Mathematics Commons^™

On The Conjugacy Problem For Automorphisms Of Trees, Kyle Douglas Beserra

Boise State University Theses and Dissertations

In this thesis we identify the complexity of the conjugacy problem of automorphisms of regular trees. We expand on the results of Kechris, Louveau, and Friedman on the complexities of the isomorphism problem of classes of countable trees. We see in nearly all cases that the complexity of isomorphism of subtrees of a given regular countable tree is the same as the complexity of conjugacy of automorphisms of the same tree, though we present an example for which this does not hold.

Number Sense In High School Mathematics Students, Vi Le Nguyen

Mathematics Theses - Archive

Understanding the real number system plays a very important role in each student’s mathematical achievement. The Texas Essential Knowledge and Skills (TEKS) for Mathematics Subchapter A. Elementary states, “For students to become fluent in mathematics, students must develop a robust sense of number” (TEKS Subchapter A Elementary, 2012). Knowledge of the real number system and number sense develops over several years. Once students get to high school, they are expected to have a large amount of knowledge about the real number system and number sense in order to effectively start and complete their high school math courses. However, many high …

A Model For Collective Dynamics In Ant Raids, Shawn D. Ryan

Mathematics and Statistics Faculty Publications

Ant raiding, the process of identifying and returning food to the nest or bivouac, is a fascinating example of collective motion in nature. During such raids ants lay pheromones to form trails for others to find a food source. In this work a coupled PDE/ODE model is introduced to study ant dynamics and pheromone concentration. The key idea is the introduction of two forms of ant dynamics: foraging and returning, each governed by different environmental and social cues. The model accounts for all aspects of the raiding cycle including local collisional interactions, the laying of pheromone along a trail, and …

A Modularized Tablet-Based Approach To Preparation For Remedial Mathematics, Kenneth A. Parker

Publications and Research

Basic arithmetic forms the foundation of the math courses that students will face in their undergraduate careers. It is therefore crucial that students have a solid understanding of these fundamental concepts. At an open- access university offering both two-year and four-year degrees, incoming freshmen who were identified as lacking in basic arithmetic skills were engaged in an experimental technology-enhanced workshop designed to provide them with a deeper understanding of arithmetic prior to their initial remedial coursework. Customized online content was created specifically for this experiment, and the first implementation (n=27) yielded statistically significant improvement, not only from pretest to post- …

Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent

Honors Theses

The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.

A Fractional Boundary Value Problem, Grant Yost

Honors Theses

We consider a fractional boundary value problem with various boundary conditions. This boundary value problem has two components, one fractional derivative of alpha degree with alpha between n-1 and n, and a fractional derivative of beta degree with beta between 0 and n-2. We prove existence and uniqueness of solutions, and show some examples that were found using a MATLAB simulation.

The Simple Zeros Of The Riemann Zeta-Function, Melissa N. Miller

Honors Theses

There have been many tables of primes produced since antiquity. In 348 BC Plato studied the divisors of the number 5040. In 1202 Fibonacci gave an example with a list of prime numbers up to 100. By the 1770's a table of number factorizations up to two million was constructed. In 1859 Riemann demonstrated that the key to the deeper understanding of the distribution of prime numbers lies in the study of a certain complex-valued function, called the zeta-function. In 1973 Montgomery used explicit formulas to study the pair correlation of the zeros of the zeta-function and their relationship to …

Opinion Formation About Childhood Immunization And Disease Spread On Networks, Shan Shan Zhao

Theses and Dissertations

People are physically and socially connected with each other. Those connections between people represent two, probably overlapping, networks: biological networks, through which physical contacts occur, or social network, through which information diffuse. In my thesis research, I am trying to answer that question in the context of pediatric disease spread on the biological network between households as well as within them and its relationship with information sharing on the social network of households (parents in that case) via "Information Cascades." I mainly focus on the Erdos-Renyi network model. In particular, I use two different but overlapping Erdos-Renyi networks for the …

Stable Local Cohomology And Cosupport, Peder Thompson

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation consists of two parts, both under the overarching theme of resolutions over a commutative Noetherian ring R. In particular, we use complete resolutions to study stable local cohomology and cotorsion-flat resolutions to investigate cosupport.

In Part I, we use complete (injective) resolutions to define a stable version of local cohomology. For a module having a complete injective resolution, we associate a stable local cohomology module; this gives a functor to the stable category of Gorenstein injective modules. We show that this functor behaves much like the usual local cohomology functor. When there is only one non-zero local cohomology …

Cohen–Macaulay Dimension For Coherent Rings, Rebecca Egg

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation presents a homological dimension notion of Cohen-Macaulay for non-Noetherian rings which reduces to the standard definition in the case that the ring is Noetherian, and is inspired by the homological notion of Cohen-Macaulay for local rings developed by Gerko. Under this notion, both coherent regular rings (as defined by Bertin) and coherent Gorenstein rings (as defined by Hummel and Marley) are Cohen-Macaulay.

