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Let $w$ be a word in alphabet $\{x,D\}$ with $m$ $x$'s and $n$ $D$'s. Interpreting "$x$" as multiplication by $x$, and "$D$" as differentiation with respect to $x$, the identity $wf(x) = x^{m-n}\sum_k S_w(k) x^k D^k f(x)$, valid for any smooth function $f(x)$, defines a sequence $(S_w(k))_k$, the terms of which we refer to as the {\em Stirling numbers (of the second kind)} of $w$. The nomenclature comes from the fact that when $w=(xD)^n$, we have $S_w(k)={n \brace k}$, the ordinary Stirling number of the second kind. Explicit expressions for, and identities satisfied by, the $S_w(k)$ have been obtained by numerous authors, and combinatorial interpretations have been presented. Here we provide a new combinatorial interpretation that retains the spirit of the familiar interpretation of ${n \brace k}$ as a count of partitions. Specifically, we associate to each $w$ a quasi-threshold graph $G_w$, and we show that $S_w(k)$ enumerates partitions of the vertex set of $G_w$ into classes that do not span an edge of $G_w$. We also discuss some relatives of, and consequences of, our interpretation, including $q$-analogs and bijections between families of labelled forests and sets of restricted partitions., Comment: To appear in Eur. J. Combin., doi:10.1016/j.ejc.2014.07.002

The recent Disneyland measles outbreak brought national attention to a growing problem: vaccine refusal—herd immunity is no longer a reality in many communities. Only 70% of children aged 19–35 months are up-to-date on immunizations, and in some communities, more than a quarter of school-age children have exemptions on file (www.doh.wa.gov/Portals/1/ Documents/Pubs/348-247-SY2014-15-ImmunizationMaps. pdf). Although they vary across the ideological spectrum, vaccine refusers tend to be well educated, white, and more affluent than people who typically experience health disparities. Prior studies have found that a diversity of motivations drive vaccine refusal, including fear that vaccines cause autism, concerns over toxins, beliefs about the benefits of measles to the immune system, distrust of government, distrust of pharmaceutical companies, and preference for a “natural” lifestyle. Arguments recommended by physicians’ groups and public health agencies to counter these beliefs do not always change minds; even parents who indicate high trust in their pediatricians may not follow doctors’ recommendations. Ultimately, people “persuade themselves to change attitudes and behavior,” and communicators must tailor messages to the beliefs, attitudes, and motivations of particular audience segments. Effective health communication about vaccines requires answering three questions

The objective of this study was to evaluate the factor structure, validity, and reliability of the Compulsive Exercise Test (CET) in an adolescent clinical eating disorder population. The data source was the Helping to Outline Paediatric Eating Disorders (HOPE) Project, a prospective ongoing registry study comprising consecutive pediatric tertiary eating disorder referrals. Adolescents (N=104; 12-17years) with eating disorders completed the CET and other measures. Factor structure, convergent validity, and internal consistency were evaluated. Despite failing to identify a factor structure, the study provided clear evidence of the multidimensionality of the measure. The total score correlated significantly with measures of eating pathology, perfectionism, and frequency of exercise for shape and weight control (r=0.32-0.70, ps0.05). More research into the multidimensional nature of compulsive exercise in clinical populations is needed. Further, research into compulsive exercise offers promise as an addition to existing cognitive behavioral models and treatments for eating disorders.

