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

Psychoendocrine validation of a short measure for assessment of perceived stress management skills in different non-clinical populations

BACKGROUND: We investigated the psychometric properties of a short questionnaire for combined assessment of different perceived stress management skills in the general population and tested whether scores relate to physiological stress reactivity. METHODS: For psychometric evaluation, we determined the factor structure of the questionnaire and investigated its measurement invariance in the participant groups and over time in three different independent samples representing the general population (total N=332). Reliability was tested by estimating test-retest reliability, internal consistency, and item reliabilities. We examined convergent and criterion validity using selected criterion variables. For endocrine validation, 35 healthy non-smoking and medication-free men in a laboratory study and 35 male and female employees in a workplace study underwent an acute standardized psychosocial stress task. We assessed stress management skills and measured salivary cortisol before and several times up to 60 min (workplace study) and 120 min (laboratory study) after stress. Potential confounders were controlled. RESULTS: The factor structure of the questionnaire consists of five scales reflecting acceptably distinct stress management skills such as cognitive strategies, use of social support, relaxation strategies, anger regulation, and perception of bodily tension. This factor structure was stable across participant groups and over time. Internal consistencies, item reliabilities, and test-retest reliabilities met established statistical requirements. Convergent and criterion validity were also established. In both endocrine validation studies, higher stress management skills were independently associated with lower cortisol stress reactivity (p's<.029). CONCLUSIONS: Our findings suggest that the questionnaire has good psychometric properties and that it relates to subjective psychological and objective physiological stress indicators. Therefore, the instrument seems a suitable measure for differential assessment of stress management skills in the general population.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.