Digital Commons Network^™

Tribute To Gene Chase, Calvin Jongsma

Faculty Work Comprehensive List

Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.

Solving Boundary Value And Initial Boundary Value Problems Of Partial Differential Equations Using Meshless Methods, Adam Johnson

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation, the methods of fundamental solutions (MFS) and the methods of particular solutions (MPS) are used to solve the boundary value problems of the Poisson and Helmholtz equations, where the particular solutions of the Poisson and Helmholtz equations in [13, 14] are used. Then the initial boundary value problems of the diffusion and wave equations are discretized into a sequence of boundary value problems of the Helmholtz equation by using either the Laplace transform or time difference methods along the lines of [8]. The Helmholtz problems are solved consequently in an iterative manner which leads to the solution …

Mathematical Modeling: Finite Element Analysis And Computations Arising In Fluid Dynamics And Biological Applications, Jorge Reyes

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is often the case when attempting to capture real word phenomena that the resulting mathematical model is too difficult and even not feasible to be solved analytically. As a result, a computational approach is required and there exists many different methods to numerically solve models described by systems of partial differential equations. The Finite Element Method is one of them and it was pursued herein.This dissertation focuses on the finite element analysis and corresponding numerical computations of several different models. The first part consists of a study on two different fluid flow models: the main governing model of fluid …

Analyzing Real Life Scenarios Through Linear And Exponential Functions Using Open Pedagogy., Lili Grigorian

Open Educational Resources

This assignment is on linear and exponential growth, which is connected to real life scenarios from students’ everyday life as well as teaches them financial responsibility and awareness of economic issues. Project has five parts. In part 1, students would use digital communication ability by creating a video about the topic from the knowledge they had prior to this project. In part 2 (the Mathematical part) they will use problem-solving and inquiry learning to better understand linear and exponential growth, in part 3 students will use global learning through reading to then annotate article and watch video to then discuss …

Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma

Faculty Work Comprehensive List

Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.

Exploring The Structure Of Partial Difference Sets With Denniston Parameters, Nicolas Ferree

Honors Theses

In this work, we investigate the structure of particular partial difference sets (PDS) of size 70 with Denniston parameters in an elementary abelian group and in a nonelementary abelian group. We will make extensive use of character theory in our investigation and ultimately seek to understand the nature of difference sets with these parameters. To begin, we will cover some basic definitions and examples of difference sets and partial difference sets. We will then move on to some basic theorems about partial difference sets before introducing a group ring formalism and using it to explore several important constructions of partial …

Staircase Arrangements Of Pillars With Distinct Heights, Andrea L. Simmons

Mathematics, Statistics, and Computer Science Honors Projects

We study the family A_n of sequences (a₁, a₂, ..., a_n) where 0 ≤ a_k ≤ k and nonzero entries are distinct. We show that these sequences are in bijection with the set partitions of [n + 1]. These sequences have a natural poset structure, and we analyze the maximal chains within this poset. Finally, we explore various subfamilies of A_n, including sequences whose largest entry is k and sequences missing the value k.

Staircase Packings Of Integer Partitions, Melody Arteaga

Mathematics, Statistics, and Computer Science Honors Projects

An integer partition is a weakly decreasing sequence of positive integers. We study the family of packings of integer partitions in the triangular array of size n, where successive partitions in the packings are separated by at least one zero. We prove that these are enumerated by the Bell-Like number sequence (OEIS A091768), and investigate its many recursive properties. We also explore their poset (partially ordered set) structure. Finally, we characterize various subfamilies of these staircase packings, including one restriction that connects back to the original patterns of the whole family.

A Brascamp-Lieb–Rary Of Examples, Anina Peersen

Mathematics, Statistics, and Computer Science Honors Projects

This paper focuses on the Brascamp-Lieb inequality and its applications in analysis, fractal geometry, computer science, and more. It provides a beginner-level introduction to the Brascamp-Lieb inequality alongside re- lated inequalities in analysis and explores specific cases of extremizable, simple, and equivalent Brascamp-Lieb data. Connections to computer sci- ence and geometric measure theory are introduced and explained. Finally, the Brascamp-Lieb constant is calculated for a chosen family of linear maps.

