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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
Honors Projects
In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …
Simulations And Queueing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann
Simulations And Queueing Theory: The Effects Of Randomly Bypassing Security, Emily Ortmann
Masters Theses & Doctoral Dissertations
We discuss queueing theory in the setting of airport security and customs. By developing queueing simulations based on mathematical models, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.
Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck
Simulations And Queueing Theory: The Effects Of Priority And Vip Thresholds, Laura Schuck
Masters Theses & Doctoral Dissertations
Everyone has experienced waiting in lines, whether it is at the airport, the grocery store, or somewhere in-between. By developing queueing simulations based on mathematical models of airport security and customs, we explore a variety of questions related to optimal queue design with respect to efficiency, feasibility, priority, and other prescribed/variable constraints.
A Mathematical Analysis Of The Game Of Chess, John C. White
A Mathematical Analysis Of The Game Of Chess, John C. White
Selected Honors Theses
This paper analyzes chess through the lens of mathematics. Chess is a complex yet easy to understand game. Can mathematics be used to perfect a player’s skills? The work of Ernst Zermelo shows that one player should be able to force a win or force a draw. The work of Shannon and Hardy demonstrates the complexities of the game. Combinatorics, probability, and some chess puzzles are used to better understand the game. A computer program is used to test a hypothesis regarding chess strategy. Through the use of this program, we see that it is detrimental to be the first …
Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme
Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme
Theses and Dissertations
The Department of Defense (DoD) enlists multiple complex systems across each of their departments. Between the aging systems going through an overhaul and emerging new systems, quality assurance to complete the mission and secure the nation‘s objectives is an absolute necessity. The U.S. Air Force‘s increased interest in Remotely Piloted Aircraft (RPA) and the Space Warfighting domain are current examples of complex systems that must maintain high reliability and sustainability in order to complete missions moving forward. DoD systems continue to grow in complexity with an increasing number of components and parts in more complex arrangements. Bathtub-shaped hazard functions arise …
Sports Analytics With Computer Vision, Colby T. Jeffries
Sports Analytics With Computer Vision, Colby T. Jeffries
Senior Independent Study Theses
Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …
Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal
Inclusion Of Blocking Power For A Complete Voting Power Analysis In The Imf, Shiwani Varal
Senior Independent Study Theses
The International Monetary Fund (IMF) calculates the voting power of a country by dividing the total of one member's votes by the total of all members' votes. This method of calculating the power of a state judges power as voting weight. However, voting weights are the total number of votes a country has in an institution, while voting power is the influence a country has on a policy decision. A better approach to calculate this voting power within an institution is by using voting power indices. However, literature only calculates the winning power, while voting power is defined as the …