Mathematics Commons^™

How To Fairly Allocate Safety Benefits Of Self-Driving Cars, Fernando Munoz, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we describe how to fairly allocated safety benefits of self-driving cars between drivers and pedestrians -- so as to minimize the overall harm.

Using Known Relation Between Quantities To Make Measurements More Accurate And More Reliable, Niklas Winnewisser, Felix Mett, Michael Beer, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Most of our knowledge comes, ultimately, from measurements and from processing measurement results. In this, metrology is very valuable: it teaches us how to gauge the accuracy of the measurement results and of the results of data processing, and how to calibrate the measuring instruments so as to reach the maximum accuracy. However, traditional metrology mostly concentrates on individual measurements. In practice, often, there are also relations between the current values of different quantities. For example, there is usually an known upper bound on the difference between the values of the same quantity at close moments of time or at …

Festival Of Research Abstracts, Spring 2024, College Of Science And Mathematics, Wright State University

Festival of Research

The collection of abstracts accepted for the Spring 2024 Festival of Research hosted by the Wright State University College of Science and Mathematics.

2-Accessibility Of The Lucas Numbers/Fibonacci Like Sequences/Wythoff Array, Cameron Lejeune

Mathematics Senior Capstone Papers

In this project we will be delving into the combinatorics side of mathematics, with basic a graph theory idea such as set coloring. It will be a continuation of a question formed by the works of Bruce M. Landman, and Aaron Robertson, ”3-Accessibility of the Fibonacci Numbers.” They were able to prove the Fibonacci Numbers to be 2-Accessible, and while they did not supply the induction proof, we were able to construct and provide a proof. This project will use their lemmas and propositions to attempt to prove 2-Accessibility of the Lucas Numbers, Fibonacci-like sequences, and the Zeckendorf-Wythoff Array.

Can Compiled Player War Predict Mlb Team Win Percentage?, Thomas Hertel

Mathematics Senior Capstone Papers

The baseball statistic Wins Above Replacement (WAR) is a complex yet effective metric for approximating the contribution of a player to his team through representing how many more wins his team ought to earn than with a AAAA player in his stead. The intent of this paper is to test whether the accumulation of player’s WAR can be extended to satisfy another discipline of SABRmetrics, i.e. predicting an entire team’s future performance, through modeling the sum’s correspondence (or lack thereof) to wins. If WAR is shown to extend in this way then franchise front offices could feasibly isolate it as …

Using Multiple Regression Analysis To Determine The Strength Of Certain Factors On Student Absenteeism, Emmitt Antwine

Mathematics Senior Capstone Papers

During the 2015-16 academic year, approximately 16% of the student population—exceeding 7 million students—were absent from school for 15 days or more. The escalation in chronic absenteeism is influenced by various factors, including poor health conditions, nonstandard work schedules of parents, socioeconomic disadvantages, changes in household compositions, frequent residential relocation, and substantial family responsibilities. Previous research on student absenteeism has examined the negative impacts that chronic absenteeism has had on students in diverse communities such as racial minorities, students with disabilities, and English Language Learners communities. We utilized information obtained from the U.S. Department of Education’s Civil Rights Data Collection …

An Exploration Of The Sums Of Two Squares And Pentagonal Numbers, Jacob Von Tress

Mathematics Senior Capstone Papers

In the field of number theory, square numbers are very significant, and finding the sums of square numbers is a topic of certain interest to mathematicians. The most immediate application for adding together two square numbers is to identify Pythagorean triples. However, apart from seeking sums of two squares that are squares themselves, interesting patterns emerge that have fascinated number theorists for decades. Particularly, the distribution of a number’s divisors can explicitly determine how many ways that number can be written as a sum of two squares. Furthermore, pentagonal numbers, similar to square numbers, can be visualized by drawing a …

Matroids Stemming From The Maximal Relaxation Of Graphic Matroids, Landen Nguyen

Mathematics Senior Capstone Papers

This research explores the base perspective for maximal relaxation of graphic matroids. We begin by covering the required knowledge of graph theory and the basics of matroid theory required to conduct this research such as definitions of matroids up to the definitions of relaxation, hyperplanes, and uniform matroids. We then analyze the conjecture in matroids obtained from simple connected graphs.

