Functional inversion for potentials in quantum mechanics

Let E = F(v) be the ground-state eigenvalue of the Schroedinger Hamiltonian H = -Delta + vf(x), where the potential shape f(x) is symmetric and monotone increasing for x > 0, and the coupling parameter v is positive. If the 'kinetic potential' bar{f}(s) associated with f(x) is defined by the transformation: bar{f}(s) = F'(v), s = F(v)-vF'(v),then f can be reconstructed from F by the sequence: f^{[n+1]} = bar{f} o bar{f}^{[n]^{-1}} o f^{[n]}. Convergence is proved for special classes of potential shape; for other test cases it is demonstrated numerically. The seed potential shape f^{[0]} need not be 'close' to the limit f.Comment: 14 pages, 2 figure

Safety Engineering with COTS components

Safety-critical systems are becoming more widespread, complex and reliant on software. Increasingly they are engineered through Commercial Off The Shelf (COTS) (Commercial Off The Shelf) components to alleviate the spiralling costs and development time, often in the context of complex supply chains. A parallel increased concern for safety has resulted in a variety of safety standards, with a growing consensus that a safety life cycle is needed which is fully integrated with the design and development life cycle, to ensure that safety has appropriate influence on the design decisions as system development progresses. In this article we explore the application of an integrated approach to safety engineering in which assurance drives the engineering process. The paper re- ports on the outcome of a case study on a live industrial project with a view to evaluate: its suitability for application in a real-world safety engineering setting; its benefits and limitations in counteracting some of the difficulties of safety en- gineering with COTS components across supply chains; and, its effectiveness in generating evidence which can contribute directly to the construction of safety cases

Klein-Gordon lower bound to the semirelativistic ground-state energy

For the class of attractive potentials V(r) <= 0 which vanish at infinity, we prove that the ground-state energy E of the semirelativistic Hamiltonian H = \sqrt{m^2 + p^2} + V(r) is bounded below by the ground-state energy e of the corresponding Klein--Gordon problem (p^2 + m^2)\phi = (V(r) -e)^2\phi. Detailed results are presented for the exponential and Woods--Saxon potentials.Comment: 7 pages, 4 figure

Projective vs metric structures

We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita connection is in the projective class and, in the positive, which finds this connection and the metric. The article also provides a basic information on invariants of projective structures, including the treatment via Cartan's normal projective connection. In particular we show that there is a number of Fefferman-like conformal structures, defined on a subbundle of the Cartan bundle of the projective structure, which encode the projectively invariant information about (M,[nabla])

Electrifying Africa: power through the public sector

A review of the need for electricity in Africa, experiences of privatisation, and the political and economic potential for development through the public sector

Iyer Laboratory Solid Tissue Chromatin Immunoprecipitation Protocol

A detailed protocol on how to perform chromatin immunoprecipitation in solid tissue samples. This protocol is used routinely in the Iyer lab.Molecular Bioscience

Hygelac's only daughter: a present, a potentate and a peaceweaver in Beowulf

[FIRST PARAGRAPH] The women of Beowulf have enjoyed extensive study in recent years, but one has escaped the limelight: the only daughter of Hygelac, king of the Geats and Beowulf’s lord. But though this daughter is mentioned only fleetingly, a close examination of the circumstances of her appearance and the words in which it is couched affords new perspectives on the role of women in Beowulf and on the nature of Hygelac’s kingship. Hygelac’s only daughter is given as part of a reward to Hygelac’s retainer Eofor for the slaying of the Swedish king Ongentheow. Beowulf refers to this reward with the unique noun ofermaðmas, traditionally understood to mean ‘‘great treasures’’. I argue, however, that ofermaðmas at least potentially means ‘‘excessive treasures’’. Developing this reading implies a less favourable assessment of Hygelac’s actions here than has previously been inferred. I argue further that the excess in Hygelac’s treasure-giving derives specifically from his gift of his only daughter, and the consequent loss to the Geats of the possibility of a diplomatic marriage through which they might end their feud with the Swedes. A reconsideration of Hygelac’s only daughter, then, offers new perspectives on the semantics of ofermaðum, on Hygelac’s kingship, and on women in Beowulf