The nonlinear and weakly dispersive Serre equations contain higher-order dispersive terms. These include mixed spatial and temporal derivative flux terms which are difficult to handle numerically. These terms can be replaced by an alternative combination of equivalent temporal and spatial terms, so that the Serre equations can be written in conservation law form. The water depth and new conserved quantities are evolved using a second-order finite-volume scheme. The remaining primitive variable, the depth-averaged horizontal velocity, is obtained by solving a second-order elliptic equation using simple finite differences. Using an analytical solution and simulating the dam-break problem, the proposed scheme is shown to be accurate, simple to implement and stable for a range of problems, including flows with steep gradients. It is only slightly more computationally expensive than solving the shallow water wave equations.

This is the second of two papers in which we estimate transition probabilities amongst levels of disability as defined in the Australian Survey of Disability, Ageing and Carers. In this paper we describe our estimation procedure, followed by its implementation, discussion of results and graduation of the estimated transition probabilities.

It has been postulated that aging is the consequence of an accelerated accumulation of somatic DNA mutations and that subsequent errors in the primary structure of proteins ultimately reach levels sufficient to affect organismal functions. The technical limitations of detecting somatic changes and the lack of insight about the minimum level of erroneous proteins to cause an error catastrophe hampered any firm conclusions on these theories. In this study, we sequenced the whole genome of DNA in whole blood of two pairs of monozygotic (MZ) twins, 40 and 100 years old, by two independent next-generation sequencing (NGS) platforms (Illumina and Complete Genomics). Potentially discordant single-base substitutions supported by both platforms were validated extensively by Sanger, Roche 454, and Ion Torrent sequencing. We demonstrate that the genomes of the two twin pairs are germ-line identical between co-twins, and that the genomes of the 100-year-old MZ twins are discerned by eight confirmed somatic single-base substitutions, five of which are within introns. Putative somatic variation between the 40-year-old twins was not confirmed in the validation phase. We conclude from this systematic effort that by using two independent NGS platforms, somatic single nucleotide substitutions can be detected, and that a century of life did not result in a large number of detectable somatic mutations in blood. The low number of somatic variants observed by using two NGS platforms might provide a framework for detecting disease-related somatic variants in phenotypically discordant MZ twins.

This paper considers the modelling of claim durations for existing claimants under income protection insurance policies. A claim is considered to be terminated when the claimant returns to work. Data used in the analysis were provided by the Life and Risk Committee of the Institute of Actuaries of Australia. Initial analysis of the data suggests the presence of a long-run probability, of the order of 7%, that a claimant will never return to work. This phenomenon suggests the use of mixed parametric regression models as a description of claim duration which include the prediction of a long-run probability of not returning to work. A series of such parametric mixture models was investigated, and it was found that the generalised F mixture distribution provided a good fit to the data and also highlighted the impact of a number of statistically significant predictors of claim duration.

This paper investigates the use of censored regression quantiles in the analysis of claim termination rates for income protection (IP) insurance. The paper demonstrates the importance of modeling quantiles given the growing interest of regulators and others in stochastic approaches to valuation of insurance liabilities and risk margins.

We have developed a novel diagrammatic approach for understanding and teaching probability theory — Probability Space diagrams [1]. Our studies of learning and instruction with Probability Space (PS) diagrams have demonstrated that they can significantly enhance students' conceptual understanding. This article illustrates the utility of PS diagrams by applying them to the explanation of some difficult concepts and notoriously counterintuitive problems in probability. We first outline the nature of the system.

Raman scattering experiments on silicon-doped GaN show that donor impurities quench the Al(LO) Raman line at 735 cm−1. This is due to interaction between lattice vibrations and the free carrier plasma. The spatial variation of the Al(LO) signal has been imaged directly using newly developed instrumentation. Features with dimension under on micron are observed in faceted GaN crystallites. The variation in free carrier concentration is attributed to preferential incorporation of donor impurities during growth.

Nano-composites allow a materials engineering approach to be exploited to realise specific characteristics in optical thin film ensembles. For example, films can be produced with refractive indices determined by their average composition on the basis of effective medium approximations, so freeing optical designers from the constraints imposed in pure materials. A summary is presented of the progress made in a fundamental study of films based on diverse materials such as fluorides and sulphides, fabricated using molecular beam deposition techniques. The film properties (eg refractive index, surface morphology, environmental stability) are correlated with microstructure (as determined by cross-sectional TEM techniques). The enhanced properties of the films are discussed in relation to the realisation of periodically modulated graded-index structures of the type required for optical filter applications.

This paper presents the results of our investigation into the possibility of increasing both the radiative cross-section and the electrical activation efficiency in erbium (Er3+) doped silicon (Si). The energy levels of the isolated Er3+ have been theoretically predicted, employing the Thomas-Fermi method. The behaviour of these levels in Si was then investigated using a Kronig-Penney approach. Initial theoretical results imply that fluorine (F), in addition to Er3+ in Si, increases the radiative cross-section of Er3+ by at least an order of magnitude, and that co-doping appears to enhance the mixing of the 4f and 5d levels and causes the Er3+ energy levels to overlap with those of the host. Photoluminescence spectra of Er3+ in Si co-doped with F also indicate an interaction with the host lattice which appears to be dependent on its electrical characteristics.

Of 219 elderly patients with a major depressive disorder (meeting RDC), 69 recovered sufficiently and consented to enter a two-year double-blind placebo-controlled trial of dothiepin. Survival analysis revealed that dothiepin reduced the relative risk of relapse by two and a half times. Past but not current serious physical illness was also associated with a favourable outcome, whereas a prolonged index depressive illness trebled the relative risk of relapse. In the light of previous research on prognosis it is suggested that elderly persons who recover from a major depressive illness should continue with antidepressant medication for at least two years, if not indefinitely.

The reactions of (Me3Si)3As with group III halides have been utilized to prepare AlAs, GaAs and InAs. The adduct (Me3Si)3AsAlCl3 has been isolated as an intermediate in the formation of AlAs from (Me3Si)3As and AICI3. The crystal structure of its toluene solvate has been determined.

A sequence of deposits ranging in date from Late-glacial to the present produced detailed evidence of environmental changes, reflecting both climatic fluctuations and the effects of human activities. A Later Mesolithic occupation horizon, with lithic industry and associated faunal remains, is dated at about 5280 bc. It was sealed by a deposit of tufa. An irregular linear excavation, dated at about 2765 bc, is interpreted as a quarry; the backfill contained Earlier Neolithic pottery and other settlement debris. The first phase of later activities is marked by the deposition of a large quantity of Peterborough ware. Later on, part of the site was ploughed over and at the same time a series of small ditches, interpreted as elements of a system of land boundaries, was dug in the adjacent area. Late Beaker and Food Vessel sherds indicate the approximate date of these events.

We consider the expansion of a function in Lr (the class of measurable functions whose rth powers are Lebesgue integrable over some interval) in terms of the eigenfunctions arising from a singular Sturm-Liouville problem defined over an infinite or semi-infinite interval. We show that if l ≦ r ≦ inline1 or if r ≧ 4 there exists f in Lr whose eigenfunction expansion is divergent in the rth mean sense, and that the terms of the series form an unbounded sequence in Lr The result extends some work of Askey and Wainger concerning the Hermite series expansions of functions in Lr(–∞, ∞).