Dobinski-type relations: Some properties and physical applications

We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.Comment: 7 pages, 1 figur

Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Combinatorial approach to generalized Bell and Stirling numbers and boson normal ordering problem

We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of Stirling and Bell numbers. The recurrence relations and closed-form expressions (Dobiski-type formulas) are obtained for these quantities by both algebraic and combinatorial methods. By extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs. This link provides a combinatorial interpretation of the numbers arising in this normal ordering problem.Comment: 10 pages, 5 figure

Some useful combinatorial formulae for bosonic operators

We give a general expression for the normally ordered form of a function F(w(a,a*)) where w is a function of boson annihilation and creation operators satisfying [a,a*]=1. The expectation value of this expression in a coherent state becomes an exact generating function of Feynman-type graphs associated with the zero-dimensional Quantum Field Theory defined by F(w). This enables one to enumerate explicitly the graphs of given order in the realm of combinatorially defined sequences. We give several examples of the use of this technique, including the applications to Kerr-type and superfluidity-type hamiltonians.Comment: 8 pages, 3 figures, 17 reference

Factors that determine the effectiveness of peer interventions in prisons in England and Wales

Epidemiological assessment of the prison population globally shows undeniable health need, with research evidence consistently demonstrating that the prevalence of ill health is higher than rates reported in the wider community. Since a meeting convened by the World Health Organisation in the mid-1990s, prisons have been regarded as legitimate settings for health promotion and a myriad of interventions have been adopted to address prisoners’ health and social need. Peer-based approaches have been a common health intervention used within the prison system, but despite their popularity little evidence exists on the approach. This paper presents findings from an expert symposium – part of a wider study which included a systematic review – designed to gather expert opinion on whether and how peer–based approaches work within prisons and if they can contribute to improving the health of prisoners. Experts were selected from various fields including the prison service, academic research and third sector organisations. Expert evidence suggested that the magnitude of success of peer interventions in prison settings is contingent on understanding the contextual environment and a recognition that peer interventions are co-constructed with prison staff at all levels of the organisation. Implications for developing peer-based interventions in prison are given which assist in developing the concept, theory and practice of the health promoting prison

Exponential Operators, Dobinski Relations and Summability

We investigate properties of exponential operators preserving the particle number using combinatorial methods developed in order to solve the boson normal ordering problem. In particular, we apply generalized Dobinski relations and methods of multivariate Bell polynomials which enable us to understand the meaning of perturbation-like expansions of exponential operators. Such expansions, obtained as formal power series, are everywhere divergent but the Pade summation method is shown to give results which very well agree with exact solutions got for simplified quantum models of the one mode bosonic systems.Comment: Presented at XIIth Central European Workshop on Quantum Optics, Bilkent University, Ankara, Turkey, 6-10 June 2005. 4 figures, 6 pages, 10 reference

Building Capacity in the Zambian Mental Health Workforce through Engaging College Educators: Evaluation of a Development Partnership in Higher Education (DelPHe) project

yesBetween 2008 and 2011 academic teaching staff from Leeds Beckett University (UK) and Chainama Hills College of Health Sciences (Zambia) worked together on a Development Partnership in Higher Education (DelPHe) project funded by the Department for International Development (DFID) via the British Council. The partnership focused on “up-scaling” the provision of mental health education which was intended to build capacity through the delivery of a range of workshops for health educators at Chainama College, Lusaka. The project was evaluated on completion using small focus group discussions (FGDs), so educators could feedback on their experience of the workshops and discuss the impact of learning into their teaching practice. This chapter discusses the challenges of scaling up the mental health workforce in Zambia; the rationale for the content and delivery style of workshops with the health educators and finally presents and critically discusses the evaluation findings.Department for International Development (DFID) via the British Counci

Gradients in compositions in the starchy endosperm of wheat have implications for milling and processing

Background: Wheat is the major food grain consumed in temperate countries. Most wheat is consumed after milling to produce white flour, which corresponds to the endosperm storage tissue of the grain. Because the starchy endosperm accounts for about 80% of the grain dry weight, the miller aims to achieve flour yields approaching this value. Scope and approach: Bioimaging can be combined with biochemical analysis of fractions produced by sequential pearling of whole grains to determine the distributions of components within the endosperm tissue. Key findings and conclusions: This reveals that endosperm is not homogeneous, but exhibits gradients in composition from the outer to the inner part. These include gradients in both amount and composition. For example, the content of gluten proteins decreases but the proportion of glutenin polymers increases from the outside to the centre of the tissue. However, the content of starch increases with changes in the granule size distribution, the proportions of amylose and amylopectin, and their thermal properties. Hence these parts of the endosperm differ in the functional properties for food processing. Gradients also exist in minor components which may affect health and processing, such as dietary fibre and lipids. The gradients in grain composition are reflected in differences in the compositions of the mill streams which are combined to give white flour (which may number over 20). These differences could therefore be exploited by millers and food processors to develop flours with compositions and properties for specific end uses

Preface (to EuroCereal 2011 special issue)

None available (preface)