Mathematics Commons^™

Problem Book On Higher Algebra And Number Theory, Ryanto Putra

Theses and Dissertations

This book is an attempt to provide relevant end-of-section exercises, together with their step-by-step solutions, to Dr. Zieschang's classic class notes Higher Algebra and Number Theory. It's written under the notion that active hands-on working on exercises is an important part of learning, whereby students would see the nuance and intricacies of a math concepts which they may miss from passive reading. The problems are selected here to provide background on the text, examples that illuminate the underlying theorems, as well as to fill in the gaps in the notes.

Mathematical Modeling Of Mers-Cov Nosocomial Epidemic, Adriana Quiroz

Theses and Dissertations

This thesis concerns about the analysis and modeling of spread of an infectious disease inside a hospital. We begin from the basic knowledge of the simple models: SIR and SEIR, to show an appropriate understanding of the epidemic dynamic process. We consider the Middle East Respiratory Syndrome Corona Virus (MERS-CoV), in Saudi Arabia, to introduce MERS-CoV SEIR ward model by developing different systems of equations in each ward (unit). We use the Next Generation Matrix method to calculate the basic reproduction number R0. Simulations of different scenarios are done using different combination of parameters.

To model MERS-CoV we established …

Disease Modeling Using Fractional Differential Equations And Estimation, Daniel P. Medina

Theses and Dissertations

Ordinary differential equations has been the most conventional approach when modeling spread of infectious diseases. Effective research has shown that using fractional-order differentiation can be a very useful and efficient extension for some mathematical models. In this thesis, fractional calculus is used to depict an SEIR model with a system of fractional-order differential equations. I also simulate the fractional-order SEIR using integer-order numerical methods. I also establish the estimation framework and show that it is accurately working.

Coupled Telegraph And Sir Model Of Information And Diseases, Jose De Jesus Galarza

Theses and Dissertations

In this work, the effect of information propagation on disease spread and vaccination uptake through networks is studied. In this model the information reaches different people at different distances from the center of information containing the health data. We use a pair of Telegraph equations to depict the vaccine and disease information propagation on a network embedded into a straight line. The Telegraph equation is coupled with an SIR (Susceptible-Infected-Recovered) model to examine the anticipated mutual influence. Numerical simulations and stability analysis were made to study the model. We show how the propagation of information about the disease impacts the …

Roman Domination In Complementary Prisms, Alawi I. Alhashim

Electronic Theses and Dissertations

The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number of complementary prisms. …

Peptide Identification: Refining A Bayesian Stochastic Model, Theophilus Barnabas Kobina Acquah

Electronic Theses and Dissertations

Notwithstanding the challenges associated with different methods of peptide identification, other methods have been explored over the years. The complexity, size and computational challenges of peptide-based data sets calls for more intrusion into this sphere. By relying on the prior information about the average relative abundances of bond cleavages and the prior probability of any specific amino acid sequence, we refine an already developed Bayesian approach in identifying peptides. The likelihood function is improved by adding additional ions to the model and its size is driven by two overall goodness of fit measures. In the face of the complexities associated …

Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, Hannah E. Green

Electronic Theses and Dissertations

To determine the function of a protein, we must know its 3-dimensional structure, which can be difficult to ascertain. Currently, predictive models are used to determine the structure of a protein from its sequence, but these models do not always predict the correct structure. To this end we use a nested graph model along with weighted invariants to minimize the errors and improve the accuracy of a predictive model to determine if we have the correct structure for a protein.

On T-Restricted Optimal Rubbling Of Graphs, Kyle Murphy

Electronic Theses and Dissertations

For a graph G = (V;E), a pebble distribution is defined as a mapping of the vertex set in to the integers, where each vertex begins with f(v) pebbles. A pebbling move takes two pebbles from some vertex adjacent to v and places one pebble on v. A rubbling move takes one pebble from each of two vertices that are adjacent to v and places one pebble on v. A vertex x is reachable under a pebbling distribution f if there exists some sequence of rubbling and pebbling moves that places a pebble on x. A pebbling distribution where every …

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

Honors Capstones

No abstract provided.

