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LSU Doctoral Dissertations

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Full-Text Articles in Physical Sciences and Mathematics

Baldcypress (Taxodium Distichum) And Their Growth And Development Under Abiotic Stressors Related To Restoration Efforts, George Washburn Mar 2023

Baldcypress (Taxodium Distichum) And Their Growth And Development Under Abiotic Stressors Related To Restoration Efforts, George Washburn

LSU Doctoral Dissertations

Baldcypresss (Taxodium distichum (L.) Rich.) forests are crucial to the Southeast coastal region for the trees’ ecosystem services. Many organizations have been trying to restore the ghost and dead forests found throughout the Gulf region through restoration events. Baldcypress seedlings and saplings face several abiotic and biotic stressors, including but not limited to elevated levels of salinity, nutrients, temperature, and light intensity. These stressors can be the limiting factor in the success or failure of these massive planting efforts.

To assess which stressors were of most concern to the restoration efforts, we conducted common garden experiments with baldcypress seedlings …


Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh Mar 2023

Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh

LSU Doctoral Dissertations

In this thesis we consider the Toeplitz operators on the weighted Bergman spaces and their analytic continuation. We proved the commutativity of the $C^*-$algebras generated by the analytic continuation of Toeplitz operators with special class of symbols that are invariant under suitable subgroups of $SU(n,1)$, and we showed that commutative $C^*-$algebras with symbols invariant under compact subgroups of $SU(n,1)$ are completely characterized in terms of restriction to multiplicity free representations. Moreover, we extended the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of the universal covering group $\widetilde{SU(n,1)}$, and we obtained the generalized Segal-Bargmann transform, where …


Stellar Binaries And Post-Merger Evolution: A Framework For Stellar Evolution And Nucleosynthesis In R Coronae Borealis Stars, Bradley Munson Mar 2023

Stellar Binaries And Post-Merger Evolution: A Framework For Stellar Evolution And Nucleosynthesis In R Coronae Borealis Stars, Bradley Munson

LSU Doctoral Dissertations

We have developed a framework for simulating binary stars through all three relevant
timescales: the dynamical merger, thermal, and nuclear evolution. The framework begins by simulating a dynamical merger in a 3-dimensional hydrodynamics adaptive mesh refinement code, Octo-Tiger, and performing a spherical averaging calculation to map the post-merger remnant into the 1-dimensional stellar evolution code, MESA. In this work, we primarily utilize this framework for simulating double white dwarf mergers, which are believed to be the progenitor to R Coronae Borealis (RCB) stars. We evolve the post-merger in MESA and compare the computed surface abundances to those observed …


Effective Connectivity Of Functional Mri Via Deep Learning Methods, Kai-Cheng Chuang Mar 2023

Effective Connectivity Of Functional Mri Via Deep Learning Methods, Kai-Cheng Chuang

LSU Doctoral Dissertations

Effective connectivity, based on functional magnetic resonance imaging (fMRI) time series signals, is the quantification of how strongly brain activity in a certain source brain region contributes to brain activity in a target brain region, independent of the contributions of other source regions. Current methods to solve this problem have several limitations. They are either unable to model nonlinear relationships between source and target signals, unable to efficiently quantify time lags in source-target relationships, unable to identify time-varying relationships, or fail to account for variability in the hemodynamic response function that converts neuron activity to a measurable signal. In this …


Hybrid Modeling For Electrochemical Systems, Luis Alejandro Briceno-Mena Feb 2023

Hybrid Modeling For Electrochemical Systems, Luis Alejandro Briceno-Mena

LSU Doctoral Dissertations

The discovery of new materials like catalysts, polymeric films, and biomolecules, is driven by industrial needs such as improving reaction or separation selectivity, enhancing therapeutic effects on medical treatments, or reducing costs of replacement. However, deployment of these advances in industrial applications is often hindered by the lack of models needed for design and optimization. Due to the novelty of materials and devices, experimental data and first principles' knowledge are scarce, making it hard to build models either via data-driven or knowledge based approaches. In this context, a way to efficiently combine domain knowledge with data could provide a pathway …


Sediment Transport And Geomorphological Evolution In The Northern Gulf Of Mexico, Kelli Moran Jan 2023

Sediment Transport And Geomorphological Evolution In The Northern Gulf Of Mexico, Kelli Moran

LSU Doctoral Dissertations

This dissertation explores the mechanisms driving sediment transport and deposition on the continental shelf and within the bays of the northern Gulf of Mexico via a suite of geophysical methods and sediment cores on a variety of timescales. This dissertation is comprised of three main chapters, each focusing on a different location, environment, and process but tied together using geophysical survey, a thematic focus on geomorphic change and sediment transport within the deltaic cycle and deltaic plain environments, and the implications this change poses for both past and future sediment transport and environmental change in response to sea level change. …


First-Principles Molecular Dynamics Study Of Liquid Iron-Rich Alloys Under Conditions Of The Earth’S Core, Dipendra Banjara Jan 2023

First-Principles Molecular Dynamics Study Of Liquid Iron-Rich Alloys Under Conditions Of The Earth’S Core, Dipendra Banjara

LSU Doctoral Dissertations

In this dissertation, we report the results of the first-principles molecular dynamics (FPMD) simulations and data analysis on the thermodynamic, structural, and transport properties of iron-rich metallic liquids considering several light and heavy elements under wide ranges of pressure and temperature that are relevant to the earth’s core. Our simulations of pure liquid iron cover the pressure range from 0 GPa at 2000 K to 380 GPa at 7000 K perhaps representing the most extensive computational study to date. We studied four molten iron-rich alloys corresponding to 2.67 atom% of Ni, Co, Mo, and W at pressures up to 380 …


Visual Analytics And Modeling Of Materials Property Data, Diwas Bhattarai Jan 2023

Visual Analytics And Modeling Of Materials Property Data, Diwas Bhattarai

LSU Doctoral Dissertations

Due to significant advancements in experimental and computational techniques, materials data are abundant. To facilitate data-driven research, it calls for a system for managing and sharing data and supporting a set of tools for effective data analysis and modeling. Generally, a given material property M can be considered as a multivariate data problem. The dimensions of M are the values of the property itself, the conditions (pressure P, temperature T, and multi-component composition X) that control the concerned property, and relevant metadata I (source, date).

Here we present a comprehensive database considering both experimental and computational sources …


Measurement Of Near-Threshold Proton Branching Ratios In 31s Important For Novae, Sudarsan Balakrishnan Jan 2023

Measurement Of Near-Threshold Proton Branching Ratios In 31s Important For Novae, Sudarsan Balakrishnan

LSU Doctoral Dissertations

Classical novae are stellar explosions that contribute to the nucleosynthesis of isotopes on the proton-rich side of the valley of stability up to 40Ca. In ONe novae, the incompletely understood reaction rate of 30P(p,γ)31S is known to strongly influence the production rate of several stable isotopes such as 30Si, 31P, and 32,33,34S. A precise measurement of this reaction rate has several potential implications towards matching astrophysical observables to the physical composition of the nova site -- the observed elemental abundance ratios of O/S and S/Al have been suggested as useful `thermometers' to gauge …


Application Of Distributed Fiber-Optic Sensing For Pressure Predictions And Multiphase Flow Characterization, Gerald Kelechi Ekechukwu Dec 2022

Application Of Distributed Fiber-Optic Sensing For Pressure Predictions And Multiphase Flow Characterization, Gerald Kelechi Ekechukwu

LSU Doctoral Dissertations

In the oil and gas industry, distributed fiber optics sensing (DFOS) has the potential to revolutionize well and reservoir surveillance applications. Using fiber optic sensors is becoming increasingly common because of its chemically passive and non-magnetic interference properties, the possibility of flexible installations that could be behind the casing, on the tubing, or run on wireline, as well as the potential for densely distributed measurements along the entire length of the fiber. The main objectives of my research are to develop and demonstrate novel signal processing and machine learning computational techniques and workflows on DFOS data for a variety of …


Estimation Of Economic Risk From Coastal Natural Hazards In Louisiana, Rubayet Bin Mostafiz Nov 2022

Estimation Of Economic Risk From Coastal Natural Hazards In Louisiana, Rubayet Bin Mostafiz

LSU Doctoral Dissertations

Louisiana, U.S.A., is among the most vulnerable areas globally to coastal natural hazards, with risk vulnerability likely increasing. The risks associated with non-tropical-cyclone hazards in Louisiana’s coastal zone have been understudied. This research enhances present and future (i.e., 2050) Louisiana risk assessment using locally-weighted, model-based hazard frequency/intensity and population projections.

