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- Genre: Doctoral Dissertation
Description
An array of north-striking, left-stepping, active normal faults is situated along the southwestern margin of the Gulf of California. This normal fault system is the marginal fault system of the oblique-divergent plate boundary within the Gulf of California. To better understand the role of upper-crustal processes during development of an obliquely rifted plate margin, gravity surveys were conducted across the normal-fault-bounded basins within the gulf-margin array and, along with optically stimulated luminescence dating of offset surfaces, fault-slip rates were estimated and fault patterns across basins were assessed, providing insight into sedimentary basin evolution. Additionally, detailed geologic and geomorphic maps were constructed along two faults within the system, leading to a more complete understanding of the role of individual normal faults within a larger array. These faults slip at a low rate (0.1-1 mm/yr) and have relatively shallow hanging wall basins (~500-3000 m). Overall, the gulf-margin faults accommodate protracted, distributed deformation at a low rate and provide a minor contribution to overall rifting. Integrating figures with text can lead to greater science learning than when either medium is presented alone. Textbooks, composed of text and graphics, are a primary source of content in most geology classes. It is essential to understand how students approach learning from text and figures in textbook-style learning materials and how the arrangement of the text and figures influences their learning approach. Introductory geology students were eye tracked while learning from textbook-style materials composed of text and graphics. Eye fixation data showed that students spent less time examining the figure than the text, but the students who more frequently examined the figure tended to improve more from the pretest to the posttest. In general, students tended to examine the figure at natural breaks in the reading. Textbook-style materials should, therefore, be formatted to include a number of natural breaks so that learners can pause to inspect the figure without the risk of losing their place in the reading and to provide a chance to process the material in small chunks. Multimedia instructional materials should be designed to support the cognitive processes of the learner.
ContributorsBusch, Melanie M. D (Author) / Arrowsmith, Ramon (Thesis advisor) / Reynolds, Stephen (Thesis advisor) / Chi, Michelene (Committee member) / Semken, Steven (Committee member) / Tyburczy, James (Committee member) / Arizona State University (Publisher)
Created2011
Description
In a large network (graph) it would be desirable to guarantee the existence of some local property based only on global knowledge of the network. Consider the following classical example: how many connections are necessary to guarantee that the network contains three nodes which are pairwise adjacent? It turns out that more than n^2/4 connections are needed, and no smaller number will suffice in general. Problems of this type fall into the category of ``extremal graph theory.'' Generally speaking, extremal graph theory is the study of how global parameters of a graph are related to local properties. This dissertation deals with the relationship between minimum degree conditions of a host graph G and the property that G contains a specified spanning subgraph (or class of subgraphs). The goal is to find the optimal minimum degree which guarantees the existence of a desired spanning subgraph. This goal is achieved in four different settings, with the main tools being Szemeredi's Regularity Lemma; the Blow-up Lemma of Komlos, Sarkozy, and Szemeredi; and some basic probabilistic techniques.
ContributorsDeBiasio, Louis (Author) / Kierstead, Henry A (Thesis advisor) / Czygrinow, Andrzej (Thesis advisor) / Hurlbert, Glenn (Committee member) / Kadell, Kevin (Committee member) / Fishel, Susanna (Committee member) / Arizona State University (Publisher)
Created2011
Description
Geoscience educators commonly teach geology by projecting a photograph in front of the class. Geologic photographs often contain animals, people, and inanimate objects that help convey the scale of features in the photograph. Although scale items seem innocuous to instructors and other experts, the presence of such items is distracting and has a profound effect on student learning behavior. To evaluate how students visually interact with distracting scale items in photographs and to determine if cueing or signaling is an effective means to direct students to pertinent information, students were eye tracked while looking at geologically-rich photographs. Eye-tracking data revealed that learners primarily looked at the center of an image, focused on faces of both humans and animals if they were present, and repeatedly returned to looking at the scale item (distractor) for the duration an image was displayed. The presence of a distractor caused learners to look at less of an image than when a distractor was not present. Learners who received signaling tended to look at the distractor less, look at the geology more, and surveyed more of the photograph than learners who did not receive signaling. The San Antonio area in the southern part of the Baja California Peninsula is host to hydrothermal gold deposits. A field study, including drill-core analysis and detailed geologic mapping, was conducted to determine the types of mineralization present, the types of structures present, and the relationship between the two. This investigation revealed that two phases of mineralization have occurred in the area; the first is hydrothermal deposition of gold associated with sulfide deposits and the second is oxidation of sulfides to hematite, goethite, and jarosite. Mineralization varies as a function of depth, whereas sulfides occurring at depth, while minerals indicative of oxidation are limited to shallow depths. A structural analysis revealed that the oldest structures in the study area include low-grade to medium-grade metamorphic foliation and ductile mylonitic shear zones overprinted by brittle-ductile mylonitic fabrics, which were later overprinted by brittle deformation. Both primary and secondary mineralization in the area is restricted to the later brittle features. Alteration-bearing structures have an average NNW strike consistent with northeast-southwest-directed extension, whereas unaltered structures have an average NNE strike consistent with more recent northwest-southeast-directed extension.
