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Articles 25561 - 25590 of 294588
Full-Text Articles in Physical Sciences and Mathematics
Ensuring The Privacy Compliance Of Voice Personal Assistant Applications, Song Liao
Ensuring The Privacy Compliance Of Voice Personal Assistant Applications, Song Liao
All Dissertations
Voice Personal Assistants (VPA) such as Amazon Alexa and Google Assistant are quickly and seamlessly integrating into people’s daily lives. Meanwhile, the increased reliance on VPA services raises privacy concerns, such as the leakage of private conversations and sensitive information. Privacy policies play an important role in addressing users’ privacy concerns and developers are required to provide privacy policies to disclose their apps’ data practices. In addition, voice apps targeting users in European countries are required to comply with the GDPR (General Data Protection Regulation). However, little is known about whether these privacy policies are informative and trustworthy on emerging …
Genomic Data Science Approaches For Understanding Human Diseases, Snehal Shah
Genomic Data Science Approaches For Understanding Human Diseases, Snehal Shah
All Dissertations
The intricate interplay of genetic predisposition, environmental influences, and lifestyle acts as the multifactorial landscape of diseases. Understanding this complexity presents a significant challenge. Molecular insights into disease mechanisms, particularly the interactions of DNA, RNA, and proteins with environmental and lifestyle factors, have revolutionized disease diagnosis, prognosis, and treatment. High-throughput technologies, such as next-generation sequencing, generate large amounts of molecular data, holding a wealth of knowledge. These datasets unveil the roles of genes and their interactions with various factors through analysis, shedding light on previously unknown molecular mechanisms underlying disease pathogenesis. Furthermore, they facilitate the discovery of biomarkers crucial for …
Relating Elasticity And Other Multiplicative Properties Among Orders In Number Fields And Related Rings, Grant Moles
Relating Elasticity And Other Multiplicative Properties Among Orders In Number Fields And Related Rings, Grant Moles
All Dissertations
This dissertation will explore factorization within orders in a number ring. By far the most well-understood of these orders are rings of algebraic integers. We will begin by examining how certain types of subrings may relate to the larger rings in which they are contained. We will then apply this knowledge, along with additional techniques, to determine how the elasticity in an order relates to the elasticity of the full ring of algebraic integers. Using many of the same strategies, we will develop a corresponding result in the rings of formal power series. Finally, we will explore a number of …
Gan With Skip Patch Discriminator For Biological Electron Microscopy Image Generation, Nishith Ranjon Roy
Gan With Skip Patch Discriminator For Biological Electron Microscopy Image Generation, Nishith Ranjon Roy
Graduate Theses and Dissertations
GAN models have been successfully used for image generation in various sections such as real-life objects like human faces, cars, animal faces, landscapes, etc. This work focuses on biological electron microscopy (EM) image generation. Unlike other real-life objects, biological EM images are obtained through electron microscopy techniques to study biological specimens. Electron microscopy offers high resolution and magnification capabilities, making it a powerful tool for visualizing biological structures at the nanoscale. However, using GAN models for biological EM image generation poses challenges due to the complex and unique arrangements of biological structures and the sparse and asymmetrical patterns in EM …
Cubic Soft Ideals On B-Algebra For Solving Complex Problems: Trend Analysis, Proofs, Improvements, And Applications, Muhammad Saeed, Hafiz Inam Ul Haq, Mubashir Ali
Cubic Soft Ideals On B-Algebra For Solving Complex Problems: Trend Analysis, Proofs, Improvements, And Applications, Muhammad Saeed, Hafiz Inam Ul Haq, Mubashir Ali
Neutrosophic Systems with Applications
In this paper, we introduce the concepts of cubic soft (CS) algebra, CS o-subalgebra, and CS ideals within the framework of B-algebra. We provide comprehensive characterizations of these new structures, elucidating their unique properties and interrelationships. Specifically, we present detailed conditions under which a CS subalgebra can be classified as a closed CS ideal. Our analysis explores the intricate relationships among closed cubic soft ideals, cubic soft subalgebras, and cubic soft o-subalgebras. By doing so, we aim to provide a deeper understanding of how these structures interact and coexist within the broader context of B-algebra The findings offer significant insights …