Mixing Measures For Trees Of Fixed Diameter, Ari Holcombe Pomerance

Mathematics, Statistics, and Computer Science Honors Projects

A mixing measure is the expected length of a random walk in a graph given a set of starting and stopping conditions. We determine the tree structures of order n with diameter d that minimize and maximize for a few mixing measures. We show that the maximizing tree is usually a broom graph or a double broom graph and that the minimizing tree is usually a seesaw graph or a double seesaw graph.

An Investigative Study Of Potential Factors That Contribute To High Under-Five Mortality Rate In Africa, David Banahene

Theses and Dissertations

Under-Five Mortality remains a significant challenge in developing countries, especially in Africa. The United Nations has implemented various measures, such as the Millennium Development Goals (MDGs) and Sustainable Development Goals (SDGs), to combat this issue. However, the success of these initiatives is uncertain. Our study investigates the social, economic, and environmental factors contributing to high Under-Five Mortality rates in African countries, using data from 1985 to 2020.We analyzed 53 African countries, partitioning them into training (45 countries) and testing data (8 countries). We conducted Multiple Linear Regression analysis and assessed the model performance using R-squared values and Root-Mean-Squared-Error (RMSE) values. …

Creation Of A College Math Club For High School Students, Lilian N. Chavez

Theses and Dissertations

This study aimed to investigate the variables that contribute to high school students' desire to join a math club, specifically the FMiM VIP Club, which is an extension of UTRGV's Follow Me into Math research project. The research utilized multiple questionnaire s to examine the combination of factors that contribute to the students' attitudes toward the math club. The participants were high school Algebra 2 students from two different schools, and the study was conducted in two stages. The first stage was conducted in the Spring of 2022, focusing on girls' math identity and their interactions with the FMiM VIP …

Data Science For Hospital Antibiotic Stewardship, Saikou Jawla

Theses and Dissertations

Antibiotics are widely used to treat bacterial infections, but their misuse leads to antibiotic resistance. Antibiotic resistance is one of the biggest threats to global health, food security, and development today. Antibiotic resistance leads to higher medical costs, prolonged hospital stays, and increased mortality. Antimicrobial stewardship is an approach to measure and improve the appropriate use of antibiotics in healthcare settings. Data science has the potential to support these programs by providing insights into antibiotic prescribing patterns, identifying areas for improvement, and predicting patient outcomes. We explored the role of data science in hospital antibiotic stewardship programs, including statistical methods …

An Analysis Of Antichimeral Ramanujan Type Congruences For Quotients Of The Rogers-Ramanujan Functions, Ryan A. Mowers

Theses and Dissertations

This paper proves the existence of antichimeral Ramanujan type congruences for certain modular forms These modular forms can be represented in terms of Klein forms and the Dedekind eta function. The main focus of this thesis is to introduce the necessary theory to characterize these specific Ramanujan type congruences and prove their antichimerality.

An Investigation Into Optimal Descent Trajectories For Multipurpose Long Range Space Vehicles Under Advanced Conditions, John M. Levis

Theses and Dissertations

In this work, we investigate the problem of fuel-optimal control of space vehicle descent trajectories. The main tool we use to establish optimality is Pontryagin’s Maximum Principle. We present a variety of scenarios with increasing complexities, including drag, wind, and moving landing platforms in the context of differing atmospheric and gravitational conditions. Throughout the paper, we use a balance of analytical and numerical techniques. Finally, observations and conclusions drawn from the investigation form the basis for suggestions into additional areas of analysis.

Effects Of Missing Data Imputation Methods On Univariate Time Series Forecasting With Arima And Lstm, Nicholas Niako

Theses and Dissertations

Missing data are common in real-life studies and missing observations within the univariate time series cause analytical problems in the flow of the analysis. Imputation of missing values is an inevitable step in the analysis of every incomplete univariate time series data. The reviewed literature has shown that the focus of existing studies is on comparing the distribution of imputed data. There is a gap of knowledge on how different imputation methods for univariate time series data affect the fit and prediction performance of time series models. In this work, we evaluated the predictive performance of autoregressive integrated moving average …

Knot Equivalence, Jacob Trubey

Electronic Theses, Projects, and Dissertations

A knot is a closed curve in R3. Alternatively, we say that a knot is an embedding f : S1 → R3 of a circle into R3. Analogously, one can think of a knot as a segment of string in a three-dimensional space that has been knotted together in some way, with the ends of the string then joined together to form a knotted loop. A link is a collection of knots that have been linked together.

