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 …

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 …

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 …

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 …