Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains,
2022
University of Nevada, Las Vegas
Positive Solutions To Semilinear Elliptic Equations With Logistic-Type Nonlinearities And Harvesting In Exterior Domains, Eric Jameson
UNLV Theses, Dissertations, Professional Papers, and Capstones
Existing results provide the existence of positive solutions to a class of semilinear elliptic PDEs with logistic-type nonlinearities and harvesting terms both in RN and in bounded domains U ⊂ RN with N ≥ 3, when the carrying capacity of the environment is not constant. We consider these same equations in the exterior domain Ω, defined as the complement of the closed unit ball in RN , N ≥ 3, now with a Dirichlet boundary condition. We first show that the existing techniques forsolving these equations in the whole space RN can be applied to the exterior domain with some …
A Survey Of The Br´Ezis-Nirenberg Problem And Related Theorems,
2022
University of Nevada, Las Vegas
A Survey Of The Br´Ezis-Nirenberg Problem And Related Theorems, Edward Huynh
UNLV Theses, Dissertations, Professional Papers, and Capstones
Nonlinear elliptic partial differential equations on bounded domains arise in several different areas of mathematics that include geometry, mathematical physics, and the calculus of variations. The Br ́ezis-Nirenberg problem is concerned with a boundary-value problem that is intimately connected to the existence of positive solutions of the Yamabe problem, of non-minimal solutions to Yang-Mills functionals, and of extremal functions to several important inequalities. Results on existence and uniqueness have been obtained in cases when the exponent is sub-critical, but such results have not been obtained when the exponent is critical due to a lack of compactness. The earliest results obtained …
Some Graph Laplacians And Variational Methods Applied To Partial Differential Equations On Graphs,
2022
University of Nevada, Las Vegas
Some Graph Laplacians And Variational Methods Applied To Partial Differential Equations On Graphs, Daniel Anthony Corral
UNLV Theses, Dissertations, Professional Papers, and Capstones
In this dissertation we will be examining partial differential equations on graphs. We start by presenting some basic graph theory topics and graph Laplacians with some minor original results. We move on to computing original Jost graph Laplacians of friendly labelings of various finite graphs. We then continue on to a host of original variational problems on a finite graph. The first variational problem is an original basic minimization problem. Next, we use the Lagrange multiplier approach to the Kazdan-Warner equation on a finite graph, our original results generalize those of Dr. Grigor’yan, Dr. Yang, and Dr. Lin. Then we …
Mathematical And Statistical Modeling With Deep Neural Networks,
2022
The University of Texas Rio Grande Valley
Mathematical And Statistical Modeling With Deep Neural Networks, Albert Romero
Theses and Dissertations
General adversarial networks (GANs) are a form of machine learning that includes two neural networks competing in a zero-sum game. One network produces artificial, while the other tries to distinguish artificial data from real. The Wasserstein general adversarial network with gradient penalty (WGAN-GP) variant of this technique is used to produce solutions for ordinary and partial differential equations.
Managing Risk For Power System Operations And Planning: Applications Of Conditional Value-At-Risk And Uncertainty Quantification To Optimal Power Flow And Distributed Energy Resources Investment,
2022
Clemson University
Managing Risk For Power System Operations And Planning: Applications Of Conditional Value-At-Risk And Uncertainty Quantification To Optimal Power Flow And Distributed Energy Resources Investment, Thanh To
All Dissertations
Renewable energy sources are indispensable components of sustainable electrical systems that reduce human dependence on fossil fuels. However, due to their intermittent nature, there are issues that need to be addressed to ensure the security and resiliency of these power systems. This dissertation formulates several practical problems, from an optimization perspective, stemming from the increasing penetration of intermittent renewable energy to power systems. A number of Optimal Power Flow (OPF) formulations are investigated and new formulations are proposed to control both operations and planning risks by utilizing the Conditional Value–at–Risk (CVaR) measure. Our formulations provide system operators and investors analysis …
Advancements In Gaussian Process Learning For Uncertainty Quantification,
2022
Clemson University
Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson
All Dissertations
Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …
A Central Compact Hybrid-Variable Method With Spectral-Like Resolution,
2022
The University of Texas at El Paso
A Central Compact Hybrid-Variable Method With Spectral-Like Resolution, Md Mahmudul Hasan
Open Access Theses & Dissertations
Numerical methods for hyperbolic conservation laws have been a driving force for theresearch in scientific computing and simulation science in the past decades, as many physical, biological, and engineering systems are governed by these equations, such as fluid mechanics, tumor growth, and virtual wind tunnel simulations. Despite the existence of many schemes in the literature, people have never stopped searching for more accurate and efficient methods for these problems. Indeed, the increasing complexity of systems in emerging applications demands better resolution of sub-grid scale phenomenon whereas classical methods usually fail to deliver high-fidelity simulation results of such systems within realistic …
Electromagnetic Modeling Of A Wind Tunnel Magnetic Suspension And Balance System,
2022
Old Dominion University
Electromagnetic Modeling Of A Wind Tunnel Magnetic Suspension And Balance System, Desiree Driver
Mechanical & Aerospace Engineering Theses & Dissertations
Wind tunnels are used to study forces and moments acting on an aerodynamic body. While most results involve some interference from the mechanical supports used to hold the model, a Magnetic Suspension and Balance System (MSBS) is void of these interferences and presents an ideal test scenario. To further investigate the feasibility of dynamic stability testing at supersonic speeds using a MSBS, a preliminary design idea is currently being developed using an existing MSBS in a subsonic wind tunnel. This review focuses on the development of a mathematical model to more accurately portray the capabilities of the 6 inch Massachusetts …
A Conservative Numerical Scheme For The Multilayer Shallow Water Equations,
2022
Clemson University
A Conservative Numerical Scheme For The Multilayer Shallow Water Equations, Evan Butterworth
All Theses
An energy-conserving numerical scheme is developed for the multilayer shallow water equations (SWE’s). The scheme is derived through the Hamiltonian formulation of the inviscid shallow water flows related to the vorticity-divergence variables. Through the employment of the skew-symmetric Poisson bracket, the continuous system for the multilayer SWE’s is shown to preserve an infinite number of quantities, most notably the energy and enstrophy. An energy-preserving numerical scheme is then developed through the careful discretization of the Hamiltonian and the Poisson bracket, ensuring the skew-symmetry of the latter. This serves as the groundwork for developing additional schemes that preserve other conservation properties …
Analyzing Suicidal Text Using Natural Language Processing,
2022
Utah State University
Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …
A Novel Data Lineage Model For Critical Infrastructure And A Solution To A Special Case Of The Temporal Graph Reachability Problem,
2022
University of Arkansas, Fayetteville
A Novel Data Lineage Model For Critical Infrastructure And A Solution To A Special Case Of The Temporal Graph Reachability Problem, Ian Moncur
Graduate Theses and Dissertations
Rapid and accurate damage assessment is crucial to minimize downtime in critical infrastructure. Dependency on modern technology requires fast and consistent techniques to prevent damage from spreading while also minimizing the impact of damage on system users. One technique to assist in assessment is data lineage, which involves tracing a history of dependencies for data items. The goal of this thesis is to present one novel model and an algorithm that uses data lineage with the goal of being fast and accurate. In function this model operates as a directed graph, with the vertices being data items and edges representing …
Relaxation Of Variational Principles For Z-Problems In Effective Media Theory,
2022
Florida Institute of Technology
Relaxation Of Variational Principles For Z-Problems In Effective Media Theory, Kenneth Beard
Theses and Dissertations
In this thesis, we consider a class of Z-problems and their associated effective operators on Hilbert spaces which arise in effective media theory, especially within the theory of composites. We provide a unified approach to obtaining solutions of the Z-problem, formulas for the effective operator in terms of generalized Schur complements, and their associated variational principles (e.g., the Dirichlet minimization principle), while allowing for relaxation of the standard hypotheses on positivity and invertibility for the classes of operators usually considered in such problems. The Hilbert space framework developed here is inspired by the methods of orthogonal projections and Hodge decompositions. …
The Biggest Loser: How Tanking In Professional Sports Impacts Fan Perception,
2022
Bryant University
The Biggest Loser: How Tanking In Professional Sports Impacts Fan Perception, Julia Ayres
Honors Projects in Mathematics
Professional sports teams are adored nationwide for their talents and the pride they bring to their city for their efforts. However, not all teams take this responsibility seriously and will lose on purpose, or tank, to gain a higher draft pick in the future. Although the long-term goals of tanking are to help the organization, many people take issue with athletes not putting in their best efforts in every game. Teams in both the NBA and NFL are guilty of tanking to gain better draft picks but not all have found success in this process. This leads to important questions …
Tracking Academic Success And Its Relationship With Student Success Center Usage And Demographics,
2022
University of Alabama in Huntsville
Tracking Academic Success And Its Relationship With Student Success Center Usage And Demographics, Samuel D. Johnson
Honors Capstone Projects and Theses
No abstract provided.
Random Variable Shape Parameter Strategy To Minimize Error In Oscillatory Radial Basis Function Approximation Method For Solving Partial Differential Equations.,
2022
Ohio Northern University
Random Variable Shape Parameter Strategy To Minimize Error In Oscillatory Radial Basis Function Approximation Method For Solving Partial Differential Equations., Quinnlan Paul Aiken
ONU Student Research Colloquium
Approximation of the functions which are the solutions of complex or difficult problems is a worthwhile endeavor. This has resulted in many ways to effectively approximate the solution of the partial differential equations. One such way to approximate the solution of the partial differential equation is Oscillatory radial basis function method. This method can approximate the solution of the partial differential equation well however relies heavily on a “shape parameter” to achieve acceptable error. Choosing this parameter was traditionally done through a trial-and-error method. Selecting shape parameters in a more analytical way has been desired. One such method is the …
Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County,
2022
Duquesne University
Impact Of Treatment Length On Individuals With Substance Use Disorders In Allegheny County, Cassie Dibenedetti, Kate Rosello
Undergraduate Research and Scholarship Symposium
Auberle social services is opening the Family Healing Center (FHC), a level 3.5 treatment program in Pittsburgh, PA that provides housing and 24-hour support for families struggling with opioid addiction. We partnered with Auberle to study characteristics of individuals receiving level 3.5 treatment and to determine whether longer treatment lengths correlate with fewer adverse outcomes. We obtained data from the Allegheny County Department of Human Services on 2,016 individuals admitted to level 3.5 treatment in 2019. The data included birth year, race, gender, admittance date, discharge date, and Children Youth and Family (CYF) incidents before and after treatment. We categorized …
Stability Analysis Of Delay-Driven Coupled Cantilevers Using The Lambert W-Function,
2022
University of South Florida
Stability Analysis Of Delay-Driven Coupled Cantilevers Using The Lambert W-Function, Daniel Siebel-Cortopassi
USF Tampa Graduate Theses and Dissertations
A coupled delay-feedback system of two cantilevers can yield greater sensitivity than that of asingle cantilever system, with potential applications in atomic force microscopy. The Lambert W-function analysis concept for delay differential equations is used to more accurately model the behavior of specific configurations of these cantilever systems. We also use this analysis concept to find parameters which yield stability for greater parameter ranges, of the delay differential equations. The Q factor, or quality factor, is the ratio of energy stored in the system, to the energy lost per fixed oscillation/movement cycle. Having stability of the cantilevers corresponds to the …
A Functional Optimization Approach To Stochastic Process Sampling,
2022
University of South Florida
A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman
USF Tampa Graduate Theses and Dissertations
The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and …
Internet Affects All Areas Of The World: A Quantitative Report On Canadians Internet Usage,
2022
Kennesaw State University
Internet Affects All Areas Of The World: A Quantitative Report On Canadians Internet Usage, Kristina Sims
Symposium of Student Scholars
The Internet has had a significant influence on modern life with Pew research reporting that 99% of American adults between the ages of 18-29 used the internet in 2021 with reported reduced internet use for older Americans. Both positive and negative consequences can be attributed to its widespread use. In attending Kennesaw State University internet use is almost mandatory to successfully complete coursework. Witnessing how active internet use is in collegiate age populations in the US is has sparked some curiosity of use in Canadian residents. The survey on "Canadian Internet Use", in the year 2018 was designed to measure …
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation,
2022
Augustana College
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, Tran April
Rose-Hulman Undergraduate Mathematics Journal
While the well-researched Finite Difference Method (FDM) discretizes every independent variable into algebraic equations, Method of Lines discretizes all but one dimension, leaving an Ordinary Differential Equation (ODE) in the remaining dimension. That way, ODE's numerical methods can be applied to solve Partial Differential Equations (PDEs). In this project, Linear Multistep Methods and Method of Lines are used to numerically solve the heat equation. Specifically, the explicit Adams-Bashforth method and the implicit Backward Differentiation Formulas are implemented as Alternative Finite Difference Schemes. We also examine the consistency of these schemes.
