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 a prediction-type adaptive Newton method and an 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 different examples

An hphp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems

In this paper we develop an $hp$-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an $hp$-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully $hp$-adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.Comment: arXiv admin note: text overlap with arXiv:1408.522

An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)In this article, we develop an adaptive procedure for the numerical solution of semilinear parabolic problems with possible singular perturbations. Our approach combines a linearization technique using Newton’s method with an adaptive discretization – which is based on a spatial finite element method and the backward Euler time-stepping scheme – of the resulting sequence of linear problems. Upon deriving a robust a posteriori error analysis, we design a fully adaptive Newton-Galerkin time-stepping algorithm. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)In this article, we develop an adaptive procedure for the numerical solution of semilinear parabolic problems with possible singular perturbations. Our approach combines a linearization technique using Newton’s method with an adaptive discretization – which is based on a spatial finite element method and the backward Euler time-stepping scheme – of the resulting sequence of linear problems. Upon deriving a robust a posteriori error analysis, we design a fully adaptive Newton-Galerkin time-stepping algorithm. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Tinkering With The Traditional To Assess And Promote Quality Instruction: Learning From A New And Unimproved Instructor Evaluation Instrument

For over 30 years survey instruments have been used in colleges of higher education to measure instructional effectiveness. Extensive research has been conducted to determine which items best capture this construct. This research study was triggered by a college of education’s enthusiastic but failed attempt to create a new and improved instructor survey based on this research. Researchers found that the new instrument was no better than its predecessor. Student halo ratings contaminated results, reliability was lower than expected, and the survey results indicated one single dimension – general teaching effectiveness.  Two associated variables of considerable interest, course relevance and rigor/demand, were also contaminated by student halo rating. Based on these findings and the extensive literature on student surveys of teaching effectiveness, we argue that traditional surveys based on conventional items may be valid for evaluating global teaching effectiveness and other summative purposes but not for the formative, self-diagnostic, and reflective purposes anticipated. New ways of evaluating teaching in higher education are presented and discussed.  The article shares insights into theory-based survey development and a plan for validation

No effect of running and laboratory housing on adult hippocampal neurogenesis in wild caught long-tailed wood mouse

BACKGROUND: Studies of adult hippocampal neurogenesis (AHN) in laboratory rodents have raised hopes for therapeutic interventions in neurodegenerative diseases and mood disorders, as AHN can be modulated by physical exercise, stress and environmental changes in these animals. Since it is not known whether cell proliferation and neurogenesis in wild living mice can be experimentally changed, this study investigates the responsiveness of AHN to voluntary running and to environmental change in wild caught long-tailed wood mice (Apodemus sylvaticus). RESULTS: Statistical analyses show that running had no impact on cell proliferation (p = 0.44), neurogenesis (p = 0.94) or survival of newly born neurons (p = 0.58). Likewise, housing in the laboratory has no effect on AHN. In addition, interindividual differences in the level of neurogenesis are not related to interindividual differences of running wheel performance (rs = -0.09, p = 0.79). There is a correlation between the number of proliferating cells and the number of cells of neuronal lineage (rs = 0.63, p < 0.001) and the number of pyknotic cells (rs = 0.5, p = 0.009), respectively. CONCLUSION: Plasticity of adult neurogenesis is an established feature in strains of house mice and brown rats. Here, we demonstrate that voluntary running and environmental changes which are effective in house mice and brown rats cannot influence AHN in long-tailed wood mice. This indicates that in wild long-tailed wood mice different regulatory mechanisms act on cell proliferation and neurogenesis. If this difference reflects a species-specific adaptation or a broader adaptive strategy to a natural vs. domestic environment is unknown

Acrylamide in almond products

Acrylamide was determined in 86 different almond products, such as roasted almonds, almond-containing bakery products, raw almonds, and marzipan. The highest acrylamide concentrations were found in dark roasted almonds, while only moderate acrylamide contents were determined in bakery products. Roasting experiments under different process conditions showed that acrylamide increases with time and that temperature has a much stronger effect on acrylamide formation than time. During roasting reducing sugars are consumed faster and to a larger extent than free asparagine, suggesting that the content of reducing sugars may be a critical factor for acrylamide formation in roasted almonds. Acrylamide was found to decrease in roasted almonds during storage at room temperatur

Potential for acrylamide formation in potatoes: data from the 2003 harvest

Reducing sugars, free amino acids, and the potential for acrylamide formation were determined in more than 50 potato samples from the 2003 harvest in Switzerland. The reducing sugar content strongly correlated with acrylamide, whereas no correlation was found between acrylamide and free asparagine or the pool of free amino acids. The reducing sugar contents and the acrylamide potentials were higher in most of the cultivars tested than in the samples from 2002. This was probably due to the hot and dry summer of 2003. Monitoring sugars and amino acids during heating at 120°C and 180°C showed that glucose and fructose reacted much faster than sucrose and the amino acids. Glutamine was consumed to a larger extent than any of the other amino acids. During prolonged storage, the reducing sugars decreased considerably while only moderate changes in the free amino acids were observed. Altogether, glucose and fructose remain the critical factors for acrylamide formation in potatoes and represent the most feasible way of reducing the formation of acrylamide in potato product

Magnetic transport in a straight parabolic channel

We study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under influence of a potential perturbation $W$. If $W$ is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any finite number of open gaps provided the confining potential is sufficiently strong. However, if $W$ depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if $W$ is small and satisfies a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists