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Full-Text Articles in Physical Sciences and Mathematics

Walking With A Robotic Exoskeleton Does Not Mimic Natural Gait: A Within-Subjects Study, Chad Swank, Sharon Wang-Price, Fan Gao, Sattam Almutairi Jan 2019

Walking With A Robotic Exoskeleton Does Not Mimic Natural Gait: A Within-Subjects Study, Chad Swank, Sharon Wang-Price, Fan Gao, Sattam Almutairi

Kinesiology and Health Promotion Faculty Publications

Background: Robotic exoskeleton devices enable individuals with lower extremity weakness to stand up and walk over ground with full weight-bearing and reciprocal gait. Limited information is available on how a robotic exoskeleton affects gait characteristics.

Objective: The purpose of this study was to examine whether wearing a robotic exoskeleton affects temporospatial parameters, kinematics, and muscle activity during gait.

Methods: The study was completed by 15 healthy adults (mean age 26.2 [SD 8.3] years; 6 males, 9 females). Each participant performed walking under 2 conditions: with and without wearing a robotic exoskeleton (EKSO). A 10-camera motion analysis system synchronized with 6 …


Sustainable Production Through Balancing Trade-Offs Among Three Metrics In Flow Shop Scheduling, Amin Abedini, Wei Li, Fazleena Badurdeen, Ibrahim S. Jawahir Jan 2019

Sustainable Production Through Balancing Trade-Offs Among Three Metrics In Flow Shop Scheduling, Amin Abedini, Wei Li, Fazleena Badurdeen, Ibrahim S. Jawahir

Institute for Sustainable Manufacturing Faculty Publications

In sustainable manufacturing, inconsistencies exist among objectives defined in triple-bottom-lines (TBL) of economy, society, and environment. Analogously, inconsistencies exist in flow shop scheduling among three objectives of minimizing total completion time (TCT), maximum completion time (MCT), and completion time variance (CTV), respectively. For continuous functions, the probability is zero to achieve the objectives at their optimal values, so is it at their worst values. Therefore, with inconsistencies among individual objectives of discrete functions, it is more meaningful and feasible to seek a solution with high probabilities that system performance varies within the …


Designing And Redesigning Products, Processes, And Systems For A Helical Economy, Ryan Bradley, Ibrahim S. Jawahir Jan 2019

Designing And Redesigning Products, Processes, And Systems For A Helical Economy, Ryan Bradley, Ibrahim S. Jawahir

Institute for Sustainable Manufacturing Faculty Publications

The Circular Economy (CE) concept has promised to unlock trillions of dollars in business value while driving a significant reduction in the world’s resource consumption and anthropogenic emissions. However, CE mainly lives in ambiguity in the manufacturing domain because CE does not address the changes needed across all of the fundamental elements of manufacturing: products, processes, and systems. Conceptually, CE is grounded in the concept of closed-loop material flows that fit within ecological limits. This grounding translates into a steady state economy, a result that is not an option for the significant portion of the world living in poverty. Therefore, …


Evaluating Reforestation Options For Surface Mines In Appalachia, Joseph Frederick Jan 2019

Evaluating Reforestation Options For Surface Mines In Appalachia, Joseph Frederick

Theses and Dissertations--Forestry and Natural Resources

During the last century coal extraction has degraded ecosystems in Appalachia, converting forested land into other cover types that have a diminished capacity to naturally progress to later stages of succession. This projects objective was to examine two options for land-use that can assist in returning the reclaimed surface mines to forested cover types, with increased ecosystem services, and a potential for economic gain.

This project examined a biomass plantation and an American chestnut trial. In the biomass trial, greatest heights for American sycamore (12.3 m) and black locust (8.0 m) were found in the fertilizer plots. Mean individual tree …


Long-Term Land Management Practices And Their Effect On Soil Health And Crop Productivity, Thomas Joseph Muratore Jr. Jan 2019

Long-Term Land Management Practices And Their Effect On Soil Health And Crop Productivity, Thomas Joseph Muratore Jr.

