MAXIMAL ARCS, ABOVE AND BEYOND

This report explores combinatorial structures in Finite Geometries by giving known constructions of maximal arcs; using maximal arcs to construct two-weight codes, partial geometries, strongly regular graphs and LDPC codes; a review on how to generalize maximal arcs to higher dimensions through Perp-Systems; and an effort in finding constructions of new Perp-Systems.

Investigation of the effect of using data collection technology on students' attitudes to science instruction

The purpose of this project was to investigate the effect of using of data collection technology on student attitudes towards science instruction. The study was conducted over the course of two years at Madison High School in Adrian, Michigan, primarily in college preparatory physics classes, but also in one college preparatory chemistry class and one environmental science class. A preliminary study was conducted at a Lenawee County Intermediate Schools student summer environmental science day camp. The data collection technology used was a combination of Texas Instruments TI-84 Silver Plus graphing calculators and Vernier LabPro data collection sleds with various probeware attachments, including motion sensors, pH probes and accelerometers. Students were given written procedures for most laboratory activities and were provided with data tables and analysis questions to answer about the activities. The first year of the study included a pretest and posttest measuring student attitudes towards the class they were enrolled in. Pre-test and post-test data were analyzed to determine effect size, which was found to be very small (Coe, 2002). The second year of the study focused only on a physics class and used Keller’s ARCS model for measuring student motivation based on the four aspects of motivation: Attention, Relevance, Confidence and Satisfaction (Keller, 2010). According to this model, it was found that there were two distinct groups in the class, one of which was motivated to learn and the other that was not. The data suggest that the use of data collection technology in science classes should be started early in a student’s career, possibly in early middle school or late elementary. This would build familiarity with the equipment and allow for greater exploration by the student as they progress through high school and into upper level science courses.

Remote sensing of volcanic plumes using the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER).

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) has been used to quantify SO2 emissions from passively degassing volcanoes. This dissertation explores ASTER’s capability to detect SO2 with satellite validation, enhancement techniques and extensive processing of images at a variety of volcanoes. ASTER is compared to the Mini UV Spectrometer (MUSe), a ground based instrument, to determine if reasonable SO2 fluxes can be quantified from a plume emitted from Lascar, Chile. The two sensors were in good agreement with ASTER proving to be a reliable detector of SO2. ASTER illustrated the advantages of imaging a plume in 2D, with better temporal resolution than the MUSe. SO2 plumes in ASTER imagery are not always discernible in the raw TIR data. Principal Component Analysis (PCA) and Decorrelation Stretch (DCS) enhancement techniques were compared to determine how well they highlight a variety of volcanic plumes. DCS produced a consistent output and the composition of the plumes was easy to identify from explosive eruptions. As the plumes became smaller and lower in altitude they became harder to distinguish using DCS. PCA proved to be better at identifying smaller low altitude plumes. ASTER was used to investigate SO2 emissions at Lascar, Chile. Activity at Lascar has been characterized by cyclic behavior and persistent degassing (Matthews et al. 1997). Previous studies at Lascar have primarily focused on changes in thermal infrared anomalies, neglecting gas emissions. Using the SO2 data along with changes in thermal anomalies and visual observations it is evident that Lascar is at the end an eruptive cycle that began in 1993. Declining gas emissions and crater temperatures suggest that the conduit is sealing. ASTER and the Ozone Monitoring Instrument (OMI) were used to determine the annual contribution of SO2 to the troposphere from the Central and South American volcanic arcs between 2000 and 2011. Fluxes of 3.4 Tg/a for Central America and 3.7 Tg/a for South America were calculated. The detection limits of ASTER were explored. The results a proved to be interesting, with plumes from many of the high emitting volcanoes, such as Villarrica, Chile, not being detected by ASTER.

Benson's Theorem for Partial Geometries

In 1970 Clark Benson published a theorem in the Journal of Algebra stating a congruence for generalized quadrangles. Since then this theorem has been expanded to other specific geometries. In this thesis the theorem for partial geometries is extended to develop new divisibility conditions for the existence of a partial geometry in Chapter 2. Then in Chapter 3 the theorem is applied to higher dimensional arcs resulting in parameter restrictions on geometries derived from these structures. In Chapter 4 we look at extending previous work with partial geometries with α = 2 to uncover potential partial geometries with higher values of α. Finally the theorem is extended to strongly regular graphs in Chapter 5. In addition we obtain expressions for the multiplicities of the eigenvalues of matrices related to the adjacency matrices of these graphs. Finally, a four lesson high school level enrichment unit is included to provide students at this level with an introduction to partial geometries, strongly regular graphs, and an opportunity to develop proof skills in this new context.