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Advanced electron diffraction methods for structural description of zeolites
Laštovičková, Anna ; Mazur, Michal (advisor) ; Tyrpekl, Václav (referee)
Electron diffraction (ED) is a powerful tool for the structure determination of crystalline materials. It offers an alternative to single crystal X-ray diffraction (SCXRD) that is often limited by the size of synthesized crystals. Electron diffraction allows analysis of materials at the nanoscale, thus it is particularly useful for samples which crystals are too small for other methods. ED utilizes electrons for collection of diffraction patterns that can be performed in a transmission electron microscope (TEM). Collected ED patterns are further analyzed allowing for the determination of unit cell parameters, lattice type, and even the crystal structure itself. Nevertheless, the effective structure determination from standard ED patterns requires in-depth expertise and data collection is time consuming. Current development of ED methods focuses on the facilitation and automatization of data collection and processing. Notably, highly advanced, continuous rotation electron diffraction (cRED) data collection takes only a few minutes enabling structure determination within a single day. In this work, I present the utilization of cRED method for the structural characterization of zeolites. These materials are often synthesized as polycrystalline samples with crystals of nanometer in size. This makes...
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An Alternative Approach to the Structure Determination of Hierarchical Archimedean Copulas
Górecki, J. ; Holeňa, Martin
Copulas offer very a flexible tool for a stochastic dependence modeling. One of the most popular classes of copulas is the class of hierarchical Archimedean copulas, which gained its popularity due to the fact that the models from the class are able to model the stochastic dependencies conveniently even in high dimensions. One critical issue when estimating a hierarchical Archimedean copula is to correctly determine its structure. The paper describes an approach to the problem of the structure determination of a hierarchical Archimedean copula, which is based on the close relationship of the copula structure and the values of measure of concordance computed on all its bivariate margins. The presented approach is conveniently summarized as a simple algorithm.
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