Department of Mathematical Sciences
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Mathematicians’ beliefs, instruction, and students’ beliefs: how related are they?
(Taylor & Francis, 2021-11-29)It is generally accepted that teachers’ beliefs impact their instructional choices, but characterizations of that relationship are limited in college settings. Furthermore, examinations of instructor beliefs, instruction, ... -
How mathematicians assign homework problems in abstract algebra courses
(2021)While many aspects of the teaching and learning of advanced mathematics have been explored, the role, construction, and values of homework have been virtually ignored. This report draws on task-based interviews with six ... -
Conceptual metaphors for isomorphism and homomorphism: Instructors’ descriptions for themselves and when teaching
(Elsevier, 2021)Group isomorphism and homomorphism are topics central to abstract algebra, yet research on instructors’ views of these concepts is limited. Based on interviews from two instructors as well as classroom video from eight ... -
A perturbed system: How tenured faculty responded to the COVID-19 shift to remote instruction
(American Chemical Society, 2020-08-13)This study investigates six university professors’ reflections on the shift to remote instruction during the Spring 2020 semester in response to the COVID-19 global pandemic. The rapid shift in instructional platform ... -
Value Distribution of L-Functions with Rational Moving Targets
(SCIRP, 2013-10-01)We prove some value-distribution results for a class of L-functions with rational moving targets. The class contains Selberg class, as well as the Riemann-zeta function. -
Mathematically optimized cryoprotectant equilibration procedures for cryopreservation of human oocytes
(BioMed Central, 2014-03-20)Background Simple and effective cryopreservation of human oocytes would have an enormous impact on the financial and ethical constraints of human assisted reproduction. Recently, studies have demonstrated the potential ... -
Science, Technology, Engineering and Mathematics Education in the United States: Areas of Current Successes and Future Needs
(Common Ground Publishing LLC, 2012)The quality of the public school teacher has the greatest in-school impact on nurturing cognitive abilities, developing content knowledge, and increasing motivation of students. This paper analyzes if, and how, professional ... -
Synergy For Science Learning: An Interdisciplinary Partnership to Improve the Quality of Science, Technology, Engineering and Mathematics Education
(Common Ground Publishing LLC, 2009)Synergy is the interaction of two or more elements to produce a combined impact greater than the sum of their separate effects. In this paper, synergy for science learning came from the amalgamation of separate, independent ... -
Existence of a Solution to the Line Contact Problem of Elastohydrodynamic Lubrication
(Cambridge University Press, 2003-06)We prove the existence of a solution to a free boundary value problem arising in elastohydrodynamic lubrication. Previously, the existence was proved only under severe restrictions on the range of the physical parameters. ... -
Structural Instability of Exponential Functions
(American Mathematical Society, 1994-07)We first prove some equivalent statements on J-stability of families of critically finite entire functions. Then, with these in hand, a conjecture concerning stability of the family of exponential functions is affirmatively ... -
An Analogue of Continued Fractions in Number Theory for Nevanlinna Theory
(American Mathematical Society, 2004-06-25)We show an analogue of continued fractions in approximation to irrational numbers by rationals for Nevanlinna theory. The analogue is a sequence of points in the complex plane which approaches a given nite set of points ... -
Finite-time singularity versus global regularity for hyper-viscous Hamilton-Jacobi-like equations
(Institute of Physics, 2003)The global regularity for the two- and three-dimensional Kuramoto-Sivashinsky equations is one of the major open questions in nonlinear analysis. Inspired by this question, we introduce in this paper and family of hyper-viscous ... -
Harmonic analysis of causal operators and their spectral properties
(Institute of Physics, 2005)The definition and study of causal operators are based on the representation theory of group algebras. We study the structure of the spectra of causal operators, obtain conditions for causal invertibility and state ... -
Matrical Filters and Crystallographic Composite Dilation Wavelets
(American Mathematical Society, 2011-07-12)In 2006 Guo, Labate, Lim, Weiss, and Wilson introduced the theory of MRA composite dilation wavelets. We continue their work by studying the filter properties of such wavelets and present several important examples. -
HOCHSCHILD COHOMOLOGY OF GROUP EXTENSIONS OF QUANTUM SYMMETRIC ALGEBRAS
(American Mathematical Society, 2010-09-16)Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an ... -
A graph-theoretic method for detecting potential Turing bifurcations
(American Institute of Physics, 2006-11-22)The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, ... -
Osmotic characteristics and fertility of murine spermatozoa collected in different solutions
(Society for Reproduction and Fertility, 2009-02)Osmotic stress is an important factor that can result in cell damage during cryopreservation. Before ejaculation or collection for cryopreservation, murine spermatozoa are stored in epididymal fluid, a physiologically ... -
Microelectromechanical systems Coulter counter for cell monitoring and counting
(American Institute of Physics, 2010)This note describes the design, fabrication, and testing of a novel microelectromechanical systems Coulter counter. The Coulter counter will be used to detect and monitor impedance changes of cells as a function of time ...
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