The subject of this work is a theoretical analysis of the Pearcey function. In optics, thin lens theory supposes that all rays focus at a unique point where the field converges. For a real lens, the focal point is replaced by a cusp, which is the end point of a caustic curve dividing the bright field region from the dark. My particular interest is the pattern of nodal points within the cusp. By investigating the stationary points for the cusp catastrophe, asymptotic approximations are found for the Pearcey function. This in turn leads to the development of finding the positions of nodal points inside, and outside a caustic. Also values for $|P|$ on a small circle surrounding a node are examined and show reasonable accuracy of order $10^{-8}$. / Thesis / Master of Science (MSc) / Identifying the nodes of the Pearcey function.

The purpose of the present study was to examine the perceptual processes associated with gender differences in leadership emergence recognition. Prior research has indicated that females are less likely to be identified as an emerging leader, even when they display identical leadership behaviors as that of their male counterparts. Unlike most of the previous research performed in this area which has obtained only static snapshots of leadership recognition, the present study used a nonlinear dynamic modeling technique, called cusp catastrophe theory. It was predicted that a nonlinear model would account for more variance than a linear model. Furthermore, it was also predicted that participants would be more resistant to recognizing a female as an emerging leader, as compared to a male. This effect was expected to be greater for male participants than female participants. Participants included 19 organizational members, who watched videos of either a male or female emerging as the leader of a four-person group. Participants recorded their perceptions of leadership through a dynamic measure. In accordance with cusp catastrophe theory, results were analyzed using the program GEMCAT II (General Multivariate Methodology for Estimating Catastrophe Models). Contrary to expectations, none of the predictions were supported. It is suggested that this was primarily due to methodological issues, rather than the relevance of cusp catastrophe modeling for leadership perceptions. Recommendations for future work in this area are provided. / Master of Science

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