Applied Mathematics Commons^™

Impact Of Stochastic Travel Times On The Military Port Selection Problem: A Stochastic Programming Approach, William M. Titus

Theses and Dissertations

This research models and analyzes the impact of stochastic travel times on port selection during a large-scale mobilization of equipment from continental United States installations to deployment locations using sealift ships. A stochastic mixed-integer programming model is developed to minimize the average arrival time of equipment into theater. The model is solved using Sample Average Approximation. In the first stage, the model selects ports to open and assigns installations, equipment, and ships to open ports. In the second stage, travel times are realized, and equipment is assigned to specific ships that are scheduled to depart. Results show that the marginal …

(Si14-02) Analysis Of Cross Diffusion Effects On Mhd Nanofluid Past An Oscillating Plate With Ramped Wall Temperature, Gopal Nanda, Harshad Patel

Applications and Applied Mathematics: An International Journal (AAM)

The primary objective of this research is to analyze the influence of cross-diffusion on the behavior of nanofluid flow, which is governed by unsteady hydrodynamics in the existence of a magnetic field. Additionally, this study considers the effects of thermal radiation and heat production. The flow occurs within a porous medium, passing through a vertically oscillating plate. The investigation focuses on two distinct nanofluid formulations, namely silver and titanium dioxide. The concept of similarity transformation is applied to simplify the governing system from partial differential equations (PDEs) to ordinary differential equations (ODEs). To obtain precise expressions for the concentration, temperature, …

(Si14-06) Influence Of Hall Effects On Rotating Mhd Casson Fluid Flow Over A Vertical Plate, Zankhana Mali, Akhil Mittal, Harshad Patel

Applications and Applied Mathematics: An International Journal (AAM)

Studies of Hall effects regarding motion of fluid due to some external forces in MHD transport of reacting Casson fluid with heat generation over an impulsively emerging vertical plate are considered in this work. This theory proposes that because of a sudden rise in temperature and an accompanying surface concentration profile, which shows an elevation with time, the boundary plate has endured rapid expansion. In a rotational environment, this characteristic occurs homogeneously inside a porous uniform material. It applies the Laplace transform method for determining the fundamental equations subject to imposed starting and side conditions. Under isothermal conditions, accurate formulae …

My Gai Study Partner For Odes, Milena C. Cuellar

Open Educational Resources

My GAI Study Partner for ODEs is a scaffolded sequence of learning activities designed to support students in an Ordinary Differential Equations (ODEs) course by integrating the use of Generative AI tools—specifically Copilot, a platform accessible to all CUNY students and faculty. The activities are rooted in experiential learning, flipped classroom strategies, and self-directed learning principles. The sequence begins with two preparatory activities that introduce students to the ethical use and foundational concepts of Generative AI, fostering digital literacy and critical reflection. These are followed by a series of main activities—initially structured (Activity 3) and later more flexible …

Advancing Defense Software Cost Estimation Through Regression, Probabilistic, And Machine Learning Models, Stephen D. Chatterton

Theses and Dissertations

Accurately estimating software costs is critical for effective project management within the Department of Defense (DoD), where early decisions shape resource allocation and risk management. This work evaluates regression-based Cost Estimating Relationships (CERs), probabilistic models, and machine learning techniques to address limitations of traditional estimation methods. Using records from two DoD repositories, the analysis applied Ordinary Least Squares (OLS) regression, Multinomial Logistic Regression (MLR), Random Forest, and neural networks to model and classify software costs, with key predictors including Source Lines of Code (SLOC), Equivalent Source Lines of Code (ESLOC), and programming hours. The findings highlight strengths and trade-offs of …

Investigation Of Node Refinement Methods In Local Adaptive Kernel Based Approximation, Shelby W. Woodrum

Theses and Dissertations

This thesis explores computational efficiency and accuracy of six node refinement methods for local adaptive kernel-based approximations of solutions to the two-dimensional Poisson equation. Using an adaptive kernel-based approximation algorithm, this research investigates performance of Delaunay triangulation-based methods (shifted barycenters and edge midpoints), refinement via approximate Fekete and discrete Leja points, and a meshless predefined shift refinement method across two domains with varying complexities. Computational experiments reveal that Delaunay triangulation-based methods achieve a practical balance between accuracy and efficiency, particularly in square domains. Refinement via approximate Fekete and discrete Leja points produce accurate results but incur greater computational costs, making …

Analyzing And Comparing Refinement Indicators For Rbf-Fd Adaptive Algorithms, Anders R. Johnson