The primary goal of this investigation was to derive a set of expressions that can be used to calculate the amphibole-melt partitioning behavior of the rare earth elements (REE) and the high field strength elements (HFSE) in natural systems. To supplement the existing data set on basaltic systems, we conducted experiments on systems where amphibole was in equilibrium with dacitic, tonalitic and low Si rhyolitic melts. These experiments, doped with La, Sm, Gd, Lu, Ta, Nb, Y, Zr, and Hf, were run at pressures of 2 and 5 kbar, temperatures between 900°C and 945°C, and oxidation conditions ranging from QFM-1 to NiNiO+1. The partitioning data obtained in this study were combined with published data to calculate two sets of expressions describing trace element partitioning. The first set models the partitioning of trace elements into amphibole using temperature, pressure and several compositional parameters, including the compositionally-compensated partition coefficients of Ti, Al, Caand SiO2, and the exchange of Fe and Mg between the crystal and the melt (DMg/DFe). The second set of expressions are slightly less precise, but require no specific knowledge of P, T, or fO2 and, for application to natural systems, can be constructed solely on the basis of information available from standard electron microprobe analyses. These expressions predict amphibole-melt partition coefficients for REE and HFSE within an internal precision of 14–40% (relative) for alkali basalt to low Si rhyolite, from 850°C to 1100°C, 2–20 kbar and oxygen fugacity from QFM-1 to NiNiO+1. Partition coefficients calculated from the expressions derived in this study were used to model the partial melting and fractional crystallization of a hypothetical amphibolite and hydrous melt, respectively. Fractionation and/or melting in amphibole-bearing systems produces a magma with a convex upward REE pattern, a characteristic common to many hornblende-bearing dacites. However, the removal or addition of an amphibole component cannot produce the strong HFSE depletion relative to the REE observed in many arc magmas.

The Armed Forces Institute of Pathology (AFIP) is well known for providing expert pathology in many specialties and educational courses for civilian and military personnel. Some of the departments at the AFIP have also developed expertise in various advanced laboratory techniques for diagnosis and research that are applicable to dermatology and are not available at most medical centers.

Summary Patellofemoral pain has been considered a difficult condition to manage effectively. Clinical trials of the McConnell programme have demonstrated excellent results from this approach. The programme aims to identify and treat the biomechanical factors which may be adversely effecting patellar tracking.

A discounted cash flow appraisal of a cryogenic-grinding (C-G) plant suitable for recycling scrap steel-radial automobile tyres is performed. The results of this appraisal are analysed using a sensitivity analysis to identify the critical variables and their break-even values for making the plant profitable. It is concluded that the C-G plant not only faces the problem of whether the initially assumed values for selling price, variable cost and volume could be achieved in the light of the structure of the rubber recycling industry but also whether the values could be achieved for sufficiently long periods for the plant to survive and become profitable. (U.K.).

Theoretical equations are established relating the transmissibility of a liquid-filled, flexible open-cell foam antivibration mount to the dimensions of the mount and the geometry and mechanical properties of the foam. The transmissibility of a foam mount is calculated by using experimentally determined values for the system parameters and compared with that for solid rubber mounts.

The granulation and re-use of conversion scrap is widespread in the plastic product manufacturing industry. However, there seems to have been little or no discussion in the literature of the economics of different recycling routes or how the incorporation of granulate affects unit cost of product manufactured to a particular design specification. This paper briefly describes different in-house size reduction arrangements: closed-loop, machine-side and centralised. An investment appraisal is made of machine-side situations using NPV analysis, for three commercially available granulators, having a wide range of throughputs. A mathematical model is established and used to predict cost relationships in products incorporating different amounts of scrap. In this model the breaking load is employed as the design criterion, assuming that the strength properties of the materials follow the simple law of mixtures for composites. The applicability of this law to these material systems is examined and an analysis made using an expression assuming an exponentional relationship between breaking stress and volume fraction of granulate.

This article briefly surveys the changes in taxation and capital investment allowances introduced in the 1984 Finance Act and discusses their likely impact on the role of investment and also the practical problems faced by investment decision-makers during the transition period. The authors present an investment appraisal model supported by a computer programme, designed to evaluate projects under a regime of varying tax rates and capital allowances. The model is applied to a ‘standard project’ to demonstrate the impact of the recent taxation changes on the profitability of investment in plant and machinery. Generally, the impact is to reduce the post-tax profitability of such investment save for exceptionally attractive ventures.