Digital Commons Network^™

Augmenting The Immersed Boundary Method With Radial Basis Functions (Rbfs) For The Modeling Of Platelets In Hemodynamic Flows, Varun Shankar, Grady B. Wright, Robert M. Kirby, Aaron L. Fogelson

Mathematics Faculty Publications and Presentations

We present a new computational method by extending the Immersed Boundary (IB) method with a geometric model based on parametric Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the modeling of platelets in hemodynamic flows, though we anticipate that our method will be useful in other applications involving surface elasticity. The efficacy of our new RBF-IB method is shown through a series of numerical experiments. Specifically, we test the convergence of our method and compare our method with the traditional IB method in terms of computational cost, maximum stable time-step size and volume loss. We …

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 …

Lower Bound For Ranks Of Invariant Forms, Harm Derksen, Zach Teitler

Mathematics Faculty Publications and Presentations

We give a lower bound for the Waring rank and cactus rank of forms that are invariant under an action of a connected algebraic group. We use this to improve the Ranestad-Schreyer-Shafiei lower bounds for the Waring ranks and cactus ranks of determinants of generic matrices, Pfaffians of generic skew-symmetric matrices, and determinants of generic symmetric matrices.

A Critical Proton Mr Spectroscopy Marker Of Alzheimer Early Neurodegenerative Change: Low Hippocampal Naa/Cr Ratio Impacts Apoe 4 Mexico City Children And Their Parents., Partha S. Mukherjee

Mathematics Faculty Publications and Presentations

Severe air pollution exposures produce systemic, respiratory, myocardial, and brain inflammation and Alzheimer’s disease (AD) hallmarks in clinically healthy children. We tested whether hippocampal metabolite ratios are associated with contrasting levels of air pollution, APOE and BMI in paired healthy children and one parent sharing the same APOE alleles. We used (1) H-MRS to interrogate bilateral hippocampal single-voxel in 57 children (12.45± 3.4 years) and their 48 parents (37.5± 6.78 years) low pollution city v Mexico City (MC). NAA/Cr, Cho/Cr, and mI/Cr metabolite ratios were analysed. The right hippocampus N-acetylaspartate/creatine (NAA/Cr) was significantly different between cohorts (p=0.007). The NAA/Cr ratio …

Generalizations And Algebraic Structures Of The Grøstl-Based Primitives, Dmitriy Khripkov, Nicholas Lacasse, Bai Lin, Michelle Mastrianni, Liljana Babinkostova (Mentor)

Idaho Conference on Undergraduate Research

With the large scale proliferation of networked devices ranging from medical implants like pacemakers and insulin pumps, to corporate information assets, secure authentication, data integrity and confidentiality have become some of the central goals for cybersecurity. Cryptographic hash functions have many applications in information security and are commonly used to verify data authenticity. Our research focuses on the study of the properties that dictate the security of a cryptographic hash functions that use Even-Mansour type of ciphers in their underlying structure. In particular, we investigate the algebraic design requirements of the Grøstl hash function and its generalizations. Grøstl is an …

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 …

How Do U.S. And Chinese Biology Students Compare In Explaining Energy Consumption Issues?, Hui Jin, Hayat Hokayem, Sasha Wang, Xin Wei

Mathematics Faculty Publications and Presentations

This qualitative study investigates how biology majors explain energy consumption issues. In particular, we focus on two energy consumption activities that account for about two-thirds of global carbon dioxide emissions in 2011: burning fossil fuels for transportation and using electricity. We conducted in-depth clinical interviews with twenty U.S. students and twenty Chinese students. We compared these two groups of students in terms of two aspects of explanation: 1) naming scientific terms in the explanation, and 2) explaining an energy consumption issue. Regarding naming, we examined the frequency of naming different terms of scientific concepts and principles in students’ explanations. Regarding …

