A Cohomological Characterization of Leibniz Central Extensions of Lie Algebras

Mainly motivated by Pirashvili's spectral sequences on a Leibniz algebra, a cohomological characterization of Leibniz central extensions of Lie algebras is given based on Corollary 3.3 and Theorem 3.5. In particular, as applications, we obtain the cohomological version of Gao's main Theorem in \cite{Gao2} for Kac-Moody algebras and answer a question in \cite{LH}.Comment: 12 pages. Proc. Amer.Math.Soc. (to appear in a simplified version

Classification of simple weight modules for the N=2N=2 superconformal algebra

In this paper, we classify all simple weight modules with finite dimensional weight spaces over the $N=2$ superconformal algebra.Comment: 18 pages, Latex, in this version we delete the Section 7 for application to the $N=1$ superconformal algebr

Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra

In this paper we investigate Lie bialgebra structures on the twisted Heisenberg-Virasoro algebra. With the classifications of Lie bialgebra structures on the Virasoro algebra, we determined such structures on the twisted Heisenberg-Virasoro algebra. Moreover, some general and useful results are obtained. With our methods and results we also can easily to determine such structures on some Lie algebras related to the twisted Heisenberg-Virasoro algebra.Comment: Latex 18page. arXiv admin note: text overlap with arXiv:0901.133

A note on the proof of magnetic flux quantization from ODLRO

It is noticed that the excellent proof of the connection of magnetic flux quantization and off-diagonal long range order (ODLRO) presented recently by Nieh, Su and Zhao suffers from an imperfection, namely, the f-factors in the case of finite translation do not satisfy $f(a)f(b)=f(a+b)$, which was employed in the proof. A corrected proof is proposed to remedy this point.Comment: 6 pages, LATEX, no figure

Visualising ergonomics data for design

Existing ergonomics data are not effectively used by designers; this is mainly because the data are not presented in a designer-friendly format. In order to help designers make better use of ergonomics data, we explored the potential of representing existing ergonomics data in a more dynamic and visual way, and making them look more relevant to design. The Cambridge Engineering Selector (CES) was adopted to turn static ergonomics data into manipulative and comparative data sets. Contextual information in a visual format was added; clearer illustrations and scenarios relevant to design were developed; design case studies were compiled and linked to the relevant ergonomics data sets – the process resulted in a new design support tool: the ErgoCES. The tool was consequently brought to both design students and professionals for evaluation. The results suggested that the ErgoCES had helped making ergonomics data more accessible to designers, and many new features (e.g. scenarios and case studies) were highly valued by the designers. Among the participants, 100% of the design students and 79% of the professionals indicated that they would use the tool when it becomes widely available.The research project is funded by the Engineering and Physical Sciences Research Council, Grant EP/F0 32145/1. The authors would like to thank all the participants for helping evaluating the tool. Hua Dong is currently sponsored by The Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning