Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras

This paper completes a series devoted to explicit constructions of finite-dimensional irreducible representations of the classical Lie algebras. Here the case of odd orthogonal Lie algebras (of type B) is considered (two previous papers dealt with C and D types). A weight basis for each representation of the Lie algebra o(2n+1) is constructed. The basis vectors are parametrized by Gelfand--Tsetlin-type patterns. Explicit formulas for the matrix elements of generators of o(2n+1) in this basis are given. The construction is based on the representation theory of the Yangians. A similar approach is applied to the A type case where the well-known formulas due to Gelfand and Tsetlin are reproduced.Comment: 29 pages, Late

Preservation of Adiabatic Invariants under Symplectic Discretization

Symplectic methods, like the Verlet method, are a standard tool for the long term integration of Hamiltonian systems as they arise, for example, in molecular dynamics. One of the reasons for the popularity of symplectic methods is the conservation of energy over very long periods of time up to small fluctuations that scale with the order of the method. In this paper, we discuss a qualitative feature of Hamiltonian systems with separated time scales that is also preserved under symplectic discretization. Specifically, highly oscillatory degrees of freedom often lead to almost preserved quantities (adiabatic invariants). Using recent results from backward error analysis and normal form theory, we show that a symplectic method, like the Verlet method, preserves those adiabatic invariants. We also discuss step-size restrictions necessary to maintain adiabatic invariants in practical computations. 1 Introduction It is well-known (see [12], for example) that symplectic discretization scheme..

UAL Elements Promotional Comics

A promotional leaflet produced by University of the Arts London at the launching of their Elements system.</p

Techie Talk: Running Different Types of Report

Lucian describes how to run different types of report from Elements.To put you in complete control of your reporting, Elements provides each of our clients with a specialist SQL-based Reporting Database which is continuously updated from the Elements operational database. This supports direct SQL querying but also allows you to analyse your Elements data using the business intelligence tool of your choice.We also offer integrated SSRS reporting, empowering our clients to create their own custom reports which can be generated directly within the Elements UI. You can use our standard templates, write your own, or have our team of experts create custom templates for you. Our reporting functionality supports a wide range of data types and formatting options including data extracts, spreadsheets, CVs, group activity reports or formatted lists of outputs and activities.You can even add visualisations such as charts, graphs, co-authorship or collaboration diagrams and even maps.We have recently added even more expanded reporting and analytics capabilities, including dashboard designers and improved analytics.</p

Automating research data harvesting to reduce researchers' workload

<p>A presentation from Daryl Naylor, Digital Science, highlighting the project carried out by Imperial College London to encourage researcher adoption of ORCIDs. </p