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Articles 14071 - 14100 of 291657

Full-Text Articles in Physical Sciences and Mathematics

Artificial Intelligence In Modern Game Development, Karan Raval May 2025

Artificial Intelligence In Modern Game Development, Karan Raval

ART 108: Introduction to Games Studies

Artificial intelligence has transformed the landscape of game development in ways early pioneers could only imagine. In my project I explore four major phases of AI evolution: classical AI methods, the rise of machine learning, the advent of transformer architectures, and a spirited debate about whether transformers truly think. To illustrate these shifts I use examples like MYCIN, which helped doctors decide treatments, and Deep Blue, which beat a world chess champion. You’ve probably lost track of time exploring an open world that adapts to your choices, right? That sense of immersion is powered by AI behind the scenes. From …


Optimized Filtrations For Stormwater Quality Improvement By Porous Media–Biochar Applications: Column Experiments And Inverse Modeling, Sumiaya Amin Preota, Chu-Lin Cheng, Myung Hwangbo, Jongsun Kim May 2025

Optimized Filtrations For Stormwater Quality Improvement By Porous Media–Biochar Applications: Column Experiments And Inverse Modeling, Sumiaya Amin Preota, Chu-Lin Cheng, Myung Hwangbo, Jongsun Kim

School of Earth, Environmental, & Marine Sciences Faculty Publications

Stormwater reuse plays a critical role under changing climates and increasing water demands. This study investigates the removal efficacy of lead (Pb2+) and ammonia (NH3) using sand and rice husk (RH) biochar for potential stormwater quality improvements and treatments. Column experiments combined with HYDRUS inverse modeling were conducted to optimize adsorption isotherms from breakthrough curves. Among linear and non-linear models, the Langmuir and Freundlich models performed better for sand and biochar, respectively. RH biochar showed much higher adsorption capacity of both Pb2+ (4.813 mg/g) and NH3 (6.188 mg/g). In contrast, sand showed a relatively limited adsorption capacity for Pb2+ (0.118 …


Controls On Nutrient And Sediment Export In A Non-Perennial Agricultural Stream, Kathleen Cutting May 2025

Controls On Nutrient And Sediment Export In A Non-Perennial Agricultural Stream, Kathleen Cutting

Graduate Theses and Dissertations

Climate change is expected to increase flow variability and intermittency in streams, changing the magnitude and timing nutrient and sediment delivery. This may exacerbate water quality issues in agricultural landscapes, where nutrient and sediment inputs are often elevated. Elevated nutrients can drive eutrophication in downstream waterways, and excess sediment loss can decrease primary productivity. Non-perennial headwater streams are particularly vulnerable to the impacts of climate change and agriculture as they serve as key sites for nutrient cycling at the terrestrial-aquatic interface. Despite their importance, the interactive effects of agriculture and stream intermittency, as well as unpaved roads in rural watersheds …


2025 May 1 - Tennessee Weekly Drought Summary, Tennessee Climate Office, East Tennessee State University May 2025

2025 May 1 - Tennessee Weekly Drought Summary, Tennessee Climate Office, East Tennessee State University

Tennessee Climate Office Weekly Drought Summaries

No abstract provided.


Silver Nanoparticles In Ammonia Sensing And Photovoltaics, Madhuka Liyanage May 2025

Silver Nanoparticles In Ammonia Sensing And Photovoltaics, Madhuka Liyanage

All Dissertations

Nanocomposite films (NCF) containing silver nanoparticles (AgNPs), separated by thin layers of silica/poly-4-vinylpyridine/polyvinylpyrrolidone, were fabricated via drop casting, spin coating, dip coating on glass substrate and drop casting on nylon filter membranes. The more uniform films were produced by drop casting on nylon filter membranes due to their solvent wicking properties. The films demonstrate electrical conductivity that varies in response to moist ammonia and water vapors. The changes in conductivity are attributed to hydrogen bonding between ammonia and water molecules with the silica/polymer layers, as well as the direct adsorption of ammonia onto the silver surface. Notably, NCFs with polyvinylpyrrolidone …


Growth, Cladding, And Characterization Of Single Crystal Optical Fiber: The Next Evolution In Directed Energy Systems, Allen Benton May 2025

Growth, Cladding, And Characterization Of Single Crystal Optical Fiber: The Next Evolution In Directed Energy Systems, Allen Benton

All Dissertations

High-power fiber lasers are steadily increasing in maximum power and rapidly approaching theoretical maximum power output from a single fiber aperture. The low thermal conductivity of silica fibers is an inherent limitation to the dissipation of heat from the fiber core, and the buildup of heat within the laser gain media is the principal driver of transverse mode instability within fiber systems. This limitation necessitates the exploration of alternate fiber host materials. Due to their high thermal conductivity, excellent transmission range, ability to host most of the optically active rare earth ions, and success as bulk laser materials, single-crystalline YAG …


Qualitative And Quantitative Analysis Of New Psychoactive Substances And Related Metabolites Using Liquid Chromatography-Ion Mobility-Mass Spectrometry (Lc-Im-Ms), Ralph Aderorho May 2025

Qualitative And Quantitative Analysis Of New Psychoactive Substances And Related Metabolites Using Liquid Chromatography-Ion Mobility-Mass Spectrometry (Lc-Im-Ms), Ralph Aderorho

All Dissertations

The increasing prevalence of novel psychoactive substances (NPS) in illicit drug markets has posed significant challenges for forensic and clinical toxicology, primarily due to the structural similarity and diversity among these compounds. This dissertation investigates the application of advanced liquid chromatography-ion mobility-mass spectrometry (LC-IM-MS/MS) techniques, using the high-resolution Structures for Lossless Ion Manipulations (SLIM) platform and the drift tube ion mobility spectrometry (DT-IMS), for the qualitative and quantitative analysis of various types of synthetic opioids, synthetic cannabinoids, psychedelics and xylazine. By combining IMS separations with mass spectrometry and targeted chemical derivatization, this work enhances the ability to distinguish and characterize …


Hydrothermal Synthesis Of Single-Crystal Magnetic Oxides, Bhakti Patel May 2025

Hydrothermal Synthesis Of Single-Crystal Magnetic Oxides, Bhakti Patel

All Dissertations

Multifunctional materials are systems that have two or more properties of interest. Some of these features are polar axes, chirality, magnetic ions, triangular arrangements, and/or magnetically silent building blocks. Various combinations of these properties can result in chiral ferromagnetism, multiferroic magnetoelectric behavior, antiferromagnetism, and quantum spin liquids and spin ices. By tuning these structure-property relations, quantum computing, memory, and sensors may be created. Large single crystals allow for a better understanding of the magnetic behavior of these crystals since they can be oriented in a magnetic field. Inorganic single crystals have a wide range of applications but growing high-quality single …


The Evolution Of Nanoparticles In Nanoparticle Doped Optical Fibers, Mary Cahoon May 2025

The Evolution Of Nanoparticles In Nanoparticle Doped Optical Fibers, Mary Cahoon

All Dissertations

Optical fiber and fiber laser technologies based on silica glass are critical to many technologies today. One method to improve the optical performance of laser fibers is engineer the local environment around the active elements in the glass. To that end, this Dissertation focused on the fabrication and characterization of fibers made with nanoparticles incorporated into the glass to control the local composition. First, the nanoparticle composition and structure was analyzed as it evolved from from the initially-synthesized form to incorporation into the dense aluminum-silicate glass. The aluminum oxide in the glass was found to be important not only to …


Robust And Efficient Solvers For Physics-Based Pde’S, Elizabeth Hawkins May 2025

Robust And Efficient Solvers For Physics-Based Pde’S, Elizabeth Hawkins

All Dissertations

This work was partially supported by the U.S. Department of Energy under award DE- SC0025292, by NSF grant DMS 2152623, and by NSF grant DMS 2011490.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Mathematical Multifaceted Integrated Capability Centers (MMICCs) program, under Field Work Proposal 22-025291 (Multifaceted Math- ematics for Predictive Digital Twins (M2dt)), Field Work Proposal 23-020467, and Computing and Information Sciences (CIS) investment area in the Laboratory Directed Research and Development program at Sandia National Laboratories. This written work is authored by an employee …


Decision Space Decomposition For Multiobjective Programs, Emma Soriano May 2025

Decision Space Decomposition For Multiobjective Programs, Emma Soriano

All Dissertations

Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca and Miguel (2017), and by the block- coordinate descent for single objective optimization problems, we present a decom- position theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements are used to retrieve the overall minimal elements. We apply this approach to strictly convex MOPs de- composing their decision space into lines. The line decomposition benefits from the fact that a multiobjective line search problem is equivalent to solving a collection of single objective …


Biophysical Studies Of Nucleic Acid - Small Molecule Recognition, Andrea Conner May 2025

Biophysical Studies Of Nucleic Acid - Small Molecule Recognition, Andrea Conner

All Dissertations

The presented work is a collection of studies performed to examine small molecule recognition of nucleic acids. Recognition of nucleic acids was examined using two types of small molecules: aminoglycosides and Hoechst dyes. Chapter One focuses on established experimental techniques (i.e. absorbance, isothermal titration calorimetry, flow cytometry, cell microscopy, etc.) in small molecule recognition of nucleic acids. The emphasis of studies in the group has been on two focus areas. (i) Thermodynamic characterization of mixed A-form and B-form DNA or RNA conformation with aminoglycosides, particularly neomycin-class. (ii) Characterization of new Hoechst-morpholine (HT-MO) derivatives’ interactions with nucleic acids.

Focus area (i) …


Learning Through Online Participation: From Breakout Rooms To Discord, Makayla Moster May 2025

Learning Through Online Participation: From Breakout Rooms To Discord, Makayla Moster

All Dissertations

For software development teams, teamwork is an essential part of their day-to-day lives. However, due to the aftermath of the COVID-19 pandemic, more companies have allowed employees to have more hybrid and remote work options than before. As more companies are adopting hybrid and remote workstyles, we need to ensure that we are preparing the next batch of young software developers to conduct teamwork in remote and hybrid settings. In this dissertation, I address the tools students use for teamwork and how to improve their teamwork inside and outside of the classroom. I present my research on improving student experiences …


Countering Deficit Narratives Through A Blackcrit Lens By Examining Case Studies Of Black College Mathematics Students’ Classroom Experiences, Akhenaton Wilbourn May 2025

Countering Deficit Narratives Through A Blackcrit Lens By Examining Case Studies Of Black College Mathematics Students’ Classroom Experiences, Akhenaton Wilbourn

All Dissertations

This dissertation examines the lived experiences of 11 Black college mathematics students at their predominantly white institution (PWI) through the lens of Black Critical Theory (BlackCrit) to counter deficit narratives about the racial achievement gap (RAG) in mathematics education courses. Deficit narratives often attribute disparities between Black and white students’ mathematical performance to assumed deficiencies in Black students’ abilities rather than systemic inequities, historical marginalization, and ongoing anti-Blackness in educational settings (Cobb & Russell, 2015; Kress, 2021). Using multiple case studies, this study explores how anti-Blackness manifests in mathematics classrooms, how students navigate tensions between multiculturalism, neoliberal educational policies, and …


Probing The 'Mev Gap': Discovery And Characterization Of Persistent And Transient Mev-Gev Gamma-Ray Sources With The Fermi Large Area Telescoope, Scott Joffre May 2025

Probing The 'Mev Gap': Discovery And Characterization Of Persistent And Transient Mev-Gev Gamma-Ray Sources With The Fermi Large Area Telescoope, Scott Joffre

All Dissertations

The MeV Gap is a moniker for the energy regime E~0.1-100 MeV that has lacked sensitive observations for the last 20 years. This is not out of scientific disinterest, but observational challenges. The only instrument currently available to make observations in the MeV Gap is the Fermi Large Area Telescope (LAT). For the first time ever, Fermi-LAT has been leveraged to push its observational capabilities to its absolute lower energy limit to end this 20-year observational gap. Observing the MeV sky is imperative for identifying some of the most luminous galaxies in the Universe known as blazars. The brightest blazars …


Toward The Application Of Natural Language Processing In Electronic Health Record Analysis For Taxonomy Development, Latoya Mcdonald May 2025

Toward The Application Of Natural Language Processing In Electronic Health Record Analysis For Taxonomy Development, Latoya Mcdonald

All Dissertations

Electronic health records (EHRs) are pivotal resources for nurse practice because they increase the timeliness and reliability of patient information at the point of care and support access by multiple healthcare providers and the individual patients themselves. However, it is widely recognized that data extraction from EHRs is challenging due to the variability in the language used in clinical care notes and the lack of standardized terminology across healthcare systems. The broad objective of this dissertation is to develop taxonomy-based classification models for nursing care by applying feature engineering approaches to EHRs that include nursing care of ostomy patients following …


Development Of Small-Molecule Inhibitors For Bacteroides, Naegleria, And Toxoplasma Microorganisms And Synthesis Of N-Heterocycles From Thiolated Ene-Ynes And Azodicarboxylates, Samuel Kwain May 2025

Development Of Small-Molecule Inhibitors For Bacteroides, Naegleria, And Toxoplasma Microorganisms And Synthesis Of N-Heterocycles From Thiolated Ene-Ynes And Azodicarboxylates, Samuel Kwain

All Dissertations

Humans and microorganisms are intricately interconnected, with microbes constituting an essential component of human biology and ecology. This interdependence necessitates a delicate balance between leveraging beneficial microbes and mitigating the impact of harmful ones. The human gut microbiome, home to trillions of microorganisms, predominantly comprises commensal species that support health. However, dysbiosis within this ecosystem has been linked to serious diseases. For instance, an overrepresentation of Bacteroides species is associated with Type I diabetes mellitus (T1D) and various chronic gut disorders, including ulcerative colitis, inflammatory bowel disease, celiac disease, and colorectal cancer. Similarly, Naegleria fowleri, a free-living amoeba, causes …


The Spectral Asymptotics Of Toeplitz Operators On Hilbert Spaces Of Analytic Functions, Trevor Camper May 2025

The Spectral Asymptotics Of Toeplitz Operators On Hilbert Spaces Of Analytic Functions, Trevor Camper

All Dissertations

Many physical systems, whether they are ocean waves or particles moving through space, can be described using the mathematical language of “partial differ- ential equations.” In many circumstances, it is useful to study how these equations amplify an input to the equation, in which case the amplification factor is called an “eigenvalue.” The usefulness of these amplification factors is that they can be used to describe properties of the physical system. In this dissertation, I have studied this amplification factor for a related set of equations called “Toeplitz operators.” In par- ticular, I have studied eigenvalues using statistical techniques. The …


The Effect Of Nuclear Isomers On S-Process Nucleosynthesis, Jaad Tannous May 2025

The Effect Of Nuclear Isomers On S-Process Nucleosynthesis, Jaad Tannous

All Dissertations

s-Process nucleosynthesis is a process in which stars produce elements of mass range A = 57 to 210. Since the days of B2FH, immense work has gone into quantifying and computing s-process yields and pathways. We expand upon said work along two fronts. The first front sets up the framework for proper treatment of nuclear isomers in network calculations. We apply the framework to study 85Kr, which is a pivotal isotope in the s-process chain that affects the abundance yields of Strontium and Rubidium isotopes. In particular, we are interested in the ratio of 88Sr/86Sr and 87Rb which are important …


A System And Method For Measuring Spatially Varying Surface Appearances With A Study Of Feathers, Jessica Baron-Lis May 2025

A System And Method For Measuring Spatially Varying Surface Appearances With A Study Of Feathers, Jessica Baron-Lis

All Dissertations

Real-world materials, particularly biological structures such as feathers exhibit complex appearances that vary spatially across their surfaces. The field of computer graphics provides a means of understanding such surfaces through material modeling which uses both analytical models and data acquired from light-surface interactions. There are many efforts within the past decade in measuring materials for graphics, but common limitations in these works include not accounting for spatially varying properties and reliance on neural networks and synthetic datasets.

Feathers from modern birds present diverse appearances due to how light interacts with their unique hierarchical microstructures. Variations in those structures lead to …


A Systemic Approach To Maximize Heterogeneous System Performance, Thomas L. Randall May 2025

A Systemic Approach To Maximize Heterogeneous System Performance, Thomas L. Randall

All Dissertations

Continuous increases in high performance computing (HPC) throughput have served as catalysts for industry and scientific advancement in countless manners that have fundamentally shaped our modern world. Our demands on compute resources continue to scale, but the limitations of Ahmdal’s law and Dennard scaling have proven increasingly difficult to overcome when approached solely through hardware or software design. Furthermore, many HPC applications fail to utilize the collective system’s performance, even on the most advanced supercomputers.

However, the resurgence of AI in the industry has promoted an explosion of hardware and software codesign that have fueled massive improvements in GPU design …


Domain Decomposition For Coupled Systems Of Fluid-Structure Interaction And Numerical Modeling For Thin Film Polymers, Amy De Castro May 2025

Domain Decomposition For Coupled Systems Of Fluid-Structure Interaction And Numerical Modeling For Thin Film Polymers, Amy De Castro

All Dissertations

We consider two primary areas of physical application in this work: fluid interaction systems with either linear elastic structures or with poroelastic structures, and thin film polymers, where the majority of the work focuses on the fluid-structure interaction systems.

In the first chapter, we present a strongly coupled partitioned method for fluid structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier (LM). We prove that both the semi-discrete and fully discrete formulations are well-posed. To derive the partitioned scheme, a Schur complement equation, which implicitly expresses the Lagrange multiplier and the fluid …


The Role Of The Neutral Wind In Observations Of High-Latitude Ionospheric Energy Transfer, Andrew M. Pepper May 2025

The Role Of The Neutral Wind In Observations Of High-Latitude Ionospheric Energy Transfer, Andrew M. Pepper

All Dissertations

Joule heating results from the collisional interaction between ions and neutrals and serves as a crucial mechanism for energy transfer between Earth's magnetosphere and ionosphere-thermosphere system, particularly at high latitudes. This dissertation investigates the modulation of Joule heating by altitude-resolved neutral winds, electric fields, and conductivity variations through multi-instrument observational analysis and modeling that incorporates both in-situ and ground-based sources to measure the main drivers of ion-neutral coupling. The observations presented consistently demonstrate a dual regulatory effect of the neutral wind on energy deposition that varies systematically with both geomagnetic activity level and proximity to auroral boundaries. In regions characterized …


Quantifying The Effects Of Urbanization On Stream Nutrient Loads And Decomposition, Caroline Anscombe May 2025

Quantifying The Effects Of Urbanization On Stream Nutrient Loads And Decomposition, Caroline Anscombe

Graduate Theses and Dissertations

Urban stream syndrome (USS) refers to the common symptoms of degradation in urban streams globally. Two symptoms of USS are increased nutrient and salt concentrations in streams, affecting ecosystem structure and function. Excess nutrients negatively impact freshwater ecosystems, placing downstream habitats at risk of eutrophication and harmful algal blooms. Excess salt runoff, derived from road salt application, is toxic to freshwater organisms and affects leaf litter decomposition, the base of aquatic food webs. Here, I aimed to quantify the effects of nutrient pollution and salinization on urban water quality and ecosystem function. Despite the widespread consequences of nutrient pollution, most …


A Dg-Algebra Structure With Divided Powers On The Generalized Taylor Resolution, Raul F, Alvarez May 2025

A Dg-Algebra Structure With Divided Powers On The Generalized Taylor Resolution, Raul F, Alvarez

Theses and Dissertations

This thesis investigates the construction of a DG Γ-algebra structure on the Generalized Taylor Resolution (GTR) associated with monomial ideals. The classical Taylor resolution is known for providing a free but generally non-minimal resolution, leading to computational challenges and inefficiencies in algebraic analysis. In contrast, the GTR preserves essential algebraic structures while optimizing the resolution process, offering a more efficient and comprehensive framework for studying monomial ideals.

We introduce a novel DG Γ-structure that incorporates divided powers into the GTR, enhancing its multiplicative and homological properties. This structure preserves strict graded commutativity and is fully compatible with the differential graded …


2022 Annual Operations And Maintenance Report 2022 Bres Annual Summary Report For Work Completed In Quadrant 2, Butte-Silver Bow Department Of Reclamation And Environmental Services May 2025

2022 Annual Operations And Maintenance Report 2022 Bres Annual Summary Report For Work Completed In Quadrant 2, Butte-Silver Bow Department Of Reclamation And Environmental Services

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.


