Mathematics Commons^™

Managing The Spread Of Alfalfa Stem Nematodes Ditylenchus Dipsaci: The Relationship Between Crop Rotation And Pest Re-Emergence, Scott Jordan

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow end-users to design better management programs and farming practices. This is of particular importance given that there are no nematicides available against alfalfa stem nematode and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties. I present a basic host-parasite model that describes the spread of the alfalfa stem nematode on alfalfa crops. With this …

Survival Analysis For Truncated Data And Competing Risks, Michael Steelman

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this project is to consider the problems of left truncation and competing risks in analyzing censored survival data, and to compare and contrast various approaches for handling these problems. The motivation for this work comes from an analysis of data from the Cache County Memory Study. Study investigators were interested in the association between early-life psychologically stressful events (e.g., parental or sibling death, or parental divorce, among others) and late-life risk of Alzheimer's disease (AD). While conventional methods for censored survival data can be applied, the presence of left truncation and competing risks (i.e., other adverse events …

Comparing Linear Mixed Models To Meta-Regression Analysis In The Greenville Air Quality Study, Lynsie M. Daley

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The effect of air quality on public health is an important issue in need of better understanding. There are many stakeholders, especially in Utah and Cache Valley, where the poor air quality as measured by PM 2.5 levels and consequent inversions can sometimes be the very worst in the nation. This project focuses on comparing two statistical methods used to analyze an important air quality data set from the Greenville Air Quality Study, focusing on a lung function response variable. A linear mixed model, with a random factor for subject, gives slope estimates and their significance for predictor variables of …

Complex Short Pulse Equation And Its Integrable Discretizations, Raul M. Guajardo

Theses and Dissertations - UTB/UTPA

In this thesis, we are mainly concerned with the complex short pulse (CSP) equation which was proposed in Physica D [1]. We present the Lax pair of the CSP equation and show the compatibility condition gives the CSP equation. Therefore, the integrability is confirmed. Then, a set of bilinear equations is proposed which yields the CSP equation through the hodograph transformation. Based on the bilinear form, general N-soliton solution is given in determinant form. Regarding two-soliton solution, a bound state can be formed if the velocities of two solitons are equal. Furthermore, a semi- and fully discrete analogues are constructed …

Generalized Markoff Equations, Euclid Trees, And Chebyshev Polynomials, Donald Joseph Mcginn

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Markoff equation is x^2+y^2+z^2 = 3xyz, and all of the positive integer solutions

of this equation occur on one tree generated from (1, 1, 1), which is called the

Markoff tree. In this paper, we consider trees of solutions to equations of the form

x^2 + y^2 + z^2 = xyz + A. We say a tree of solutions satisfies the unicity condition

if the maximum element of an ordered triple in the tree uniquely determines the

other two. The unicity conjecture says that the Markoff tree satisifies the unicity

condition. In this paper, we show that there exists …

A Comparison Of Recent Results On The Unicity Conjecture Of The Markoff Equation, Brandon John Metz

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis we discuss the positive integer solutions to the equation known as the Markoff equation

x² + y² + z² = 3xyz.

Each solution to the equation is a permutation of a triple (x,y,z) with [mathematical equation refer to PDF] which is called a Markoff triple and each integer of the triple is referred to as a Markoff number.

In 1913, Frobenius conjectured that given an ordered Markoff triple (x,y,z), then both x and y are uniquely determined by z. In other words, if both (x₁,y₁,z) and (x₂,y_{2 …}

Situational Assessment Using Graph Comparison, Pavan Kumar Pallapunidi

UNLV Theses, Dissertations, Professional Papers, and Capstones

In strategic operations, the assessment of any given situation is very important and may trigger the development of a mission plan. The mission plan consists of various actions that should be executed in order to successfully mitigate the situation. For a new mission plan to be designed or implemented, the effect of the previous mission plan should be accessed. These mission plans use various sensors to collect the data which can be very large and aggregate them to obtain detailed information of the situation. In order to implement an effective mission plan the current situation has to be assessed effectively. …

Exploring Ways Of Identifying Outliers In Spatial Point Patterns, Jie Liu

Electronic Theses and Dissertations

This work discusses alternative methods to detect outliers in spatial point patterns.

Outliers are defined based on location only and also with respect to associated variables. Throughout the thesis we discuss five case studies, three of them come from experiments with spiders and bees, and the other two are data from earthquakes in a certain region. One of the main conclusions is that when detecting outliers from the point of view of location we need to take into consideration both the degree of clustering of the events and the context of the study. When detecting outliers from the point of …

Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei

Electronic Theses and Dissertations

In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.

