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Algorithmic Methods for Mixed Recurrence Equations, Zeros of Classical Orthogonal Polynomials and Classical Orthogonal Polynomial Solutions of Three-Term Recurrence Equations
Using an algorithmic approach, we derive classes of mixed recurrence equations satisfied by classical orthogonal polynomials. Starting from certain structure relations satisfied by classical orthogonal polynomials or their connection formulae, we show that our mixed recurrence equations are structurally valid. However, they couldn't be easily obtained with classical methods and for this reason, our algorithmic approach is important. The main algorithmic tool used here is an extended version of Zeilberger's ...
Applicability of ordinal-array-based indicators to strange nonchaotic attractors
(Universität Kassel, 2017-06-12)
Time series are useful for modeling systems behavior, for predicting some events (catastrophes, epidemics, weather, . . . ) or for classification purposes (pattern recognition, pattern analysis). Among the existing data analysis algorithms, ordinal pattern based algorithms have been shown effective when dealing with simulation data. However, when applied to quasi-periodically forced systems, they fail to detect SNA and tori as regular dynamics. In this work we address this concern by defining ordinal array (OA) ...