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Full-Text Articles in Physical Sciences and Mathematics

Projection-Domain Low-Count Quantitative Spect (Lc-Qspect) Methods For Radiopharmaceutical Therapies (Rpts), Zekun Li Aug 2024

Projection-Domain Low-Count Quantitative Spect (Lc-Qspect) Methods For Radiopharmaceutical Therapies (Rpts), Zekun Li

McKelvey School of Engineering Graduate Student Theses & Dissertations

Radiopharmaceutical therapies (RPTs) using α- or β-particle-emitting isotopes are becoming increasingly important in cancer treatment. Reliable (accurate and precise) quantification of absorbed doses in lesions and vital organs is important for the safety and effectiveness of these therapies. Quantitative single-photon emission computed tomography (SPECT) provides a mechanism for such dose quantifications by quantifying the regional activity uptake. This dissertation aims to develop methodologies for reliable SPECT-based regional uptake quantification for patients treated with α-particle-emitting RPTs (α-RPTs). A significant challenge with conventional reconstruction-based quantitative (RBQ) SPECT methods is the ill-posed nature of image reconstruction, which is further complicated by the limited …


Topic Modeling On Document Networks With Dirichlet Optimal Transport Barycenter, Ce Zhang, Hady Wirawan Lauw Aug 2024

Topic Modeling On Document Networks With Dirichlet Optimal Transport Barycenter, Ce Zhang, Hady Wirawan Lauw

Research Collection School Of Computing and Information Systems

Text documents are often interconnected in a network structure, e.g., academic papers via citations, Web pages via hyperlinks. On the one hand, though Graph Neural Networks (GNNs) have shown promising ability to derive effective embeddings for such networked documents, they do not assume a latent topic structure and result in uninterpretable embeddings. On the other hand, topic models can infer semantically interpretable topic distributions for documents by associating each topic with a group of understandable key words. However, most topic models mainly focus on plain text within documents and fail to leverage network structure across documents. Network connectivity reveals topic …


Draft Final Horseshoe Bend Effluent Line (Hbel) Discharge Structure Surface Enhancements Work Plan, Pioneer Technical Services, Inc. Aug 2024

Draft Final Horseshoe Bend Effluent Line (Hbel) Discharge Structure Surface Enhancements Work Plan, Pioneer Technical Services, Inc.

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.


Canine Parasites In Southern Nevada Urban Dog Parks: Paravec Study, Miklo Azrael A. Alcala Aug 2024

Canine Parasites In Southern Nevada Urban Dog Parks: Paravec Study, Miklo Azrael A. Alcala

UNLV Theses, Dissertations, Professional Papers, and Capstones

While dogs are one of humans’ greatest companions, they also serve as hosts for a multitude of parasites. Urban dog parks serve as environments where the transmission of diseases is likely to occur. Exposure to infective agents, contained within the soil, intermediate hosts (e.g., rodents, rabbits), and feces, can directly affect the health of dogs and their owners. Other factors that can further influence canine health include age, previous diagnoses of parasites/diseases, and migration. Many dog owners visit dog parks to encourage socialization and exercise. Such activities are meant to improve health, but unawareness of microbiological organisms can lead to …


New Insights Into The Diverse Intraplate Volcanism Present Within The Howland And Baker Island United States Exclusive Economic Zone, Nicholas Foresta Aug 2024

New Insights Into The Diverse Intraplate Volcanism Present Within The Howland And Baker Island United States Exclusive Economic Zone, Nicholas Foresta

UNLV Theses, Dissertations, Professional Papers, and Capstones

The origin of oceanic volcanism has been attributed to various mechanisms, such as upwelling mantle plumes, lithospheric extension driven decompression melting, and small-scale convective cells in the asthenosphere. Discovering the range of magmatic drivers present in the ocean basins aids in understanding mantle geodynamics and tectonic processes. A recent seafloor exploration campaign within the Howland and Baker Island (HBI) U.S. Exclusive Economic Zone (EEZ; approximately near the equator and the International Date Line) resulted in the collection of multiple lava flow samples, which offer valuable insights into the complex origins and dynamics of intraplate seamounts. According to current absolute plate …


Image Processing Techniques For Water Droplet Penetration Time And Contact Angle Estimation, Sai Balaji Jai Kumar Aug 2024