Four Colorful Methods For Finding The Chromatic Polynomial, Emerson Statom

Mathematics Senior Capstone Papers

Mathematicians apply algebraic graph theory to address and interpret problems arising out of data structures and optimization. For example, graph coloring problems have intrigued mathematicians and computer scientists alike. The chromatic polynomial was created to help solve such problems. This research aims to create a greater understanding of the underlying structures behind chromatic polynomials by analyzing the algebraic, deletion-contraction, and color partition methods. Each method has differing applications, but by viewing them all together, this research hopes to show the depth of this most interesting subject in a condensed manner.

Factors That Contribute To Completing Gateway Math Course At Southern University, Emma Colvin

Mathematics Senior Capstone Papers

At Southern University in Shreveport, Louisiana, there are several pathways students can take to complete the institution’s required Gateway Math Courses (GMC). The GMC consists of Math 133, Math 135, and Math 136. Currently, there is a significantly low passing rate for these courses potentially due to several factors such as the student’s math ACT score, the student’s age, whether or not the student took optional developmental math courses beforehand, and whether or not the student took these courses online or in person.

Congruences Of The Sums Of The First Rp Fibonacci Numbers, Tyler Warzynak

Mathematics Senior Capstone Papers

This paper serves as an extension/application of a method detailed by Chang et. al. in two separate papers which worked with sums modulo p for combinatorial sequences, positive integers r, and prime numbers p. Using a known formula, the Fibonacci numbers were converted into a sum of binomial coefficients to apply the aforementioned method. A hypothesis was formed using computational methods, where a pattern was observed to hold for the first 50,000 prime numbers. This claim was then proven following the methodology from Chang et. al. using properties of Laurent polynomials, definitions and theorems related to the Fibonacci numbers, and …

Abstract Measures On Totally Ordered Sets, Gregory Whitehurst

Mathematics Senior Capstone Papers

Two specific notions of integration were the motivation of this paper: Riemann-Stieltjes and Lebesgue-Stieltjes integration. The question that arose from these notions was the idea of generalization. How can Stieltjes integration be generalized to an arbitrary measure? The buildup to this question requires a beautiful combination of measure theory and order theory to deliver a measure on totally ordered sets that provide structure for a potential generalization. This paper shows that the set of chains in a totally ordered set is a σ-algebra and defines cumulative cardinality measure on (X, Σ) in an attempt to give insight on the structure …

Does The ”Freshman 15” Exist?, Peyton Albritton

Mathematics Senior Capstone Papers

This experiment was performed to determine whether the environmental changes of adapting from high school to college impact a student’s weight. Using a Google form, we collected data from 58 college students in two Psychology 102 classes, with ages ranging from seventeen to twenty-two. The students were asked a series of questions regarding their age and gender, as well as their eating, sleeping, and activity habit changes. Data was analyzed using hypothesis testing and a t-test.

Injuries On Artificial Turf Vs. Natural Grass In The Nfl, Robert Emory

Mathematics Senior Capstone Papers

The purpose of this research is to determine if artificial turf causes more injuries than natural grass. By referencing different statistics from a sample of games from the 2023 National Football League season. Out of the ten games sampled, five were played on natural grass and five were played on artificial turf. We ran the data collected from these games through two different regression analysis models that output p-values to show what truly caused the injuries. Our model uses a player’s position, height, weight, age, and snap counts along with the field surface type to see how if an injury …

Comparison Of Linear Control Techniques For The Underactuated Nonlinear Quadcopter System, Ian Golsby

Mathematics Senior Capstone Papers

Uncrewed Aerial Vehicles (UAVs) are a prevalent technology in many fields. They must be lightweight, efficient, and stable in order to carry out their objectives or support a payload. The control system that maintains a UAV’s attitude directly contributes to the stability and efficiency of the UAV, and more efficient UAVs can be made more lightweight by reducing battery size. Because the UAV has only four degrees of control (one per motor) but requires twelve dimensions to describe its orientation and position over time, it is considered an under-actuated nonlinear complex system. In this study, we compare various linear control …

A Closer Look At The Structure Of Uniquely Pancyclic Graphs, Zak Kilpatrick

Mathematics Senior Capstone Papers

In this paper we will consider uniquely pancyclic graphs which are described as graphs on n vertices which have a unique cycle of size k for each integer k from 3 to n. To date, there are only seven known graphs of this type. To narrow down what a uniquely pancyclic graph could look like in order to aid the search in finding new ones, the focus of this paper is on the different ways the three and four cycles for these graphs can occur.

