Applied Mathematics Commons^™

Mathematical Modeling Of Awareness-Driven Interventions For Gender-Based Violence Control In A Closed Population, Furaha M. Chuma, Edward K. Ngailo, Zubeda S. Mussa

Tanzania Journal of Science

Gender-based violence (GBV) remains a critical global health issue with profound social, economic, and psychological implications. Despite concerted efforts to address this challenge, traditional intervention approaches often fall short of effectively mitigating its prevalence. In recent years, there has been growing recognition of the potential impact of awareness-based interventions in addressing various social and health crises. This paper introduces a modeling framework to explore the efficacy of awareness-based interventions in influencing the dynamics of the GBV epidemic within a closed population. A detailed sensitivity analysis, utilizing a normalized sensitivity index method, reveals that the violence transfer rate between perpetrators and …

Modelling The Impact Of Multiple Control Strategies On The Spread Of Phyllody Disease In Sesame, Augustino I. Msigwa, Furaha M. Chuma

Tanzania Journal of Science

Phyllody disease, caused by phytoplasma and transmitted by insect vectors such as leafhoppers, poses a serious threat to the productivity of sesame (Sesamum indicum) as it has caused substantial yield and oil-quality losses worldwide, with documented seed-yield reductions ranging from 38% to as high as 80% in severe outbreaks, particularly in Africa and India. Understanding phyllody dynamics is therefore critical to safeguard yields and trade. While some modeling efforts exist for sesame phyllody (for example, statistical and prediction-focused approaches), mechanistic transmission models (SEIR) assessing its full impact remain scarce. This study therefore develops and analyses impact of multiple control strategies …

Modeling And Forecasting Wholesale Gasoline Prices In Tanzania Using Arima And Neural Network Autoregressive Models, Thadei D. Sagamiko, Edward K. Ngailo

Tanzania Journal of Science

Fluctuations in wholesale gasoline prices significantly impact the economy of import-dependent countries like Tanzania, making accurate forecasting essential for policymakers and market participants. This study forecasts monthly wholesale gasoline prices in Dar es Salaam by comparing the Autoregressive Integrated Moving Average (ARIMA) model with a Neural Network Autoregressive (NNAR) model. Using data from January 2015 to December 2024 from the Energy and Water Utilities Regulatory Authority (EWURA), the models were evaluated. The ARIMA(1,1,1) model was identified as the best-fitting linear model, but the NNAR(11,7) model demonstrated superior accuracy. On the holdout test set, the NNAR model achieved a lower Mean …

A Parallel Interval Modeling Framework For Nonlinear Systems: Application To A Modified Duffing Oscillator, Roman Voliansky, Nina Volianska

Northeast Journal of Complex Systems (NEJCS)

The paper presents a mathematical framework for converting nonlinear dynamical systems into parallel forms. This framework replaces the exact system motion equations with interval equations, enabling the representation of nonlinear functions over piecewise linear domains. Such representation enables the description of system motions using linear-like differential equations, which can be analyzed and manipulated using well-known control methods. One such method is eigenvalue analysis, a powerful tool in classical control theory since many techniques rely on the system’s characteristic polynomial and its eigenvalues. We apply this method to define interval system eigenvalues and track their variation during system operation. These eigenvalues …

Lipscomb University Parking Garage Analysis, Morgan Hayes, Reagan Maxwell, Daniel Diaz Tortolero, Dominick Dingus, Michael Ent

Student Scholar Symposium

Many students struggle to easily find parking during the school day at Lipscomb University, and this problem will only be emphasized with the potential removal of the nearby Stokes parking lot (containing 255 spaces). To combat this need and help provide additional room for university growth, we propose the addition of a parking garage west of the Fields engineering building, between Belmont Boulevard and Grandview Drive. This garage would be separated from the current garage behind Fields and be slightly larger, containing about 500 spaces over five levels. We evaluate the current number of parking spaces needed at Lipscomb based …

Gauge Invariance And Repeated Time Isolated Solution Discontinuities, James Glimm, James Glimm, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

The main conclusion of this paper is (a) a gauge structure for the underlying physics, at or above a critical dimension, forces multiple time isolated solution discontinuities (blowups). The main conclusion (b) is that the solution is one Sobolev index more singular that the natural Hilbert space H. Proofs are given for Navier-Stokes fluids.

