A coalition in a graph (Formula presented.) consists of two disjoint sets of vertices V 1 and V 2, neither of which is a dominating set but whose union (Formula presented.) is a dominating set. A coalition partition in a graph G of order (Formula presented.) is a vertex partition (Formula presented.) such that every set Vi of π either is a dominating set consisting of a single vertex of degree n–1, or is not a dominating set but forms a coalition with another set (Formula presented.) which is not a dominating set. In this paper we introduce this concept and study its properties.

No description available.

Stress can be defined as the mental, physical, and emotional response of humans to stressors encountered in their personal or professional environment. Stressors are introduced in various activities, especially those found in dynamic task conditions when multiple task requirements must be performed. Stress and stressors have been described as activators and inhibitors of human performance. The ability to manage high levels of acute stress is an important determinant of successful performance in any occupation. In situations where performance is critical, personnel must be prepared to operate successfully under hostile or extreme stress conditions; therefore training programs and engineered systems must be tailored to assist humans in fulfilling these demands. To effectively design appropriate training programs for these conditions, it is necessary to quantitatively describe stress. A series of theoretical stress models have been developed in previous research studies; however, these do not provide quantification of stress levels nor the impact on human performance. By modeling acute stress under dynamic task conditions, quantitative values for stress and its impact on performance can be assessed. Thus, this research was designed to develop a predictive model for acute stress as a function of human performance and task demand. Initially, a four factor two level experimental design (2 (Noise) x 2 (Temperature) x 2 (Time Awareness) x 2 (Workload)) was performed to identify reliable physiological, cognitive and behavioral responses to stress. Next, multivariate analysis of variance (n=108) tests were performed, which showed statistically significant differences for physiological, cognitive and behavioral responses. Finally, fuzzy set theory techniques were used to develop a comprehensive stress index model. Thus, the resulting stress index model was constructed using input on physiological, cognitive and behavioral responses to stressors as well as characteristics inherent to the type of task performed and personal factors that interact as mediators (competitiveness, motivation, coping technique and proneness to boredom). Through using this stress index model to quantify and characterize the affects of acute stress on human performance, these research findings can inform proper training protocols and help to redesign tasks and working conditions that are prone to create levels of acute stress that adversely affect human performance.

This thesis explores Russell’s Paradox and the comparative analysis of Zermelo-Fraenkel set theory, von Neumann-Bernays-Gödel set theory, and Russell’s Type Theory from a mathematical Platonist perspective, focusing on the ontology of sets. Our conclusion posits that, although these theories have made significant attempts in addressing Russell’s paradox and other inconsistencies of naïve set theory, we currently lack a proper language for expressing set theory that fully captures the underlying Platonic world of sets. Consequently, it is impossible to definitively refute or accept any of the given theories as the ultimate solution the paradox.

No description available.

No description available.

No description available.

No description available.

No description available.

A Julia set for a complex function 𝑓 is the set of all points in the complex plane where the iterates of 𝑓 do not form a normal family. A picture of the Julia set for a function can be generated with a computer by coloring pixels (which we consider to be small squares) based on the behavior of the point at the center of each pixel. We consider the accuracy of computer generated pictures of Julia sets. Such a picture is said to be accurate if each colored pixel actually contains some point in the Julia set. We extend previous work to show that the pictures generated by an algorithm for the family λe² are accurate, for appropriate choices of parameters in the algorithm. We observe that the Julia set for meromorphic functions with polynomial Schwarzian derivative is the closure of those points which go to infinity under iteration, and use this as a basis for an algorithm to generate pictures for such functions. A pixel in our algorithm will be colored if the center point becomes larger than some specified bound upon iteration. We show that using our algorithm, the pictures of Julia sets generated for the family λtan(z) for positive real λ are also accurate. We conclude with a cautionary example of a Julia set whose picture will be inaccurate for some apparently reasonable choices of parameters, demonstrating that some care must be exercised in using such algorithms. In general, more information about the nature of the function may be needed. / Ph. D.