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Roots Of Quaternionic Polynomials And Automorphisms Of Roots, Olalekan Ogunmefun 2023 East Tennessee State University

Roots Of Quaternionic Polynomials And Automorphisms Of Roots, Olalekan Ogunmefun

Electronic Theses and Dissertations

The quaternions are an extension of the complex numbers which were first described by Sir William Rowan Hamilton in 1843. In his description, he gave the equation of the multiplication of the imaginary component similar to that of complex numbers. Many mathematicians have studied the zeros of quaternionic polynomials. Prominent of these, Ivan Niven pioneered a root-finding algorithm in 1941, Gentili and Struppa proved the Fundamental Theorem of Algebra (FTA) for quaternions in 2007. This thesis finds the zeros of quaternionic polynomials using the Fundamental Theorem of Algebra. There are isolated zeros and spheres of zeros. In this thesis, we …


Impact Of Cover Crop Species Diversity On Soil Nutrient Availability And Crop Productivity, Amanda Kramer 2023 University of Tennessee, Knoxville

Impact Of Cover Crop Species Diversity On Soil Nutrient Availability And Crop Productivity, Amanda Kramer

Masters Theses

Cover crops provide multiple environmental benefits that improve both soil and water quality; however, farmers only utilize them on approximately 5% of harvested U.S. cropland. Low adoption rates are attributed to yield impact concerns, seed and planting costs, and lack of advocacy. This study, which began in October 2019, assessed the effects of nitrogen rate and cover crop diversity on weed biomass, soil coverage, in-situ residue decomposition, soil nitrogen and phosphorus availability, and cash crop yield to better understand the costs and benefits of cover crop adoption at two locations in Tennessee (Milan and Spring Hill). Treatments were replicated 4 …


The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi 2023 Western University

The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi

Electronic Thesis and Dissertation Repository

Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a …


Using Integral Projection Models To Explore Management Strategies For Silver Carp (Hypophthalmichthys Molitrix), Cameron Coles, Elizabeth Balas, James Peirce, Greg Sandland, Richard Erickson 2023 Cornell University

Using Integral Projection Models To Explore Management Strategies For Silver Carp (Hypophthalmichthys Molitrix), Cameron Coles, Elizabeth Balas, James Peirce, Greg Sandland, Richard Erickson

Spora: A Journal of Biomathematics

Silver carp (Hypophthalmichthys molitrix) are planktivorous fish that were originally introduced to the United States for use in fish production ponds and have since escaped these enclosures and are invading the Mississippi River Basin. The silver carp invasion of the Illinois River has a myriad of negative effects on native ecosystems. In this paper, we introduce key dependencies that are likely important in the population dynamics of silver carp: length-dependent egg production and density-dependent growth. Using movement data between two adjacent pools of the Illinois River, we conduct numerical simulations to explore the theoretical effect of harvesting and …


Commutators On Fock Spaces, Daniel Alpay, Paula Cerejeiras, Uwe Kähler, Trevor Kling 2023 Chapman University

Commutators On Fock Spaces, Daniel Alpay, Paula Cerejeiras, Uwe Kähler, Trevor Kling

Mathematics, Physics, and Computer Science Faculty Articles and Research

Given a weighted ℓ2 space with weights associated with an entire function, we consider pairs of weighted shift operators, whose commutators are diagonal operators, when considered as operators over a general Fock space. We establish a calculus for the algebra of these commutators and apply it to the general case of Gelfond–Leontiev derivatives. This general class of operators includes many known examples, such as classic fractional derivatives and Dunkl operators. This allows us to establish a general framework, which goes beyond the classic Weyl–Heisenberg algebra. Concrete examples for its application are provided.


Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment, Tyler Evans 2023 Southern Methodist University

Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment, Tyler Evans

Mathematics Theses and Dissertations

For decades, it has been observed that broad-beam irradiation of semiconductor surfaces can lead to spontaneous self-organization into highly regular patterns, sometimes at length scales of only a few nanometers. Initial theory was largely based on erosion and redistribution of material occurring on fast time scales, which are able to produce good agreement with certain aspects of surface evolution. However, further experimental and theoretical work eventually led to the realization that numerous effects are active in the irradiated target, including stresses associated with ion-implantation and the accumulation of damage leading to the development of a disordered, amorphous layer atop the …


The Use Of Probability In Quantum Mechanics To Calculate Measurement Outcomes, Hannah E. Collins 2023 Gettysburg College

The Use Of Probability In Quantum Mechanics To Calculate Measurement Outcomes, Hannah E. Collins

CAFE Symposium 2023

The concept of probability can help measure some of the possible outcomes of different experiments in the field of quantum mechanics. Those experiments include Thomas Young's double slit experiment, the Schrödinger equation, the wave function, and the Born Rule, which all make use of probability to predict the placement of certain subatomic particles including photons of light, in the experiments. In this project, the manner in which probability does this is explored in depth.


U.S. Energy Information Administration Information Resources, Bert Chapman 2023 Purdue University

U.S. Energy Information Administration Information Resources, Bert Chapman

Libraries Faculty and Staff Presentations

Provides information about the resources produced by U.S. Department of Energy's Energy Information Administration. These resources cover energy statistics for U.S., states, the United States, and foreign countries. They also cover energy products as varied as coal, natural gas, nuclear energy, petroleum, and renewable energy.


Estimate Of The Random Match Frequency Of Acquired Characteristics In A Forensic Footwear Database, Alyssa N. Smale 2023 West Virginia University

Estimate Of The Random Match Frequency Of Acquired Characteristics In A Forensic Footwear Database, Alyssa N. Smale

Graduate Theses, Dissertations, and Problem Reports

When analyzing footwear impression evidence, one of the goals of an examiner is to determine if an exemplar shoe could be the source of an impression found at a crime scene. This opinion is based on an assessment of the similarity of class characteristics and randomly acquired characteristics (RACs) between the known and questioned impressions, as well as the rarity of the observed characteristics. The primary aim of this research was to estimate the random match frequency of randomly acquired characteristics (RAC-RMF) within a forensic footwear database to determine the frequency of RACs with geometric similarity occurring in the same …


Reviving Knowledges Through Play And Resistance: The Case Of Navajo Conceptions Of Space, Daniel Ness, Richard D. Sawyer 2022 St. John's University

Reviving Knowledges Through Play And Resistance: The Case Of Navajo Conceptions Of Space, Daniel Ness, Richard D. Sawyer

Northwest Journal of Teacher Education

The authors explore a possible cause of epistemicidal predispositions of the dominant Eurocentric curricula. They posit that one way to determine a plausible contributing factor of this increasing devastation is to consider epistemicide through the lens of intellectual development. To do this, the authors examine parallel patterns of behavior in the domains of developmental and cognitive psychology. The authors then discuss an alternative framework to the Western conception of space within formal K-12 education by presenting the Navajo conception of space and play. Throughout the paper, the authors argue that all students—and especially those living in poverty in commercially constructed, …


Orbit Propagation And Determination Algorithms For Satellite Ground Stations, Shamma Esmaeel Jamali 2022 United Arab Emirates University

Orbit Propagation And Determination Algorithms For Satellite Ground Stations, Shamma Esmaeel Jamali

Theses

The satellite orbital parameters are essential for satellite operations. With these parameters, it is possible to estimate the satellite position in the recent past and near future, which is essential to effectively plan satellite operations and associate satellite telemetry with geographical locations.
However, for small or medium satellite operators who do not possess the infrastructure required to track their satellites, the problem of determining the satellite orbit is problematic. To access the orbit for their satellites, these organizations have to rely on third parties such as Celestrak. These entities provide the service free of charge but do not provide orbital …


Electrocatalysis By Design: Low Dissolution Counter Electrode And Highly Efficient Nanostructured Electrocatalysts, Menna Hasan 2022 American University in Cairo

Electrocatalysis By Design: Low Dissolution Counter Electrode And Highly Efficient Nanostructured Electrocatalysts, Menna Hasan

Theses and Dissertations

Water Electrolysis is one of the most promising techniques to generate H2 gas, which is an alternative clean source of energy. Hydrogen provides almost three times the energy provided by gasoline, helping to solve the global warming problem caused by the currently used fossil fuels. As any electrochemical reaction is composed of two half reactions, a setup of working and counter electrodes is used to study the catalytic activity towards the targeted reaction, where each electrode carries one of the two-half reactions. In this dissertation, the stability of a number of the commonly used counter electrodes was examined to identify …


Open Source Solutions In Experimental Design: An Introduction To The Symposium, Richelle L. Tanner, Kirt L. Onthank 2022 Chapman University

Open Source Solutions In Experimental Design: An Introduction To The Symposium, Richelle L. Tanner, Kirt L. Onthank

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

The Open Science movement has increased dramatically in popularity with deserved calls to action around transparency, access to resources, and inclusion in our field. However, its practical applications within experimental design have been slow to uptake, with researchers unsure where to even start with the dizzying array of open source hardware and software solutions available. The perceived time investment and unknown cost, especially in implementing open source hardware, has stagnated the implementation of inexpensive experimental solutions, but we sought to increase awareness to lower the barrier to participation in this space. While there are countless technical and financial advantages to …


On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen 2022 Chapman University

On Superoscillations And Supershifts In Several Variables, Yakir Aharonov, Fabrizio Colombo, Andrew N. Jordan, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen

Mathematics, Physics, and Computer Science Faculty Articles and Research

The aim of this paper is to study a class of superoscillatory functions in several variables, removing some restrictions on the functions that we introduced in a previous paper. Since the tools that we used with our approach are not common knowledge we will give detailed proof for the case of two variables. The results proved for superoscillatory functions in several variables can be further extended to supershifts in several variables.


Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs 2022 University of Nebraska at Omaha

Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

UNO Student Research and Creative Activity Fair

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding to …


Virtual Expeditions Facilitated By Open Source Solutions Broaden Student Participation In Natural History Research, Richelle L. Tanner, Talia Y. Moore 2022 Chapman University

Virtual Expeditions Facilitated By Open Source Solutions Broaden Student Participation In Natural History Research, Richelle L. Tanner, Talia Y. Moore

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

From its genesis in the Victorian era as an activity for the elite to today's emphasis on “Big Data” and continuous monitoring, natural history has a prominent role in scientific discoveries for many fields. However, participation in field expeditions is limited by funding, space, accessibility, and safety constraints. Others have detailed the active exclusion of minoritized groups from field expeditions and harm/discrimination faced by the few who do participate, but we provide one solution to broaden opportunities for participation in natural history: Virtual Expeditions. Virtual Expeditions are broadly defined as open source, web-facilitated research activities designed to analyze bulk-collected digital …


(R1507) Mathematical Modeling And Analysis Of Seqiahr Model: Impact Of Quarantine And Isolation On Covid-19, Manoj Kumar Singh, . Anjali 2022 Banasthali Vidyapith

(R1507) Mathematical Modeling And Analysis Of Seqiahr Model: Impact Of Quarantine And Isolation On Covid-19, Manoj Kumar Singh, . Anjali

Applications and Applied Mathematics: An International Journal (AAM)

At the moment in time, an outbreak of COVID-19 is transmitting on from human to human. Different parts have different quality of life (e.g., India compared to Russia), which implies the impact varies in each part of the world. Although clinical vaccines are available to cure, the question is how to minimize the spread without considering the vaccine. In this paper, via a mathematical model, the transmission dynamics of novel coronavirus with quarantine and isolation facilities have been proposed. The examination of the proposed model is set in motion with the boundedness and positivity of the solution, sole disease-free equilibrium, …


In-Phantom Film Measurements Of Two Treatment Planning Systems For Single-Fraction Spine Sbrt, Michael J. Taylor 2022 Louisiana State University and Agricultural and Mechanical College

In-Phantom Film Measurements Of Two Treatment Planning Systems For Single-Fraction Spine Sbrt, Michael J. Taylor

LSU Master's Theses

Purpose: Treatment planning accuracy for spine stereotactic body radiation therapy (SBRT) varies depending on the dose calculation algorithm utilized in the treatment planning system (TPS). This project compared the end-to-end accuracy between spine SBRT plans calculated in a convolution-superposition based TPS (TPSCS) and Monte Carlo based TPS (TPSMC) with radiochromic film measurements. The hypothesis was that TPSMC would calculate the dose gradient in the critical region between the vertebral body and the spinal cord more accurately than TPSCS.

Methods: Single-fraction spine SBRT treatments following RTOG 0631 and local institutional guidelines were planned in …


Use Of Consumer Grade Small Unmanned Aerial Systems (Suas) For Mapping Storm Damage In Forested Environments, James Dewey Cox 2022 Mississippi State University

Use Of Consumer Grade Small Unmanned Aerial Systems (Suas) For Mapping Storm Damage In Forested Environments, James Dewey Cox

Theses and Dissertations

Storm damages to forested environments pose significant challenges to landowners, land managers, and conservationists alike. Damage scope and scale assessments can be difficult, costly, and time consuming with conventional pedestrian survey techniques. Consumer grade sUAS technology offers an efficient, cost-effective way to accurately assess storm damage in small to moderate sized survey areas (less than 10 km²). Data were collected over a 0.195 km² area of damaged timber within the Kisatchie National Forest in Central Louisiana using a DJI Mavic 2 Pro drone. Collected imagery was processed into an orthomosaic using Agisoft Metashape Professional with a resulting ground sampling distance …


The Impact Of Sea-Level Rise In Numerically Modeled Landfalling Hurricanes: Katrina And The Gulf Coast., Serenity Nadirah Mercuri 2022 University of Louisville

The Impact Of Sea-Level Rise In Numerically Modeled Landfalling Hurricanes: Katrina And The Gulf Coast., Serenity Nadirah Mercuri

Electronic Theses and Dissertations

With climate change, landfalling hurricanes become an increasing threat to coastal regions. However, the interactions between the coastal landscape and landfalling hurricanes are often overlooked when addressing sea-level rise outside of inundation and independent of sea surface temperature. This study analyzed the potential impacts regarding structure and intensity as a result of sea-level rise in the Gulf of Mexico using the WRF-ARW numerical model coupled with a 1D ocean model. Analysis showed that 10 m windspeed from landfall forward was higher in modified coastlines, and minimum sea-level pressure post-landfall was consistently lower for modified runs where storms maintain a higher …


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