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Articles 61 - 90 of 3930
Full-Text Articles in Physical Sciences and Mathematics
Simulation Of Fluid Flow Based On Navier Stokes Equations, Ricardo Marquez, Javier Perez
Simulation Of Fluid Flow Based On Navier Stokes Equations, Ricardo Marquez, Javier Perez
Undergraduate Research Symposium Posters
This work presents a computational study of incompressible flow based on the Navier-Stokes equations using finite element method. The Crank-Nicolson approximation is used for discretizing the time derivative. The study consists of investigating the effect of the choice of finite elements and the size of the time step in obtaining the numerical velocity and pressure. This is illustrated with FreeFEM++ simulations of the von Karman benchmark flow problem. Profiles of drag, lift and pressure drop will be presented in time.
The Mathematics Of Motion: Applying Derivatives To Fluid Systems, Sayla Daily
The Mathematics Of Motion: Applying Derivatives To Fluid Systems, Sayla Daily
Undergraduate Research Symposium Posters
Mathematical modeling through differential equations provides a basis for understanding change in physical and engineering systems. My project explores the transition from single-variable derivatives to multivariable partial derivatives and their applications in describing engineering applications. Beginning with the Fundamental Theorem of Calculus, derivatives are introduced as measures of change, quantifying relationships such as velocity and acceleration. The study then extends to partial derivatives, which represents systems influenced by multiple variables, including spatial and temporal factors. These principles are applied to model fluid motion, and pressure gradients, including the Navier–Stokes equations governing fluid dynamics. By linking mathematics with engineering applications, this …
Preparing For The Artificial Intelligence (Ai) Economy In The Mountain West, 2025, Kian Parikh, Taylor Volk, Maisoon Faris, Kristian Thymianos, William E. Brown Jr.
Preparing For The Artificial Intelligence (Ai) Economy In The Mountain West, 2025, Kian Parikh, Taylor Volk, Maisoon Faris, Kristian Thymianos, William E. Brown Jr.
Economic Development & Workforce
This fact sheet presents data from the Brainly report, “Here Are the States Most (and Least) Prepared to Win the AI Race in 2025” for the five Mountain West states of Arizona, Colorado, New Mexico, Nevada, and Utah. This fact sheet highlights the national and individual rankings of four key metrics for each Mountain West state: the fixed percentage of businesses using artificial intelligence (AI); the number of AI jobs per 1,000 workers; the number of AI-related degrees per 10,000 people ages 20-24; and federal funding for small business technology innovation per $1 million of gross domestic product (GDP).
Artificial Intelligence (Ai) And The Anthropic Economic Index In The Mountain West, 2025, Cason Noll, Olivia K. Cheche, William E. Brown Jr.
Artificial Intelligence (Ai) And The Anthropic Economic Index In The Mountain West, 2025, Cason Noll, Olivia K. Cheche, William E. Brown Jr.
Economic Development & Workforce
This fact sheet presents 2025 data on the state of artificial intelligence (AI) adoption among the five Mountain West states of Arizona, Colorado, Nevada, New Mexico, and Utah. The data are sourced from the “Anthropic Economic Index,” which provides data on Claude.ai (an AI large language model) and its adoption across all 50 U.S. states and Washington, D.C. This fact sheet focuses on Claude.ai usage, the most common topic Claude.ai has been used for, and augmentation and automation shares for each Mountain West state.
U.S. Water Infrastructure: Diving Into Needs And Recent Policy Developments, Joseph Kane
U.S. Water Infrastructure: Diving Into Needs And Recent Policy Developments, Joseph Kane
Brookings Scholar Lecture Series
As part of the Brookings Scholar Lecture Series, Brookings Mountain West presents a lecture titled, "U.S. Water Infrastructure: Diving Into Needs and Recent Policy Developments" by Brookings fellow in Brookings Metro, Joseph Kane. Whether providing drinking water, treating wastewater, or managing stormwater, water infrastructure in the United States spans a wide range of human-made and natural systems. In turn, the enormous scale and variety of these systems is leading to an array of challenges: aging and vulnerable infrastructure; fragmented governance and siloed planning across different geographies; a lack of financial, technical, and managerial capacity; difficulties adapting to new industrial and …
U.S News & World Report 2025 Graduate Program Rankings, Unlv & Unr, Dre Boyd-Weatherly, Caitlin J. Saladino, William E. Brown Jr.
