Relations Between Coefficients of Fractional Parentage

For each of the (9/2), (11/2) and (13/2) single j shells we have only one state with J=j V=3 for a five particle system. For four identical particles there can be more than one state of seniority four. We note some ``ratio'' relations for the coefficients of fractional parentage for the four and five identical particle systems

Investigation of polymeric coatings by electrodeless discharge Final report

Polymeric films deposited by electrical discharge from hydrocarbon

Educational Attainment and Skill Utilisation in the Irish Labour Market: An EU Comparison. Quarterly Economic Commentary Special Article, WINTER 2017

In recent years the Irish economy has experienced strong economic growth accompanied by significant improvements in the labour market. The unemployment rate in the second quarter of 2017 stands at 6.2 per cent (CSO, 2017), its lowest rate in nine years. In light of these improvements in the labour market, we examine the nature of current employment in Ireland with respect to the intensity of use of certain skills and the mismatch between the skills possessed by employees and those required to do their jobs. Furthermore, we consider the possible future sources of skilled labour supply by examining the characteristics of those currently unemployed and inactive in the labour market, as well as the ability of Ireland to attract high-skilled migrant workers. Our analysis reveals a high degree of skill underutilisation among Irish employees. The percentage of Irish workers reporting education or skill levels in excess of those required to do their job is the third highest of 28 EU countries. Our findings also indicate that, as was the case in recent decades, immigration may play an important role as a source of skilled labour in a tightening labour market

Enabling local rapid change solutions to the Climate Emergency

Three quarters of UK Local Authorities (LAs) have declared Climate Emergencies. Most include an ambition for carbon neutrality by 2030. Yet a lack of clarity on a national policy framework through to 2030 means that LAs now face the challenge of creating an enabling environment to respond to urgent Climate Emergency targets. This paper reviews the implications of the LA Climate Emergency Declarations for local policy making in respect of low carbon retrofit. It will focus on evidence from a council whose dedicated project team is creating and implementing 2030 Climate response strategies, as well as built environment practitioners who have expertise to deliver retrofit services. Using documentary evidence and expert testimony, this paper will explore the gaps in creating an enabling environment/policy roadmap to 2030, the role might local government play in delivering large scale domestic retrofit, and how to align the various stakeholder groups. The paper finds that despite the simplistic term ‘retrofit’, the domestic retrofit landscape is far from simple. It is not a homogenous entity, rather a complex, multi-layered and segmented eco-system. We propose reviewing this segmentation through the lens of ‘first-mover’ which would help clarify where efforts should be focused, and which measures could be taken to accelerate consumer engagement. The authors discover there is potential for Local Authorities to develop novel approaches to retrofit processes, by taking the role of ‘middle actor’, reshaping the customer journey and engaging a range of stakeholders to stimulate local economies and deliver on social and environmental goals. Open collaboration with third sector organisations can provide access to research, resources, and networks to help deploy rapid change solutions

Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density

We argue that a technique called analytic perturbation theory leads to a well-defined method for analytically continuing the running coupling constant from the spacelike to the timelike region, which allows us to give a self-consistent definition of the running coupling constant for timelike momentum. The corresponding $\beta$-function is proportional to the spectral density, which confirms a hypothesis due to Schwinger.Comment: 11 pages, 2 figure

Computer recommendations for an automatic approach and landing system for V/STOL aircraft. Volume 2 - Equations

Automatic approach and landing system for V/STOL aircraf

Dirac Cat States in Relativistic Landau Levels

We show that a relativistic version of Schrodinger cat states, here called Dirac cat states, can be built in relativistic Landau levels when an external magnetic field couples to a relativistic spin 1/2 charged particle. Under suitable initial conditions, the associated Dirac equation produces unitarily Dirac cat states involving the orbital quanta of the particle in a well defined mesoscopic regime. We demonstrate that the proposed Dirac cat states have a purely relativistic origin and cease to exist in the non-relativistic limit. In this manner, we expect to open relativistic quantum mechanics to the rich structures of quantum optics and quantum information.Comment: Revtex4, color figures, submitted for publicatio

Taming Landau singularities in QCD perturbation theory: The analytic approach 2.0

The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools together with key applications. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion's electromagnetic form factor in the spacelike region and the Higgs-boson decay into a $b\bar b$ pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the four-loop level an accuracy of the order of 1%, avoiding difficulties inherent in the standard perturbative expansion. The obtained results are compared with estimates from fixed-order and contour-improved QCD perturbation theory. Using the brand-new Higgs mass value of about 125 GeV, measured at the Large Hadron Collider (CERN), a prediction for $\Gamma_{H\to b\bar{b}}=2.4 \pm 0.15 {\rm MeV}$ is extracted.Comment: v3: 23 pages, 7 figures, Invited topical article published in Particles and Nuclei with update using the CERN Higgs discovery. Abridged version presented as plenary talk at International Conference on Renormalization Group and Related Topics (RG 2008), Dubna, Russia, September 1 - 5, 2008. v4 typo in Eq. (3) correcte