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Full-Text Articles in Physical Sciences and Mathematics

Assessment Of Local Ecological Knowledge, Oyster Predation, And Habitat Function To Improve Management Of Nearshore Habitats, Cynthia Evelyn Marie Lupton May 2026

Assessment Of Local Ecological Knowledge, Oyster Predation, And Habitat Function To Improve Management Of Nearshore Habitats, Cynthia Evelyn Marie Lupton

Theses and Dissertations

Coastal ecosystems along the northern Gulf of Mexico are ecologically and economically vital yet increasingly threatened by environmental change, habitat degradation, and knowledge gaps that complicate restoration and management efforts. This dissertation integrates social and ecological approaches to improve understanding of predator dynamics, stakeholder perceptions, and habitat function related to nearshore habitats. Thereby, providing information that can inform adaptive management and restoration in the region through addressing three overarching objectives: 1) evaluate stakeholder perceptions of oyster (Crassostrea virginica) predation and management practices; 2) quantify environmental and habitat factors influencing oyster drill (Stramonita haemastoma complex) abundance; and, 3) assess the influence …


Unbounded Derivations On Algebras Associated With Monothetic Groups: An Expository Thesis, Britton Phillips May 2026

Unbounded Derivations On Algebras Associated With Monothetic Groups: An Expository Thesis, Britton Phillips

Theses and Dissertations

This thesis is an expository exploration of the paper Unbounded Derivations in Algebras Associated with Monothetic Groups. Monothetic groups will be utilized to create a minimal system that gives rise to two C*-algebras, and once we have these algebras, unbounded derivations will be able to be defined on them. These derivations are able to be classified and decomposed into ”special” derivations, and these decompositions help simplify the comparisons between derivations on different algebras. In particular, we emphasize the classification, covariance properties, innerness and approximate innerness, and the lifting behavior of these derivations.


From Natural Language To Cryptographic Protocol Specifications: Evaluating Llms For Cpsa Generation, Martin Duclos May 2026

From Natural Language To Cryptographic Protocol Specifications: Evaluating Llms For Cpsa Generation, Martin Duclos

Theses and Dissertations

Formal verification can prove the security properties of cryptographic protocols, but translating natural language specifications into formal models requires specialized expertise, limiting the broader adoption of formal verification methods. This dissertation investigates whether large language models (LLMs) can lower this barrier by automatically generating Cryptographic Protocol Shapes Analyzer (CPSA) models from natural language protocol specifications. We evaluate three complementary strategies for improving LLM-based CPSA code generation through systematic experimentation across 104 protocols and 15 language models. First, we analyze prompt engineering and find that moderate structured guidance yields the most accurate outputs, while excessive prompt complexity degrades performance. Second, we …


Evaluation And Mitigation Of Bias And Toxicity In Open-Source Large Language Models Using Crows-Pairs And Bold, Sai Harika Gade May 2026

Evaluation And Mitigation Of Bias And Toxicity In Open-Source Large Language Models Using Crows-Pairs And Bold, Sai Harika Gade

Theses and Dissertations

This thesis evaluates bias and harmful language generation in five open-source language models and tests practical mitigation methods that do not require retraining. Two masked models are assessed with a sentence-pair benchmark for stereotype preference, and three generative models are assessed with a prompt-based benchmark for harmful continuations across demographic domains. The study uses a unified experimental workflow to compare model behavior, summarize differences across bias categories, and measure changes after intervention. Results show that the masked models favor stereotypical content above a random baseline, while the generative models usually produce low average toxicity but still show uneven risk across …


Integrating Augmented Reality Visualizations Into Data Science Notebooks Using Microsoft Hololens 2, Derek Willis May 2026

Integrating Augmented Reality Visualizations Into Data Science Notebooks Using Microsoft Hololens 2, Derek Willis

Theses and Dissertations

Data-science notebooks support iterative analysis but are limited to two-dimensional (2D) displays. This work presents an approach to extend such environments with rapid augmented reality (AR) visualization while preserving conventional 2D workflows. An opensource R package was developed to convert notebook objects into three-dimensional (3D) models, export them in the Graphics Language Transmission Format (glTF), and transfer directly to a Microsoft HoloLens 2 via a USB connection for viewing in the native 3D Viewer application. The proposed workflow eliminates manual conversion and transfer steps required by earlier methods. A user study employing a post-session questionnaire indicated that participants found the …


Establishing A Comprehensive Framework For Sfrt Lattice Treatments: Optimization, Planning, And Clinical Evaluation, Gregory M. Gill May 2026

Establishing A Comprehensive Framework For Sfrt Lattice Treatments: Optimization, Planning, And Clinical Evaluation, Gregory M. Gill

UNLV Theses, Dissertations, Professional Papers, and Capstones

Spatially fractionated radiation therapy (SFRT) using lattice radiotherapy (LRT) has emerged as a promising treatment technique for bulky, nonresectable tumors by delivering spatially heterogeneous dose distributions consisting of high-dose vertices embedded within lower-dose regions. Although early clinical experiences have demonstrated potential therapeutic benefit, widespread clinical implementation of LRT remains limited due to the absence of standardized treatment planning workflows, consistent optimization strategies, and clearly defined evaluation metrics for heterogeneous dose distributions. The objective of this study is to develop and evaluate a structured framework to support efficient, reproducible, and safe clinical implementation of LRT.

To address these challenges, a comprehensive …


A Modified Maximum Likelihood Estimation Algorithm For Modeling Threshold Exceedances With The Generalized Pareto Distribution, Jeffrey Harkness May 2026

A Modified Maximum Likelihood Estimation Algorithm For Modeling Threshold Exceedances With The Generalized Pareto Distribution, Jeffrey Harkness

UNLV Theses, Dissertations, Professional Papers, and Capstones

A modified maximum likelihood estimation (MLE) algorithm is proposed for modeling threshold exceedances with the generalized Pareto distribution (GPD). The algorithm addresses multiple issues with an approach originally published in the Journal Computational Statistics and Data Analysis (Castillo and Serra, 2015). The modified algorithm is intended to be comparatively simple to understand and implement, accurate in the handling of boundary conditions, relatively fast and reliable for most data sets, and relatively easy to transfer between computer languages by leveraging existing optimization routines.

A reproducibility study of work in recent literature published in the journal Extremes (Belzile, et al., 2023) is …


Iterative Silver-Label Refinement For Temporal Information Extraction In Biomedical Literature, Chan Lee May 2026

Iterative Silver-Label Refinement For Temporal Information Extraction In Biomedical Literature, Chan Lee

UNLV Theses, Dissertations, Professional Papers, and Capstones

Temporal information extraction plays a critical role in the biomedical domain, where the ability to identify events and their temporal relationships is central to interpreting research findings. However, annotated corpora for this task remain scarce and costly to produce and the existing models developed for clinical text do not transfer well. This work bridges that gap through iterative silver-label refinement. A temporal model originally trained on news-domain data is adapted to biomedical text through cycles of automatic labeling, targeted correction, and retraining without the need for comprehensive manual annotation.

Key contributions include a practical iterative refinement methodology demonstrating that the …


Thermal Physiological Ecology Of The Relict Leopard Frog At Hot And Cold Springs, Robert P. Pelletier Iii May 2026

Thermal Physiological Ecology Of The Relict Leopard Frog At Hot And Cold Springs, Robert P. Pelletier Iii

UNLV Theses, Dissertations, Professional Papers, and Capstones

The relict leopard frog (Rana onca) once ranged across drainages in southern Nevada, northwestern Arizona, and southwestern Utah. Following a decline, the species only persisted in a few geothermally influenced hot springs, which led to the perspective that hot springs were high-quality habitat. Rana onca has been under intensive, multiagency management and the species has been translocated to establish additional populations, including at cold-water sites. Three research studies are presented into the thermal physiological ecology of R. onca with the aim of informing conservation strategy. The research was focused at a thermally influenced hot spring and a cold-water spring to …


Methylation-Dependent Regulatory Pathway That Governs The Stability Of The Sox Family Proteins And Related Developmental Regulators, Keshari Gayathri Rajawasam May 2026

Methylation-Dependent Regulatory Pathway That Governs The Stability Of The Sox Family Proteins And Related Developmental Regulators, Keshari Gayathri Rajawasam

UNLV Theses, Dissertations, Professional Papers, and Capstones

The SRY (Sex-determining Region Y) protein is a transcription factor encoded on the Y chromosome and is the key regulator responsible for initiating male sex determination in mammals. During early embryonic development, SRY activates the genetic program that leads to testis formation by promoting the expression of downstream genes involved in male gonadal differentiation. Mutations or dysregulation of SRY can lead to disorders of sex development such as male-to-female sex conversion and hermaphroditism, highlighting its critical role in sex determination.

