Department of Mathematics
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Departmental Publications, Department of Mathematics [5]
Newsletters, annual reports, and other departmental publications 
Scholarly Works, Department of Mathematics [233]
Research articles, presentations, and other scholarship
Recent Submissions

Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents
(MDPI, 20201023)There are two main strategies for improving the projectionbased reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, ... 
Transfer Entropy Analysis of Interactions between Bats Using Position and Echolocation Data
(MDPI, 20201019)Many animal species, including many species of bats, exhibit collective behavior where groups of individuals coordinate their motion. Bats are unique among these animals in that they use the active sensing mechanism of ... 
Students' metarepresentational competence with matrix notation and Dirac notation in quantum mechanics
(20200825)This article shares analysis regarding quantum mechanics students' metarepresentational competence (MRC) that is expressed as they engaged in solving an expectation value problem, which involves linear algebra concepts. ... 
A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem
(Hindawi, 20170912)Let 𝑋 be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇 : 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be maximal monotone, 𝑆:𝑋→2𝑋∗ be bounded and of type (𝑆₊), and 𝐶 : 𝐷(𝐶) → 𝑋∗ ... 
Fiberoptic Seismology
Distributed Acoustic Sensing (DAS) is an emerging technology that repurposes a fiberoptic cable as a dense array of strain sensors. This technology repeatedly pings a fiber with laser pulses, measuring optical phase ... 
Mathematical model of broadly reactive plasma cell production
(Nature Research, 2020)Strainspecific plasma cells are capable of producing neutralizing antibodies that are essential for clearance of challenging pathogens. These neutralizing antibodies also function as a main defense against disease ... 
Longtime Reynolds averaging of reduced order models for fluid flows: Preliminary results
(20191022)We perform a preliminary theoretical and numerical investigation of the timeaverage of energy exchange among modes of Reduced Order Models (ROMs) of fluid flows. We are interested in the statistical equilibrium problem, ... 
Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network
(MDPI, 20200323)Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a ... 
Editorial for Special Issue “Drop, Bubble and Particle Dynamics in Complex Fluids”
(MDPI, 20200102)The presence of drops, bubbles, and particles affects the behavior and response of complex multiphase fluids [...] 
A Linear Algorithm for Ambient Seismic Noise Double Beamforming Without Crosscorrelations
(20200102)Geoscientists and engineers are increasingly using denser arrays for continuous seismic monitoring, and often turning to ambient seismic noise interferometry for lowcost nearsurface imaging. While ambient noise interferometry ... 
Modelling Allee effects in a transgenic mosquito population during range expansion
(Taylor & Francis, 20180427)Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo matefinding Allee effects such that their ability to successfully ... 
On the diagonal subalgebra of an Ext algebra
(201704)Let R be a Koszul algebra over a field k and M be a linear Rmodule. We study a graded subalgebra Delta(M) of the Extalgebra Ext(R)*(M, M) called the diagonal subalgebra and its properties. Applications to the Hochschild ... 
The emergence of fast oscillations in a reduced primitive equation model and its implications for closure theories
(20170627)The problem of emergence of fast gravitywave oscillations in rotating, stratified flow is reconsidered. Fast inertiagravity oscillations have long been considered an impediment to initialization of weather forecasts, and ... 
Examining Mathematics Anxiety of Undergraduates Using a BrainBased Measurement, EEG
(Scientific Research Publishing, 20190527)This paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times from ... 
How soap bubbles freeze
(Springer Nature, 20190618)Droplets or puddles tend to freeze from the propagation of a single freeze front. In contrast, videographers have shown that as soap bubbles freeze, a plethora of growing ice crystals can swirl around in a beautiful effect ... 
Linked withinhost and betweenhost models and data for infectious diseases: a systematic review
(PeerJ, 20190619)The observed dynamics of infectious diseases are driven by processes across multiple scales. Here we focus on two: withinhost, that is, how an infection progresses inside a single individual (for instance viral and immune ... 
Individual and situational factors related to undergraduate mathematics instruction
(20190628)Abstract Background In the US, there is significant interest from policy boards and funding agencies to change students’ experiences in undergraduate mathematics classes. Even ... 
Bridging Frameworks for Understanding Numerical Cognition
(LeibnizInstitute for Psychology Information (ZPID), 20180607)As noted by Berch (2016) and others (e.g., Bruer, 1997), divergent frameworks and epistemologies exacerbate the challenges of interdisciplinary research. After all, theoretical frameworks frame even the way we pose questions. ... 
A note on best approximation and invertibility of operators on uniformly convex Banach spaces
(Hindawi Publishing Corp, 19910101)It is shown that if X is a uniformly convex Banach space and S a bounded linear operator onX for which ?IS?=1, then S is invertible if and only if ?I12S? <1. From this it follows thatif S is invertible on X then either ...