Applied Mathematics Commons^™

Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan

Electrical and Computer Engineering ETDs

Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …

Operations On Submodules With The Multiplicative And Quotient Properties, Jiekai Pang

Mathematics & Statistics ETDs

Inspired by the works of Petro, Epstein, Vassilev, and Morre, this thesis aims to study the generalized definitions of the semiprime operation, weakly prime operation, and standard closure operation on rings, that is, the multiplicative operation, weakly multiplicative operation, and standardly multiplicative operation on submodules. Then, we will use Matlis duality to induce the dual notions of these definitions on submodules of Matlis-dualizable Artinian modules. In order to understand the dual notion of the standardly multiplicative operation, that is, the standardly quotient operation, we will classify the operations on the injective hull of residue field of the ring K[[x,y]]/(xy) which …

Investigating The Efficacy Of Prompt Engineering Techniques For Research Survey Paper Generation Using Large Language Models, Innocent Obed Awidi

Theses and Dissertations

The recent advancements in large language models (LLMs), such as ChatGPT, offer promising potential for automating academic writing tasks. This study investigates the efficacy of prompt engineering techniques in guiding LLMs to generate high-quality research survey papers, specifically exploring their application in the fields of artificial intelligence (AI) in drug development and large language model customization for classification. Using a mixed-methods approach, this research assessed the impact of prompt engineering on the coherence, relevance, and overall quality of generated content through quantitative and qualitative analyses. Techniques including prompt refinement, contextual prompting, and iterative prompting were systematically applied to enhance the …

Mathematics In Amusement Parks, Kacey Laumann

Honors Projects

This project focuses specifically on the Walt Disney World Park, Magic Kingdom. I started by collecting data through the MyDisneyExperience app. By recording the data, I was then able to create polynomial functions to the fifth the degree. Each attraction received a function which allowed me to predict the wait times for that attraction. Then, by graphing the functions and analyzing the graph using calculus the “best time” and “worst time” to go to the attraction were found. After the analysis the information is used to build a unique schedule for a guest. Then the guest receives this schedule after …

(R2100) Optimality Conditions Of A Topsis Optimization Model And Its Application On Interval-Valued Data, Sudipta Roy, Sandip Chatterjee

Applications and Applied Mathematics: An International Journal (AAM)

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is widely used in the field of multi-criteria decision analysis. Despite its popularity and widespread application, little attention has been given to the mathematical foundation that underlies the TOPSIS algorithm. The existing literature on this subject is far from comprehensive, leaving many aspects of the algorithm unexplored. This paper aims to address this gap in the literature by delving into the optimization problem associated with TOPSIS. Unlike traditional interval analysis theory, which only covers a limited scope, our approach extends to a broader range of scenarios and offers …

(R2111) Effect Of Stenotic-Aneurysmal Arterial Regime On Unsteady Magnetohydrodynamic Non-Newtonian Blood Flow With Heat Radiation, Babatunde A. Joseph, Dada M. Sunday, Bello A.J. Funsho, Akeem B. Disu, Alamu-Awoniran F., Danas James Y.

Applications and Applied Mathematics: An International Journal (AAM)

The study aims to investigate the effect of magneto-hydrodynamic on a non-Newtonian unsteady blood flow with internal heat energy in the presence of blood ironic properties characterized by stenosis. The formulated mathematical equations resulted in differential forms and were solved analytically by Differential Transform Method. The obtained solutions were displayed by graphs showing different flow physiognomies like blood velocity, temperature profile, Nusselt number, wall shear stress and stream function.

The results indicated that velocity profile increases as magnetic field, Darcy number and aneurysmal artery rise, while it decreases as heat radiation, Reynold number, and Casson parameter speedup. The temperature profile …

A New Reduced Basis Method For Parabolic Equations Based On Single-Eigenvalue Acceleration, Qijia Zhai, Qingguo Hong, Xiaoping Xie

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts the backward Euler scheme and conforming simplicial finite elements for the temporal and spatial discretizations, respectively. Under the assumption that the time step size is sufficiently small, and time steps are not very large, we show that the singular value distribution of the high-fidelity solution matrix U is close to that of a rank one matrix. We select the eigenfunction associated to the principal eigenvalue of the …

(R2101) Analysis Of Map/Ph/1 Queueing Inventory System With Two Commodity, Working Vacation, (S, S) Replenishment Policy, Essential And Optional Repair, G. Ayyappan, N. Arulmozhi

Applications and Applied Mathematics: An International Journal (AAM)

We examine a queueing inventory model with single server which can offer two types of inventory items: main item (commodity I) and complementary item (commodity II). We assume both commodities have a finite capacity Si, i = 1, 2. Customers reach the system by following the Markovian arrival process (MAP). The service times are considered to be phase-type (PH) distribution. We have considered no customer in the system, even inventory level is positive; the server will start the working vacation, and any customer that arrives during working vacation, the server provides slow service. If an item is not available, the …

(R2108) Global Asymptotic Stability Analysis Of Discrete Time Population Model With Allee Effect Through Lyapunov Function, Govind Jha, Neeraj Kumar, Sarita Jha

Applications and Applied Mathematics: An International Journal (AAM)

This study explores the idea of stability analysis by using Lyapunov functions in discrete time population models; this work focuses on the nth generation. Further, this investigation aims to extend global stability concepts to discrete-time models and considers the influence of the Allee effect on population dynamics. Mathematical formulations and specific modelling approaches are utilized to investigate the behavior of the population system. The results reveal a larger range of stability in comparison to previous findings, emphasizing the effectiveness of the Lyapunov function approach. Specifically highlighted here are the extension of global stability concepts to the nth generation providing insights …

(R2099) Boundedness And Square Integrability In Neutral Differential Equations With Delay And Exponential Stability In Nonlinear Differential Equations Of Third-Order, Fatima Abdellaoui, Mebrouk Rahmane

Applications and Applied Mathematics: An International Journal (AAM)

The Lyapunov second method is an eigenvalue-based technique which consist of finding a Lyapunov function candidate for studying the stability of dynamical systems which is hard to deal with especially in most of nonlinear cases. Studying the stability and some of other qualitative behaviors based on the Lyapunov second method is research topic of actuality because of the wide range of applications of the differential equations. Many authors in the literature have used the second method of Lyapunov in the study of some qualitative behaviors from which the stability, the boundedness and the square integrability of solutions for various kinds …

(R2090) Analysis Of Heat And Mass Transfer In Mhd Boundary Layer Flow Of Chemically Reacting Fluid, Dharati Sheth, Manisha Patel, Dilip Joshi

Applications and Applied Mathematics: An International Journal (AAM)

Analysis of the effects of heat and mass transfer on the chemically responding boundary layer flow of a Casson fluid across a porous stretched sheet in the existence of a crosswise magnetic field is the aim of the existing work. The partial differential equations that control the current flow problems can be converted into similarity equations by applying the right similarity technique. Our goal is to use the DTM-Pade approximation to analytically solve the derived similarity equations. The transformed similarity equations are a group of nonlinear ordinary differential equations for the present flow problem. The analytical approach of the differential …

Bounding The Convex Hull Relaxation Of The Unit Commitment Problem With The Shapley-Folkman Theorem, Lauren Henderson

All Theses

The Unit Commitment (UC) problem finds an optimal schedule for a set of generators by minimizing the total operation cost subject to demand and operational constraints. The UC problem is often modeled with a mixed-integer linear program (MILP). We employ the Shapley-Folkman Theorem to provide a bound on the size of fractional solutions of its convex hull relaxation. This result is used to obtain a bound on the optimality gap between the MILP and the convex hull relaxation, which is further tightened using several problem-specific properties of UC. We conduct extensive numerical experiments to study the tightness of this threshold, …

Locally Varying Geostatistical Machine Learning For Spatial Prediction, Francky Fouedjio, Emet Arya

Research outputs 2022 to 2026

Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction. Nonetheless, under these methods, the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area. This assumption, known as spatial stationarity, is very questionable in real-world situations due to the influence of contextual factors. Therefore, allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable. However, existing machine learning techniques accounting for the spatially varying relationship between the dependent variable …

(R2104) On The Qualitative Results Of Riemann-Liouville Fractional Order Nonlinear Neutral Singular Systems With Mixed Delays, Abdullah Yiğit, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, we discuss new conditions for asymptotic stability of nonlinear Riemann- Liouville fractional mixed-delay neutral singular systems. By constructing a set of improved Lyapunov-Krasovski˘ı functionals (LKFs), we establish some new delay-dependent conditions in terms of matrix inequality, which guarantees that the systems are asymptotically stable. In the particular case, we give four numerical examples with their solutions and graphs via MATLAB software demonstrating the practical applicability of these proven conditions. With this study, some conditions existing in the literature are developed and generalized.

(R2113) A Numerical Method For Solving Linear First-Order Volterra Integro-Differential Equations With Integral Boundary Condition, Zelal Temel, Musa Cakir

Applications and Applied Mathematics: An International Journal (AAM)

We investigate an efficient numerical method for the linear first-order Volterra integro-differential equations with integral boundary condition. To solve this problem, boundaries are determined for its derivative and the solution. The numerical solutions of the problem are modeled over a uniform mesh using the composite right-side rectangle concept for the integral component and the implicit difference rules for the differential component. Next, the stability and convergence of the numerical approach are discussed. The numerical experiments are presented confirming the accuracy of the proposed scheme.

(R2098) Dynamic Analysis Of Stochastic Leslie-Gower Biological Predator-Prey Model With Prey Cannibalism, Sada Nand Prasad, Itendra Kumar Universiry Of Delhi, India, Pawan Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the dynamical analysis of a stochastic Leslie–Gower biological predator– prey model. Earlier, the Leslie–Gower model was studied in the context of biological systems, including cases involving cannibalism. In our model, we investigate the dynamic properties of a stochastic Leslie–Gower predator–prey ecological system using the stability of invariant measures on invariant sets, where the invariant measures are shown to be ergodic. We also conduct a threshold analysis to study the stochastic persistence and extinction of species. Stochastic bifurcation is also examined. The theoretical results are supported by numerical simulations and examples. Intra-species competition is considered and …

(R2102) Chaos Measure In A Discrete Sir Epidemic Model With Constant Recovery, Sonia Aneja, Itendra Kumar, Sada Nand Prasad

Applications and Applied Mathematics: An International Journal (AAM)

A discrete SIR epidemic model with constant recovery and bilinear incidence rate is investigated for emergence of regular and chaotic behaviour in the context of non linear dynamics and different viable settings. The Euler’s discretization method is employed to transform the continuous epidemic model into discrete model which has been used as the study model. Attention is paid to various bifurcation plots obtained by varying certain system parameters while keeping other parameters constant. Bifurcations indicate regular evolution followed by chaos. Regular and chaotic attractors have been drawn in the process. As part of chaos measure, numerical studies are extended to …

(R2097) Impact Of Inclined Magnetic Field On Two Immiscible Viscous Fluids Flow In A Porous Channel With Variable Permeability: A Finite Difference Technique, Angad Prasad, P. K. Singh

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the flow of two immiscible, viscous, incompressible, and electrically conducting fluids in a horizontal channel containing a porous material under an inclined magnetic field. The flow is propelled by a consistent pressure gradient. These two fluids have different viscosities in two separate layers of equal width. The fluid in the upper layer has a lower viscosity compared to the fluid in the lower layer. The Permeability of a porous medium is variable with the transverse direction. The Brinkman equation is employed to describe fluid flow within a porous medium. Numerical solutions for velocity and volumetric …

Enhancing Mathematical Models For Covid-19 Pandemic Response: A Philippine Study, Timothy Robin Teng, Elvira De Lara-Tuprio, Ma. Regina Justina Estuar, Christian Pulmano, Lu Christian S. Ong, Zachary Pangan, Lenard Paulo V. Tamayo, Jasper John V. Segismundo, Mark Anthony C. Tolentino, Alyssa Nicole N. Ty

Mathematics Faculty Publications

Mathematical models supported by a robust automated data pipeline proved to be useful tools for a data-driven and science-based response and policy-making during the COVID-19 pandemic in the Philippines. In the first year of the pandemic, FASSSTER (Feasibility Analysis on Syndromic Surveillance using Spatio-Temporal Epidemiological modeleR) used a compartmental model to generate scenario-based projections of COVID-19 cases. The emergence of the Delta variant, however, and the administration of vaccines over the second half of 2021 caused significant changes in the Philippine pandemic landscape. This necessitated making adjustments to the model to better capture the local disease transmission dynamics and address …

Bayesian Lasso Regularized Quantile Regression And Its Applications, Priscilla Kissi-Appiah

Theses and Dissertations

Since the pioneering work of (Koenker and Bassett Jr 1978), quantile regression has been a popular regression technique that helps researchers investigate a whole distribution of the response variable. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the response variable and can provide a more comprehensive picture of modeling via exploring the conditional quantiles of the response variable. In this research, we study the lasso regularized quantile regression from a Bayesian perspective. We develop an efficient sampling algorithm to generate posterior samplings for making posterior inference by using a location-scale …