The Witt ring of a field gives the structure of the isometry classes of quadratic forms over that field. In particular, the Witt ring provides an algebraic invariant for fields away from characteristic $2$, which also allow us to study the orderings we can put on that field. During the latter quarter of the 20th century, abstract Witt rings, a wider class of rings that had the structure of a Witt ring but constructed independently from fields, were introduced. In this thesis, we will use what is known about the structure of Witt rings over quadratic extensions of fields in order to come up with an analog that extends over to abstract Witt rings.

In this paper, we study linked bilinear pairings and their associated Witt rings. An open problem is to classify all linked quaterionic pairings. The Elementary Type Conjecture [1] asserts that every finite linked quaternionic pairing can be built from symplectic pairings using direct sums and group extensions iteratively. We investigate the validity of this conjecture by studying an infinite quaternionic pairing and its sub- pairings motivated by certain structures arising in Henselian dyadic valued fields.

Let $F$ be a field and $E$ an extension of $F$ with $[E:F]=d$ where the characteristic of $F$ is zero or prime to $d$. We assume $\mu_{d^2}\subset F$ where $\mu_{d^2}$ are the $d^2$th roots of unity. This thesis studies the problem of determining the cohomological kernel $H^n(E/F):=\ker(H^n(F,\mu_d) \rightarrow H^n(E,\mu_d))$ (Galois cohomology with coefficients in the $d$th roots of unity) when the Galois closure of $E$ is a semi-direct product of cyclic groups. The main result is a six-term exact sequence determining the kernel as the middle map and is based on tools of Positelski \cite{Positselski}. When $n=2$ this kernel is the relative Brauer group ${\rm Br}(E/F)$, the classes of central simple algebras in the Brauer group of $F$ split in the field $E$. In the case where $E$ has degree $d$ and the Galois closure of $E$, $\tE$ has Galois group ${\rm Gal}(\tE/F)$ a dihedral group of degree $2d$, then work of Rowen and Saltman (1982) \cite{RowenSaltman} shows every division algebra $D$ of index $d$ split by $E$ is cyclic over $F$ (that is, $D$ has a cyclic maximal subfield.) This work, along with work of Aravire and Jacob (2008, 2018) \cite{AJ08} \cite{AJ18} which calculated the groups $H^n_{p^m}(E/F)$ in the case of semi-direct products of cyclic groups in characteristic $p$, provides motivation for this work.

Diisopropylaminoborane (BH2-N(iPr)2) is prepared by reacting lithium diisopropylaminoborohydride (iPr-LAB) with trimethylsilyl chloride (TMSCl). Aliphatic, aromatic, and heteroaromatic (diisopropylamino)boranes are readily synthesized at ambient temperature (0 °C) in 1h by the reaction of Grignard reagents with (BH2-N(iPr)2). Two contending reaction pathways have tentatively been identified. In one pathway, bromomagnesium hydride (HMgBr) acts as the leaving group from the initially formed bromomagnesium organo(diisopropylamino)borohydride, affording the product organodiisopropylaminoborane (RBH-N(iPr)2). The increased sterics and the diminished Lewis acidity of (RBH-N(iPr)2) prevents it from further reacting with Grignard reagents. In the second pathway, the product may be formed by a hydride transfer from bromomagnesium organo(diisopropylamino)borohydride to the starting material (BH2-N(iPr)2). It was found that only 1.2 equivalents of (BH2-N(iPr)2) was required for greater than 95% conversion to the organo(diisopropylamino)borane. During the mechanistic investigation, bromomagnesium diisopropylaminoborohydride was identified as a byproduct and was subsequently synthesized from diisopropylamine borane and methylmagnisum chloride. This borylation reaction can be carried out under Barbier conditions, where (BH2-N(iPr)2) traps the in situ formed Grignard reagent from the corresponding organic halide and magnesium metal. Simple acid hydrolysis of the product organo(diisopropylamino)borane leads to the corresponding boronic acid in good to excellent yield.

Grignard reagents (aliphatic, aromatic, heteroaromatic, vinyl or allylic) react with one equivalent of 4,4,5,5-tetramethyl-1,3,2-dioxaborolane, (pinacolborane, PinBH) at ambient temperature in tetrahydrofuran (THF) to afford the corresponding pinacol boronates. Initially formed dialkoxy alkylborohydride intermediate quickly eliminates hydridomagnesium bromide (HMgBr) and affords the product boronic ester in very good yield. Hydridomagnesium bromide (HMgBr), in turn disproportionates to a 1:1 mixture of magnesium hydride (MgH2) and magnesium bromide (MgBr2) on addition of pentane to the reaction mixture. DFT calculations (Gaussian09) at the B3LYP/6-31G(d) level of theory show that disproportionation of HMgBr to MgH2 and MgBr2 is viable in the coordinating ethereal solvents. This reaction also can be carried out under Barbier conditions where the neat PinBH is added to the flask prior to the in situ formation of Grignard reagent from the corresponding organic halide and magnesium metal. Pinacol boronic ester synthesis under Barbier conditions does not give Wurtz coupling side products from reactive halides, such as benzylic and allylic halides. The reaction between PinBH and various Grignard reagents is an efficient, mild and general method for the synthesis of pinacol boronates.

The early twentieth century saw a remarkable boon in the amount of new repertoire being written for the viola as a solo instrument. Specifically, the rise in composing unaccompanied, multi-movement sonatas and suites for viola in these decades was noteworthy. This document came of a desire to probe deeper into the socio-cultural context of fin de siècle and interwar Europe, in order to better understand what factors might have contributed to this prolific output of repertoire for the genre. By exploring the works of several composers - specifically pieces by Max Reger, Paul Hindemith, and Ladislav Vycpálek - a conscious choice was made not to focus on any one composer, style, or individual piece. These solo viola works were not written in a vacuum, but were products of composers who were deeply embedded in the cultural milieu of their time. These composers and this genre needed placing within a larger socio-historical framework. Both the composers and their compositions are considered here as part of the interrelated culture of those heady years, when the emergent aesthetics of a variety of modernist strains - historicist modernism, neoclassicism, neue sachlichkeit to name a few - began to take root. Such an approach allows for unexpected connections and relationships between key figures and aesthetic concepts to materialize more readily, providing a vibrant portrait of the brash and often contradictory age that produced such a wealth of solo repertoire for a long-ignored instrument.

This dissertation is dedicated to the idea that the cultural phenomenon of wellness—understood as an ethos of self-directed healthcare—provides a generative framework for thinking through the formal and critical dimensions of a diverse selection of novels published in the years between 2013-2019. How, it asks, do the novels examined in each chapter serve as a social and formal site for analyzing the zeitgeist of wellness? In what ways do these fictional accounts of wellness influence the novel on the level of genre? How does the history, culture, and politics of wellness work discursively to shape these fictional worlds? To what effect? And how might the critical concerns of these novels be enriched or best understood from the perspective of wellness? These formal questions open up an equally compelling set of broader sociopolitical critiques of wellness including the manifold ways it obfuscates the structural violence of the U.S. healthcare system, the decline of the welfare state, and the disappearance of social services. Moreover, the formal presence of wellness in the novels prompts readers to consider how it operates as a moral and ethical framework for judging and stigmatizing those who “fail” to embody signs of wellness or to take control of their health, allowing larger systemic failures to be redirected back onto the individual. At stake in wellness’ incorporation and ubiquity is the continued shift away from alternative systems of care whereby a reified model of self-directed healthcare maintains rather than subverts the hegemony of western biomedicine. Within these texts, one finds an urgency to articulate new modes of wellbeing rooted in collectivity and interdependence. In answering these questions, my dissertation hopes to make the case for the usefulness of wellness to critical discussions of recent literary production.

In 1980, Murray Marshall proved that the category of

Quaternionic Structures is naturally equivalent to the category of

abstract Witt rings. This paper develops a combinatorial theory

for finite Quaternionic Structures in the case where $1=-1$,

by demonstrating an equivalence between finite quaternionic

structures and Steiner Triple Systems (STSs) with suitable block

colorings. Associated to these STSs are Block Intersection Graphs (BIGs)

with induced vertex colorings. This equivalence allows for

a classification of BIGs corresponding to the basic indecomposable Witt rings via their associated quaternionic structures. Further, this paper classifies the BIGs associated

to the Witt rings of so-called elementary type, by providing

necessary and sufficient conditions for a BIG associated to

a product or group extension.

Magnesium has the potential to become an indispensable structural material alongside aluminum due to its low density. However, magnesium is currently held back in its use as a result of its low strength and poor ductility with relatively limited structural applications. This dissertation presents the results for a processing route that was used to achieve a high-strength and thermally stable magnesium-based bulk nanocomposite in order to increase the applicability of magnesium-based alloys. This processing route included the gas atomization of Mg-4Y-3RE (WE43) powders which were treated by cryomilling (mechanical ball milling in liquid nitrogen) followed by consolidation by spark plasma sintering (SPS) in order to obtain a bulk material. The resulting bulk nanocomposite consisted of approximately 15-20% by volume fraction of extremely fine MgO nanoparticles/grains (< 10 nm) with a bimodally distributed Mg matrix consisting of nanocrystalline (~10 nm) and coarse grains (~1 �m). Besides Mg and MgO, no other phases were detected suggesting that the rare earth elements were elementally segregated to the grain boundaries. The microstructure contained a quasi-duplex structure consisting of two distinct regions with one of these regions containing only the coarse Mg grains with the other region containing all of the nanocrystalline Mg grains, MgO nanoparticles, and rare earth elements. Focused ion beam (FIB) was used to prepare 4 �m micropillars in order to determine the bulk compressive yield strength along with nanoindentation to evaluate the elastic modulus and hardness. Micropillar compression revealed a compressive yield strength of 325 MPa (compared to 190 MPa for traditional processing consisting of casting and a T6 heat-treatment) with nanoindentation demonstrating an elastic modulus of about 60 GPa and a hardness of 1.25 GPa. The nanocomposite also showed remarkable thermal stability with no observable differences in both its microstructure as well as in its mechanical properties even up to an extremely severe heat-treatment at 450 �C (0.9Tm) for 100 hours. The thermal stability was attributed to a combination of the MgO nanoparticles as well as the rare earth elements segregated to the grain boundaries acting as grain boundary pinning sites with the thermal stability of the nanocrystalline regions confining the growth of the discontinuous coarse-grained Mg regions.