SRY belongs to the SOX (SRY-related HMG-box) family of transcription factors, which includes the proteins SOX1, SOX2 and SOX3. These …


Effect Of The Sava Syndemic On Hiv Viral Suppression Among People Living With Hiv In The United States: A Scoping Review And Meta-Analysis, Jacquelyn Rodriguez May 2026

Effect Of The Sava Syndemic On Hiv Viral Suppression Among People Living With Hiv In The United States: A Scoping Review And Meta-Analysis, Jacquelyn Rodriguez

UNLV Theses, Dissertations, Professional Papers, and Capstones

The SAVA syndemic highlights the interconnected and mutually reinforcing nature of substance use, violence victimization, and HIV/AIDS. The synergistic interaction of these conditions creates structural and behavioral barriers that disrupt the HIV care continuum and contribute to significant health inequities. Achieving a suppressed viral load is a critical clinical outcome for people living with HIV, while viral non-suppression can be an indicator of poor health, elevated transmission risk, and disease progression. Still, the association between SAVA factors and viral suppression/non-suppression outcomes within U.S. populations remains inconsistently characterized due to heterogeneous methodologies and variable inclusion of high-risk groups. This mixed-methods study …


Fast Radio Bursts And Long Period Radio Transients: Radiation Mechanisms And Propagation Effects, Yuanhong Qu May 2026

Fast Radio Bursts And Long Period Radio Transients: Radiation Mechanisms And Propagation Effects, Yuanhong Qu

UNLV Theses, Dissertations, Professional Papers, and Capstones

Fast Radio Bursts (FRBs) are bright radio bursts with the highest brightness temperatures in the radio sky. In this thesis, we investigate the trigger mechanisms, radiation mechanisms, and propagation effects of FRBs. Two general classes of coherent radiation mechanisms are considered in two categories: pulsar-like models invoking emission originating within the magnetar magnetosphere, and GRB-like models, which attribute the emission to relativistic magnetized shocks occurring far away from the central engine. We use the general observed properties (polarization features and spectra bandwidths) of repeating FRBs to constrain the physical conditions needed for these two mechanisms. We propose that crust quakes …


Validation And Implementation Of Automated Planning Optimization In Utah Valley Hospital, Oluwatobi Adeniji May 2026

Validation And Implementation Of Automated Planning Optimization In Utah Valley Hospital, Oluwatobi Adeniji

UNLV Theses, Dissertations, Professional Papers, and Capstones

The increasing complexity of modern radiotherapy demands planning workflows that are efficient, standardized, and dosimetrically robust across diverse disease sites. Knowledge-based planning (KBP) systems such as RapidPlan offer a data-driven approach to automate and improve treatment planning by learning geometric–dosimetric relationships from high-quality clinical plans. In this work, I am evaluating the performance, generalizability, and clinical applicability of vendor-provided RapidPlan models across seven anatomical sites: intracranial SRS, prostate SBRT, right and left lung SBRT, liver SBRT, head and neck, and glioblastoma. Subsequently, a complementary institution-specific SRS model tailored to single-isocenter multitarget workflows was created. Seventy retrospectively selected patients were replanned …


Unknowing Sacrifices: Public Health And Radiation Illness In New Mexico And Nevada, 1940s-1960s, Beatriz Avila-Marquez May 2026

Unknowing Sacrifices: Public Health And Radiation Illness In New Mexico And Nevada, 1940s-1960s, Beatriz Avila-Marquez

UNLV Theses, Dissertations, Professional Papers, and Capstones

The detonation of the first atomic bomb in the early morning of July 16, 1945, in New Mexico welcomed the atomic age that forever changed the world. After that day, thousands of lives were lost due to nuclear weapons, and hundreds of thousands more continued to suffer from the effects of atomic testing. The Atomic Energy Commission, fueled by the arms race of the Cold War, chose Nevada to continue the United States’ nuclear weapons testing. Knowledge of the dangers of radiation exposure, the effects of radiation, and techniques to prevent exposure are now available in part due to the …


“A Land No One Would Want”: Environmental Activism And The Rejection Of ‘Wasteland’ Narratives In Southern Nevada, Steven Butler May 2026

“A Land No One Would Want”: Environmental Activism And The Rejection Of ‘Wasteland’ Narratives In Southern Nevada, Steven Butler

UNLV Theses, Dissertations, Professional Papers, and Capstones

This paper traces events within the history of environmental activism in Southern Nevada. The first chapter discusses the proposed high level nuclear waste repository at Yucca Mountain. The second chapter examines the closure of the Reid Gardner Generating Station in Moapa, Nevada. The third chapter details the Southern Nevada Water Authority’s Groundwater Development Project. Each of the three chapters is linked by common themes within the history of Southern Nevada environmental activism, including dedicated coalition-building and the refusal of “wastelanding” of the region.


Preservation Of Sedimentary Rubidium Isotopic Signatures In Subduction Zones: Insights From The Schistes Lustrés Hp-Uhp Metasediments, Western Alps, Mary Clarich May 2026

Preservation Of Sedimentary Rubidium Isotopic Signatures In Subduction Zones: Insights From The Schistes Lustrés Hp-Uhp Metasediments, Western Alps, Mary Clarich

UNLV Theses, Dissertations, Professional Papers, and Capstones

When oceanic plates bend and sink into the mantle at subduction zones, they carry sediments from the surface down into the mantle. The recycled sediments contain elements, that are depleted in the mantle, thereby influencing the composition of the mantle wedge and the formation of arc magmas, which are the building blocks of juvenile continental crust. However, it remains poorly constrained how much these elements, particularly fluid-mobile elements such as rubidium (Rb), are lost into fluids during metamorphic dehydration, and how much is transported to sub-arc depths where arc magmas are generated. Rubidium in subducting sediments is mainly hosted in …


Agentic Synthetic Data Generation For Automated Model Development, Frederick Eugene Diehl May 2026

Agentic Synthetic Data Generation For Automated Model Development, Frederick Eugene Diehl

Theses and Dissertations

Large Language Model research has made large strides in capabilities from sentiment analysis to writing code. These advancements have been realized thanks to research into specific capabilities such as prompting techniques. Language models today have demonstrated the ability to create content, transform, and classify. These capabilities are not limited to academic exploration but also found in commercial products that are positioning themselves from application augmentation to personal assistants. These commercial products tend to steer towards single actions such as “summarize this article” or “write a function that performs action...” In parallel research has continued to advance towards more advanced constructs …


Automatically Constructed Preference Pairs For Chain-Of-Thought: Consistency Gains With Accuracy Tradeoffs, Cameron Scolari, Lanyu Shang May 2026

Automatically Constructed Preference Pairs For Chain-Of-Thought: Consistency Gains With Accuracy Tradeoffs, Cameron Scolari, Lanyu Shang

Honors Thesis

We investigate preference optimization over chain-of-thought (CoT) reasoning using automatically constructed preference signals derived from the accuracy and internal consistency of a model. Our results show that framing reasoning as a preference learning problem improves both the accuracy of the final answer and the structure of the model outputs. We observe a non-monotonic relationship between performance and the Direct Preference Optimization (DPO) scaling parameter β, where moderate values maximize accuracy while lower values improve stability, highlighting a tradeoff between optimization strength and reliable generation. We further identify a tradeoff between reasoning consistency and accuracy. Increasing the consistency weight improves agreement …


Local And Indigenous Knowledge, Innovation, And Sustainable Development: Creating Sustainable Futures Amidst Crisis Conditions At The Community Level, Carlos Andrés Arias May 2026

Local And Indigenous Knowledge, Innovation, And Sustainable Development: Creating Sustainable Futures Amidst Crisis Conditions At The Community Level, Carlos Andrés Arias

Dissertations and Theses

In 1987, the Brundtland Commission's Our Common Future (1987) made clear the need to reject longstanding development processes and focus on sustainable development. The Commission stressed that actual sustainable development integrates three elements: social development, economic development, and environmental protection. Though developed nations have achieved economic growth through conventional and extractive development practices, these practices have intensified natural disasters driven by climate change, increased food insecurity, and deepened poverty. This has acutely impacted Indigenous and local communities, many of whom face crisis conditions, such as war, terrorism, civil disorder, and their aftermath. Even so, many of these communities successfully implement …


Pwnagotchi: Deauthentication Attacks, Wpa Handshakes, And Wireless Network Security, Emily Musgrove May 2026

Pwnagotchi: Deauthentication Attacks, Wpa Handshakes, And Wireless Network Security, Emily Musgrove

Computer Science Honors Papers

Wireless networks are the foundation of modern device communication infrastructure. This project examines the security implications of automated WPA/WPA2 handshake collection using the Pwnagotchi, a portable Wi-Fi network auditing and penetration testing device. The paper provides a technical analysis of WPA and WPA2 authentication mechanisms, including the structure of the 4-way handshake, the creation of cryptographic keys, and the role of deauthentication attacks in forcing reconnections for handshake capture. Additionally, the project explores the vulnerabilities associated with using legacy wireless security protocols such as WEP and TKIP to allow for older technologies that continue to require such encryption methods. This …


Synthergy: Social Deduction And Deception In Llm-Powered Agents, Lauren Campbell, Andrew Forney May 2026

Synthergy: Social Deduction And Deception In Llm-Powered Agents, Lauren Campbell, Andrew Forney

Honors Thesis

Synthergy is an online social deduction game designed to enable comparative analysis of how large language model-powered agents engage in social deduction and deception under conditions of asymmetric information. Inspired by social deduction games such as Town of Salem, Throne of Lies, and Mafia, the game consists of two factions, Harmony and Discord, to which agents are secretly assigned. Agents must infer others’ affiliations through dialogue, in-game abilities, and voting behavior. To evaluate agent behavior, we conducted 100 simulated games across six agent types: a random baseline agent (RandomSynth), an LLM-based agent (Synth), a chain-of-thought agent (CoT Synth), a Bayesian …


A Governance-Aware Multi-Agent Framework For Enhancing Fairness & Temporal Accuracy In Disaster Response Systems, Md. Ashfaqur Rahman May 2026

A Governance-Aware Multi-Agent Framework For Enhancing Fairness & Temporal Accuracy In Disaster Response Systems, Md. Ashfaqur Rahman

Theses and Dissertations

Large Language Models (LLMs) have demonstrated significant potential in disaster-response decision support, however, their deployment in high-stakes humanitarian settings raises critical concerns regarding factual reliability, fairness, temporal validity, and governance compliance. Hallucinated outputs, demographic bias, and outdated recommendations can directly impact vulnerable populations and undermine public trust. This dissertation proposes a governance-aware multi-agent framework designed to enhance fairness and temporal accuracy in disaster-response systems through structured Retrieval-Augmented Generation (RAG), verification-driven orchestration, and adaptive correction mechanisms.The proposed architecture decomposes response generation into specialized agents responsible for real-time retrieval, fact-checking, bias auditing, temporal validation, threshold-based correction, and monitoring. By embedding governance constraints …


Modeling Velocity Distributions Of Interstellar Neutral Hydrogen In The Heliosphere, Lucas Robert Dyke May 2026

Modeling Velocity Distributions Of Interstellar Neutral Hydrogen In The Heliosphere, Lucas Robert Dyke

Dartmouth College Ph.D Dissertations

As interstellar neutral hydrogen (ISN H) is the most abundant neutral element in the helio- sphere, the region within which the solar wind interacts with the portion of the interstellar medium through which our solar system moves through, it is integral that we aim to under- stand its many properties and interactions within this region. This work details the synthesis and use of a model of ISN H, using trajectory methods to backtrace from a target point at a radial distance of 1 au where explorer probes like Interstellar Boundary Explorer (IBEX) and Interstellar Mapping and Acceleration Probe (IMAP) reside. …


A Mathematical & Computational Study Of Voting Power In Social Choice Systems, Madison T. Gambon May 2026

A Mathematical & Computational Study Of Voting Power In Social Choice Systems, Madison T. Gambon

Undergraduate Honors Theses

This thesis develops a computational framework for measuring the vulnerability of voting rules to coordinated strategic manipulation. While classical results show that most voting systems are theoretically manipulable, less is known about the magnitude of coordination required to alter outcomes or how that magnitude varies across institutional designs. I define the minimal manipulating coalition size k* as the smallest number of voters whose strategic ballot changes can overturn a sincere election outcome under a given rule. To enable cross-election comparison, I introduce the normalized manipulation threshold θ = k*/n . Using algorithmic search procedures and Monte Carlo simulation, I estimate …


Dynamic Trust Calibration, Bruno Miranda Henrique May 2026

Dynamic Trust Calibration, Bruno Miranda Henrique

Dartmouth College Ph.D Dissertations

Trust calibration between humans and Artificial Intelligence (AI) is crucial for optimal decision-making in collaborative settings. Excessive trust can lead users to accept AI-generated outputs without question, overlooking critical flaws, while insufficient trust may result in disregarding valuable insights from AI systems, hindering performance. Despite its importance, there is currently no definitive and objective method for measuring trust calibration between humans and AI. Current approaches lack standardization and consistent metrics that can be broadly applied across various contexts, and they don’t distinguish between the formation of opinions and subsequent human decisions. This thesis brings a novel and objective method for …


Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard May 2026

Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard

LSU Doctoral Dissertations

Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …


“The New Normal”: California’S Escalating Wildfire Crisis, Alexandra Vasquez May 2026

“The New Normal”: California’S Escalating Wildfire Crisis, Alexandra Vasquez

Student Theses 2015-Present

This paper addresses the current state of California's wildfire epidemic and how the increasing effects of climate change have worsened the fires, harming residents' health and the state's economy. The wildfires are shaped by factors such as climate change, land-use choices, and policy designs. California wildfires have worsened substantially in the 21st century, with the worst burns in the 2020 season setting a record of 4.2 to 4.5 million acres destroyed. Given current policies and the administration's disinterest in combating climate change, understanding wildfire history and data is essential to improving California's wildfire resilience, creating sustainable land management practices, and …


Sage: Contention-Aware Sensitivity Adjustment For Spin Lock Exiting In Vms, Sam Thomas Stowers May 2026

Sage: Contention-Aware Sensitivity Adjustment For Spin Lock Exiting In Vms, Sam Thomas Stowers

Theses - ALL

To address the severe multi-threaded performance degradation caused by lock contention in oversubscribed cloud environments, this thesis examines and improves on the Pause Loop Exit (PLE) mechanism used by hypervisors to deschedule unproductive virtual CPUs (vCPUs). These oversubscribed environments introduce contention which frequently leads to Lock Holder Preemption (LHP), where a hypervisor preempts a vCPU holding a critical spinlock, causing waiting vCPUs to waste cycles spinning. To mitigate LHP, hardware mechanisms trigger PLE events to inform hypervisors of spinning vCPUs, relying on a PLE_gap parameter to differentiate spinlock instances. The PLE_gap dictates spinlock detection sensitivity—a component of the virtualization stack …


Geometric Approaches To Memory Formation In Soft Matter, Gentian Muhaxheri May 2026

Geometric Approaches To Memory Formation In Soft Matter, Gentian Muhaxheri

Dissertations - ALL

The primary focus of this dissertation is the development of a geometric framework for understanding memory formation in systems composed of interacting hysteretic elements, or hysterons. Using tools from bifurcation and catastrophe theory, this work provides a description of how complex memory behaviors emerge from the structure of the system's configuration space and the system bifurcations under external driving. As a concrete model system, we study networks of connected rubber balloons subjected to different inflation protocols. Under pressure control, the system maps naturally onto a Preisach-type system of non-interacting hysterons and exhibits return point memory. In contrast, under volume control, …


Global Invertibility Of Sobolev Mappings And Energy Minimizers With Prescribed Jacobian, Sabrina Traver May 2026

Global Invertibility Of Sobolev Mappings And Energy Minimizers With Prescribed Jacobian, Sabrina Traver

Dissertations - ALL

We prove two main results at the intersection of Geometric Function Theory and Nonlinear Elasticity. The first is a Sobolev variant of the Inverse Function Theorem, which generalizes a famous result of John Ball. It uses Classical Sobolev Theory as well as the Degree Function, which was initially a topological tool. The second result is the existence and uniqueness (up to rotation) of a radially-symmetric minimizer for Sobolev mappings with prescribed Jacobian. This result generalizes recent work of André Guerra, Lukas Koch, and Sauli Lindberg.