Physical Sciences and Mathematics Commons^™

Euler And Gauss On The Hypergeometric Function -- A Comparison, Alexander Aycock

Euleriana

We present several results stated by Euler on what is today called the Gaussian hypergeometric function. For this purpose, we compare the results found by Gauss to Euler's results.

The Extent To Which The Earth's Motion Is Perturbed By The Moon, More Accurately Investigated: An English Translation Of E139, Patrick T. Headley

Euleriana

In Tabulae astronomicae solis et lunae (Solar and lunar astronomical tables) (E87), published in 1746, Euler made a first attempt to correct his astronomical tables for the gravitational attraction of the Earth toward the Moon, simply by accounting for the difference between the position of the Earth and the center of gravity of the Earth-Moon system. In this article Euler revisited the problem, noting that this center of gravity would not itself take an elliptical path around the Sun. To model the motion more accurately, Euler considered the separate gravitational attractions of the Sun and Moon acting on the Earth. …

About Infinite Algebraic Curves Whose Indefinite Lengths Equal An Elliptic Arc: An English Translation Of E780, Derek R. Aoki

Euleriana

Euler continues his study of algebraic curves with equal arc length, a subject to which he returned several times. After a brief review, he introduces an infinite family of curves with the same indefinite length as a given ellipse. However, this first family is by his own admission poorly motivated, so he derives directly a different but related family of curves with the same indefinite length as a given ellipse.

Historical Beginnings To Modern Results, Christopher Goff, Erik Tou

Euleriana

An introduction to the contents in Volume 6 (Issue 1) of Euleriana.

The Need For Developing Psychologically Informed Physical Therapy Education, Dustin Cox

Journal of Applied Disciplines

Chronic pain presents a multifaceted challenge for healthcare providers, often impacting patients' physical, emotional, and psychological well-being. Research indicates that individuals with chronic pain process pain through emotional and reward pathways in the brain, underscoring the need for integrative treatment approaches. Evidence supports the effectiveness of combining psychological interventions with physical rehabilitation to improve outcomes. Acceptance and Commitment Therapy (ACT), a mindfulness-based behavioral therapy, has shown promise in addressing the psychological dimensions of chronic pain. However, physical therapists often lack formal training in ACT. This study protocol was designed to explore effective methods for educating physical therapists in ACT principles …

Optimizing And Fortifying Ai Software Through The Lens Of Artifact Synthesis, Jieke Shi

Dissertations and Theses Collection (Open Access)

Artificial Intelligence (AI) has transformed the software landscape, ushering in a new era of intelligent systems that increasingly shape our daily lives. This transformation is evident in various domains, including Software Engineering (SE), where Large Language Models (LLMs) support many development tools, and control systems, where self-driving cars and autonomous drones rely on deep learning models for real-time decision-making. These AI systems are collectively referred to as AI software, with the former categorized as AI4SE software (AI for Software Engineering) and the latter as AI4Control software (AI for Control). As AI software becomes central to modern computing infrastructure, its reliability …

Averaging Principle For A General Class Of Periodic Functions In Discrete Spaces, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

In this work, we develop a periodic averaging principle for arbitrary discrete time domains, leveraging a novel definition of periodicity. This definition does not rely on the classical requirement for the time domain itself to be periodic. We implement this averaging principle across diverse discrete time domains and explore a range of periodic functions within this extended context. The paper contains several examples with numerical simulations, providing visual demonstrations of our results. This highlights the versatility of our averaging principle and its potential to understand dynamics of nonautonomous recurrences with complex temporal patterns.

Controllability Of The Semilinear Benjamin–Bona–Mahony Dynamic Equation On Homogeneous Time Scales, Martin Bohner, Cosme Duque, Hugo Leiva

Mathematics and Statistics Faculty Research & Creative Works

This work investigates the approximate controllability and free-time approximate controllability of a generalized semi linear Benjamin–Bona–Mahony type dynamic equation defined on homogeneous time scales, subject to homogeneous Dirichlet boundary conditions. To accomplish this, the problem is framed within an abstract setting, employing the -semigroup theory on time scales. Moreover, we apply a technique introduced by Bashirov et al. [1, 2], which enables us to avoid relying on fixed point theorems.

Plaster Creek Watershed Management Plan: Chloride Addendum, Plaster Creek Stewards

Watershed Reports

This addendum complements the 2008 Plaster Creek Watershed Management Plan (WMP), which tells the full story of the Plaster Creek Watershed’s current condition, impairments, and need for restoration. This addendum focuses on chloride, an emerging pollutant of concern in Michigan that was not addressed in Plaster Creek’s 2008 WMP. This addendum meets the nine elements required by the United States Environmental Protection Agency (EPA) for a watershed management plan to be officially approved; as such, its content and layout are intended for a technical audience.

“It’S A Lot More To It Than Just Research”: Integrating Critical Data Literacy And Reasoning With Data Into A Stem Summer Camp, Marc T. Sager, Saki L. Milton, Candace Walkington

Publications

Purpose: This study explores how middle-grade girls from predominantly underrepresented and underserved racially and ethnically minoritized (UUREM) backgrounds developed critical data literacy (CDL) through participation in a week-long residential STEM camp. Given the increasing importance of data science education in a data-driven world, this research examines how informal learning environments can support CDL development among youth from historically marginalized groups.

Design/Methodology/Approach: The study draws on qualitative interview data from eleven participants, and their group-produced artifacts to investigate how the camp experience supported engagement with data and the development of CDL. Interviews explored participants' experiences with data collection, organization, analysis, and …

(Si16-04) Some Fixed Point Theorems On Chatterjea Type Contractions, Irom Shashikanta Singh, Y. Mahendra Singh

Applications and Applied Mathematics: An International Journal (AAM)

This paper establishes the existence of fixed points related to strict Chatterjee contractive mappings by relaxing the compactness of the underlying spaces and the continuity of the mapping involved, using altering distance functions and comparison functions in the general setting of metric spaces. Several non-trivial and illustrative examples are provided to demonstrate, support, and validate the obtained theoretical results. In addition, a theorem that can characterize the completeness of metric spaces through the existence of fixed points is rigorously proven and discussed. Furthermore, a theorem on strict Chatterjea-type modulus contractive mappings without continuity assumptions and with relaxed compactness conditions is …

(Si16-06) Equations Of Geodesics In Two-Dimensional Finsler Manifold With A Special Cubic (Α, Β)-Metric, Sejal Prajapati, Brijesh Kumar Tripathi, V. K. Chaubey

Applications and Applied Mathematics: An International Journal (AAM)

Geodesics represent the shortest path between two points in curved spacetime and are vital in the study of Finsler manifolds. Matsumoto and Park first derived the geodesic equation as a secondorder differential equation in a two-dimensional Finsler manifold with Randers, Kropina, and Matsumoto metrics. Building on this foundation, our paper presents the geodesic differential equation for a two-dimensional Finsler manifold using a special cubic power metric. In this two-dimensional setting, this work also looks at certain well-known geometric curves and analyzes their variants as solutions to the geodesic differential equation. Additionally, this work examines the geometric applications of the geodesic’s …

(Si16-07) Computing The Kirchhoff Index And The Wiener Index Of Spiro Para Hexagonal Cylinder Chain, Md Selim Reja, Sk. Md. Abu Nayeem

Applications and Applied Mathematics: An International Journal (AAM)

In graph theory, the Kirchhoff index serves as a metric to evaluate the complexity of a graph. It is determined by adding up the resistance distances between every pair of vertices in the graph. In a network created from the given graph by substituting each edge by a unit resistor, the resistance distance between a pair of specified vertices is equivalent to the electrical resistance between them in the constructed network. Basically, it measures the convenience with which data or flow can move between various locations in a network that the graph represents. In terms of graph matrices, the Kirchhoff …

(Si16-11) Seasonal And Temporal Optimization Of Solar Energy Harvesting In Smart Iot Lighting Infrastructure, Abhijit Paul, Rishabh Pipalwa, Sabyasachi Mondal North - Eastern Hill University, Shillong, India

Applications and Applied Mathematics: An International Journal (AAM)

