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 Creator:
 Patno, Janina Silvana P
 Description:
 We consider the problem of sending a message in a communication network. Our networks are modeled by graphs. In our graphs we want to send a message from a vertex s, the sender, to a vertex r, the receiver, via paths from s tor. One difficulty we may encounter if we try sending the message along every possible s, rpath is that the receiver r will be flooded, so we focus our attention on certain finite protocols for sending the message from s to r. We study the probability that such a protocol successfully sends a message from s to r if the edges of the network live with probability p. We present some results and some open problems on this topic. Keywords: network, communication, protocol, twoterminal graph, twoterminal reliability polynomial
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Safaralian, Leila
 Description:
 Digitized as part of the "Retrospective Thesis and Dissertation Digitization Project." No abstract is available.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Sastre, Iane
 Description:
 This work is based on the article" A Guide to Entropy and the Second Law of Thermodynamics" [1] by E. H. Lieb of Princeton University and J. Yngvason of Vienna University. The article appeared on the May 1998 issue of Notices of the American Mathematical Society. The authors present a thermodynamic system as a set of states, define an ordering < on the set, and develop axioms for the ordering relation. These axioms lead to the construction of a realvalued function S (entropy) which encodes <. The encoding of < by S strongly depends of the comparability of states both within one system and in compound systems. Thus much of the work is dedicated to showing that the Comparison Hypothesis holds for simple and compound systems. The article is mainly expository, in the sense that, for the most part, it offers no proof of the results. This work intends to expand the expository nature of the article by providing a proof for each of the stated results. In addition to providing a proof for each result, two other approaches to the Second Law of Thermodynamics are explored.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Spangler, Megan
 Description:
 We start by familiarizing ourselves with edge covers. We review several interesting results for covers using triangles and covers using cycles. We then consider covering a graph with cuts. Determining the minimum total number of edges in a cut cover of a graph, called its cut cover size, is an NPcomplete problem. We investigate some special cases of graphs for which the cut cover size can be easily determined. The main result of this thesis is that the cut cover size of a graph is bounded from above by 2e  n + 1 when the graph is connected and has e edges and n vertices. Before proving the main result, we look at specific cases where the bound holds with equality, namely in trees, odd cycles and most complete graphs. We then make a key observation that the main result is related to a known upper bound using the maximum size of a stable cut. This observation gives us a simpler inequality to consider. We prove the main result by proving the simpler inequality by induction. Finally, we prove that equality holds in the bound precisely for those connected graphs all of whose blocks are complete graphs Kn(n =I 4,8) or odd cycles e2k+!.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 DePalma, Eli D
 Description:
 Digitized as part of the "Retrospective Thesis and Dissertation Digitization Project." No abstract is available.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Eddo, Timothy J
 Description:
 Computing the k dominant singular values of a matrix A by computing the singular value decomposition may require an exorbitant amount time when A is large sparse and rectangular. Instead, the iterative Lanczos method may be used to compute a partial tridiagonal decomposition of AT A as an intermediate step in computing the k dominant singular values of A. We discuss the problematic loss of orthogonality among the Lanczos vectors that is apparent when implementing the Lanczos method in finite precision along with two methods often used as a remedy: full reorthogonalization and partial reorthogonalization. We implement a hybrid Lanczosbased routine for computing the k dominant singular values derived from two existing routines. Keywords: Lanczos method, partial reorthogonalization, restarts, singular values, SVD.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Shinsato, Tina
 Description:
 Over the past century golf has become an obsession among many Americans. With the popularity of any sport, the opportunity to gamble will usually follow. It is clear that a matchup between a casual golfer and an avid golfer would not be fair. Therefore a method was created to equalize the game: the golf handicap system. This opened the door for tournaments between amateurs as well side bets between neighbors thus leading to the arguable question; Does the golf handicap create a fair game? Using data from a local golf country club, the question of fairness will be addressed in terms of the player against the course rating and the player randomly paired with another player. Point estimates and interval estimates will pave the way for hypothesis testing. Through the use of the ttest, !proportion Ztest and Wilcoxon matched pairs test, inferences about the hanidcap system will be made based on the statistical analysis. Key words: Golf; Handicap; Fairness; Statistics; Confidence interval; Significance; Hypothesis tests.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Jones, Jessica M
 Description:
 The focus of this thesis is to use Galois Theory to prove results in Number Theory. As a result, we begin by familiarizing ourselves with some significant results in Galois Theory. We then proceed to discuss other pertinent results in Algebraic Number Theory. This discussion provides the tools necessary to prove key theorems later in the text. The first five chapters, along with Chapters 8 and 10, are included to provide the reader with background information. As a result, the reader will find that not every result in these chapters is followed by a proof. The first main result we discuss in full is Kummer's Theorem. This theorem connects factoring a polynomial mod p with factoring p once it has been lifted to the ring of integers. A proof of the well known Quadratic Reciprocity Law follows which incorporates Kummer's Theorem and results in Galois Theory. The remaining text is devoted to the KroneckerWeber Theorem which states that every Abelian extension of Q is contained in a cyclotomic extension. We conclude the discussion of the KroneckerWeber Theorem with a few concrete examples.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 McNulty, Anne
 Description:
 This paper begins with the definition of an elliptic curve. We define the group law on elliptic curves and discuss methods for finding points on elliptic curves. We discuss torsion points and the use of division polynomials to calculate them. We investigate different bounds on torsion points and discuss the PrasadYogananda Conjecture. We empirically examine the coefficient in the PrasadYogananda Conjecture.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Reeves, Tonya
 Description:
 A repetition is a sequence of symbols in which the first half is the same as the second half. An edgecoloring of a graph is repetitionfree if there is no path with a color pattern that is a repetition. The minimum number of colors so that a graph has an edgecoloring that is repetition free is called the Thue edgechromatic number. In this thesis we investigate the Thue edgechromatic number of kary trees, that is trees in which every vertex has at most k children. Specifically we obtain new upper and lower bounds for the Thue edgechromatic number of binary trees, and present a new general method for obtaining repetitionfree edgecolorings of kary trees from what we call kspecial sequences. We present examples of kspecial sequences as well as algorithms for generating and verifying kspecial sequences and repetitionfree colorings of kary trees.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics