Applied Mathematics Commons^™

Looking Good: The Math Behind Computer Vision*, Corbin Weiss

Campus Research Month

Exploring the mathematical foundations of a Multilayer Perceptron (MLP), a foundational approach to computer vision. Then expanding this understanding to create a visualization of the representation of reality in the MLP.

Unraveling The Impact Of Curricular Complexity On Graduation Time: A Causal Analysis In Higher Education, Ameer Slim

Mathematics & Statistics ETDs

This study examines the causal relationship between program complexity and graduation time at UNM. While program complexity is recognized as a factor influencing student outcomes, its precise impact on graduation timelines remains underexplored. Using comprehensive cohort data, this study employs causal inference methods, including generalized propensity scores, to estimate the effect of complexity on time-to-degree. Findings reveal that higher program complexity extends graduation timelines, even after controlling for demographics and academic preparedness. Socioeconomic factors also play a role. Specifically, programs with more Pell Grant recipients and lower median high school GPAs tend to have lower complexity levels. These results provide …

Unfitted Finite Element Methods For Shape Optimization And Liquid Crystals, Jeremy T. Shahan

LSU Doctoral Dissertations

We present an approach to shape optimization problems that uses an unfitted finite element method (FEM). The domain geometry is represented, and optimized, using a (dis- crete) level set function and we consider objective functionals that are defined over bulk domains. For a discrete objective functional, defined in the unfitted FEM framework, we show that the exact discrete shape derivative essentially matches the shape derivative at the continuous level. In other words, our approach has the benefits of both optimize-then- discretize and discretize-then-optimize approaches.

Specifically, we establish the shape Fréchet differentiability of discrete (unfitted) bulk shape functionals using both the …

Fibonacci Product Cordial Labeling Of Generalized Triangular Snake And Other Graphs, Anthony S. Arial, Soumya Bhoumik

SACAD: Scholarly Activities

A Fibonacci Product Cordial labeling is an assignment of Fibonacci numbers to the vertices of a graph in a way that determines edge labels based on the product of vertex labels, modulo 2. The labeling is valid if the number of edges labeled 0 and 1 differ by at most 1. If a graph allows such a labeling, it is called a Fibonacci Cordial graph. We explore various snake graphs and Helm graphs that can have this type of labeling.

Irreversible K-Threshold Number Ck(G) And Saturation Probability P[G] For Corona Product And Double Corona Product Graphs, Eric J. Moon, Soumya Bhoumik, Paul Flesher

SACAD: Scholarly Activities

We discuss the Irreversible k-conversion process for graphs, where a vertex becomes saturated and remains saturated indefinitely if at least k of its neighbors are saturated. We investigate sets S₀, which when initially saturated, lead to complete graph saturation. We are interested in the minimum |S₀| = C_k(G), called the k-threshold number. We consider the construction of the Corona Product Graphs (of C_n and K_p). Additionally, we extend our analysis by defining and exploring Double Corona Product Graphs (of C_n and K_p). Then we incorporate …

Exploring Electrical Impedance Tomography Techniques For Breast Cancer Detection In Three Dimensions, Emily Jean Mader Corcoran

Dissertations (1934 -)

Electrical Impedance Tomography (EIT) is an imaging modality whose reconstruction problem is severely ill-posed; large changes in the interior conductivity can present as small changes in the data. Due to this ill-posedness, reconstructed images generally have low spatial resolution. However, EIT remains a promising area of study for many medical imaging applications, including breast imaging. In this dissertation, a proof of concept study is discussed in Project 1: "Machine Learning for Breast Cancer Detection" wherein machine learning techniques are used to classify breast tumors as malignant or benign from simulated EIT voltage data. Promising results in terms of accuracy and …

Acoustic-Gravity Wave Propagation Based On Solutions To The Generalized Multi-Component Transport Equations, Benedict PiñEyro

Doctoral Dissertations and Master's Theses

Nonlinear atmospheric models have provided important insight into acoustic waves generated by natural and man-made hazards, which may steepen into shocks or N-waves while also dissipating when propagating in the thermosphere. Although models have yielded results that agree with observations of ionospheric perturbations, dynamical models for the diffusive and stratified lower thermosphere often use single gas approximations with height-dependent physical properties that omit the dynamics of the major and minor constituents. Thus, the inter-species diffusion associated with these flows (e.g. variations of mean molecular weight, and specific heat) are not accounted for. This approximation is simpler and less computationally expensive …

