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

Spectral bounds for the cutoff Coulomb potential

The method of potential envelopes is used to analyse the bound-state spectrum of the Schroedinger Hamiltonian H = -Delta -v/(r+b), where v and b are positive. We established simple formulas yielding upper and lower energy bounds for all the energy eigenvalues.Comment: 11 pages, 2 figure

Relativistic N-boson systems bound by pair potentials V(r_{ij}) = g(r_{ij}^2)

We study the lowest energy E of a relativistic system of N identical bosons bound by pair potentials of the form V(r_{ij}) = g(r_{ij}^2) in three spatial dimensions. In natural units hbar = c = 1 the system has the semirelativistic `spinless-Salpeter' Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} + \sum_{j>i=1}^N g(|r_i - r_j|^2), where g is monotone increasing and has convexity g'' >= 0. We use `envelope theory' to derive formulas for general lower energy bounds and we use a variational method to find complementary upper bounds valid for all N >= 2. In particular, we determine the energy of the N-body oscillator g(r^2) = c r^2 with error less than 0.15% for all m >= 0, N >= 2, and c > 0.Comment: 15 pages, 4 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

Deaf children need language, not (just) speech

Deaf and Hard of Hearing (DHH) children need to master at least one language (spoken or signed) to reach their full potential. Providing access to a natural sign language supports this goal. Despite evidence that natural sign languages are beneficial to DHH children, many researchers and practitioners advise families to focus exclusively on spoken language. We critique the Pediatrics article ‘Early Sign Language Exposure and Cochlear Implants’ (Geers et al., 2017) as an example of research that makes unsupported claims against the inclusion of natural sign languages. We refute claims that (1) there are harmful effects of sign language and (2) that listening and spoken language are necessary for optimal development of deaf children. While practical challenges remain (and are discussed) for providing a sign language-rich environment, research evidence suggests that such challenges are worth tackling in light of natural sign languages providing a host of benefits for DHH children – especially in the prevention and reduction of language deprivation.Accepted manuscrip

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])

Bounds for Hamiltonians with arbitrary kinetic parts

A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds. A semiclassical interpretation of the generic formula obtained for the eigenvalues supports a new definition of the effective particle mass used in solid state physics. An analytical toy model with a Gaussian dependence in the momentum is studied in order to check the validity of the method.Comment: Improved version with new refernce

A chain theorem for 4-connected matroids

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Challenges to Slovakia and Poland health policy decisions: use of investment treaties to claim compensation for reversal of privatisation/liberalisation policies

Investment treaties, and possibly the EU Treaty itself, are being used by multinational companies Penta and Eureko to try and force the Slovak government to pay compensation for reversing health privatisation and liberalisation policies. Similar action has been used against the Polish government by Eureko to win compensation worth nearly 2 billion Euros and a policy commitment to further privatisation