Mathematics Commons^™

Existence Of Exact Zero Divisors And Totally Reflexive Modules In Artinian Rings, Basanti Sharma Poudyal

Mathematics Dissertations - Archive

In this dissertation, we consider commutative local Artinian rings (A, m, k), which are rings that satisfy the descending chain condition on ideals. First, we investigate the existence of exact zero divisors in Artinian Gorenstein rings. We say that a pair of elements (a, b) in m is an exact pair of zero divisors in A if ann(a) = (b) and ann(b) = (a). It is known that a generic Artinian Gorenstein ring of socle degree 3 contains at least one pair of exact zero divisors. We are interested in the existence of exact pairs of zero divisors in the …

Mri Analysis Of White Matter Myelin Water Content In Multiple Sclerosis: A Novel Approach Applied To Finding Correlates Of Cortical Thinning, Michael Dayan, Sandra M. Hurtado Rua, Elizabeth Monohan, Kyoko Fujimoto, Sneha Pandya, Eve M. Locastro, Tim Vartanian, Thanh D. Nguyen, Ashish Raj, Susan A. Gauthier

Mathematics and Statistics Faculty Publications

A novel lesion-mask free method based on a gamma mixture model was applied to myelin water fraction (MWF) maps to estimate the association between cortical thickness and myelin content, and how it differs between relapsing-remitting (RRMS) and secondary-progressive multiple sclerosis (SPMS) groups (135 and 23 patients, respectively). It was compared to an approach based on lesion masks. The gamma mixture distribution of whole brain, white matter (WM) MWF was characterized with three variables: the mode (most frequent value) m1 of the gamma component shown to relate to lesion, the mode m2 of the component shown to be associated with normal …

Mathematical Evolution, Jeremiah Farrell, William Johnston

Scholarship and Professional Work - LAS

Crossword puzzle featured in the May 2017 issue of American Mathematical Monthly.

An Exploratory Study Of Fifth-Grade Students’ Reasoning About The Relationship Between Fractions And Decimals When Using Number Line-Based Virtual Manipulatives, Scott Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Understanding the relationship between fractions and decimals is an important step in developing an overall understanding of rational numbers. Research has demonstrated the feasibility of technology in the form of virtual manipulatives for facilitating students’ meaningful understanding of rational number concepts. This exploratory dissertation study was conducted for the two closely related purposes: first, to investigate a sample of fifth-grade students’ reasoning regarding the relationship between fractions and decimals for fractions with terminating decimal representations while using virtual manipulative incorporating parallel number lines; second, to investigate the affordances of the virtual manipulatives for supporting the students’ reasoning about the decimal-fraction …

Use Of Generalized Gamma Distribution In Modeling, Hongbo Yu

Mathematics Theses - Archive

In this study, we have considered analysis of lifetime or survival data with right censoring, which is the most common form of censoring encountered in practice. Assuming a fully parametric setup, the main objective is to consider a wider family of distributions for the lifetime and then find the maximum likelihood estimates of the model parameters using some optimization technique available in R statistical software. In this work, the generalized gamma distribution is considered as the distribution for the lifetime which is flexible in the sense that it contains some of the commonly used lifetime distributions, such as Weibull, gamma, …

Application Of Symplectic Integration On A Dynamical System, William Frazier

Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic …

Assessing Non-Atomicity In Groups Of Divisibility, Brandon G. Goodell

All Dissertations

An integral domain D is atomic if every non-zero non-unit is a product of irreducibles. More generally, D is quasi-atomic if every non-zero non-unit divides some product of atoms. Arbitrary integral domains, however, cannot be assumed to be quasi-atomic in general; factorization in a non-atomic D can be subtle. We outline a novel method of qualifying the quasi-atomicity of D by studying ascending filtrations of localizations of D and the associated groups of divisibility. This approach yields structure theorems, cochain complexes, and cohomological results. We take care to present examples of integral domains exhibiting the spectrum of factorization behavior and …

The Elvis Problem A Minimal Time Problem With Constant Dynamics, Emily Ribando-Gros

Honors Capstones

No abstract provided.