Modeling Droplet Levitation Over A Heated Liquid Surface, Jacob E. Davis

Mathematics Theses and Dissertations

Research into the interactions between droplets and liquid surfaces is of importance for a number of practical applications. These applications range from spray cooling techniques in engineering, to infectious disease transmission, to the distribution of aerosolized pharmaceuticals and various challenges in particle transport in multiphase flows. In this study, we focus on the dynamics of a slowly condensing droplet, suspended above an evaporating liquid layer. The key objective of the present study is to formulate comprehensive mathematical models that describe the phenomena of diffusion and heat transfer occurring within this system. Using this, we model the flow around the droplet …

Dual Quaternions For Gravity Recovery Missions, Ryan Kinzie

Doctoral Dissertations and Master's Theses

A dual quaternion-based modeling, state estimation and control approach is introduced as a better alternative to the traditional methods which are currently utilized for gravity recovery missions. The proposed modeling and control approach was verified against and compared to the tangent bundle to Special Euclidean Group 3 through MATLAB simulations. The dual quaternion-based approach shows superior performance over traditional linearized and uncoupled methodologies, in both modeling accuracy of spacecraft translational position, and the ability to control the pose of a test mass relative to its host spacecraft. Utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a …

Stability Analysis In The Twist-Bend Nematic Liquid Crystal Model, Zhenqiang Li

Mathematics & Statistics Theses & Dissertations

The recently discovered twist-bend nematic liquid crystal (LC) phase is characterized by a nanoscale helical modulation of the nematic director n, forming a conical helix along the z-axis at an oblique angle θ. While many models assume a constant cone angle and equal elastic constants K11 = K22 = K33, this dissertation removes both assumptions by considering a fully anisotropic elastic energy with K11 ≠ K22 ≠ K33, and allowing θ to vary spatially. We analyze the stability of this system under frustrated and free boundary conditions using variational methods. …

Predicting Battery Efficiency: A Theoretical Approach, Haiti Schafers

SACAD: Scholarly Activities

The Kansas ElectroRally Races continuously demand faster electric vehicles (EV). When designing a vehicle one of the most important components is the battery. This study was designed to find the following; What is the optimal throttle percentage to run a 36V 20Ah (768Wh) LiFePO4 Rechargeable Battery Pack[1].

The optimal throttle percentage was found with methods detailed in a different section. Based on the performance of the older cars this study choose to focus on 50% and 70%, while obtaining other relevant data to further that inference.

Stability Criteria For The Generalized El Borhamy-Rashad-Sobhy Equation, Mohamed El-Borhamy Assoc.Prof, Essam Eddin Rashad Prof., Fathi Mousa Dr., Mai Hamouda

Journal of Engineering Research

This article is concerned with the study of stability criteria for one of the generalization form of El Borhamy-Rashad Sobhy equation, which is a linear second-order ordinary differential equation with periodically time varying coefficients. Many engineering applications can be represented by this generalization, for instance, including the modeling of RLC circuit with time varying inductance, resistance and capacitance, and the vibration of a stretched string, whose mass per unit length is periodic, under a periodic motion. An approximate solution is derived by using the Wenhl-Kramers-Brillonin (WKB) approach. A method of constructing Liapunov function is employed to derive extra conditions for …

Greatest Common Divisors And Lucas’S Theorem, John Ferdinands, Timothy Ferdinands

University Faculty Publications and Creative Works

Weconsider a sequence of greatest common divisors of the coefficients of a binomial expansion and use a classical result due to Lucas to show that the greatest common divisor is always 1. Our result generalizes a problem found in the Problem Section of Mathematics Magazine.

The "Distributed Ghost" With Independence - A Study On Computational Ability Of Skewed Asynchronous Cellular Automata, Shrey Salvi, Shlok Shelat, Sumit Adak, Souvik Roy

Northeast Journal of Complex Systems (NEJCS)

This paper explores the computational ability of ``distributed ghost" cellular automata (CA) \cite{10.1162/artl_e_00450} after introducing independence in the updating scheme. Traditionally, the CA system dictates all cells to update together following the concept of the global clock. To introduce independence in the system, CA researchers have introduced the notion of fully asynchronous updating scheme with atomicity property where, again, the CA system dictates two neighbouring cells not to update together. In this study, we explore the skewed asynchronous system after breaking the atomicity property. Specifically, we study the computational ability of the proposed skewed asynchronous system in the context of …

Analysis Of Systematic Trade-Offs Between Military And Healthcare Expenditure Alongside Gdp Growth Of Select Asian And Western Exporting Economies In The 21st Century, Rahul Balamurugan, Carlos Gershenson, Preethi Nanjundan, Hiroki Sayama

Northeast Journal of Complex Systems (NEJCS)