Somewhat Surprisingly, (Subjective) Fuzzy Technique Can Help To Better Combine Measurement Results And Expert Estimates Into A Model With Guaranteed Accuracy: Digital Twins And Beyond, Niklas Winnewisser, Michael Beer, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To understand how different factors and different control strategies will affect a system -- be it a plant, an airplane, etc. -- it is desirable to form an accurate digital model of this system. Such models are known as digital twins. To make a digital twin as accurate as possible, it is desirable to incorporate all available knowledge of the system into this model. In many cases, a significant part of this knowledge comes in terms of expert statements, statements that are often formulated by using imprecise ("fuzzy") words from natural language such as "small", "very possible", etc. To translate …

The Impacts Of Covid-19 On The U.S. Life Insurance Industry: A Study Of Pandemic Mortality Rates, Allison Wheaton

Honors Projects in Mathematics and Economics

The COVID-19 pandemic has had substantial and widespread impacts around the world that are not yet completely understood but will likely be experienced for years to come. This research seeks to analyzed and quantify the pandemic’s effects on the life insurance industry in the United States through the use of mortality models. Because the life insurance industry relies on the ability to accurately predict an individual’s mortality, it is necessary to investigate the impacts of the pandemic on mortality predictions and accuracy. Impairment factors were developed using pandemic mortality data and applied to existing mortality tables to compare expected and …

Statistics Pedagogy: Modernizing Introductory College Statistics Courses For Students With Non-Stem Majors, Samantha Hazan

Honors Projects in Mathematics and Economics

With the growing role of technology in society, statistics and statistical literacy have become ever more important. In reaction to this, many colleges now require students, regardless of major, to take an introductory statistics course. The intention behind this is to create a workforce of people who are capable of reasoning about statistics. While good intentioned, preliminary research suggests that current statistics curriculum is not effective in instilling the necessary skills to achieve statistical literacy, particularly for students not majoring in a STEM field. For this reason, this thesis looks to empirically evaluate how the disjuncture between teaching statistics and …

How Difficult Is It To Comprehend A Program That Has Significant Repetitions: Fuzzy-Related Explanations Of Empirical Results, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In teaching computing and in gauging the programmers' productivity, it is important to property estimate how much time it will take to comprehend a program. There are techniques for estimating this time, but these techniques do not take into account that some program segments are similar, and this similarity decreases the time needed to comprehend the second segment. Recently, experiments were performed to describe this decrease. These experiments found an empirical formula for the corresponding decrease. In this paper, we use fuzzy-related ideas to provide commonsense-based theoretical explanation for this empirical formula.

Why Bernstein Polynomials: Yet Another Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many computational situations -- in particular, in computations under interval or fuzzy uncertainty -- it is convenient to approximate a function by a polynomial. Usually, a polynomial is represented by coefficients at its monomials. However, in many cases, it turns out more efficient to represent a general polynomial by using a different basis -- of so-called Bernstein polynomials. In this paper, we provide a new explanation for the computational efficiency of this basis.

How To Make A Decision Under Interval Uncertainty If We Do Not Know The Utility Function, Jeffrey Escamilla, Vladik Kreinovich

Departmental Technical Reports (CS)

Decision theory describes how to make decisions, in particular, how to make decisions under interval uncertainty. However, this theory's recommendations assume that we know the utility function -- a function that describes the decision maker's preferences. Sometimes, we can make a recommendation even when we do not know the utility function. In this paper, we provide a complete description of all such cases.

Shall We Place More Advanced Students In A Separate Class?, Shahnaz Shahbazova, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In every class, we have students who are more advanced and students who are more behind. From this viewpoint, it seems reasonable to place more advanced students in a separate class. This should help advanced students progress faster, and it should help other students as well, since the teachers in the remaining class can better attend to their needs. However, empirically, this does not work: when we form a separate class, the overall amount of gained knowledge decreases. In this paper, we provide a possible explanation for this seemingly counterintuitive phenomenon.

