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Full-Text Articles in Physical Sciences and Mathematics

Measurement Of The Prompt J/Psi Pair Production Cross Section In Pp Collisions At Sqrt(S) = 8 Tev With Cms, Grant Valentine Riley Dec 2017

Measurement Of The Prompt J/Psi Pair Production Cross Section In Pp Collisions At Sqrt(S) = 8 Tev With Cms, Grant Valentine Riley

Doctoral Dissertations

The cross section for the prompt production of J/ψ [J/Psi] meson pairs in proton-proton collisions at √ s[sqrt(s)] = 8 TeV at the LHC from a sample corresponding to an integrated luminosity of 20.2±0.5 fb−1 [inverse femtobarns] has been measured with the CMS detector. It provides unique insight into particle production and proton structure in proton-proton (pp) collisions. The two J/ψ mesons are fully reconstructed in their µ +µ −[mu+ mu-] decay. An acceptance region is defined by the individual J/ψ transverse momentum pT J/ψ [J/Psi pT] and rapidity |y J/ψ| [J/Psi Rapidity]. The total fiducial cross section assuming unpolarized …


Development Of High-Performing Polydimethylsiloxane-Based Membranes For Carbon Dioxide Separation, Tao Hong Dec 2017

Development Of High-Performing Polydimethylsiloxane-Based Membranes For Carbon Dioxide Separation, Tao Hong

Doctoral Dissertations

Membrane separation is highlighted as one of the most promising approaches to mitigate the excessive CO2 [carbon dioxide] emission, due to its significant reduction of energy cost compared with many conventional separation techniques. Unfortunately, the separation performance of current membranes does not meet the practical CO2/N2 [nitrogen] separation requirements. And due to the huge volume of industrial flue gas, membranes with exceptionally high permeability are needed for practical reasons.

Currently, the separation mechanism of most polymeric membranes is based on size-sieving. However, this method is not sufficient for CO2/N2 separations due to the …


An Exploration Of Basic Processes For Aqueous Electrochemical Production Of Hydrogen From Biomass Derived Molecules, Brian Fane Dec 2017

An Exploration Of Basic Processes For Aqueous Electrochemical Production Of Hydrogen From Biomass Derived Molecules, Brian Fane

Doctoral Dissertations

Polymer electrolyte membrane fuel cells(PEMFCs) are energy conversion devices with significant potential. The factors preventing them from becoming widespread concern production and distribution of hydrogen. Developing an efficient hydrogen infrastructure with an approachable rollout plan is an essential step towards the future of fuel cells. Water electrolysis is limited by the thermodynamics of the process, which leads to high electrical consumption and significant materials challenges. Alternative methods for cleanly generating hydrogen while using a lower cell voltage are required. PEM based electrolyzers can operate with a "depolarized anode", whereby they become significantly less power hungry.

This thesis explores two techniques …


Design And Synthesis Of Analogs Of Myo-Inositol, Serine, And Cysteine To Enable Chemical Biology Studies, Tanei J. Ricks Dec 2017

Design And Synthesis Of Analogs Of Myo-Inositol, Serine, And Cysteine To Enable Chemical Biology Studies, Tanei J. Ricks

Doctoral Dissertations

Phosphorylated myo-inositol compounds including inositol phosphates (InsPs) as well as the phosphatidylinositol polyphosphate lipids (PIPns) are critical biomolecules that regulate many of the most important biological processes and pathways. They are aberrant in many disease states due to their regulatory function. The same is true of the phospholipid phosphatidylserine (PS) which can serve as a marker to begin apoptosis. However, the full scope of activities of these structures is not clear, particularly since techniques that enable global detection and analysis of the production of these compounds spatially and temporally are lacking. With all of these obstacles in …


Search For The Decays Of 113ba, Yongchi Xiao Dec 2017

Search For The Decays Of 113ba, Yongchi Xiao

Doctoral Dissertations

The search for new alpha-emitters in the region above tin-100 was carried out in Japan Atomic Energy Agency (JAEA) tandem accelerator in Tokai, Japan. This work aimed to discover barium-113 produced via the fusion-evaporation reaction nickel-58(nickel-58,3n)barium-113 and observation through its alpha-decay chain from barium-113 to xenon-109 to tellurium-105 and tin-101. In the proof of principle experiment in March 2014, the alpha-decay chain of xenon-109 was observed with Double-sided Silicon Strip Detector (DSSD) and digital electronics at JAEA Recoil Mass Separator (RMS). The first discovery-oriented barium-113 experiment was carried out in December 2014 searching for its alpha-decay, ground-state to ground-state beta-decay …


Multiscale Modeling Approach To Understand Active Sites In Non-Conventional Catalyst Layers For Fuel Cell Applications, Diana Constanza Orozco Gallo Dec 2017

Multiscale Modeling Approach To Understand Active Sites In Non-Conventional Catalyst Layers For Fuel Cell Applications, Diana Constanza Orozco Gallo

Doctoral Dissertations

Fuel cells development required stable, active and more abundant catalytic materials. Oxygen reduction reaction (ORR) is the key process to enhance better activity and reduce the fabrication costs. Pt-based has proven to be the best catalyst for ORR and greater efforts has been made in terms of reducing the Pt content in the electrodes, reduce electrode thickness and enhance better catalytic activities. To overcome many of the challenges present, the catalyst layer studies are the great importance in the fuel cell community. Understanding catalyst layer with new catalytic materials, and configurations requires the development of methodological approach to relate structure, …


From Pyrochlore To The Tripod Kagome Lattice: Magnetism Of New Compound Family A2re3sb3o14 (A = Mg, Zn; Re = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb), Zhiling Dun Dec 2017

From Pyrochlore To The Tripod Kagome Lattice: Magnetism Of New Compound Family A2re3sb3o14 (A = Mg, Zn; Re = Pr, Nd, Gd, Tb, Dy, Ho, Er, Yb), Zhiling Dun

Doctoral Dissertations

Geometrical frustration refers to the inability of a complex system to satisfy all its competing interactions within an underlying topological constrained lattice. The two-dimensional kagome lattice is one of the most frustrated lattices and has been a favorite in the theoretical condensed matter community. However, the large variety of exotic states predicted in kagome lattices lies in contrast to a paucity of experimental systems, making new kagome lattice compounds highly desired.

In this dissertation, I shall provide a systematic study of the structural and magnetic properties of a new compounds family, A2RE3Sb3O14 (A = Mg, Zn; RE = Pr, Nd, …


Development And Implementation Of Redox-Active Olefin Polymerization Catalysts, William Curtis Anderson Jr. Dec 2017

Development And Implementation Of Redox-Active Olefin Polymerization Catalysts, William Curtis Anderson Jr.

Doctoral Dissertations

Investigating homogeneous polymerization catalysts has been a thriving area of chemistry in the academic realm for several decades now, and has helped drive the development of a range of materials, from designer plastics to cheap commodity polymers. Billions of pounds of these materials are produced every year, which ensures that continuing research in the area will be necessary to improve current processes and enable more economic use of our resources.

This dissertation showcases the Long group’s research in homogeneous polymerization catalysis and our impact on the field thus far. We show that intelligent design of redox-active catalysts allows for a …


Impact Of Soil Water Content On Bermudagrass Athletic Field Performance, Kyley Hampton Dickson Dec 2017

Impact Of Soil Water Content On Bermudagrass Athletic Field Performance, Kyley Hampton Dickson

Doctoral Dissertations

Soil water content (SWC) influences the consistency and performance of athletic fields. Two studies were conducted at the University of Tennessee Center for Athletic Field Safety (Knoxville, TN) to determine SWC impact on the performance of hybrid bermudagrass [Cynodon dactylon (L.) Pers. x C. transvaalensis, Burtt-Davy, ‘Tifway’] on silt loam (cohesive) and sand root zone conforming to United States Golf Association (USGA) specifications (noncohesive) root zones. Soil water content treatments for the cohesive soil averaged 0.10 m3/m3 (+/- 0.035), 0.17 m3/m3 (+/- 0.035), 0.26 m3/m3 (+/- 0.035), and 0.35 …


Transport Of Water And Ions Through Single-Walled Armchair Carbon Nanotubes: A Molecular Dynamics Study, Michelle Patricia Aranha Dec 2017

Transport Of Water And Ions Through Single-Walled Armchair Carbon Nanotubes: A Molecular Dynamics Study, Michelle Patricia Aranha

