Bounding The Norm Of Matrix Powers,
2013
Brigham Young University - Provo
Bounding The Norm Of Matrix Powers, Daniel Ammon Dowler
Theses and Dissertations
In this paper I investigate properties of square complex matrices of the form Ak, where A is also a complex matrix, and k is a nonnegative integer. I look at several ways of representing Ak. In particular, I present an identity expressing the kth power of the Schur form T of A in terms of the elements of T, which can be used together with the Schur decomposition to provide an expression of Ak. I also explain bounds on the norm of Ak, including some based on the element-based expression of …
Integral Traces Of Weak Maass Forms Of Genus Zero Odd Prime Level,
2013
Brigham Young University - Provo
Integral Traces Of Weak Maass Forms Of Genus Zero Odd Prime Level, Nathan Eric Green
Theses and Dissertations
Duke and Jenkins defined a family of linear maps from spaces of weakly holomorphic modular forms of negative integral weight and level 1 into spaces of weakly holomorphic modular forms of half integral weight and level 4 and showed that these lifts preserve the integrality of Fourier coefficients. We show that the generalization of these lifts to modular forms of genus 0 odd prime level also preserves the integrality of Fourier coefficients.
The Spacetime Geometry Of A Null Electromagnetic Field,
2013
Department of Physics, Utah State University
The Spacetime Geometry Of A Null Electromagnetic Field, Charles G. Torre
Presentations and Publications
We give a set of local geometric conditions on a spacetime metric which are necessary and sufficient for it to be a null electrovacuum, that is, the metric is part of a solution to the Einstein-Maxwell equations with a null electromagnetic field. These conditions are restrictions on a null congruence canonically constructed from the spacetime metric, and can involve up to five derivatives of the metric. The null electrovacuum conditions are counterparts of the Rainich conditions, which geometrically characterize non-null electrovacua. Given a spacetime satisfying the conditions for a null electrovacuum, a straightforward procedure builds the null electromagnetic field from …
A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing,
2013
Louisiana Tech University
A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi
Doctoral Dissertations
DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …
Lattice Point Counting And Height Bounds Over Number Fields And Quaternion Algebras,
2013
Claremont McKenna College
Lattice Point Counting And Height Bounds Over Number Fields And Quaternion Algebras, Lenny Fukshansky, Glenn Henshaw
CMC Faculty Publications and Research
An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit applications of a particular estimate of this sort to several counting problems in number theory: counting integral points and units of bounded height over number fields, counting points of bounded height over positive definite quaternion algebras, and counting points of bounded height with a fixed support over global function fields. Our arguments use a collection of height comparison inequalities for heights over a number …
Minimization Of Average Sensitivity As A Method Of Selecting Fuzzy Functions And Operations: Successes And Limitations,
2013
The University of Texas at El Paso
Minimization Of Average Sensitivity As A Method Of Selecting Fuzzy Functions And Operations: Successes And Limitations, Riya George, Suresh Subramanian, Alejandro Vega, Olga Kosheleva
Departmental Technical Reports (CS)
Fuzzy logic is an extension of the standard 2-valued logic -- with two possible truth values 0 ("false") and ("true") -- to values (degrees of certainty) represented by arbitrary numbers from the interval [0,1]. One of the main challenges in fuzzy logic is that we need to extend the usual logical operations from the set {0,1} to the entire interval, and there are many possible extensions. One promising technique for selecting a reasonable extension is to take into account that the fuzzy degrees of certainty are themselves only known with uncertainty; so, it makes sense to select an operation which …
Developing Effective Mathematics Teachers Through National Science Foundation Funded Math And Science Partnership Grants,
2013
University of Montana
Developing Effective Mathematics Teachers Through National Science Foundation Funded Math And Science Partnership Grants, Ruth M. Heaton, Wendy M. Smith
The Mathematics Enthusiast
Every year the National Science Foundation (NSF) gathers together leadership teams of funded Math and Science Partnership programs (MSP) at a Learning Network Conference in Washington, D.C. The purpose of the annual conference is to bring together teams of MSP leaders who represent institution higher education (IHE) faculty from STEM disciplines, IHE education faculty, school partners, and project evaluators, to give them an opportunity to learn across projects, and provide opportunities for individual projects to reflect on their progress. For the last two years, 2011 and 2012, we were part of the conference’s organizing committee. During the two‐day conference, project …
Integrating Disciplinary Perspectives: The Poincaré Institute For Mathematics Education,
2013
University of Montana
Integrating Disciplinary Perspectives: The Poincaré Institute For Mathematics Education, Montserrat Teixidor-I-Bigas, Analúcia D. Schliemann, David W. Carraher
The Mathematics Enthusiast
We describe the development of the Poincaré Institute, an NSF‐MSP supported program developed through Tufts University Departments of Mathematics, Education, and Physics and by TERC, in partnership with nine school districts in Massachusetts, New Hampshire, and Maine. We focus on the challenges of developing an inter‐disciplinary program aimed at improving the teaching and learning of mathematics from grades 5 to 9, the choice of mathematical and educational content of the program, the course structure, and the progress of the first cohort of participant teachers. We also outline the changes we are implementing for future cohorts.