An important question in the mathematical study of knot theory is that of how we can tell when two knots are, or are …

Reverse Mathematics Of Ramsey's Theorem, Nikolay Maslov

Electronic Theses, Projects, and Dissertations

Reverse mathematics aims to determine which set theoretic axioms are necessary to prove the theorems outside of the set theory. Since the 1970’s, there has been an interest in applying reverse mathematics to study combinatorial principles like Ramsey’s theorem to analyze its strength and relation to other theorems. Ramsey’s theorem for pairs states that for any infinite complete graph with a finite coloring on edges, there is an infinite subset of nodes all of whose edges share one color. In this thesis, we introduce the fundamental terminology and techniques for reverse mathematics, and demonstrate their use in proving Kőnig's lemma …

Roots Of Quaternionic Polynomials And Automorphisms Of Roots, Olalekan Ogunmefun

Electronic Theses and Dissertations

The quaternions are an extension of the complex numbers which were first described by Sir William Rowan Hamilton in 1843. In his description, he gave the equation of the multiplication of the imaginary component similar to that of complex numbers. Many mathematicians have studied the zeros of quaternionic polynomials. Prominent of these, Ivan Niven pioneered a root-finding algorithm in 1941, Gentili and Struppa proved the Fundamental Theorem of Algebra (FTA) for quaternions in 2007. This thesis finds the zeros of quaternionic polynomials using the Fundamental Theorem of Algebra. There are isolated zeros and spheres of zeros. In this thesis, we …

A Case Study In Bivariate Spline Spaces, Ryann Lee Firestine

Graduate Theses and Dissertations (2019 - present)

Loosely speaking, splines are piece-wise polynomial functions which are continuously differentiable of order r. The individual polynomial segments are degree less than or equal to d. Splines are typically associated with approximation theory, computer-aided graphic design, and partial differential equations. Due to the wide variety of applications, mathematicians became interested in better understanding the behavior of the vector spaces containing splines in various setting and values r and d. In particular, many focused on formulating the dimension of these vector spaces. In the 1980s, commutative algebra was first applied to the study of spline spaces. In our work, we use …

Recursive Forms For Determinant Of K-Tridiagonal Toeplitz Matrices, Eugene Agyei-Kodie

Open Access Theses & Dissertations

Toeplitz matrices have garnered renewed interest in recent years due to their practical applications in engineering and computational sciences. Additionally, research has shown their connection to other matrices and their significance in matrix theory. For example, one study demonstrated that any matrix can be expressed as the product of Toeplitz matrices \citep{ye2016every}, while another showed that any square matrix is similar to a Toeplitz matrix \citep{mackey1999every}.

Numerous studies have examined various properties of Toeplitz matrices, including ideals of lower triangular Toeplitz matrices \citep{dogan9some}, matrix power computation with band Toeplitz structures \citep{dogan2017matrix}, and norms of Toeplitz matrices. Moreover, the use of …

Flexible Models For The Estimation Of Treatment Effect, Habeeb Abolaji Bashir

Open Access Theses & Dissertations

Estimation of treatment effect is an important problem which is well studied in the literature. While the regression models are one of the most commonly used techniques for the estimation of treatment effect, they are prone to model misspecification. To minimize the model misspecification bias, flexible nonparametric models are introduced for the estimation. Continuing this line of research, we propose two flexible nonparametric models that allow the treatment effect to vary across different levels of covariates. We provide estimation algorithms for both these models. Using simulations and data analysis, we illustrate the usefulness of the proposed methods.

