a b s t r a c tFollowing the results of Rüschendorf and Uckelmann (2002) [20], we introduce the completely mixable distributions on R and prove that the distributions with monotone density and moderate mean are completely mixable. Using this method, we solve the minimization problem min X i ∼P Ef (X 1 + · · · + X n ) for convex functions f and marginal distributions P with monotone density. Our results also provide valuable implications in variance minimization, bounds for the sum of random variables and risk theory.

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Recent building emergency management research has highlighted the need for the effective utilization of dynamically changing building information. BIM (building information modelling) can play a significant role in this process due to its comprehensive and standardized data format and integrated process. This paper introduces a BIM based virtual environment supported by virtual reality (VR) and a serious game engine to address several key issues for building emergency management, for example, timely two-way information updating and better emergency awareness training. The focus of this paper lies on how to utilize BIM as a comprehensive building information provider to work with virtual reality technologies to build an adaptable immersive serious game environment to provide real-time fire evacuation guidance. The innovation lies on the seamless integration between BIM and a serious game based virtual reality (VR) environment aiming at practical problem solving by leveraging state-of-the-art computing technologies. The system has been tested for its robustness and functionality against the development requirements, and the results showed promising potential to support more effective emergency management.

A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling known as maximal ordering. With an appropriate choice of filters, second-order error bounds in the position and in the parallel velocity, and first-order error bounds in the normal velocity are obtained with respect to the scaling parameter. The proof compares the modulated Fourier expansions of the exact and the numerical solutions. Numerical experiments illustrate the error behaviour of the filtered Boris algorithm.

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