Results suggest that property risks associated with extreme cold temperature and tornado are and will remain costlier than those for hail and lightning. Property risks of extreme cold temperature and hail are projected to decrease with the expected warming temperatures, with those of all four of these hazards peaking in …


Compilation Optimizations To Enhance Resilience Of Big Data Programs And Quantum Processors, Travis D. Lecompte Nov 2022

Compilation Optimizations To Enhance Resilience Of Big Data Programs And Quantum Processors, Travis D. Lecompte

LSU Doctoral Dissertations

Modern computers can experience a variety of transient errors due to the surrounding environment, known as soft faults. Although the frequency of these faults is low enough to not be noticeable on personal computers, they become a considerable concern during large-scale distributed computations or systems in more vulnerable environments like satellites. These faults occur as a bit flip of some value in a register, operation, or memory during execution. They surface as either program crashes, hangs, or silent data corruption (SDC), each of which can waste time, money, and resources. Hardware methods, such as shielding or error correcting memory (ECM), …


Design, Synthesis, And Characterization Of Nqo1-Activatable Luminescent Probes, Ovini Vionika Weeratung Kankanamge Nov 2022

Design, Synthesis, And Characterization Of Nqo1-Activatable Luminescent Probes, Ovini Vionika Weeratung Kankanamge

LSU Doctoral Dissertations

Being among the top ten causes of death, cancer has constantly been able to grab the attention of researchers all around the world. While several treatment methods prevail to cure cancer, the seriousness of this medical condition requires continuous work in the development of novel treatments as well as scientific advancements in order to achieve early detection of the disease. Luminescence imaging is an emerging field in both diagnosis of diseases, as well as a means to provide guidance in clinical surgeries. While there exist only a few contrasting agents approved by the Food and Drug Administration, the need for …


Sers Platform For Single Fiber Endoscopic Probes, Debsmita Biswas Nov 2022

Sers Platform For Single Fiber Endoscopic Probes, Debsmita Biswas

LSU Doctoral Dissertations

Molecular detection techniques have huge potential in clinical environments. In addition to many other molecular detection techniques, endoscopic Raman spectroscopy has great ability in terms of minimal invasiveness and real-time spectra acquisition. However, Raman Effect is low in sensitivity, limiting the application. Surface-Enhanced Raman Scattering (SERS), addresses this limitation. SERS brings rough nano-metallic surfaces in contact with specimen molecules which enormously enhances Raman signals. This provides Raman spectroscopy with immense capabilities for diverse fields of applications.

Generally, in clinical probe applications, the spectrometer is brought near the target molecules for detection. Typically, optical fibers are used to couple spectrometers to …


From Biowaste To Product: The Functionalization Of Biochar For Agricultural And Environmental Applications, Baoyue Zhou Nov 2022

From Biowaste To Product: The Functionalization Of Biochar For Agricultural And Environmental Applications, Baoyue Zhou

LSU Doctoral Dissertations

Biochar is a porous carbonated substance that is manufactured through pyrolysis of biomass feedstocks in an oxygen-deficiency environment. The production of biochar from agricultural waste materials provides a potential solution for eliminating pollution while improving carbon sequestration. While biochar is shown to provide multiple benefits to soil health and fertility, its use in environmental remediation has been hampered by its low affinity for hazardous anionic species and the difficulty in isolating from water phase. To overcome these obstacles, various efforts have been made to modify biochar surface chemistry and morphology.

Fe/Mg co-doped biochar composites from sugarcane harvest residue were prepared …


Polymer Mimetics For Soil Modeling And Detection Of Biomarkers, Md Ragib Hasan Nov 2022

Polymer Mimetics For Soil Modeling And Detection Of Biomarkers, Md Ragib Hasan

LSU Doctoral Dissertations

The population of the world is increasing day by day and is expected to reach 9.8 billion by the year 2050. The ever-increasing demand for agricultural products is putting an unprecedented strain on the world's soils as the human population continues to expand. Soil degradation caused by over-farming and the agrochemicals (fertilizers, pesticides, etc.) used in agriculture is a growing problem, although its causes remain murky. In addition, little is understood about the molecular-level interactions of substances that are subsequently introduced to soils, such as agricultural chemicals (ACs). Therefore, it is expected that these constraints may be circumvented by the …


