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

Lions-type compactness and Rubik actions on the Heisenberg group

In this paper we prove a Lions-type compactness embedding result for symmetric unbounded domains of the Heisenberg group. The natural group action on the Heisenberg group TeX is provided by the unitary group U(n) × {1} and its appropriate subgroups, which will be used to construct subspaces with specific symmetry and compactness properties in the Folland-Stein’s horizontal Sobolev space TeX. As an application, we study the multiplicity of solutions for a singular subelliptic problem by exploiting a technique of solving the Rubik-cube applied to subgroups of U(n) × {1}. In our approach we employ concentration compactness, group-theoretical arguments, and variational methods.

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.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Congenital hypotrichosis and partial anodontia in a crossbred beef calf

Clinical examination, skin biopsies, skull radiographs, and DNA analysis of a 2-day-old Red Angus-Charolais-Simmental cross bull calf confirmed the diagnosis of congenital hypotrichosis and anodontia defect (HAD), also called anhidrotic ectodermal dysplasia, which is a rare anomaly caused by a deletion in the bovine EDA gene on the X chromosome.

Executive functions and their differential contribution to sustained attention in 5- to 8-year-old children

ABSTRACT Everyday routine in general and school settings in particular make high demands on children's abilities to sustain their focus of attention over longer time periods. School tasks thus require the child to accomplish the task on an appropriate level of performance while maintaining the focus of attention even under repetitious or distracting conditions. However, sustained attention (SA) may be a more heterogeneous construct than commonly assumed as it requires the individual not only to sustain attentional capacities but also to store and maintain the task rule (working memory), to inhibit inappropriate responses (inhibition), and to switch according to requirements (switching). It might thus involve processes counted among executive functions (EF). In the present study, performance in EF tasks (covering the core components inhibition, switching, and working memory) and in a SA task was assessed in 118 children, aged between 5;0 and 8;11 years. Similar age-dependent performance trajectories were found in EF components and SA, indicating ongoing performance improvements between 5 until at least 8 years of age in SA and in EF. Interrelations between single EF components and SA showed to be small to moderate. Finally, different patterns of SA performance predictions were found in age-homogeneous subgroups with inhibition being crucial for SA performance in the youngest and switching in the oldest age group. Taken as a whole, even though similarities in assumed developmental trajectories and substantial interrelations point to common underlying processes in EF and SA, age-dependent patterns of explained variance indicate clear discriminability.

Cloning, sequencing and partial functional characterization of the 5' region of the human p75 tumor necrosis factor receptor-encoding gene (TNF-R)

A 1887-bp region at the 5' flank of the human p75 tumor necrosis factor receptor (p75 TNF-R)-encoding gene was found to be active in driving expression of the luc (luciferase-encoding) reporter gene, suggesting that it contains the promoter for the receptor. Rather unexpectedly, a 1827-bp region at the 3' end of the first intron of the p75 TNF-R gene also displayed promoter activity. This activity may be artefactual, reflecting only the presence of an enhancer in this region; yet it also raises the possibility that p75 TNF-R is controlled by more than one promoter and that it encodes various forms of the receptor, or even other proteins. We present here the nucleotide sequences of the 5' flanking and intron regions. Possible implications for the transcriptional regulation of the p75 TNF-R gene are discussed.