Suicide in later life is a pressing public health concern, which has likely been exacerbated by the COVID-19 pandemic. Many older adults who need mental health treatment do not have access to necessary services and training for mental health providers to support older adults experiencing suicidality is limited. One solution is developing interventions based in a public health approach to suicide prevention, whereby natural helpers who provide community services are mobilised to respond to older persons-at-risk. Home-delivered meal (HDM) services, for example, are one effective means to reach older adults who are isolated due to being homebound and may be instrumental in preventing suicide. This study examined the experiences of 20 HDM volunteers who received Applied Suicide Intervention Skills Training (ASIST), an evidence-based suicide intervention programme. Phenomenological analysis yielded findings centred on three areas demonstrating the impact of the ASIST training on HDM volunteers: putting asist skills into practice; response to ASIST skills; and role transformation. Implications for integrating suicide prevention efforts with HDM services and directions for future research are discussed.

Spherulitic and felted green to brown minerals are described from various volcanic rocks of the Western Ochils, Stirlingshire. They fill amygdales and replace pyroxenes and appear to be an interlayered series of sheet silicates from celadonite to vermiculite. The minerals are hydrothermal in origin and suggest the presence of a potassium-rich hydrous fluid at a late stage in the volcanic history.

Grey seals (Halichoerus grypus) are a species of conservation concern that require Marine Protected Area management and population status assessment under the EU Habitats Directive. Aerial surveys are commonly used to monitor grey seal pup production at their globally important UK colonies. However, in Wales more than half of pups are born in cryptic breeding habitats such as sea caves. These cryptic habitats preclude the use of aerial monitoring methods and necessitate ground-based counts, which are costly in resources. In this study, we compare a ground-based pup production census with a reduced effort plot-sampling survey to estimate pup production, derive a total population size and assess cost effectiveness. Pup production in North Wales was estimated at 91 (95% confidence interval: 70–112) by the plot-sampling design and was a good approximation of the ‘true’ value of 96 derived from the census. The total population size in North Wales was estimated at between 242 and 307 grey seals. The plot-sampling design reduced survey effort by 46% and saved 30% on logistical costs compared to the full census. We outline the suitability of this method as part of a monitoring programme for grey seal pup production and suggest our approach may be applicable to other regions where grey seals use cryptic breeding habitat.

For the class of continuous games where σi and fi {σi, φ(σ1, …, σN)} are the strategy of and payoff to player i for i = 1, …, N, it is proved that the set of weak type I optima defined in Paper I conicide with the set of solution of a matrix condition. The latter condition restricts the equilibrium solutions of an adjustment process. Numerical results for N = 2 and N = 3 indicate that the set of all equilibrium solutions coincides with the above sets. The optima of types I to IV from Paper I are described fairly completely for the given class of games.

In this, the first of three papers, we examine conditions, derived previously, which specify the equilibrium solutions of an adjustment process for N players engaged in a game with continuous (in fact, continuously differentiable) payoff functions, where each player's strategy is to choose a single real number. It is equivalent to the basic form of quantity-variation competition between N firms. The conditions are related to a new optimum which takes account of the ability of firms, or coalitions of firms, to discipline another firm that tries to increase its own profit. Closely related optima are also introduced and analysed. The new optima occupy N-dimensional regions in the strategy space, and contain the optima of Cournot, Pareto, von-Neumann and Morgenstern, and Nash as special cases.

Mixing rules model how the physical properties of a polymer, such as its relaxation modulus G(t), depend on the distribution w(m) of its molecular weights m. They are of practical importance because, among other things, they allow estimates of the molecular weight distribution (MWD) w(m) of a polymer to be determined from measurements of its physical properties including the relaxation modulus. The two most common mixing rules are “single” and “double” reptation. Various derivations for these rules have been published. In this paper, a conditional probability formulation is given which identifies that the fundamental essence of “double” reptation is the discrete binary nature of the “entanglements”, which are assumed to occur in the corresponding topological model of the underlying polymer dynamics. In addition, various methods for determining the MWD are reviewed, and the computation of linear functionals of the MWD motivated and briefly examined.

The new optima and equilibria discussed in the preceding two papers are compared with the results of bargaining experiments between two and three players performed by Fouraker and Siegel. Experiments where players have complete or incomplete information are considered. There is clear evidence that the new optima are operating, and that traditional optima–Cournot, Pareto and competitive (threat)–are less satisfactory in explaining the course of the whole bargaining process.

We derive asymptotic forms for the distributions of k-point scan statistics as the interval L under study becomes infinite, while k and the window length are held fixed. In the Poisson case the intensity is also held fixed. In the uniform case the number of points N becomes infinite and N/L tends to a limit, representing a limiting intensity. These results are made explicit for k = 3, and in the Poisson case provide approximations which are typically accurate to six or seven figures, even for small L.

The application of carbon steel corrosion allowance containers for the long term encapsulation of HLW or spent fuel requires data on the likely rates of corrosion attack so that the metal thickness needed to prevent penetration can be estimated. This paper describes a joint mathematical modelling and experimental approach to the evaluation of the rate of localised corrosion.

The perturbed angular correlation (PAC) method was used to study vacancy trapping at 111In atoms in quenched Al single crystals containing up to 10 ppm In. During annealing from 200–230 K, two different electric field gradients appeared, characterized by the interaction frequencies ν 01 = 67 MHz with asymmetry parameter η = 0.41, and νQ2 = 133 MHz with η = 0. The assignment of ν01 to a single vacancy-In atom pair is discussed. The results indicate that the migration energy of single vacancies in Al is = 0.55 eV.

A plantation is modelled in terms of discs of random size centred on the points of a two-dimensional lattice, together with rules for partitioning the union of these discs. The resulting sets are functions of random sequences, and some properties of these functions are deduced. Results are given which relate various properties of measurements on a plantation to measurements of individual plants and of plants in isolation. These include limit theorems for complete plantations and for samples. They also lead to a rigorous demonstration of certain well-known empirical relations between typical measurements and survival frequencies and to some new relations which are amenable to test. The model is a formulation of computer simulations which have had success in describing competition in plantations, but are too costly for routine forest management.

Consider a renewal process on the nonnegative real line with non-arithmetic distribution function F(x). Denote by V(x; t) the distribution function of the forward recurrence time from t, t ≤ 0. If t is chosen at random with distribution function Ф(t), the corresponding unconditional forward recurrence time has distribution function

This paper contains a detailed study of the Poisson cluster process on the real line, concentrating on two aspects; first, the asymptotic distribution of the number of points in [0,t) as t→ ∞ for both transient and equilibrium cluster processes and, secondly, a general formula for the probability generating function of the equilibrium process. Asymptotic formulae for cumulants of the process are also derived. The results obtained generalize those of previous writers. The approach is analytical, in contrast to the probabilistic treatment of P. A. W. Lewis.

This paper is concerned with certain aspects of the theory and application of the probability generating functional (p.g.fl) of a point process on the real line. Interest in point processes has increased rapidly during the last decade and a number of different approaches to the subject have been expounded (see for example [6], [11], [15], [17], [20], [25], [27], [28]). It is hoped that the present development using the p.g.ff will calrify and unite some of these viewpoints and provide a useful tool for solution of particular problems.

Newman (1970) introduced an interesting new class of point processes which he called Gauss-Poisson. They are characterized, in the most general case, by two measures. We determine necessary and sufficient conditions on these measures for the resulting point process to be well defined, and proceed to a systematic study of its properties. These include stationarity, ergodicity, and infinite divisibility. We mention connections with other classes of point processes and some statistical results. Our basic approach is through the probability generating functional of the process.

Recent years have seen a material growth in the annuity business of British offices and in many instances what was a relatively insignificant part of the offices' activities has now assumed considerable importance. In fact in the case of some offices, the amount of the liability in respect of annuity business exceeds that in respect of assurances.