Doctoral Dissertations

The narrow hydrophobic interior of a carbon nanotube (CNT) poses a barrier to the transport of water and ions, and yet, unexpectedly, numerous experimental and simulation studies have confirmed fast water transport rates comparable to those seen in biological aquaporin channels. These outstanding features of high water permeability and high solute rejection of even dissolved ions that would typically require a lot of energy for separation in commercial processes makes carbon nanotubes an exciting candidate for desalination membranes. Extending ion exclusion beyond simple mechanical sieving by the inclusion of electrostatics via added functionality to the nanotube bears promise to not …


Analysis Of Primary Stripper Foils At The Spallation Neutron Source By An Electron Beam Foil Test Stand, Eric Paul Barrowclough Dec 2017

Analysis Of Primary Stripper Foils At The Spallation Neutron Source By An Electron Beam Foil Test Stand, Eric Paul Barrowclough

Doctoral Dissertations

Diamond films are used at the Spallation Neutron Source (SNS) as the primary charge exchange foils (i.e., stripper foils) of the accelerated 1 GeV (Gigaelectron volts) hydride ions. The most common type of film used is a nanocrystalline diamond film, typically 17 mm x 45 mm (millimeter) with an aerial density of 350 μg/cm2 (microgram per square centimeter). The diamond film is deposited on a corrugated silicon substrate using plasma-assisted chemical vapor deposition. After the growth of the diamond film, 30 mm of the silicon substrate is etched away, leaving a freestanding diamond foil with a silicon handle that …


Exploration Of Equal Tune Transverse Coupling In The Spallation Neutron Source Accumulator Ring, Robert Edward Potts Iii Dec 2017

Exploration Of Equal Tune Transverse Coupling In The Spallation Neutron Source Accumulator Ring, Robert Edward Potts Iii

Doctoral Dissertations

The development of hadron machines is one of the main areas of focus in accelerator technology and is specifically called out as a priority in the high energy physics 10-year plan[70]. The trend for future accelerators is to move towards very high-intensity high-power accelerators to be used as proton drivers for secondary particles, target stations, and high-energy accelerators. These accelerators require lower beam losses and more stringent beam controls to maintain typical loss levels and meet specific final beam distributions.

This study focuses on the recently documented coupling resonance in the Spallation Neutron Source (SNS) accumulator ring. It was previously …


Memory Response: Exposure History Dependence Of Microbial Mediated Transformations Of Substrates In Groundwater, Charles Joseph Paradis Dec 2017

Memory Response: Exposure History Dependence Of Microbial Mediated Transformations Of Substrates In Groundwater, Charles Joseph Paradis

Doctoral Dissertations

The flow, transport, and reactivity of dissolved-phase constituents in an unconfined and shallow aquifer were characterized, in situ, by utilizing the single-well push-pull test method. In the first study, the re-oxidation/mobility of uranium, in the presence of nitrate oxidant, was shown to be mitigated by preferential oxidation/mobilization of solid-phase, reduced, sulfur-bearing species. These results indicated that establishing conditions conducive to uranium reduction and the formation of reduced sulfur-bearing species can increase the efficacy of sustained uranium reduction/immobility in the presence of re-mobilizing oxidants. In the second study, the analytical solution to describe the one-dimensional displacement of the center of …


Numerical Studies Of Iron Based Superconductors Using Spin-Fermion Models, Christopher Brian Bishop Dec 2017

Numerical Studies Of Iron Based Superconductors Using Spin-Fermion Models, Christopher Brian Bishop

Doctoral Dissertations

The iron pnictide and iron chalchogenide superconductors are studied numerically using classical Monte Carlo techniques to reproduce experimental data and make predictions about the nature of the relevant interactions. The focus will be using Spin-Fermion models in a classical approximation to explore the phase diagram and calculate important physical properties of these materials over a wide range of temperatures.


Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics, John Timothy Cummings Dec 2017

Mathematical Modeling Of Mixtures And Numerical Solution With Applications To Polymer Physics, John Timothy Cummings

Doctoral Dissertations

We consider in this dissertation the mathematical modeling and simulation of a general diffuse interface mixture model based on the principles of energy dissipation. The model developed allows for a thermodynamically consistent description of systems with an arbitrary number of different components, each of which having perhaps differing densities. We also provide a mathematical description of processes which may allow components to source or sink into other components in a mass conserving, energy dissipating way, with the motivation of applying this model to phase transformation. Also included in the modeling is a unique set of thermodynamically consistent boundary conditions which …


Local Moments And Itinerant Electrons: Gaining New Insights Through Investigating Electronic And Dynamical Properties, Nicholas Steven Sirica Aug 2017

Local Moments And Itinerant Electrons: Gaining New Insights Through Investigating Electronic And Dynamical Properties, Nicholas Steven Sirica

Doctoral Dissertations

Magnetic materials are often categorized in terms of either a purely local or a purely itinerant picture despite the fact that the vast majority actually fall within a spectrum that ranges between these two extremes. It is from such a starting point that this thesis aims at developing an understanding of how the complex interplay between local moments and itinerant electrons ultimately affects the electronic and dynamical properties. Such ideas are explored in greater detail using two materials as case studies: the chiral helimagnet Cr1/3NbS2 [Cr intercalated Niobium Disulfide] and YFe2Ge2 [Yttrium Iron Germanide] …


On Laser-Induced Plasma Containing Hydrogen, Ghaneshwar Gautam Aug 2017

On Laser-Induced Plasma Containing Hydrogen, Ghaneshwar Gautam

Doctoral Dissertations

Laser-induced micro-plasma dynamics are investigated in laboratory air, ultra-high-pure hydrogen gas, and hydrogen-nitrogen gas mixtures. The dissertation focuses on atomic spectroscopy of hydrogen in the visible region.

Line-of-sight measurements are analyzed to obtain spatial distributions of electron densities and excitation temperatures. The studies include evaluation of self-absorption phenomena. The plasma dynamics occur initially well above re-entry speeds and diminish to hypersonic and then supersonic expansions. Expansion velocities are measured that are above three hundred times the speed of sound in standard atmosphere. Optical breakdown is induced by using pulsed laser radiation. Emission spectra are collected by employing a spectrometer equipped …


First-Principles Study Of Point Defect Behavior At Interfaces And In-Plane Strain Fields, Jianqi Xi Aug 2017

First-Principles Study Of Point Defect Behavior At Interfaces And In-Plane Strain Fields, Jianqi Xi

Doctoral Dissertations

Interfaces in solid materials are the so-called boundaries, separating crystals with the same structure and chemistry but different orientations, e.g. grain boundaries (GBs), different stacking sequences, e.g. stacking faults (SFs), or crystals with different structures and/or chemistries as well as orientations, e.g. the interface between substrate and thin film. In this study, first-principles calculations are used to investigate the defect behavior at different interfaces and in-plane strain fields, such as stacking fault (SF) in silicon carbide (SiC), in-plane strain field near interfaces in potassium tantalate (KTaO3), and grain boundary in ceria (CeO2).

Results show that the …


Metal Oxyhalides And Halides For Use As Electrode Materials In Li-Ion Batteries, Jonathan Mark Powell Aug 2017

Metal Oxyhalides And Halides For Use As Electrode Materials In Li-Ion Batteries, Jonathan Mark Powell

Doctoral Dissertations

Synthesis of select metal halides and oxyhalides are explored in the form of direct fluorination using a fluidized bed reactor system, direct chlorination using hydrogen chloride gas, and a degradation dehydration reaction as novel methods towards the synthesis of these select metal halides and oxyhalides. The flexibility of the direct fluorination technique is demonstrated by the ability to vary the degree of fluorination based on the reaction conditions of temperature, time, and fluorine concentration. Conversion electrodes in the form of metal halides and metal oxyhalides are investigated as both anode and cathode materials for lithium ion batteries. The resulting electrochemical …


Surface Modification Of Icy Satellites: Space Weathering Of The Large Moons Of Uranus And Alluvial Fan Formation On Saturn’S Moon Titan, Richard John Cartwright Aug 2017

Surface Modification Of Icy Satellites: Space Weathering Of The Large Moons Of Uranus And Alluvial Fan Formation On Saturn’S Moon Titan, Richard John Cartwright

Doctoral Dissertations

The surfaces of icy satellites are continually modified by space weathering and geologic processes. This dissertation explores the processes changing the surface compositions of the large moons of Uranus and mechanisms for development of possible alluvial fans on the Saturnian moon, Titan. On the Uranian satellites, I hypothesize that the origin and distribution of carbon dioxide ice results from charged particle bombardment, and that spectrally red material originated on retrograde irregular satellites. On Titan, I hypothesize that landforms identified as alluvial fans at low and mid latitudes were formed by sheetfloods, whereas possible alluvial fans at high latitudes were formed …


Total Absorption Spectroscopy Of Neutron Rich Nuclei Across The N=50 Neutron Shell Closure, Kathleen Conner Goetz Aug 2017

Total Absorption Spectroscopy Of Neutron Rich Nuclei Across The N=50 Neutron Shell Closure, Kathleen Conner Goetz

Doctoral Dissertations

Decay spectroscopy of neutron rich nuclei near doubly magic 78Ni [78-Nickel] is relevant to nuclear structure and astrophysics as well as reactor and neutrino physics. β-decay [beta-decay] calorimetry studies are essential to reconstruct the decay strength function and is used to overcome the problems arising from the high density of states leading to nuclear Pandemonium. The Modular Total Absorption Spectrometer, currently located in HRIBF at the Oak Ridge National Laboratory, collected data on 25 fission products of 238U [238-Uranium] during a run in March 2015. Analysis of the 84,85,86Br [84, 85 and 86-Bromine] data from the …


Electronic And Magnetic Materials Under External Stimuli, Kenneth Robert O'Neal Aug 2017

Electronic And Magnetic Materials Under External Stimuli, Kenneth Robert O'Neal

Doctoral Dissertations

The interaction between spin, charge, and lattice degrees of freedom leads to exotic and useful properties in multifunctional materials. This delicate balance of energy scales allows external stimuli such as temperature, magnetic field, or pressure to drive to novel phases. As a local probe technique, spectroscopy can provide insight into the microscopic mechanism of the phase transitions. In this dissertation I present spectroscopic studies of functional materials under extreme conditions.

Nanomaterials have attracted attention because nanoscale confinement affects various material properties and often reduces energy scales or suppress phase transitions. Combining Raman and infrared spectroscopies reveals that the breakdown mechanism …


Measurement Of Heavy Flavor Yield And Azimuthal Anisotropy At Forward Angles In Cu + Au Collisions At A Center-Of-Mass Collision Energy Per Nucleon Of 200 Gev, Brandon Kyle Schmoll Aug 2017

Measurement Of Heavy Flavor Yield And Azimuthal Anisotropy At Forward Angles In Cu + Au Collisions At A Center-Of-Mass Collision Energy Per Nucleon Of 200 Gev, Brandon Kyle Schmoll

Doctoral Dissertations

Heavy flavor quarks are produced early in heavy ion collisions and will experience the full evolution of the Quark Gluon Plasma (QGP). Measurements at forward rapidity may be influenced as much, or more, by the cold nuclear matter effects as by the hot nuclear matter effects associated with a QGP. As the medium evolves, the initial spatial anisotropy of participants is converted to an azimuthal anisotropy in the momentum space of outgoing particles. Therefore, the momentum spectra modification and anisotropy parameters provide useful information about the heavy quark interaction with the bulk medium.

Asymmetric heavy ion collisions, such as Cu+Au, …


New Optical And Electrochemical Probes For Trace Chemicals With Health And Environmental Impacts, Thomas Stewart Carpenter Aug 2017

New Optical And Electrochemical Probes For Trace Chemicals With Health And Environmental Impacts, Thomas Stewart Carpenter

Doctoral Dissertations

The work in this dissertation focuses on the development of probes for the analysis of trace chemicals in samples with health and environmental impacts. A paper, Cu(copper)-based colorimetric probe was developed for the detection of toxic hydrogen sulfide (H2S) gas. A modified Kipp’s apparatus was used to generate desired concentrations of H2S in a total volume of 1.35 L (liters). The probe shows a qualitative response down to 60 ppb (parts per billion), indicating its ability to be used in industrial settings as a replacement for the commonly used lead acetate strips. When used in conjunction …


Synthesis, Characterization, And Reactive Modification Of 2-Vinyl-4,4-Dimethyl Azlactone Polymers, Bethany Michelle Aden Aug 2017

Synthesis, Characterization, And Reactive Modification Of 2-Vinyl-4,4-Dimethyl Azlactone Polymers, Bethany Michelle Aden

Doctoral Dissertations

Polymeric materials possessing specific functionality have been designed for use in applications such as membranes, biocompatible coatings, lubricants, and tissue engineering. Because the chemical nature of the repeat units set the properties offered by the polymer, the ability to reactively modify polymer chains to integrate specific functionality expands the range of potential applications. Thus, reactive modification of polymer thin films provides a useful route to confer new properties to the underlying material, with the range, strength and type of interaction across the interface dictated by the display of functional groups decorating the surface. To address the links between design, in …


Efficient Methods For Multidimensional Global Polynomial Approximation With Applications To Random Pdes, Peter A. Jantsch Aug 2017

Efficient Methods For Multidimensional Global Polynomial Approximation With Applications To Random Pdes, Peter A. Jantsch

Doctoral Dissertations

In this work, we consider several ways to overcome the challenges associated with polynomial approximation and integration of smooth functions depending on a large number of inputs. We are motivated by the problem of forward uncertainty quantification (UQ), whereby inputs to mathematical models are considered as random variables. With limited resources, finding more efficient and accurate ways to approximate the multidimensional solution to the UQ problem is of crucial importance, due to the “curse of dimensionality” and the cost of solving the underlying deterministic problem.

The first way we overcome the complexity issue is by exploiting the structure of the …


Various Topics On Graphical Structures Placed On Commutative Rings, Darrin Weber Aug 2017

Various Topics On Graphical Structures Placed On Commutative Rings, Darrin Weber

Doctoral Dissertations

In this dissertation, we look at two types of graphs that can be placed on a commutative ring: the zero-divisor graph and the ideal-based zero-divisor graph. A zero-divisor graph is a graph whose vertices are the nonzero zero-divisors of a ring and two vertices are connected by an edge if and only if their product is 0. We classify, up to isomorphism, all commutative rings without identity that have a zero-divisor graph on 14 or fewer vertices.

An ideal-based zero-divisor graph is a generalization of the zero-divisor graph where for a ring R and ideal I the vertices are { …


Data Analysis Methods Using Persistence Diagrams, Andrew Marchese Aug 2017

Data Analysis Methods Using Persistence Diagrams, Andrew Marchese

Doctoral Dissertations

In recent years, persistent homology techniques have been used to study data and dynamical systems. Using these techniques, information about the shape and geometry of the data and systems leads to important information regarding the periodicity, bistability, and chaos of the underlying systems. In this thesis, we study all aspects of the application of persistent homology to data analysis. In particular, we introduce a new distance on the space of persistence diagrams, and show that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Moreover, we introduce a clustering framework directly …


Generalizations Of Coarse Properties In Large Scale Spaces, Kevin Michael Sinclair Aug 2017

Generalizations Of Coarse Properties In Large Scale Spaces, Kevin Michael Sinclair

Doctoral Dissertations

Many results in large scale geometry are proven for a metric space. However, there exists many large scale spaces that are not metrizable. We generalize several concepts to general large scale spaces and prove relationships between them. First we look into the concept of coarse amenability and other variations of amenability on large scale spaces. This leads into the definition of coarse sparsification and connections with coarse amenability. From there, we look into an equivalence of Sako's definition of property A on uniformly locally finite spaces and prove that finite coarse asymptotic definition implies it. As well, we define large …


Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake Aug 2017

Numerical Methods For Non-Divergence Form Second Order Linear Elliptic Partial Differential Equations And Discontinuous Ritz Methods For Problems From The Calculus Of Variations, Stefan Raymond Schnake

Doctoral Dissertations

This dissertation consists of three integral parts. Part one studies discontinuous Galerkin approximations of a class of non-divergence form second order linear elliptic PDEs whose coefficients are only continuous. An interior penalty discontinuous Galerkin (IP-DG) method is developed for this class of PDEs. A complete analysis of the proposed IP-DG method is carried out, which includes proving the stability and error estimate in a discrete W2;p-norm [W^2,p-norm]. Part one also studies the convergence of the vanishing moment method for this class of PDEs. The vanishing moment method refers to a PDE technique for approximating these PDEs by a …