Image Processing Techniques For Water Droplet Penetration Time And Contact Angle Estimation, Sai Balaji Jai Kumar

UNLV Theses, Dissertations, Professional Papers, and Capstones

Water droplet behavior on soil surfaces plays a critical role in numerous environmental processes, including soil erosion, hydrological dynamics, and ecosystem health. Accurate characterization of soil water repellency, quantified by parameters such as water droplet penetration time (WDPT) and contact angles (WDCA), is essential for informed decision-making in agricultural management, forestry practices, and land-use planning. Despite the significance of these parameters, challenges exist in reliably estimating them due to the complex and dynamic nature of soil-water interactions. This thesis address challenges in estimating WDPT and WDCA, by leveraging state-of-the-art image processing techniques and machine learning algorithms. The research focuses on …


Scoring Single-Sample Pathway Expression Level Using Graph Autoencoder, Eunyoung Jang Aug 2024

Scoring Single-Sample Pathway Expression Level Using Graph Autoencoder, Eunyoung Jang

UNLV Theses, Dissertations, Professional Papers, and Capstones

Single-sample pathway analysis (ssPA) is a bioinformatics technique used to assess the activity of biological pathways in individual samples, rather than relying on aggregated data from multiple samples. This approach allows for the detection of pathway activation or suppression in single samples, making it a valuable approach in research and clinical applications where individual variability is critical. In this paper, we propose a deep-learning method that scores individual pathway expression levels using a graph autoencoder. The proposed method provides insights into the biological processes and leverages the high dimensionality of gene expression data by setting the nodes in the neural …


Evaluation Of Electrochemical Corrosion, Electrodeposition, And Other Electroanalytical Methods As Investigative Forensic Techniques For Advancing Metal Substrate Analysis, Crystal C. Kitanovski Aug 2024

Evaluation Of Electrochemical Corrosion, Electrodeposition, And Other Electroanalytical Methods As Investigative Forensic Techniques For Advancing Metal Substrate Analysis, Crystal C. Kitanovski

UNLV Theses, Dissertations, Professional Papers, and Capstones

Friction ridge skin, bearing unique patterns of epidermal ridges commonly known as fingerprints, has served as a crucial tool for identification since ancient times, with its utilization dating back to Chinese culture around 221 B.C. Today, friction ridge skin impressions remain vital evidence in forensic investigations, aiding in the identification of suspects. While fingerprints, palm prints, and footprints can all serve as identifying markers, this dissertation focuses specifically on fingerprints, broadly classified as visible or latent. Latent fingerprints, though invisible to the naked eye, constitute the majority of prints collected from crime scenes, necessitating physical, chemical, or physicochemical processing for …


Interpretable And Evidential Deep Learning For Medical Image Analysis, Sai Chandra Kosaraju Aug 2024

Interpretable And Evidential Deep Learning For Medical Image Analysis, Sai Chandra Kosaraju

UNLV Theses, Dissertations, Professional Papers, and Capstones

Automatic histopathological Whole Slide Image (WSI) analysis has been highlighted along with the advancements in microscopic imaging techniques, but manual examination and diagnosis of WSIs are time-consuming and tiresome. Recently, deep convolutional neural networks have succeeded in histopathological image analysis. Especially, Convolutional Neural Networks CNN models such as Inception and DenseNet have achieved effective performance. However, automatic histopathological WSI analysis still has significant drawbacks such as considering deep learning as black-box models, predicting disease independently on a small part of images (patch images) extracted from WSIs, limitations in predicting a single slide-based score for a patient, and capturing disease-specific morphology …


The Development Of Environmental Dna (Edna) Sampling For Arbovirus Vector Surveillance In Southern Nevada, Katharine Brooke Major Aug 2024

The Development Of Environmental Dna (Edna) Sampling For Arbovirus Vector Surveillance In Southern Nevada, Katharine Brooke Major

UNLV Theses, Dissertations, Professional Papers, and Capstones

Vector-borne diseases account for 17% of all infectious diseases worldwide and are responsible for more than 700,000 deaths annually. Two-thirds of the global population are at risk of arthropod-borne RNA viruses (arboviruses), spread by mosquitoes, ticks, and sandflies, with these pathogens accounting for 37% of all emerging human diseases. Arboviruses are becoming increasingly important causes of neurological disease in the United States, presenting a significant public health problem. In the absence of available vaccines and efficacious treatment options, accurate, rapid, and cost-effective surveillance of arbovirus vectors is critical for monitoring species distribution and mitigating disease transmission risk. Currently, mosquito vector …


