Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Health informatics education for clinicians and managers - What's holding up progress?

This paper reports outcomes of a national survey of health informatics (HI) education and training carried out in the UK. A questionnaire to elicit details of HI and IT skills teaching was derived from a national consensus document (Learning to Manage Health Information, LtMHI). Forms were sent to all pre-qualification medical and nursing schools and to a stratified sample of postgraduate and post-registration programmes. Three case studies were carried out in acute hospital trusts to gain insight into opportunities for continuing professional development in health informatics and IT. Our evidence suggests that in the UK, health informatics is not yet integrated into the clinical curriculum. Nearly all the pre-qualification courses made some provision for teaching IT skills. Nonetheless, many respondents felt that students did not receive sufficient training. There was considerable variation in the amount of HI teaching provided in the different educational sectors. The case studies suggested very little HI training was provided for clinical staff and take-up of provision was not monitored. A number of factors are holding up progress, the most important being a lack of staff with the knowledge and skills to provide academic leadership. The paper outlines some steps that need to be taken to ensure health informatics is embedded in all clinical curricula. © 2003 Elsevier Ireland Ltd. All rights reserved

Smeared heat-kernel coefficients on the ball and generalized cone

We consider smeared zeta functions and heat-kernel coefficients on the bounded, generalized cone in arbitrary dimensions. The specific case of a ball is analysed in detail and used to restrict the form of the heat-kernel coefficients $A_n$ on smooth manifolds with boundary. Supplemented by conformal transformation techniques, it is used to provide an effective scheme for the calculation of the $A_n$. As an application, the complete $A_{5/2}$ coefficient is given.Comment: 23 pages, JyTe

Differentiation and dynamics of competitiveness impacts from the EU ETS

We summarises the main factors that differentiate impacts of the EU ETS on profitability and market share. By examining sampling a range of sectors, we present some simple metrics and indicators to help judge the nature of potential impacts. We also consider briefly the mitigation response to these impacts by sectors, and how they may evolve over time. The broad conclusion confirms the aggregate findings presented in the existing literature - most participating sectors are likely to profit under the current ETS structure out to 2012 at the cost of a modest loss of market share, but this may not hold for individual companies and regions. The period 2008-12 can assist participating sectors to build experience and financial reserves for longer term technology investments and diversification, providing the continuation and basic principles of the EU ETS post-2012 is quickly defined and incentives are in place for sectors to pursue this.Emissions trading, industrial competitiveness, spillovers, allowance allocation, perverse incentives.

Schrödinger operators with δ and δ′-potentials supported on hypersurfaces

Self-adjoint Schrödinger operators with δ and δ′-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity results on the functions in their domains are obtained, and analogues of the Birman–Schwinger principle and a variant of Krein’s formula are shown. Furthermore, Schatten–von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ′-potentials, and the Schrödinger operator without a singular interaction are proved. An immediate consequence of these estimates is the existence and completeness of the wave operators of the corresponding scattering systems, as well as the unitary equivalence of the absolutely continuous parts of the singularly perturbed and unperturbed Schrödinger operators. In the proofs of our main theorems we make use of abstract methods from extension theory of symmetric operators, some algebraic considerations and results on elliptic regularity

Evolution of size-dependent flowering in a variable environment: construction and analysis of a stochastic integral projection model

Understanding why individuals delay reproduction is a classic problem in evolutionary biology. In plants, the study of reproductive delays is complicated because growth and survival can be size and age dependent, individuals of the same size can grow by different amounts and there is temporal variation in the environment. We extend the recently developed integral projection approach to include size- and age-dependent demography and temporal variation. The technique is then applied to a long-term individually structured dataset for Carlina vulgaris, a monocarpic thistle. The parameterized model has excellent descriptive properties in terms of both the population size and the distributions of sizes within each age class. In Carlina, the probability of flowering depends on both plant size and age. We use the parameterized model to predict this relationship, using the evolutionarily stable strategy approach. Considering each year separately, we show that both the direction and the magnitude of selection on the flowering strategy vary from year to year. Provided the flowering strategy is constrained, so it cannot be a step function, the model accurately predicts the average size at flowering. Elasticity analysis is used to partition the size- and age-specific contributions to the stochastic growth rate, λs. We use λs to construct fitness landscapes and show how different forms of stochasticity influence its topography. We prove the existence of a unique stochastic growth rate, λs, which is independent of the initial population vector, and show that Tuljapurkar's perturbation analysis for log(λs) can be used to calculate elasticities

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio

Global Theory of Quantum Boundary Conditions and Topology Change

We analyze the global theory of boundary conditions for a constrained quantum system with classical configuration space a compact Riemannian manifold $M$ with regular boundary $\Gamma=\partial M$. The space \CM of self-adjoint extensions of the covariant Laplacian on $M$ is shown to have interesting geometrical and topological properties which are related to the different topological closures of $M$. In this sense, the change of topology of $M$ is connected with the non-trivial structure of \CM. The space \CM itself can be identified with the unitary group \CU(L^2(\Gamma,\C^N)) of the Hilbert space of boundary data L^2(\Gamma,\C^N). A particularly interesting family of boundary conditions, identified as the set of unitary operators which are singular under the Cayley transform, \CC_-\cap \CC_+ (the Cayley manifold), turns out to play a relevant role in topology change phenomena. The singularity of the Cayley transform implies that some energy levels, usually associated with edge states, acquire an infinity energy when by an adiabatic change the boundary condition reaches the Cayley submanifold \CC_-. In this sense topological transitions require an infinite amount of quantum energy to occur, although the description of the topological transition in the space \CM is smooth. This fact has relevant implications in string theory for possible scenarios with joint descriptions of open and closed strings. In the particular case of elliptic self--adjoint boundary conditions, the space \CC_- can be identified with a Lagrangian submanifold of the infinite dimensional Grassmannian. The corresponding Cayley manifold \CC_- is dual of the Maslov class of \CM.Comment: 29 pages, 2 figures, harvma