Using Feynman's Technique To Evaluate Non-Elementary Integrals Used In Physics, Dominick Dingus, Christopher Wengert, Madouna Barsoum

Student Scholar Symposium

In numerous physical applications, such as those in the fields of optics and thermodynamics, the quantitative description of various phenomena requires evaluating certain definite integrals whose antiderivatives cannot be expressed using elementary functions. As a result, these integrals are typically evaluated numerically using a suitable program. However, it is possible to evaluate some of these types of integrals using a strategy known as Feynman’s Technique, an approach named after Richard Feynman, the American physicist who popularized the method during the mid-20th century. This project aims to highlight the usage of Feynman’s Technique for evaluating some of these integrals while applying …

Assessing The Electrical Efficiency Of The Thompson Coil, Christopher Wengert, Dominick Dingus, Madouna Barsoum, Jacqueline Ceballos, Michael Ent, Jackson Stephens

Student Scholar Symposium

The Thompson Coil is a well-known system used in undergraduate electromagnetism courses to demonstrate electromagnetic induction. Traditionally, the system employs a “jumping ring” to visualize induced currents. This project seeks to repurpose this phenomenon for practical energy transfer by replacing the jumping ring with a wire coil, allowing the measurement of the power delivered to an electric load. Using Faraday’s Law of Induction, 𝜖 = −𝑑Φ𝐵 /𝑑𝑡 , where Φ𝐵 represents the magnetic flux, the induced electromotive force (EMF) in the receiving coil is determined. Finally, the system’s power transfer efficiency is evaluated using the formula 𝜂 =𝑃𝑜𝑢𝑡/ 𝑃𝑖𝑛 ×100% …

Complex Numbers And Phone Signals, Ava Barrett, Rebecca Brazeal, Javier Gutierrez

Student Scholar Symposium

Though widely used, complex numbers are often introduced in coursework without real-world context. Our team examines their application in electromagnetic waves and communication systems, focusing on how they help model and analyze phone signals. By connecting concepts from physics and math, we demonstrate their role in signal modulation and transmission. Through this project, we aim to highlight the practical importance of complex numbers in modern technology and provide a clearer understanding of their use in communication systems that power everyday devices like smartphones.

Advanced Soliton Structures And Elliptic Wave Patterns In A Sixth-Order Nonlinear Schrödinger Equation Using Improved Modified Extended Tanh Function Method, Mina Fahim, Hamdy Mohamed Ahmed, Islam Samir, Kamal Dib

Basic Science Engineering

In this work, a sixth–order extension of the nonlinear Schrödinger equation (NLSE) within its integrable hierarchy is investigated to model higher–order nonlinear and dispersive effects relevant to optical fiber systems and nonlinear wave propagation. By employing the Improved Modified Extended Tanh Function Method, a comprehensive family of exact analytical solutions is derived, encompassing bright and dark solitons, singular soliton structures, and singular periodic solutions. In addition, solution families expressed in terms of Jacobi elliptic functions, Weierstrass doubly periodic elliptic functions, and exponential profiles are obtained. The novelty of this study lies in extending the analytical framework of the NLSE hierarchy …

Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev

Honors Scholar Theses

This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the …

On Sharpest Tail Bounds For Functions Of Tail Bounded Random Variables, Stephen Harrison

Mathematics & Statistics ETDs

Consider n real/complex, independent/dependent random variables with respective tail bounds and g a measurable function of the r.v.’s. Consider f the “sharpest” tail bound of g (sharpest in the sense, if f were any less, then for some X1, ..., Xn satisfying the conditions, g(X1, ..., Xn) would not satisfy the tail f). Significant research has been done to approximate f often with high accuracy. These results are often of the form, for g in this family, and tail bounds of Xk in this family, f is bounded by some f′ with high accuracy. However, the question “what would it …

Spectral Methods And Wavelets In Quantitative Finance Problems, Davood Damircheli

Theses and Dissertations

This dissertation leverages advanced spectral methods and wavelet techniques to address complex quantitative finance models, enhancing the computation of financial derivatives and risk assessments. Building on foundational studies, this research extends these methods to broader, intricate financial contexts. The first section explores fractional-order generalized Chebyshev wavelets (FOCW) applied to fractional advection equations, relevant in both mathematics and physics. Using a regularized beta function to compute the Riemann-Liouville fractional integral operator, this study introduces a novel numerical scheme with robust accuracy, confirmed through error analysis and empirical tests. The second part examines the fractional Black-Scholes equations for option pricing under subdiffusive …

