Analysis Commons^™

The General Solution Analysis Of Homogeneous Linear Equations, Jacob Schwamb, Edward Whipple

Discovery Day - Daytona Beach

The general solution analysis of homogeneous linear equations are any systems of equations in which all constant terms are equal to zero is classified as a homogeneous linear equation. Some key characteristics of homogeneous linear equations are that there are “zero” solutions, where every system has at least a single solution where all variables are zero, also all solutions to any homogenous linear equation is linearly independent, along with having preserved homogeneity, where if any variable (x) may be added to the system, then any scalar multiple of the variable is also a solution. The General solution of any homogeneous …

A Compact Representation Of Oscillatory Limits Via Asymptotic Value Distributions, Ibrahim Arnous, Eric M. Rodarte, Chirag Kumar

Discovery Day - Daytona Beach

Classical limits describe asymptotic behavior through convergence to a single value, but many important oscillatory functions do not converge in this sense. Standard examples such as sin(𝑥) as 𝑥→∞ and sin(1/x) as x→0 instead display stable distributions of values over time. This project examines how such behavior can be described using a measure-theoretic framework, particularly through occupation measures and, in sequence-based settings, Young measures. The objective is to present this perspective in a clear and accessible way while introducing the Ansatz representation, a compact notation for recording the support and density of an asymptotic value distribution when the limiting measure …

Differentiating The Impossible: Feynman's Trick In Applications Of Modern Physics, Yaohua Zhao

Discovery Day - Daytona Beach

We discuss Feynman’s method of differentiating with respect to a parameter inside an integral and explore its significance on selective topics of modern physics. This powerful technique allows us to integrate functions that may seem impossible. Depending on the underlying parameters, the Feynman method becomes a unifying framework that connects mathematical concepts to many parameter-dependent equations in modern physics. In statistical mechanics, this appears directly in the partition function, where derivatives with respect to temperature-related parameters yield thermodynamic quantities such as internal energy and heat capacity; this demonstrates how parameter dependence gives rise to macroscopic behaviors observable at a larger …

Engineering Path Trajectories With Gravitational Fields, Eliane Dean, Aidan Hart, Isabel Noot, Nathan Browning, Valeria Villazon Fito

Discovery Day - Daytona Beach

This project explores how vector calculus concepts play a role in aerospace engineering though spacecraft trajectory design. In particular, the notion of vector fields is used to model the gravitational force, whose work done is expressed through line integrals. By taking the curl of the gravitational field and showing it is zero, the field is recognised as conservative, implying that the work done by gravity is path independent. This property is conceptually linked to gravitational potential energy and the principle of energy conservation. The results are then applied to spacecraft motion, where engineers use energy-base methods to determine efficient trajectories …

Visualizing The Invisible: Simulating Electromagnetic Field In 3d Space With Matlab, Aashman Gupta, Eliane Dean, Riley Esperanca, Hailey Grabinski, Jacob Summerhays, Ameya Sute

Discovery Day - Daytona Beach

Electromagnetic field behaviours in free space are defined by Maxwell’s Equations, which couple the temporal and spatial variations of electric and magnetic fields through partial derivatives. These derivatives quantify the rate of change of each field’s vector component with respect to position and time in a 3D lattice, forming the basis for numerical field analysis. This research will develop a mathematical and computational framework using multivariable calculus to model, simulate, and visualize electromagnetic wave propagation in free space using MATLAB. Gradient, divergence, and curl operations are implemented to compute local field variations and energy transfer. The resulting data are used …

On The Fractional Laplacian Type Operator, Maysam Abdulnaser Zain

Thesis/ Dissertation Defenses

In this thesis, we study analytical structures arising from Dunkl theory and their applications to harmonic analysis and fractional Laplacian operators. Dunkl operators are differential-difference operators associated with finite reflection groups, providing a natural generalization of the classical Fourier analysis through the introduction of root systems and multiplicity functions. Within this framework, several classical transforms appear as special cases of the (k,a)-generalized Fourier transform. We study the generalized Fourier transform, its kernel, and the associated translation operator and convolution structures. Using these tools, we construct the corresponding heat kernel and analyze the associated heat semigroup. Our main contribution concerns the …

Effectiveness Of The Guided Discovery Method In Teaching The Surface Area Of A Cylinder, Paul Ahortu

2026 Symposium

This study investigates the impact of the guided discovery instructional method on students’ understanding of the surface area of a cylinder. A quasi-experimental pre-test–post-test design was conducted with 100 senior high school students in Cape Coast, Ghana, divided into experimental and comparison groups..

Results showed a substantial improvement in performance for students exposed to guided discovery, with mean scores increasing from 1.25 (pre-test) to 9.43 (post-test) and a large effect size (Cohen’s d = 2.70). Statistical analysis also revealed significant gender differences in achievement.

These findings indicate strong improvement following the guided discovery intervention and suggest its potential to enhance …

From Counting To Advanced Math: How Five Simple Axioms Shape The Mathematical Landscape, Joy Skaggs

ATU Scholars Symposium

In the late nineteenth and early twentieth centuries, mathematics faced a foundational crisis: Greog Cantor’s set theory led to an interesting self-referencing paradox in math and questions about the logical consistency of mathematics. From this crisis, two opposing viewpoints emerged: the Formalists and the Intuitionists. The Formalists praised Cantor’s work as a way to place math on a secure logical foundation, ensuring the discipline’s purity, however the Intuitionists despised Cantor’s work and heralded Cantor as a charlatan and corrupter of the youth. The leader of the Formalists, David Hilbert, proposed a formal system of rigorous proofs to build a complete …

Exploration Of Euclidean Distances In Five-Dimensional Color Space As Proof-Of-Concept For Identification Of Promising Alternatives To Platinum-Based Cancer Drug Candidates, Kiomi Tanakura, Elena G. Harvey

Student Scholar Symposium

Cisplatin, cis-Pt(NH₃)₂Cl₂, is one of the most successful anticancer drugs of all time. However, it has some negative aspects, including toxicity to healthy cells, side effects, and cost. Our goal in this project is to design metal-based anticancer drugs that would be less expensive, less toxic, and more efficient for cancer patients than cisplatin. To begin this research we calculated Euclidean distances - as used by computerized recognition systems - to compare the properties of colors within seasonal palettes that are proven and visible to the eye. These Euclidean distances were then used …

An Analysis On The Time Effectiveness Of Speeding While Driving A Vehicle, Joy Skaggs

ATU Scholars Symposium

Speeding is responsible for roughly a third of all crashes, often coming at a deadly cost. The National Highway Traffic Safety Administration reports many negative consequences, such as a greater likelihood of loss of vehicle control, reduced protection equipment effectiveness, increased stopping distance, crash severity, and fuel consumption (National Highway Traffic Safety Administration, n.d.). Yet despite these costs, drivers continue to speed. In fact, in our fast paced world, speeding is so normalized that it’s uncommon to encounter a driver following the speed limit. Hawaiian psychology professor Leon James explains it best: people have twisted their definitions of speeding to …

A Study Of The Sum Of Divisors, Henry M. Willie

Miners Solving for Tomorrow Research Conference

No abstract provided.

Kroger Post-Pandemic Customer Segmentation, Mario Mata, Joey Truitt, Renn Spigelmyer, Dhanuja Kasturiratna, Lisa Holden, Nitish Baidya, Hanna Tafari

Posters-at-the-Capitol

The grocery retail industry landscape has changed greatly in the wake of the pandemic. Specifically, delivery and pickup services have become more popular and customer buying habits have evolved. At the same time, improvements in data collection and analysis have allowed grocery marketing strategies to become highly individualized.

We worked with 84.51, an analytics firm, to identify customer segments for the Kroger Company based on data from 2023. Using clustering techniques, we organized customers into groups, or segments, based on similar characteristics. We identified and profiled four distinct groups of customers. Three segments were characterized by high frequency and spending …

Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effects Of Persistent Post-Concussion Syndrome, Jackson Flemming, Olivia Schleifer, Megan Powell

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Employee Attrition: Analyzing Factors Influencing Job Satisfaction Of Ibm Data Scientists, Graham Nash

Symposium of Student Scholars

Employee attrition is a relevant issue that every business employer must consider when gauging the effectiveness of their employees. Whether or not an employee chooses to leave their job can come from a multitude of factors. As a result, employers need to develop methods in which they can measure attrition by calculating the several qualities of their employees. Factors like their age, years with the company, which department they work in, their level of education, their job role, and even their marital status are all considered by employers to assist in predicting employee attrition. This project will be analyzing a …

Analysis Of The Discrete Cosine Transform Coefficients, Dillon C. Mckinley

ATU Scholars Symposium

No abstract provided.

Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

UNO Student Research and Creative Activity Fair

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding to …

Artsy Chaos: The Secret Life Of A Class Of Trigonometric Sums, Kaleb Swieringa, Joelena Brown, Rachael Harbaugh, Francis Nadolny

ONU Student Research Colloquium

We start from classical trigonometric sums (of terms such as k^n*cos(k), k^n*sin(k) - where n is a positive integer). These classical sums allow fairly straightforward closed form representations. In our work we considered changing the arguments of the trigonometric factors to powers (so that they get replaced by cos(k^a) and sin(k^a) - for a positive real exponent that may or may not be an integer), while also introducing in any term of such a sum a "rotational" factor of the form omega^k, where "omega" is a complex number of modulus 1 (that may or may not be a root of …

Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie Dibenedetti, Kate Rosello

Undergraduate Research and Scholarship Symposium

Auberle social services is opening the Family Healing Center (FHC), a level 3.5 treatment program in Pittsburgh, PA that provides housing and 24-hour support for families struggling with opioid addiction. We partnered with Auberle to study characteristics of individuals receiving level 3.5 treatment and to determine whether longer treatment lengths correlate with fewer adverse outcomes. We obtained data from the Allegheny County Department of Human Services on 2,016 individuals admitted to level 3.5 treatment in 2019. The data included birth year, race, gender, admittance date, discharge date, and Children Youth and Family (CYF) incidents before and after treatment. We categorized …

Session 5: Equipment Finance Credit Risk Modeling - A Case Study In Creative Model Development & Nimble Data Engineering, Edward Krueger, Landon Thompson, Josh Moore

SDSU Data Science Symposium

This presentation will focus first on providing an overview of Channel and the Risk Analytics team that performed this case study. Given that context, we’ll then dive into our approach for building the modeling development data set, techniques and tools used to develop and implement the model into a production environment, and some of the challenges faced upon launch. Then, the presentation will pivot to the data engineering pipeline. During this portion, we will explore the application process and what happens to the data we collect. This will include how we extract & store the data along with how it …

Question Answering By Bert, Suman Karanjit

Student Academic Conference

No abstract provided.

An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith

Student Scholar Showcase

Blood flow to the tissue of the hands and digits is efficiently regulated by vasoconstriction and vasodilation. Through a series of cadaveric dissection, we examined arteries in the hands and digits, including ulnar artery, radial artery, palmar arteries, and digital arteries, for their distribution (branching) patterns and morphological parameters (e.g., thickness, length between branches, external and internal diameters). Using data directly collected from three female cadavers as input variables to our mathematical model, we simulated vasoconstriction (-20% and -10% diameter) and vasodilation (+10% and +20 diameter) to evaluate the extent of changes in blood volume and flow within the arteries. …

Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller

UNO Student Research and Creative Activity Fair

Description: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my …

Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, Deyshon Ward, Kazi Javed

Posters-at-the-Capitol

The goal was to make a renewable fuel by using catalysts to remove oxygen molecules from fats. This is a current issue that society faces today because nonrenewable fossil fuels hurt the environment more than they help it. There are two components that make up a heterogeneous catalyst, a support and a reduced metal active phase. The active metal phases Nickel, Palladium, Platinum have been studied in the past on an alumina and carbon supports. We were investigating other supports using Nickel as the active phase component to determine the effect the support has on the catalyst removing oxygen of …

Building A Better Risk Prevention Model, Steven Hornyak

National Youth Advocacy & Resilience Conference

This presentation chronicles the work of Houston County Schools in developing a risk prevention model built on more than ten years of longitudinal student data. In its second year of implementation, Houston At-Risk Profiles (HARP), has proven effective in identifying those students most in need of support and linking them to interventions and supports that lead to improved outcomes and significantly reduces the risk of failure.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, Anqi Zhang, Lawrence Theller, Bernard A. Engel

The Summer Undergraduate Research Fellowship (SURF) Symposium

Urbanization increases runoff by changing land use types from less impervious to impervious covers. Improving the accuracy of a runoff assessment model, the Long-Term Hydrologic Impact Assessment (L-THIA) Model, can help us to better evaluate the potential uses of Low Impact Development (LID) practices aimed at reducing runoff, as well as to identify appropriate runoff and water quality mitigation methods. Several versions of the model have been built over time, and inconsistencies have been introduced between the models. To improve the accuracy and consistency of the model, the equations and parameters (primarily curve numbers in the case of this model) …

Using Nitrate, Chloride, Sodium, And Sulfate To Calculate Groundwater Age, Kimm Crawford, Terry Lee

Sinkhole Conference 2015

Regression analysis is used to identify monotonic trends to assign water age using ion data from two large well water databases from southeast Minnesota (SE MN). Nitrate (NO3-N), chloride (Cl), sodium (Na), and sulfate (SO4) ions in the commonly used aquifers in SE MN can be used as groundwater tracers since they are either entirely or partly anthropogenic in their sources, their loading occurs on a regional scale, and they are almost entirely conserved. Ion concentrations over time are used to establish six trend patterns. Two patterns are unchanging (background and stable above background), and four are changing (linear up, …

Spatiotemporal Crime Analysis, James Q. Tay, Abish Malik, Sherry Towers, David Ebert

The Summer Undergraduate Research Fellowship (SURF) Symposium

There has been a rise in the use of visual analytic techniques to create interactive predictive environments in a range of different applications. These tools help the user sift through massive amounts of data, presenting most useful results in a visual context and enabling the person to rapidly form proactive strategies. In this paper, we present one such visual analytic environment that uses historical crime data to predict future occurrences of crimes, both geographically and temporally. Due to the complexity of this analysis, it is necessary to find an appropriate statistical method for correlative analysis of spatiotemporal data, as well …

Applied Analysis Of Ionic Polymer Metal-Composite Actuators, Siul Ruiz, Benjamin Mead, Woosoon Yim

College of Engineering: Graduate Celebration Programs

• IPMC is a type of smart material called an electroactive polymer
• Consists of an ionic polymer such as Nafion or Flemion and a conducive metal such as platinum or gold
• COMSOL multi-physics simulations accurately model the experimental displacement results
• Optimization performed using the multi-physics model to find the maximum deflection, force, and twisting
• Using the closed loop control system accurate IPMC tip location can be achieved
• This control system has been extended to function using a computer mouse as an input