Theses and Dissertations

Recent progress has been made in the development of collocation-based iterative algorithms that approximate solutions to PDEs. These algorithms rely on the ability to identify regions within a domain where a finer discretization is required. Such iterative algorithms are beneficial particularly when solution functions have highly localized behavior. This thesis proposes an indicator for node refinement that is constructed by approximating the forward error. This proposed indicator also helps to establish confidence in the accuracy of a given solution estimate. The proposed error estimator is theoretically examined and compared with contemporary refinement indicators. It is shown that an iterative algorithm, …

Grassmannian Codes From Stratified Frames, William J. Brinkley

Theses and Dissertations

An equichordal tight fusion frame (ECTFF) is a finite sequence of equi-dimensional subspaces of a Euclidean space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ECTFF is an optimal Grassmannian code with respect to the chordal distance. We introduce a method for constructing an ECTFF from any finite sequence of unit norm tight frames that happen to be stratified in a certain sense. We moreover show how to construct stratified unit norm tight frames from a difference family for a finite abelian group, as well as from a suitable combination of a resolvable balanced incomplete block design …

Greening The Workplace: Can Sustainable Practices Reduce Anxiety And Enhance Meaningful Work Engagement?, Cyril Tom T. Sunny, Peter Muttungal, Benny G. Davidson

Northeast Journal of Complex Systems (NEJCS)

This academic research examines the relationship between job engagement, green work climate, job-related anxiety, meaningfulness at work within the organization. It draws attention to identify the significant relations among all these factors and highlights the role of a green work climate in promoting meaningful work and alleviating job-related anxiety. The research emphasizes a diverse sample of employees from various organisations using structural modelling to find the mediating roles of job engagement and work meaningfulness in the correlation between organizational practices, environmental sustainability, and employee satisfaction. The study finds that a green work climate significantly enhances meaningful work experiences and reduces …

Exploration Of Differential Equation Models For Phage-Bacteria Population Dynamics, John Lawrence Palacios, Rebecca A. Segal

Spora: A Journal of Biomathematics

Bacteriophages are viruses that infect and replicate within bacteria. Lytic phages cause the bacterial cell to burst, killing the bacteria. These types of phages can be used to treat patients with antibiotic-resistant bacterial infections. As a step in developing successful treatment protocols, we aim to understand the population dynamics of phages and bacteria using an in vitro model. We model the dynamics using the Campbell model, which consist of a delay differential equation (DDE), as a base model. We extended the model by including the emergence of phage resistance. We then compared the DDE model with a parallel ordinary differential …

Impact Of Node Failures On Productivity In Multilayer Supply Chain Networks: An Influence Network Analysis In The Indian Electronics Sector, Surendra Orupalli, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

Supply chain networks are essential for the delivery of goods and information, but disruptions such as natural disasters or trade embargoes can severely impact them. Resilience of entire networks under different types of disruptions when nodes or edges fail has been extensively studied. However, the extent to which the failure of a particular company affects another company of interest within a network has not been widely explored. To address this, we created a multilayer physical supply chain network of companies in an electronics supply chain concentrated in India. Through systematic node removal simulations, we examined how the productivity of one …

A Novel Preprocessing Model For Multi Modal Brain Mri Image Classification For Stroke Prognosis, Alwin Joseph, Chandra J

Northeast Journal of Complex Systems (NEJCS)

Magnetic Resonance Imaging (MRI) is an imaging technique used for the diagnosis and observing the progression in various neurological disorders. Stroke is one of the prominent neurological disorders that creates significant impacts in the patients. It occurs when the blood supply to part of the brain is interrupted or reduced, preventing brain tissues from getting oxygen and nutrients. Multimodal data from various modalities help clinicians in proper prognosis of stroke. Ischemic Stroke Lesion Segmentation Challenge (ISLES22) provides data of stroke data for various stroke patients, the dataset consists of three modalities of data – Fluid Attenuated Inversion Recovery (FLAIR), Apparent …

Modeling Covid-19 Spread And Effects Of Non-Pharmaceutical Interventions On A College Campus, Jakob Kotas, Priscilla Perey Ratonel

CODEE Journal

We consider an extension to the classical SIR compartmental model from mathematical epidemiology as applied to the spread of COVID-19 on a college campus. While the classical SIR model does not allow for recovered individuals to lose immunity, we alter the equations to allow for such (due to the rise of new variants), leading to a SIRS-type model. We study the system of ODEs analytically and through numerical simulation. Finally we discuss a quantitative approach for how college administrators can decide when to implement stricter non-pharmaceutical interventions (social distancing, mask mandates, quarantine, etc.) to eradicate the infection from the campus …

