Matching Items (5)
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- All Subjects: Mathematics
- Creators: Department of Chemistry and Biochemistry
- Member of: Barrett, The Honors College Thesis/Creative Project Collection
Description
This paper focuses on the Szemerédi regularity lemma, a result in the field of extremal graph theory. The lemma says that every graph can be partitioned into bounded equal parts such that most edges of the graph span these partitions, and these edges are distributed in a fairly uniform way. Definitions and notation will be established, leading to explorations of three proofs of the regularity lemma. These are a version of the original proof, a Pythagoras proof utilizing elemental geometry, and a proof utilizing concepts of spectral graph theory. This paper is intended to supplement the proofs with background information about the concepts utilized. Furthermore, it is the hope that this paper will serve as another resource for students and others to begin study of the regularity lemma.
ContributorsByrne, Michael John (Author) / Czygrinow, Andrzej (Thesis director) / Kierstead, Hal (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2015-05
Description
Metal-organic frameworks (MOFs) are a new set of porous materials comprised of metals or metal clusters bonded together in a coordination system by organic linkers. They are becoming popular for gas separations due to their abilities to be tailored toward specific applications. Zirconium MOFs in particular are known for their high stability under standard temperature and pressure due to the strength of the Zirconium-Oxygen coordination bond. However, the acid modulator needed to ensure long range order of the product also prevents complete linker deprotonation. This leads to a powder product that cannot easily be incorporated into continuous MOF membranes. This study therefore implemented a new bi-phase synthesis technique with a deprotonating agent to achieve intergrowth in UiO-66 membranes. Crystal intergrowth will allow for effective gas separations and future permeation testing. During experimentation, successful intergrown UiO-66 membranes were synthesized and characterized. The degree of intergrowth and crystal orientations varied with changing deprotonating agent concentration, modulator concentration, and ligand:modulator ratios. Further studies will focus on achieving the same results on porous substrates.
ContributorsClose, Emily Charlotte (Author) / Mu, Bin (Thesis director) / Shan, Bohan (Committee member) / Chemical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Mathematics education, defined briefly by both students' understanding and teacher instruction, is a cause for concern in the United States. A 1998 comprehensive study conducted by The Third International Mathematics and Science Study (TIMSS) shows that preadolescent mathematics education is comparatively less effective in this country than it is in other countries. The purposes of the present investigation were to understand why mathematics education has its short-comings in the United States, to analyze the most effective ways to help middle grade students learn mathematics, and to examine instructional methods for improving student understanding. The focus is on effective instructional methods because this is an aspect that teachers can directly control and influence. A thorough review of neurological findings and learning theories strongly gave insight into how the preadolescent brain learns best and the investigation further examined the effectiveness of research-based findings by executing a lesson in a 6th grade mathematics classroom and analyzing student results.
ContributorsPatel, Jay Narendra (Author) / Brass, Amber (Thesis director) / White, Darcy (Committee member) / Klem-Deleon, Olga (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor) / School of Historical, Philosophical and Religious Studies (Contributor)
Created2013-05
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
Styrene, a component of many rubber products, is currently synthesized from petroleum in a highly energy-intensive process. The Nielsen Laboratory at Arizona State has demonstrated a biochemical pathway by which E. coli can be engineered to produce styrene from the amino acid phenylalanine, which E. coli naturally synthesizes from glucose. However, styrene becomes toxic to E. coli above concentrations of 300 mg/L, severely limiting the large-scale applicability of the pathway. Thus, styrene must somehow be continuously removed from the system to facilitate higher yields and for the purposes of scale-up. The separation methods of pervaporation and solvent extraction were investigated to this end. Furthermore, the styrene pathway was extended by one step to produce styrene oxide, which is less volatile than styrene and theoretically simpler to recover. Adsorption of styrene oxide using the hydrophobic resin L-493 was attempted in order to improve the yield of styrene oxide and to provide additional proof of concept that the flux through the styrene pathway can be increased. The maximum styrene titer achieved was 1.2 g/L using the method of solvent extraction, but this yield was only possible when additional phenylalanine was supplemented to the system.
ContributorsMcDaniel, Matthew Cary (Author) / Nielsen, David (Thesis director) / Lind, Mary Laura (Committee member) / McKenna, Rebekah (Committee member) / Barrett, The Honors College (Contributor) / Department of Chemistry and Biochemistry (Contributor) / Chemical Engineering Program (Contributor)
Created2013-05