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Comparison of Design Optimality Criteria of Reduced Models for Response Surface Designs in a Spherical Design Region: Author: Chomtee, Boonorm; Date: 2003-05-15; Program: Statistics; Abstract: In this dissertation, the major objective is to compare 3 and 4 factor response surface designs in a spherical design region by studying design optimality criteria (D, A, G, and IV-criteria) over sets of reduced models. Hence, theoretical and computational details of evaluating optimality criteria for reduced models for response surface designs in a spherical design region have been described. Specifically, robustness results of the spherical response surface designs and the comparison of design optimality criteria of the response surface designs across the full second-order model and sets of ...; Download File | View full details

Return Map Characterizations of Singular Solutions for a Model of Bursting with Two Slow Variables: Author: Griffiths, Roger Evan; Date: 2003-05-15; Program: Mathematics; Abstract: Various physiological systems display bursting electrical activity (BEA). There exist numerous three variable models to describe this behavior. However, four variables may be required to explain some qualitative features of BEA. In this dissertation a model with two slow and two fast variables is presented. For some parameter values the system has stable equilibria while for other values there exist bursting solutions. A singular construction of the latter solutions corresponds to the existence of a fixed point of a one dimensional map. The map is the composition of two maps derived from the s...; Download File | View full details