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])

Methodological issues in estimating the impact of private equity buyouts on employment

Claims by private equity firms that they create employment are based on deeply flawed research, and are worthless as contributions to the debate

Private equity and employment - the Davos/WEF/Harvard study

The World Economic Forum at Davos has published a major study showing that workplaces of firms taken over by private equity have 10% less employees 5 years after the takeover, than other similar workplaces. The rate of plant closures, opening, acquisitions and disposals is twice as high as in other firms, and the net effect is still a job loss of 3.6%-4.5% after only 2 years, compared with other firms. Firms taken over by private equity are also more likely to go bankrupt than publicly quoted firms

Take the Money and Run: Detainment Incident to a Search Warrant in Bailey v. United States

This commentary previews an upcoming Supreme Court case, Bailey v. United States, in which the Court will examine the scope of permissible non-arrest seizures in the context of a detainment incident to a search warrant. The case offers the Court an opportunity to clarify its holding in Michigan v. Summers--that occupants of premises being searched pursuant to a valid warrant may be detained during the search--by determining whether such a detainment is permissible when the occupants have left the premises

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