U.S News & World Report 2025 Graduate Program Rankings, Unlv & Unr, Dre Boyd-Weatherly, Caitlin J. Saladino, William E. Brown Jr.
Higher Education
This fact sheet presents 2025 graduate program rankings for the University of Nevada, Las Vegas (UNLV) and for the University of Nevada, Reno (UNR) based on the data published in spring 2025 by U.S. News & World Report. The graduate program categories reported include business, education, engineering, fine arts, law, medicine and health care, sciences and mathematics, and social sciences and humanities.
A Comprehensive Study On The Use Of Sub-Coherent Self Heterodyne Linewidth Estimations, Genevieve Gutierrez
A Comprehensive Study On The Use Of Sub-Coherent Self Heterodyne Linewidth Estimations, Genevieve Gutierrez
UNLV Theses, Dissertations, Professional Papers, and Capstones
A fundamental requirement for many precision spectroscopic applications is the development of stable lasers with narrow linewidths. However, accurately verifying laser linewidths becomes increasingly challenging as the linewidth decreases. In the field of frequency metrology, the delayed self-heterodyne technique has long been regarded as one of the most reliable and accessible methods for linewidth characterization, favored for its low equipment cost and reproducible results. Traditionally, self-heterodyne measurements employ an optical delay line significantly longer than the coherence length of the laser, with analysis performed via either the instantaneous power spectral density or the noise power spectral density. However, the use …
The Compositional And Dynamical Properties Of Exoplanets, Cody James Shakespeare
The Compositional And Dynamical Properties Of Exoplanets, Cody James Shakespeare
UNLV Theses, Dissertations, Professional Papers, and Capstones
The solid surface density profile of protoplanetary discs, and the composition of these solids, can be formed through sequential condensation models of dust precipitating from the cooling gas of the solar nebula. I continue developing a code that reproduces the chemical compositions of most chondrites as well as the bulk compositions of the rocky planets using our partial condensation model with an evolving disc. I extend this validated code to exoplanet systems with different initial elemental ratios, like the carbon-to-oxygen ratio and estimated stellar abundances over the age of the universe. I have improved this dust condensation code to include …
Autonomous Uav Swarm Formation Utilizing Gradient-Driven Contour Mapping For Radiation Source Localization, Edgar Amalyan
Autonomous Uav Swarm Formation Utilizing Gradient-Driven Contour Mapping For Radiation Source Localization, Edgar Amalyan
UNLV Theses, Dissertations, Professional Papers, and Capstones
This thesis presents a drone swarm for radiation mapping to aid source localization. The Department of Energy advocates employing UAVs for this task, but existing approaches remain inefficient and impractical in real-world scenarios. Three custom drones are built and flight-tested. A control algorithm to follow a contour, a constant-intensity path, is designed using a gradient fit. By knowing the source’s direction, the drone swarm can fly in the optimal trajectory at every step, leaving nothing to assumption. A program is created that implements formation flight and autonomous navigation. It is tested via a software-in-the-loop simulation utilizing radiation sources and detectors …
The Dual Impact Of Moral Injury: Links To Ptsd Symptoms And Disinhibited Externalizing In U.S. Combat Veterans, Bianca S. Islas
The Dual Impact Of Moral Injury: Links To Ptsd Symptoms And Disinhibited Externalizing In U.S. Combat Veterans, Bianca S. Islas
UNLV Theses, Dissertations, Professional Papers, and Capstones
Moral injury is an experience of psychological distress that occurs when a person’s morals are violated by themselves or others, including institutions and organizations. Such violations of morality can be impairing and have high rates of comorbidity with internalizing disorders (posttraumatic stress, depression, anxiety, suicidality), which may indicate that moral injury is a transdiagnostic construct. This study had four aims, which were accomplished using from a nationally representative, probability-based sample of 1,353 US military veterans. In the first aim, we created structural models of moral injury using the Moral Injury Events Scale (for which a bifactor structure with a specific …
Rna’S Symphony: Harmonizing Splice Junctions And Exon Counts For A Novel Approach To Differential Splicing Analysis, Jelard Aquino
Rna’S Symphony: Harmonizing Splice Junctions And Exon Counts For A Novel Approach To Differential Splicing Analysis, Jelard Aquino
UNLV Theses, Dissertations, Professional Papers, and Capstones
