4,504 research outputs found

    Standard and Non-standard Extensions of Lie algebras

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    We study the problem of quadruple extensions of simple Lie algebras. We find that, adding a new simple root α+4\alpha_{+4}, it is not possible to have an extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links and no loops between the dots, while it is possible if α+4\alpha_{+4} is a Borcherds imaginary simple root. We also comment on the root lattices of these new algebras. The folding procedure is applied to the simply-laced triple extended Lie algebras, obtaining all the non-simply laced ones. Non- standard extension procedures for a class of Lie algebras are proposed. It is shown that the 2-extensions of E8E_{8}, with a dot simply linked to the Dynkin-Kac diagram of E9E_{9}, are rank 10 subalgebras of E10E_{10}. Finally the simple root systems of a set of rank 11 subalgebras of E11E_{11}, containing as sub-algebra E10E_{10}, are explicitly written.Comment: Revised version. Inaccurate statements corrected. Expanded version with added reference

    Very Extended E8E_8 and A8A_8 at low levels, Gravity and Supergravity

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    We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended AD3A_{D-3} and E8E_8 (i.e. E11E_{11}) at low levels in terms of AD1A_{D-1} and A10A_{10} representations respectively. The results are consistent with the conjectured very extended A8A_8 and E11E_{11} symmetries of gravity and maximal supergravity theories given respectively in hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference expanded

    Covariance estimation for multivariate conditionally Gaussian dynamic linear models

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    In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the computation of confidence bounds of the forecasts. We develop an on-line, non-iterative Bayesian algorithm for estimation and forecasting. It is empirically found that, for a range of simulated time series, the proposed covariance estimator has good performance converging to the true values of the unknown observation covariance matrix. Over a simulated time series, the new method approximates the correct estimates, produced by a non-sequential Monte Carlo simulation procedure, which is used here as the gold standard. The special, but important, vector autoregressive (VAR) and time-varying VAR models are illustrated by considering London metal exchange data consisting of spot prices of aluminium, copper, lead and zinc.Comment: 21 pages, 2 figures, 6 table

    Powder removal from Ti-6Al-4V cellular structures fabricated via electron beam melting

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    Direct metal fabrication systems like electron beam melting (EBM) and direct metal laser sintering (also called selective laser melting) are gaining popularity. One reason is the design and fabrication freedom that these technologies offer over traditional processes. One specific feature that is of interest is mesh or lattice structures that can be produced using these powder-bed systems. One issue with the EBM process is that the powder trapped within the structure during the fabrication process is sintered and can be hard to remove as the mesh density increases. This is usually not an issue for the laser-based systems since most of them work at a low temperature and the sintering of the powder is less of an issue. Within the scope of this project, a chemical etching process was evaluated for sintered powder removal using three different cellular structures with varying mesh densities. All meshes were fabricated via EBM using Ti6Al4V Footnote Information powder. The results are promising, but the larger the structures, the more difficult it is to completely remove the sintered powder without affecting the integrity of the mesh structure

    CFD Analysis of Premixed Methane Chlorination Reactors with Detailed Chemistry

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    With the implementation of efficient algorithms for the accurate calculation of reaction source terms, computational fluid dynamics (CFD) is now a powerful tool for the simulation and design of chemical reactors with complex kinetic schemes. The example studied in this work is the methane chlorination reaction for which the detailed chemistry scheme has 152 reactions and 38 species. The adiabatic, jet-stirred chlorination reactor used for the CFD simulations is an insulated right cylinder with a coaxial premixed feed stream at one end. In order for this reactor to remain lit, recirculation of hot products is crucial, and hence, reactor stability is sensitive to both macroscale and microscale mixing. By neglecting density variations, a Lagrangian composition probability density function (PDF) code with a novel chemistry tabulation algorithm (in-situ adaptive tabulation or ISAT) for handling complex reactions is used to simulate the species concentrations and temperature field inside of the reactor. In addition, a reduced mechanism with 21 reactions and 15 species is tested for accuracy against the detailed chemistry scheme, a simplified CSTR model is used to illustrate the shortcomings of zero-dimensional models, and a pair-wise mixing stirred reactor (PMSR) model is used to show the stabilizing effect of micromixing on reactor stability. The CFD simulations are generally in good agreement with results from pilot-scale reactors for the outlet temperature and major species

    Detection of Drugs of Abuse by Raman Spectroscopy

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    Raman spectroscopy can provide rapid, sensitive, non-destructive analysis of a variety of drug types (e.g. amphetamines, alkaloids, designer drugs and date rape drugs). This review concentrates on developments in the past 15 years. It considers identification and quantification of drugs of abuse in different types of forensic evidence, including bulk street drugs as well as traces found in drinks, on fibres/clothing, in fingerprints, on fingernails, on bank notes and in body fluids
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