Volatility Modeling Of Time Series Using Fractal And Self-Similarity Models, William Kubin

Open Access Theses & Dissertations

The study uses various methods to compare financial and geophysical time series scaling parameters and long-term memory behavior. The Cantor Detrended Fluctuation Analysis (CDFA) method is proposed to provide more accurate estimates of Hurst exponents. The CDFA method is applied to real-time series and the results are verified. The study also analyzes the memory behavior of daily Covid-19 cases before and after the announcement of effective vaccines. Low and high-frequency dataâ??s influence on the Hurst Index estimation is investigated, and a new PCDFA method is proposed. The stability of the Dow Jones Industrial Average is analyzed using a multi-scale normalized …

Investigating The Effect Of Greediness On The Coordinate Exchange Algorithm For Generating Optimal Experimental Designs, William Thomas Gullion

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Design of Experiments (DoE) is the field of statistics concerned with helping researchers maximize the amount of information they gain from their experiments. Recently, researchers have been turning to optimal experimental designs instead of classical/catalog experimental designs. One of the most popular algorithms used today to generate optimal designs is the Coordinate Exchange (CEXCH) Algorithm. CEXCH is known to be a greedy algorithm, which means it tends to favor immediate, locally best designs instead of globally optimal designs. Previous research demonstrated that this tradeoff was efficacious in that it reduced the cost of a single run of CEXCH and allowed …

Evaluation Of Black Holes In An Evolving Universe, John P. Naan

Theses and Dissertations

There are various solutions to the Einstein field equations that represent different physical assumptions, but how to represent multiple black holes within an expanding universe remains an area of open interest. The first step to resolving this question involves evaluating spacetime models that contain a single black hole in an expanding universe. Here, we are primarily interested in understanding the energy distribution of black hole models by solving Einstein's equations using the associated spacetime metric and comparing the propagation of waves within the model against other known spacetime models. Specifically, we will evaluate the combined Schwarschild-de Sitter solution under a …

Congruences For Quotients Of Rogers-Ramanujan Functions, Maria Del Rosario Valencia Arevalo

Theses and Dissertations

In 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n) modulo powers of the primes 5,7,11. In this work, we study Ramanujan type congruences modulo powers of primes p = 7,11,13,17,19,23 satisfied by the Fourier coefficients of quotients the Rogers-Ramanujan Functions G(τ) and H(τ) and the Dedekind eta function η(5τ). In addition to deriving new congruences, we develop the foundational theory of modular forms to motivate and prove the results. The work includes proofs of congruences facilitated by Python/SageMath code.

Machine Learning-Based Data And Model Driven Bayesian Uncertanity Quantification Of Inverse Problems For Suspended Non-Structural System, Zhiyuan Qin

All Dissertations

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and …

Framing How We Think About Curves, Megan Sattler

Mathematical Sciences Undergraduate Honors Theses

A frame defines a basis at a point in R^n, and we can frame a curve by placing one at every point along it. This thesis investigates adapted framed curves in R^2 and R^3 in which they are used to provide information about how a curve twists and turns. We derive differential information from the frames that describe how they change and consequently how the curve changes. We also deduce special properties of each framing and discuss how the differential information suffices to describe the shape of curves.

The Development Of Sociomathematical Norms In The Transition To Tertiary Exam-Oriented Individualistic Mathematics Education In An East Asian Context, Woong Lim, Hyunkyoung Yoon, Younggon Bae, Oh Nam Kwon

School of Mathematical & Statistical Sciences Faculty Publications

This study investigates social, mathematical, and sociomathematical norms perceived by college students in an engineering mathematics course and examines the students’ sense of mathematics as signals of individual merit. Data sources include a survey and one-on-one interviews with 38 students. The findings help illustrate student perceptions of academic social norms in a large-lecture course represented by the acquisition model of learning in college, detached from communal and collaborative disciplinary practices. Findings provide insights into the local educational context of an East Asian country as a case study when exam-oriented mathematics is institutionalized as normalcy.

Invariants Of 3-Braid And 4-Braid Links, Mark Essa Sukaiti

Theses

In this study, we established a connection between the Chebyshev polynomial of the first kind and the Jones polynomial of generalized weaving knots of type W(3,n,m).
Through our analysis, we demonstrated that the coefficients of the Jones polynomial of weaving knots are essentially the Whitney numbers of Lucas lattices which allowed us to find an explicit formula for the Alexander polynomial of weaving knots of typeW(3,n).
In addition to confirming Fox’s trapezoidal conjecture, we also discussed the zeroes of the Alexander Polynomial of weaving knots of type W(3,n) as they relate to Hoste’s conjecture. In addition, …