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])

Anti-Bourgeois Theory

In his celebrated 2009 memoir Returning to Reims, the Parisian intellectual and theorist Didier Eribon travels home for the first time in thirty years following the death of his father. There he tries to account for the change in politics of his working class family over the period he has been away: from supporting the Communist Party to voting for the National Front. But Eribon also discusses the transition he himself has undergone as a result of having escaped his working class culture and environment through education, and how this has left him unsure whom it is he is actually writing for. He may be addressing the question of what it means to grow up poor and gay, however he is aware few working class people are ever likely to read his book.At the same time, Eribon emphasizes that his non-conforming identity has left him with a sense of just how important it is to display a ‘lack of respect for the rules’ of bourgeois liberal humanist ‘decorum that reign in university circles’, and that insist ‘people follow established norms regarding “intellectual debate” when what is at stake clearly has to do with political struggle’. Together with his friend Édouard Louis and partner Geoffroy de Lagasnerie, Eribon wants to ‘rethink’ the antihumanist theoretical tradition of Foucault, Derrida, Cixous et al. to produce a theory ‘in which something is at stake’: a theory that speaks about ‘class, exploitation, violence, repression, domination, intersectionality’, and yet has the potential to generate the same kind of power and excitement as ‘a Kendrick Lamar concert’. With ‘Anti-Bourgeois Theory’ I likewise want to reinvent what it means to theorise by showing a certain lack of respect for the rules of bourgeois decorum the university hardly ever questions. I want do so, however, by also breaking with those bourgeois liberal humanist conventions of intellectual debate that – for all his emphasis on rebelling ‘in and through’ the technologies of knowledge production – continue to govern the antihumanist theoretical tradition Eribon and his collaborators are associated with. Included in these conventions are culturally normative ideas of the human subject, the proprietorial author, the codex print book, critical reflection, linear thought, the long-form argument, self-expression, originality, creativity, fixity and copyright. I will argue that even the current landfill of theoretical literature on the posthuman and the Anthropocene is merely a form of bourgeois liberal humanism that is padded with nonhuman stuffing – technologies, objects, animals, insects, plants, fungi, compost, microbes, stones, geological formations – to make it appear different. Can we not do better than this?<br/

State aid and public services in Europe: the limitations of the EC package

This critique of the EC 2005 proposals on state aid and the implications for public services presents the historical and legal context, their impact on the expansion of private sector activity in the market for public services, a critical analysis of the proposals, and a discussion contrasting the route of encouraging competitive tendering with the possibility of exempting public services operating in the general interest