Multiple Hypothesis Testing Under Dependence, Nabaneet Das

Doctoral Theses

We have examined various aspects of multiple hypothesis testing under dependence. Traditional algorithms designed to control the error arising from multiplicity become severely conservative when the hypotheses exhibit positive dependence, resulting in a loss of power. There is a paucity of literature explicating the behaviour of traditional algorithms when the hypotheses are dependent. In the realm of multiple testing, a popular multiplicity correction is the Bonferroni correction, which is perhaps the oldest classical approach for controlling the Family-Wise Error Rate (FWER) at a desired level, regardless of dependence among hypotheses. However, under the global null and equicorrelated normal model, the …

Leveraging Network Science For Customer Segmentation And Product Recommendation, Ali Nasirzonouzi

Northeast Journal of Complex Systems (NEJCS)

The rapid growth in e-commerce has forced the development and implementation of enhanced customer segmentation and recommendation systems, improving business results and improving customer experience. Traditional approaches, such as RFM analysis and clustering algorithms like K-means, are very helpful in many situations but usually fail to catch complex interdependencies among customers and products. This paper proposes a new approach using network science methodologies, a bipartite graph model, toward the advancement of customer segmentation and product recommendation. It implements a bipartite graph of customers and products using the "Online Retail II" dataset and proceeds with community detection, segmenting customers into unique …

Influence Of Oil Density On Self-Propelled Motion Of Belousov-Zhabotinsky Reaction Droplet, Vivek Bharat Meshram, Anupama Sebastian, Puthiyapurayil Sibeesh, T K Shajahan

Northeast Journal of Complex Systems (NEJCS)

Belousov-Zhabotinsky reaction serves as an example of the nonlinear chemical oscillator in which the reacting substance undergoes sequential oxidation and reduction. A droplet containing the BZ reaction, when placed within the oily environment, can self-propel. In this experimental work, we explore the effect of oil medium density on the BZ reaction droplet dynamics. In an oil medium with lower density, the BZ droplet exhibits higher speed and effective diffusivity but a shorter lifetime. Both the distance and speed of the droplet initially increase with droplet volume. However, beyond a critical volume, the distance decreases while the speed stays constant. Interestingly, …

Integrating Neural Networks For Predictive Torque Control And Obstacle Avoidance In Autonomous Robot, Viswanath Kodali, Harsha Vardhan Borra, Kiran P

Northeast Journal of Complex Systems (NEJCS)

In the field of robotics, precise motion control and accurate computation of joint forces are critical for ensuring optimal performance. Traditional methods, such as using the Jacobian matrix for joint angle determination and Euler-Lagrange equations for torque computation, are reliable but computationally intensive, making them less suitable for real-time applications. This paper presents an advanced approach to improving the productivity and efficiency of a 3-Degree of Freedom (DOF) robotic arm by utilizing Artificial Neural Network (ANN). The proposed system dynamically predicts joint angles and torque, enabling faster and more efficient motion control.

To address the challenge of obstacle avoidance in …

Optimized Hiv/Aids Resource Allocation In Ohio: A Linear Programming Approach, Godfred Ahenkroa Kesse

Data Science and Data Mining

This study employs a linear and integer programming approach to optimize HIV resource allocation in Ohio, aiming to minimize new infections and enhance the impact of limited resources. With the advances in HIV prevention and treatment, Ohio faces challenges in addressing disparities in access to healthcare, particularly among high-risk populations. The proposed model integrates data on infection rates, transmission patterns, demographic factors, and cost-effectiveness to provide a decision-support framework for policymakers. Using epidemiological data and equity constraints, the model prioritizes high-risk regions and populations while ensuring fair resource distribution. Results indicate that increased funding allocations significantly enhance the potential to …

Project Title: Maximizing The Volume Of A Cardboard Box To Save Trees– An Application Of Polynomial Functions To Address Global Issues [Mathematics], Lucie Mingla

Open Educational Resources

MAT 115 College Algebra & Trigonometry/Precalculus

Project Title: Maximizing the Volume of a Cardboard Box to Save Trees– An Application of Polynomial Functions to Address Global Issues

Reflective Narrative:

This project was inspired by my participation in the "Designing and Implementation of STEM Co-Curricular Activities" CTL seminar in Spring 2023. I am grateful to Drs. Bukurie Gjoci, Daniel Gertner, Ingrid Veras, and Midas Tsai, along with fellow participants, for their invaluable feedback that helped shape its development. The project was implemented in two College Algebra and Trigonometry courses. I participated in two seminars to further develop this project. The Community …

Translation Of: Dupin'sche Hyperflächen In E^4, Manuscripta Math By Ulrich Pinkall, Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an English translation of the article "Dupin'sche Hyperflächen in E⁴" by Ulrich Pinkall, which was originally published in manuscripta math. 51 (1985), 89-119.

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in German. All references should be made to the original paper.