Developing Effective Mathematics Teaching: Assessing Content And Pedagogical Knowledge, Student-Centered Teaching, And Student Engagement,
2013
University of Montana
Developing Effective Mathematics Teaching: Assessing Content And Pedagogical Knowledge, Student-Centered Teaching, And Student Engagement, Serigne M. Gningue, Roger Peach, Barbara Schroder
The Mathematics Enthusiast
The Mathematics Teacher Transformation Institutes (MTTI) program attempts to develop math teacher leaders in part by providing content, inquiry and leadership courses aimed at making them more effective teachers. We assessed progress by observing teacher leaders’ teaching practices, and encouraging them to introduce or extend studentcentered pedagogy in their classrooms. We found there was little relationship between our measures of mathematics content knowledge and student‐centered pedagogy. But teachers who employed student‐centered pedagogy tended to have more highly‐engaged math students in their classrooms.
Making Explicit The Commonalities Of Msp Projects: Learning From Doing,
2013
University of Montana
Making Explicit The Commonalities Of Msp Projects: Learning From Doing, Marilyn Strutchens, W. Gary Martin
The Mathematics Enthusiast
The seven projects discussed in the preceding articles are funded by the National Science Foundation (NSF) Math and Science Partnership (MSP) program (Hamos et al., 2009), which began in 2002. One of the main goals of the MSP program is to build capacity and integrate the work of higher education, especially its STEM disciplinary faculty, with that of K‐12 to strengthen and reform mathematics and science education (Hamos et al., 2009). Thus, the MSP program brought together three sets of people (disciplinary faculty, teacher educators, and school system personnel) who do not usually work together to reform the mathematics and …
Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations,
2013
Louisiana Tech University
Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii
Doctoral Dissertations
The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …
Statistical Analysis Of Student Performance In Mathematics Courses,
2013
Valparaiso University
Statistical Analysis Of Student Performance In Mathematics Courses, Katie Merkling, Hannah Dorman, Nicolle Kinzel
Symposium on Research and Creative Expression (SORCE)
We examined the effect of taking AP Calculus in high school on final letter grades in Calculus I, II, and III at Valparaiso University. The data used in our study was obtained from the registrar and included demographic information, entrance exam scores (ACT, SAT, AP, etc.), Valpo GPA for each semester, and final letter grades in all math courses from Spring 2008-Summer 2012. We performed multiple statistical analyses, such as chi-square tests, two-sample t-tests, and multiple regressions, using the statistical software package R. Our results show that students who took AP Calculus in high school on average received higher final …
Genomic Analysis Of Stress Response Against Arsenic In Caenorhabditis Elegans,
2013
Food and Drug Administration
Genomic Analysis Of Stress Response Against Arsenic In Caenorhabditis Elegans, Surasri N. Sahu, Jada Lewis, Isha Patel, Serdar Bozdag, Jeong H. Lee, Robert Sprando, Hediye Nese Cinar
Mathematics, Statistics and Computer Science Faculty Research and Publications
Arsenic, a known human carcinogen, is widely distributed around the world and found in particularly high concentrations in certain regions including Southwestern US, Eastern Europe, India, China, Taiwan and Mexico. Chronic arsenic poisoning affects millions of people worldwide and is associated with increased risk of many diseases including arthrosclerosis, diabetes and cancer. In this study, we explored genome level global responses to high and low levels of arsenic exposure in Caenorhabditis elegans using Affymetrix expression microarrays. This experimental design allows us to do microarray analysis of dose-response relationships of global gene expression patterns. High dose (0.03%) exposure caused stronger global …
Counting The Number Of Squares Reachable In K Knight's Moves.,
2013
Rochester Institute of Technology
Counting The Number Of Squares Reachable In K Knight's Moves., Amanda M. Miller, David L. Farnsworth
Articles
from its initial position on an infinite chessboard are derived. The number of squares reachable in exactly k moves are 1, 8, 32, 68, and 96 for k = 0, 1, 2, 3, and 4, respectively, and 28k – 20 for k ≥ 5. The cumulative number of squares reach- able in k or fever moves are 1, 9, 41, and 109 for k = 0, 1, 2, and 3, respectively, and 14k-squared – 6k + 5 for k ≥ 4. Although these formulas are known, the proofs that are presented are new and more mathematically accessible then preceding proofs.
Mathematical Habits Of Mind For Teaching: Using Language In Algebra Classrooms,
2013
University of Montana
Mathematical Habits Of Mind For Teaching: Using Language In Algebra Classrooms, Ryota Matsuura, Sarah Sword, Mary Beth Piecham, Glenn Stevens, Al Cuoco
The Mathematics Enthusiast
The notion of mathematical knowledge for teaching has been studied by many researchers, especially at the elementary grades. Our understandings of this notion parallel much of what we have read in the literature, but are based on our particular experiences over the past 20 years, as mathematicians engaged in doing mathematics with secondary teachers. As part of the work of Focus on Mathematics, Phase II MSP, we are developing, in collaboration with others in the field, a research program with the ultimate goal of understanding the connections between secondary teachers’ mathematical knowledge for teaching and secondary students’ mathematical understanding and …
Tme Volume 10, Number 3,
2013
University of Montana
Phase Transition Of Boolean Networks With Partially Nested Canalizing Functions,
2013
University of Nebraska at Omaha
Phase Transition Of Boolean Networks With Partially Nested Canalizing Functions, Kayse Jansen, Mihaela Teodora Matache
Mathematics Faculty Publications
We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the …
2013 (Summer),
2013
University of Dayton
2013 (Summer), University Of Dayton. Department Of Mathematics
Colloquia
Abstracts of the talks given at the 2013 Summer Colloquium.
Optimal Control Modeling And Simulation, With Application To Cholera Dynamics,
2013
Old Dominion University
Optimal Control Modeling And Simulation, With Application To Cholera Dynamics, Chairat Modnak
Mathematics & Statistics Theses & Dissertations
The theory of optimal control, a modern extension of the calculus of variations. has found many applications in a wide range of scientific fields, particularly in epidemiology with respect to disease prevention and intervention. In this dissertation. we conduct optimal control modeling, simulation and analysis to cholera dynamics. Cholera is a severe intestinal infectious disease that remains a serious public health threat in developing countries. Transmission of cholera involves complex interactions between the human host, the pathogen, and the environment. The worldwide cholera outbreaks and their increasing severity, frequency and duration in recent years underscore the gap between the complex …
Spectral Stability Of Weak Detonations In The Majda Model,
2013
Brigham Young University - Provo
Spectral Stability Of Weak Detonations In The Majda Model, Jeffrey James Hendricks
Theses and Dissertations
Using analytical and numerical Evans-function techniques, we examine the spectral stability of weak-detonation-wave solutions of Majda's scalar model for a reacting gas mixture. We provide a proof of monotonicity of solutions. Using monotonicity we obtain a bound on possible unstable eigenvalues for weak-detonation-wave solutions that improves on the more general bound given by Humpherys, Lyng, and Zumbrun. We use a numerical approximation of the Evans function to search for possible unstable eigenvalues in the bounded region obtained by the energy estimate. For the parameter values tested, our results combined with the result of Lyng, Raoofi, Texier, and Zumbrun demonstrate that …