Modeling Private Debt Using U.S. Consumer Expenditure Data, Stsiapan Dziamentsyeu

Honors Capstones

This project models private household debt among U.S. consumers using data from the Consumer Expenditure Survey (CES) between 2013 and 2023. The analysis focuses on identifying how demographic and economic characteristics, such as income, housing expenditures, education, and occupation, relate to non-mortgage “other” loan balances. After initial model development produced poor residual behavior due to zero-inflation from imputed debt values, the analysis was refined to include only households reporting verifiable debt. Multiple modeling techniques, including AIC-based variable selection and Lasso regularization, were compared under a five-fold cross-validation framework. The Lasso model achieved superior predictive accuracy (RMSE = 1.55, MAE = …

Math Meets Climate: The Energy Balance Model, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to the mathematics of Earth’s climate through the classical energy balance model. Students analyze how incoming solar radiation, outgoing thermal radiation, and temperature-dependent albedo interact to determine Earth’s equilibrium temperature. Using analytical calculations and computational tools, students identify equilibrium states, assess their stability, and interpret the results through the lens of dynamical systems and bifurcation theory. The activity builds conceptual understanding of climate feedbacks, greenhouse effects, and tipping behavior using a transparent, one-variable model. Designed for applied mathematics and interdisciplinary STEM courses, this assignment emphasizes computation, physical interpretation, and real-world relevance. It is released as a …

Understanding Enso Through Mathematical Models, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to conceptual models of the El Niño–Southern Oscillation (ENSO) and guides them through a structured investigation of their physical and mathematical foundations. Students analyze the recharge–oscillator and delayed–oscillator frameworks, explore how differential equations capture ocean–atmosphere interactions, and evaluate parameter-driven changes in oscillatory behavior. A key component of the work is the guided use of generative AI as a research tool: students employ AI models to locate peer-reviewed literature, interrogate model extensions, and refine their understanding of complex mechanisms, while synthesizing all final explanations in their own words. By blending classical climate modeling with modern AI-supported inquiry, …

A Harmonious Equation: How To Facilitate The Interdisciplinary Nature Of The Arts In A High School Math Classroom, Myah Medendorp

Honors Theses

The education system is constantly evolving and advancing, and the teaching methods should advance along with it. Musical involvement has long been cited as having a positive effect on mathematical proficiency and being an easy way to boost mathematical performance but is most often used in an elementary school setting and the early learning years. Are there ways to use this scientific relationship to boost performance and engagement in a secondary school environment?

This literature review functionalization takes a closer look at this relationship and how it can be implemented effectively in a high school math classroom beyond the young …

Global-Local Method For Poroelasticity Problems With Localized Pressure Effects, Hemantha Kunwar

Math Department Colloquium Series

In many poroelasticity applications, pressure effects are confined to a small region, making it inefficient and possibly unnecessary to solve the full system across the entire domain. Instead, we propose to solve the poroelasticity problem locally, where pressure effects are significant, and use a simpler linear elasticity model elsewhere. This creates a coupled elasticity–poroelasticity problem with transmission conditions. To solve this coupled problem, we propose a new non-intrusive global–local algorithm that iteratively solves the elasticity problem in the entire (global) domain and the poroelasticity problem only in a local domain, ensuring proper transmission conditions across the interface. This approach, which …

Extensions Of Weighted Integral Inequalities For Ga-Convex Functions In Connection With Fejér’S Result, Muhammad Amer Latif

Publications and Research

No abstract provided.

(R2136) Dimensionless Modeling And Analytical Insights Into Botanical Biofiltration Systems For Voc Reduction, N. Jeeva, K. M. Dharmalingam, M. Veeramuni

Applications and Applied Mathematics: An International Journal (AAM)

This paper investigates the mathematical modeling of volatile organic compound (VOC) removal using a botanical biofiltration system, an effective biological treatment method. It examines mass balance concentrations in the gas and biofilm phases, highlighting their significance in VOC degradation and indoor air quality enhancement. The governing equations of the proposed model are converted into a dimensionless form, resulting in second-order nonlinear differential equations. Derived from mass transfer and reaction kinetics principles, these equations incorporate specific boundary conditions to capture gas-biofilm interactions and VOC removal dynamics in biofiltration. The modified Adomian decomposition method (MADM) is utilized to derive analytical solutions for …