Abstract. In this article we consider partitioned Runge-Kutta (PRK) methods for Hamiltonian partial differential equations (PDEs) and present some sufficient conditions for multi-symplecticity of PRK methods of Hamiltonian PDEs.

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Abstract:Micro Learning through open educational resources (OERs) is becoming increasingly popular. However, adaptive micro learning support remains inadequate by current OER platforms. To address this, our smart system, Micro Learning as a Service (MLaaS), aims to deliver personalized OER with micro learning to satisfy their real-time needs. In this paper, we focus on constructing a knowledge base to support the decision-making process of MLaaS. MLaas is built using a top-down approach. A conceptual graph-based ontology construction is first developed. An educational data mining and learning analytic strategy is then proposed for the data level. The learning resource adaptation still requires learners' historical information. To compensate for the absence of this information initially (aka 'cold start'), we set up a predictive ontology-based mechanism. As the first resource is delivered to the beginning of a learner's learning journey, the micro OER recommendation is also optimized using a tailored heuristic.