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Schur Rings Over Projective Special Linear Groups, David R. Wagner
Schur Rings Over Projective Special Linear Groups, David R. Wagner
Theses and Dissertations
This thesis presents an introduction to Schur rings (S-rings) and their various properties. Special attention is given to S-rings that are commutative. A number of original results are proved, including a complete classification of the central S-rings over the simple groups PSL(2,q), where q is any prime power. A discussion is made of the counting of symmetric S-rings over cyclic groups of prime power order. An appendix is included that gives all S-rings over the symmetric group over 4 elements with basic structural properties, along with code that can be used, for groups of comparatively small order, to enumerate all …
Weakly Holomorphic Modular Forms In Prime Power Levels Of Genus Zero, David Joshua Thornton
Weakly Holomorphic Modular Forms In Prime Power Levels Of Genus Zero, David Joshua Thornton
Theses and Dissertations
Let N ∈ {8,9,16,25} and let M#0(N) be the space of level N weakly holomorphic modular functions with poles only at the cusp at infinity. We explicitly construct a canonical basis for M#0(N) indexed by the order of the pole at infinity and show that many of the coefficients of the elements of these bases are divisible by high powers of the prime dividing the level N. Additionally, we show that these basis elements satisfy an interesting duality property. We also give an argument that extends level 1 results …
Existence Of A Periodic Brake Orbit In The Fully Symmetricplanar Four Body Problem, Ammon Si-Yuen Lam
Existence Of A Periodic Brake Orbit In The Fully Symmetricplanar Four Body Problem, Ammon Si-Yuen Lam
Theses and Dissertations
We investigate the existence of a symmetric singular periodic brake orbit in the equal mass, fully symmetric planar four body problem. Using regularized coordinates, we remove the singularity of binary collision for each symmetric pair. We use topological and symmetry tools in our investigation.
Periodic Points And Surfaces Given By Trace Maps, Kevin Gregory Johnston
Periodic Points And Surfaces Given By Trace Maps, Kevin Gregory Johnston
Theses and Dissertations
In this thesis, we consider the properties of diffeomorphisms of R3 called trace maps. We begin by introducing the definition of the trace map. The group B3 acts by trace maps on R3. The first two chapters deal with the action of a specific element of B3,called αn. In particular, we study the fixed points of αn lying on a topological subspace contained in R3, called T . We investigate the duality of the fixed points of the action ofαn, which will be defined later in the thesis.Chapter 3 involves the study of the fixed points of an element called …
Machine Learning For Disease Prediction, Abraham Jacob Frandsen
Machine Learning For Disease Prediction, Abraham Jacob Frandsen
Theses and Dissertations
Millions of people in the United States alone suffer from undiagnosed or late-diagnosed chronic diseases such as Chronic Kidney Disease and Type II Diabetes. Catching these diseases earlier facilitates preventive healthcare interventions, which in turn can lead to tremendous cost savings and improved health outcomes. We develop algorithms for predicting disease occurrence by drawing from ideas and techniques in the field of machine learning. We explore standard classification methods such as logistic regression and random forest, as well as more sophisticated sequence models, including recurrent neural networks. We focus especially on the use of medical code data for disease prediction, …
American Spread Option Pricing With Stochastic Interest Rate, An Jiang
American Spread Option Pricing With Stochastic Interest Rate, An Jiang
Theses and Dissertations
In financial markets, spread option is a derivative security with two underlying assets and the payoff of the spread option depends on the difference of these assets. We consider American style spread option which allows the owners to exercise it at any time before the maturity. The complexity of pricing American spread option is that the boundary of the corresponding partial differential equation which determines the option price is unknown and the model for the underlying assets is two-dimensional.In this dissertation, we incorporate the stochasticity to the interest rate and assume that it satisfies the Vasicek model or the CIR …
Weak Cayley Table Groups Of Wallpaper Groups, Rebeca Ann Paulsen
Weak Cayley Table Groups Of Wallpaper Groups, Rebeca Ann Paulsen
Theses and Dissertations
Let G be a group. A Weak Cayley Table mapping ϕ : G → G is a bijection such that ϕ(g1g2) is conjugate to ϕ(g1)ϕ(g2) for all g1, g2 in G. The set of all such mappings forms a group W(G) under composition. We study W(G) for the seventeen wallpaper groups G.