Alternative Splicing (AS) plays a critical role in transcriptome complexity and cell-type-specific gene regulation, yet its analysis remains methodologically fragmented, especially in the context of noisy and sparse single-cell RNA sequencing (scRNA-seq) data. This dissertation addresses key computational challenges in AS detection by evaluating existing tools, developing integrative frameworks, and proposing new strategies for improving analysis accuracy in both bulk and single-cell contexts. In chapter 1, I present a comprehensive literature review of computational tools designed for detecting and quantifying AS from bulk and scRNA-seq data. This review outlines major methodological paradigms, including exon-based and splice junction-based approaches, and evaluates …
Hot Spring Associated Infectious Diseases In The Great Basin And Southwest, Matthew Bentz
Hot Spring Associated Infectious Diseases In The Great Basin And Southwest, Matthew Bentz
UNLV Theses, Dissertations, Professional Papers, and Capstones
Like all bodies of freshwater, natural hot springs can harbor pathogenic microorganisms that carry the threat of infectious disease. The unique chemistry, increased temperature, and popularity for bathing may alter the risk profile of hot springs compared to other natural bodies of water. Despite this risk, the role of hot springs as a reservoir for infectious diseases remains understudied, particularly within the context of regional public health. Nevada and the Great Basin/Southwest have increasingly promoted hot springs for the purposes of tourism, and they share a strong link to the cultural heritage of the region. The unknown risk profile and …
Understanding Ore Deposit Scale Controls On Au Enrichment In Carlin-Type Au Mineralization: A High-Resolution Study Of The Rita K Deposit, Conner T. Callaway
Understanding Ore Deposit Scale Controls On Au Enrichment In Carlin-Type Au Mineralization: A High-Resolution Study Of The Rita K Deposit, Conner T. Callaway
UNLV Theses, Dissertations, Professional Papers, and Capstones
Controls on the distribution of gold (Au) within the Rita K Carlin-type deposit are poorly understood. The primary Au-bearing carbonate unit Wispy, is a bioturbated muddy limestone with debris flow clasts that range in size but are typically >5 cm occurring in the lower sections. The orebody is described as a syncline-anticline pair that hosts high-grade Au ore in the fold hinges. The spatial relationship between Au mineralization and fold hinges suggests that shortening due to folding is an important mechanism producing Au-enriched zones. However, the exact mechanism of Au enrichment and deposit-scale controls on Au distribution and fluid evolution …
Empowering Science With The World's First High Accuracy And High Throughput Functional Assay, Christopher Giacoletto
Empowering Science With The World's First High Accuracy And High Throughput Functional Assay, Christopher Giacoletto
UNLV Theses, Dissertations, Professional Papers, and Capstones
Understanding the functional consequences of genetic mutations remains a central challenge in modern biology, with far-reaching implications for human health and disease. While early systematic methods like alanine scanning and phage display provided foundational insights into protein structure and function, the emergence of high-throughput approaches—such as Multiplexed Assays of Variant Effect (MAVEs)—and predictive tools powered by artificial intelligence have vastly expanded our ability to profile mutational landscapes. However, these methods are often constrained by trade-offs between accuracy, scalability, and biological relevance.This dissertation presents the development and application of the GigaAssay, the world’s first high-throughput functional assay capable of delivering both …
Mechanisms Of Gold Enrichment In Seafloor Massive Sulfide Deposits: A Study On The Higashi-Aogashima Hydrothermal Field, Claudia Martinez
Mechanisms Of Gold Enrichment In Seafloor Massive Sulfide Deposits: A Study On The Higashi-Aogashima Hydrothermal Field, Claudia Martinez
UNLV Theses, Dissertations, Professional Papers, and Capstones
The study of Seafloor Massive Sulfides (SMS) deposit formation is vital for assessing both the economic potential and environmental risks posed by future marine mining projects. Metal-rich SMS deposits form in hydrothermal vent systems within tectonically active regions, such as back-arc basins, where faults enhance crustal permeability, enabling fluid migration driven by magmatic heat sources at depth in the crust. Currently our understanding of SMS formation processes is based on bulk-rock geochemical and isotopic data, lacking the necessary spatial and temporal resolution to understand ore forming processes. As a result, critical gaps remain in understanding the exact mechanisms responsible for …
