Abstract. Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on L p X (R 2 ) with p ∈ (1, ∞). Moreover, replacing equality by a linear equivalence, this is found to be a typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given. As a corollary we obtain that the norm of the real part of the Beurling-Ahlfors operator equals p

We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.

The present research examines the longitudinal average impact of frequency of use of Internet and social networking sites (SNS) on subjective well-being of adolescents in Germany. Based on five-wave panel data that cover a period of nine years, we disentangle between-person and within-person effects of media use on depressive symptomatology and life satisfaction as indicators of subjective well-being. Additionally, we control for confounders such as TV use, self-esteem, and satisfaction with friends. We found that frequency of Internet use in general and use of SNS in particular is not substantially related subjective well-being. The explanatory power of general Internet use or SNS use to predict between-person differences or within-person change in subjective well-being is close to zero. TV use, a potentially confounding variable, is negatively related to satisfaction with life, but it does not affect depressive symptomatology. However, this effect is too small to be of practical relevance.

When covering violations of social norms by public figures, the mass media depict the resulting damages and attribute responsibility to actors. These depictions of responsibility constitute frames that elicit reactions from recipients. A theory regarding the effects of these media frames on cognitions, emotions, and opinions is presented. Content analyses of the media coverage of four cases and corresponding surveys were conducted. The findings indicate that the cognitions, emotions, and opinions of recipients cannot be sufficiently explained by learning of media input; recipients process the content based on individual frames. They complement fragmentary media frames and generate consistent impressions based on media cues. Their judgments and emotional reactions go beyond the media's depictions and induce corresponding behavioral intentions.

Bone milling reduces the quantity of osteoblasts. Bone obtained by the ball reamer supplies a smaller number of cells than bone obtained by other methods. Unmilled spongy bone chips appear to offer the greatest amount of viable osteoblasts.