Department of Mathematics
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Faculty Works, Department of Mathematics [158]
Research articles, presentations, and other scholarship
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Existence Theorems on Solvability of Constrained Inclusion Problems and Applications
(20180712)Let 𝑋 be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space 𝑋∗. Let𝑇 : 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be a maximal monotone operator and 𝐶 : 𝑋 ⊇ 𝐷(𝐶) → 𝑋∗ be bounded and continuous ... 
Multiscale immunoepidemiological modeling of withinhost and betweenhost HIV dynamics: systematic review of mathematical models
(PeerJ, 20170928)Objective The objective of this study is to conduct a systematic review of multiscale HIV immunoepidemiological models to improve our understanding of the synergistic impact between the HIV viralimmune dynamics at the ... 
Outlier Detection for Sensor Systems (ODSS): A MATLAB Macro for Evaluating Microphone Sensor Data Quality
(MDPI, 20171013)Microphone sensor systems provide information that may be used for a variety of applications. Such systems generate large amounts of data. One concern is with microphone failure and unusual values that may be generated as ... 
A structural equation model looking at student’s participatory behavior and their success in Calculus I
(20171110)Abstract Background Government projections in the USA indicate that the country will need a million more science, technology, engineering, and mathematics (STEM) graduates ... 
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∗ ... 
Factors contributing to students and instructors experiencing a lack of time in college calculus
(SpringerOpen, 20170614)Background: Calculus is a foundational course for STEMintending students yet has been shown to dissuade students from pursuing STEM degrees. In this report, we examine factors related to students and instructors reporting ... 
Simulating WithinVector Generation of Malaria Parasite Diversity
(PLOS, 20170522)Plasmodium falciparum, the most virulent human malaria parasite, undergoes asexual reproduction within the human host, but reproduces sexually within its vector host, the Anopheles mosquito. Consequently, the mosquito stage ... 
Understanding the complex patterns observed during hepatitis B Virus therapy
(MDPI, 20170519)Data from human clinical trials have shown that the hepatitis B virus (HBV) follows complex profiles, such as biphasic, triphasic, stepwise decay and rebound. We utilized a deterministic model of HBV kinetics following ... 
A New Topological Degree Theory for Perturbations of Demicontinuous Operators and Applications to Nonlinear Equations with Nonmonotone Nonlinearities
(Hindawi, 20161018)Let 𝑋 be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇 : 𝑋 ⊇ 𝐷(𝑇)→ 2𝑋∗ be maximal monotone of type 𝚪𝜙 𝑑 (i.e., there exist 𝑑 ≥ 0 and a nondecreasing ... 
An ObjectOriented Framework for Versatile Finite Element Based Simulations of Neurostimulation
(Hindawi, 20151021)Computational simulations of transcranial electrical stimulation (TES) are commonly utilized by the neurostimulation community, and while vastly different TES application areas can be investigated, the mathematical equations ... 
Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems
(Hindawi, 20150809)Let 𝑋 be a real locally uniformly convex reflexive separable Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇: 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be maximal monotone and 𝑆 : 𝑋 ⊇ 𝐷(𝑆) → 𝑋∗ quasibounded generalized ... 
Multiscale Coupling of Transcranial Direct Current Stimulation to Neuron Electrodynamics: Modeling the Influence of the Transcranial Electric Field on Neuronal Depolarization
(Hindawi Publishing Corporation, 20141023)Transcranial direct current stimulation (tDCS) continues to demonstrate success as a medical intervention for neurodegenerative diseases, psychological conditions, and traumatic brain injury recovery. One aspect of tDCS ... 
JigCell Run Manager (JCRM): a tool for managing large sets of biochemical model parametrizations
(20151224)Background Most biomolecular reaction modeling tools allow users to build models with a single list of parameter values. However, a common scenario involves different parameterizations of the model to account for the results ... 
A Network Biology Approach to Denitrification in Pseudomonas aeruginosa
(20150223)Pseudomonas aeruginosa is a metabolically flexible member of the Gammaproteobacteria. Under anaerobic conditions and the presence of nitrate, P. aeruginosa can perform (complete) denitrification, a respiratory process of ... 
Predicting the combined effect of multiple genetic variants
(20150730)Background Many genetic variants have been identified in the human genome. The functional effects of a single variant have been intensively studied. However, the joint effects of multiple variants in the same genes have ... 
Cohomology of Finite Groups
(University of Essen, 1992)This is a short lecture course on the cohomology of finite groups. Topics include Künneth formula, cup products and cohomology ring, differential graded algebras, Evens norm map and the Steenrod operations. 
Pulse propagation in a randomly perturbed ocean: Single pulse statistics
(Acoustical Society of America, 198010)A statistical theory of broadband single pulse propagation in a random ocean is presented. The mutual coherence function of the received signal is derived using an analysis based upon coupled mode theory. As propagation ... 
Dynamics of selfdriven microcantilevers
(American Institute of Physics, 20020401)The small amplitude thermal vibrations of the microcantilever of an atomic force microscope can be enhanced via a delayed feedback system. This is verified experimentally for a triangular cantilever, and modeled theoretically ... 
Convergence theorems for intermediate problems. II
(Cambridge University Press, 2002)Convergence theorems for the practical eigenvector free methods of Gay and Goerisch are obtained under a variety of hypotheses, so that our theorems apply to both traditional boundaryvalue problems and atomic problems. ...