Investigating Information Extraction And Language Models In Medical Domain Text Processing, Pouyan Nahed
Investigating Information Extraction And Language Models In Medical Domain Text Processing, Pouyan Nahed
UNLV Theses, Dissertations, Professional Papers, and Capstones
This dissertation demonstrates that carefully adapted language-model pipelines can transform unstructured clinical-trial and pharmacological prose into reliable, low-latency structured data. Four interconnected studies support this claim.Tri-AL platform. An open-source dashboard ingests all 440 k+ ClinicalTrials.gov records—including every historical revision—into a normalized schema and parses the 20 GB XML archive over 10x faster than a BeautifulSoup baseline, while exposing hooks for demographic analytics and supporting integration of user-defined modules. Clinical trial summarization. An encoder–decoder model is trained on 57k description–summary pairs to condense clinical trials into a few sentences. ROUGE evaluation shows a 20% improvement over the baseline, while graph-based evaluation …
Pylro: A Python Calculator For Analyzing Long-Range Structural Order, Kevin Parrish
Pylro: A Python Calculator For Analyzing Long-Range Structural Order, Kevin Parrish
UNLV Theses, Dissertations, Professional Papers, and Capstones
We present PyLRO, an open-source Python calculator designed to detect, quantify, and display long-range order in periodic structures. The program’s design methodology, workflow, and approach to order quantification are thoroughly described and demonstrated using a simple toy model. Great care is considered in the detailing of the calculation logic, as is standard in the development of computational methods. Additionally, we apply PyLRO to a series of metastable AlPO4 structural intermediates from a prior high-pressure study, demonstrating how to compute and visualize structural order in all directions on a Miller sphere. We further highlight the program’s capabilities through a high-throughput analysis …
The Chemistry Workforce In The Mountain West, 2022, Sean Curry, Otoniel Ramos, Mohit Pande, Olivia K. Cheche, Caitlin J. Saladino, William E. Brown Jr.
The Chemistry Workforce In The Mountain West, 2022, Sean Curry, Otoniel Ramos, Mohit Pande, Olivia K. Cheche, Caitlin J. Saladino, William E. Brown Jr.
Economic Development & Workforce
This fact sheet presents 2022 data on the industrial chemistry workforce in five Mountain West states: Arizona, Colorado, Nevada, New Mexico, and Utah. The American Chemistry Council’s (ACC’s) report, “2023 Guide to the Business of Chemistry,” offers insights into the chemistry industry’s role in the U.S. economy. This fact sheet focuses on 2022 state-level data related to the number of chemistry establishments, the number of individuals employed in the industry, and the average wages and salaries of industry workers in the Mountain West.
Poly(Pyridinium Salt)S Containing 9,9-Bis(4- Aminophenyl)Fluorene Moieties With Various Organic Counterions Exhibiting Both Lyotropic Liquid-Crystalline And Light-Emitting Properties, Pradip K. Bhowmik, David King, Haesook Han, Andras F. Wacha, Matti Knaapila
Poly(Pyridinium Salt)S Containing 9,9-Bis(4- Aminophenyl)Fluorene Moieties With Various Organic Counterions Exhibiting Both Lyotropic Liquid-Crystalline And Light-Emitting Properties, Pradip K. Bhowmik, David King, Haesook Han, Andras F. Wacha, Matti Knaapila
Chemistry and Biochemistry Faculty Research
Main-chain conjugated and non-conjugated polyelectrolytes are an important class of materials that have many technological applications ranging from fire-retardant materials to carbon-nanotube composites, nonlinear optical materials, electrochromic materials for smart windows, and optical sensors for biomolecules. Here, we describe a series of poly(pyridinium salt)s-fluorene containing 9,9-bis(4-aminophenyl)fluorene moieties with various organic counterions that were synthesized using ring-transmutation polymerization and metathesis reactions, which are non-conjugated polyelectrolytes. Their chemical structures were characterized by Fourier transform infrared (FTIR), proton (1H) and fluorine 19 (19F) nuclear magnetic resonance (NMR) spectrometers, and elemental analysis. They exhibited polyelectrolytic behavior in dimethyl sulfoxide. Their lyotropic liquid-crystalline phases were …
"Opting Out Of Ai”: Exploring Perceptions, Reasons, And Concerns Behind Faculty Resistance To Generative Ai, Aya Shata
Hank Greenspun School of Journalism and Media Studies Faculty Research
