New G₂-holonomy cones and exotic nearly Kahler structures on S⁶ and S³ x S³

There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kaehler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G_{2}: the metric cone over a Riemannian 6-manifold M has holonomy contained in G_{2} if and only if M is a nearly Kaehler 6-manifold. A central problem in the field has been the absence of any complete inhomogeneous examples. We prove the existence of the first complete inhomogeneous nearly Kaehler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kaehler structure on the 6-sphere and on the product of a pair of 3-spheres. We conjecture that these are the only simply connected (inhomogeneous) cohomogeneity one nearly Kaehler structures in six dimensions

Infinitely many new families of complete cohomogeneity one G₂-manifolds: G₂ analogues of the Taub-NUT and Eguchi-Hanson spaces

We construct infinitely many new 1-parameter families of simply connected complete noncompact G_2-manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geometry. However, the nature of the asymptotic geometry changes at two special parameter values: at one special value we obtain a unique member of each family with asymptotically conical (AC) geometry; on approach to the other special parameter value the family of metrics collapses to an AC Calabi-Yau 3-fold. Our infinitely many new diffeomorphism types of AC G_2-manifolds are particularly noteworthy: previously the three examples constructed by Bryant and Salamon in 1989 furnished the only known simply connected AC G_2-manifolds. We also construct a closely related conically singular G_2 holonomy space: away from a single isolated conical singularity, where the geometry becomes asymptotic to the G_2-cone over the standard nearly Kaehler structure on the product of a pair of 3-spheres, the metric is smooth and it has ALC geometry at infinity. We argue that this conically singular ALC G_2-space is the natural G_2 analogue of the Taub-NUT metric in 4-dimensional hyperKaehler geometry and that our new AC G_2-metrics are all analogues of the Eguchi-Hanson metric, the simplest ALE hyperKaehler manifold. Like the Taub-NUT and Eguchi-Hanson metrics, all our examples are cohomogeneity one, i.e. they admit an isometric Lie group action whose generic orbit has codimension one

Bridging the gap: exploring the attitudes and beliefs of nurses and patients about coexisting traditional and biomedical healthcare systems in a rural setting in KwaZulu-Natal

Objectives: Health care in South Africa takes place within a diverse cultural context and includes perceptions about health that strongly link to cultural beliefs and values. Biomedical healthcare professionals, particularly nurses, are exposed to and expected to cope with cultural challenges on a daily basis, with little or no training on how to do so. In this paper, we explore nurse and patient attitudes to and beliefs about how the systems of health care coexist, what issues this raises and how nurses and patients address these issues in their daily practice.Design: The study employed an exploratory, qualitative research design.Setting and subjects: Four in-depth focus group discussions were conducted with nurses and patients at a deep rural, district hospital in northern KwaZulu-Natal. Participants were selected based on their availability and willingness to contribute to the discussion.Results: Traditional and biomedical healthcare systems coexist and are used simultaneously with the healthcare- seeking pattern of patients traversing multiple systems of care. Currently, patients and nurses have developed strategies to address this by steering a pragmatic course to minimise risks, and by doing so, bridging the gap between the two healthcare mediums.Conclusion: Further research is required to understand which illnesses are primarily seen as traditional, how this gap can be effectively addressed, and how different healthcare co-delivery models can best be utilised and evaluated.Keywords: health worker, traditional health care, biomedical health care, cultur

Lake Itasca State Park Myxomycetes: An Annotated Checklist

A lack of published information regarding Minnesota Myxomycetes prompted attempts to document species from Lake Itasca State Park in Clearwater county, in the northwest part of the state. Seventy-five species are herein recorded from 341 collections made during the years 1959, 1971,and 1975-78

Computational Materials Techniques for Thermal Protection Solutions: Materials and Process Design

Integrated computational materials techniques that span the atomistic and continuum scales have the potential to aid the design and manufacturing of thermal protection materials. Two cases demonstrating the practical application of these methods are discussed. Case one examines the selection of a high temperature coating for carbon/carbon, with the target application being a solar thermal propulsion heat exchanger. The performance of various refractory metal and metal-carbide coatings is characterized considering extreme thermal (3500 degrees Kelvin) and chemical (hydrogen flows) conditions. The recession rate, hydrogen leakage, and likelihood of mechanical failure are characterized and provide directions for further experimental investigation. Case two examines the process optimization of a heat shield material composed of a woven silica fiber preform and cyanate ester resin. Frequently, internal voids were found to be present in this composite after the resin infusion and curing stages of manufacturing. Using the manufacturing conditions, computations indicate that both water adsorption and resin cure shrinkage are contributing factors to void formation. The results suggest an alternative process configuration for curing that would mitigate voids

Special Lagrangian cones with higher genus links

For every odd natural number g=2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in C^3 over a closed Riemann surface of genus g, using a geometric PDE gluing method.Comment: 48 page

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps

The most fruitful approach to studying low energy soliton dynamics in field theories of Bogomol'nyi type is the geodesic approximation of Manton. In the case of vortices and monopoles, Stuart has obtained rigorous estimates of the errors in this approximation, and hence proved that it is valid in the low speed regime. His method employs energy estimates which rely on a key coercivity property of the Hessian of the energy functional of the theory under consideration. In this paper we prove an analogous coercivity property for the Hessian of the energy functional of a general sigma model with compact K\"ahler domain and target. We go on to prove a continuity property for our result, and show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive in the degree 1 sector. We present numerical evidence which suggests that the Hessian is globally coercive in a certain equivariance class of the degree n sector for n>1. We also prove that, within the geodesic approximation, a single CP^1 lump moving on S^2 does not generically travel on a great circle.Comment: 29 pages, 1 figure; typos corrected, references added, expanded discussion of the main function spac

Kinetic analysis of microcalorimetric data derived from microbial growth: Basic theoretical, practical and industrial considerations

We report here a mathematical framework for the quantitative interpretation of exponential bacterial growth measured with isothermal microcalorimetry. The method allows determination of many parameters that define the exponential growth phase. To automate the analysis, we also wrote a coding program, so that the approach could be embedded in a commercial setting. As an exemplar, we apply the method to a commercial probiotic product. The outcome was that we could identify characteristic parameters of growth (including rate constant and doubling time), and hence authenticate product quality, within 15 h. This compares favourably with the current 7–10 days required for conventional microbiological assessment (to allow release of product for bottling and marketing) via plating methods. The method would lend itself to growth analysis of single and mixed bacterial cultures