Theses and Dissertations--Plant and Soil Sciences

Agricultural intensification reliant on monocrops could change soil health in a way that does not support maximum crop productivity. Twenty-nine-year-old no-till field plots at the University of Kentucky Spindletop research farm showed a significant reduction in corn yields from continuous corn plots compared to those from plots in various types of rotation. The objective of this study was to determine what role soil microbes might play in yield reduction and how management and time effects microbial community structure. Samples were collected from the following treatments: continuous corn (CC), continuous soybean (SS), a 2-year corn/soybean rotation (CCSS), Corn in rotation with …


A New Independence Measure And Its Applications In High Dimensional Data Analysis, Chenlu Ke Jan 2019

A New Independence Measure And Its Applications In High Dimensional Data Analysis, Chenlu Ke

Theses and Dissertations--Statistics

This dissertation has three consecutive topics. First, we propose a novel class of independence measures for testing independence between two random vectors based on the discrepancy between the conditional and the marginal characteristic functions. If one of the variables is categorical, our asymmetric index extends the typical ANOVA to a kernel ANOVA that can test a more general hypothesis of equal distributions among groups. The index is also applicable when both variables are continuous. Second, we develop a sufficient variable selection procedure based on the new measure in a large p small n setting. Our approach incorporates marginal information between …


Serial Testing For Detection Of Multilocus Genetic Interactions, Zaid T. Al-Khaledi Jan 2019

Serial Testing For Detection Of Multilocus Genetic Interactions, Zaid T. Al-Khaledi

Theses and Dissertations--Statistics

A method to detect relationships between disease susceptibility and multilocus genetic interactions is the Multifactor-Dimensionality Reduction (MDR) technique pioneered by Ritchie et al. (2001). Since its introduction, many extensions have been pursued to deal with non-binary outcomes and/or account for multiple interactions simultaneously. Studying the effects of multilocus genetic interactions on continuous traits (blood pressure, weight, etc.) is one case that MDR does not handle. Culverhouse et al. (2004) and Gui et al. (2013) proposed two different methods to analyze such a case. In their research, Gui et al. (2013) introduced the Quantitative Multifactor-Dimensionality Reduction (QMDR) that uses the overall …


Procure-To-Pay Software In The Digital Age: An Exploration And Analysis Of Efficiency Gains And Cybersecurity Risks In Modern Procurement Systems, Drew Lane Jan 2019

Procure-To-Pay Software In The Digital Age: An Exploration And Analysis Of Efficiency Gains And Cybersecurity Risks In Modern Procurement Systems, Drew Lane

MPA/MPP/MPFM Capstone Projects

Procure-to-Pay (P2P) softwares are an integral part of the payment and procurement processing functions at large-scale governmental institutions. These softwares house all of the financial functions related to procurement, accounts payable, and often human resources, helping to facilitate and automate the process from initiation of a payment or purchase, to the actual disbursal of funds. Often, these softwares contain budgeting and financial reporting tools as part of the offering. As such an integral part of the financial process, these softwares obviously come at an immense cost from a set of reputable vendors. In the case of government, these vendors mainly …


Does The Emission Trading System Reduce Greenhouse Gas Emissions & Coal Consumption And Lead To An Increase In Renewable Energy? – Evidence From Oecd Member Countries, Pilmu Ryu Jan 2019

Does The Emission Trading System Reduce Greenhouse Gas Emissions & Coal Consumption And Lead To An Increase In Renewable Energy? – Evidence From Oecd Member Countries, Pilmu Ryu

MPA/MPP/MPFM Capstone Projects

The Emission Trading System (ETS) on greenhouse gas (GHG) is a climate change policy well-known as a market-based mitigation mechanism. However, policymakers have faced strong opposition of many stakeholders and failed to persuade them in the process to introduce the ETS. Objective evidence on ETS impact not only provides information to policymakers but also may help alleviate controversy between stakeholders and policymakers. Also, empirical results on ETS will be able to contribute to the theoretical economic study of cap-and-trade. In this context, this research aims at empirical analyses of ETS impact with regard to GHG emissions, coal consumption, and renewable …


Evaluating The Impact Of Fine Particulate Matter Pollution Standards On Mortality Rates In The Southeastern United States, Lauren Wice Jan 2019

Evaluating The Impact Of Fine Particulate Matter Pollution Standards On Mortality Rates In The Southeastern United States, Lauren Wice

MPA/MPP/MPFM Capstone Projects

The Environmental Protection Agency (EPA) continuously monitors six criteria pollutants that are known to have impacts on public health and welfare. One of these pollutants, fine particulate matter, or PM2.5 (which includes particles that are smaller than 2.5 micrometers in diameter), is easily inhalable and can enter the lining of the lungs and the bloodstream, posing a great risk to human health. Standards for allowable concentrations of PM2.5 were amended in 1997, 2006, and again in 2012, becoming increasingly stringent each time. According to the EPA, health organizations, and other research studies, these particles can specifically contribute to …


An Inverse Eigenvalue Problem For The Schrödinger Equation On The Unit Ball Of R3, Maryam Ali Al Ghafli Jan 2019

An Inverse Eigenvalue Problem For The Schrödinger Equation On The Unit Ball Of R3, Maryam Ali Al Ghafli

Theses and Dissertations--Mathematics

The inverse eigenvalue problem for a given operator is to determine the coefficients by using knowledge of its eigenfunctions and eigenvalues. These are determined by the behavior of the solutions on the domain boundaries. In our problem, the Schrödinger operator acting on functions defined on the unit ball of $\mathbb{R}^3$ has a radial potential taken from $L^2_{\mathbb{R}}[0,1].$ Hence the set of the eigenvalues of this problem is the union of the eigenvalues of infinitely many Sturm-Liouville operators on $[0,1]$ with the Dirichlet boundary conditions. Each Sturm-Liouville operator corresponds to an angular momentum $l =0,1,2....$. In this research we focus on …


Electronic Properties Of Atomically Thin Material Heterostructures, M. Javad Farrokhi Jan 2019

Electronic Properties Of Atomically Thin Material Heterostructures, M. Javad Farrokhi

Theses and Dissertations--Physics and Astronomy

There is a movement in the electronic industry toward building electronic devices with dimensions smaller than is currently possible. Atomically thin 2D material, such as graphene, bilayer graphene, hBN and MoS2 are great candidate for this goal and they have a potential set of novel electronic properties compare to their bulk counterparts due to the exhibition of quantum confinement effects. To this goal, we have investigated the electric field screening of multilayer 2D materials due to the presence of impurity charge in the interface and vertical electric fifield from back gate. Our result shows a dramatic difference of screening behavior …


Variability In Groundwater Flow And Chemistry In The Houzhai Karst Basin, Guizhou Province, China, Joshua M. Barna Jan 2019

Variability In Groundwater Flow And Chemistry In The Houzhai Karst Basin, Guizhou Province, China, Joshua M. Barna

Theses and Dissertations--Earth and Environmental Sciences

Understanding how karst aquifers store and transmit water and contaminants is an ongoing problem in hydrogeology. Flowpath and recharge heterogeneity contribute to the complexity of these systems. This thesis explores karst-conduit connectivity and water chemistry variability in the Houzhai catchment in Guizhou province, China. Artificial tracer tests were conducted during both the monsoon and dry seasons to understand temporal variability in connectivity and water velocity between karst features. Multiple flowpaths through the catchment are activated during the monsoon season and partially abandoned during the dry season. Additionally, gradient reversals during monsoonal high-flow events and as a result of pumping can …


Mineral Exploration And Sustainable Development: A Case Study In The Republic Of South Sudan, Cosmas Pitia Kujjo Jan 2019

Mineral Exploration And Sustainable Development: A Case Study In The Republic Of South Sudan, Cosmas Pitia Kujjo

Theses and Dissertations--Earth and Environmental Sciences

South Sudan, a new country formed in 2011, has been planning to develop its mineral sector by allocating exploration licenses to investors. This decision requires preliminary knowledge of geology and mineral occurrences, both of which are unavailable because the country has been engaged in a civil war for more than 50 years. Exploration of mineral resources in South Sudan has lagged behind its petroleum industry, except for artisanal gold mining, which is practiced intermittently by local communities. Freely available satellite gravity and remote-sensing data were used to map the basement architecture as well as zones of hydrothermal alteration in the …


The Role Of Angular Momentum In The Interplay Between Disk Galaxies And Their Host Dark Matter Halos: Corollaries For The Hubble Fork Diagram, Angela Collier Jan 2019

The Role Of Angular Momentum In The Interplay Between Disk Galaxies And Their Host Dark Matter Halos: Corollaries For The Hubble Fork Diagram, Angela Collier

Theses and Dissertations--Physics and Astronomy

A majority of disk galaxies host stellar bars that regulate and amplify the flow of angular momentum, J, between disks and their parent dark matter (DM) halos. These bars constitute the prime factor driving internal galaxy evolution. Yet, a non-negligible fraction of disks lack this morphological feature, which led to adoption of the Hubble Fork Diagram. The complex evolution of barred galaxies has been studied by means of numerical simulations, complemented by observations. Despite prolonged efforts, many fundamental questions remain, in part because cosmological simulations still lack the necessary resolution to account for resonant interactions and simulations of isolated …


Determining Rates Of Landscape Response To Tectonic Forcing Across A Range Of Temporal Scales And Erosional Mechanisms: Teton Range, Wy, Meredith Swallom Jan 2019

Determining Rates Of Landscape Response To Tectonic Forcing Across A Range Of Temporal Scales And Erosional Mechanisms: Teton Range, Wy, Meredith Swallom

Theses and Dissertations--Earth and Environmental Sciences

Understanding how mountain landscapes respond to variations in tectonic forcing over a range of temporal scales in active mountain belts remains as a prominent challenge in tectonic and geomorphological studies. Although a number of empirical and numerical studies have examined this problem, many of them were complicated by issues of scale and climatic variability. More specifically, the relative efficiencies of fluvial and glacial erosion, which are presumably controlled by climate, are difficult to unravel. The Teton Range in Wyoming, which results from motion on the crustal-scale Teton fault, is an ideal natural laboratory for addressing this challenge as the tectonic …


Characterizations Of Linear Ground Motion Site Response In The New Madrid And Wabash Valley Seismic Zones And Seismicity In The Northern Eastern Tennessee Seismic Zone And Rome Trough, Eastern Kentucky, Nicholas Von Seth Carpenter Jan 2019

Characterizations Of Linear Ground Motion Site Response In The New Madrid And Wabash Valley Seismic Zones And Seismicity In The Northern Eastern Tennessee Seismic Zone And Rome Trough, Eastern Kentucky, Nicholas Von Seth Carpenter

Theses and Dissertations--Earth and Environmental Sciences

The central and eastern United States is subject to seismic hazards from both natural and induced earthquakes, as evidenced by the 1811-1812 New Madrid earthquake sequence, consisting of at least three magnitude 7 and greater earthquakes, and by four magnitude 5 and greater induced earthquakes in Oklahoma since 2011. To mitigate seismic hazards, both earthquake sources and their effects need to be characterized.

Ground motion site response can cause additional damage to susceptible infrastructure and buildings. Recent studies indicate that Vs30, one of the primary site-response predictors used in current engineering practice, is not reliable. To investigate site response in …


Extension Of A Quaternary-Active Shear Zone Across The Reelfoot Fault Stepover Arm: Evidence From P- And Sh-Wave Seismic Reflection Imaging, Brooks Rosandich Jan 2019

Extension Of A Quaternary-Active Shear Zone Across The Reelfoot Fault Stepover Arm: Evidence From P- And Sh-Wave Seismic Reflection Imaging, Brooks Rosandich

Theses and Dissertations--Earth and Environmental Sciences

Many seismic hazard source parameters such as slip rate, total displacement, strain accommodation, geographic fault location, etc. are poorly constrained in the New Madrid seismic zone (NMSZ). This is in large part due to the masking effect of the thick Mississippi embayment sediment package on seismogenic structures and features. Consequently, much of the subsurface geologic characterization needed for understanding seismic hazard sources requires geophysical imaging. Recent seismic reflection surveys 12 km NE of the Reelfoot Fault stepover arm of the NMSZ have suggested a northeast-oriented transpressional fault zone extending across the Reelfoot Fault stepover arm where its dextral displacement at …


Rule Mining And Sequential Pattern Based Predictive Modeling With Emr Data, Orhan Abar Jan 2019

Rule Mining And Sequential Pattern Based Predictive Modeling With Emr Data, Orhan Abar

Theses and Dissertations--Computer Science

Electronic medical record (EMR) data is collected on a daily basis at hospitals and other healthcare facilities to track patients’ health situations including conditions, treatments (medications, procedures), diagnostics (labs) and associated healthcare operations. Besides being useful for individual patient care and hospital operations (e.g., billing, triaging), EMRs can also be exploited for secondary data analyses to glean discriminative patterns that hold across patient cohorts for different phenotypes. These patterns in turn can yield high level insights into disease progression with interventional potential. In this dissertation, using a large scale realistic EMR dataset of over one million patients visiting University of …


Optimal Gateway Placement In Low-Cost Smart Cities, Oluwashina Madamori Jan 2019

Optimal Gateway Placement In Low-Cost Smart Cities, Oluwashina Madamori

Theses and Dissertations--Computer Science

Rapid urbanization burdens city infrastructure and creates the need for local governments to maximize the usage of resources to serve its citizens. Smart city projects aim to alleviate the urbanization problem by deploying a vast amount of Internet-of-things (IoT) devices to monitor and manage environmental conditions and infrastructure. However, smart city projects can be extremely expensive to deploy and manage partly due to the cost of providing Internet connectivity via 5G or WiFi to IoT devices. This thesis proposes the use of delay tolerant networks (DTNs) as a backbone for smart city communication; enabling developing communities to become smart cities …


Investigation Of Thiol-Containing Biomarkers And Their Role In The Exposome, Tracy Gastineau-Stevens Jan 2019

Investigation Of Thiol-Containing Biomarkers And Their Role In The Exposome, Tracy Gastineau-Stevens

Theses and Dissertations--Chemistry

Exposomics is an emerging area of study that looks at how the environment around a person or persons affects their overall health. Biomarkers have emerged as useful tools to better understand how the exposome affects a person. In this work, we investigate two potential endogenous biomarkers, homocysteine and glutathione that have been previously implicated in a number of diseases that have been linked to environmental causes. We also investigated an environmental exposure, the fungicide Ziram, which epidemiologically has been linked to diseases. In our investigation, we utilized capillary electrophoresis and capillary electrophoresis-mass spectrometry to develop a method for homocysteine and …


Oleic Acid Vesicles: Formation, Mechanisms Of Reactivity, And Uses In Determination Of Terpene Activity, Laura A. Walther Jan 2019

Oleic Acid Vesicles: Formation, Mechanisms Of Reactivity, And Uses In Determination Of Terpene Activity, Laura A. Walther

Theses and Dissertations--Chemistry

This dissertation will focus on the volatile compounds released upon the burning of incense which are numerous and varied. The first part of this dissertation is the gas chromatography-mass spectral (GC-MS) analysis of burning incense collected via solid phase microextraction (SPME) with the aim of developing a library of compounds found in incense as used in the Orthodox church.

The second part of this dissertation has the aim of developing a method for forming oleic acid bilayer vesicle membranes and a fluorescence spectroscopy method by which the reactivities of these vesicles can be analyzed. These reactivities include permeability, fluidity, aggregation, …


Modeling The Condensed-Phase Behavior Of Π-Conjugated Polymers, Walker Mask Jan 2019

Modeling The Condensed-Phase Behavior Of Π-Conjugated Polymers, Walker Mask

Theses and Dissertations--Chemistry

It is well established that the morphology and physical properties of an organic semiconducting (OSC) material regulate its electronic properties. However, structure-function relationships remain difficult to describe in polymer-based OSC, which are of particular interest due to their robust mechanical properties. If relationships among the molecular and bulk levels of structure can be found, they can aid in the design of improved materials. To explore and detail important structure-function relationships in polymer-based OSC, this work employs molecular dynamics (MD) simulations to study various π-conjugated polymers in different environments. Two independent investigations are discussed in this work. One investigation examines how …


Bottom-Up Lignomics: Towards The Development Of Adduct Electrospray Ionization Mass Spectrometric Methods To Characterize And Sequence Lignin Oligomers, Shardrack O. Asare Jan 2019

Bottom-Up Lignomics: Towards The Development Of Adduct Electrospray Ionization Mass Spectrometric Methods To Characterize And Sequence Lignin Oligomers, Shardrack O. Asare

Theses and Dissertations--Chemistry

Lignin, the second most abundant naturally occurring polymer found in plant cell wall has the potential of becoming an alternative source for the production of chemical synthons for the pharmaceuticals and other chemical industries. While much gain has been made towards the development of degradation methods to break down lignin, effective analytical methods are still required to rapidly and accurately identify the products of lignin breakdown experiments. The goal of this work was to develop mass spectrometric methods for the characterization of lignin oligomers based on the study of model lignin compounds.

Unlike peptides and oligosaccharides, lignin model compounds that …


Oxidative Depolymerization Of Lignin To Low Molecular Weight Aromatics, Yang Song Jan 2019

Oxidative Depolymerization Of Lignin To Low Molecular Weight Aromatics, Yang Song

Theses and Dissertations--Chemistry

To date, most lignocellulosic biorefinery strategies have focused on optimizing conversion of cellulose to ethanol, leaving lignin as an underutilized biomass constituent. Lignin is engineered by nature with the intent to protect plants from chemical and biological attack; this leaves lignin with high structural irregularity and recalcitrance, rendering conversion of the lignin macromolecule to valuable products particularly challenging. Nevertheless, given that the economics of cellulosic ethanol production are strongly dependent on the value that can be obtained for the lignin co-product, the successful valorization of lignin is a crucial step in the transition towards a bio-based economy.

This thesis focuses …


Bounding The Number Of Compatible Simplices In Higher Dimensional Tournaments, Karthik Chandrasekhar Jan 2019

Bounding The Number Of Compatible Simplices In Higher Dimensional Tournaments, Karthik Chandrasekhar

Theses and Dissertations--Mathematics

A tournament graph G is a vertex set V of size n, together with a directed edge set EV × V such that (i, j) ∈ E if and only if (j, i) ∉ E for all distinct i, jV and (i, i) ∉ E for all iV. We explore the following generalization: For a fixed k we orient every k-subset of V by assigning it an orientation. That is, every facet of the (k − 1)-skeleton of the ( …


Undergraduate Mathematics Students’ Connections Between Their Group Homomorphism And Linear Transformation Concept Images, Jeffrey Slye Jan 2019

Undergraduate Mathematics Students’ Connections Between Their Group Homomorphism And Linear Transformation Concept Images, Jeffrey Slye

Theses and Dissertations--Mathematics

It is well documented that undergraduate students struggle with the more formal and abstract concepts of vector space theory in a first course on linear algebra. Some of these students continue on to classes in abstract algebra, where they learn about algebraic structures such as groups. It is clear to the seasoned mathematician that vector spaces are in fact groups, and so linear transformations are group homomorphisms with extra restrictions. This study explores the question of whether or not students see this connection as well. In addition, I probe the ways in which students’ stated understandings are the same or …


Lattice Simplices: Sufficiently Complicated, Brian Davis Jan 2019

Lattice Simplices: Sufficiently Complicated, Brian Davis

Theses and Dissertations--Mathematics

Simplices are the "simplest" examples of polytopes, and yet they exhibit much of the rich and subtle combinatorics and commutative algebra of their more general cousins. In this way they are sufficiently complicated --- insights gained from their study can inform broader research in Ehrhart theory and associated fields.

In this dissertation we consider two previously unstudied properties of lattice simplices; one algebraic and one combinatorial. The first is the Poincar\'e series of the associated semigroup algebra, which is substantially more complicated than the Hilbert series of that same algebra. The second is the partial ordering of the elements of …


Approximations In Reconstructing Discontinuous Conductivities In The Calderón Problem, George H. Lytle Jan 2019

Approximations In Reconstructing Discontinuous Conductivities In The Calderón Problem, George H. Lytle

Theses and Dissertations--Mathematics

In 2014, Astala, Päivärinta, Reyes, and Siltanen conducted numerical experiments reconstructing a piecewise continuous conductivity. The algorithm of the shortcut method is based on the reconstruction algorithm due to Nachman, which assumes a priori that the conductivity is Hölder continuous. In this dissertation, we prove that, in the presence of infinite-precision data, this shortcut procedure accurately recovers the scattering transform of an essentially bounded conductivity, provided it is constant in a neighborhood of the boundary. In this setting, Nachman’s integral equations have a meaning and are still uniquely solvable.

To regularize the reconstruction, Astala et al. employ a high frequency …


On The Role Of Ill-Conditioning: Biharmonic Eigenvalue Problem And Multigrid Algorithms, Kasey Bray Jan 2019

On The Role Of Ill-Conditioning: Biharmonic Eigenvalue Problem And Multigrid Algorithms, Kasey Bray

Theses and Dissertations--Mathematics

Very fine discretizations of differential operators often lead to large, sparse matrices A, where the condition number of A is large. Such ill-conditioning has well known effects on both solving linear systems and eigenvalue computations, and, in general, computing solutions with relative accuracy independent of the condition number is highly desirable. This dissertation is divided into two parts.

In the first part, we discuss a method of preconditioning, developed by Ye, which allows solutions of Ax=b to be computed accurately. This, in turn, allows for accurate eigenvalue computations. We then use this method to develop discretizations that yield accurate computations …