Building Toward A Text-Based Intervention For Parents Of Suicidal Adolescents Seeking Emergency Department Care: A Pilot Randomized Controlled Trial., Ewa Czyz, Inbal Nahum-Shani, Cynthia Ewell Foster, Valerie Micol, Amanda Jiang, Nadia Al-Dajani, Alejandra Arango, Maureen Walton, Victor Hong, Sheikh Iqbal Ahamed, Cheryl King May 2025

Building Toward A Text-Based Intervention For Parents Of Suicidal Adolescents Seeking Emergency Department Care: A Pilot Randomized Controlled Trial., Ewa Czyz, Inbal Nahum-Shani, Cynthia Ewell Foster, Valerie Micol, Amanda Jiang, Nadia Al-Dajani, Alejandra Arango, Maureen Walton, Victor Hong, Sheikh Iqbal Ahamed, Cheryl King

Computer Science Faculty Research and Publications

Objective: The growing demand for emergency department (ED) care for suicidal ideation and attempts in adolescents calls for effective interventions preventing post-ED recurrence of suicidal crises. Parents are tasked with implementing postdischarge suicide prevention recommendations, often with little support. To address this need, this study examined a parent-facing texting intervention targeting parental engagement in suicide prevention activities to lower youth suicide risk after discharge. Method: A pilot randomized controlled trial was conducted with 120 parents (83.3% mothers) and their adolescents (ages 13–17, 65.8% female, 75.0% White) presenting to an ED with suicide risk concerns. Parents were randomized to a control …


Functional Consequences Of Lysine Acetylation Of Phosphofructokinase Isozymes, Xinyu Lin, Nour Fatema, Qinglei Gan, Chenguang Fan May 2025

Functional Consequences Of Lysine Acetylation Of Phosphofructokinase Isozymes, Xinyu Lin, Nour Fatema, Qinglei Gan, Chenguang Fan

Chemistry & Biochemistry Faculty Publications and Presentations

Phosphofructokinase (Pfk) catalyzes the phosphorylation of fructose 6-phosphate and is a key regulatory point in the glycolysis pathway. Multiple lysine residues in both Pfk isozymes, PfkA and PfkB, have been identified to be acetylated in Escherichia coli by proteomic studies, but no studies have been implemented to further characterize these acetylation events. To investigate the role of Pfk acetylation, the genetic code expansion strategy was used to generate homogeneously acetylated Pfk variants at target lysine sites that have been reported to be acetylated in nature. We found that acetylation of K309 of PfkA and K27 of PfkB decreased PfK enzyme …


A Comprehensive Review Of Carbon Sequestration And Its Assessment Techniques Using Remote Sensing And Geospatial Methods, Imen Ben Salem May 2025

A Comprehensive Review Of Carbon Sequestration And Its Assessment Techniques Using Remote Sensing And Geospatial Methods, Imen Ben Salem

All Works

Global warming has elevated carbon sequestration as a critical strategy for mitigating climate change, while enhancing sustainability in productivity. Agricultural land use systems contribute substantially to CO2 emissions due to crop residues, shifting cultivation practices, low-biomass crops, land degradation, and deforestation. The significant rise in CO2 emissions over the past thirty years is associated with burning fossil fuels, leading to substantial environmental changes, including global warming. Remote sensing (RS) and Geographic Information Systems (GIS) are advanced geospatial technologies that facilitate the rapid evaluation of terrestrial carbon stock over extensive regions. An integrated RS-GIS approach for carbon stock estimation and precision …


Relaxation Maximum-Based Iteration Method For Solving The Generalized Absolute Value Equation, Ximing Fang, Zhidong Wang, Zhijun Qiao May 2025

Relaxation Maximum-Based Iteration Method For Solving The Generalized Absolute Value Equation, Ximing Fang, Zhidong Wang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The generalized absolute value equation (GAVE) has wide applications in scientific computing. Establishing a high performance computing method to solve the GAVE is a hot research topic in recent years. In this paper, with the aid of the maximum function, the GAVE is decomposed of two equations, and then we present the relaxation maximum-based (RM) iteration method. To see the feasibility of the method, we discuss the necessary and sufficient conditions for the GAVE to have a unique solution. Next, the convergence analysis of the RM iteration is discussed under some convergence conditions. Moreover, some numerical examples of low and …