors. Results: A total of 139 patients with a diagnosis of severe mental illness participated in the study. The unadjusted prevalence of metabolic syndrome was 35%. The relative risk of metabolic syndrome in comparison with the general Hong Kong population was 2.008 (95% CI 1.59-2.53, p < 0.001). In a logistic regression model sleep disruption and being prescribed first generation antipsychotics were significantly associated with the syndrome, whilst eating less than 3 portions of fruit/vegetables per day and being married were weakly associated. Conclusion The results demonstrate that metabolic syndrome is highly prevalent and that physical health inequalities in patients with severe mental illness in Hong Kong are similar to those observed in western countries. The results provide sufficient evidence to support the need for intervention studies in this setting and reinforce the requirement to conduct regular physical health checks for all patients with severe mental illness

Variance Control in Weak Value Measurement Pointers

The variance of an arbitrary pointer observable is considered for the general case that a complex weak value is measured using a complex valued pointer state. For the typical cases where the pointer observable is either its position or momentum, the associated expressions for the pointer's variance after the measurement contain a term proportional to the product of the weak value's imaginary part with the rate of change of the third central moment of position relative to the initial pointer state just prior to the time of the measurement interaction when position is the observable - or with the initial pointer state's third central moment of momentum when momentum is the observable. These terms provide a means for controlling pointer position and momentum variance and identify control conditions which - when satisfied - can yield variances that are smaller after the measurement than they were before the measurement. Measurement sensitivities which are useful for estimating weak value measurement accuracies are also briefly discussed.Comment: submitted to Phys Rev