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- Creators: Barrett, The Honors College
- Creators: Debussy, Claude, 1862-1918
Description
In 1959, Iwasawa proved that the size of the $p$-part of the class groups of a $\mathbb{Z}_p$-extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large. Broadly, I construct conditions to verify if a given $m$ is indeed sufficiently large. More precisely, let $CG_m^i$ (class group) be the $\epsilon_i$-eigenspace component of the $p$-Sylow subgroup of the class group of the field at the $m$-th level in a $\mathbb{Z}_p$-extension; and let $IACG^i_m$ (Iwasawa analytic class group) be ${\mathbb{Z}_p[[T]]/((1+T)^{p^m}-1,f(T,\omega^{1-i}))}$, where $f$ is the associated Iwasawa power series. It is expected that $CG_m^i$ and $IACG^i_m$ be isomorphic, providing us with a powerful connection between algebraic and analytic techniques; however, as of yet, this isomorphism is unestablished in general. I consider the existence and the properties of an exact sequence $$0\longrightarrow\ker{\longrightarrow}CG_m^i{\longrightarrow}IACG_m^i{\longrightarrow}\textrm{coker}\longrightarrow0.$$ In the case of a $\mathbb{Z}_p$-extension where the Main Conjecture is established, there exists a pseudo-isomorphism between the respective inverse limits of $CG_m^i$ and $IACG_m^i$. I consider conditions for when such a pseudo-isomorphism immediately gives the existence of the desired exact sequence, and I also consider work-around methods that preserve cardinality for otherwise. However, I primarily focus on constructing conditions to verify if a given $m$ is sufficiently large that the kernel and cokernel of the above exact sequence have become well-behaved, providing similarity of growth both in the size and in the structure of $CG_m^i$ and $IACG_m^i$; as well as conditions to determine if any such $m$ exists. The primary motivating idea is that if $IACG_m^i$ is relatively easy to work with, and if the relationship between $CG_m^i$ and $IACG_m^i$ is understood; then $CG_m^i$ becomes easier to work with. Moreover, while the motivating framework is stated concretely in terms of the cyclotomic $\mathbb{Z}_p$-extension of $p$-power roots of unity, all results are generally applicable to arbitrary $\mathbb{Z}_p$-extensions as they are developed in terms of Iwasawa-Theory-inspired, yet abstracted, algebraic results on maps between inverse limits.
ContributorsElledge, Shawn Michael (Author) / Childress, Nancy (Thesis advisor) / Bremner, Andrew (Committee member) / Fishel, Susanna (Committee member) / Jones, John (Committee member) / Paupert, Julien (Committee member) / Arizona State University (Publisher)
Created2013
Description
In 1984, Sinnott used $p$-adic measures on $\mathbb{Z}_p$ to give a new proof of the Ferrero-Washington Theorem for abelian number fields by realizing $p$-adic $L$-functions as (essentially) the $Gamma$-transform of certain $p$-adic rational function measures. Shortly afterward, Gillard and Schneps independently adapted Sinnott's techniques to the case of $p$-adic $L$-functions associated to elliptic curves with complex multiplication (CM) by realizing these $p$-adic $L$-functions as $Gamma$-transforms of certain $p$-adic rational function measures. The results in the CM case give the vanishing of the Iwasawa $mu$-invariant for certain $mathbb{Z}_p$-extensions of imaginary quadratic fields constructed from torsion points of CM elliptic curves.
In this thesis, I develop the theory of $p$-adic measures on $mathbb{Z}_p^d$, with particular interest given to the case of $d>1$. Although I introduce these measures within the context of $p$-adic integration, this study includes a strong emphasis on the interpretation of $p$-adic measures as $p$-adic power series. With this dual perspective, I describe $p$-adic analytic operations as maps on power series; the most important of these operations is the multivariate $Gamma$-transform on $p$-adic measures.
This thesis gives new significance to product measures, and in particular to the use of product measures to construct measures on $mathbb{Z}_p^2$ from measures on $mathbb{Z}_p$. I introduce a subring of pseudo-polynomial measures on $mathbb{Z}_p^2$ which is closed under the standard operations on measures, including the $Gamma$-transform. I obtain results on the Iwasawa-invariants of such pseudo-polynomial measures, and use these results to deduce certain continuity results for the $Gamma$-transform. As an application, I establish the vanishing of the Iwasawa $mu$-invariant of Yager's two-variable $p$-adic $L$-function from measure theoretic considerations.
In this thesis, I develop the theory of $p$-adic measures on $mathbb{Z}_p^d$, with particular interest given to the case of $d>1$. Although I introduce these measures within the context of $p$-adic integration, this study includes a strong emphasis on the interpretation of $p$-adic measures as $p$-adic power series. With this dual perspective, I describe $p$-adic analytic operations as maps on power series; the most important of these operations is the multivariate $Gamma$-transform on $p$-adic measures.
This thesis gives new significance to product measures, and in particular to the use of product measures to construct measures on $mathbb{Z}_p^2$ from measures on $mathbb{Z}_p$. I introduce a subring of pseudo-polynomial measures on $mathbb{Z}_p^2$ which is closed under the standard operations on measures, including the $Gamma$-transform. I obtain results on the Iwasawa-invariants of such pseudo-polynomial measures, and use these results to deduce certain continuity results for the $Gamma$-transform. As an application, I establish the vanishing of the Iwasawa $mu$-invariant of Yager's two-variable $p$-adic $L$-function from measure theoretic considerations.
