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Alternative Strategies for Thermoelectric Materials Development - Springer
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Alternative Strategies for Thermoelectric Materials DevelopmentA. P. Gon?alvesAffiliated withDepartment Química, Instituto Tecnológico e Nuclear/CFMC-UL, C. GodartAffiliated withCNRS, ICMPE, CMTR
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, 1 June 2015, Pages 208–218
An approach to cluster separability in a partition, ,
Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31000 Osijek, CroatiaIn this paper, we consider the problem of cluster separability in a minimum distance partition based on the squared Euclidean distance. We give a characterization of a well-separated partition and provide an operational criterion that gives the possibility to measure the quality of cluster separability in a partition. Especially, the analysis of cluster separability in a partition is illustrated by implementation of the k-means algorithm.2000 MSC62H30; 68T10; 90C26; 90C27; 91C20; 47N10KeywordsClustering; Data mining; Cluster separability; Separability balls
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Limits in PMF of Teichmuller geodesics
We consider the limit set in Thurston's compactification PMF of Teichmueller space of some Teichmueller geodesics defined by quadratic differentials with minimal but not uniquely ergodic vertical foliations. We show that a) there are quadratic differentials so that the limit set of the geodesic is a unique point, b) there are quadratic differentials so that the limit set is a line segment, c) there are quadratic differentials so that the vertical foliation is ergodic and there is a line segment as limit set, and d) there are quadratic differentials so that the vertical foliation is ergodic and there is a unique point as its limit set. These give examples of divergent Teichmueller geodesics whose limit sets overlap and Teichmueller geodesics that stay a bounded distance apart but whose limit sets are not equal. A byproduct of our methods is a construction of a Teichmueller geodesic and a simple closed curve $\gamma$ so that the hyperbolic length of the geodesic in the homotopy class of gamma varies between increasing and decreasing on an unbounded sequence of time intervals along the geodesic.
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