Hydrogeologic Investigation Of A Covered Karst Terrain, Joseph Peter Honings Oct 2022

Hydrogeologic Investigation Of A Covered Karst Terrain, Joseph Peter Honings

LSU Doctoral Dissertations

Increasing demand for water for agricultural use within the Dougherty Plain of the Southeastern United States has depleted surface water bodies. In karstic landscapes, such as the Dougherty Plain in southwest Georgia where the linkages between surface and ground waters are close, there is a need to understand the physical characteristics of the subsurface that allow these close linkages. Having a better understanding of the subsurface characteristics will aid numerical modeling efforts that underpin policy decisions and economic analyses. Two common features on this karstic landscape are draws and geographically isolated wetlands. Using LiDAR, aerial imagery, and ground-penetrating radar, this …


A Cluster Structure On The Coordinate Ring Of Partial Flag Varieties, Fayadh Kadhem Oct 2022

A Cluster Structure On The Coordinate Ring Of Partial Flag Varieties, Fayadh Kadhem

LSU Doctoral Dissertations

The main goal of this dissertation is to show that the (multi-homogeneous) coordinate ring of a partial flag variety C[G/P_K^−] contains a cluster algebra for every semisimple complex algebraic group G. We use derivation properties and a canonical lifting map to prove that the cluster algebra structure A of the coordinate ring C[N_K] of a Schubert cell constructed by Goodearl and Yakimov can be lifted, in an explicit way, to a cluster structure \hat{A} living in the coordinate ring of the corresponding partial flag variety. Then we use a minimality condition to prove that the cluster algebra \hat{A} is equal …


Synthesis Of Carbon Nanohoops And Macrocycles Via Alkyne Metathesis, Xin Zhou Oct 2022

Synthesis Of Carbon Nanohoops And Macrocycles Via Alkyne Metathesis, Xin Zhou

LSU Doctoral Dissertations

Cycloparaphenyleneacetylene (CPPA) and cycloparaphenylene (CPP) are called carbon nanohoops; they are fully conjugated macrocycles with radially oriented aromatic groups. Though many syntheses of CPPA and CPP were reported, in the macrocyclization step, the yields were usually not satisfying, as the reactions were irreversible. Our group utilizes alkyne metathesis to address this problem. Chapter 1 provides backgrounds and an introduction to the carbon nanohoops and alkyne metathesis.

Chapter 2 details the synthesis of the [3]CPP4A and [3]CPP5A, with good macrocyclization yields via alkyne metathesis. This study showed the error-correction ability of alkyne metathesis, especially with nonsymmetric substrates. …


Controlling Electro-Magnetic Functionality Of Ruthenates By Heterostructure Design, Zeeshan Ali Oct 2022

Controlling Electro-Magnetic Functionality Of Ruthenates By Heterostructure Design, Zeeshan Ali

LSU Doctoral Dissertations

Perovskite oxides (ABO3) show wide range of functionalities originating from interplay of structural, spin, charge, and orbital degrees of freedoms. The bulk perovskite structure could be controlled via conventional chemical substitution, though exploiting heterostructure engineering novel ground states could be observed which otherwise are absent in bulk. In this thesis, the interest is to explore the electro-magnetic phenomena as complex oxides are confined in heterostructures.

I first investigate electromagnetic properties of ultrathin epitaxial ruthenate: SrRuO3 (SRO); spatially confined between SrTiO3 (STO) i.e., STO5-SROn-STO5 with n = 1- and 2-unit cells. It …


A Numerical And Machine Learning Investigation Of Water Quality In The Northern Gulf Of Mexico, From Estuaries To Shelf, Yanda Ou Oct 2022

A Numerical And Machine Learning Investigation Of Water Quality In The Northern Gulf Of Mexico, From Estuaries To Shelf, Yanda Ou

LSU Doctoral Dissertations

In this study, numerical and machine learning (ML) models are developed and adapted to investigate the water quality of the Barataria Estuary and the Louisiana-Texas (LaTex) Shelf in northern Gulf of Mexico. By using a 3-D hydrodynamic ROMS model, the salinity variability of the Barataria Estuary is found highly influenced by the Mississippi River discharges and man-made river diversion systems. The Mississippi River freshwater can intrude into the estuary through the middle and the east passes. Sensitivity tests indicate that decreases in lower estuarine salinity due to the elevated Mississippi River discharges are more apparent than the salinity increases due …


Understanding Consumers' Use Experience On Electrically Heated Jacket: A Study On Online Review Using Topic Modeling, Md Nakib-Ul Hasan Aug 2022

Understanding Consumers' Use Experience On Electrically Heated Jacket: A Study On Online Review Using Topic Modeling, Md Nakib-Ul Hasan

LSU Doctoral Dissertations

The demand for heated jackets is anticipated to be fuelled by frequent temperature drops, severe winter weather, and increasing outdoor activities. Electrically heated jackets (EHJ) are primarily marketed through online distribution channels and expansion of online sales channels is expected to boost the global market. Consumers are increasingly relying on online reviews from other consumers to help them decide what to buy. Businesses also actively monitor and manage their online reviews to build trust in their brand and make it more likely that customers will buy. Traditional approaches for assessing customer behavior, such as market research surveys and focus groups, …


Computational Imaging For Shape Understanding, Yuqi Ding Aug 2022

Computational Imaging For Shape Understanding, Yuqi Ding

LSU Doctoral Dissertations

Geometry is the essential property of real-world scenes. Understanding the shape of the object is critical to many computer vision applications. In this dissertation, we explore using computational imaging approaches to recover the geometry of real-world scenes. Computational imaging is an emerging technique that uses the co-designs of image hardware and computational software to expand the capacity of traditional cameras. To tackle face recognition in the uncontrolled environment, we study 2D color image and 3D shape to deal with body movement and self-occlusion. Especially, we use multiple RGB-D cameras to fuse the varying pose and register the front face in …


Novel Synthetic Routes To Functionalized Tetrahydrobenzofurans And Chiral A-Quaternary A'-Hydroxy Ketones, Fatimat Oluwayemisi Badmus Jul 2022

Novel Synthetic Routes To Functionalized Tetrahydrobenzofurans And Chiral A-Quaternary A'-Hydroxy Ketones, Fatimat Oluwayemisi Badmus

LSU Doctoral Dissertations

Various naturally occurring organic compounds possess unique biological activities and have found exclusive applications in pharmaceuticals and agrochemicals. Their undeniable significance has necessitated the discovery and development of novel reactions that unveil advanced chemical transformations. This dissertation will detail our new approaches towards the synthesis of functionalized tetrahydrobenzofurans and chiral α-quaternary α’-hydroxy ketones. The transformations in these approaches were enabled by the chemistries of oxyallyl cations, Grignard reaction and Claisen rearrangement.

Chapter 1 introduces oxyallyl cations, their generation, reactions and applications. Our previous contributions, in the form of silyloxyallyl cations, to solve the regioselective issues associated with unsymmetrical oxyallyl cations …


Scheduling Many-Task Computing Applications For A Hybrid Cloud, Shifat Perveen Mithila Jul 2022

Scheduling Many-Task Computing Applications For A Hybrid Cloud, Shifat Perveen Mithila

LSU Doctoral Dissertations

A centralized scheduler can become a bottleneck for placing the tasks of a many-task application on heterogeneous cloud resources. Previously, it was demonstrated that a decentralized vector scheduling approach based on performance measurements can be used successfully for this task placement scenario. In this dissertation, we extend this approach to task placement based on latency measurements. Each node collects performance metrics from its neighbors on an overlay graph, measures the communication latency, and then makes local decisions on where to move tasks. We present a decentralized and a centralized algorithm for configuring the overlay graph based on latency measurements and …


Development Of 1,2-Cis-Selective Glycosylation Protocols And Multistep Synthesis Of Glycans From Acinetobacter Baumannii., Dancan Kamau Njeri Jul 2022

Development Of 1,2-Cis-Selective Glycosylation Protocols And Multistep Synthesis Of Glycans From Acinetobacter Baumannii., Dancan Kamau Njeri

LSU Doctoral Dissertations

Access to various oligosaccharides has been made possible by glycosylation reactions. This is mainly through chemical synthesis and enzymatic approaches. Herein, I talk about glycosylation through chemical synthesis. In general, glycosylation reactions lead to a mixture of 1,2-cis and 1,2-trans stereoisomers. Stereoselective access to 1,2-trans isomer is highly developed; it efficiently relies on neighboring group participation. However, efficient access to 1,2-cis selective glycosylation is still a work in progress. In Chapter 1, I highlight notable efforts developed so far that address the 1,2-cis selectivity challenge in glycosylation.

In Chapter 2, I demonstrate how I improved …


Determining The 3d Structure And Dynamics Of Mouse Notch1 Epidermal Growth Factor-Like Repeat 26 Using Nuclear Magnetic Resonance Spectroscopy, Kendra D. Jenkins Jul 2022

Determining The 3d Structure And Dynamics Of Mouse Notch1 Epidermal Growth Factor-Like Repeat 26 Using Nuclear Magnetic Resonance Spectroscopy, Kendra D. Jenkins

LSU Doctoral Dissertations

NOTCH is a transmembrane protein that transmits signals between cells in direct contact and alters gene expression. The signaling pathway is important because it is involved in cell fate determination. The NOTCH1 extracellular domain has 36 epidermal growth factor-like (EGF) repeats that are responsible for ligand binding. Mutations in the EGF-like repeats cause various neurological and developmental disorders. NOTCH1 signaling initiates when DSL ligands bind to EGF11-12, the minimum Ligand Binding Domain (LBD). The Abruptex region of the NOTCH1 protein (EGF24-29) is a highly glycosylated, flexible region with calcium binding sites that regulates NOTCH1 signaling and binding by interacting with …


Consequences Of Gulf Of Mexico Estuarine Tropical Cyclone Disturbance Regimes For Fish Assemblage Dynamics Conditionally Depend On Life-History Traits And Niche Characteristics, Stephen Edward Potts Jul 2022

Consequences Of Gulf Of Mexico Estuarine Tropical Cyclone Disturbance Regimes For Fish Assemblage Dynamics Conditionally Depend On Life-History Traits And Niche Characteristics, Stephen Edward Potts

LSU Doctoral Dissertations

Tropical cyclones (TC) are intense, localized disturbances that can potentially cause extensive damage to ecosystems. This dissertation is motivated by a need for interdisciplinary study of TC-ecosystem dynamics with applications to ecology, geography, and analytical methodology. I explore concept linkages between TC dynamics and ecosystems to characterize TC-ecosystem relationships as ecological disturbance regimes. This dissertation tests hypotheses and relationships of TC effects on estuarine fish assemblages in the north-western Gulf of Mexico. I explore concepts in TC-ecosystem relationships to link biotic dynamics with physical disturbance.

In Chapter 2, I compared spatial performance of generalized linear models (GLMs) and generalized additive …


On A Relation Between Ado And Links-Gould Invariants, Nurdin Takenov Jul 2022

On A Relation Between Ado And Links-Gould Invariants, Nurdin Takenov

LSU Doctoral Dissertations

In this thesis we consider two knot invariants: Akutsu-Deguchi-Ohtsuki(ADO) invariant and Links-Gould invariant. They both are based on Reshetikhin-Turaev construction and as such share a lot of similarities. Moreover, they are both related to the Alexander polynomial and may be considered generalizations of it. By experimentation we found that for many knots, the third order ADO invariant is a specialization of the Links-Gould invariant. The main result of the thesis is a proof of this relation for a large class of knots, specifically closures of braids with five strands.


Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, Vishwa Nirmika Dewage Jul 2022

Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, Vishwa Nirmika Dewage

LSU Doctoral Dissertations

The Fock space $\mathcal{F}(\mathbb{C}^n)$ is the space of holomorphic functions on $\mathbb{C}^n$ that are square-integrable with respect to the Gaussian measure on $\mathbb{C}^n$. This space plays an essential role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Grudsky and Vasilevski showed in 2002 that radial Toeplitz operators on $\mathcal{F}(\mathbb{C})$ generate a commutative $C^*$-algebra $\mathcal{T}^G$, while Esmeral and Maximenko showed that $C^*$-algebra $\mathcal{T}^G$ is isometrically isomorphic to the $C^*$-algebra $C_{b,u}(\mathbb{N}_0,\rho_1)$. In this thesis, we extend the result to $k$-quasi-radial symbols acting on the Fock space $\mathcal{F}(\mathbb{C}^n)$. …