Compactifications of discrete quantum groups

Given a discrete quantum group A we construct a certain Hopf *-algebra AP which is a unital *-subalgebra of the multiplier algebra of A. The structure maps for AP are inherited from M(A) and thus the construction yields a compactification of A which is analogous to the Bohr compactification of a locally compact group. This algebra has the expected universal property with respect to homomorphisms from multiplier Hopf algebras of compact type (and is therefore unique). This provides an easy proof of the fact that for a discrete quantum group with an infinite dimensional algebra the multiplier algebra is never a Hopf algebra

Mobility and distance decay at the aggregated and individual level

Most crimes are committed near to where the offender lives; this has been observed both at the aggregate and at the offender level. At the aggregate level, as the distance increases there is a decline in the number of offences committed, and initially this decline is quite slow. This pattern has been described by a number of researchers, and results in a distance decay curve. Near-home offending has also been observed at the level of the individual offender, although it has been debated whether distance decay actually exists at the level of the individual offender. We therefore believe it is important to distinguish near-home offending from decay, i.e. the gradual decline in offences as distances increase. This paper studies mobility patterns and decay curves on serious property crimes in Belgium. First, aggregated patterns are discussed and categorised. Second, individual offenders are analysed. It becomes clear through studying offender patterns that offender mobility and decay are not intertwined at the individual level to the same extent as they are at the aggregate level. This suggests that it is important, particularly when studying individual offenders, to clarify whether (average) distances or decay are being considered