The Groups Acting On The Riemann Sphere, Ruba Yousef Wadi

Theses

In this Master thesis we consider the group actions, with emphasis on the group of general Möbius transformations of one complex valuable acting on the Riemann sphere. We study some invariant subspaces of Riemann sphere under the actions of natural groups of transformations, including the invariant quantities in Hyperbolic Geometry that is a beautiful area of Mathematics. We use analytic and algebraic points of view to describe some group actions on Riemann sphere; in particular, we present the relationships between isometries of hyperbolic plane, Möbius transformations, and groups of matrices. Keywords: Group actions, Riemann sphere, general Möbius transformations, transitivity, hyperbolic

A Fixed-Inverse Binary Misclassification Model Under Possible False-Positive Misclassification, Asmerom Tesfamichael, Kent Riggs

Bright Ideas Conference

In this project, we develop a particular statistical model for binary data that allows for the possibility of false-positive misclassification. To account for the misclassification, the model incorporates a two-stage sampling scheme.

• Next, we apply maximum likelihood methods to find estimators of the primary prevalence parameter p as well as the false-positive misclassification rate parameter ϕ. In addition, we derive confidence intervals for p based on inverting Wald, score and likelihood ratio statistics.

• Also, we graphically compare coverage and width properties of the Wald-based, score-based, and likelihood ratio-based confidence intervals for p through a Monte Carlo simulation. The …

Using Independent Bernoulli Random Variables To Model Gender Hiring Practices, Kimberly D. Hildebrand

Departmental Honors & Graduate Capstone Projects

Gender bias is a problem in the workforce at large. In order for society to progress it is important that hiring practices do not use gender as a competitive factor. Hiring practices based on gender can be represented statistically using Bernoulli Random Variables and the Beta and Binomial distributions.Using the moment generating function (MGF) of the Bernoulli and Binomial Distributions, it is possible to calculate the expected value (mean) and variance for the number of women hires for n positions. The probability generating function (PGF) of a sample size n can be used to find the probability of hiring a …

Scientific Awareness At Ursinus College, Frank G. Devone

Mathematics Honors Papers

Ursinus College prides itself on creating well-rounded students, and recent initiatives, such as the Fellowships in the Ursinus Transition to the Undergraduate Research Experience Program and the Center for Science and the Common Good suggest that science is a vital part of the Ursinus liberal arts mission. A scientific awareness pilot survey was administered to a sample of Ursinus students drawn from the Class of 2014 and students residing at Ursinus during summer 2014. Experience and data collected from this pilot were used to create a final survey which was made available to all students at Ursinus College. The survey …

Wavelet Analysis Of Non-Stationary Signals With Applications, Maria Dorothea Van Der Walt

Dissertations

The empirical mode decomposition (EMD) algorithm, introduced by N.E. Huang et al in 1998, is arguably the most popular mathematical scheme for non-stationary signal decomposition and analysis. The objective of EMD is to separate a given signal into a number of components, called intrinsic mode functions (IMF's), after which the instantaneous frequency (IF) and amplitude of each IMF are computed through Hilbert spectral analysis (HSA). On the other hand, the synchrosqueezed wavelet transform (SST), introduced by I. Daubechies and S. Maes in 1996 and further developed by I. Daubechies, J. Lu and H.-T. Wu in 2011, is first applied to …

Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok

Mathematics Honors Papers

This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.

The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …

Estimation In The Exponentiated Kumaraswamy Dagum Distribution With Censored Samples, Broderick O. Oluyede, Shujiao Huang

Mathematical Sciences: Faculty Publications

In a recent note, Huang and Oluyede (2014) proposed a new model called the exponentiated Kumaraswamy Dagum (EKD) distribution with applications to income and lifetime data. In this note, this distribution is shown to be a very competitive model for describing censored observations in lifetime reliability problems. This work shows that in certain cases, the EKD distribution performs better than other parametric model such as the exponentiated Kumaraswamy Weibull distribution and its sub-models, which include some of the commonly used models in survival analysis and reliability analysis, such as the exponentiated Weibull, Weibull and exponential distributions.

Packing Densities Of Colored And Non-Colored Patterns, Matthew R. Just

GS4 Student Scholars Symposium

Pattern packing concerns finding an optimal permutation that contains the maximum number of occurrences of a given pattern and computing the corresponding packing density. In many instances such an optimal permutation can be characterized directly and the number of occurrences of the pattern in interest may be enumerated explicitly. In more complicated patterns a direct characterization may be more challenging, however computational results for long permutations can help provide an indirect characterization of the general form of an optimal permutation. Much work has been done on the study of pattern packing in layered patterns, as the optimal permutation of a …

2015 Sonia Kovalevsky Math For Girls Day Program, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

10th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program on April 24, 2015.