ContributorsCoyan, Joshua (Author) / Reynolds, Stephen (Thesis advisor) / Arrowsmith, Ramon (Committee member) / Chi, Michelene (Committee member) / Piburn, Michael (Committee member) / Semken, Steven (Committee member) / Arizona State University (Publisher)
Created2011
Description
A central concept of combinatorics is partitioning structures with given constraints. Partitions of on-line posets and on-line graphs, which are dynamic versions of the more familiar static structures posets and graphs, are examined. In the on-line setting, vertices are continually added to a poset or graph while a chain partition or coloring (respectively) is maintained. %The optima of the static cases cannot be achieved in the on-line setting. Both upper and lower bounds for the optimum of the number of chains needed to partition a width $w$ on-line poset exist. Kierstead's upper bound of $\frac{5^w-1}{4}$ was improved to $w^{14 \lg w}$ by Bosek and Krawczyk. This is improved to $w^{3+6.5 \lg w}$ by employing the First-Fit algorithm on a family of restricted posets (expanding on the work of Bosek and Krawczyk) . Namely, the family of ladder-free posets where the $m$-ladder is the transitive closure of the union of two incomparable chains $x_1\le\dots\le x_m$, $y_1\le\dots\le y_m$ and the set of comparabilities $\{x_1\le y_1,\dots, x_m\le y_m\}$. No upper bound on the number of colors needed to color a general on-line graph exists. To lay this fact plain, the performance of on-line coloring of trees is shown to be particularly problematic. There are trees that require $n$ colors to color on-line for any positive integer $n$. Furthermore, there are trees that usually require many colors to color on-line even if they are presented without any particular strategy. For restricted families of graphs, upper and lower bounds for the optimum number of colors needed to maintain an on-line coloring exist. In particular, circular arc graphs can be colored on-line using less than 8 times the optimum number from the static case. This follows from the work of Pemmaraju, Raman, and Varadarajan in on-line coloring of interval graphs.
ContributorsSmith, Matthew Earl (Author) / Kierstead, Henry A (Thesis advisor) / Colbourn, Charles (Committee member) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2012
Description
Research on combinatorics education is sparse when compared with other fields in mathematics education. This research attempted to contribute to the dearth of literature by examining students' reasoning about enumerative combinatorics problems and how students conceptualize the set of elements being counted in such problems, called the solution set. In particular, the focus was on the stable patterns of reasoning, known as ways of thinking, which students applied in a variety of combinatorial situations and tasks. This study catalogued students' ways of thinking about solution sets as they progressed through an instructional sequence. In addition, the relationships between the catalogued ways of thinking were explored. Further, the study investigated the challenges students experienced as they interacted with the tasks and instructional interventions, and how students' ways of thinking evolved as these challenges were overcome. Finally, it examined the role of instruction in guiding students to develop and extend their ways of thinking. Two pairs of undergraduate students with no formal experience with combinatorics participated in one of the two consecutive teaching experiments conducted in Spring 2012. Many ways of thinking emerged through the grounded theory analysis of the data, but only eight were identified as robust. These robust ways of thinking were classified into three categories: Subsets, Odometer, and Problem Posing. The Subsets category encompasses two ways of thinking, both of which ultimately involve envisioning the solution set as the union of subsets. The three ways of thinking in Odometer category involve holding an item or a set of items constant and systematically varying the other items involved in the counting process. The ways of thinking belonging to Problem Posing category involve spontaneously posing new, related combinatorics problems and finding relationships between the solution sets of the original and the new problem. The evolution of students' ways of thinking in the Problem Posing category was analyzed. This entailed examining the perturbation experienced by students and the resulting accommodation of their thinking. It was found that such perturbation and its resolution was often the result of an instructional intervention. Implications for teaching practice are discussed.