Isomorphisms Of Landau-Ginzburg B-Models, Nathan James Cordner
Isomorphisms Of Landau-Ginzburg B-Models, Nathan James Cordner
Theses and Dissertations
Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted A and B) that are constructed from a nondegenerate quasihomogeneous polynomial W and a related group of symmetries G. In 2013, Tay proved that given two polynomials W1, W2 with the same quasihomogeneous weights and same group G, the corresponding A-models built with (W1, G) and (W2, G) are isomorphic. An analogous theorem for isomorphisms between orbifolded B-models remains to be found. This thesis investigates isomorphisms between B-models using polynomials in two variables in search of such a theorem. In particular, several examples are given showing the relationship between continuous …
Construction And Isomorphism Of Landau-Ginzburg B-Model Frobenius Algebras, Matthew Robert Brown
Construction And Isomorphism Of Landau-Ginzburg B-Model Frobenius Algebras, Matthew Robert Brown
Theses and Dissertations
Landau-Ginzburg Mirror Symmetry provides for the construction of two algebraic objects, called the A- and B-models. Special cases of these models–constructed using invertible polynomials and abelian symmetry groups–are well understood. In this thesis, we consider generalizations of the B-model, and specifically address the associativity of the multiplication in these models. We also prove an explicit B-model isomorphism for a class of polynomials in three variables.
Modeling Individual Health Care Utilization, Matthew Aaron Webb
Modeling Individual Health Care Utilization, Matthew Aaron Webb
Theses and Dissertations
Health care represents an increasing proportion of global consumption. We discuss ways to model health care utilization on an individual basis. We present a probabilistic, generative model of utilization. Leveraging previously observed utilization levels, we learn a latent structure that can be used to accurately understand risk and make predictions. We evaluate the effectiveness of the model using data from a large population.
The Principles Of Effective Teaching Student Teachershave The Opportunity To Learn In An Alternativestudent Teaching Structure, Danielle Rose Divis
The Principles Of Effective Teaching Student Teachershave The Opportunity To Learn In An Alternativestudent Teaching Structure, Danielle Rose Divis
Theses and Dissertations
Research has shown that the focus of mathematics student teaching programs is typically classroom management and non-mathematics specific teaching strategies. However, the redesigned BYU student teaching structure has proven to help facilitate a greater focus on mathematics-specific pedagogy and student mathematics during post-lesson reflection meeting conversations. This study analyzed what specific principles of NCTM’s standards of effective teaching were discussed in the reflection meetings of this redesigned structure. This study found that the student teachers extensively discussed seven of the eight principles NCTM considers to be necessary for effective mathematics teaching. Other pedagogical principles pertaining to student mathematical learning not …
The Solenoid And Warsawanoid Are Sharkovskii Spaces, Tyler Willes Hills
The Solenoid And Warsawanoid Are Sharkovskii Spaces, Tyler Willes Hills
Theses and Dissertations
We extend Sharkovskii's theorem concerning orbit lengths of endomorphisms of the real line to endomorphisms of a path component of the solenoid and certain subspaces of the Warsawanoid. In particular, Sharkovskii showed that if there exists an orbit of length 3 then there exist orbits of all lengths. The solenoid is the inverse limit of double covers over the circle, and the Warsawanoid is the inverse limit of double covers over the Warsaw circle. We show Sharkovskii's result is true for path components of the solenoid and certain subspaces of the Warsawanoid.
