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 Creator:
 Hultman, Jason
 Description:
 Hospital emergency room patients often experience lengthy delays while waiting for an open bed and treatment. Some patients become frustrated and leave without being seen, which results in lost hospital revenue. Hospital administrators are responding with the introduction of new protocols to improve response times. One popular protocol goes by the name of FastTrack. This thesis focuses on proposing a mathematical model for FastTrack and using a combination of mathematical theory and simulation to analyze system performance. Prior efforts to analyze system performance have been data driven and taken place after implementation. The work here is predictive in nature. Through the application of theory and simulations, we demonstrate that an appropriately implemented FastTrack protocol can reduce the average wait times for certain classes of patients without significantly impacting the average wait for other patient classes. We also suggest a revised protocol involving a threshold for treating FastTrack patients that seems to improve efficiency.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Knapp, Randall G
 Description:
 This is a survey of various results concerning the extremity of graphs and digraphs. Given a graph, there are various subsets of the vertex set that can be interpreted as the "extremity of the graph"; we investigate several of these: the periphery, the set of vertices eccentric to the center, and the margin. We ·generalize the concept of periphery and margin to digraphs. Topics covered include the following: finding families of graphs such that the vertices in the periphery are the same as the vertices that are eccentric to the center, finding conditions on the product of two graphs which insure that the resulting periphery and set of vertices eccentric to the center are equal, studying graphs where each vertex of the graph has exactly one eccentric vertex, and finding conditions which allow us to construct supergraphs of a given graph such that the periphery or margin of the supergraph is isomorphic to the given graph. This last topic is also investigated in the context of digraphs.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Santana, Michael
 Description:
 This thesis focuses on two ideas in tournament theory: cycle intersections in tournaments (i.e., intersection spectra of tournaments) and some work done on score sequences of tournaments. Chapter 2 deals with the intersection spectrum of a specific family of tournaments, and Chapter 4 restricts the intersection spectrum of strong tournaments to characterize new families of strong tournaments. Previous work by Brualdi and Li, as well as, Poet and Shader, characterizes what are known as upset tournaments by their score sequences. Chapter 3 extends this characterization to kupset tournaments, again based on their score sequences (in particular, their score arrangements). Chapter 5 provides a new proof of a wellknown characterization of score sequences of tournaments. At the very end of this thesis is an Appendix that contains many drawings of tournaments referred to in the body of this work. It also contains the Graph Theory Hymn as a special tribute to Bohdan Zelinka whose work on cyclically simple tournaments gave the inspiration for this thesis. Keywords: tournaments, upset tournaments, intersection spectrum, score sequences
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Singh, Leena
 Description:
 Digitized as part of the "Retrospective Thesis and Dissertation Project." No abstract is available.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Martinez, Martha
 Description:
 The purpose of this paper is to utilize algebraicgeometric ideas in the study of polynomials for which the associated polynomial functions are permuta tions of a given finite field. Polynomials of this type are called permutation polynomials. Due to the complexity of such geometric approach, we will concentrate on the specific study of lowdegree polynomials over finite fields of characteristic 2. Nevertheless, the methods to be presented can be ap plied to the study of polynomials of any degree over finite fields of arbitrary characteristic. Chapter 2 in this paper discusses criteria used in the determination of permutation polynomials, as well as elementary theoretical results. Other, more sophisticated results and some applications of permutation polyno mials are discussed in Chapter 3. In Chapter 4, we relate concepts and ideas from both algebra and algebraic geometry to the study of lowdegree polynomials over finite fields of characteristic 2; more specifically, we use algebraic geometry to classify permutation polynomials of degree up to 5 in characteristic 2. These same techniques are then applied, in Chapter 5, to the classification of general permutation polynomials (an important type of permutation polynomials) of degree 8 over finite fields of characteristic 2. To our knowledge, this is the first time this classification has been carried out.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Caldwell, James David
 Description:
 This paper examines the problem of rank ordering a set of players or objects on the basis of a tournament arising from a complete set of pairwise comparisons.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Hermiz, Rani
 Description:
 The SPHAERICA (in English: Spherics) of Menelaus of Alexandria (dating to roughly 100 AD) is among the oldest known works on spherical geometry and trigonometry. Spherical geometry is the study of geometric objects on the surface of a sphere and spherical trigonometry is the study of relationships among sides and angles in triangles on a sphere, where the sides are arcs of “great circles.” The SPHAERICA was originally written in Koiné Greek, but editions in this language are no longer extant. One of the oldest complete editions still available is Abu Nasr Mansur’s “improved” edition in Arabic. Other editions exist in Arabic, Hebrew, Latin, and German, but none in English. In this thesis I give an English translation of Abu Nasr Mansur’s edition, and discuss certain aspects of the text from a modern point of view.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Hernandez Hernandez, Jesus
 Description:
 This thesis explores bond percolation on rary trees and then moves on to 3regular infinite trees. The last chapter explores bond percolation on the square lattice where horizontal bonds are open in a periodic fashion.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Newberg, Steven
 Description:
 A moduli problem seeks to find a bijection between a class of objects and a topological space that describes the parameters of the class of objects. We will present the moduli problem for a type of curve used in cryptography, elliptic curves. The topological space describing elliptic curves is the quotient of the complex plane by the action of matrices in SL_2(Z), which we call a modular curve. Taking a quotient of the upper half of the complex plane by subgroups of SL_2(Z) also give moduli spaces of elliptic curves but include some extra structure. There are special points on modular curves, which we will discuss and give methods for finding.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Mulvany, Justin
 Description:
 A multiclass processor sharing queue consists of a single server and a buffer that contains jobs that require service. At each time, the server simultaneously processes the work associated with each job in the buffer at a rate equal to the reciprocal number of jobs in system. The processor sharing queue is meant to be a mathematical idealization of a computer server time sharing algorithm [10]. Unlike its single class counterpart, a multiclass processor queue works on inhomogeneous jobs; i.e., some jobs may take longer to serve than others. A critical fluid model of a multiclass processor sharing queue describes the average behavior of the queue. We propose a strategy for analyzing the long run behavior of critical fluid model solutions using a notion of relative entropy. This generalizes the work in [13] concerning single class processor sharing queues by incorporating a term that accounts for the equilibration of the distribution of work across job classes. The potential application of this relative entropy approach is substantiated via simulations.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics