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Articles 541 - 570 of 2316

Full-Text Articles in Physical Sciences and Mathematics

The Double Prior Selection For The Parameter Of Exponential Life Time Model Under Type Ii Censoring, Ronak M. Patel, Achyut C. Patel May 2017

The Double Prior Selection For The Parameter Of Exponential Life Time Model Under Type Ii Censoring, Ronak M. Patel, Achyut C. Patel

Journal of Modern Applied Statistical Methods

A comparison of double informative priors assumed for the parameter of exponential life time model is considered. Three different sets of double priors are included, and the results are compared with a forth single prior. The data is Type II censored and Bayes estimators for the parameter and reliability are carried out under a squared error loss function in the cases of the four different sets of prior distributions. The predictive distribution was derived for future failure time and also for the remaining ordered failure times after the first r failure times have been observed. Corresponding Bayes credible equal tail …


Jmasm43: Teereg: Trimmed Elemental Estimation (R), Wei Jiang, Matthew S. Mayo May 2017

Jmasm43: Teereg: Trimmed Elemental Estimation (R), Wei Jiang, Matthew S. Mayo

Journal of Modern Applied Statistical Methods

Trimmed elemental regression is robust to outliers and violations of model assumptions. Its properties and statistical inference were evaluated using bias-corrected and accelerated bootstrap confidence intervals. An R package named TEEReg is developed to compute the trimmed elemental estimates and the corresponding bootstrap confidence intervals. Two examples are provided to demonstrate its usage.


Outlier Impact And Accommodation On Power, Hongjing Liao, Yanju Li, Gordon P. Brooks May 2017

Outlier Impact And Accommodation On Power, Hongjing Liao, Yanju Li, Gordon P. Brooks

Journal of Modern Applied Statistical Methods

The outliers’ influence on power rates in ANOVA and Welch tests at various conditions was examined and compared with the effectiveness of nonparametric methods and Winsorizing in minimizing the impact of outliers. Results showed that, considering both power and Type I error, a nonparametric test is the safest choice to control the inflation of Type I error with a decent sample size and yield relatively high power.


Book Review: Multivariate Statistical Methods, A Primer, C. R. Rao May 2017

Book Review: Multivariate Statistical Methods, A Primer, C. R. Rao

Journal of Modern Applied Statistical Methods

Multivariate Statistical Methods, A Primer, 4th Ed. Bryan F. J. Manly and Jorge A. Navarro Alberto. NY: Chapman & Hall / CRC Press. 2016. 264 p. ISBN 10: 1498728960 / ISBN 13: 978-1498728966


Jmasm44: Implementing Multiple Ratio Imputation By The Emb Algorithm (R), Masayoshi Takahashi May 2017

Jmasm44: Implementing Multiple Ratio Imputation By The Emb Algorithm (R), Masayoshi Takahashi

Journal of Modern Applied Statistical Methods

Although single ratio imputation is often used to deal with missing values in practice, there is a paucity of discussion regarding multiple ratio imputation. Code in the R statistical environment is presented to execute multiple ratio imputation by the Expectation-Maximization with Bootstrapping (EMB) algorithm.


Investigations Of The Spatial And Temporal Variations Of Sr And Nd Isotopes In Sediments From Two Indian Rivers: Implications To Source Identification, Sonali Pradhan, Jing Zhang, Mark Baskaran, Prabhaker Vasant Shirodkar, Ying Wu, Umesh Kumar Pradhan Apr 2017

Investigations Of The Spatial And Temporal Variations Of Sr And Nd Isotopes In Sediments From Two Indian Rivers: Implications To Source Identification, Sonali Pradhan, Jing Zhang, Mark Baskaran, Prabhaker Vasant Shirodkar, Ying Wu, Umesh Kumar Pradhan

Environmental Science and Geology Faculty Research Publications

Radiogenic isotopes of Sr and Nd provide crucial information on chemical and physical erosion processes, therefore used as tracers for fingerprinting the sources of fluvial sediments. Moreover, elemental geochemistry, 87Sr/86Sr and 143Nd/144Nd signatures in silicate fractions of sediments primarily reflect intricate controls of characteristics and provenance of sediment. A suite of sediment samples collected from two rivers of India, Narmada (large) and Netravati (small) were analyzed for elemental concentrations, 87Sr/86Sr and 143Nd/144Nd in silicate as well as acid-leachable fractions. 87Sr/86Sr in acid-leachable sediment fractions from both the rivers (0.7094 ± 0.0002 for Narmada and 0.7158 ± 0.003 for Netravati) showed …


Velocity Variations And Uncertainty From Transdimensional P-Wave Tomography Of North America, Scott Burdick, Vedran Lekić Mar 2017

Velocity Variations And Uncertainty From Transdimensional P-Wave Tomography Of North America, Scott Burdick, Vedran Lekić

Environmental Science and Geology Faculty Research Publications

High-resolution models of seismic velocity variations constructed using body-wave tomography inform the study of the origin, fate and thermochemical state of mantle domains. In order to reliably relate these variations to material properties including temperature, composition and volatile content, we must accurately retrieve both the patterns and amplitudes of variations and quantify the uncertainty associated with the estimates of each. For these reasons, we image the mantle beneath North America with P-wave traveltimes from USArray using a novel method for 3-D probabilistic body-wave tomography. The method uses a Transdimensional Hierarchical Bayesian framework with a reversible-jump Markov Chain Monte Carlo algorithm …


Investigation Of Firn Aquifer Structure In Southeastern Greenland Using Active Source Seismology, Lynn N. Montgomery, Nicholas Schmerr, Scott Burdick, Richard R. Forster, Lora Koenig, Anatoly Legchenko, Stefan Ligtenberg, Clément Miège, Olivia L. Miller, D. Kip Solomon Feb 2017

Investigation Of Firn Aquifer Structure In Southeastern Greenland Using Active Source Seismology, Lynn N. Montgomery, Nicholas Schmerr, Scott Burdick, Richard R. Forster, Lora Koenig, Anatoly Legchenko, Stefan Ligtenberg, Clément Miège, Olivia L. Miller, D. Kip Solomon

Environmental Science and Geology Faculty Research Publications

In spring of 2011, a perennial storage of water was observed in the firn of the southeastern Greenland Ice Sheet (GrIS), a region of both high snow accumulation and high melt. This aquifer is created through percolation of surface meltwater downward through the firn, saturating the pore space above the ice-firn transition. The aquifer may play a significant role in sea level rise through storage or draining freshwater into the ocean. We carried out a series of active source seismic experiments using continuously refracted P-waves and inverted the first P-arrivals using a transdimensional Bayesian approach where the depth, velocity, and …


Memorium: Bhamidipati Lakshmidhara Kanakadri Somayajulu (1937-2016), Mark Baskaran, R. Ramesh Jan 2017

Memorium: Bhamidipati Lakshmidhara Kanakadri Somayajulu (1937-2016), Mark Baskaran, R. Ramesh

Environmental Science and Geology Faculty Research Publications

The demise of B. L. K. Somayajulu, an illustrious nuclear geochemist, brings great sadness to the community of geo- logists, geochemists and oceanographers in India and elsewhere.


A Review Of The Multiple-Sample Tests For The Continuous-Data Type, Dewi Rahardja Jan 2017

A Review Of The Multiple-Sample Tests For The Continuous-Data Type, Dewi Rahardja

Journal of Modern Applied Statistical Methods

For continuous data, various statistical hypotheses testing methods have been extensively discussed in the literature. In this article a review is provided of the multiple-sample continuous-data testing methods. It includes traditional methods, such as the two-sample t-test, Welch ANOVA test, etc., as well as newly-developed ones, such as the various Multiple Comparison Procedure (MCP). A roadmap is provided in a figure or diagram format as to which methods are available in the literature. Additionally, the implementation of these methods in popular statistical software packages such as SAS is also presented. This review will be helpful to determine which continuous-data testing …


Factor Analysis By Limited Scales: Which Factors To Analyze?, Stan Lipovetsky Jan 2017

Factor Analysis By Limited Scales: Which Factors To Analyze?, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Factor Analysis (FA) and Principal Component Analysis (PCA) are well-known main tools of the multivariate statistics for data analysis, reduction, and visualization. Commonly, the analysis and interpretation of their solutions is performed for each of several main eigenvectors with variances explaining a big part of the total variability in data. The recommendation is to determine if all the main vectors are really needed in the analysis, or some of them should be skipped if they correspond to the absence of the analyzing features. A simple criterion for identifying redundant vectors of loadings is their negative correlation with the vector of …


Prediction Of Percent Change In Linear Regression By Correlated Variables, Stan Lipovetsky Jan 2017

Prediction Of Percent Change In Linear Regression By Correlated Variables, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Multiple linear regression can be applied for predicting an individual value of dependent variable y by the given values of independent variables x. But it is not immediately clear how to estimate percent change in y due to changes in predictors, especially when those are correlated. This work considers several approaches to this problem, including its formulation via predictors adjusted by their correlation structure. Ordinary least squares regression is used, together with Shapley value regression and another model based on solving some system of differential equations. Numerical estimations performed for a real marketing research data demonstrate meaningful results. The considered …


The In Vivo Effect Of Oil Palm Phenolics (Opp) In Atherogenic Diet Induced Rats Model Of Alzheimer’S Disease (Ad), Yan Wu Jan 2017

The In Vivo Effect Of Oil Palm Phenolics (Opp) In Atherogenic Diet Induced Rats Model Of Alzheimer’S Disease (Ad), Yan Wu

Wayne State University Dissertations

Alzheimer’s disease (AD) is the most common cause of dementia in the aging population. It is characterized by cognitive decline and deposition of ß-amyloid plaques in the hippocampus. It has been shown that hypercholesterolemia induced by high cholesterol diet is associated with AD development. Increased level of oxidative stress has also been observed in AD patients. An important strategy to treat or delay the impairment is based on dietary modification, using food supplements. OPP, a water soluble fraction from oil palm fruit, rich in phenolics has been found to possess significant antioxidant activities. Its beneficial effects on cardiovascular diseases, diabetes …


Synthesis Of Discrete Transition Metal (Ni, Fe, Co, Mn) Phosphide Nanoparticles: Compositional Effect On Catalytic And Magnetic Properties, Da Li Jan 2017

Synthesis Of Discrete Transition Metal (Ni, Fe, Co, Mn) Phosphide Nanoparticles: Compositional Effect On Catalytic And Magnetic Properties, Da Li

Wayne State University Dissertations

This dissertation research is focused on the synthesis, characterization of binary and ternary transition metal (Ni, Co, Fe, Mn) phosphide nanomaterials and their catalytic and magnetic properties.

A phase-control strategy enabling the arrested-precipitation synthesis of nanoparticles of Ni5P4 and NiP2 is presented. The composition and purity of the product can be tuned by changing key synthetic levers, including the metal precursor, the oleylamine (OAm) and Trioctylphosphine (TOP) concentrations, temperature, time and the presence or absence of a moderate temperature soak step to facilitate formation of Ni and/or Ni-P amorphous nanoparticle intermediates.

New CoxFe2-xP nanoparticles (0 ≤ x ≤ 2), Co2-xMnxP …


Commissioning Of The Large Angle Beamstrahlung Monitor At Superkekb, Salvatore Di Carlo Jan 2017

Commissioning Of The Large Angle Beamstrahlung Monitor At Superkekb, Salvatore Di Carlo

Wayne State University Dissertations

The Large Angle Beamstrahlung Monitor (LABM) is a device capable to monitor

the beam-beam collisions. The LABM measures the beamstrahlung light emitted

at large angle during the collisions of electron and positron beams. The properties

of the beamstrahlung, spectrum and polarization, are fundamentally related to the

size and relative position of the beams. Measuring the beamstrahlung, the LABM

delivers information about the size of the beams and their relative position at the

interaction point. The LABM will be part of the instrumentation of SuperKEKB,

a new e+e− collider that aims to reach the world record luminosity of 8×10^35 cm^-2 s^-1. …


Nanostructured Lithium Iron Silicate/Carbon Composites As Cathode Material For Next Generation Of Lithium-Ion Batteries, Ajay Kumar Jan 2017

Nanostructured Lithium Iron Silicate/Carbon Composites As Cathode Material For Next Generation Of Lithium-Ion Batteries, Ajay Kumar

Wayne State University Dissertations

Lithium iron silicate (Li2FeSiO4) has the potential as cathode material for next generation lithium ion batteries because of its high specific theoretical capacity (330 mA h g-1), low cost, environmental benignity, and improved safety. However, itsintrinsically poor electronic conductivity and slow lithium ion diffusion in the solid phase limits its applications. To address these issues, we studied mesoporous Li2FeSiO4/C composites synthesized by sol-gel (SG) and solvothermal (ST) methods using tri-block copolymer (P123) as carbon source and structure directing agent. The Li2FeSiO4/C (ST) composites show improved electrochemical performance compared to Li2FeSiO4/C (SG). At C/30 rate, Li2FeSiO4/C (ST) delivered the discharge capacity …


Selective Atomic Layer Deposition Of Transition Metal Thin Films, Marissa Marie Kerrigan Jan 2017

Selective Atomic Layer Deposition Of Transition Metal Thin Films, Marissa Marie Kerrigan

Wayne State University Dissertations

Atomic layer deposition (ALD) affords highly conformal thin films with precise thickness control due to its self-limited growth mechanism. ALD enables the increasing demands for smaller feature sizes in microelectronics devices to be met. Area-selective ALD growth is receiving attention in the fabrication of microelectronic devices, since it can eliminate complicated etching steps from the fabrication process and minimizes expensive and toxic reagent use. Selectivity can be achieved by tailoring the surface chemistry of the precursor and substrate. To date, few area-selective ALD processes have been reported for metallic films. Thin films of cobalt metal deposited selectively are of considerable …


Product Development Resilience Through Set-Based Design, Stephen H. Rapp Jan 2017

Product Development Resilience Through Set-Based Design, Stephen H. Rapp

Wayne State University Dissertations

Often during a system Product Development program external factors or requirements change, forcing system design change. This uncertainty adversely affects program outcome, adding to development time and cost, production cost, and compromise to system performance. We present a development approach that minimizes the impacts, by considering the possibility of changes in the external factors and the implications of mid-course design changes. The approach considers the set of alternative designs and the burdens of a mid-course change from one design to another in determining the relative value of a specific design. The approach considers and plans parallel development of alternative designs …


Design, Synthesis And Biological Evaluation Of Histone Deacetylase (Hdac) Inhibitors: Saha (Vorinostat) Analogs And Biaryl Indolyl Benzamide Inhibitors Display Isoform Selectivity, Ahmed Negmeldin Jan 2017

Design, Synthesis And Biological Evaluation Of Histone Deacetylase (Hdac) Inhibitors: Saha (Vorinostat) Analogs And Biaryl Indolyl Benzamide Inhibitors Display Isoform Selectivity, Ahmed Negmeldin

Wayne State University Dissertations

HDAC proteins have emerged as interesting targets for anti-cancer drugs due to their involvement in cancers, as well as several other diseases. Several HDAC inhibitors have been approved by the FDA as anti-cancer drugs, including SAHA (suberoylanilide hydroxamic acid, Vorinostat). Unfortunately, SAHA inhibits most HDAC isoforms, which limit its use as a pharmacological tool and may lead to side effects in the clinic. In this work we were interested in developing isoform selective HDAC inhibitors, which may decrease or eliminate the side effects associated with non-selective inhibitors treatment. In addition, isoform selective HDAC inhibitors can be used as biological tools …


Development Of Chemical Tools To Investigate Protein S-Glutathionylation In Response To Metabolic Alteration, Kusal Theekshana Gayan Samarasinghe Jan 2017

Development Of Chemical Tools To Investigate Protein S-Glutathionylation In Response To Metabolic Alteration, Kusal Theekshana Gayan Samarasinghe

Wayne State University Dissertations

Oxidative stress is a common characteristic of age-related diseases such as vascular diseases, diabetes and cancer. Many diseases are known to be regulated by glutathionylation. Glutathionylation is referred to as the formation of disulfide bond between a protein cysteine and a glutathione. To understand the molecular mechanisms behind the disease initiation and progression, identification of such glutathionylated proteins is important. Even though existing methods have been widely used, several limitations of these methods hinder the identification of such proteins in disease conditions. Therefore, we developed a versatile chemical method that generates clickable glutathione inside the cells. In this method, we …


Ligand Binding Studies Of A Peptide Targeting Helix 69 Of 23s Rrna In Bacterial Ribosomes, Hyosuk Seo Jan 2017

Ligand Binding Studies Of A Peptide Targeting Helix 69 Of 23s Rrna In Bacterial Ribosomes, Hyosuk Seo

Wayne State University Dissertations

In the development of finding a peptide targeting H69 of 23S rRNA in bacterial ribosomes, phage display was employed at pH 5.5, a buffer condition previously reported of H69 preferring a closed conformation. After sequencing, several peptides were chosen through sequence alignment, followed by preparation using solid-phase peptide synthesis. The peptides were characterized using MALDI-TOF and purified with HPLC. A truncated peptide TARHIY was selected from FID assay. Through binding studies using ESI-MS, SPR, BLItz, and NMR, the binding properties of the peptide to H69 were determined, such as binding affinity, stoichiometry, and interaction site. The peptide exhibited moderate binding …


The Development Of Chemical Methods To Discover Kinase Substrates And Map Cell Signaling With Gamma-Modified Atp Analog-Dependent Kinase-Catalyzed Phosphorylation, Dissanayaka Mudiyanselage Maheeka Madhubashini Embogama Jan 2017

The Development Of Chemical Methods To Discover Kinase Substrates And Map Cell Signaling With Gamma-Modified Atp Analog-Dependent Kinase-Catalyzed Phosphorylation, Dissanayaka Mudiyanselage Maheeka Madhubashini Embogama

Wayne State University Dissertations

Kinase-catalyzed phosphorylation plays an important role in cell physiology by regulating a myriad of cellular functions. Thus aberrant kinase activity is implicated in various diseases. Methods are needed to discover kinase substrates and map signaling pathways to explore biology and to help drug discovery. A few techniques are currently available to discover kinase substrate and map cell signaling. However, to augment kinase substrate discovery approaches, it is essential to develop alternative techniques. Pflum has recently discovered cosubstrate promiscuity of protein kinases with gamma-modified ATP analogs. Here, kinase-catalyzed biotinylation with ATP-biotin was used to develop novel tools to discover kinase substrates …


A New Three-Dimensional (3d) Particle Coincidence Imaging System And Its Applications In Strong Field Studies Of Reaction Dynamics In Atoms And Molecules, Yunfei Lin Jan 2017

A New Three-Dimensional (3d) Particle Coincidence Imaging System And Its Applications In Strong Field Studies Of Reaction Dynamics In Atoms And Molecules, Yunfei Lin

Wayne State University Dissertations

Electron‐electron interaction is an important and interesting research theme both in chemistry and physics. Experimental study of electron correlation is hindered by the long dead time (the time within which no more than two electrons can be detected) of electron detection system. We developed a new three‐dimensional (3D) particle coincidence imaging system to remove this restriction. The detection system employs a new strategy: It uses a fast‐frame camera to record positional information on 2D MCPs/phosphor detector (so the particle velocities in two dimensions can be measured); It utilizes a high‐speed digitizer to pick up the signal from MCP lead, off‐line …


Clinical Applications Of Advanced Rotational Radiation Therapy, Adrian Nalichowski Jan 2017

Clinical Applications Of Advanced Rotational Radiation Therapy, Adrian Nalichowski

Wayne State University Dissertations

Purpose: With a fast adoption of emerging technologies, it is critical to fully test and understand its limits and capabilities. In this work we investigate new graphic processing unit (GPU) based treatment planning algorithm and its applications in helical tomotherapy dose delivery. We explore the limits of the system by applying it to challenging clinical cases of total marrow irradiation (TMI) and stereotactic radiosurgery (SRS). We also analyze the feasibility of alternative fractionation schemes for total body irradiation (TBI) and TMI based on reported historical data on lung dose and interstitial pneumonitis (IP) incidence rates.

Methods and Materials: An anthropomorphic …


Interaction-Driven Phenomena And Wigner Transition In Two-Dimensional Systems, Talbot Anderson Knighton Jan 2017

Interaction-Driven Phenomena And Wigner Transition In Two-Dimensional Systems, Talbot Anderson Knighton

Wayne State University Dissertations

The formation of a quantum Wigner Cyrstal (WC) is one of the most anticipated predictions of electron-electron interaction. This is expected to occur in zero magnetic field when the Coulomb energy $E_C$ dominates over the Fermi energy $E_F$ (at a ratio $r_s \equiv E_C/E_F \sim 37$) for temperatures $T \ll E_F / k_B$. The extremely low $T$ and ultra dilute carrier concentrations necessary to meet these requirements are difficult to achieve. Alternatively, a perpendicular magnetic $B$-field can be used to quench the kinetic energy. As $B$ increases, various energies compete to produce the ground state. High purity systems with large …


Gas-Phase Ion Spectroscopy Of Nucleobases And Mononucleotides: Models For Higher Order Nucleic Acids, Yuan-Wei Nei Jan 2017

Gas-Phase Ion Spectroscopy Of Nucleobases And Mononucleotides: Models For Higher Order Nucleic Acids, Yuan-Wei Nei

Wayne State University Dissertations

Experiments examining the structures and stabilities of protonated and sodium cationized nucleobases, and deprotonated DNA and RNA mononucleotides are presented and discussed in this dissertation. These studies were carried out using the infrared multiple photon dissociation (IRMPD) action spectroscopy technique that utilizes a Fourier transform ion cyclotron mass spectrometer (FT-ICR MS) coupled to a free electron laser (FEL) located at the Radboud University Nijmegen. Ionic species of these biologically important complexes were generated using an electrospray ionization source and then mass isolated to have their infrared (IR) spectra measured by the experimental apparatus. Detailed analysis of the IR spectra measured …


Synthesis Of Netilmicin And Apramycin Derivatives For The Treatment Of Multidrug-Resistant Infectious Diseases, Amr Sayed Motawi Sonousi Jan 2017

Synthesis Of Netilmicin And Apramycin Derivatives For The Treatment Of Multidrug-Resistant Infectious Diseases, Amr Sayed Motawi Sonousi

Wayne State University Dissertations

The ever-growing bacterial resistance to existing antibiotics is alarming to humanity. Many researchers decided to revisit aminoglycosides with renewed emphasis on chemical modification as they have long been used as highly potent antibiotics for treating severe bacterial infections. The bactericidal effect of aminoglycosides is mainly due to protein synthesis inhibition by binding to the A-site of the bacterial ribosomes. However, the high potency and the broad spectrum of aminoglycosides has been outweighed by their side effects, especially ototoxicity, and by the resistance of pathogens. The goal of this research was the modification of existing aminoglycosides to develop derivatives which are …


Exploring Potential Energy Surfaces Of Chemical Reactions Using Electronic Structure Methods, Bishnu Thapa Jan 2017

Exploring Potential Energy Surfaces Of Chemical Reactions Using Electronic Structure Methods, Bishnu Thapa

Wayne State University Dissertations

This dissertation includes three topics: molecular dynamics in strong laser fields, pKa’s and redox potential calculations of bio–organic molecules, and oxidative damage of the nucleobases. Electronic structure calculations are used to provide a deeper understanding of experimental observations as well as to predict new results.

Chapters 2, 3 and 4 investigate the fragmentation and isomerization reactions of small monocations in the presence of strong laser fields. In the presence of intense laser pulses with 800 nm wavelengths, Born-Oppenheimer classical trajectory simulations were performed to investigate the dynamics of methanol monocation on the ground state potential energy surface (Chapter 2). With …


Classical And Quantum Mechanical Simulations Of Condensed Systems And Biomolecules, Hedieh Torabifard Jan 2017

Classical And Quantum Mechanical Simulations Of Condensed Systems And Biomolecules, Hedieh Torabifard

Wayne State University Dissertations

This work describes the fundamental study of two enzymes of Fe(II)/-KG super family enzymes (TET2 and AlkB) by applying MD and QM/MM approaches, as well as the development of multipolar-polarizable force field (AMOEBA/GEM-DM) for condensed systems (ionic liquids and water).

TET2 catalytic activity has been studied extensively to identify the potential source of its substrate preference in three iterative oxidation steps. Our MD results along with some experimental data show that the wild type TET2 active site is shaped to enable higher order oxidation. We showed that the scaffold stablished by Y1902 and T1372 is required for iterative oxidation. The …


Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications, Ren Zhao Jan 2017

Polynomial Preserving Recovery For Weak Galerkin Methods And Their Applications, Ren Zhao

Wayne State University Dissertations

Gradient recovery technique is widely used to reconstruct a better numerical gradient from a finite element solution, for mesh smoothing,

a posteriori error estimate and adaptive finite element methods. The PPR technique generates a higher order approximation of the gradient on a patch of mesh elements around each mesh vertex. It can be used for different finite element methods for different problems. This dissertation presents recovery techniques for the weak Galerkin methods and as well as applications of gradient recovery on various of problems, including elliptic problems, interface problems, and Stokes problems.

Our first target is to develop a boundary …