378 research outputs found
Geostrategies of the European neighbourhood policy
The debate about the European Neighbourhood Policy (ENP) has, in essence, been about borders and bordering. Such departures could contribute â and often do so â to a rather fixed geopolitical vision of what the EU is about and how it aims to run and to organize the broader European space. However, this article aims to retain space for viewing the ENP as a developmental and somewhat fluid process. A conceptual framework, based on outlining three geopolitical models and a series of different geopolitical strategies employed by the EU in regard to its borders, is hence employed in order to be able to tell a more dynamic story regarding the developing nature of the ENP and the EU's evolving nature more generally. The complexity traced informs us that various geostrategies may be held at the same time at the external border. Moreover, the dominance of one geostrategy may be replaced by another or a different combination of them with regard to the same neighbourhood. It is, more generally, argued that if anything it is precisely this dynamism that should be championed as a valuable resource, avoiding the tendency to close off options through the reification of particular visions of the nature of the EU and its borders
Unambiguous Morphic Images of Strings
We study a fundamental combinatorial problem on morphisms in free semigroups: With
regard to any string α over some alphabet we ask for the existence of a morphism Ï such
that Ï(α) is unambiguous, i.e. there is no morphism T with T(i) â Ï(i) for some symbol
i in α and, nevertheless, T(α) = Ï(α). As a consequence of its elementary nature, this
question shows a variety of connections to those topics in discrete mathematics which
are based on finite strings and morphisms such as pattern languages, equality sets and,
thus, the Post Correspondence Problem.
Our studies demonstrate that the existence of unambiguous morphic images essen-
tially depends on the structure of α: We introduce a partition of the set of all finite
strings into those that are decomposable (referred to as prolix) in a particular manner
and those that are indecomposable (called succinct). This partition, that is also known
to be of major importance for the research on pattern languages and on finite fixed
points of morphisms, allows to formulate our main result according to which a string α
can be mapped by an injective morphism onto an unambiguous image if and only if α is
succinct
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