A Computational Study Of Icart's Function, Thomas Simmons

Honors Projects

A hash function maps some elements of a larger, initial set to elements of a smaller, resultant set. By nature, this leads to collisions and, sometimes, not all elements in the smaller set will be mapped to as a result. The set in consideration here is all points on an elliptic curve. This is a special class of curve with two variables, which takes the form here as y² = x³ + ax + b. A hash function is useful in offering a deterministic way to map an input to a pair of x and y values …

Explorations Of The Collatz Conjecture (Mod M), Glenn Micah Jackson Jr

Honors College Theses

The Collatz Conjecture is a deceptively difficult problem recently developed in mathematics. In full, the conjecture states: Begin with any positive integer and generate a sequence as follows: If a number is even, divide it by two. Else, multiply by three and add one. Repetition of this process will eventually reach the value 1. Proof or disproof of this seemingly simple conjecture have remained elusive. However, it is known that if the generated Collatz Sequence reaches a cycle other than 4, 2, 1, the conjecture is disproven. This fact has motivated our search for occurrences of 4, 2, 1, and …

Gallai-Ramsey And Vertex Proper Connection Numbers, Emily C. Chizmar

Honors College Theses

Given a complete graph G, we consider two separate scenarios. First, we consider the minimum number N such that every coloring of G using exactly k colors contains either a rainbow triangle or a monochromatic star on t vertices. This number is known for small cases and generalized for larger cases for a fixed k. Second, we introduce the vertex proper connection number of a graph and provide a relationship to the chromatic number of minimally connected subgraphs. Also a notion of total proper connection is introduced and a question is asked about a possible relationship between the total proper …

Fostoria Intermediate Elementary School Family Math Night, Chelsea Nye

Honors Projects

This is a Family Math Night that was planned and held at Fostoria Intermediate Elementary School in Fostoria, Ohio. It includes the Research Questions, Literature Review, Proposed Activity, Methodology, and Expected Results as well as the Annotated Bibliography and Timeline for Completion from my research and planning. Following the Proposal are 20 mathematical activity or game lesson plans and direction sheets that were planned for the Family Math Night. There are 5 different mathematical activities or games for each grade level 3-6, each meeting a different domain in the Common Core State Standards. At the end there is two general …

Multidecompositions Of Complete Graphs Into A Graph Pair Of Order 6, Yizhe Gao, Mark Daniel Roberts, Faculty Advisor

John Wesley Powell Student Research Conference

A graph is a mathematical structure consisting of a set of objects called vertices and a set of 2-element subsets of vertices, called edges. The complete graph on n vertices is the graph with n vertices and an edge between any pair of distinct vertices. Let C₆ denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on n vertices into copies of C₆ and its complement with at least one copy of each graph. We provide necessary and sufficient conditions on n for the existence such a structure.

Hurwitz Monodromy And Full Number Fields, David P. Roberts, Akshay Venkatesh

Mathematics Publications

We give conditions for the monodromy group of a Hurwitz space over the configuration space of branch points to be the full alternating or symmetric group on the degree. Specializing the resulting coverings suggests the existence of many number fields with surprisingly little ramification —for example, the existence of infinitely many A_m or S_m number fields unramified away from {2,3,5}.

Euler's Multiple Solutions To A Diophantine Problem, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate

Senior Honors Theses

Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a …

How Visualization Can Improve The Understanding Of Mathematics, Mariah Martin

Undergraduate Research Conference

High school students have a difficult time taking the new End-Of-Course exams in math. Why are students having this difficulty? This could be because students lack the understanding of visualization in mathematics. Visualization can be helpful to certain students who think this way, while also confusing to those same students, and others as well. However, to what extent do high stakes tests, such as the End-Of-Course exams in Algebra I and II, incorporate mathematical visualization? How can visualization help improve the understanding of mathematics? This review will explain the advantages and disadvantages of incorporating visualization in these exams, how students …

Analysis Of Accounting Wages Within The Largest Cities Of Texas, Zuleima Espino, Delyla Frederick, Allyson Gallier, Halee Morehead

Undergraduate Research Conference

No abstract provided.

Construction Of Spline Type Orthogonal Scaling Functions And Wavelets, Tung Nguyen

Honors Projects

In this paper, we present a method to construct orthogonal spline-type scaling functions by using B-spline functions. B-splines have many useful properties such as compactly supported and refinable properties. However, except for the case of order one, B-splines of order greater than one are not orthogonal. To induce the orthogonality while keeping the above properties of B-splines, we multiply a class of polynomial function factors to the masks of the B-splines so that they become the masks of a spline-type orthogonal compactly-supported and refinable scaling functions in L₂. In this paper we establish the existence of this class …

Discovering Geometric And Topological Properties Of Ellipsoids By Curvatures, Lina Wu, Shihshu Walter Wei, Jia Liu, Ye Li

Publications and Research

Aims/ Objectives: We are interested in discovering the geometric, topological and physical properties of ellipsoids by analyzing curvature properties on ellipsoids. We begin with studying ellipsoids as a starting point. Our aim is to find a way to study geometric, topological and physical properties from the analytic curvature properties for convex hyper-surfaces in the general setting.

Study Design: Multiple-discipline study between Differential Geometry, Topology and Mathematical Physics.

Place and Duration of Study: Department of Mathematics (Borough of Manhattan Community College-The City University of New York), Department of Mathematics (University of Oklahoma), Department of Mathematics and Statistics (University of West Florida), …