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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 order to cope with the decreasing availability of symphony jobs and collegiate faculty positions, many musicians are starting to pursue less traditional career paths. Also, to combat declining audiences, musicians are exploring ways to cultivate new and enthusiastic listeners through relevant and engaging performances. Due to these challenges, many community-based chamber music ensembles have been formed throughout the United States. These groups not only focus on performing classical music, but serve the needs of their communities as well. The problem, however, is that many musicians have not learned the business skills necessary to create these career opportunities. In this document I discuss the steps ensembles must take to develop sustainable careers. I first analyze how groups build a strong foundation through getting to know their communities and creating core values. I then discuss branding and marketing so ensembles can develop a public image and learn how to publicize themselves. This is followed by an investigation of how ensembles make and organize their money. I then examine the ways groups ensure long-lasting relationships with their communities and within the ensemble. I end by presenting three case studies of professional ensembles to show how groups create and maintain successful careers. Ensembles must develop entrepreneurship skills in addition to cultivating their artistry. These business concepts are crucial to the longevity of chamber groups. Through interviews of successful ensemble members and my own personal experiences in the Tetra String Quartet, I provide a guide for musicians to use when creating a community-based ensemble.
ContributorsDalbey, Jenna (Author) / Landschoot, Thomas (Thesis advisor) / McLin, Katherine (Committee member) / Ryan, Russell (Committee member) / Solis, Theodore (Committee member) / Spring, Robert (Committee member) / Arizona State University (Publisher)
Created2013
Description
American Primitive is a composition written for wind ensemble with an instrumentation of flute, oboe, clarinet, bass clarinet, alto, tenor, and baritone saxophones, trumpet, horn, trombone, euphonium, tuba, piano, and percussion. The piece is approximately twelve minutes in duration and was written September - December 2013. American Primitive is absolute music (i.e. it does not follow a specific narrative) comprising blocks of distinct, contrasting gestures which bookend a central region of delicate textural layering and minimal gestural contrast. Though three gestures (a descending interval followed by a smaller ascending interval, a dynamic swell, and a chordal "chop") were consciously employed throughout, it is the first gesture of the three that creates a sense of unification and overall coherence to the work. Additionally, the work challenges listeners' expectations of traditional wind ensemble music by featuring the trumpet as a quasi-soloist whose material is predominately inspired by transcriptions of jazz solos. This jazz-inspired material is at times mimicked and further developed by the ensemble, also often in a soloistic manner while the trumpet maintains its role throughout. This interplay of dialogue between the "soloists" and the "ensemble" further skews listeners' conceptions of traditional wind ensemble music by featuring almost every instrument in the ensemble. Though the term "American Primitive" is usually associated with the "naïve art" movement, it bears no association to the music presented in this work. Instead, the term refers to the author's own compositional attitudes, education, and aesthetic interests.
ContributorsJandreau, Joshua (Composer) / Rockmaker, Jody D (Thesis advisor) / Rogers, Rodney I (Committee member) / Demars, James R (Committee member) / Arizona State University (Publisher)
Created2014
Description
This project is a practical annotated bibliography of original works for oboe trio with the specific instrumentation of two oboes and English horn. Presenting descriptions of 116 readily available oboe trios, this project is intended to promote awareness, accessibility, and performance of compositions within this genre.
The annotated bibliography focuses exclusively on original, published works for two oboes and English horn. Unpublished works, arrangements, works that are out of print and not available through interlibrary loan, or works that feature slightly altered instrumentation are not included.
Entries in this annotated bibliography are listed alphabetically by the last name of the composer. Each entry includes the dates of the composer and a brief biography, followed by the title of the work, composition date, commission, and dedication of the piece. Also included are the names of publishers, the length of the entire piece in minutes and seconds, and an incipit of the first one to eight measures for each movement of the work.
In addition to providing a comprehensive and detailed bibliography of oboe trios, this document traces the history of the oboe trio and includes biographical sketches of each composer cited, allowing readers to place the genre of oboe trios and each individual composition into its historical context. Four appendices at the end include a list of trios arranged alphabetically by composer's last name, chronologically by the date of composition, and by country of origin and a list of publications of Ludwig van Beethoven's oboe trios from the 1940s and earlier.
The annotated bibliography focuses exclusively on original, published works for two oboes and English horn. Unpublished works, arrangements, works that are out of print and not available through interlibrary loan, or works that feature slightly altered instrumentation are not included.
Entries in this annotated bibliography are listed alphabetically by the last name of the composer. Each entry includes the dates of the composer and a brief biography, followed by the title of the work, composition date, commission, and dedication of the piece. Also included are the names of publishers, the length of the entire piece in minutes and seconds, and an incipit of the first one to eight measures for each movement of the work.
In addition to providing a comprehensive and detailed bibliography of oboe trios, this document traces the history of the oboe trio and includes biographical sketches of each composer cited, allowing readers to place the genre of oboe trios and each individual composition into its historical context. Four appendices at the end include a list of trios arranged alphabetically by composer's last name, chronologically by the date of composition, and by country of origin and a list of publications of Ludwig van Beethoven's oboe trios from the 1940s and earlier.
ContributorsSassaman, Melissa Ann (Author) / Schuring, Martin (Thesis advisor) / Buck, Elizabeth (Committee member) / Holbrook, Amy (Committee member) / Hill, Gary (Committee member) / Arizona State University (Publisher)
Created2014
Description
Since the seminal work of Tur ́an, the forbidden subgraph problem has been among the central questions in extremal graph theory. Let ex(n;F) be the smallest number m such that any graph on n vertices with m edges contains F as a subgraph. Then the forbidden subgraph problem asks to find ex(n; F ) for various graphs F . The question can be further generalized by asking for the extreme values of other graph parameters like minimum degree, maximum degree, or connectivity. We call this type of question a Tura ́n-type problem. In this thesis, we will study Tura ́n-type problems and their variants for graphs and hypergraphs.
Chapter 2 contains a Tura ́n-type problem for cycles in dense graphs. The main result in this chapter gives a tight bound for the minimum degree of a graph which guarantees existence of disjoint cycles in the case of dense graphs. This, in particular, answers in the affirmative a question of Faudree, Gould, Jacobson and Magnant in the case of dense graphs.
In Chapter 3, similar problems for trees are investigated. Recently, Faudree, Gould, Jacobson and West studied the minimum degree conditions for the existence of certain spanning caterpillars. They proved certain bounds that guarantee existence of spanning caterpillars. The main result in Chapter 3 significantly improves their result and answers one of their questions by proving a tight minimum degree bound for the existence of such structures.
Chapter 4 includes another Tur ́an-type problem for loose paths of length three in a 3-graph. As a corollary, an upper bound for the multi-color Ramsey number for the loose path of length three in a 3-graph is achieved.
Chapter 2 contains a Tura ́n-type problem for cycles in dense graphs. The main result in this chapter gives a tight bound for the minimum degree of a graph which guarantees existence of disjoint cycles in the case of dense graphs. This, in particular, answers in the affirmative a question of Faudree, Gould, Jacobson and Magnant in the case of dense graphs.
In Chapter 3, similar problems for trees are investigated. Recently, Faudree, Gould, Jacobson and West studied the minimum degree conditions for the existence of certain spanning caterpillars. They proved certain bounds that guarantee existence of spanning caterpillars. The main result in Chapter 3 significantly improves their result and answers one of their questions by proving a tight minimum degree bound for the existence of such structures.
Chapter 4 includes another Tur ́an-type problem for loose paths of length three in a 3-graph. As a corollary, an upper bound for the multi-color Ramsey number for the loose path of length three in a 3-graph is achieved.
ContributorsYie, Jangwon (Author) / Czygrinow, Andrzej (Thesis advisor) / Kierstead, Henry (Committee member) / Colbourn, Charles (Committee member) / Fishel, Susanna (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2018
ContributorsPagano, Caio, 1940- (Performer) / Mechetti, Fabio (Conductor) / Buck, Elizabeth (Performer) / Schuring, Martin (Performer) / Spring, Robert (Performer) / Rodrigues, Christiano (Performer) / Landschoot, Thomas (Performer) / Rotaru, Catalin (Performer) / Avanti Festival Orchestra (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-02
ContributorsSchuring, Martin (Performer) / Stromberg, Eric (Performer) / Campbell, Andrew (Pianist) (Performer) / ASU Library. Music Library (Publisher)
Created2018-08-19
ContributorsDe La Cruz, Nathaniel (Performer) / LoGiudice, Rosa (Contributor) / Tallino, Michael (Performer) / McKinch, Riley (Performer) / Li, Yuhui (Performer) / Armenta, Tyler (Contributor) / Gonzalez, David (Performer) / Jones, Tarin (Performer) / Ryall, Blake (Performer) / Senseman, Stephen (Performer)
Created2018-10-10
Description
The repertoire for guitar and piano duo is small in comparison with other chamber music instrumentation; therefore, it is important to broaden this repertoire. In addition to creating original compositions, arrangements of existing works contribute to this expansion.
This project focuses on an arrangement of Bachianas Brasileiras No. 1 by Brazilian composer Heitor Villa-Lobos (1887-1959), a work originally conceived for cello ensemble with a minimum of eight cellos. In order to contextualize the proposed arrangement, this study contains a brief historical listing of the repertoire for guitar and piano duo and of the guitar works by Villa-Lobos. Also, it includes a description of the Bachianas Brasileiras series and a discussion of the arranging methodology that shows how the original musical ideas of the composer were adapted using techniques that are idiomatic to the guitar and piano. The full arrangement is included in Appendix A.
This project focuses on an arrangement of Bachianas Brasileiras No. 1 by Brazilian composer Heitor Villa-Lobos (1887-1959), a work originally conceived for cello ensemble with a minimum of eight cellos. In order to contextualize the proposed arrangement, this study contains a brief historical listing of the repertoire for guitar and piano duo and of the guitar works by Villa-Lobos. Also, it includes a description of the Bachianas Brasileiras series and a discussion of the arranging methodology that shows how the original musical ideas of the composer were adapted using techniques that are idiomatic to the guitar and piano. The full arrangement is included in Appendix A.
ContributorsFigueiredo Bartoloni, Fabio (Author) / Koonce, Frank (Thesis advisor) / Suzuki, Kotoka (Committee member) / Landschoot, Thomas (Committee member) / Arizona State University (Publisher)
Created2016
Description
Higher-rank graphs, or k-graphs, are higher-dimensional analogues of directed graphs, and as with ordinary directed graphs, there are various C*-algebraic objects that can be associated with them. This thesis adopts a functorial approach to study the relationship between k-graphs and their associated C*-algebras. In particular, two functors are given between appropriate categories of higher-rank graphs and the category of C*-algebras, one for Toeplitz algebras and one for Cuntz-Krieger algebras. Additionally, the Cayley graphs of finitely generated groups are used to define a class of k-graphs, and a functor is then given from a category of finitely generated groups to the category of C*-algebras. Finally, functoriality is investigated for product systems of C*-correspondences associated to k-graphs. Additional results concerning the structural consequences of functoriality, properties of the functors, and combinatorial aspects of k-graphs are also included throughout.
ContributorsEikenberry, Keenan (Author) / Quigg, John (Thesis advisor) / Kaliszewski, Steven (Thesis advisor) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2016