University of Paderborn

About: University of Paderborn is a education organization based out in Paderborn, Nordrhein-Westfalen, Germany. It is known for research contribution in the topics: Computer science & Context (language use). The organization has 6684 authors who have published 16929 publications receiving 323154 citations.

Finite-time blow-up in low-dimensional Keller–Segel systems with logistic-type superlinear degradation

Abstract: We consider radially symmetric solutions of the Keller–Segel system with generalized logistic source given by $$\begin{aligned} \left\{ \begin{array}{l} u_t = \Delta u - abla \cdot (u abla v) + \lambda u - \mu u^\kappa , \\ 0 = \Delta v - v + u, \end{array} \right. \qquad \qquad (\star ) \end{aligned}$$ under homogeneous Neumann boundary conditions in the ball $$\Omega =B_R(0) \subset \mathbb {R}^n$$ for $$n\ge 3$$ and $$R>0$$ , where $$\lambda \in \mathbb {R}, \mu >0$$ and $$\kappa >1$$ . Under the assumption that $$\begin{aligned} \kappa < \left\{ \begin{array}{ll} \frac{7}{6} &{}\quad \text {if } n\in \{3,4\}, \\ 1+ \frac{1}{2(n-1)} &{}\quad \text {if } n \ge 5, \end{array} \right. \end{aligned}$$ a condition on the initial data is derived which is seen to be sufficient to ensure the occurrence of finite-time blow-up for the corresponding solution of ( $$\star $$ ). Moreover, this criterion is shown to be mild enough so as to allow for the conclusion that in fact any positive continuous radial function on $$\overline{\Omega }$$ is the limit in $$L^1(\Omega )$$ of a sequence $$(u_{0k})_{k\in \mathbb {N}}$$ of continuous radial initial data which are such that for each $$k\in \mathbb {N}$$ the associated initial-boundary value problem for ( $$\star $$ ) exhibits a finite-time explosion phenomenon in the above sense. In particular, this apparently provides the first rigorous detection of blow-up in a superlinearly dampened but otherwise essentially original Keller–Segel system in the physically relevant three-dimensional case.

Transfer and typological proximity in the context of second language processing

Abstract: In this article, the issue of cross-linguistic influence in second language acquisition is examined from a processing perspective. Applying Processability Theory as the theoretical framework we claim that second language (L2) learners can only produce forms they are able to process.We thus argue that the first language (L1) influence on the L2 is developmentally moderated. Data were collected from German L2 learners with Swedish as their L1. Twenty informants participated in the study, 10 in their first year of German (13 years of age) and 10 in their second year of German (14 years of age). Both languages involved are typologically very close but not mutually intelligible. The results show that Swedish learners of German do not transfer the verb-second structure from their L1 to the L2 even though this structure is identical in both languages.Instead they start out with canonical word order and subsequently produce an intermediate structure (adv NPsubj V X), which is ungrammatical in the L1 and the L2. These observations support the idea of a developmentally moderated transfer. The results clearly contradict the predictions from the 'full transfer/full access' hypothesis (Schwartz and Sprouse, 1994; 1996). (Less)

Induced Representations of Locally Compact Groups

Abstract: 1. Basics 2. Induced representations 3. The imprimitivity theorem 4. Mackey analysis 5. Topologies on dual spaces 6. Topological Frobenius properties 7. Further applications References Index.