Weighted Distributions: A Brief Review, Perspective And Characterizations, Aamir Saghir, Gholamhossein G. Hamedani, Sadaf Tazeem, Aneeqa Khadim

Mathematics, Statistics and Computer Science Faculty Research and Publications

The weighted distributions are widely used in many fields such as medicine, ecology and reliability, to name a few, for the development of proper statistical models. Weighted distributions are milestone for efficient modeling of statistical data and prediction when the standard distributions are not appropriate. A good deal of studies related to the weight distributions have been published in the literature. In this article, a brief review of these distributions is carried out. Implications of the differing weight models for future research as well as some possible strategies are discussed. Finally, characterizations of these distributions based on a simple relationship …

Identification Of Dynamic Outliers, Kangkana Sarmah Baruah

Theses, Dissertations and Culminating Projects

Several methods for performing the identification of outliers are described when dealing with functional data. The methods studied include prediction intervals for detection of dynamic functional outliers as well as related methods from the functional data literature. A comparison of methods is performed using metrics for dynamic outlier identification. Simulations and applications to environmental studies illustrate the applicability of the methods. Results obtained from simulation and application to real dataset suggest that Dynamic Function-on-Function Regression is a preferable method for detecting dynamic outliers. This method can detect outliers at a very high identification rate. Identification rate of dynamic outliers increases …

Quantum Mechanics For Non-Hermitian Hamiltonians With Pt Symmetries, Gustavo D. Duarte

Theses, Dissertations and Culminating Projects

Quantum Mechanics is an axiomatic theory. One of its axioms states that every observable of a physical system is associated with a Hermitian operator allowing the reality of the energy spectrum and a complete set of eigenfunctions. Furthermore, because of the Hermicity imposed on the observable described by the Hamiltonian H, the time evolution of the system is preserved. In recent years, researchers have shown that the Hermicity requirement may be relaxed by a weaker condition described by the combined actions of P and T symmetries on the operator. Under this new regimen some non-Hermitian Hamiltonians have real spectra such …

Joint Modelling Of Longitudinal Measurements And Time-To-Event Data : Application To Hiv Study, Mirna Walid Halawani

Theses, Dissertations and Culminating Projects

Longitudinal and survival data are frequently collected in biomedical studies. The research questions of interest in these studies often require separate analysis of the outcomes. But in many occasions interest also lies in studying their association structures, such as in biomarker research, where the clinical studies are designed to identify biomarkers with strong prognostic capabilities for event time outcomes. In the separate analyses, a linear mixed-effects model is used for modeling the longitudinal data to study the changing trend of the response overtime when controlling some covariates and a survival model is used to model the time-to-event data. A common …

Constructing Magic Squares Of Squares Modulo Certain Prime Numbers, Nicholas Ryan Bilynsky

Theses, Dissertations and Culminating Projects

A magic square is a square table of numbers such that each row, column, or diagonal adds up to the same sum. This research is inspired by an open question posed by Martin Labar in 1984. The open question states: “Can a 3 x 3 magic square be constructed using nine distinct perfect squares?” Though unsolved, this question sheds light on the existence of a Magic Square of Squares modulo a prime number p. For over two thousand years, many mathematicians have looked at these magical properties. In this thesis, the focus is on certain prime numbers p in the …

Spin Viscosity Effects In Planar Ferrofluid Couette Flow Of Ferrofluids, LucíA Cataldo Ottieri

Theses, Dissertations and Culminating Projects

Previous studies of planar Couette flow of ferro-fluids in a transverse time-independent external magnetic field are extended to include the effects by spin diffusion. We numerically study the modification in the internal rotation of particles in a colloidal ferro-fluid. In particular, we consider a ferro-fluid between two concentric cylinders, and apply a radial magnetic field inversely proportional to the radial variable. We consider the influence of shear effects by assuming a constant magnetic field while varying the rotation rate of the inner cylinder, and the effects of the balance between shear and magnetic stresses by varying the values of the …

Stochastic Improvisation Of Jazz Solos, Tevin Rouse

Theses, Dissertations and Culminating Projects

We propose using stochastic methods to generate new Jazz solos in the style of an artist of interest. To accomplish this, we implement several Markov models that use an artist’s known solos in order to mimic their pitch selection tendencies. Construction of two unique solos were generated for each artist considered as well as analysis of the characteristics the solos possessed in comparison to the artist’s original solo. This software implementation seeks to offer a new method for creating computer music compositions.