Research on Generative Artificial Intelligence (GAI) in higher education primarily focuses on faculty use and experiences, with limited attention given to why some abstain from using it. Drawing from Innovation Resistance Theory, this study aims to address this gap by exploring the perceptions of both faculty users and non-users of GAI, identifying the reasons and concerns why they avoid GAI. A survey of 294 full-time higher education faculty from two mid-size U.S. public universities was conducted. Using qualitative and quantitative analysis, results show that over one-third of the faculty members opted out of using GAI for five primary reasons: not …
Planting Seeds, Changing Minds: A Narrative Analysis Of Environmental Children’S Books, Julianna Jovillar
Planting Seeds, Changing Minds: A Narrative Analysis Of Environmental Children’S Books, Julianna Jovillar
UNLV Theses, Dissertations, Professional Papers, and Capstones
Children’s books are some of the earliest forms of entertainment and education a person will interact with in their lifetime. Simultaneously weaving a tale and teaching a lesson, children’s books, therefore, have the great potential to communicate important lessons and mindsets at young ages. Utilizing narrative theory (Fisher, 1984) and ecocriticism (Glotfelty, 1996), while also considering environmental ideologies and narrative components (Bloomfield, 2024), this study explores the functions of environmental children’s books and how they might communicate environmental messaging and encourage ecological thinking. Following a narrative analysis of 46 environmental children’s books, the results of this study indicate that there …
Cross-Correlation Studies Of The Cosmological 21 Cm Signal And High-Redshift Galaxy Distributions, Simon Matin
Cross-Correlation Studies Of The Cosmological 21 Cm Signal And High-Redshift Galaxy Distributions, Simon Matin
UNLV Theses, Dissertations, Professional Papers, and Capstones
The Epoch of Reionization (EoR) marks a critical phase in cosmic history, during which time the first stars and galaxies ionized the surrounding neutral hydrogen gas. A powerful way to probe this period is by cross-correlating the 21 cm signal from neutral hydrogen with high-redshift galaxy distributions. In this study, we analyze the 21 cm-galaxy cross-power spectrum using simulated sky maps and explore its redshift evolution, revealing a transition from positive correlation at early times (high redshift) to anti-correlation at later stages of reionization (low redshift). Our results highlight the sensitivity of the cross-power spectrum to the evolving ionized structure …
Specters Of Change: A Rhetorical And Qualitative Analysis Of Environmental Ghost Stories From Las Vegas Locals, Rachel J. Wuester
Specters Of Change: A Rhetorical And Qualitative Analysis Of Environmental Ghost Stories From Las Vegas Locals, Rachel J. Wuester
UNLV Theses, Dissertations, Professional Papers, and Capstones
This thesis explores “environmental ghost stories,” a term created to represent narratives that blend emotions and memories of ecological loss to make sense of environmental change. This project utilizes a mixed-methods approach that blends narrative theory, environmental rhetoric, and qualitative interviews to examine the narratives of chronic and acute changes experienced by long-term residents of Las Vegas, Nevada. Participants (N = 15) were required to have resided in the Las Vegas valley for a minimum of twenty years in order to have had the opportunity to witness both chronic and acute changes to their environment. Using a phronetic iterative approach …
Anonymous Cyber Threat Intelligence Sharing On Blockchain, Chol Hyun Park
Anonymous Cyber Threat Intelligence Sharing On Blockchain, Chol Hyun Park
UNLV Theses, Dissertations, Professional Papers, and Capstones
In cybersecurity, sharing of cyber threat intelligence (CTI) plays a pivotal role in our collective defense against emerging threats. However, the current paradigm of CTI sharing is one that participants are reluctant to share due to serious concerns about privacy and the potential exposure of sensitive information.We provide a comprehensive look at the potential of blockchain technology in cybersecurity, highlighting its advantages in creating an immutable, transparent, and decentralized ledger for CTI sharing. We also explore the mechanism of decentralized identity (DID) and explain how ZKP can be used to verify the authenticity of shared data without compromising the anonymity …
Dry And Wet Deposition Of Atmospheric Microplastics In Las Vegas, Nevada, Laine Adame
Dry And Wet Deposition Of Atmospheric Microplastics In Las Vegas, Nevada, Laine Adame
UNLV Theses, Dissertations, Professional Papers, and Capstones
Plastics have been one of the most widely used man-made materials since their inception, and production is expected to grow by five percent every year. Plastic waste has become a growing global environmental issue. Primary MPs are plastics that are created to be intentionally tiny for their specific functional purpose. Secondary microplastics (MPs) are byproducts of plastic waste occurring due to the breakdown of larger plastics resulting in the presence and accumulation of MPs in the environment. MPs are defined as tiny particles of plastic between 5 mm and 1 μm in size. MPs have been found in the deep …
