Digital Commons Network^™

Nonlinear Partial Differential Equations, Their Solutions, And Properties, Prasanna Bandara

Boise State University Theses and Dissertations

Although valuable understanding of real-world phenomena can be gained experimentally, it is often the case that experimental investigations can be found to be limited by financial, ethical or other constraints making such an approach impractical or, in some cases, even impossible. To nevertheless understand and make predictions of the natural world around us, countless processes encountered in the physical and biological sciences, engineering, economics and medicine can be efficiently described by means of mathematical models written in terms of ordinary or/and partial differential equations or their systems. Fundamental questions that arise in the modeling process need care that relies on …

The Classical Theory Of Rearrangements, Monica Josue Agana

Boise State University Theses and Dissertations

One type of conditionally convergent series that has long been considered by mathematicians is the Alternating Harmonic Series and its sum under various types of rearrangements. The purpose of this thesis is to introduce results from the classical theory of rearrangements dating back to the 19th and early 20th century. We will look at results by mathematicians such as Ohm, Riemann, Schlömilch, Pringsheim, and Sierpiński. In addition, we show examples of each classical result by applying the Alternating Harmonic Series under the different types of rearrangements, and also introducing theorems by Lévy and Steinitz, and Wilczyński which are modern extensions …

Temporal And Spatial Nutrient Trends Of The Lower Boise River, Southwest Idaho, Brian M. Yelen

Boise State University Theses and Dissertations

Elevated nutrients, orthophosphate and nitrate, in the Lower Boise River (LBR) in southwest Idaho may be attributed to contamination from agriculture runoff draining into tributaries and/or waste water treatment plants (WWTP). To better understand the sources and associated spatial and temporal dynamics of nutrient loading to the LBR, a series of high resolution synoptic sampling events were conducted. Six separate synoptic sampling events were conducted along approximately 65 miles, from upstream near the city of Boise to the confluence with the Snake River, seasonally from July 2012 to October 2013 with a sampling increment of approximately 0.5 miles. The samples …

Tracking And Characterization Of Moving Acoustic Sources Using An Infrasound Array At Volcán Santiaguito, Guatemala, Brian R. Terbush

Boise State University Theses and Dissertations

Active volcanic processes produce large amounts of acoustic energy within the infrasound band (0-20 Hz). Infrasound-sensitive microphones are often installed in addition to other forms of volcano monitoring equipment to increase the ability to remotely detect volcanic activity. In this study, an array of microphones was deployed without any additional sensor types for 36 hours at Santiaguito, Guatemala, to test the detection capabilities of a standalone microphone array. Array processing was applied to the recorded data, through frequency-domain beamforming and calculating a Fisher statistic (F). A changing F-threshold value was applied to differentiate between desired detections, or …

Defining Antecedent Topography At Coral Pink Sand Dunes, Kane County, Utah: The Influence Of Structural Controls On Dune-Field Boundary Conditions And Holocene Landscape Evolution, Elizabeth Janna Rozar

Boise State University Theses and Dissertations

Dune fields are transient features that record climate signatures through changes in mobility, morphology, and patterning. Aeolian geomorphologists are increasingly recognizing the important role that pre-existing, antecedent topography plays in controlling boundary conditions that affect changes in dune patterning. However, the dynamic relationship between antecedent topography and climate-sensitive boundary conditions is relatively unexplored. Here, I define antecedent topography for the Coral Pink Sand Dunes in southern Utah and show that structural controls play an important role in shaping antecedent geomorphic conditions of this dune field. I use ground-based terrestrial laser scanning (TLS) to produce a high-resolution digital elevation model (DEM), …

Multi-Component Active Source Rayleigh Wave Analysis, Gabriel Gribler

Boise State University Theses and Dissertations

Determining how a building site will respond to earthquake ground shaking plays a critical role in proper construction practices. One critical constraint on how a site responds is the near surface shear wave seismic velocity distribution. One commonly used method for indirectly estimating shear wave velocities is Multichannel Analysis of Surface Waves (MASW), which utilizes a spread of vertical geophones to measure Rayleigh wave dispersion. With this approach, phase velocity vs. frequency dispersion curve picks can be used to estimate shear wave velocities with depth. I investigate the use of two (vertical and horizontal inline) component seismic signals to record …

Stable Isotopes Reveal A Disconnect Between Biotic And Abiotic Hydrological Processes In A Seasonally-Dry, Semi-Arid Watershed, Ryan James Mccutcheon

Boise State University Theses and Dissertations

Until recently, it had been thought that humid catchment woody plants transpired primarily mobile soil water that would otherwise flow to streams or recharge groundwater. However, several recent studies have suggested that trees in seasonally-dry humid catchments use primarily tightly-bound, immobile soil water that does not fully mix with new precipitation or participate in translatory flow. McDonnell (2014) called this existence of two, hydrologically-distinct, water pools “the two water worlds hypothesis.” This ecohydrological behavior has important implications for understanding a wide range of catchment processes, including the spatial and temporal variability of evapotranspiration and nutrient cycling, and our abilities to …

Impacts Of Changing Snowmelt Timing On Non-Irrigated Crop Yield, Erin Murray

Boise State University Theses and Dissertations

As climate changes, the final date of spring snowmelt is projected to occur earlier in the year within the western United States. This earlier snowmelt timing may impact crop yield in snow-dominated watersheds by changing the timing of water delivery to agricultural fields. There is considerable uncertainty about how agricultural impacts of snowmelt timing may vary by region, crop type, and practices like irrigation vs. dryland farming. We utilize parametric regression techniques to isolate the magnitude of impact snowmelt timing has had on historical crop yield independently of climate and physiographic variables that also impact yield. To do this, we …

Automatic Detection And Denoising Of Signals In Large Geophysical Datasets, Gabriel O. Trisca

Boise State University Theses and Dissertations

To fully understand the complex interactions of various phenomena in the natural world, scientific disciplines such as geology and seismology increasingly rely upon analyzing large amounts of observations. However, data collection is growing at a faster rate than what is currently possible to analyze through traditional approaches. These datasets, supplied by the increasing use of sensors and remote sensing, require specialized computer programs to effectively analyze complex and expansive volumes of data.

Elaborating on existing geophysical data processing approaches for infrasound data collected from an avalanche-prone area, this project proposes new techniques for processing large geophysical datasets. These improved techniques …

Monodromy Representation Of The Braid Group, Phillip W. Hart

Boise State University Theses and Dissertations

In the mid 1980s, it was realized that solutions to what is known as the Knizhnik- Zamolodchikov equation, or KZ equation, provided a pathway to representations of the braid group B_n on n strands, with early mathematical treatments of the topic by Kohno and Drinfel'd. Such representations are typically referred to as monodromy representations of the braid group along solutions of the KZ equation. These linear representations are of great interest within topology, integral to the construction of isotopy invariants of knots and links, such as the well known Jones polynomial. More current discussions of the KZ equation and …

The Impact Of A Quantitative Reasoning Instructional Approach To Linear Equations In Two Variables On Student Achievement And Student Thinking About Linearity, Paul Thomas Belue

Boise State University Theses and Dissertations

A control group and an experimental group of college students at a community college in the Pacific Northwest were taught a unit on linear equations in two variables. The control group was taught using a traditional instructional approach that focused on learning procedures and the experimental group was taught using a quantitative reasoning instructional approach that focused on learning proportional and functional reasoning. Both groups were then given the same unit assessment that had 10 procedural understanding items and 10 conceptual understanding items related to linear equations in two variables. The assessment was given to determine the impact of the …

Student Understanding Of Function And Success In Calculus, Daniel I. Drlik

Boise State University Theses and Dissertations

The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus.

A major …

Seismic Imaging To Constrain Groundwater Models For A Better Understanding And Management Of Water Quality In Coastal Benin, West Africa: A Saltwater Intrusion Problem, Kyle Michael Lindsay

Boise State University Theses and Dissertations

The coastal city of Cotonou in Bénin, West Africa, is a large population center that is facing a serious threat to the sustainability of its fresh water supply. Cotonou relies on groundwater derived from the Godomey aquifer for its domestic water supply. The aquifer is undergoing saltwater intrusion due to an increase in pumping to accommodate a growth in population. Hence, there is substantial interest in better characterizing the groundwater system for the purpose of determining appropriate management strategies to ensure sustainability of this freshwater resource.

I collected seismic reflection data along 15 transects to characterize the geometry of the …

The Relationship Between Elementary Teachers' Self-Efficacy For Teaching Mathematics And Their Mathematical Knowledge For Teaching, Meagan Mckinney

Boise State University Theses and Dissertations

This study examined the relationship between elementary teachers’ mathematical knowledge for teaching (MKT) and their self-efficacy for teaching mathematics. Self-efficacy and MKT are of high importance with implications in regards to quality of instruction and the Common Core State Standards for mathematics. Using the Content Knowledge for Teaching Mathematics (CKT-M) instrument, data for this study were collected from thirty-five elementary school teachers participating in the Improving Teachers’ Monitoring of Learning Grant at the time. The data were concerned with these teachers’ self-efficacy with the pedagogy and content of mathematics using the Self-Efficacy for Teaching Mathematics Instrument (SETMI). Qualitative data were …