Divergence Measures And Aggregation Operators For Single-Valued Neutrosophic Sets With Applications In Decision-Making Problems, Surender Singh, Sonam Sharma
Divergence Measures And Aggregation Operators For Single-Valued Neutrosophic Sets With Applications In Decision-Making Problems, Surender Singh, Sonam Sharma
Neutrosophic Systems with Applications
Single-valued neutrosophic sets (SVNSs) facilitate the representation of uncertain information more extensively than conventional methods. The study of divergence measures of SVNSs is important due to their applications in different areas like multi-criteria decision-making (MCDM), pattern recognition, cluster analysis, machine learning, etc., In this paper, we introduce a divergence measure for SVNSs. The suggested divergence measure is applied to cluster analysis for the classification of imprecise data. For establishing the reasonability and advantage of the suggested divergence measure in a clustering problem over the existing measures, a comparative assessment is also presented. Furthermore, we introduce, an inferior ratio method for …
Rotational State-To-State Transition Rate Coefficients For H2O + H2O Collisions At Nonequilibrium Conditions, Bikramaditya Mandal, Michal Zoltowski, Martin Cordiner, François Lique, Dmitri Babikov
Rotational State-To-State Transition Rate Coefficients For H2O + H2O Collisions At Nonequilibrium Conditions, Bikramaditya Mandal, Michal Zoltowski, Martin Cordiner, François Lique, Dmitri Babikov
Chemistry Faculty Research and Publications
Aims. The goal is to develop a database of rate coefficients for rotational state-to-state transitions in H2O + H2O collisions that is suitable for the modeling of energy transfer in nonequilibrium conditions, in which the distribution of rotational states of H2O deviates from local thermodynamic equilibrium.
Methods. A two-temperature model was employed that assumed that although there is no equilibrium between all possible degrees of freedom in the system, the translational and rotational degrees of freedom can be expected to achieve their own equilibria independently, and that they can be approximately characterized by Boltzmann …
La1-Xsrxcoo3 Perovskite: Antimicrobial Properties And Pvdf Based Piezoelectric Nanogenerator For Energy Storage Through Self-Induced Polling, S M. Anyet Ullah Shohag
La1-Xsrxcoo3 Perovskite: Antimicrobial Properties And Pvdf Based Piezoelectric Nanogenerator For Energy Storage Through Self-Induced Polling, S M. Anyet Ullah Shohag
Theses and Dissertations
Piezoelectric Nanogenerators (PENGs), which can produce electrical energy from mechanical energy via ferroelectric effect, are one of the ambient sources of green energy. PENGs have gathered a huge attention due to cost-effectiveness, mechanical stability, and easy installation process. In this experiment, different weight percent of Sr2+ doped Lanthanum Cobaltite (La1- XSrXCoO3) perovskite, a ferroelectric material, was synthesizes by using a simple combination of sol-gel and molten-salt process and then characterization by X-ray diffraction, and scanning electron microscopy ensures the uniform morphology of nano cubes. Poly (vinylidene difluoride) (PVDF), N,N-dimethylformamide and acetone solution were used to make a flexible film using …
Exploratory Analysis In Rio Grande Valley Real Estate Development, Mathew C. Sosa
Exploratory Analysis In Rio Grande Valley Real Estate Development, Mathew C. Sosa
Theses and Dissertations
The aim of this thesis is to apply exploratory data analysis and machine learning (ML) to answer critical questions in real estate development within the Rio Grande Valley (RGV). The real estate development sector is highly dynamic and relies on multiple integrated systems and planning to bring new homes to the market. Customer Relationship Management (CRM) software and real estate listing services, such as Redfin, are utilized to manage the customer lifecycle and analyze the local market, respectively. Two of the most crucial aspects of the customer lifecycle are the first home tour and deal closing. This paper explores the …
Tales In The Teeth: Using Isotopic Analysis To Understand The Paleoecology And Social Behavior Of Brontotheres Of The Intermountain Basins During The Middle Eocene, John Michael Michalski
Tales In The Teeth: Using Isotopic Analysis To Understand The Paleoecology And Social Behavior Of Brontotheres Of The Intermountain Basins During The Middle Eocene, John Michael Michalski
All Graduate Reports and Creative Projects, Fall 2023 to Present
