Ab initio based simulations have been proven in the past to be and still are a valuable and indispensable tool in the field of III‐nitride semiconductors. They have been successfully used to explain, describe and guide growth and characterization experiments and to address a large variety of material problems at different length scales. In the present report we review on five selected topics which span different length scales, various method developments, and diverse material properties that have been theoretically addressed within the research group “Physics of nitride‐based, nanostructured, light emitting devices.”
Let be a continuous function with and . If is convex, then , , is the characteristic function of an absolutely continuous probability distribution. The criterion complements Pólya's theorem and applies to characteristic functions with various types of behavior at the origin. In particular, it provides upper bounds on Kuttner's function , , which gives the minimal value of such that is a characteristic function. Specifically, . Furthermore, improved lower bounds on Kuttner's function are obtained from an inequality due to Boas and Kac.
Some of the recent developments concerning the synthesis, properties and applications of functionalised ionic liquids are highlighted. Various strategies are presented, including functionalisation of the cation, anion or both cation and anion in the same ionic liquid, leading to what has been termed dual-functionalised ionic liquids. Particular attention is given to the application of functionalised ionic liquids as reaction media, to stabilise nanoparticles/modify surfaces and to generate porous materials. 相似文献