ContributorsHalani, Aviva (Author) / Roh, Kyeong Hah (Thesis advisor) / Fishel, Susanna (Committee member) / Saldanha, Luis (Committee member) / Thompson, Patrick (Committee member) / Zandieh, Michelle (Committee member) / Arizona State University (Publisher)
Created2013
Description
A tiling is a collection of vertex disjoint subgraphs called tiles. If the tiles are all isomorphic to a graph $H$ then the tiling is an $H$-tiling. If a graph $G$ has an $H$-tiling which covers all of the vertices of $G$ then the $H$-tiling is a perfect $H$-tiling or an $H$-factor. A goal of this study is to extend theorems on sufficient minimum degree conditions for perfect tilings in graphs to directed graphs. Corrádi and Hajnal proved that every graph $G$ on $3k$ vertices with minimum degree $delta(G)ge2k$ has a $K_3$-factor, where $K_s$ is the complete graph on $s$ vertices. The following theorem extends this result to directed graphs: If $D$ is a directed graph on $3k$ vertices with minimum total degree $delta(D)ge4k-1$ then $D$ can be partitioned into $k$ parts each of size $3$ so that all of parts contain a transitive triangle and $k-1$ of the parts also contain a cyclic triangle. The total degree of a vertex $v$ is the sum of $d^-(v)$ the in-degree and $d^+(v)$ the out-degree of $v$. Note that both orientations of $C_3$ are considered: the transitive triangle and the cyclic triangle. The theorem is best possible in that there are digraphs that meet the minimum degree requirement but have no cyclic triangle factor. The possibility of added a connectivity requirement to ensure a cycle triangle factor is also explored. Hajnal and Szemerédi proved that if $G$ is a graph on $sk$ vertices and $delta(G)ge(s-1)k$ then $G$ contains a $K_s$-factor. As a possible extension of this celebrated theorem to directed graphs it is proved that if $D$ is a directed graph on $sk$ vertices with $delta(D)ge2(s-1)k-1$ then $D$ contains $k$ disjoint transitive tournaments on $s$ vertices. We also discuss tiling directed graph with other tournaments. This study also explores minimum total degree conditions for perfect directed cycle tilings and sufficient semi-degree conditions for a directed graph to contain an anti-directed Hamilton cycle. The semi-degree of a vertex $v$ is $min{d^+(v), d^-(v)}$ and an anti-directed Hamilton cycle is a spanning cycle in which no pair of consecutive edges form a directed path.
ContributorsMolla, Theodore (Author) / Kierstead, Henry A (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Spielberg, Jack (Committee member) / Arizona State University (Publisher)
Created2013
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
Science, Technology, Engineering & Mathematics (STEM) careers have been touted as critical to the success of our nation and also provide important opportunities for access and equity of underrepresented minorities (URM's). Community colleges serve a diverse population and a large number of undergraduates currently enrolled in college, they are well situated to help address the increasing STEM workforce demands. Geoscience is a discipline that draws great interest, but has very low representation of URM's as majors. What factors influence a student's decision to major in the geosciences and are community college students different from research universities in what factors influence these decisions? Through a survey-design mixed with classroom observations, structural equation model was employed to predict a student's intent to persist in introductory geology based on student expectancy for success in their geology class, math self-concept, and interest in the content. A measure of classroom pedagogy was also used to determine if instructor played a role in predicting student intent to persist. The targeted population was introductory geology students participating in the Geoscience Affective Research NETwork (GARNET) project, a national sampling of students in enrolled in introductory geology courses. Results from SEM analysis indicated that interest was the primary predictor in a students intent to persist in the geosciences for both community college and research university students. In addition, self-efficacy appeared to be mediated by interest within these models. Classroom pedagogy impacted how much interest was needed to predict intent to persist, in which as classrooms became more student centered, less interest was required to predict intent to persist. Lastly, math self-concept did not predict student intent to persist in the geosciences, however, it did share variance with self-efficacy and control of learning beliefs, indicating it may play a moderating effect on student interest and self-efficacy. Implications of this work are that while community college students and research university students are different in demographics and content preparation, student-centered instruction continues to be the best way to support student's interest in the sciences. Future work includes examining how math self-concept may play a role in longitudinal persistence in the geosciences.