Towards An Optimal Design: What Can We Recommend To Elon Musk?, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

Elon Musk's successful "move fast and break things" strategy is based on the fact that in many cases, we do not need to satisfy all usual constraints to be successful. By sequentially trying smaller number of constraints, he finds the smallest number of constraints that are still needed to succeed -- and using this smaller number of constrains leads to a much cheaper (and thus, more practical) design. In this strategy, Musk relies on his intuition -- which, as all intuitions, sometimes works and sometimes doesn't. To replace this intuition, we propose an algorithm that minimizes the worst-case cost of …

Normalized Ground State Of A Mixed Dispersion Nonlinear Schrodinger Equation With Combined Power-Type Nonlinearities, Zhouji Ma, Xiaojun Chang, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

We study the existence of normalized ground state solutions to a mixed dispersion fourth-order nonlinear Schrodinger equation with combined power-type nonlinearities. By analyzing the subadditivity of the ground state energy with respect to the prescribed mass, we employ a constrained minimization method to establish the existence of ground state that corresponds to a local minimum of the associated functional. Under certain conditions, by studying the monotonicity of ground state energy as the mass varies, we apply the constrained minimization arguments on the Nehari-Pohozaev manifold to prove the existence of normalized ground state solutions.

Visualizing The Standard Deviation Via Revolution Using R/Rstudio, Hieu Nguyen '25, Trung Pham '25, Mamunur Rashid, Jyotirmoy Sarkar

Student Research

The standard deviation is a commonly used statistical measure to quantify the level of variation present in a set of numbers or in a random variable. Sarkar and Rashid (2016) introduced an interpretation of the population standard deviation as the radius of a cylinder with a volume equivalent to that of the solid of revolution when the 2-D graph of the empirical cumulative distribution function is revolved about the vertical line through the mean. This article demonstrates step-by-step how to use the RevSD package in R/RStudio to visualize the standard deviation of data using this innovative technique. The RevSD package …

Discrete Macaulay-Steiner Geometry, Nikola Kuzmanovski

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

This thesis is concerned with discrete isoperimetric inequalities and Hilbert functions. Two generalizations of the Ahlswede-Cai local global principle are presented. These results give positive answers to two questions posed by Harper. One of these results is achieved by proving uniqueness of the lexicographic and colexicographic orders in two dimensions. The other result generalizes the technique which is commonly known as compression and includes almost all previously published results in this direction. The Ahlswede-Cai local global principle is a direct corollary of this result. Optimal downsets are studied in rectangles and triangles. All optimal downsets are found. The main result …

Syllabus For Oer Version Of Math 20100, Thea Pignataro

Open Educational Resources

Syllabus for OER version of first semester calculus with analytic geometry for physical sciences and engineering.

Mediating Effect Of Bmi On The Association Of Economic Status And Coexistence Of Hypertension And Diabetes In Bangladesh: A Counterfactual Framework-Based Weighting Approach, Foyez , Md. Jamal Hossain Ahmmed, Md. Jamal Hossain, Md Tareq Ferdous Khan, Muhammad Mahabub Rahaman Manik, Saimon Shahriar, Dulal Chandra Nandi, Md Parvej Hussain

Mathematics and Statistics Faculty Publications

Background and Aims

Non-communicable diseases such as hypertension and diabetes are matters of huge concern worldwide, with an increasing trend in prevalence over the previous decade. First of all, this study aimed to evaluate the association between economic status (ES) and body mass index (BMI), ES and comorbidity of hypertension and diabetes, and BMI and comorbidity independently. Second, it explored the mediating role of BMI in the association between ES and comorbidity of hypertension and diabetes. Finally, it investigated whether the mediating effect differs with the place of residence, gender, and education levels.

Methods

A total of 11,291 complete cases …

Circle Packings From Tilings Of The Plane, Philip Rehwinkel , '22, Ian Whitehead, David Yang , '24, Mengyuan Yang , '25

Mathematics & Statistics Faculty Works

We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The existence and uniqueness of these packings are guaranteed by infinite versions of the Koebe–Andreev–Thurston theorem. We prove structure theorems giving a complete description of the symmetry groups for these packings. And we give several examples to illustrate their number-theoretic and group-theoretic significance.