This work is motivated by Glaz's question regarding whether a notion of Cohen-Macaulay exists for coherent rings which satisfies certain properties and agrees with the usual notion when the ring is Noetherian. Hamilton and Marley gave …

Rainbow Matchings And Hamilton Cycles In Random Graphs, Deepak Bal, Alan Frieze

Department of Mathematics Faculty Scholarship and Creative Works

Let HPn,m,k be drawn uniformly from all m-edge, k-uniform, k-partite hypergraphs where each part of the partition is a disjoint copy of [n]. We let HPn,m,k(κ) be an edge colored version, where we color each edge randomly from one of κ colors. We show that if κ=n and m=Knlogn where K is sufficiently large then w.h.p. there is a rainbow colored perfect matching. I.e. a perfect matching in which every edge has a different color. We also show that if n is even and m=Knlogn where K is sufficiently large then w.h.p. there is a rainbow colored Hamilton cycle in …

Self-Monitoring Practices, Attitudes, And Needs Of Individuals With Bipolar Disorder: Implications For The Design Of Technologies To Manage Mental Health, Elizabeth L. Murnane, Dan Cosley, Pamara Chang, Shion Guha, Ellen Frank, Geri K. Gay, Mark Matthews

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective To understand self-monitoring strategies used independently of clinical treatment by individuals with bipolar disorder (BD), in order to recommend technology design principles to support mental health management.

Materials and Methods Participants with BD (N = 552) were recruited through the Depression and Bipolar Support Alliance, the International Bipolar Foundation, and WeSearchTogether.org to complete a survey of closed- and open-ended questions. In this study, we focus on descriptive results and qualitative analyses.

Results Individuals reported primarily self-monitoring items related to their bipolar disorder (mood, sleep, finances, exercise, and social interactions), with an increasing trend towards the use of digital …

The Eagle Programming Language, Samuel G. Horlbeck Olsen

Mathematics, Statistics, and Computer Science Honors Projects

C remains the dominant systems programming language despite many new languages attempting to take its place. Modern languages generally value abstraction and safety over speed and direct control of hardware. They are therefore not well suited to the low-level tasks for which C was designed. This paper introduces a novel programming language, Eagle, which represents a fast, elegant alternative to C. It allows low-level programming while providing optional modern features like reference counting, closures, generators, and classes. In addition to specifying this language and reviewing the current alternatives, the paper describes the implementation of a working Eagle compiler. The language …

Bases For Mckay Centralizer Algebras, Lucas Gagnon

Mathematics, Statistics, and Computer Science Honors Projects

The finite subgroups of the special unitary group SU2 have been classified to be isomorphic to one of the following groups: cyclic, binary dihedral, binary tetrahedral, binary octahedral, and binary icosahedral, of order n, 4n, 24, 48, and 120, respectively. Associated to each group is a representation graph, which by the McKay correspondence is a Dynkin diagram of type Aˆ n−1, Dˆ n+2, Eˆ 6, Eˆ 7, or Eˆ 8. The centralizer algebra Zk(G) = EndG(V ⊗k ) is the algebra of transformations that commute with G acting on the k-fold tensor product of the defining representation V = C …

Building Voters: Exploring Interdependent Preferences In Binary Contexts, Ian Calaway

Mathematics, Statistics, and Computer Science Honors Projects

In this thesis we develop a new method for constructing binary preference orders for given interdependent structures, called characters. We introduce the preference space, which is a vector space of preference vectors. The preference vectors correspond to binary preference orders. We show that the hyperoctahedral group, Z2 o Sn, describes the symmetries of binary preferences orders and then define an action of Z2 o Sn on our preference vectors. We find a natural basis for a preference space. These basis vectors are indexed by subsets of proposals. We show that when completely separable binary preference vectors are decomposed using this …

Global Supply Sets In Graphs, Christian G. Moore

Electronic Theses and Dissertations

For a graph G=(V,E), a set S⊆V is a global supply set if every vertex v∈V\S has at least one neighbor, say u, in S such that u has at least as many neighbors in S as v has in V \S. The global supply number is the minimum cardinality of a global supply set, denoted γgs (G). We introduce global supply sets and determine the global supply number for selected families of graphs. Also, we give bounds on the global supply number for general graphs, trees, and grid graphs.

Lie Symmetry To Nonlinear Oscillator Systems And Applications, Xiaoyan Li

Theses and Dissertations

In this paper, we apply the theory of Lie symmetry to study a generalized second-order nonlinear differential equation, which includes several physical nonlinear oscillators such as force-free Helmholtz oscillator, force-free Duffing and Duffing-van der Pol oscillators, modified Emden-type equation and its hierarchy etc, and investigate the dynamical properties of this rather general equation. We identify and classify several new integrable cases for arbitrary values of exponents, which determine the tangent vector as well as the infinitesimal generator. Using the Lie point symmetry, we find the useful infinitesimal generators and canonical coordinates, and obtain the first integrals of the second-order nonlinear …

On Hypergroups Of Order At Most 6, Jordy C. Lopez

Theses and Dissertations

This thesis surveys recent results on hypergroups as defined by Frédéric Marty in [3] and [4] and their relation to association schemes as presented in [5]. We show that every association scheme is a hypergroup. Then, we compile a few general results on hypergroups needed for our investigation of hypergroups with three, four and six elements. From [1] and [7], we give examples of hypergroups that do not come from finite schemes and from no scheme at all. Our main result occurs when considering hypergroups S with six elements that have a non-normal closed subset T of order 2 with …

The Complete Structure Of Linear And Nonlinear Deformations Of Frames On A Hilbert Space, Devanshu Agrawal

Electronic Theses and Dissertations

A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show …

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …