Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Demographic model of the Swiss cattle population for the years 2009-2011 stratified by gender, age and production type

Demographic composition and dynamics of animal and human populations are important determinants for the transmission dynamics of infectious disease and for the effect of infectious disease or environmental disasters on productivity. In many circumstances, demographic data are not available or of poor quality. Since 1999 Switzerland has been recording cattle movements, births, deaths and slaughter in an animal movement database (AMD). The data present in the AMD offers the opportunity for analysing and understanding the dynamic of the Swiss cattle population. A dynamic population model can serve as a building block for future disease transmission models and help policy makers in developing strategies regarding animal health, animal welfare, livestock management and productivity. The Swiss cattle population was therefore modelled using a system of ordinary differential equations. The model was stratified by production type (dairy or beef), age and gender (male and female calves: 0-1 year, heifers and young bulls: 1-2 years, cows and bulls: older than 2 years). The simulation of the Swiss cattle population reflects the observed pattern accurately. Parameters were optimized on the basis of the goodness-of-fit (using the Powell algorithm). The fitted rates were compared with calculated rates from the AMD and differed only marginally. This gives confidence in the fitted rates of parameters that are not directly deductible from the AMD (e.g. the proportion of calves that are moved from the dairy system to fattening plants).

An adaptive Newton-method based on a dynamical systems approach

The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

Differential Responses of Herbivores and Herbivory to Management in Temperate European Beech

Forest management not only affects biodiversity but also might alter ecosystem processes mediated by the organisms, i.e. herbivory the removal of plant biomass by plant-eating insects and other arthropod groups. Aiming at revealing general relationships between forest management and herbivory we investigated aboveground arthropod herbivory in 105 plots dominated by European beech in three different regions in Germany in the sun-exposed canopy of mature beech trees and on beech saplings in the understorey. We separately assessed damage by different guilds of herbivores, i.e. chewing, sucking and scraping herbivores, gall-forming insects and mites, and leaf-mining insects. We asked whether herbivory differs among different forest management regimes (unmanaged, uneven-aged managed, even-aged managed) and among age-classes within even-aged forests. We further tested for consistency of relationships between regions, strata and herbivore guilds. On average, almost 80 of beech leaves showed herbivory damage, and about 6 of leaf area was consumed. Chewing damage was most common, whereas leaf sucking and scraping damage were very rare. Damage was generally greater in the canopy than in the understorey, in particular for chewing and scraping damage, and the occurrence of mines. There was little difference in herbivory among differently managed forests and the effects of management on damage differed among regions, strata and damage types. Covariates such as wood volume, tree density and plant diversity weakly influenced herbivory, and effects differed between herbivory types. We conclude that despite of the relatively low number of species attacking beech; arthropod herbivory on beech is generally high. We further conclude that responses of herbivory to forest management are multifaceted and environmental factors such as forest structure variables affecting in particular microclimatic conditions are more likely to explain the variability in herbivory among beech forest plots.

Marital split-up and widowhood in old age: Differential impact on psychological and social well-being

Marital split-up and spousal loss are among the most stressful critical life events. Numerous studies have documented their detrimental effects on well-being, yet the large individual differences in psychological adaptation are still not well understood. Whereas in old age bereavement is normative and can be anticipated, divorce is an “off-time” transition for this age group. In contrast to bereavement which has been amply studied, research on later life divorce is still missing despite the increasing relevance of the topic due to the significant increase of divorces in older age. Based on a modified and extended view of Amato’s divorce-stress-adjustment model (2000), the aim of this contribution is to explore the differential impact of marital split-up and widowhood in older age on psychological (life satisfaction) and social well-being (social loneliness), and the adaptation to these critical life events. Our analyses are based on data gathered in a questionnaire study, which is part of the Swiss National Centre of Competence in Research LIVES. In a first step we compared three groups of individuals aged 60 to 75 years: a sample of 251 persons with a marital split-up (127 women; 123 men), a sample of 270 widowed persons (170 women; 100 men), and a group of 221 continuously married people (110 women; 111 men), which served as control group. In a second step, we investigated the role of socio-demographic variables, intrapersonal and interpersonal resources and variables of the context of loss as predictors for the psychological adaptation to a marital break-up and loss in old age. First results by ANCOVA indicate significant differences with regard to life satisfaction among the three groups, with divorced persons with the lowest scores, followed by the bereaved ones, and the married controls with the highest. Regarding social loneliness, divorced individuals report higher social loneliness than the bereaved group and the married controls (no significant difference between widowed and the married). In both loss groups, financial and intrapersonal resources, as well as the emotional valence of the loss are the most important predictors for the psychological and social adaptation. However, happiness in the past relationship is an important resource regarding the indicators for adaptation for the widowers, but not for individuals with a marital dissolution.

Differential effects of long and short carbon nanotubes on the gas-exchange region of the mouse lung

Abstract We hypothesise that inflammatory response and morphological characteristics of lung parenchyma differ after exposure to short or long multi-walled carbon nanotubes (MWCNT). Mice were subjected to a single dose of vehicle, short or long MWCNT by pharyngeal aspiration. Bronchoalveolar lavage fluid (BALF) obtained at 24 h was analysed for inflammatory reaction and lung tissue was analysed for morphological alterations using stereology. Short MWCNT had stronger potential to induce polymorphonuclear cells whereas long MWCNT increased interleukin-6 levels in BALF. Alveolar septal fibrosis was only observed with short MWCNT. Type II pneumocyte hypertrophy was only detected with long MWCNT. There was no reduction in total alveolar surface area and no sign of type II cell hyperplasia. We observed mild inflammatory and pathological responses to short and long MWCNT in the lung parenchyma depending on the size of the applied MWCNT.