Isotopic analysis has been a common practice used in paleontology to study ancient ecosystems, and the lives of animals therein. Oxygen isotopic analysis is of particular importance not only because of its use in studying paleoecology, diet, and migration, but also its use in studying mountain elevation, and its impact on ancient ecosystems. I use stable oxygen isotopic analysis to study the habits and ecology of brontotheres from intermountain basins surrounding the Uinta Mountains of Utah and Wyoming, USA. I studied the oxygen isotopes from 16 fossil specimens of teeth, most of which belonged to brontotheres, including the genera Palaeosyops …
Staying Fresh: Unconventional Approaches Towards Advancing Energy Sustainability, Water Resources, And Community Resiliency In The Southwestern United States, Judith Hoyt
Open Access Theses & Dissertations
This dissertation addresses critical challenges in urban heat management, sustainable energy resource utilization, and water quality communication through three studies. Study 1 investigates the impact of roof color on urban heat islands in Tucson, Arizona where approximately 70% of roofs display high albedo (i.e., light) colors. Energy consumption simulations conducted indicate that converting dark- to light-colored roofs could save Tucson approximately $1,400,000 annually in energy costs, highlighting the potential of cool roofs for energy savings and improved thermal comfort. Study 2 assesses the sources of lithium in subsurface waters in West Texas and South Central New Mexico. Water chemistry data …
Neural Networks For Decisions Under Uncertainty, Edwin Tomy George
Neural Networks For Decisions Under Uncertainty, Edwin Tomy George
Open Access Theses & Dissertations
Neural networks are used in many real-world applications, ranging from classification tasks to medical diagnostics. For each task, a neural network is typically able to make predictions due to its ability to extract meaningful patterns from processing large amounts of data. Thus, given the increases in available data in recent decades, the performance of neural networks in making accurate predictions has greatly increased. However, this data often comes with ingrained uncertainties due to measurement errors or the inherent variability of individual data points. Neural networks can learn despite the errors in the overall data, but what if we want them …
Experimental And Theoretical Investigation Of The Coordination Of 8-Hydroxquinoline Inhibitors To Biomimetic Zinc Complexes And Histone Deacetylase 8 (Hdac8), Anthony M. Baudino, Harris F. Ciaccio, Michael J. Turski, Xavier A. Akins, Phoebus Sun Cao, Elisa Morales, Roger D. Sommer, Adam R. Johnson, Donald J. Wink, Kyle A. Grice, Kari Stone
Experimental And Theoretical Investigation Of The Coordination Of 8-Hydroxquinoline Inhibitors To Biomimetic Zinc Complexes And Histone Deacetylase 8 (Hdac8), Anthony M. Baudino, Harris F. Ciaccio, Michael J. Turski, Xavier A. Akins, Phoebus Sun Cao, Elisa Morales, Roger D. Sommer, Adam R. Johnson, Donald J. Wink, Kyle A. Grice, Kari Stone
Chemistry Department Faculty Articles
Zinc is integral to diverse biological functions, acting catalytically, structurally, and supportively in essential enzyme cycles, despite its limited amounts in the body. Targeting zinc enzymes with potent drugs, such as Vorinostat, demonstrates the therapeutic efficacy of zinc-binding ligands, notably in cutaneous T-cell lymphoma treatments. Our study merges experimental and theoretical approaches to analyze the coordination of 8-hydroxylquinoline (8HQ) inhibitors with biomimetic zinc complexes and human histone deacetylase 8 (HDAC8), a monozinc hydrolase enzyme. Assessing 10 8HQ derivatives for structural and electronic characteristics against these models, we observe minimal inhibition efficacy, corroborated through protein–ligand docking analyses, highlighting the complexities of …
Semantic Linguistic User Profiles For Automatic Computational Narrative Creation For Scientific Models, Angel Uriel Ortega Castillo
Semantic Linguistic User Profiles For Automatic Computational Narrative Creation For Scientific Models, Angel Uriel Ortega Castillo
Open Access Theses & Dissertations
The outcomes of scientific models can be hard to understand given the need for context, domain knowledge, and many variables and data being used. This research aims to provide users of scientific models with understandable information that can be automatically generated. For the context of this research, understandable is defined as being correctly interpreted (i.e., with respect to the original intent of the data). Scientific information can be conveyed to users in the form of a narrative or visualizations, and these are not necessarily separate from each other, but rather complimentary. One of the objectives of this research is to …
Random Forest For High-Dimensional Data, George Ekow Quaye
Random Forest For High-Dimensional Data, George Ekow Quaye
Open Access Theses & Dissertations