On Efficient Position Dependent Computation Of Radiation Near Accretion Disks, Kara Jeanette Smith
On Efficient Position Dependent Computation Of Radiation Near Accretion Disks, Kara Jeanette Smith
UNLV Theses, Dissertations, Professional Papers, and Capstones
Accretion onto super massive black holes (SMBH) plays a vital role in explaining our observations of active galactic nuclei (AGN). One key aspect of observations of AGN is the prevalence of massive outflows which transport matter and energy away from the galactic core. These outflows are characterized by highly blueshifted absorption lines as radiation from the accretion disk is absorbed by gas which is moving toward us. Radiation pressure on spectral lines is expected to play a vital role in launching and accelerating these winds. At the other end of the spectrum of black hole masses, accretion disks in X-ray …
Climate Change And Hydropower Development Impacts In The Lower Mekong Basin, Nudthawud Homtong
Climate Change And Hydropower Development Impacts In The Lower Mekong Basin, Nudthawud Homtong
UNLV Theses, Dissertations, Professional Papers, and Capstones
The Mekong River Basin is vital to East and Southeast Asia, supporting over 60 million people and sustaining critical ecological systems. However, the basin faces dual threats from climate change and hydropower development, jeopardizing its ecological balance, hydrological patterns, and resource reliability. This research focuses on the Lower Mekong Basin (LMB), where aggressive hydropower expansion and climate variability have intensified concerns about sustainable water management. The study is divided into three interconnected parts. Part I examines spatial and temporal precipitation patterns in the Chi-Mun Basin (CMB) and Lower Mekong River (LMR) from 1950 to 2008, using linear regression and Mann-Kendall …
“Do You Even Lift, Bro?”: Correlates Of Muscle Dysmorphia Symptomatology In Filipino Male University Students, Pamela Paula C. Pioquinto
“Do You Even Lift, Bro?”: Correlates Of Muscle Dysmorphia Symptomatology In Filipino Male University Students, Pamela Paula C. Pioquinto
UNLV Theses, Dissertations, Professional Papers, and Capstones
Muscle Dysmorphia (MD) is a subtype of Body Dysmorphic Disorder (BDD) and is marked by the desire to increase muscularity and reduce body fat. MD is typically more prevalent among younger male populations, and it often drives comorbid disorders, including substance abuse, eating disorders, and social anxiety. Despite the growing literature on MD, it remains understudied in certain racial/ethnic populations, such as Filipinos. Acculturation, defined as the process in which an individual adopts, acquires, and adapts to a new cultural environment as a result of immigration, influences body image by reshaping an individual’s perceptions of beauty and muscularity standards. Guided …
Detection And Quantification Of Total Airborne Fungi And Coccidioides Species In Environmental Samples, Theresa T. Roehr
Detection And Quantification Of Total Airborne Fungi And Coccidioides Species In Environmental Samples, Theresa T. Roehr
UNLV Theses, Dissertations, Professional Papers, and Capstones
Fungal exposure can cause acute and chronic illnesses or exacerbate existing illnesses. Some fungi are opportunistic pathogens and can lead to serious systemic fungal infections. In 2020, more than 150 million cases of severe fungal infections were reported globally resulting in an estimated 1.7 million deaths. Coccidioidomycosis, or Valley fever, is classified as a serious fungal infection caused by the fungi Coccidioides immitis and C. posadasii. These particular fungi are prevalent in the soil of the Southwestern United States, including Las Vegas, Nevada. In 2024, there were a total of 269 cases of Valley fever reported in Nevada, and …
On The Special Cases Of Carmichael’S Totient Conjecture, Christopher Saito
On The Special Cases Of Carmichael’S Totient Conjecture, Christopher Saito
UNLV Theses, Dissertations, Professional Papers, and Capstones
Euler’s totient function, φ(n), is the arithmetic function defined as the number of positive integers less than or equal to n that are relatively prime to n. In his 1922 paper [3], Professor R. D. Carmichael conjectured that for each positive integer n, there exists at least one positive integer m̸ = n such that φ(m) = φ(n).In this thesis, we consider some relevant literature and explore Carmichael’s totient conjecture for particular values of φ(n) = k. Our main consideration will be the set X_k = {n ∈ N : φ(n) = k}. In identifying X_k for k = 2^t, …