Special subgroups of regular semigroups

This work was partially supported by the Portuguese Foundation for Science and Technology through the grant UID/MAT/00297/2013 (CMA).Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.PostprintPeer reviewe

Towards a generalisation of formal concept analysis for data mining purposes

In this paper we justify the need for a generalisation of Formal Concept Analysis for the purpose of data mining and begin the synthesis of such theory. For that purpose, we first review semirings and semimodules over semirings as the appropriate objects to use in abstracting the Boolean algebra and the notion of extents and intents, respectively. We later bring to bear powerful theorems developed in the field of linear algebra over idempotent semimodules to try to build a Fundamental Theorem for K-Formal Concept Analysis, where K is a type of idempotent semiring. Finally, we try to put Formal Concept Analysis in new perspective by considering it as a concrete instance of the theory developed

The Third Way for the Third Sector: Using Design to Transfer Knowledge and Improve Service in a Voluntary Community Sector Organisation

This paper describes a two-year Knowledge Transfer Partnership that concluded in September 2011. Knowledge Transfer Partnerships (KTP) is a UK-wide activity that helps organisations to improve their competitiveness and productivity by making better use of knowledge, technology and skills within universities, colleges and research organisations. This paper details the outcome of a KTP between Age UK Newcastle and Northumbria University’s School of Design that aimed to use Design approaches to improve the charity’s services. This paper will describe the recent context for organisations operating in the Voluntary Community Sector and discuss the relevance of a Design approach to both the improvement of customer services in this circumstance, as well as the transfer of knowledge to a capacity-starved organisation. It will also document how Design was used to achieve both of these aims, and the resulting impact of this engagement on the organisation and stakeholders

On the transition to dripping of an inverted liquid film

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on a periodic domain assuming either a fixed fluid volume or a fixed flow rate for a hierarchy of models: two lubrication models with either linearised curvature or full curvature (the LCM and FCM, respectively), and the full equations of Stokes flow. Of particular interest is the breakdown of travelling-wave solutions as the plate inclination angle is increased. For any fixed volume the LCM reaches the horizontal state where it attains a cosine-shaped profile. For sufficiently small volume, the FCM and Stokes solutions attain a weak Young-Laplace equilibrium profile, the approach to which is described by an asymptotic analysis generalising that of Kalliadasis & Chang (1994) for the LCM. For large volumes, the bifurcation curves for the FCM and Stokes model have a turning point so that the fully inverted state is never reached. For fixed flow rate the LCM blows up at a critical angle that is well predicted by asymptotic analysis. The bifurcation curve for the FCM either has a turning point or else reaches a point at which the surface profile has an infinite slope singularity, indicating the onset of multi-valuedness. The latter is confirmed by the Stokes model which can be continued to obtain overturning surface profiles. Overall the thin-film models either provide an accurate prediction for dripping onset or else supply an upper bound on the critical inclination angle

Congruences associated with inverse transversals

An inverse transversal of a regular semigroup $S$ is an inverse subsemigroup of $S$ that contains a unique inverse $x^\circ$ of every element $x$ of $S$. Here we consider the congruences on such a semigroup, considered as an algebra of type (2, 1). The structure of such semigroups being known, with 'building bricks' the inverse subsemigroup $S^\circ$ and the sub-bands $I = \{xx^\circ; x\in S\},\Lambda = \{x^\circ x; x\in S\}$, we investigate how congruences on $S$ are related to congruences on these building bricks

A Cone Jet-Finding Algorithm for Heavy-Ion Collisions at LHC Energies

Standard jet finding techniques used in elementary particle collisions have not been successful in the high track density of heavy-ion collisions. This paper describes a modified cone-type jet finding algorithm developed for the complex environment of heavy-ion collisions. The primary modification to the algorithm is the evaluation and subtraction of the large background energy, arising from uncorrelated soft hadrons, in each collision. A detailed analysis of the background energy and its event-by-event fluctuations has been performed on simulated data, and a method developed to estimate the background energy inside the jet cone from the measured energy outside the cone on an event-by-event basis. The algorithm has been tested using Monte-Carlo simulations of Pb+Pb collisions at $\sqrt{s}=5.5$ TeV for the ALICE detector at the LHC. The algorithm can reconstruct jets with a transverse energy of 50 GeV and above with an energy resolution of $\sim30$.Comment: 13 pages, 7 figure

A cohort study of influences, health outcomes and costs of patients' health-seeking behaviour for minor ailments from primary and emergency care settings

To compare health-related and cost-related outcomes of consultations for symptoms suggestive of minor ailments in emergency departments (EDs), general practices and community pharmacies

Absolute and convective instabilities in non-local active-dissipative equations arising in the modelling of thin liquid films

Absolute and convective instabilities in a non-local model that arises in the analysis of thin-film flows over flat or corrugated walls in the presence of an applied electric field are discussed. Electrified liquid films arise, for example, in coating processes where liquid films are deposited onto a target surfaces with a view to producing an evenly coating layer. In practice, the target surface, or substrate, may be irregular in shape and feature corrugations or indentations. This may lead to non-uniformities in the thickness of the coating layer. Attempts to mitigate film-surface irregularities can be made using, for example, electric fields. We analyse the stability of such thin-film flows and show that if the amplitude of the wall corrugations and/or the strength of the applied electric field is increased the convectively unstable flow undergoes a transition to an absolutely unstable flo

Towards a Full Census of the Obscure(d) Vela Supercluster using MeerKAT

Recent spectroscopic observations of a few thousand partially obscured galaxies in the Vela constellation revealed a massive overdensity on supercluster scales straddling the Galactic Equator (l $\sim$ 272.5deg) at $cz \sim 18000$km/s. It remained unrecognised because it is located just beyond the boundaries and volumes of systematic whole-sky redshift and peculiar velocity surveys - and is obscured by the Milky Way. The structure lies close to the apex where residual bulkflows suggest considerable mass excess. The uncovered Vela Supercluster (VSCL) conforms of a confluence of merging walls, but its core remains uncharted. At the thickest foreground dust column densities (|b| < 6 deg) galaxies are not visible and optical spectroscopy is not effective. This precludes a reliable estimate of the mass of VSCL, hence its effect on the cosmic flow field and the peculiar velocity of the Local Group. Only systematic HI-surveys can bridge that gap. We have run simulations and will present early-science observing scenarios with MeerKAT 32 (M32) to complete the census of this dynamically and cosmologically relevant supercluster. M32 has been put forward because this pilot project will also serve as precursor project for HI MeerKAT Large Survey Projects, like Fornax and Laduma. Our calculations have shown that a survey area of the fully obscured part of the supercluster, where the two walls cross and the potential core of the supercluster resides, can be achieved on reasonable time-scales (200 hrs) with M32.Comment: 10 pages, 3 figures, accepted for publication, Proceedings of Science, workshop on "MeerKAT Science: On the Pathway to the SKA", held in Stellenbosch 25-27 May 201