Let Ω \subset \mathbb{R}^{n} be a domain and let α < n − 1. We prove the Concentration-Compactness Principle for the embedding of the space W_{0}^{1}L^{n} log^{\alpha } L(Ω) into an Orlicz space corresponding to a Young function which behaves like (t^{n/n-1-\alpha }) for large t. We also give the result for the embedding into multiple exponential spaces. Our main result is Theorem 1.6 where we show that if one passes to unbounded domains, then, after the usual modification of the integrand in the Moser functional, the statement of the Concentration-Compactnes Principle is very similar to the statement in the case of a bounded domain. In particular, in the case of a nontrivial weak limit the borderline exponent is still given by the formula P: = \left( {1 - \left\| {\Phi (|\nabla u|)} \right\|_{L^1 (\mathbb{R}^n )} } \right)^{ - 1/(n - 1)} ., Robert Černý., and Obsahuje seznam literatury
There are at least two significantly different approaches to the conceptualisation of social capital. Advocates of the most influential stream define social capital primarily as an attribute of societies, as an innate characteristic of the social environment based on the high degree of interpersonal and institutional trust facilitating people's co-operation. Adherents of the other stream define social capital in terms of mutually beneficial exchanges based on social connections and informal networks allowing individuals to achieve their own particular goals. The former approach prevails in 'western' countries, while the latter one prevails in the study of social change in post-communist societies where social capital drawing from interpersonal trust seems to be rather low. The aim of this article is to contribute to the conceptualisation and measurement of social capital, with a special emphasis on its role in post-communist societies. The authors attempt to develop a measurement model for the two distinct dimensions of social capital mentioned above. The measurement model for the two dimensions of social capital is developed and tested by confirmatory factor analysis. The authors proceed by testing the hypothesis that social capital defined as trust is only weakly linked to social stratification, while social capital defined as a person's involvement in mutually beneficial exchanges shows significant variation between groups defined by relevant stratification variables. The analysis was performed on the data from the Social Networks survey carried out in the Czech Republic in 2001 under the International Social Survey Programme.