Einstein metrics on tangent bundles of spheres

We give an elementary treatment of the existence of complete Kahler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.Comment: 9 page

The use of conversation mapping to frame key perceptual issues facing the general dental practice system in England

<b>Objective</b>: To demonstrate the use of a novel qualitative methodology namely conversation mapping, which can be used to capture differences in stakeholder perspectives and give a root definition of the problem in a complex policy area. The methodology is used in the context of the changes introduced in the English general dental practice system in April 2006, to investigate the key issues facing the system, as perceived by general dental practitioners (GDPs). <b>Basic research design</b>: From a broad trigger statement, three transformational statements were produced. Each participant recorded their contribution on a hard diagrammatic form as a ‘map’, with others responding with their own written comment, thus generating three conversation maps. Thematic analysis resulted in the generation of a preliminary model summarising key perceptual issues. <b>Results</b>: The five emergent themes identified were: financing, dentists’ wants/needs, the role of the public and patients, system goals and policy level decision making. Financing was identified as the core category to which all other categories were related. <b>Conclusions</b>: Conversation mapping, a methodology arising from a systems approach, can be used to develop a ‘rich picture’ of an oral health care system in order to define the core problem within this policy area. Findings suggest that GDPs identify the financing of the system as a fundamental source of problems within the general dental practice system. This appears to be at variance with the perception of policy makers, who report a more limited view, identifying the system of remuneration as the ‘heart of the problem’

Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation

Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter equation. Such solutions do not depend on a spectral parameter, and to date there has been little investigation into extending these solutions such that they do depend on a spectral parameter. Here we first explicitly construct the matrix elements of the generators for all irreducible representations of quantum doubles of the dihedral groups $D_n$. These results may be used to determine constant solutions of the Yang--Baxter equation. We then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter equation with spectral parameter and give several examples, including a new 21-vertex model. We also describe this approach in terms of minimal-dimensional representations of the quantum doubles of the alternating group $A_4$ and the symmetric group $S_4$.Comment: 19 pages, no figures, changed introduction, added reference

SU(3) monopoles and their fields

Some aspects of the fields of charge two SU(3) monopoles with minimal symmetry breaking are discussed. A certain class of solutions look like SU(2) monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding the monopoles. For large cloud size the relative moduli space metric splits as a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2) monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4 which corresponds to its radius and SO(3) orientation. We solve for the long-range fields in this region, and examine the energy density and rotational moments of inertia. The moduli space metric for these monopoles, given by Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.

Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry

The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model describes local interactions between non-Abelian anyons, with fusion rules given by the tensor product decompositions of the irreducible representations of D(D_3). The Bethe ansatz equations which characterise the exact solution are found through the use of functional relations satisfied by a set of mutually commuting transfer matrices.Comment: 19 page