L^2-Betti numbers and Plancherel measure

We compute $L^2$-Betti numbers of postliminal, locally compact, unimodular groups in terms of ordinary dimensions of reduced cohomology with coefficients in irreducible unitary representations and the Plancherel measure. This allows us to compute the $L^2$-Betti numbers for semi-simple Lie groups with finite center, simple algebraic groups over local fields, and automorphism groups of locally finite trees acting transitively on the boundary.Comment: 11 page

L^2-Betti Numbers of Locally Compact Groups

We introduce a notion of $L^2$-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of $L^2$-Betti numbers of countable discrete groups for lattices. In this way, several new computations are obtained for countable groups, including lattices in algebraic groups over local fields, and Kac-Moody lattices. We also extend the vanishing of reduced $L^2$-cohomology for countable amenable groups, a well known theorem due to Cheeger and Gromov, to cover all amenable, second countable, unimodular locally compact groups.Comment: The latest update replaces the old preprint with the authors thesis. This is the final versio

Oil generation from coal source rocks: the influence of depositional conditions and stratigraphic age

Although it was for many years believed that coals could not act as source rocks for commercial oil accumulations, it is today generally accepted that coals can indeed generate and expel commercial quantities of oil. While hydrocarbon generation from coals is less well understood than for marine and lacustrine source rocks, liquid hydrocarbon generation from coals and coaly source rocks is now known from many parts of the world, especially in the Australasian region (MacGregor 1994; Todd et al. 1997). Most of the known large oil accumulations derived from coaly source rocks have been generated from Cenozoic coals, such as in the Gippsland Basin (Australia), the Taranaki Basin (New Zealand), and the Kutei Basin (Indonesia). Permian and Jurassic coal-sourced oils are known from, respectively, the Cooper Basin (Australia) and the Danish North Sea, but in general only minor quantities of oil appear to be related to coals of Permian and Jurassic age. In contrast, Carboniferous coals are only associated with gas, as demonstrated for example by the large gas deposits in the southern North Sea and The Netherlands. Overall, the oil generation capacity of coals seems to increase from the Carboniferous to the Cenozoic. This suggests a relationship to the evolution of more complex higher land plants through time, such that the highly diversified Cenozoic plant communities in particular have the potential to produce oil-prone coals. In addition to this overall vegetational factor, the depositional conditions of the precursor mires influenced the generation potential. The various aspects of oil generation from coals have been the focus of research at the Geological Survey of Denmark and Greenland (GEUS) for several years, and recently a worldwide database consisting of more than 500 coals has been the subject of a detailed study that aims to describe the oil window and the generation potential of coals as a function of coal composition and age

Graph colouring for office blocks

The increasing prevalence of WLAN (wireless networks) introduces the potential of electronic information leakage from one company's territory in an office block, to others due to the long-ranged nature of such communications. BAE Systems have developed a system ('stealthy wallpaper') which can block a single frequency range from being transmitted through a treated wall or ceiling to the neighbour. The problem posed to the Study Group was to investigate the maximum number of frequencies ensure the building is secure. The Study group found that this upper bound does not exist, so they were asked to find what are "good design-rules" so that an upper limit exists