The exponential growth of data has led to a rapid increase in high-dimensional datasets across various domains, presenting significant challenges in data analysis, particularly in predictive modeling tasks. Traditional Random Forest (RF), while robust, often struggles with datasets filled with numerous noisy or non-informative features, compromising both performance and accuracy. This study introduces an advanced algorithm, High-Dimensional Random Forests (HDRF), designed to address these challenges by integrating robust multivariate feature selection techniques directly into the decision tree construction process. Unlike standard RF, HDRF incorporates ridge regression-based variable screening at each decision split, enhancing its ability to identify and utilize the …
Quantum Circuit Optimization Leveraging Multi-Qubit Exchange Interactions In Spin Qubits, Miguel Gonzalo Rodriguez
Quantum Circuit Optimization Leveraging Multi-Qubit Exchange Interactions In Spin Qubits, Miguel Gonzalo Rodriguez
Open Access Theses & Dissertations
This thesis looks into how multi-qubit exchange interactions can be used to improve quantumcircuits in semiconductor quantum devices. Pairwise interactions between qubits are a common tenet of traditional quantum computing paradigms, although they can impose complexity and depth constraints on circuits. In order to improve the efficiency and scalability of quantum circuits, this research explores the theoretical underpinnings and practical uses of multi-qubit interactions. A thorough theoretical framework is formulated, outlining the mathematical equivalence of a unitary matrix representing interactions between multiple qubits. We obtain the timeevolution operator by analyzing the Hamiltonian of three spin-1/2 particles. A number of quantum …
Seismic Imaging Of Mcmurdo Ice Shelf Near Williams Airfield, Yeshey Seldon
Seismic Imaging Of Mcmurdo Ice Shelf Near Williams Airfield, Yeshey Seldon
Open Access Theses & Dissertations
Seismic exploration has played a crucial role in understanding the Earth's interior and has been successfully employed in various regions, including Antarctica. This research focuses on analyzing a 1000-m seismic line on McMurdo Ice Shelf near Williams Airfield, as part of the Thwaites Interdisciplinary Margin Evolution (TIME) project. The McMurdo Ice Shelf, covering an expansive area within the Ross Ice Shelf, has undergone significant changes due to evolving oceanic and atmospheric conditions. The presence of Circumpolar Deep Water (CDW) has recently impacted the ice shelf, with warmer ocean waters causing basal melting and changes in wind patterns affecting ice flow …
Investigating Styles Of Contraction And Overprinting By Rio Grande Rift Extension In The Southern Indio Mountains, Western Texas, David W. West
Investigating Styles Of Contraction And Overprinting By Rio Grande Rift Extension In The Southern Indio Mountains, Western Texas, David W. West
Open Access Theses & Dissertations
Laramide-style intracontinental deformation occurred throughout a large area in the western United States from the late Cretaceous through the Eocene. This event is largely investigated and viewed from classic exposures in Colorado and Wyoming, extending south to southern New Mexico. In this region the Laramide orogen merges with the Mexican fold and thrust belt (MFTB) and the northern limits of the Mexican orogen along a blurry boundary. In the Indio Mountain range in western Texas, Cretaceous sediments were deposited in the Jurassic-Cretaceous Chihuahua trough. They were inverted due to contraction and emplaced adjacent to the Diablo Plateau. This region lies …
A Uniformly Most Powerful Test For The Mean Of A Beta Distribution, Richard Ntiamoah Kyei
A Uniformly Most Powerful Test For The Mean Of A Beta Distribution, Richard Ntiamoah Kyei
Electronic Theses and Dissertations
The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, …
Computational Models That Exploit Spatial, Temporal, And Voltage-Current Relationships In The Electrochemical Generation-Collection Of Redox-Active Molecules, Miguel Angel Abrego Tello
Computational Models That Exploit Spatial, Temporal, And Voltage-Current Relationships In The Electrochemical Generation-Collection Of Redox-Active Molecules, Miguel Angel Abrego Tello
Graduate Theses and Dissertations
The numerical studies in this dissertation explore the application of redox cycling, an advanced electrochemical technique, for analyzing bioelectrochemical systems with a particular focus on small-volume samples and involves electrodes that can be activated to oxidize and reduce, separated by varying distances and featuring different geometries. The redox cycling approach facilitates the spatio-temporal interrogation of kinetics, mass transport, and the quantification and identification of chemical systems. We optimize a previously fabricated neural probe design on an SU-8 substrate, featuring coplanar arrays of nine microband electrodes suited for in vivo applications. Through comprehensive in situ and in silico redox cycling studies …