Implementing Radformation At Personalized Radiation Oncology: Enhancing Efficiency And Precision, Devin J. Peart Aug 2024

Implementing Radformation At Personalized Radiation Oncology: Enhancing Efficiency And Precision, Devin J. Peart

UNLV Theses, Dissertations, Professional Papers, and Capstones

RadMachine is a data quality management application implemented at Personalized Radiation Oncology (PRO) to streamline quality assurance (QA) tests. It offers various functions assisting medical physicists in a radiation oncology clinic, including inputting, analyzing, managing, exporting, and monitoring QA data. Physicists create test lists following the recommendations provided by the American Association of Medical Physics (AAPM). These lists track results for units such as the Varian Edge, Varian BRAVOS, and Siemens SOMATOM go.Open Pro CT scanner. Ancillary equipment used for testing also has assigned test lists to store calibration factors and receive calibration expiration reminders. The primary goal of utilizing …


Mining Gambling Data For Modeling Gambling Behavior Patterns, Piyush Aniruddha Puranik Aug 2024

Mining Gambling Data For Modeling Gambling Behavior Patterns, Piyush Aniruddha Puranik

UNLV Theses, Dissertations, Professional Papers, and Capstones

Understanding player behavior for responsible gambling research is a difficult task due to the lack of data on players’ activities. Past studies in this area are largely limited to publicly available behavioral data or aggregated players data. Problem gambling in gamblers is typically identified only after they have already been addicted or have already been engaging in problematic gambling behavior. Furthermore, “risky” gambling behavior has historically been difficult to define due to the varying patterns of gambling activity that could potentially be attributed to it.In this dissertation we illustrate the methodology and algorithms used to engineer financial data for further …


A Heuristic Approach To Operations And Control Of Btm-Ders For Bill Management And Grid Services, Md Arshad Rashid Shaon Aug 2024

A Heuristic Approach To Operations And Control Of Btm-Ders For Bill Management And Grid Services, Md Arshad Rashid Shaon

UNLV Theses, Dissertations, Professional Papers, and Capstones

Behind-The-Meter (BTM) distributed energy resources (DERs) have emerged as a critical and transformative force within the energy sector. These decentralized energy assets, which include solar photovoltaic (PV) systems, battery energy storage systems (BESS), and thermostatically controlled loads (TCLs), are increasingly essential for empowering customers by granting them greater control over their energy production and consumption, thereby reducing reliance on centralized power sources. Additionally, they have the potential to play a pivotal role in enhancing grid resilience by providing grid services. This study investigates the management of customer electricity bills and grid services through the integration of various BTM-DERs, particularly solar …


Uvc And Planetary Habitability: Insights From Desert Lichens And Cyanobacteria, Tejinder Singh Aug 2024

Uvc And Planetary Habitability: Insights From Desert Lichens And Cyanobacteria, Tejinder Singh

UNLV Theses, Dissertations, Professional Papers, and Capstones

An important question in astrobiology is whether life can exist under the levels of UVC radiation found on Archean Earth, Mars, and exoplanets. We investigated this question by studying the UVC survival of colonial cyanobacterium and lichens that grow in harsh desert environments and possess natural sunscreens. We irradiated them nonstop in a desiccated state with a UVC flux closely representing the upper limit on those planets: 55-60 W/m². After irradiation, we rehydrated and assessed their survival using chlorophyll fluorometry and by counting the number of viable colonies that formed on agar plates. All three study organisms survived two to …


Effects Of Climate Change On (Semi)-Arid Ecosystems In The Southwestern United States, Charlotte Van Der Nagel Aug 2024

Effects Of Climate Change On (Semi)-Arid Ecosystems In The Southwestern United States, Charlotte Van Der Nagel

UNLV Theses, Dissertations, Professional Papers, and Capstones

Climate change is considered amongst the most severe threats to terrestrial and aquatic ecosystems globally. Ecosystems in the southwestern United States have specifically been impacted by intense drought conditions since 2000. Higher temperatures combined with altered precipitation stresses many ecosystems; however, ecosystem specific responses to such stressors may vary. Here, the effects of climate change on semi-arid ecosystems are analyzed for some of the most vulnerable ecosystems in the southwestern United States: lacustrine, riparian, and dryland ecosystems.

Lakes and reservoirs in arid environments often serve as drinking water sources and recreational areas where high water quality is essential. Climate change …


Probing The Ecological Functions Of Thermophiles Using Cultivation-Dependent And Cultivation-Independent Techniques, Dengxun Lai Aug 2024

Probing The Ecological Functions Of Thermophiles Using Cultivation-Dependent And Cultivation-Independent Techniques, Dengxun Lai

UNLV Theses, Dissertations, Professional Papers, and Capstones

High-temperature geothermal springs are ecosystems that resemble early Earth, offering insights into the origins and early evolution of life. In these unique ecosystems, thermophilic microorganisms thrive. However, our knowledge of thermophiles remains limited. A major challenge is that many thermophiles remain uncultivated. The primary goal of this dissertation was to explore the diversity, metabolism, and ecological functions of thermophiles using cultivation-dependent and cultivation-independent approaches. Chapter 1 provides a broad overview of geothermal spring ecosystems and thermophiles, along with a roadmap of the dissertation. Chapter 2 documents a study on the response of specific thermophiles from Gongxiaoshe (GXS) Hot Spring in …


Forecasting Commercial Vehicle Miles Traveled (Vmt) In Urban California Areas, Steve Chung, Jaymin Kwon, Yushin Ahn Aug 2024

Forecasting Commercial Vehicle Miles Traveled (Vmt) In Urban California Areas, Steve Chung, Jaymin Kwon, Yushin Ahn

Mineta Transportation Institute

This study investigates commercial truck vehicle miles traveled (VMT) across six diverse California counties from 2000 to 2020. The counties—Imperial, Los Angeles, Riverside, San Bernardino, San Diego, and San Francisco—represent a broad spectrum of California’s demographics, economies, and landscapes. Using a rich dataset spanning demographics, economics, and pollution variables, we aim to understand the factors influencing commercial VMT. We first visually represent the geographic distribution of the counties, highlighting their unique characteristics. Linear regression models, particularly the least absolute shrinkage and selection operator (LASSO) and elastic net regressions are employed to identify key predictors of total commercial VMT. LASSO regression …


Techno-Economic And Environmental Assessments Of Produced Water Treatment Technologies For Beneficial Reuse, Elora Afrin Aug 2024

Techno-Economic And Environmental Assessments Of Produced Water Treatment Technologies For Beneficial Reuse, Elora Afrin

Water Resources Science and Technology Theses and Graduate Research Reports (Archived)

Produced water (PW) is a bulk portion of byproduct generated during oil and gas extraction operations and can be potentially reused for various purposes. However, the treatment costs and associated environmental issues call for a multitude of factors for proper management. This research aims to evaluate the viability of technologies for treating PW in terms of their technical performance, cost-effectiveness, and environmental considerations. Technologies evaluated include well-established processes such as electrodialysis (ED), electrodialysis reversal (EDR), ion exchange, chemical oxidation, electrocoagulation (EC), chemical coagulation (CC), nanofiltration (NF) etc. Associated case studies have been studied. However, except EC and CC, other technologies …


Utilizing Unmanned Aerial Systems (Uas) And Computer Software To Assess Effects Of Cover Crops On Cash Crop Volumetric Mass And Plant Height, Carlos Andres Garcia Patlan Aug 2024

Utilizing Unmanned Aerial Systems (Uas) And Computer Software To Assess Effects Of Cover Crops On Cash Crop Volumetric Mass And Plant Height, Carlos Andres Garcia Patlan

Theses and Dissertations

Sustainability in agriculture starts with the health of soil-- from its productivity and fertility, to its ability to retain water during droughts and allow for drainage during rain. One approach of improving soil health is the use of cover crops, a practice associated with improved nutrient availability in soils, the promotion of soil biodiversity and organic matter to improve density and structure, effective weed management, and ultimately improved yields of subsequent cash crops. Assessing the cumulative impacts of cover crops is difficult, with various metrics and indicators. Crop dry weight may be a way to predict the effects cover crops …


Intrinsic Universality In Tile Automata And Related Results, Elise C. Grizzell Aug 2024

Intrinsic Universality In Tile Automata And Related Results, Elise C. Grizzell

Theses and Dissertations

The Tile Automata (TA) model describes self-assembly systems in which monomers can build structures and transition with an adjacent monomer to change their states. This paper shows that seeded TA is a non-committal intrinsically universal model of self-assembly. We present a single universal Tile Automata system containing approximately 4600 states that can simulate (a) the output assemblies created by any other Tile Automata system Γ, (b) the dynamics involved in building Γ’s assemblies, and (c) Γ’s internal state transitions. It does so in a non-committal way: it preserves the full non-deterministic dynamics of a tile’s potential attachment or transition by …


Development Of A Flow Cytometry Method For The Identification And Enumeration Of Enterococcus Faecalis, Riza Magbitang Aug 2024

Development Of A Flow Cytometry Method For The Identification And Enumeration Of Enterococcus Faecalis, Riza Magbitang

Master's Theses

A multi-color flow cytometry method coupled with fluorescent staining was developed to detect and quantify E. faecalis concentrations in coastal waters as an alternative to the traditional membrane filtration method. The developed method was used to characterize E. faecalis during batch growth and yielded consistent results across the various physiological states of the cells. Additionally, the application of propidium iodide (i.e., a viability stain), afforded the method the ability to differentiate between cells with intact and compromised cell membranes, which raises the potential of quantifying cells that are in viable-but-non-culturable (VBNC) state. Initial field test using natural seawater samples spiked …


Integration Of Matlab And Machine Learning To Accelerate Evaluation Of Biological Activity In Agricultural Soils And Promote Soil Health Improvement Goals, Andrew Stiven Ortiz Balsero Aug 2024

Integration Of Matlab And Machine Learning To Accelerate Evaluation Of Biological Activity In Agricultural Soils And Promote Soil Health Improvement Goals, Andrew Stiven Ortiz Balsero

Department of Agricultural and Biological Systems Engineering: Dissertations, Theses, and Student Research

Traditionally, assessments of soil biological activity have been confined to laboratory settings, creating a disconnect with practical in-field methods. To bridge this gap, cotton fabric degradation has been used to illustrate soil microbial activity under different management practices. While effective, these demonstrations are subjective and labor-intensive.

Researchers have explored using image processing software like ImageJ and Adobe Photoshop to streamline this process. Although these tools accurately quantified fabric degradation under varying soil conditions, the methods remained labor-intensive and complex. Consequently, these methods were still not ideal for on-farm use by agricultural practitioners.

To further address labor and complexity limitations, the …


Virtual Unknotting Numbers For Families Of Virtual Torus Knots, Kaitlin R. Tademy Aug 2024

Virtual Unknotting Numbers For Families Of Virtual Torus Knots, Kaitlin R. Tademy

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A virtual torus knot T(p,q,VC) sits in the intersection of the well-understood torus knot and the not-so-well-understood virtual knot, making it an intriguing object to study.

The unknotting number of a classical knot K is defined unambiguously. However, "the" unknotting number when K is a virtual knot is not as clear to define, since virtual knots have both classical and virtual crossings. We will define virtual unknotting number vu(K) as the minimum number of (classical) crossing changes required to unknot K. Under this definition of virtual unknotting, not all …


Emergent Phenomena In Ferroelectric-Dielectric And Ferroelectric-Graphene Heterostructures, Tianlin Li Aug 2024

Emergent Phenomena In Ferroelectric-Dielectric And Ferroelectric-Graphene Heterostructures, Tianlin Li

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

This dissertation explores the emergent phenomena in epitaxial ferroelectric oxide-based heterostructures, including the negative capacitance (NC) effect in ferroelectric-dielectric systems, ferroelectric gate imposed mobility limit in graphene field-effect transistors, and ferroelectric domain-induced graphene-superlattices.

We carry out a phenomenological study of the NC effect in PbZr0.2Ti0.8O3/SrTiO3 capacitors. The Landau free-energy profile predicts a critical thickness ratio for the ferroelectric-dielectric phase transition, consistent with the observed abrupt change in remnant polarization. A static NC state is observed in the low thickness ratio region, which is compromised by the emergence of multidomain in the moderate ratio …


We're Swarming Again! Swarming, Collectivity, And Trope: The Case Of Extinction Rebellion, Tyler J. Behymer Aug 2024

We're Swarming Again! Swarming, Collectivity, And Trope: The Case Of Extinction Rebellion, Tyler J. Behymer

Department of Communication Studies: Dissertations, Theses, and Student Research

This thesis explores the rhetoric of the eco-movement Extinction Rebellion, focusing on the use of swarming and nature tropes to mobilize collective action and revivify contemporary notions of collectivity. Drawing on rhetoric of social movement scholarship, cultural studies, and psychoanalysis, this essay theorizes swarming as a tropological economy that expands the conditions of propriety in the context of collectivity. Through an analysis of Extinction Rebellion’s discourse, this study demonstrates how the naturalization of swarming tropes works in various ways to rewild conventional political discourse, galvanize disruptive collective assembly, and challenge green neoliberalism.

Advisor: Casey Ryan Kelly


Gevrey Class Estimates Towards Null Controllability Of A Fluid Structure Interaction System, Dylan Mcknight Aug 2024

Gevrey Class Estimates Towards Null Controllability Of A Fluid Structure Interaction System, Dylan Mcknight

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Fluid-Structure Interaction concerns the interaction of parabolic fluids and hyperbolic elastic structures via numerous mechanisms such as boundary coupling and pressure. These models find application in blood flow, fluid flow in the eye, and air flow over plane wings. Parabolic equations are well known for “infinite speed of propagation,” which manifests itself via a uniform bound on the resolvent of the infinitesimal generator of the associated strongly continuous semigroup. Qualitatively, a solution of a parabolic pde with rough initial data is immediately smooth for any positive time. A priori, it is not clear whether a fluid structure interaction inherits any …


Search For Physics Beyond The Standard Model In Top Quark Production With Additional Leptons In The Context Of Effective Field Theory, Furong Yan Aug 2024

Search For Physics Beyond The Standard Model In Top Quark Production With Additional Leptons In The Context Of Effective Field Theory, Furong Yan

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

The dissertation presents a search for new physics impacting top quark productions within the framework of effective field theory (EFT). Potential new physics effects are parameterized in terms of 26 dimension-six EFT operators into the event yields of six distinct top production processes in the detector level. The analysis targets multilepton final states consisting of two leptons of the same charge, three leptons and four leptons. The events are further categorized and binned in terms of kinematic distributions in order to gain sensitivity to the new physics effects. A likelihood function is formulated based on the predicted distribution in each …


On Regularity Of Graph C*-Algebras, Gregory Joseph Faurot Aug 2024

On Regularity Of Graph C*-Algebras, Gregory Joseph Faurot

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

We prove that for any countable directed graph E with Condition (K), the corresponding graph C*-algebra C*(E) has nuclear dimension at most two. We also prove that the nuclear dimension of certain extensions is at most one, which can be applied to certain graphs to achieve the optimal upper bound of one. Finally, we generalize some previous results for O∞ -stability of graph algebras, and prove some partial results for Z-stability.

Advisor: Christopher Schafhauser


Phylogenetic And Biogeographic Patterns Of Devonian Proetid Trilobites, Katherine Jane Jordan Aug 2024

Phylogenetic And Biogeographic Patterns Of Devonian Proetid Trilobites, Katherine Jane Jordan

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Ecological disruption events such as mass extinctions can result in the permanent alteration in clades and ecosystems. A pivotal time of change during the history of life on Earth can be seen in the Devonian Period. During this time, major transitions in marine and terrestrial system resulted in a different world at the end of the period in comparison to the beginning. One such group most heavily impacted were trilobites. Trilobites were reduced to one order by the end of the Devonian: Proetida. My dissertation focuses on phylogenetic, biogeographic, and paleocommunity patterns of this group, known as the last of …


Making Sandwiches: A Novel Invariant In D-Module Theory, David Lieberman Aug 2024

Making Sandwiches: A Novel Invariant In D-Module Theory, David Lieberman

Department of Mathematics: Dissertations, Theses, and Student Research

Say I hand you a shape, any shape. It could be a line, it could be a crinkled sheet, it could even be a the intersection of a cone with a 6-dimensional hypersurface embedded in a 7-dimensional space. Your job is to tell me about the pointy bits. This task is easier when you can draw the shape; you can you just point at them. When things get more complicated, we need a bigger hammer.

In a sense, that “bigger hammer” is what the ring of differential operators is to an algebraist. Then we will say some things and stuff …