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Full-Text Articles in Physical Sciences and Mathematics

Metal-Ligand Cooperative Catalysis And Methods For Metal Removal From Organic Transformations, John-Paul J. Bow Aug 2015

Metal-Ligand Cooperative Catalysis And Methods For Metal Removal From Organic Transformations, John-Paul J. Bow

Electronic Thesis and Dissertation Repository

Organometallic catalysis has revolutionized the synthesis of complex organic molecules. Methods for C-C, C-X and C-H bond formation and cleavage are exploited throughout the areas of fine chemicals synthesis, with major applications for pharmaceuticals. This situation raises duel challenges: 1) high-performance catalysts for environmentally and economically sustainable synthesis and 2) efficient methods of catalyst (i.e. metal) removal must be identified. This work tackles both of these areas. The highly tunable cooperative PR2NR'2 ligands have been implemented for the first time for catalytic organic transformations. I show that [Ru(Cp)(PtBu2NBn2)(MeCN)][PF6 …


Self-Assembly And Stimuli-Responsive Properties Of Amphiphilic Self-Immolative Block Co-Polymers, Thomas Mackenzie Gungor Aug 2015

Self-Assembly And Stimuli-Responsive Properties Of Amphiphilic Self-Immolative Block Co-Polymers, Thomas Mackenzie Gungor

Electronic Thesis and Dissertation Repository

In recent years, degradable polymers have become increasingly researched for their applications in drug delivery systems, adhesives, and tissue engineering. Self-immolative polymers (SIPs) are of particular utility due to predictable end-to-end backbone depolymerization after a stimuli-responsive end-cap cleavage. There are examples of incorporating a hydrophobic SIP into an amphiphilic block-copolymer, followed by self-assembly in aqueous media forming various nanoparticle morphologies. However, their self-assembly behaviour has not been described in detail, and there are no general synthetic methods that allow for their synthesis with good control over the relative hydrophilic block ratio, the major factor controlling their morphology. This thesis presents …


A Study Of Green’S Relations On Algebraic Semigroups, Allen O'Hara Aug 2015

A Study Of Green’S Relations On Algebraic Semigroups, Allen O'Hara

Electronic Thesis and Dissertation Repository

The purpose of this work is to enhance the understanding regular algebraic semigroups by considering the structural influence of Green's relations. There will be three chief topics of discussion.

  • Green's relations and the Adherence order on reductive monoids
  • Renner’s conjecture on regular irreducible semigroups with zero
  • a Green’s relation inspired construction of regular algebraic semigroups

Primarily, we will explore the combinatorial and geometric nature of reductive monoids with zero. Such monoids have a decomposition in terms of a Borel subgroup, called the Bruhat decomposition, which produces a finite monoid, R, the Renner monoid. We will explore the structure of …


Conduits Of Communion: Monstrous Affections In Algonquin Traditional Territory, Ian S.G. Puppe Aug 2015

Conduits Of Communion: Monstrous Affections In Algonquin Traditional Territory, Ian S.G. Puppe

Electronic Thesis and Dissertation Repository

This project investigates the legacies of shifting land tenure and stewardship practices on what is now known as the Ottawa Valley watershed (referred to as the Kitchissippi by the Omamawinini or Algonquin people), and the effects that this central colonization project has had on issues of identity and Nationalism on Canadians, diversely identified as settler-colonists of European or at least “Old World” descent and First Nations, Métis and Inuit (Lawrence 2012).

Focusing on historical and contemporary political and social issues related to Algonquin Provincial Park and its establishment, this project explores; 1) Competing claims levied by First Nations Peoples, local …


Fourier Inequalities In Lorentz And Lebesgue Spaces, Javad Rastegari Koopaei Aug 2015

Fourier Inequalities In Lorentz And Lebesgue Spaces, Javad Rastegari Koopaei

Electronic Thesis and Dissertation Repository

Mapping properties of the Fourier transform between weighted Lebesgue and Lorentz spaces are studied. These are generalizations to Hausdorff-Young and Pitt’s inequalities. The boundedness of the Fourier transform on $R^n$ as a map between Lorentz spaces leads to weighted Lebesgue inequalities for the Fourier transform on $R^n$ .

A major part of the work is on Fourier coefficients. Several different sufficient conditions and necessary conditions for the boundedness of Fourier transform on unit circle, viewed as a map between Lorentz $\Lambda$ and $\Gamma$ spaces are established. For a large range of Lorentz indices, necessary and sufficient conditions for boundedness are …


Identification Of Ancient Maya Agriculture In The Periphery Of Motul De San José, Alexandra E. Smofsky Aug 2015

Identification Of Ancient Maya Agriculture In The Periphery Of Motul De San José, Alexandra E. Smofsky

Electronic Thesis and Dissertation Repository

Agricultural systems were investigated in the Motul de San José periphery, an ancient Maya polity in Guatemala, using soil geochemical techniques. The δ13C values of soil organic matter delineated areas of ancient maize agriculture at the satellite center of Kante’t’u’ul. A new method to locate areas of former cacao cultivation or processing was developed using HPLC to detect theobromine, an alkaloid of the cacao plant, preserved in soils. Extraction of spiked soils revealed that theobromine adsorption is inversely correlated with organic matter content of soils. Detection of naturally occurring theobromine was successful, demonstrating its utility as a tracer. …


Stimuli-Responsive Polymersomes And Surface Functionalized Dendrimersomes: Platforms For Biomedical Applications, J Trevor Mcintosh Aug 2015

Stimuli-Responsive Polymersomes And Surface Functionalized Dendrimersomes: Platforms For Biomedical Applications, J Trevor Mcintosh

Electronic Thesis and Dissertation Repository

Amphiphilic block copolymers (BCPs) and dendrimers are known to self-assemble in aqueous solution to form a number of aggregate morphologies. These different architectures are largely a function of the hydrophilic volume or weight fractions of the different components of the polymer system. One possible morphology is a vesicle, also referred to as a polymersome or dendrimersome when BCPs or dendrimers, respectively, are used. Vesicles are multi-functional, supramolecular, bilayer assemblies, whose potential for stimuli-responsiveness and surface functionalization make them promising materials for a variety of biomedical applications. This thesis demonstrates the use of UV-sensitive block copolymers forming photodegradable vesicles, as well …


Mechanistic Studies Of Donor-Acceptor Cyclopropanes, Tristan Chidley Aug 2015

Mechanistic Studies Of Donor-Acceptor Cyclopropanes, Tristan Chidley

Electronic Thesis and Dissertation Repository

Cyclopropane 1,1-diesters have been investigated as a source of donor-acceptor cyclopropanes, providing an understanding of the mechanism of reaction between these cyclopropanes and nitrosoarenes, as well as azo dicarboxylates. Cross-over experiments have been utilized to provide key pieces of experimental evidence that help generate a theoretical model of the reactions. By understanding these reactions with precision, the avenue to expand the reaction scope and develop other useful reactions is opened up. This allows the chemistry to be better utilized, providing easier access to important molecules when needed, and contributes to advancing the field of synthetic organic chemistry.

In addition, cyclobutane …


Coinage Metal Silylphosphido Complexes Stabilized By N-Heterocyclic Carbene Ligands, Bahareh Khalili Najafabadi Aug 2015

Coinage Metal Silylphosphido Complexes Stabilized By N-Heterocyclic Carbene Ligands, Bahareh Khalili Najafabadi

Electronic Thesis and Dissertation Repository

N-Heterocyclic carbenes (NHCs) are strong σ-donating ligands and thus, promising candidates for decorating and stabilizing metal-phosphide nanoclusters. While much research has been focused on the coordination of NHC ligands to different coinage metal centers in order to synthesize mononuclear organometallic complexes, their application in nanocluster chemistry has been relatively unexplored. The work described in this thesis involves employment of NHC ligands for stabilizing coinage metal t-butylthiolate and silylphosphido complexes. These complexes are promising molecular precursors for formation of larger NHC-stabilized nanoclusters.

In particular, the ligation of NHCs to [CuStBu] and [AgStBu] was developed as an …


Combinatorial Polynomial Identity Theory, Mayada Khalil Shahada Aug 2015

Combinatorial Polynomial Identity Theory, Mayada Khalil Shahada

Electronic Thesis and Dissertation Repository

This dissertation consists of two parts. Part I examines certain Burnside-type conditions on the multiplicative semigroup of an (associative unital) algebra $A$.

A semigroup $S$ is called $n$-collapsing if, for every $a_1,\ldots, a_n \in S$, there exist functions $f\neq g$ on the set $\{1,2,\ldots,n\}$ such that \begin{center} $s_{f(1)}\cdots s_{f(n)} = s_{g(1)}\cdots s_{g(n)}$. \end{center} If $f$ and $g$ can be chosen independently of the choice of $s_1,\ldots,s_n$, then $S$ satisfies a semigroup identity. A semigroup $S$ is called $n$-rewritable if $f$ and $g$ can be taken to be permutations. Semple and Shalev extended Zelmanov's Fields Medal writing solution of the Restricted …


Development Of A Small Animal Conformal Irradiator With Dual Energy X-Ray Computed Tomography Imaging For Kilovoltage Dosimetry, Michael D. Jensen Aug 2015

Development Of A Small Animal Conformal Irradiator With Dual Energy X-Ray Computed Tomography Imaging For Kilovoltage Dosimetry, Michael D. Jensen

Electronic Thesis and Dissertation Repository

External beam radiotherapy has become technically sophisticated with image guided radiation therapy (IGRT) and intensity modulated radiation therapy (IMRT). These technologies allow for precise delivery of radiation to geometric targets in cancer patients. However, many questions remain on how to best define targets based on biological information, such as functional imaging, and how to combine radiation with other cancer therapies. To help answer these questions, small animal preclinical studies are needed to generate data to inform clinical trials. However, the precise radiation delivery capabilities of IGRT and IMRT have not been available in the preclinical labs. To enable translational experiments …


Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi Aug 2015

Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi

Electronic Thesis and Dissertation Repository

This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.

In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties of the generalized …


Computational Studies Of Compressed Diborane And Engineered Narrow-Gap Semiconductors, Amin Torabi Aug 2015

Computational Studies Of Compressed Diborane And Engineered Narrow-Gap Semiconductors, Amin Torabi

Electronic Thesis and Dissertation Repository

The research contained in this thesis is two-fold: understanding the behavior of diborane under pressure, and engineering wide-gap semiconductors in order to promote their optical eciency. Each of these themes are further explained below.

Diborane (B2H6), is a prototypical electron-deficient molecule and has received a great deal of attention in recent years due to its unique and peculiar structure, as well as its potential applications as a hydrogen-storage material. At high pressures, vibrational spectroscopy analysis have revealed several changes in the spectral profile that suggest occurrence of polymorphic transformations; however, the new crystal structures at high …


Field Scale Application Of Nanoscale Zero Valent Iron: Mobility, Contaminant Degradation, And Impact On Microbial Communities, Chris M.D. Kocur Aug 2015

Field Scale Application Of Nanoscale Zero Valent Iron: Mobility, Contaminant Degradation, And Impact On Microbial Communities, Chris M.D. Kocur

Electronic Thesis and Dissertation Repository

This thesis began by verifying that nanoscale zero valent iron (nZVI) synthesis methods could be scaled up and implemented at the field scale in a safe manner. This led to successful demonstration of nZVI injection and mobility under constant head gravity injection into a contaminated utility corridor in Sarnia, Ontario. Where field studies have fallen short in the past was linking the somewhat qualitative field geochemical parameters to other evidence of nZVI transport. Definitive nZVI detection was elusive in previous field studies due to the highly reactive nature of the particles caused by their high surface area. nZVI was detected …


Healthy And Unhealthy Statistics: Examining The Impact Of Erroneous Statistical Analyses In Health-Related Research, Britney Allen Aug 2015

Healthy And Unhealthy Statistics: Examining The Impact Of Erroneous Statistical Analyses In Health-Related Research, Britney Allen

Electronic Thesis and Dissertation Repository

Sound statistical analyses are essential to the advancement of medicine. Although certainly not always the case, far too many publications are based on weak or inappropriate statistical methodology, leading to questionable results. Statistical reporting guidelines and standards for research are being introduced which should help curb this problem. Wide recognition of the need for statistical methodologies aligned with research questions and study designs, and the impact when this is not the case, would help prevent this problem. In this thesis, I illustrate the consequences of erroneous statistical analyses on data from an observational study on Multiple Sclerosis and I investigate …


The Effect Of Diversification On The Dynamics Of Mobile Genetic Elements In Prokaryotes: The Birth-Death-Diversification Model, Nicole E. Drakos Jul 2015

The Effect Of Diversification On The Dynamics Of Mobile Genetic Elements In Prokaryotes: The Birth-Death-Diversification Model, Nicole E. Drakos

Electronic Thesis and Dissertation Repository

Mobile genetic elements (MGEs) are ubiquitous among prokaryotes, and have important implications to many areas, such as the evolution of certain genes, bioengineering and the spread of antibiotic resistance. In order to understand the complex dynamics of MGEs, mathematical models are often used. One model that has been used to describe the dynamics of mobile promoters (a class of MGEs) is the birth-death-diversification model. This model is unique in that it allows MGEs to diversify to create new families. In this thesis, I analyze the dynamics of this model; in particular, I examine equilibrium distributions, extinction probabilities and mean time …


Strategies For Photochemical And Thermal Modification Of Materials, Sara Ghiassian Jul 2015

Strategies For Photochemical And Thermal Modification Of Materials, Sara Ghiassian

Electronic Thesis and Dissertation Repository

The modification of materials/surfaces is central to numerous applications ranging from opto-electronic devices to biomedical implants and drug delivery. Thus, there exists a high motivation for improving the methodologies which can be employed in order to modify surfaces in a selective and efficient fashion. One of the major goals of surface engineering is to control the chemical composition at the material interface. The fine control of the surface properties is a field of intense research as the performance of functional materials is strongly related to the processes and interactions that are occurring at the materials’ interface.

In general, the modification …


Complementary Mass Spectrometry Methods For Characterizing Protein Folding, Structure, And Dynamics, Siavash Vahidi Jul 2015

Complementary Mass Spectrometry Methods For Characterizing Protein Folding, Structure, And Dynamics, Siavash Vahidi

Electronic Thesis and Dissertation Repository

Proteins are involved in virtually every biochemical process. A comprehensive characterization of factors that govern protein function is essential for understanding the biomedical aspects of human health. This dissertation aims to develop complementary mass spectrometry-based methods and apply them to solve problems pertaining to the area of protein structure, folding and dynamics.

‎Chapter 1 uses fast photochemical oxidation of proteins (FPOP) to characterize partially disordered conformers populated under semi-denaturing conditions. In FPOP, ·OH generated by laser photolysis of H2O2 introduces oxidative modifications at solvent accessible side chains. By contrast, buried sites are protected from radical attack. Using …


Hydrogen Exchange Mass Spectrometry For Studying Protein-Ligand Interactions, Modupeola A. Sowole Jul 2015

Hydrogen Exchange Mass Spectrometry For Studying Protein-Ligand Interactions, Modupeola A. Sowole

Electronic Thesis and Dissertation Repository

Hydrogen deuterium exchange (HDX) coupled with mass spectrometry is widely used for probing protein structure and dynamics. Protein-ligand interactions usually induce a reduction in the measured HDX rates an effect that may be ascribed to stabilization of the protein structure. This work aims to improve the general understanding of the changes in HDX patterns associated with ligand binding.

We initially applied HDX for studying differences between oxy-hemoglobin (Oxy-Hb) and aquomet-hemoglobin (Chapter 2). The results show that the α and β subunits respond differently to the oxy to aquomet transition with the heme binding pocket being destabilized in both cases. The …


From Solution Into The Gas Phase: Studying Protein Hydrogen Exchange And Electrospray Ionization Using Molecular Dynamics Simulation, Robert G. Mcallister Jul 2015

From Solution Into The Gas Phase: Studying Protein Hydrogen Exchange And Electrospray Ionization Using Molecular Dynamics Simulation, Robert G. Mcallister

Electronic Thesis and Dissertation Repository

Here, we apply Molecular Dynamics (MD) simulations to investigate fundamental aspects of structural mass spectrometry (MS). We first examine microscopic phenomena underlying Hydrogen/Deuterium exchange (HDX). HDX interrogates structural dynamics of proteins by measuring the rate of Deuterium uptake into backbone amides. We perform microsecond MD simulations on ubiquitin to investigate this process. We find that HDX protection often cannot be explained by H‑bonding or solvent accessibility considerations. These findings caution against non-critical use of HDX data in structural contexts. We next use MD to examine the Electrospray ionization (ESI) mechanism of proteins. ESI is a soft ionization technique resulting in …


Using Ion Mobility Spectrometry To Study Protein Conformations In The Gas Phase, Yu Sun Jun 2015

Using Ion Mobility Spectrometry To Study Protein Conformations In The Gas Phase, Yu Sun

Electronic Thesis and Dissertation Repository

The question whether electrosprayed protein ions retain solution-like conformations remains a matter of debate. One way to address this issue involves comparisons of collision cross sections measured by travelling wave ion mobility spectrometry (TWIMS) with the values calculated for model structures. It is often implied that nanoESI is more conducive for the retention of solution structure than regular ESI. Focusing on four different proteins we demonstrated that collision cross section values and collisional unfolding profiles are virtually indistinguishable under both conditions. Calibration can be challenging because differences in the extent of collisional activation for TWIMS and drift tube calibrant data …


Algorithms To Compute Characteristic Classes, Martin Helmer Jun 2015

Algorithms To Compute Characteristic Classes, Martin Helmer

Electronic Thesis and Dissertation Repository

In this thesis we develop several new algorithms to compute characteristics classes in a variety of settings. In addition to algorithms for the computation of the Euler characteristic, a classical topological invariant, we also give algorithms to compute the Segre class and Chern-Schwartz-MacPherson (CSM) class. These invariants can in turn be used to compute other common invariants such as the Chern-Fulton class (or the Chern class in smooth cases).

We begin with subschemes of a projective space over an algebraically closed field of characteristic zero. In this setting we give effective algorithms to compute the CSM class, Segre class and …


Strength Study Of Zircon Under High Pressure, Ievgeniia Morozova Jun 2015

Strength Study Of Zircon Under High Pressure, Ievgeniia Morozova

Electronic Thesis and Dissertation Repository

Zircon (ZrSiO4) is a strong accessory mineral that can retain U, Th and Hf within its structure. This makes zircon an important material in geochemical and geochronological studies. In addition, the strong thermal shock resistance of zircon allows for dating the formations of melt and impact events and to separate shocked and potentially shocked country rocks. However, the deformation mechanism and microstructure behavior of zircon at high pressure is poorly understood. Therefore, this work aims to study the deformation and texture of zircon in situ at high pressure and room temperature, and also to examine the microstructure of …


Bioaccumulation And Concentration Of Mercury In Rivers And Streams Of The Hudson Bay Lowland, Ashley Warnock Jun 2015

Bioaccumulation And Concentration Of Mercury In Rivers And Streams Of The Hudson Bay Lowland, Ashley Warnock

Electronic Thesis and Dissertation Repository

Methylmercury (MeHg) is a neurotoxin that biomagnifies in northern aquatic food webs to high enough concentrations to cause concern for human consumption. The Hudson Bay Lowland of Canada is projected to experience climate and land-use impact in the immediate future, and these environmental stressors may affect the exposure to and subsequent bioaccumulation of MeHg in subarctic fish populations. The focus of this research is to evaluate the spatial variability in total and MeHg in water, sediment, and biota within and across a range of subarctic streams and river reaches of the Hudson Bay Lowland. This data was then used to …


The Lithotectonic Setting And Paragenetic History Of Deposit No.1, Mary River District, North Baffin Island, Sean A. Fulcher May 2015

The Lithotectonic Setting And Paragenetic History Of Deposit No.1, Mary River District, North Baffin Island, Sean A. Fulcher

Electronic Thesis and Dissertation Repository

Baffinland Iron Mines Corporation is currently extracting the highest grade BIF-hosted direct shipping iron ore in the world from their flagship Deposit No.1 on north Baffin Island. This deposit and several other prospects are hosted within the isoclinally folded Mary River Group, a Neoarchean greenstone belt terrane hosting Algoma-type BIF, ultramafics volcaniclastics and sediment. Mary River Group supracrustals are juxtaposed against Mesoarchean basement gneisses due to a regional Transhudson Orogen overprint, forming a regional dome-keel tectonic framework.

Detail mapping and core logging of Deposit No.1 combined with geochemistry and geochronology reveal the footwall rocks, previously interpreted as gneisses, volcanics and …


Studies Of Periodic And Quasiperiodic Gold Nanohole Arrays And Their Applications, Zhaoliang Yang May 2015

Studies Of Periodic And Quasiperiodic Gold Nanohole Arrays And Their Applications, Zhaoliang Yang

Electronic Thesis and Dissertation Repository

Wavelength to refractive index sensitivity and resonance wavelength position are two very important performance characteristics for nanohole array based surface plasmon resonance sensors while these characteristics are mostly researched on periodic nanohole arrays, instead of quasiperiodic nanohole arrays. This thesis deduces theoretical equations about the wavelength to refractive index sensitivity and resonance wavelength position of quasiperiodic nanohole arrays. Theoretical analysis shows that wavelength to refractive index sensitivity is not associated with geometry pattern, hole size or pitch but with the wavelength. A novel surface plasmon resonance platform is built by transferring gold films patterned with quasiperiodic nanohole arrays to the …


High Pressure And High Temperature Study Of Magnesiochromite And Its Geophysical Implications, N M Tauhid Belal Khan May 2015

High Pressure And High Temperature Study Of Magnesiochromite And Its Geophysical Implications, N M Tauhid Belal Khan

Electronic Thesis and Dissertation Repository

Magnesiochromite (MgCr2O4) is commonly found in the Earth’s crust, upper mantle, meteorites, and possibly in lunar crust. Synchrotron X-ray diffraction measurements of MgCr2O4 using double-sided laser heating diamond anvil cell showed the dissociation of MgCr2O4 to Cr2O3+MgO at ~15 GPa and to Mg2Cr2O5+Cr2O3 below and above ~1500 K, respectively. At above 20 GPa, only a single phase CaTi2O4-type structure of MgCr2O4 was observed at 1400-2000 K. Fitting the pressure-volume data …


Using Cellular Automata And Lattice Boltzmann Methods To Model Cancer Growth: Analysis Of Combination Treatment Outcomes, Jenna L. Butler May 2015

Using Cellular Automata And Lattice Boltzmann Methods To Model Cancer Growth: Analysis Of Combination Treatment Outcomes, Jenna L. Butler

Electronic Thesis and Dissertation Repository

In Canada it is estimated that 76,600 people will die of cancer in 2014. Cancer, a collection of over 200 diseases, has differences existing between globally, between individuals and overtime in one individual. Treatment options are similarly varied. These differences make selecting the best possible treatment for every type of cancer very challenging. In addition, with no single cure for cancer, treatments are often combined in different ways to form the best overall option. In an attempt to synthesize the properties of these diseases into a collection of common cellular changes, Hanahan and Weinberg proposed ``the hallmarks of cancer" -- …


Exploring The Chemistry Of Phosphorus For Photopolymer Applications, Ryan Guterman May 2015

Exploring The Chemistry Of Phosphorus For Photopolymer Applications, Ryan Guterman

Electronic Thesis and Dissertation Repository

Prior to this thesis, phosphorus-containing polymers and photopolymerization represented two distinct, non-overlapping fields of study. This thesis examined the prospect of combining these two approaches to create a system possessing the benefits of both techniques. By exploiting the chemistry of phosphorus, and using photopolymerization as a fabrication method, new materials were developed and assessed for their use in various applications.

Among the many phosphorus compounds that may be used in polymer science, phosphonium salts and primary phosphines were of specific focus. First, highly fluorinated phosphonium monomers were developed to create photopolymerized hydrophobic surfaces. A structure-activity relationship was established, as both …


Combinatorial Techniques In The Galois Theory Of P-Extensions, Michael Rogelstad May 2015

Combinatorial Techniques In The Galois Theory Of P-Extensions, Michael Rogelstad

Electronic Thesis and Dissertation Repository

A major open problem in current Galois theory is to characterize those profinite groups which appear as absolute Galois groups of various fields. Obtaining detailed knowledge of the structure of quotients and subgroup filtrations of Galois groups of p-extensions is an important step toward a solution. We illustrate several techniques for counting Galois p-extensions of various fields, including pythagorean fields and local fields. An expression for the number of extensions of a formally real pythagorean field having Galois group the dihedral group of order 8 is developed. We derive a formula for computing the Fp-dimension of an n-th …