Search Constraints
« Previous 
37,371  37,380 of 43,684

Next »
Search Results
 Creator:
 Lovelace, Joshua Walter
 Description:
 This thesis will briefly go over definitions and properties of continuous time Markov chains and describe the definition of reversibility and conditions for positive recurrence. We then discuss the evolution of the Markov chains studied in [12] which have state spaces consisting of the finite rooted subtrees of the infinite, regular, rooted, positional, dary tree. We summarize how the author of [12] used reversibility to prove a positive recurrence result for these chains. For the main results of the thesis, we analyze a Markov chain with a state space consisting of the set of finite rooted trees with unbounded degree. This chain was proposed and analyzed in [4] without reference to reversibility. Here, we identify a reversible measure for that chain and show nnder what conditions the measure is summable, and therefore give an alternate proof of the positive recurrence result in [4] using more probabilistic methods. Finally, the reversible measure is used to discuss the behavior of the chain, when it is positive recurrent. Keywords: Reversible Markov chains, Trees, Positive recurrence, Spanning trees
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Melcher, Michael
 Description:
 A monochromatic sink in an arccolored tournament is a vertex that can be reached by every other vertex in the tournament by a monochromatic path. A rainbow k cycle in an arccolored tournament is a cycle with k arcs such that no two arcs in the cycle have the same color. Motivated by a conjecture ofP. Erdos and a conjecture by Sands, Sauer, and Woodrow, we investigate the existence of monochromatic sinks in certain tournaments without rainbow 3cycles; the tournaments considered are tournaments obtained from special arc reversals of transitive tournaments. Among the tournaments investigated are upset tournaments, tournaments that are obtained by reversing the arcs in a path from the source to the sink in a transitive tournament. Results from the literature and some open problems are be discussed. Keywords: graph theory, tournament, arccolorings, monochromatic paths, upset tournaments
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Sanders, Gina
 Description:
 In this thesis, we investigate a coloring problem on a special class of graphs. A proper coloring of a graph is a coloring of the vertices of the graph so that vertices joined by an edge get different colors. A starcoloring of a graph is a proper coloring of a graph with the additional constraint that there are no 2colored paths on four vertices. A graph is said to be kstarcolorable if it can be starcolored with no more than k colors. It is well known that all outerplanar graphs are 6starcolorable. We prove that all outerplanar bipartite graphs are 5starcolorable and that there is a family of graphs that requires five colors. Keywords: graphs, starcoloring, planar, outerplanar, bipartite
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Brich, Jennifer
 Description:
 This thesis focuses on the formalization of basic topics in commutative algebra using the proof assistant Isabelle. This written exposition will provide an overview of the work that was completed to formalize the following objectives in Isabelle: 1. Define a Noetherian ring using three di!erent characterizations. 2. Show the existence of factorization in a Noetherian domain. 3. Show the uniqueness of factorization in a principal ideal domain. 4. Lay the ground work needed to prove unique factorization in K[x1, ..., xn], where K is a UFD. Chapter 1 provides a brief introduction to formalization and a detailed outline of the five theory files that were formalized for this project. Chapter 2 explains the fundamentals of formalization in Isabelle and serves as a reference guide to the formal work completed for my thesis. In Chapters 3 through 7, we explore the outlined mathematical concepts in greater detail. In each of these five chapters we will define and prove the results that were formalized in each of the theory files. This exposition ends with a few closing remarks about this project and ideas for future development in Isabelle, using the work from this thesis. After the exposition an appendix is provided that gives all of the Isabelle file that were produced for this project.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Stewart, Mary
 Description:
 In this thesis, we study finite simple groups as well as the Classification Theorem, which classifies all such groups. We will see by the Classification Theorem that all simple groups are one of the following four types: cyclic of prime order, alternating on n elements for n 2: 5, of Lietype, or sporadic. We prove that the cyclic groups of prime order are the only finite simple Abelian groups, and that the alternating groups on n elements are indeed simple for n 2: 5. We also prove that all groups in a specific family of Lietype groups, namely PSL2 (q), where q is a power of a prime and q > 3, are simple. Even though all finite simple groups have currently been classified, we explore some methods used to show certain groups are not simple. Through this, we are able to classify all simple groups of order through 360, as well as provide some more general results that cover infinitely many groups. Keywords: groups, simple groups, Sylow Theorems, JordanHolder Theorem, Classification Theorem
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Timmons, Craig
 Description:
 The focus of this thesis is star coloring planar graphs. A star coloring of a planar graph is a proper coloring in which no path on four vertices is colored with just two colors. A graph G is said to be kstarcolorable if G has a star coloring with at most k colors. The fewest number of colors needed to star color a graph G is called the star chromatic number of G. It is known that all planar graphs of girth at least seven can be star colored using at most 9 colors. We prove that all planar graphs of girth at least seven can be star colored using at most 7 colors. Also, we improve upon the current known bounds for star colorings of families of planar graphs of girth at least eight. It is known that there exists a planar graph that requires at least 10 colors to star color. We prove that there are planar bipartite graphs requiring at least 8 colors to star color, and that there are planar graphs of girth 5 requiring at least 6 colors to star color. Finally, we prove that there are planar graphs of girth 6 requiring at least 5 colors to star color. Keywords: graphs, starcoloring, planar, girth, outerplanar
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Wilson, Jason R
 Description:
 A major part of topology is the study of properties of topological spaces that are invariant under homeomorphisms. Such properties allow us to classify spaces. Some basic examples are compactness and connectedness. Although quite useful, these properties cannot, for example, distinguish between a torus and a sphere. Algebraic topology uses algebra to attach more sophisticated invariants to spaces. In particular, singular homology associates a sequence of abelian groups to a space known as the homology. After first reviewing general topology as well as some necessary ideas from homological algebra, this thesis establishes the basics of singular homology. Although showing that the homology of a space is a topological invariant is easy, computing the homology of nontrivial spaces is quite challenging. This leads us to develop a very general computational tool known as the MayerVietoris Sequence. With this tool in hand, we can compute the homology of spaces such as circles and spheres. Finally, we prove our main result, the Brouwer FixedPoint Theorem.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Mariscal, Eduardo
 Description:
 The thesis goal is to prove unique prime factorization (UPF) for ideals in a cyclotomic integers in the most elementary and efficient way. This way it can later be formally verified. The reason is to help prepare a formal verification of Fermat's Last Theorem (FLT) for regular primes. This thesis could be used as blueprint to formally verifying UPF. Once formally verify, UPF will be added to the Archives of Formal Proofs (AFP). AFP is an electronic journal that serves as a library of proofs, examples, scientific developments, which have beed formally verified using the proof assistant Isabelle. Not only UPF will be added to the AFP but also all the math that took to formally verifing it. And this by itself is a major contribution to AFP. By having UPF in the AFP it will be easier to formally verify FLT for regular primes since the UPF for ideal is essential to the proof. Formally verifying FLT for regular primes can be a future thesis for another master student. Special thanks to Dr. Wayne Aitken, my Thesis Advisor. Thanks to his collaboration, guidance, patience,. and contribution, this thesis was made possible. Also thanks to my siblings and mother for supporting me through out this long journey. Keywords: Unique prime factorization, Fermat's Last Theorem for regular primes, Formal Verification, Isabelle, Cyclotomic fields.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics
 Creator:
 Ellinger, Paul N
 Description:
 Digitized as part of the "Retrospective Thesis and Dissertation Project." No abstract is available. Item only available to the CSUSM community. Authentication with campus user name and password required.
 Resource Type:
 Thesis
 Campus Tesim:
 San Marcos
 Department:
 Mathematics