On the set of hypercyclic vectors for the differentiation

Let D be the differentiation operator Df = f' acting on the Fréchet space H of all entire functions in one variable with the standard (compact-open) topology. It is known since the 1950’s that the set H(D) of hypercyclic vectors for the operator D is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the set H(D) contains (up to the zero function) a non-trivial subalgebra of H or an infinite-dimensional closed linear subspace of H. In the present article both questions are answered affirmatively.

Use of microtechnologies for intensifying industrial processes

The use of new technologies based on microstructured reactors in industrial processes, including the obtainment of hydrogen peroxide, the catalytic oxidation of ammonia, the utilization of rocket fuels, fine organic synthesis, polymerization, and phase transfer catalysis, were considered. The transition to microtechnologies considerably increases the performance of the process; at the same time, the product yield increases as compared with periodically operating reactors, which allows for a reduction of costs at the separation stage of the reaction mixture and the extraction of the reaction products.

Imprecise probabilistic query answering using measures of ignorance and degree of satisfaction

In conditional probabilistic logic programming, given a query, the two most common forms for answering the query are either a probability interval or a precise probability obtained by using the maximum entropy principle. The former can be noninformative (e.g.,interval [0; 1]) and the reliability of the latter is questionable when the priori knowledge isimprecise. To address this problem, in this paper, we propose some methods to quantitativelymeasure if a probability interval or a single probability is sufficient for answering a query. We first propose an approach to measuring the ignorance of a probabilistic logic program with respect to a query. The measure of ignorance (w.r.t. a query) reflects howreliable a precise probability for the query can be and a high value of ignorance suggests that a single probability is not suitable for the query. We then propose a method to measure the probability that the exact probability of a query falls in a given interval, e.g., a second order probability. We call it the degree of satisfaction. If the degree of satisfaction is highenough w.r.t. the query, then the given interval can be accepted as the answer to the query. We also prove our measures satisfy many properties and we use a case study to demonstrate the significance of the measures. © Springer Science+Business Media B.V. 2012

On the Condition Number Distribution of Complex Wishart Matrices

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

Models of Mental Health

A good understanding of the different theoretical models is essential when working in the field of mental health. Not only does it help with understanding experiences of mental health difficulties and to find meaning, but it also provides a framework for expanding our knowledge of the field.

As part of the Foundations of Mental Health Practice series, this book provides a critical overview of the theoretical perspectives relevant to mental health practice. At the core of this book is the idea that no single theory is comprehensive on its own and each theory has its limitations. Divided in to two parts, Part I explores traditional models of mental health and covers the key areas: bio-medical perspectives, psychological perspectives and social perspectives, whilst Part II looks at contemporary ideas that challenge and push these traditional views. The contributions, strengths and limitations of each model are explored and, as a result, the book encourages a more holistic, open approach to understanding and responding to mental health issues.

Together, these different approaches offer students and practitioners a powerful set of perspectives from which to approach their study and careers. Each model is covered in a clear and structured way with supporting exercises and case studies. It is an essential text for anyone studying or practising in the field of mental health, including social workers, nurses and psychologists.

General practitioners’ management of the long-term sick role

In this paper, we use qualitative research techniques to examine the role of general practitioners in the management of the long-term sickness absence. In order to uncover the perspectives of all the main agents affected by the actions of general practitioners, a case study approach focussing on one particular employment sector, the public health service, is adopted. The role of family physicians is viewed from the perspectives of health service managers, occupational health physicians, employees / patients, and general practitioners. Our argument is theoretically framed by Talcott Parsons’s model of the medical contribution to the sick role, along with subsequent conceptualisations of the social role and position of physicians. Sixty one semi-structured interviews and three focus group interviews were conducted in three Health and Social Care Trusts in Northern Ireland between 2010 and 2012. There was a consensus among respondents that general practitioners put far more weight on the preferences and needs of their patients than they did on the requirements of employing organisations. This was explained by respondents in terms of the propinquity and longevity of relationships between doctors and their patients, and by the ideology of holistic care and patient advocacy that general practitioners viewed as providing the foundations of their approach to patients. The approach of general practitioners was viewed negatively by managers and occupational health physicians, and more positively by general practitioners and patients. However, there is some evidence that general practitioners would be prepared to forfeit their role as validators of sick leave. Given the imperatives of both state and capital to reduce the financial burden of long-term sickness, this preparedness puts into doubt the continued role of general practitioners as gatekeepers to legitimate long-term sickness absence.

Characterisations of the weak expectation property

We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C∗ -algebras. By Kirchberg’s work on WEP, these results give new formulations of Connes’ embedding problem.