A Real-Time Iot-Based Data Acquisition And Monitoring System For Photovoltaic Applications, Adam Barbosa, Hamza Mubarak, Fazel Mohammadi, Mohammad J. Sanjari, Mehrdad Saif
A Real-Time Iot-Based Data Acquisition And Monitoring System For Photovoltaic Applications, Adam Barbosa, Hamza Mubarak, Fazel Mohammadi, Mohammad J. Sanjari, Mehrdad Saif
Electrical & Computer Engineering and Computer Science Faculty Publications
The transition to low-carbon energy systems, driven by climate change and fossil fuel scarcity, highlights technologies, such as Photovoltaic (PV) technology, for sustainable energy generation. This paper focuses on enhancing the efficiency of PV monitoring systems by leveraging Internet of Things (IoT) technology for accurate and real-time monitoring of essential parameters, such as voltage, current, and output power. Significant gaps in cost-effective and reliable IoT integration for PV monitoring are addressed, with an emphasis on predictive modeling. In this regard, a low-cost real-time IoT-based data acquisition and monitoring system for PV systems, as a proof of concept for future endeavors …
Differential Behavior Of Conformational Dynamics In Active And Inactive States Of Cannabinoid Receptor 1, Ugochi H. Isu, Adithya Polasa, Mahmoud Moradi
Differential Behavior Of Conformational Dynamics In Active And Inactive States Of Cannabinoid Receptor 1, Ugochi H. Isu, Adithya Polasa, Mahmoud Moradi
Chemistry & Biochemistry Faculty Publications and Presentations
Cannabinoid receptor 1 (CB1) is a G protein-coupled receptor that regulates critical physiological processes including pain, appetite, and cognition. Understanding the conformational dynamics of CB1 associated with transitions between inactive and active signaling states is imperative for developing targeted modulators. Using microsecond-level all-atom molecular dynamics simulations, we identified marked differences in the conformational ensembles of inactive and active CB1 in apo. The inactive state exhibited substantially increased structural heterogeneity and plasticity compared to the more rigidified active state in the absence of stabilizing ligands. Transmembrane helices TM3 and TM7 were identified as distinguishing factors modulating the state-dependent dynamics. TM7 …
Engineering Central Substitutions In Heptamethine Dyes For Improved Fluorophore Performance, Lei Guo, Meek Yang, Bin Dong, Seth Lewman, Alex Van Horn, Shang Jia
Engineering Central Substitutions In Heptamethine Dyes For Improved Fluorophore Performance, Lei Guo, Meek Yang, Bin Dong, Seth Lewman, Alex Van Horn, Shang Jia
Chemistry & Biochemistry Faculty Publications and Presentations
As a major family of red-shifted fluorophores that operate beyond visible light, polymethine dyes are pivotal in light-based biological techniques. However, methods for tuning this kind of fluorophores by structural modification remain restricted to bottom-up synthesis and modification using coupling or nucleophilic substitutions. In this study, we introduce a two-step, late-stage functionalization process for heptamethine dyes. This process enables the substitution of the central chlorine atom in the commonly used 4′-chloro heptamethine scaffold with various aryl groups using aryllithium reagents. This method borrows the building block and designs from the xanthene dye community and offers a mild and convenient way …
Recent Advances In Magnetic Feˣ⁺/Tio₂ Microfibers For Wastewater Treatment As Climate Change Mitigation, Misriani Misriani, Yang Tian, Z. Ryan Tian
Recent Advances In Magnetic Feˣ⁺/Tio₂ Microfibers For Wastewater Treatment As Climate Change Mitigation, Misriani Misriani, Yang Tian, Z. Ryan Tian
Chemistry & Biochemistry Faculty Publications and Presentations
Chemical dyeing and finishing processes used in the clothing and textile industries are among the main contributors that can increase the impact of climate change. Photocatalysis using nanosized titanium dioxide (TiO2) has been continuously developed as a promising technology for purifying dye wastewater into simpler and environmentally friendly components. In addition, the decoration of iron cations (Fe2+) and (Fe3+) increases the reusability of the photocatalyst due to their magnetic properties, which are easy to collect for the recycling process. Magnetic Fex+/TiO2 microfibers have been successfully prepared using a hydrothermal method using …
Querymate: A Custom Llm Powered By Llamacpp, Pegah Khosravi
Querymate: A Custom Llm Powered By Llamacpp, Pegah Khosravi
Open Educational Resources
No abstract provided.
