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Full-Text Articles in Physical Sciences and Mathematics
Applying The Poincaré Recurrence Theorem To Billiards, Aaron Smith
Applying The Poincaré Recurrence Theorem To Billiards, Aaron Smith
Honors Theses
The Poincaré recurrence theorem is one of the first and most fundamental theorems of ergodic theory. When applied to a dynamical system satisfying the theorem's hypothesis, it roughly states that the system will, within a finite amount of time, return to a state arbitrarily close to its initial state. This result is intriguing and controversial, providing a contradiction with the Second Law of Thermodynamics known as the recurrence paradox. Here, we treat a set of pool balls on a billiard table as a dynamical system that satisfies the hypotheses of the Poincaré recurrence theorem. We prove that time is a …
Title Ix Compliance: A Comparison Of Division I Equality, Jacqueline Leake
Title Ix Compliance: A Comparison Of Division I Equality, Jacqueline Leake
Honors Theses
The passage of Title IX of the Education Amendments of 1972 has had a significant impact on college athletics. However, there is still a large disparity between opportunities offered for men and women. This study determined the true gender equality within Division I athletics. Inequalities were assessed in the areas of athletic participation, athletically related student aid, recruiting expenses, and total expenses. Data from these areas were gathered from the Equity in Athletics Disclosure Analysis Cutting Tool. Ratios and the difference between the ideal and current values were calculated for each category. Institutions were ranked in each category, as well …