Migration At The Provincial Level In China: Effects Of The Economic Motivation And Migration Cost, Mengran Zhang

Renée Crown University Honors Thesis Projects - All

Since 1978 when China relaxed the restriction om internal migration, thousands of millions of labors have moved from hometowns to other places in search of better jobs and higher incomes in 30 years. This study looks at the internal migration at provincial level from 1995 to 2000 and also analyzes how the different wages levels in different provinces or in rural and urban areas in the same province affect the migration. By looking at the percentage of migrants to the destination provinces (region) from the home province to the total migrants from the home province, the study assesses the to …

A Unified Inter-Host And In-Host Model Of Antibiotic Resistance And Infection Spread In A Hospital Ward, Lester Caudill, Barry Lawson

Department of Math & Statistics Faculty Publications

As the battle continues against hospital-acquired infections and the concurrent rise in antibiotic resistance among many of the major causative pathogens, there is a dire need to conduct controlled experiments, in order to compare proposed control strategies. However, cost, time, and ethical considerations make this evaluation strategy either impractical or impossible to implement with living patients. This paper presents a multi-scale model that offers promise as the basis for a tool to simulate these (and other) controlled experiments. This is a “unified” model in two important ways: (i) It combines inter-host and in-host dynamics into a single model, and (ii) …

Eit Imaging Of Admittivities With A D-Bar Method And Spatial Prior: Experimental Results For Absolute And Difference Imaging, Sarah J. Hamilton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body's surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a …

Residues, Bernoulli Numbers And Finding Sums, Mohammed Saif Alotaibi

Graduate Theses/Dissertations

A large number of infinite sums, such as , cannot be found by the methods of real analysis. However, many of them can be evaluated using the theory of residues. In this thesis we characterize several methods of summations using residues, including methods integrating residues and the Bernoulli numbers. In fact, with this technique we derive some summation formulas for particular Finite Sums and Infinite Series that are difficult or impossible to solve by the methods of real analysis.

The Classification Problem For Models Of Zfc, Samuel Dworetzky

Boise State University Theses and Dissertations

Models of ZFC are ubiquitous in modern day set theoretic research. There are many different constructions that produce countable models of ZFC via techniques such as forcing, ultraproducts, and compactness. The models that these techniques produce have many different characteristics; thus it is natural to ask whether or not models of ZFC are classifiable. We will answer this question by showing that models of ZFC are unclassifiable and have maximal complexity. The notions of complexity used in this thesis will be phrased in the language of Borel complexity theory.

In particular, we will show that the class of countable models …

Classification Of Vertex-Transitive Structures, Stephanie Potter

Boise State University Theses and Dissertations

When one thinks of objects with a significant level of symmetry it is natural to expect there to be a simple classification. However, this leads to an interesting problem in that research has revealed the existence of highly symmetric objects which are very complex when considered within the framework of Borel complexity. The tension between these two seemingly contradictory notions leads to a wealth of natural questions which have yet to be answered.

Borel complexity theory is an area of logic where the relative complexities of classification problems are studied. Within this theory, we regard a classification problem as an …

A Snapshot Of The Alignment Of University Students’ Mathematical Problem Solving Practices To A Likert Scale Assessment Of Mathematical Problem Solving, Duy Phan

Mathematics Theses - Archive

This study investigates the alignment of students' actual problem-solving practices and compares them to the outcomes on a Likert scale mathematical problem solving (MPS) assessment. The Likert scale survey items developed by the Mathematical Problem Solving Item Development Project (MPSI) to gather information on undergraduate's MPS in five domains: sense-making, representing/connecting, reviewing, justifying, and challenge (Epperson, Rhoads, and Campbell, 2016). This snapshot investigation analyzes two individual undergraduate student interviews to characterize the students' MPS practices. Data analysis suggests a promising alignment between the MPSI survey results and students' actual practices. The analysis also establishes preliminary reliability of the MPSI survey …

