Town Centre Statistics Through the Internet

April 28-2

Cyclic growth in Atlantic region continental crust

Atlantic region continental crust evolved in successive stages under the influence of regular, approximately 400 Ma-long tectonic cycles. Data point to a variety of operative tectonic processes ranging from widespread ocean floor consumption (Wilson cycle) to entirely ensialic (Ampferer-style subduction or simple crustal attenuation-compression). Different processes may have operated concurrently in some or different belts. Resolving this remains the major challenge

On commuting varieties of parabolic subalgebras

Let $G$ be a connected reductive algebraic group over an algebraically closed field $k$, and assume that the characteristic of $k$ is zero or a pretty good prime for $G$. Let $P$ be a parabolic subgroup of $G$ and let $\mathfrak p$ be the Lie algebra of $P$. We consider the commuting variety $\mathcal C(\mathfrak p) = \{(X,Y) \in \mathfrak p \times \mathfrak p \mid [X,Y] = 0\}$. Our main theorem gives a necessary and sufficient condition for irreducibility of $\mathcal C(\mathfrak p)$ in terms of the modality of the adjoint action of $P$ on the nilpotent variety of $\mathfrak p$. As a consequence, for the case $P = B$ a Borel subgroup of $G$, we give a classification of when $\mathcal C(\mathfrak b)$ is irreducible; this builds on a partial classification given by Keeton. Further, in cases where $\mathcal C(\mathfrak p)$ is irreducible, we consider whether $\mathcal C(\mathfrak p)$ is a normal variety. In particular, this leads to a classification of when $\mathcal C(\mathfrak b)$ is normal.Comment: 19 pages; minor update

Defining and delineating the central areas of towns for statistical monitoring using continuous surface representations

The increasing availability of very high spatial resolution data using the unit postcode as its geo-reference is making possible new kinds of urban analysis andmodelling. However, at this resolution the granularity of the data used to representurban functions makes it difficult to apply traditional analytical and modellingmethods. An alternative suggested here is to use kernel density estimation totransform these data from point or area 'objects' into continuous surfaces of spatialdensities. The use of this transformation is illustrated by a study in which we attemptto develop a robust, generally applicable methodology for identifying the centralareas of UK towns for the purpose of statistical reporting and comparison.Continuous density transformations from unit post code data relating to a series ofindicators of town centredness created using ArcView are normalised and thensummed to give a composite ?Index of Town Centredness?. Selection of key contourson these index surfaces enables town centres to be delineated. The work results froma study on behalf of DETR