Mexico City Normal Weight Children Exposed To High Concentrations Of Ambient Pm2.5 Show High Blood Leptin And Endothelin-1, Vitamin D Deficiency, And Food Reward Hormone Dysregulation Versus Low Pollution Controls. Relevance For Obesity And Alzheimer Disease, Partha S. Mukherjee

Mathematics Faculty Publications and Presentations

Millions of Mexico, US and across the world children are overweight and obese. Exposure to fossil-fuel combustion sources increases the risk for obesity and diabetes, while long-term exposure to fine particulate matter (PM _2.5) and ozone (O₃) above US EPA standards is associated with increased risk of Alzheimer’s disease (AD). Mexico City Metropolitan Area children are chronically exposed to PM_2.5 and O₃ concentrations above the standards and exhibit systemic, brain and intrathecal inflammation, cognitive deficits, and Alzheimer disease neuropathology. We investigated adipokines, food reward hormones, endothelial dysfunction, vitamin D and apolipoprotein E (APOE) relationships in …

Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence

Mathematics Faculty Publications and Presentations

We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in Pⁿ whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.

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 …

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 …

Order-Preserving Derivative Approximation With Periodic Radial Basis Functions, Edward Fuselier, Grady B. Wright

Mathematics Faculty Publications and Presentations

In this exploratory paper we study the convergence rates of an iterated method for approximating derivatives of periodic functions using radial basis function (RBF) interpolation. Given a target function sampled on some node set, an approximation of the m ^th derivative is obtained by m successive applications of the operator “interpolate, then differentiate”- this process is known in the spline community as successive splines or iterated splines. For uniformly spaced nodes on the circle, we give a sufficient condition on the RBF kernel to guarantee that, when the error is measured only at the nodes, this iterated method approximates …

A Refinement Of Michener’S Example Classification, Laurie O. Cavey, Margaret T. Kinzel

Mathematics Faculty Publications and Presentations

In this paper we propose a refinement of Michener’s (1978) well-known example classification based on data from university mathematicians. The refinement takes into account the mathematician’s perspective on the role of examples in doing mathematics. More specifically, our work provides insight into the ways in which mathematicians talk about using examples in their scholarly work and their work with students. The proposed classification has the potential to inform our work as teachers as we strive to create opportunities to engage students in authentic mathematical work.

Image Denoising By A Local Clustering Framework, Partha Sarathi Mukherjee, Peihua Qiu

Mathematics Faculty Publications and Presentations

Images often contain noise due to imperfections in various image acquisition techniques. Noise should be removed from images so that the details of image objects (e.g., blood vessels, inner foldings, or tumors in the human brain) can be clearly seen, and the subsequent image analyses are reliable. With broad usage of images in many disciplines—for example, medical science—image denoising has become an important research area. In the literature, there are many different types of image denoising techniques, most of which aim to preserve image features, such as edges and edge structures, by estimating them explicitly or implicitly. Techniques based on …

Extension Of Chebfun To Periodic Functions, Grady B. Wright, Mohsin Javed, Hadrien Montanelli, Lloyd N. Trefethen

Mathematics Faculty Publications and Presentations

Algorithms and underlying mathematics are presented for numerical computation with periodic functions via approximations to machine precision by trigonometric polynomials, including the solution of linear and nonlinear periodic ordinary differential equations. Differences from the nonperiodic Chebyshev case are highlighted.

Identifying Similar Polygons: Comparing Prospective Teachers’ Routines With A Mathematician’S, Sasha Wang

Mathematics Faculty Publications and Presentations

This paper reports two prospective teachers' and a mathematician's ways of identifying similar triangle and hexagons through the analysis of routines, a characteristic of geometric discourse. The findings show that visual recognition was a common approach for the mathematician as wells as the two prospective teachers. However, when asked for justification, their routines of identifying similar polygons diverged. The paper also discusses the implication of classroom discourse practices to enhance prospective teachers' communication and reasoning skills while learning geometric concepts such as similarity.