English Language Learners In The Mathematics Classroom, Julia Mccormick

Senior Honors Projects

Mathematics is often considered a universal language. Most of us have heard this statement from a math teacher at some point throughout our academic careers. However, for students moving to the United States from another country with minimal fluency in English, this is clearly not the case. They may walk into math class, a subject area in which they may have excelled in their native country, and see the words “polynomial”, “coefficient”, and “differentiate” on the board. Regardless of their experiences in their native language, there are disconnects and cultural differences between languages and skills emphasized that prevents mathematics from …

Solving A Rubik’S Cube: An Analysis Of Problem Solving Strategies, Nicole Kerrigan

Senior Honors Projects

Stumbling upon a difficult problem to solve is inevitable. A difficult problem is defined as a problem in which the solution is not easily discovered for a typical person. These problems can range from real-life situations, such as quitting an addiction or finding a cure for cancer, to recreational puzzles such as a game of chess or a Rubik’s Cube. Due to their complexity, and in some cases lack of information on the subject, it is easy to get frustrated and not try when one encounters such a problem. For this reason, it is imperative to have a skill set …

Time Dependent Solution For An Incompressible Viscous Fluid Flow In A Cavity, Bishnu Parajuli

Theses and Dissertations

The Finite Element Method is used to find the time dependent solution for an incompressible viscous fluid flow in a cavity in two dimension. The governing equations for this system are the continuity equation and the momentum equation. We use finite element method to obtain the dependent variables. Here we derive weak formulation and develop finite element model by using Galerkin Method. Then we compute velocity components of the fluid for a square cavity. The numerical results are presented.

Multi-Type Branching Processes Model Of Nosocomial Epidemic, Zeinab Nageh Mohamed

Theses and Dissertations

The potency of an infectious disease to spread between different types of susceptible individuals in a hospital determines the fate of controlling nosocomial epidemics. I use a multi-type branching process with a joint negative binomial offspring distribution to study nosocomial epidemics. In particular, I estimate the basic reproduction number R0 and study its relationship with the offspring distribution’s parameters at different and fixed number of generations. Also, I study the effect of contact tracing on estimates of R0.

Observations On Convexity, Chad A. Huckaby

Electronic Theses and Dissertations

This thesis will explore convexity as it pertains to sets of complex-valued functions. These include preliminary looks at established linear and polynomially convex hulls, along with the development of new types of convex hulls. These types will include, but are not limited to the hulls determined by inversions, shift inversions, and Mobius transformations. A convex hull must be preceded by the set of functions involved. These hulls are the smallest convex sets that contain the original set. Justifications and precise definitions are included within the body of the work.

Languages, Geodesics, And Hnn Extensions, Maranda Franke

Department of Mathematics: Dissertations, Theses, and Student Research

The complexity of a geodesic language has connections to algebraic properties of the group. Gilman, Hermiller, Holt, and Rees show that a finitely generated group is virtually free if and only if its geodesic language is locally excluding for some finite inverse-closed generating set. The existence of such a correspondence and the result of Hermiller, Holt, and Rees that finitely generated abelian groups have piecewise excluding geodesic language for all finite inverse-closed generating sets motivated our work. We show that a finitely generated group with piecewise excluding geodesic language need not be abelian and give a class of infinite non-abelian …

Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson

Dissertations

As a result of stiff systems of ODEs, difficulties arise when using time stepping methods for PDEs. Krylov subspace spectral (KSS) methods get around the difficulties caused by stiffness by computing each component of the solution independently. In this dissertation, we extend the KSS method to a circular domain using polar coordinates. In addition to using these coordinates, we will approximate the solution using Legendre polynomials instead of Fourier basis functions. We will also compare KSS methods on a time-independent PDE to other iterative methods. Then we will shift our focus to three families of orthogonal polynomials on the interval …

A New Approach To Ramanujan's Partition Congruences, Mayra C. Huerta

Theses and Dissertations

MacMahon provided Ramanujan and Hardy a table of values for p(n) with the partitions of the first 200 integers. In order to make the table readable, MacMahon grouped the entries in blocks of five. Ramanujan noticed that the last entry in each block was a multiple of 5. This motivated Ramanujan to make the following conjectures, p(5n+4) ≡ 0 (mod 5); p(7 n+5) ≡ 0 (mod 7); p(11n+6) ≡ 0 (mod 11) which he eventually proved.

The purpose of this thesis is to give new proofs for Ramanujan's partition …