Compression Bodies And Their Boundary Hyperbolic Structures, Vinh Xuan Dang
Compression Bodies And Their Boundary Hyperbolic Structures, Vinh Xuan Dang
Theses and Dissertations
We study hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary. We consider individual hyperbolic structures as well as special regions in the space of all such hyperbolic structures. We use some properties of the boundary hyperbolic structures on C to establish an interesting property of cusp shapes of tunnel number one manifolds. This extends a result of Nimershiem in [26] to the class of tunnel number one manifolds. We also establish convergence results on the geometry of compression bodies. This extends the work of Ito in [13] from the punctured-torus case …
Alternating Direction Implicit Method With Adaptive Grids For Modeling Chemotaxis In Dictyostelium Discoideum, Christopher F. Loomis
Alternating Direction Implicit Method With Adaptive Grids For Modeling Chemotaxis In Dictyostelium Discoideum, Christopher F. Loomis
Theses and Dissertations
Dictyostelium discoideum (Dd) is a model organism, studied for reasons from cell movement to chemotaxis to human disease control. Creating a computer model of the life cycle of Dd has garnered great interest, one part of which is the Aggregation Stage, where thousands of amoeba gather together to form a slug. Chemotaxis is the mechanism through which this is accomplished. This thesis develops two- and three-dimensional alternating direction implicit code which solves the diffusion equation on an adaptive grid. The calculated values for both two and three dimensions are checked against the actual solution and error results are provided. Comparisons …
A Nonabelian Landau-Ginzburg B-Model Construction, Ryan Thor Sandberg
A Nonabelian Landau-Ginzburg B-Model Construction, Ryan Thor Sandberg
Theses and Dissertations
The Landau-Ginzburg (LG) B-Model is a significant feature of singularity theory and mirror symmetry. Krawitz in 2010, guided by work of Kaufmann, provided an explicit construction for the LG B-model when using diagonal symmetries of a quasihomogeneous, nondegenerate polynomial. In this thesis we discuss aspects of how to generalize the LG B-model construction to allow for nondiagonal symmetries of a polynomial, and hence nonabelian symmetry groups. The construction is generalized to the level of graded vector space and the multiplication developed up to an unknown factor. We present complete examples of nonabelian LG B-models for the polynomials x^2y + y^3, …
Evaluation And Refinement Of Generalized B-Splines, Ian Daniel Henriksen
Evaluation And Refinement Of Generalized B-Splines, Ian Daniel Henriksen
Theses and Dissertations
In this thesis a method for direct evaluation of Generalized B-splines (GB-splines) via the representation of these curves as piecewise functions is presented. A local structure is introduced that makes the GB-spline curves more amenable to the integration used in constructing bases of higher degree. This basis is used to perform direct computation of piecewise representation of GB-spline bases and curves. Algorithms for refinement using these local structures are also developed.
Investigations Into Non-Degenerate Quasihomogeneous Polynomials As Related To Fjrw Theory, Scott C. Mancuso
Investigations Into Non-Degenerate Quasihomogeneous Polynomials As Related To Fjrw Theory, Scott C. Mancuso
Theses and Dissertations
The motivation for this paper is a better understanding of the basic building blocks of FJRW theory. The basics of FJRW theory will be briefly outlined, but the majority of the paper will deal with certain multivariate polynomials which are the most fundamental building blocks in FJRW theory. We will first describe what is already known about these polynomials and then discuss several properties we proved as well as conjectures we disproved. We also introduce a new conjecture suggested by computer calculations performed as part of our investigation.
Nonlocally Maximal Hyperbolic Sets For Flows, Taylor Michael Petty
Nonlocally Maximal Hyperbolic Sets For Flows, Taylor Michael Petty
Theses and Dissertations
In 2004, Fisher constructed a map on a 2-disc that admitted a hyperbolic set not contained in any locally maximal hyperbolic set. Furthermore, it was shown that this was an open property, and that it was embeddable into any smooth manifold of dimension greater than one. In the present work we show that analogous results hold for flows. Specifically, on any smooth manifold with dimension greater than or equal to three there exists an open set of flows such that each flow in the open set contains a hyperbolic set that is not contained in a locally maximal one.
Octahedral Extensions And Proofs Of Two Conjectures Of Wong, Kevin Ronald Childers
Octahedral Extensions And Proofs Of Two Conjectures Of Wong, Kevin Ronald Childers
Theses and Dissertations
Consider a non-Galois cubic extension K/Q ramified at a single prime p > 3. We show that if K is a subfield of an S_4-extension L/Q ramified only at p, we can determine the Artin conductor of the projective representation associated to L/Q, which is based on whether or not K/Q is totally real. We also show that the number of S_4-extensions of this type with K as a subfield is of the form 2^n - 1 for some n >= 0. If K/Q is totally real, n > 1. This proves two conjectures of Siman Wong.
Topics Pertaining To The Group Matrix: K-Characters And Random Walks, Randall Dean Reese
Topics Pertaining To The Group Matrix: K-Characters And Random Walks, Randall Dean Reese
Theses and Dissertations
Linear characters of finite groups can be extended to take k operands. The basics of such a k-fold extension are detailed. We then examine a proposition by Johnson and Sehgal pertaining to these k-characters and disprove its converse. Probabilistic models can be applied to random walks on the Cayley groups of finite order. We examine random walks on dihedral groups which converge after a finite number of steps to the random walk induced by the uniform distribution. We present both sufficient and necessary conditions for such convergence and analyze aspects of algebraic geometry related to this subject.
Analysis Of Multiple Collision-Based Periodic Orbits In Dimension Higher Than One, Skyler C. Simmons
Analysis Of Multiple Collision-Based Periodic Orbits In Dimension Higher Than One, Skyler C. Simmons
Theses and Dissertations
We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many of these orbits feature regularizable collisions between the masses. We demonstrate existence of the periodic orbits after performing the appropriate regularization. Stability, including linear stability, for the orbits is then computed using a technique due to Roberts. We point out other interesting features of the orbits as appropriate. When applicable, the results are extended to a broader family of orbits with similar behavior.
The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
The Steiner Problem On Closed Surfaces Of Constant Curvature, Andrew Logan
Theses and Dissertations
The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region in the covering space that is guaranteed to contain T. We will then provide an algorithm for solving the n-point Steiner problem on such a surface.
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
Theses and Dissertations
Understanding cell motion facilitates the understanding of many biological processes such as wound healing and cancer growth. Constructing mathematical models that replicate amoeboid cell motion can help us understand and make predictions about real-world cell movement. We review a force-based model of cell motion that considers a cell as a nucleus and several adhesion sites connected to the nucleus by springs. In this model, the cell moves as the adhesion sites attach to and detach from a substrate. This model is then reformulated as a random process that tracks the attachment characteristic (attached or detached) of each adhesion site, the …
The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen
The Existence Of A Discontinuous Homomorphism Requires A Strong Axiom Of Choice, Michael Steven Andersen
Theses and Dissertations
Conner and Spencer used ultrafilters to construct homomorphisms between fundamental groups that could not be induced by continuous functions between the underlying spaces. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This led us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We …
A Covering System With Minimum Modulus 42, Tyler Owens
A Covering System With Minimum Modulus 42, Tyler Owens
Theses and Dissertations
We construct a covering system whose minimum modulus is 42. This improves the previous record of 40 by P. Nielsen.
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor
Theses and Dissertations
Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of …
Connecting Galois Representations With Cohomology, Joseph Allen Adams
Connecting Galois Representations With Cohomology, Joseph Allen Adams
Theses and Dissertations
In this paper, we examine the conjecture of Avner Ash, Darrin Doud, David Pollack, and Warren Sinnott relating Galois representations to the mod p cohomology of congruence subgroups of the general linear group of n dimensions over the integers. We present computational evidence for this conjecture (the ADPS Conjecture) for the case n = 3 by finding Galois representations which appear to correspond to cohomology eigenclasses predicted by the ADPS Conjecture for the prime p, level N, and quadratic nebentype. The examples include representations which appear to be attached to cohomology eigenclasses which arise from D8, S3, A5, and S5 …
Hecke Eigenvalues And Arithmetic Cohomology, William Leonard Cocke
Hecke Eigenvalues And Arithmetic Cohomology, William Leonard Cocke
Theses and Dissertations
We provide algorithms and documention to compute the cohomology of congruence subgroups of the special linear group over the integers when n=3 using the well-rounded retract and the Voronoi decomposition. We define the Sharbly complex and how one acts on a k-sharbly by the Hecke operators. Since the norm of a sharbly is not preserved by the Hecke operators we also examine the reduction techniques described by Gunnells and present our implementation of said techniques for n=3.
Hölder Extensions For Non-Standard Fractal Koch Curves, Joshua Taylor Fetbrandt
Hölder Extensions For Non-Standard Fractal Koch Curves, Joshua Taylor Fetbrandt
Theses and Dissertations
Let K be a non-standard fractal Koch curve with contraction factor α. Assume α is of the form α = 2+1/m for some m ∈ N and that K is embedded in a larger domain Ω. Further suppose that u is any Hölder continuous function on K. Then for each such m ∈ N and iteration n ≥ 0, we construct a bounded linear operator Πn which extends u from the prefractal Koch curve Kn into the whole of Ω. Unfortunately, our sequence of extension functions Πnu are not bounded in norm in the limit because the upper bound is …
A New Public-Key Cryptosystem, Christopher James Hettinger
A New Public-Key Cryptosystem, Christopher James Hettinger
Theses and Dissertations
Public key cryptosystems offer important advantages over symmetric methods, but the most important such systems rely on the difficulty of integer factorization (or the related discrete logarithm problem). Advances in quantum computing threaten to render such systems useless. In addition, public-key systems tend to be slower than symmetric systems because of their use of number-theoretic algorithms. I propose a new public key system which may be secure against both classical and quantum attacks, while remaining simple and very fast. The system's action is best described in terms of linear algebra, while its security is more naturally explained in the context …