The Science of a Lost Medieval Graveyard: The Ballyhanna Research Project

he Science of Lost Medieval Gaelic Graveyard tells the story of the discovery in 2003 of a graveyard and the foundations of a small forgotten stone church at Ballyhanna, in Ballyshannon, Co. Donegal, as part of the N15 Bundoran–Ballyshannon Bypass archaeological works. This led to the excavation of one of the largest collections of medieval burials ever undertaken on this island. Over 1,200 individuals were excavated from the site at Ballyhanna during the winter of 2003–4, representing 1,000 years of burial through the entire Irish medieval period. The discovery led to the establishment of a cross-border research collaboration—the Ballyhanna Research Project—between Queen’s University Belfast and the Institute of Technology, Sligo, which has brought to life this lost Gaelic graveyard.

This book shows how cutting-edge scientific research may aid our understanding and interpretation of archaeology and reveal new insights into past societies. For example, the use of ancient DNA analysis represented the first biomolecular archaeological evaluation of a medieval population to date and provided evidence that cystic fibrosis was much less prevalent in the medieval period than today. The Science of Lost Medieval Gaelic Graveyard is about a community who lived in Gaelic Ireland, about their lifestyles, health and diet. It tells us of their deaths and of their burial traditions, and through examining all of these aspects, it reveals the ebb and flow of their lives.

The book is accompanied by a CD-ROM which includes supplementary information from the Ballyhanna Research Project and the original excavation and survey reports for all of the archaeological sites on the N15 Bundoran–Ballyshannon Bypass.

A kinetic analysis methodology to elucidate the roles of metal, support and solvent for the hydrogenation of 4-phenyl-2-butanone over Pt/TiO2

The rate and, more importantly, selectivity (ketone vs aromatic ring) of the hydrogenation of 4-phenyl-2-butanone over a Pt/TiO2 catalyst have been shown to vary with solvent. In this study, a fundamental kinetic model for this multi-phase reaction has been developed incorporating statistical analysis methods to strengthen the foundations of mechanistically sound kinetic models. A 2-site model was determined to be most appropriate, describing aromatic hydrogenation (postulated to be over a platinum site) and ketone hydrogenation (postulated to be at the platinum–titania interface). Solvent choice has little impact on the ketone hydrogenation rate constant but strongly impacts aromatic hydrogenation due to solvent-catalyst interaction. Reaction selectivity is also correlated to a fitted product adsorption constant parameter. The kinetic analysis method shown has demonstrated the role of solvents in influencing reactant adsorption and reaction selectivity.

A Pilot Study of Reciprocal Peer Tutoring in Irish Medium Schools

A pilot study to investigate the effects of mathematics peer tutoring in Irish medium primary schools was undertaken. Five schools and 90 students took part in the pilot. Materials and resources that had previously been shown to work in English medium Scottish schools were translated into Irish by CCEA. Irish medium teachers attended three professional development days. Teachers implemented the peer tutoring techniques during mathematics lessons during a period of 16 weeks. Changes in attainment were measures with an Irish translation of the Scottish Survey of Achievement Mathematics Test. Results were positive. Student attainment was significantly raised during the 16-week implementation period by over one standard deviation. This equated to one-year’s worth of mathematics development during this time period. Results must be treated with caution. No control group was used in the pilot study. However, results are very promising and indicate that reciprocal role peer tutoring may be a useful pedagogy in Irish medium education. Further work would be required to establish this definitively.

Mathematics Learning Support in Ireland in 2015

The provision of mathematics learning support in higher-level institutions on the island of Ireland has developed rapidly in recent times with the number of institutions providing some form of support doubling in the past seven years. The Irish Mathematics Learning Support Network aims to inform all mathematics support practitioners in Ireland on relevant issues. Consequently it was decided that a detailed picture of current provision was necessary. A comprehensive online survey was conducted to amass the necessary data. The ultimate aim of the survey is to benefit all mathematics support practitioners in Ireland, in particular those in third-level institutions who require further support to enhance the mathematical learning experience of their students. The survey reveals that the majority of Irish higher-level institutions provide mathematics learning support to some extent, with 65% doing so through a support centre. Learners of service mathematics are the primary users: first-year science, engineering and business undergraduates, with non-traditional students being a sizeable element. Despite the growing recognition for the need to offer mathematics learning support almost half of the centres are subject to annual review. Further, less than half the support offerings have a dedicated full-time manager, while 60% operate with a staff of five or fewer. The elevation of mathematics support as a viable and worthwhile career in order to attract and retain high quality staff is seen by many respondents as the crucial next phase of development.