Self-shrinkers of the mean curvature flow in arbitrary codimension

For hypersurfaces of dimension greater than one, Huisken showed that compact self-shrinkers of the mean curvature flow with positive scalar mean curvature are spheres. We will prove the following extension: A compact self-similar solution in arbitrary codimension and of dimension greater than one is spherical, i.e. contained in a sphere, if and only if the mean curvature vector \be H\ee is non-vanishing and the principal normal \be\nu\ee is parallel in the normal bundle. We also give a classification of complete noncompact self-shrinkers of that type.Comment: 19 pages, 1 figur

Reducing behaviour problems in young people through social competence programmes

There is a relatively strong relationship between the concepts of behavioural problems and social competence, in that social competence is regarded as one of the most important protective factors in the prevention of behavioural problems. This paper argues that the concept of social competence should include social skills, social practice and empathic understanding. It identifies the components that form part of an effective social competence programme, including enhancing an understanding of social situations, increasing the generation of adequate social skills, improving the management of provocations which may lead to uncontrolled anger, and developing empathic understanding. The evidence also suggests that effective social competence programmes for children and young people should be multi modal and consist of mixed groups of pupils with and without difficulties. The paper concludes with a brief description of Aggression Replacement Training as an example of a programme which follows the recommended guidelines.peer-reviewe

Deservingness Transfers

This article seeks to cause trouble for a brand of consequentialism known as ‘desertarianism’. In somewhat different ways, views of this kind evaluate outcomes more favourably, other things equal, the better the fit between the welfare different people enjoy and the welfare they each deserve. These views imply that we can improve outcomes by redistributing welfare to fit desert, which seems plausible enough. Unfortunately, they also imply that we can improve outcomes by redistributing desert to fit welfare: in other words, by making happy people more deserving, at the cost of making unhappy people less deserving. Extant versions of desertarianism predict that such ‘deservingness transfers’ are improvements and that we ought to carry them out. Even worse, they will sometimes rank deservingness transfers higher than simply benefitting deserving people who are poorly off

The uncertainty in regional innovation policy: some ration-ales and tools for learning in policy making

This paper deals with two major dilemmas in regional innovation policy making: The dilemma that theory does not provide sufficient answers for the formulation of specific innovation policy measures addressing the problem configurations of single regions and the dilemma that role models are used as a substitute for orientation. In order to support policy learning, different approaches like evaluation, the development of innovation strategies and regional foresight are discussed. --

Pulse propagation in time dependent randomly layered media

We study cumulative scattering effects on wave front propagation in time dependent randomly layered media. It is well known that the wave front has a deterministic characterization in time independent media, aside from a small random shift in the travel time. That is, the pulse shape is predictable, but faded and smeared as described mathematically by a convolution kernel determined by the autocorrelation of the random fluctuations of the wave speed. The main result of this paper is the extension of the pulse stabilization results to time dependent randomly layered media. When the media change slowly, on time scales that are longer than the pulse width and the time it takes the waves to traverse a correlation length, the pulse is not affected by the time fluctuations. In rapidly changing media, where these time scales are similar, both the pulse shape and the random component of the arrival time are affected by the statistics of the time fluctuations of the wave speed. We obtain an integral equation for the wave front, that is more complicated than in time independent media, and cannot be solved analytically, in general. We also give examples of media where the equation simplifies, and the wave front can be analyzed explicitly. We illustrate with these examples how the time fluctuations feed energy into the pulse