This study explores the complexity in the trade-offs between military expenditure, healthcare expenditure, and GDP growth across select Asian nations and major weapon-exporting countries, examining how nations allocate finite resources between national security and human well-being over the past two decades. Using a systems science approach, the research integrates Granger causality testing to analyze temporal and directional relationships among GDP growth, military expenditure, and healthcare expenditure, uncovering their dynamic interdependencies. The methodology includes trend and slope analysis, Granger causality testing, outlier detection, and clustering to identify heterogeneity in resource allocation strategies. Developed, weapon-exporting nations exhibit complementary trends, with strong causality …

(Si14-13) Study Of Micropolar Ferrofluid In Non-Linear Stretching Sheet With Magnetic Field Effects, Harshad Patel, Rakesh Darji, Akhil Mittal, Monika Khanna

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with mixed convection two-dimensional flow of micropolar ferrofluid when magnetic field presence in the system. The effects of different types of physical parameter like thermal radiation, thermophoresis and Brownian motion are considered in non-linear stretching sheet. The governing system of PDE is convert in dimensionless system of ODE using dimensionless variable 𝜂𝜂. The suitable HAM is applied for solving the governing problems and obtained the results of linear velocity, micro rotational velocity, temperature, and concentration. Behaviors of different physical parameters effects are discussed through a graph. The Numerical values of skin friction, rate of heat transfer …

(Si14-03) Time Proportional Non-Instantaneous Deterioration Decisions For Vendor Managed Inventory System, Hetal Patel, Hardik Soni, Ajay Gor

Applications and Applied Mathematics: An International Journal (AAM)

This article formulates a model for optimizing inventory replenishment decisions for the products that experience non-instantaneous deterioration by allowing partial backlogging. Two-level supply chain (SC) is considered in vendor-managed inventory (VMI) model which contains ‘single-retailer and single-supplier’ for studying the performance. The model considers two constant demand rates which differ from others when deterioration in the product commences. In addition, the general function of time is considered for deterioration rate. Theoretical results are derived to compute the replenishment cycle length. Lastly, the benefit of VMI policy is illustrated through numerical examples. Further, explanation of some features of the VMI model …

(Si14-15) Heat Source/Sink And Chemical Reaction Effects On Micropolar Mhd Nano Fluid Flow In Stretching/Shrinking Sheet, Tejal Nagar, Harshad Patel, Akhil Mittal, Vikas Kori

Applications and Applied Mathematics: An International Journal (AAM)

This paper deals with the effects of a non-uniform heat source/sink and chemical reaction on micropolar nanofluid flow in a stretching and shrinking sheet. The flow is considered as a laminar mixed convective two-dimensional steady flow. In this flow, water is considered as a base fluid, whereas iron oxide is considered to be a conventional fluid. The governing non-linear system of PDEs are transformed into a system of ODEs using the similarity transformation, and HAM is employed for obtaining solutions. For more understanding of the effects of various physical conditions, approximate results are obtained, and expressed graphically. From the results, …

(Si14-11) Analysing Co-Current Imbibition Phenomenon In Heterogeneous Reservoir Using Multistep Hybrid Differential Transform Finite Difference Method, Aruna Sharma, Amit Parikh

Applications and Applied Mathematics: An International Journal (AAM)

The primary focus of this study is to analyse the co-current imbibition phenomenon in an inclined heterogeneous reservoir. This phenomenon occurs during the secondary oil recovery process. Capillary force is responsible for the displacement of a non-wetting phase by a wetting phase, and this phenomenon is called spontaneous imbibition. Imbibition is of two types and can be differentiated based on the direction in which the wetting phase (water) and non-wetting phase (oil) move. If the two phases flow in the same direction, it is called co-current imbibition, and if they flow in the opposite direction, it is called counter-current imbibition. …

Smoothed Particle Hydrodynamics For Free-Surface Flows And Time Series Forecasting Approach For Computational Fluid Dynamics, Huali Ye

Doctoral Dissertations

With the increase in computing power, numerical simulation has become an essential approach to solving problems in engineering and science. Numerical simulations provide a platform for theoretical validation and facilitate novel discovery. Even though extensive mesh-based numerical methods are utilized, significant limitations exist, particularly in Computational Fluid Dynamics (CFD). Because of the grid distortion, issues related to large deformations, moving interfaces, and free surfaces may lead to considerable computational errors, constraining their efficacy in numerous applications. As a mesh-free method, Smoothed Particle Hydrodynamics (SPH) was introduced in 1977 and has been widely applied in many fields such as astrophysics and …

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, …

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 …

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 …

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 …

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 …

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 …