Average Frobenius Distributions For Elliptic Curves: Extremal Primes And Koblitz's Conjecture, Luke M. Giberson

All Dissertations

No abstract provided.

Chaos To Permanence - Through Control Theory, Sherli Koshy Chenthittayil

All Dissertations

Work by Cushing et al. [18] and Kot et al. [60] demonstrate that chaotic behavior does occur in biological systems. We demonstrate that chaotic behavior can enable the survival/thriving of the species involved in a system. We adopt the concepts of persistence/permanence as measures of survival/thriving of the species [35]. We utilize present chaotic behavior and a control algorithm based on [66, 72] to push a non-permanent system into permanence. The algorithm uses the chaotic orbits present in the system to obtain the desired state. We apply the algorithm to a Lotka-Volterra type two-prey, one-predator model from [30], a ratio-dependent …

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 …

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 …

Irrational Eigenvalues Of The Discrete Laplacian: A Study Of Simplical Complexes, Brian Bollen

Psychology

We study the behavior of eigenvalues of the discrete Laplacian of an abstract simplicial complex K when subdividing a single face of K . We show that if K is a simplex, performing this kind of restricted subdivision twice on a single face produces irrational eigenvalues for the discrete Laplacian.

Statistical Analysis Of Markovian Queueing Models Of Limit Order Books, Yiyao Luo

Arts & Sciences Graduate Student Theses and Dissertations

The objective of this thesis is to investigate the suitability of some Markovian queueing models in being able to effectively describe the dynamical properties of a limit order book more specifically. We review and compare the assumptions proposed by Huang et al.[Quantitative Finance,12,547-557(2012)] and Cont et al.[SIAM Journal for Financial Mathematics,4,1- 25(2013)], and estimate the intensity parameters in both ways, based on real data of a stock on the Nasdaq Stock Market. Trough comparing by cumulative distribution functions of first-passage time to state 0, we will hsow that the estimators of Cont’s model fit our data better and we put …

Statistical Models To Predict Popularity Of News Articles On Social Networks, Ziyi Liu

Arts & Sciences Graduate Student Theses and Dissertations

Social networks have changed the way that we obtain information. Content creators and, specifically news article authors, have in interest in predicting the popularity of content, in terms of the number of shares, likes, and comments across various social media platforms. In this thesis, I employ several statistical learning methods for prediction. Both regression-based and classification-based methods are compared according to their predictive ability, using a database from the UCI Machine Learning Repository.

Market Risk Management For Financial Institutions Based On Garch Family Models, Qiandi Chen

Arts & Sciences Graduate Student Theses and Dissertations

The financial stock market turned out to rise and fall suddenly and sharply in recent years, which means that volatility and uncertainty is very significant in market and measuring the market risk accurately is of great importance. I collect the historical close price of S&P 500 Financials Sector Index from January 19th 2011 to January 31st 2017, and use the daily logarithm yield as time series data to build 2 ARMA models and 5 GARCH family models using t-distribution. Then I calculate future 10 days’ relative VAR in 1-day horizon under 99\% confidence level based on the selected model. E-GARCH …

On Post-Selection Confidence Intervals In Linear Regression, Xinwei Zhang

Arts & Sciences Graduate Student Theses and Dissertations

The general goal of this thesis is to investigate and examine some issues about post-selection inference which arises from the setting where statistical inference is carried out after a datadriven model selection step. In this setting, the classical inference theory which requires a fixed priori model becomes invalid since the selected model is a result of random event. Hence, a common practice in applied research which ignores the model selection and builds up confidence interval will result in misleading or even false conclusion. In this thesis, specifically, we first discusses some examples to show how the classical inference theory loses …

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 …

Combinatorial Games On Graphs, Trevor K. Williams

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Combinatorial Games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games and some educational tools are presented which were developed by the author in the pursuit of the solution of these games.