ContributorsZinzer, Scott Michael (Author) / Childress, Nancy (Thesis advisor) / Bremner, Andrew (Committee member) / Fishel, Susanna (Committee member) / Jones, John (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2015
ContributorsDebussy, Claude, 1862-1918 (Composer)
ContributorsDebussy, Claude, 1862-1918 (Composer)
ContributorsDebussy, Claude, 1862-1918 (Composer)
ContributorsDebussy, Claude, 1862-1918 (Composer)
ContributorsDebussy, Claude, 1862-1918 (Composer)
Description
Geology and its tangential studies, collectively known and referred to in this thesis as geosciences, have been paramount to the transformation and advancement of society, fundamentally changing the way we view, interact and live with the surrounding natural and built environment. It is important to recognize the value and importance of this interdisciplinary scientific field while reconciling its ties to imperial and colonizing extractive systems which have led to harmful and invasive endeavors. This intersection among geosciences, (environmental) justice studies, and decolonization is intended to promote inclusive pedagogical models through just and equitable methodologies and frameworks as to prevent further injustices and promote recognition and healing of old wounds. By utilizing decolonial frameworks and highlighting the voices of peoples from colonized and exploited landscapes, this annotated syllabus tackles the issues previously described while proposing solutions involving place-based education and the recentering of land within geoscience pedagogical models. (abstract)
ContributorsReed, Cameron E (Author) / Richter, Jennifer (Thesis director) / Semken, Steven (Committee member) / School of Earth and Space Exploration (Contributor, Contributor) / School of Sustainability (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The ASU COVID-19 testing lab process was developed to operate as the primary testing site for all ASU staff, students, and specified external individuals. Tests are collected at various collection sites, including a walk-in site at the SDFC and various drive-up sites on campus; analysis is conducted on ASU campus and results are distributed virtually to all patients via the Health Services patient portal. The following is a literature review on past implementations of various process improvement techniques and how they can be applied to the ABCTL testing process to achieve laboratory goals. (abstract)
ContributorsKrell, Abby Elizabeth (Co-author) / Bruner, Ashley (Co-author) / Ramesh, Frankincense (Co-author) / Lewis, Gabriel (Co-author) / Barwey, Ishna (Co-author) / Myers, Jack (Co-author) / Hymer, William (Co-author) / Reagan, Sage (Co-author) / Compton, Carolyn (Thesis director) / McCarville, Daniel R. (Committee member) / Industrial, Systems & Operations Engineering Prgm (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
The US National Academy of Sciences and The Royal Society have recently released a detailed report on the causes and effects of global climate change.1 This report states that the Earth’s climate is rapidly changing due to human activity. Specifically, the burning of fossil fuels to satisfy the energy demands of rising global population has resulted in unprecedented levels of greenhouse gasses in the atmosphere. These high levels of greenhouse gasses are serving to warm the surface of the planet resulting in extreme weather events. Thus, controlling the atmospheric CO2 level is motivating a great deal of scientific research in the area of carbon capture and storage (CCS).
Despite the great strides being made in the areas of alternative energy and solar-energy conversion, consumption of fossil fuels for energy generation will likely continue into the foreseeable future. This is primarily motivated by economic factors inasmuch as fossil fuels are a proven resource base with robust harvesting and distribution infrastructure.2 Presently, there are more than 8,000 stationary CO2 emission sources with an annual output of 13,466 megatons of CO2 per year.2 In this context, development of systems that ameliorate the output of greenhouse gasses from stationary CO2 sources, such as coal and natural gas burning power plants, is urgently needed.
In this document the utility of sulfur nucleophiles for CCS schemes is explored. The main thrust of the research has been utilizing electrogenerated sulfur nucleophiles to capture CO2, which can be electrochemically recovered from the resulting thiocarbonates while concomitantly regenerating the masked capture agent. Further, a temperature swing CO2 capture scheme that employs benzylthiolate as the CO2 sorbent is proposed and methods of manipulating the release temperature and kinetics were investigated. These reports represent the first application of organosulfur compounds toward CCS technologies and there are a number of newly reported compounds. The appendix deviates from the theme of the first four chapters to describe the functionalization of poly(2,6-dimethyl-1,4-phenylene oxide) with ferrocene moieties by the copper catalyzed azide-alkyne coupling reaction. This material is discussed within the context of anion recognition and sensing applications.
Despite the great strides being made in the areas of alternative energy and solar-energy conversion, consumption of fossil fuels for energy generation will likely continue into the foreseeable future. This is primarily motivated by economic factors inasmuch as fossil fuels are a proven resource base with robust harvesting and distribution infrastructure.2 Presently, there are more than 8,000 stationary CO2 emission sources with an annual output of 13,466 megatons of CO2 per year.2 In this context, development of systems that ameliorate the output of greenhouse gasses from stationary CO2 sources, such as coal and natural gas burning power plants, is urgently needed.
In this document the utility of sulfur nucleophiles for CCS schemes is explored. The main thrust of the research has been utilizing electrogenerated sulfur nucleophiles to capture CO2, which can be electrochemically recovered from the resulting thiocarbonates while concomitantly regenerating the masked capture agent. Further, a temperature swing CO2 capture scheme that employs benzylthiolate as the CO2 sorbent is proposed and methods of manipulating the release temperature and kinetics were investigated. These reports represent the first application of organosulfur compounds toward CCS technologies and there are a number of newly reported compounds. The appendix deviates from the theme of the first four chapters to describe the functionalization of poly(2,6-dimethyl-1,4-phenylene oxide) with ferrocene moieties by the copper catalyzed azide-alkyne coupling reaction. This material is discussed within the context of anion recognition and sensing applications.
ContributorsRheinhardt, Joseph (Author) / Buttry, Daniel A. (Thesis advisor) / Angell, Charles A. (Committee member) / Chizmeshya, Andrew V. G. (Committee member) / Arizona State University (Publisher)
Created2018