This study investigates the seasonal and temporal optimization of solar energy harvesting in a smart IoT-enabled streetlighting infrastructure by focusing on the theoretical determination of optimal solar panel tilt angles. The proposed system incorporates auto-adjusted solar panels integrated with an IoT network comprising sensors, microcontrollers, and streetlights. A key innovation lies in the implementation of a modified MQTT communication protocol, which enables efficient, localized decision-making and data exchange among components. Simulation results indicate that the modified MQTT protocol significantly reduces communication delay and power consumption compared to the conventional MQTT approach, thereby enhancing the overall system performance. Detailed analysis of …

A Survey On Heterogeneous Computing Using Smartnics And Emerging Data Processing Units, Nathan Tibbetts, Sifat Ibtisum, Satish Puri

Computer Science Faculty Research & Creative Works

The emergence of new, off-path smart network cards (SmartNICs), known generally as Data Processing Units (DPU), has opened a wide range of research opportunities. Of particular interest is the use of these and related devices in tandem with their host's CPU, creating a heterogeneous computing system with new properties and strengths to be explored, capable of accelerating a wide variety of workloads. This survey begins by providing the motivation and relevant background information for this new field, including its origins, a few current hardware offerings, major programming languages and frameworks for using them, and associated challenges. We then review and …

A Diffuse Interface Model And Fully Decoupled, Energy-Stable Scheme For The Two-Phase Ferrofluid Flows In Porous Media, Guo Dong Zhang, Shuai Zhou, Yunqing Huang, Xiaoming He, Xiaofeng Yang

Mathematics and Statistics Faculty Research & Creative Works

We propose a new diffuse interface model for two-phase porous media ferrofluid flows, employing the phase-field method and establishing an associated energy law. This thermodynamically consistent multi-physics model integrates the Cahn-Hilliard equations, Darcy equations, the magnetostatic equation, and magnetization equations. To efficiently solve the system by addressing its inherent nonlinearities, coupling, and saddle-point structure, we incorporate several advanced techniques, including the SAV-ZEC method to handle nonlinearities and couplings, a reformulated approach to decouple the linear coupling of the magnetic potential and magnetization, and the pressure projection method to decouple velocity and pressure. This results in a numerical scheme that is …

Alfred Russel Wallace Notes 39. What About Wallace's 'Agnosticism'...?, Charles H. Smith

Faculty/Staff Personal Papers

Alfred Russel Wallace (1823−1913) seems to have distinguished his earlier years of agnosticism from his later period as a spiritualist, but a closer look at the situation suggests he actually remained an agnostic all the way through to the end of his life. The confusion is occasioned by a lack of terminology that can be applied to his position, which most closely resembles a Spinozian manner of thinking.

The Enthalpy Of Formation Of Acetylenes And Aromatic Nitro Compounds For A Group Contribution Method With “Chemical Accuracy”, R. J. Meier, Paul R. Rablen

Chemistry & Biochemistry Faculty Works

In this paper we provide the Group Contribution parameters for acetylenes and aromatic nitro compounds fitting with a recently developed Group Contribution method with chemical accuracy (1 kcal/mol) for the heat of formation of organics. These additional parameters widen the applicability of the Group Contribution method. We also provide further G4 quantum calculated values as reference when no experimental data are available and compare to previously reported G4 data.

An Seir Model On Time Scales With Discrete Applications To Tuberculosis, E. Akın, G. Yeni, D. Konur, S. R. Işık, M. R. Işık

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose a novel dynamical model on time scales consisting of new parameters to investigate the transmission dynamics of tuberculosis (TB), one of the deadliest infectious diseases worldwide, characterized by a long latency stage. The dynamical TB model, governed by the Susceptible–Exposed–Infected–Recovered (SEIR) framework within a unified form, yields a continuous model with a non-saturated incidence rate on the real numbers and discrete models with saturated incidence rates when different time domains are chosen. We analyze the stability of the equilibrium points of both the continuous TB model on the set of real numbers and the discrete …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Homogeneous Syringe-Sharing Network, Seun Ale, Que Thi Nguyet Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model assumes homogeneous mixing among syringe-sharing agents, without any form of heterogeneity in the agents interactions or syringe-sharing attitude. All syringe-sharing PWID are treated as identical in terms of their interaction frequency and syringe-sharing probability. Interactions are generated dynamically using proximity-based sampling at each timestep (one day), allowing agents to form syringe-sharing interactions based on spatial closeness. The number of daily interaction events is fixed at the population level, and each syringe-sharing agent has the same probability …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission With Inter- And Intra-Group Structural And Behavioural Heterogeneous Syringe-Sharing Networks (5), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework and behavioural heterogeneity through group-specific syringe-sharing rates with additional intra-group variability. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. In addition to differences in the number of daily interaction opportunities across groups, agents in each group are assigned syringe-sharing probabilities that vary at the individual level around their …

Automated Machine Learning For High-Resolution Daily And Hourly Methane Emission Mapping For Rice Paddies Over South Korea: Integrating Modis, Era5-Land, And Soil Data, Jiah Jang, Seung Hee Kim, Menas Kafatos, Jaeil Cho, Gayoung Yoo, Sujong Jeong, Yangwon Lee

Institute for ECHO Articles and Research

Agriculture is a major global source of methane (CH4), and accurate emission estimates are essential for refining national greenhouse gas inventories and supporting climate-resilient policies. This study develops a high-resolution estimation framework for CH4 emissions from Korean rice paddies by integrating multi-source datasets, including Moderate Resolution Imaging Spectroradiometer (MODIS) vegetation indices, European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis Version 5 (ERA5)-Land meteorological variables, and Harmonized World Soil Database (HWSD) soil properties. Using CH4 flux observations from four global rice ecosystems (Italy, Japan, South Korea, and USA), we constructed parallel daily and hourly machine learning models using an automated machine …

Identifying Priorities To Guide Extension Water Quality Programming In Utah, Clare Entwistle, Sarah Erwin, Stephanie Vaughn

Outcomes and Impact Quarterly

Utah State University Extension water quality faculty conducted a statewide water quality needs assessment to identify priority contaminants and resource gaps. The results found that elevated nutrient levels and sedimentation were the top concerns where additional resources would be beneficial. In addition, insufficient funding for improvements and low public engagement were identified as key challenges in addressing water quality issues. Results revealed current unmet needs with regional variation to inform Extension resource allocation and programming.

An Explainable Transformer-Based Model For Phishing Email Detection: A Large Language Model Approach, Mohammad Amaz Uddin, Md Mahiuddin, Iqbal H. Sarker

Research outputs 2022 to 2026

Phishing email is a serious cyber threat that tries to deceive users by sending false emails with the intention of stealing confidential information or causing financial harm. Attackers, often posing as trustworthy entities, exploit technological advancements and sophistication to make the detection and prevention of phishing more challenging. Despite extensive academic research, phishing detection remains an ongoing and formidable challenge in the cybersecurity landscape. In this research paper, we present a fine-tuned transformer-based masked language model, RoBERTa (Robustly Optimized BERT Pretraining Approach), for phishing email detection. In the detection process, we employ a phishing email dataset and apply the preprocessing …

Explainable Artificial Intelligence Models For Detecting Suspicious Bank Transactions, Narasimha Kumar Narasapuram, Syed Afaq Ali Shah, Mohd Fairuz Shiratuddin, Ferdous Sohel

Research outputs 2022 to 2026

Detecting financial crime is a complex challenge due to evolving criminal strategies and fragmented detection systems, particularly in the areas of money laundering and fraud. While it is easy to implement, traditional rule-based approaches lack adaptability to new threats, and machine learning models, though more effective, often function as opaque "black boxes," limiting their practical use in regulated domains like banking, where interpretability and accountability are essential. This research presents a novel framework that combines intrinsic and post-hoc XAI techniques to detect suspicious bank transactions. Intrinsic methods provide model-inherent transparency, while post-hoc methods offer behavior-level explanations, enabling robust cross-verification of …

Software Engineering In The Age Of Coding Agents: Failure Modes And Rejection Patterns, Mahd Mohd Hindi

Theses

This thesis investigates the real-world behavior of LLM-driven coding agents that generate code changes and submit pull requests (PRs) to public software repositories. As these tools evolve from autocomplete-style assistants into more autonomous agents, their contributions increasingly interact with socio-technical review processes (human reviewers, bots, CI/CD gates, and project norms). The thesis focuses on understanding why agent-generated PRs are accepted or rejected and what these outcomes reveal about current agent limitations in practical development workflows.

