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

An Analysis of Efficiency Improvements in Room Air Conditioner

In 1976, the U.S. Congress passed the National Energy Conservation Policy Act (NECPA) P.L. 95-619, which requires the imposition of minimum efficiency standards on eight major household appliances. The law required that the proposed standards be both technologically feasible and economically justifiable. One of the appliances for standards consideration was the room air conditioner (RAC). In 1980 the Department of Energy first proposed minimum efficiency standards on new room air conditioners on seven other appliances[1]. In 1983, "no standard" standards were issued by DOE for all eight appliances because the energy savings of standards were not significant enough to justify minimum efficiency standards.[2] The "no standard" standards were challenged in court ion 1984. In 1985, the "no standard" standards were ruled unlawful [3]. In 1983 However, due to a court challenge of the 1982 standards, they were not allowed. In 1987, Congress passed the National Appliance Energy Conservation Act (NAECA), P.L. 100-12 which specified minimum efficiency levels for major appliances, including RACs (Table 1.1). The minimum efficiency standards for RACs must be met by January 1, 1990. Periodically, the Department of Energy can publish amendments to the standards after analyses have been performed to determine their technical and economic feasibility. This report summarizes the results of an engineering analysis used to evaluate the technical feasibility of improving the efficiency of RACs. The objectives of this study included: (1) evaluation and selection of a suitable RAC design model, (2) selection of design options that can be used to improve RAC performance, and (3) development of high efficiency RAC designs

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

Hierarchical Dobinski-type relations via substitution and the moment problem

We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). They turn out to be of Sheffer-type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a)the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.Comment: 14 pages, 31 reference

An Analysis of Efficiency Improvements in Residential Sized Heat Pumps and Central Air Conditioners

This report summarizes: (1) the performance improvements possible for central air conditioners and heat pumps using conventional design improvements, (2) the development of a methodology for estimating the seasonal performance of variable speed heat pumps and air conditioners, and (3) the estimated maximum efficiency levels that are technically feasible for variable speed heat pumps and air conditioners. This report builds on the work summarized in an earlier report from the Energy Systems Laboratory[2]

Exact and explicit probability densities for one-sided Levy stable distributions

We study functions g_{\alpha}(x) which are one-sided, heavy-tailed Levy stable probability distributions of index \alpha, 0< \alpha <1, of fundamental importance in random systems, for anomalous diffusion and fractional kinetics. We furnish exact and explicit expression for g_{\alpha}(x), 0 \leq x < \infty, satisfying \int_{0}^{\infty} exp(-p x) g_{\alpha}(x) dx = exp(-p^{\alpha}), p>0, for all \alpha = l/k < 1, with k and l positive integers. We reproduce all the known results given by k\leq 4 and present many new exact solutions for k > 4, all expressed in terms of known functions. This will allow a 'fine-tuning' of \alpha in order to adapt g_{\alpha}(x) to a given experimental situation.Comment: 4 pages, 3 figures and 1 tabl

Quantum statistical properties of some new classes of intelligent states associated with special quantum systems

Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems with a known discrete spectrum as well as the generalized coherent states with known nonlinearity function $f (n)$. As some physical appearance of the proposed formalism, a few new classes of intelligent states associated with \textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'} and \textit{`hydrogen-like spectrum'} have been realized. Finally, the nonclassicality of the obtained states has been investigated. To achieve this purpose the quantum statistical properties using the Mandel parameter and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been established numerically.Comment: 13page

Low protein wheat for bread making

Nitrogen (N) is the major mineral that determines crop yield, but it is also an important determinant of grain quality, particularly in wheat. It is required for the synthesis of grain proteins, with gluten forming the major protein fraction in wheat grain. Because of the high protein content required for bread making, the requirement for N applied to bread-making wheats may be above the optimum required for yield, by up to 50 kg N/ha. For example, Dampney et al. (1995) reported that to produce grain containing 13% protein, about 60 kgN/ha above the yield optimum was required. N fertiliser is a major cost for farmers, with a high-energy requirement for manufacture and potentially harmful environmental footprint. Therefore, it is important to reduce the requirement for producing breadmaking wheat, either by improving the efficiency of N use within the plant or by developing new types of wheat that allow the use of lower protein contents for bread making. This project focused on the latter strategy. It aimed to identify and characterise types of wheat with good bread-making quality at low grain protein content. Forty wheat genotypes were grown on 6 sites for 2 years, with a sub-set of 30 grown on the same sites for a third year. All were grown in 3 randomised replicate plots and at 2 levels of N fertilisation: 150 kgN/ha (low) and 250 kgN/ha (conventional). This generated over 4000 grain samples that were analysed for protein content. Samples from 4 sites were bulked for detailed analysis, excluding sites associated with technical problems or unusually high or low contents of protein or responses to fertilisation. Whereas all 40 genotypes were studied in the first year, the number was reduced to 30 in year 2 and to 20 in year 3, based on the analysis of the samples from years 1 and 2, respectively. Campden BRI milled the samples and carried out Extensograph and Farinograph analyses of all flours. The mixing and bread-making performances were subsequently determined by 6 commercial partners, who used three different bread-making processes. SE-HPLC analyses of gluten polymer size distribution was determined on all samples from year 1 and the low N samples from years 2 and 3. This comparison showed that five cultivars (called Group 1) performed well at both high and low N and over all three years: Crusoe and Gallant (current UK nabim Group 1), Rumor and Nelson (German varieties bred to show high quality at low grain protein) and Genius (Danish bread-making cultivar). In addition, two cultivars (called Group 2) performed better when grown at low N than at high N: Skyfall (current UK nabim Group 1 cultivar) and Mv Lucilla (Hungarian high protein breadmaking cultivar). A comparison between these two groups of cultivars and the whole set of cultivars was carried out focusing on four parameters: grain N, grain protein deviation (GPD), gluten protein profiles by SE-HPLC and dough rheology (R/E) measured by Extensograph. This showed that: 1. The selected (Groups 1 and 2) wheats had higher %N, GPD, dough elasticity and proportions of glutenin polymers ((%F1+%F2)/(%F3+%F4)) than the non-selected cultivars. 2. In addition, the Group 2 wheats (which performed better at low N) had higher proportions of high molecular weight glutenin polymers (%F1, (%F3+%F4)/%F1). Although these cultivars include two German lines bred to perform well at low N, they also include three highly successful recent UK cultivars: Crusoe, Gallant and Skyfall. Hence, modern cultivars, which have been selected for performance in high-input systems, may also perform well under low N inputs. We conclude that good bread-making performance at low N fertiliser resulted from two factors: efficient translocation of N into the grain and increased proportions of glutenin in gluten, which resulted in greater dough elasticity. Breeding should, therefore, focus on increasing the efficiency of N use combined with high gluten protein elasticity

Quantum information and triangular optical lattices

The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or fermionic, can be employed to generate a variety of novel spin-1/2 models that include effective three-spin interactions. Such interactions can be employed to simulate specific one or two dimensional physical systems that are of particular interest for their condensed matter and entanglement properties. In particular, connections between the scaling behaviour of entanglement and the entanglement properties of closely spaced spins are drawn. Moreover, three-spin interactions are well suited to support quantum computing without the need to manipulate individual qubits. By employing Raman transitions or the interaction of the atomic electric dipole moment with magnetic field gradients, one can generate Hamiltonians that can be used for the physical implementation of geometrical or topological objects. This work serves as a review article that also includes many new results.Comment: 17 pages, 16 figues, based on talk presented by J. K. Pachos at CEWQO 200