Conjugacy classes of parabolic subalgebras in complex semi-simple lie algebras

For a complex semi simple Lie algebra g, Richardson's dense orbit theorem gives a map between conjugacy classes of parabolic subalgebras in g and conjugacy classes of nilpotent elements. Unfortunately, this map is not surjective, in general, and hence does not give a direct classification of the nilpotent conjugacy classes in g. Despite this, the theorem is used by Bala and Carter to produce an indirect classification of the nilpotent conjugacy classes in g. The map is not injective, either, and this thesis attempts to discover a necessary and sufficient condition for two parabolic subalgebras to give the same nilpotent conjugacy class under the above map. Springer conjectured that associated parabolics would give the same nilpotent conjugacy class. The problem was also raised in another form by Dixmier in his work concerning the distribution of nilpotent polarisable elements in g. He conjectured a generalisation of Kostant's results on the regular nilpotent elements. We prove both these conjectures correct, the method of proof being inspired by Dixmier's work. Unfortunately, the necessary and sufficient condition is clearly more complicated than this and we give two examples (one trivial, one non-trivial) of non-associated parabolics giving the same nilpotent conjugacy class under Richard son's ma

The statistical mechanics of multi-index matching problems with site disorder

We study the statistical mechanics of multi-index matching problems where the quenched disorder is a geometric site disorder rather than a link disorder. A recently developed functional formalism is exploited which yields exact results in the finite temperature thermodynamic limit. Particular attention is paid to the zero temperature limit of maximal matching problems where the method allows us to obtain the average value of the optimal match and also sheds light on the algorithmic heuristics leading to that optimal matchComment: 11 pages 11 figures, RevTe

Structure determination of a 4-pyrone from the liverwort <i>Plagiochila bifaria</i> (Sw.) Lindenb. (Plagiochilaceae)

The centenary of the presentation in 1907 of the "polyketide" hypothesis by Collie, along with his use of a 4-pyrone as an example, is marked by reporting the discovery and isolation of 2-(3,4-dimethoxyphenethyl)-6-methyl-4-pyrone from &lt;i&gt;Plagiochila bifaria&lt;/i&gt;. This compound dominates the phytochemical profile of the deuteriochloroform extract of a Venezuelan specimen of &lt;i&gt;P. bifaria&lt;/i&gt; and the structure was determined using spectroscopic techniques, especially 2D NMR. This natural product is novel because it contains what appears to be the first example of a monocyclic 4-pyrone that has a polyketide origin. The hypothetical pathway for cyclization of a triketocarboxylic acid to a 4-pyrone was known to be applicable to model systems but no examples of natural products from this route were known. This compound is the same as one of a series of compounds observed previously in an extract of a Brazilian specimen of &lt;i&gt;P. bifaria&lt;/i&gt;; the working structures that were proposed earlier require revision. The mass spectral characteristics are the same as those reported (parent and base peak) in 1987 for the major component observed in the GC-MS profile of an extract of a specimen of &lt;i&gt;P. bifaria&lt;/i&gt; from Peru. The roles played by Birch and Robinson in the renaissance of the polyketide hypothesis almost fifty years after its initial launch are considered. Based on evidence from their publications, they worked independently of each other. It appears Robinson always had knowledge of Collie's hypothesis when developing ideas about structural relations of natural products whereas Birch initially was unaware of both Collie's and Robinson's ideas on the subject

Nurturing the acorn: helping a small software company onto the CMM ladder

We report on an interaction between a University and a small software development company within the framework of a Teaching Company Scheme. By exploiting the peculiar environment offered by a TCS, the University was able to help the company introduce measures to improve their software development process. Not only have these measures moved the company from level 1 to level 2 of the Capability Maturity Model; they are doubtless also responsible, at least in part, for the company's survival. The fundamental features of the environment which supported this success are discussed, and it is suggested how the approach might be applied elsewhere, either within or independently of a funding framework such as TCS

On the binary codes with parameters of triply-shortened 1-perfect codes

We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary $(n=2^m-3, 2^{n-m-1}, 4)$ code $C$, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of an equitable partition of the $n$-cube into six cells. An arbitrary binary $(n=2^m-4, 2^{n-m}, 3)$ code $D$, i.e., a code with parameters of a triply-shortened Hamming code, is a cell of an equitable family (but not a partition) from six cells. As a corollary, the codes $C$ and $D$ are completely semiregular; i.e., the weight distribution of such a code depends only on the minimal and maximal codeword weights and the code parameters. Moreover, if $D$ is self-complementary, then it is completely regular. As an intermediate result, we prove, in terms of distance distributions, a general criterion for a partition of the vertices of a graph (from rather general class of graphs, including the distance-regular graphs) to be equitable. Keywords: 1-perfect code; triply-shortened 1-perfect code; equitable partition; perfect coloring; weight distribution; distance distributionComment: 12 page

Characteristics of Cosmic Time

The nature of cosmic time is illuminated using Hamilton-Jacobi theory for general relativity. For problems of interest to cosmology, one may solve for the phase of the wavefunctional by using a line integral in superspace. Each contour of integration corresponds to a particular choice of time hypersurface, and each yields the same answer. In this way, one can construct a covariant formalism where all time hypersurfaces are treated on an equal footing. Using the method of characteristics, explicit solutions for an inflationary epoch with several scalar fields are given. The theoretical predictions of double inflation are compared with recent galaxy data and large angle microwave background anisotropies.Comment: 20 pages, RevTex using Latex 2.09, Submitted to Physical Review D Two figures included in fil

Further Studies of the Distributional Effects of Road Pricing

This Working Paper extends the study reported in Working Paper 400, which used the MVA START model for London, disaggregated into three income groups for each of car owners and non car owners, to investigate the distributional effects of road pricing in London. At the time of that study, it was not possible to obtain, from the disaggregate model, output on trips, flows and speeds. The further work reported in this Working Paper has involved extending the evaluation procedures to provide output on trips, flows and speeds; assessing the results from the previous study in tms of these indicators, and testing a fourth charging structure. In all, four charging structures were tested. It is concluded that the additional charging structure tested here, with the original LPAC charging structure, but with charging extended to the off peak in inner London, is by far the most effective in terms of overall benefits, and is similar in its distributional effects to the original LPAC structure

Some Results on the Identification and Estimation of Vector ARMAX Processes

This paper addresses the problem of identifying echelon canonical forms for a vector autoregressive moving average model with exogenous variables using finite algorithms. For given values of the Kronecker indices a method for estimating the structural parameters of a model using ordinary least squares calculations is presented. These procedures give rise, rather naturally, to a technique for the determination of the structural indices based on the use of conventional model selection criteria. A detailed analysis of the statistical properties of the estimation and identification procedures is given and some evidence on the practical significance of the results obtained is also provided. Modifications designed to improve the performance of the methods are presented. Some discussion of the practical significance of the results obtained is also provided.ARMAX model, consistency, echelon canonical form, efficiency, estimation, identification, Kronecker invariants, least squares, selection criterion, structure determination, subspace algorithm.

Urban road user charging and workplace parking levies

In this chapter we will briefly describe the provision made for the introduction of road user charging and workplace parking levies in the Transport Act 2000 and equivalent legislation for London and Scotland. After reviewing the background to these provisions, we will discuss the practical issues and policy questions which arise for any local authority wishing to take advantage of their new powers. Our discussion will draw attention to developments that have occurred since the passing of the Act and conclude on the prospects for charging schemes in the UK