The main objective of this thesis is to systematically characterize rejection patterns and failure modes of agent-generated pull requests in real repositories. Specifically, the thesis …

In Vitro Pharmacological Evaluation Of Novel Cmpi Derivatives As Selective Positive Allosteric Modulators Of The Alpha4 Beta2 Nicotinic Acetylcholine Receptor, Josue Gaona, Nataly Sanchez, Wilder Felix, Nathalia Menegasso, Brisa Cea, Ganesh Thakur, Ayman K. Hamouda

School of Medicine Student Publications and Presentations

Nicotinic acetylcholine receptors (nAChRs) contribute to the pathogenesis of neurodegenerative diseases such as Parkinson’s disease (PD), where degeneration of dopaminergic and cholinergic neurons disrupts neurotransmission. The (α4)₃(β2)₂ nAChR subtype is expressed on affected neuronal populations and represents a promising therapeutic target. Positive allosteric modulators (PAMs) may enhance receptor function while preserving endogenous signaling. We evaluated chemical derivatives of CMPI [3-(2-chlorophenyl)-5-(5-methyl-1-(piperidin-4-yl)-1H-pyrazol-4-yl)isoxazol] as selective PAMs of (α4)₃(β2)₂ nAChRs. Two-electrode voltage-clamp recordings were performed in Xenopus laevis oocytes expressing defined receptor stoichiometries to assess potentiation and generate dose–response curves. Cytotoxicity was assessed in HEK cells using the MTT assay. Substitutions at the pyrazole …

Transfer Learning Neural Networks For Nuclear Forensic Image Morphology Using Image Splitting Techniques, Niko A. Petrocelli, Lee C. Lambert, Brett J. Borghetti, Abigail A. Bickley

Faculty Publications

Manual morphological analysis of actinide particles from scanning electron microscope (SEM) imagery is a critical component of nuclear forensics but is prone to significant inter-analyst variability. To address this challenge, this work develops and evaluates an automated classification method using deep learning. We introduce a methodology based on partitioning 1906 SEM images, representing 13 classes of uranium compounds, into smaller patches for analysis. Three convolutional neural network (CNN) architectures of increasing complexity were compared: a custom baseline CNN, a simple transfer learning model using ResNet50v1, and a complex model featuring hierarchical feature extraction and a spatial attention mechanism built upon …

Using Ensemble Disagreement To Stabilize Conformal Prediction Under Distribution Shift, Patrick D. Murphy

Master's Theses

Semantic segmentation of eelgrass from drone imagery is crucial for coastal habitat monitoring, restoration, and management, as these habitats continue to see rapid changes due to climate change and human influence. However, the reliability of generalizing a deployed classification model relies on both high-accuracy segmentation as well as robust uncertainty quantification that holds up when conditions change over years or locations. Conformal prediction (CP) is a method that converts a classifier's output into prediction sets with a guaranteed average coverage level for in-distribution data. However, the “vanilla” conformal score can often under-cover in hard or out-of-distribution (OOD) regions under drift. …

The Application, Construction, And Validation Of Hidden Markov Model Profiles For Carbonic Anhydrase Enzymes, Samuel F. Kaplan

Master's Theses

Carbonic anhydrases (CAs) catalyze the reversible hydration of CO2 and have evolved independently at least eight times, resulting in structurally distinct enzyme families (α, β, γ, δ, ζ, η, θ, ι). Traditional sequence alignment methods struggle to classify these convergently evolved proteins because their sequential similarity does not reliably indicate functional or evolutionary relationships. Many CA sequences in public databases are annotated generically without family assignments, and prior computational approaches have focused predominantly on the three well characterized families (α, β, γ), leaving the five recently discovered classes without robust classification tools. Family level assignment is often a prerequisite for …