On Neumann Boundary Conditions For Nonlocal Models With Finite Horizon, Scott Alex Hootman-Ng
On Neumann Boundary Conditions For Nonlocal Models With Finite Horizon, Scott Alex Hootman-Ng
Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–
Nonlocal models are have recently seen an explosive interest and development in the context of fracture mechanics, diffusion, image processing, population dynamics due to their ability to approximate differential-like operators with integral operators for inherently discontinuous solutions. Much of the work in the field focuses on how concepts from partial differential equations (PDEs) can be extended to the nonlocal domain. Boundary conditions for PDEs are crucial components for applications to physical problems, prescribing data on the domain boundary to capture the behavior of physical phenomena accurately with the underlying model. In this thesis we specifically examine a Neumann-type boundary condition …
Equilibria And Effective Transition Rates In Linear Networks, Sayani Ghosh
Equilibria And Effective Transition Rates In Linear Networks, Sayani Ghosh
All Dissertations
Investigating equilibration in nucleosynthetic processes is crucial for understanding stellar chemical abundances in nuclear astrophysical scenarios. While current computational models are effective at predicting final species abundances at the end of these stellar processes, they fail to provide insights into the evolution of equilibrium. Without this deeper understanding, it is challenging to determine the impact of individual reaction rates on timescales and the resultant equilibrium.
In this work, we model nucleosynthetic processes as directed graphs. We develop theorems that allow us to express the mass fractions of species as spanning arborescences of these graphs. By obtaining eigenvalues in terms of …
Studying The Chemistry-Property Relationship In Magnetic And Optical Materials: Spin S = 3/2 Systems Of Neodymium, Manganese, And Cobalt Oxyanions, Xudong Huai
All Dissertations
This dissertation describes the design and tunability of new magnetic and optical materials, emphasizing the intricate relationship between their crystal structures and their optical, electronic, and magnetic properties.
Two new frustrated magnets, ANd(SO4)2 (A = Rb, Cs), were designed and synthesized to examine the influence of the the counter cation A site in Nd lanthanide materials featuring a distorted triangular magnetic lattice with S = 3/2. This work demonstrates how the tunability of magnetic and photoluminescent properties can be achieved through the A sites, with findings validated through density functional theory calculations.
AMnTeO6 (A = Ca, …
Remote Onboarding Of Software Developers: Leveraging Virtual Reality And Ai Tools, James Dominic
Remote Onboarding Of Software Developers: Leveraging Virtual Reality And Ai Tools, James Dominic
All Dissertations
Software development teams add newcomers to accommodate the increasing demand, complexity of software solutions, and turnover. Onboarding newcomers is expensive and error-prone. It can take up to three years for a newcomer to become an expert on a project. Onboarding techniques described in the current literature focus on collocated teams. As more teams are adopting remote and distributed team structures, I address this research gap in understanding remote onboarding for software developers. I present my research on the use of Virtual Reality (VR) for remote software developer onboarding. I discuss a VR remote pair programming environment. With positive outcomes, pair …
Some Experiments In Additive Number Theory, Yunan Wang
Some Experiments In Additive Number Theory, Yunan Wang
All Dissertations
This dissertation explores fundamental conjectures in number theory, focusing on the distribution patterns of representation functions in prime pairs. The work concentrates on twin primes, cousin primes, and primes separated by six units, offering a fresh heuristic interpretation of the Hardy-Littlewood correction factor. The analysis progresses to investigate the partition function for prime pairs in the form $(p, p+k)$, specifically for $k = 2, 4, 6$. The study culminates in the derivation of a general formula for prime pairs $(p, p+d)$, where $d$ is an even integer. Drawing on the insights gleaned from examining the correction factor, this dissertation proposes …