ContributorsKraft, Katrien J. van der Hoeven (Author) / Husman, Jenefer (Thesis advisor) / Semken, Steven (Thesis advisor) / Baker, Dale R. (Committee member) / McConnell, David (Committee member) / Arizona State University (Publisher)
Created2014
Description
Every graph can be colored with one more color than its maximum degree. A well-known theorem of Brooks gives the precise conditions under which a graph can be colored with maximum degree colors. It is natural to ask for the required conditions on a graph to color with one less color than the maximum degree; in 1977 Borodin and Kostochka conjectured a solution for graphs with maximum degree at least 9: as long as the graph doesn't contain a maximum-degree-sized clique, it can be colored with one fewer than the maximum degree colors. This study attacks the conjecture on multiple fronts. The first technique is an extension of a vertex shuffling procedure of Catlin and is used to prove the conjecture for graphs with edgeless high vertex subgraphs. This general approach also bears more theoretical fruit. The second technique is an extension of a method Kostochka used to reduce the Borodin-Kostochka conjecture to the maximum degree 9 case. Results on the existence of independent transversals are used to find an independent set intersecting every maximum clique in a graph. The third technique uses list coloring results to exclude induced subgraphs in a counterexample to the conjecture. The classification of such excludable graphs that decompose as the join of two graphs is the backbone of many of the results presented here. The fourth technique uses the structure theorem for quasi-line graphs of Chudnovsky and Seymour in concert with the third technique to prove the Borodin-Kostochka conjecture for claw-free graphs. The fifth technique adds edges to proper induced subgraphs of a minimum counterexample to gain control over the colorings produced by minimality. The sixth technique adapts a recoloring technique originally developed for strong coloring by Haxell and by Aharoni, Berger and Ziv to general coloring. Using this recoloring technique, the Borodin-Kostochka conjectured is proved for graphs where every vertex is in a large clique. The final technique is naive probabilistic coloring as employed by Reed in the proof of the Borodin-Kostochka conjecture for large maximum degree. The technique is adapted to prove the Borodin-Kostochka conjecture for list coloring for large maximum degree.
ContributorsRabern, Landon (Author) / Kierstead, Henry (Thesis advisor) / Colbourn, Charles (Committee member) / Czygrinow, Andrzej (Committee member) / Fishel, Susanna (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2013
Description
Understanding the evolution of the Himalayan-Tibetan orogen is important because of its purported effects on global geodynamics, geochemistry and climate. It is surprising that the timing of initiation of this canonical collisional orogen is poorly constrained, with estimates ranging from Late Cretaceous to Early Oligocene. This study focuses on the Ladakh region in the northwestern Indian Himalaya, where early workers suggested that sedimentary deposits of the Indus Basin molasse sequence, located in the suture zone, preserve a record of the early evolution of orogenesis, including initial collision between India and Eurasia. Recent studies have challenged this interpretation, but resolution of the issue has been hampered by poor accessibility, paucity of robust depositional age constraints, and disputed provenance of many units in the succession. To achieve a better understanding of the stratigraphy of the Indus Basin, multispectral remote sensing image analysis resulted in a new geologic map that is consistent with field observations and previously published datasets, but suggests a substantial revision and simplification of the commonly assumed stratigraphic architecture of the basin. This stratigraphic framework guided a series of new provenance studies, wherein detrital U-Pb geochronology, 40Ar/39Ar and (U-Th)/He thermochronology, and trace-element geochemistry not only discount the hypothesis that collision began in the Early Oligocene, but also demonstrate that both Indian and Eurasian detritus arrived in the basin prior to deposition of the last marine limestone, constraining the age of collision to older than Early Eocene. Detrital (U-Th)/He thermochronology further elucidates the thermal history of the basin. Thus, we constrain backthrusting, thought to be an important mechanism by which Miocene convergence was accommodated, to between 11-7 Ma. Finally, an unprecedented conventional (U-Th)/He thermochronologic dataset was generated from a modern river sand to assess steady state assumptions of the source region. Using these data, the question of the minimum number of dates required for robust interpretation was critically evaluated. The application of a newly developed (U-Th)/He UV-laser-microprobe thermochronologic technique confirmed the results of the conventional dataset. This technique improves the practical utility of detrital mineral (U-Th)/He thermochronology, and will facilitate future studies of this type.
ContributorsTripathy, Alka (Author) / Hodges, Kip V (Thesis advisor) / Semken, Steven (Committee member) / Van Soest, Matthijs C (Committee member) / Whipple, Kelin X (Committee member) / Christensen, Philip R. (Philip Russel) (Committee member) / Arizona State University (Publisher)
Created2011