Applied Mathematics Commons^™

An Analysis Of The Impact Of The Csu Peer Leader Program On Student Performance In 2014-2015, Harrison E. Sharitt

Theses and Dissertations

In efforts to retain students and increase student performance, Columbus State implemented a Peer Leader program. With access to archival data on the CSU Peer Leader Program, the goal of this project was to determine if the program at CSU had a significant impact on students’ course performance. The impact of the program was assessed by performing multiple regression analyses and ANOVA. Preliminary results showed that Columbus State’s Peer Leader program had a small, but statistically significant, positive impact on students’ final course grades.

Illustrating Pit Initiation And Evolution In Aluminum Alloys According To A 3-Dimensional Cellular Automata Based Model, Kathryn Stalker

Williams Honors College, Honors Research Projects

The objective of this work is to develop a cellular automata based model of pitting initiation and subsequent three-dimensional evolution of pit shapes. Here, a cellular automaton is a collection of cells, each of which may be in one of two states, metallic or electrolyte, arranged over a grid. Pit initiation is implemented over a 2-dimensional grid representative of the metal surface while pit propagation is resolved over a 3-dimensional grid which describes a subsection of the bulk metal. The size of the bulk metal will be on the order of millimeters, and a layer of electrolyte, in which chloride …

Price Signaling In A Two-Market Duopoly, Matthew Hughes

Williams Honors College, Honors Research Projects

Within any industry, firms typically produce related products over multiple subsequent periods in an attempt to build consumer loyalty and achieve continued sales. Apple releases new iPhones and car companies produce new models every year, relying on consumers believing each new product is of high quality. Firms rely on the spillover effects from previous markets, where firms are able to more easily demonstrate their product's quality to the consumers before purchase. The goal is to find a range of prices which allows the high quality firm to distinguish its type to consumers via the price pH and if spillover effects …

Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda

Williams Honors College, Honors Research Projects

Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z₉≀(Z₃ × Z₃) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.

Diffusive Behavior Of Physically Cross-Linked Hydrogels, Morgan A. Stilke

Williams Honors College, Honors Research Projects

A hydrogel is a water swollen polymeric network that has the potential to transform a variety of biomedical applications because of its biocompatibility and water content. Unfortunately, hydrogels typically have poor mechanical robustness. The majority of the content is water, while the remaining structure consists of a physical network, a covalent network, or a combination of both, yielding strength and toughness. There are several strategies attempted to improve mechanical properties including double network hydrogels comprised of two interpenetrating networks: one being a highly crosslinked sacrificial network and the other being a weakly crosslinked network that maintains reversibility after deformation. However, …

Comparing The Growth Of The Prime Numbers To The Natural Numbers, Michael A. Brilleslyper, Nathan Wakefield, A. J. Wallerstein, Bradley Warner

Department of Mathematics: Faculty Publications

We define a new method of measuring the rate of divergence for an increasing positive sequence of integers. We introduce the growth function for such a sequence and its associated growth limit. We use these tools to study the divergence rate for the natural numbers, polynomial and exponential-type sequences, and the prime numbers. We conclude with a number of open questions concerning general properties and characterizations of growth functions and the set of possible growth limits.

Characterizing Mathematics Graduate Student Teaching Assistants’ Opportunities To Learn From Teaching, Yvonne Lai, Wendy Smith, Nathan Wakefield, Erica R. Miller, Julia St. Goar, Corbin M. Groothuis, Kelsey M. Wells

Department of Mathematics: Faculty Publications

Exemplary models to inform novice instruction and the development of graduate teaching assistants (TAs) exist. What is missing from the literature is the process of how graduate students in model professional development programs make sense of and enact the experiences offered. A first step to understanding TAs’ learning to teach is to characterize how and whether they link observations of student work to hypotheses about student thinking and then connect those hypotheses to future teaching actions. A reason to be interested in these connections is that their strength and coherence determine how well TAs can learn from experiences. We found …

R0 Analysis Of A Benthic-Drift Model For A Stream Population, Qihua Huang, Yu Jin, Mark A. Lewis

Department of Mathematics: Faculty Publications

One key issue for theory in stream ecology is how much stream flow can be changed while still maintaining an intact stream ecology, instream flow needs (IFNs); the study of determining IFNs is challenging due to the complex and dynamic nature of the interaction between the stream environ- ment and the biological community. We develop a process-oriented benthic-drift model that links changes in the flow regime and habitat availability with population dynamics. In the model, the stream is divided into two zones, drift zone and benthic zone, and the population is divided into two interacting compartments, individuals residing in the …

Simple Adaptive Control For Positive Linear Systems With Applications To Pest Management, Chris Guiver, Christina Edholm, Yu Jin, Markus Mueller, Jim Powell, Richard Rebarber, Brigitte Tenhumberg, Stuart Townley

Department of Mathematics: Faculty Publications

Pest management is vitally important for modern arable farming, but models for pest species are often highly uncertain. In the context of pest management, control actions are naturally described by a nonlinear feedback that is generally unknown, which thus motivates a robust control approach. We argue that adaptive approaches are well suited for the management of pests and propose a simple high-gain adaptive tuning mechanism so that the nonlinear feedback achieves exponential stabilization. Furthermore, a switched adaptive controller is proposed, cycling through a set of given control actions, that also achieves global asymptotic stability. Such a model in practice allows …

Topic Analysis Of Tweets On The European Refugee Crisis Using Non-Negative Matrix Factorization, Chong Shen

CMC Senior Theses

The ongoing European Refugee Crisis has been one of the most popular trending topics on Twitter for the past 8 months. This paper applies topic modeling on bulks of tweets to discover the hidden patterns within these social media discussions. In particular, we perform topic analysis through solving Non-negative Matrix Factorization (NMF) as an Inexact Alternating Least Squares problem. We accelerate the computation using techniques including tweet sampling and augmented NMF, compare NMF results with different ranks and visualize the outputs through topic representation and frequency plots. We observe that supportive sentiments maintained a strong presence while negative sentiments such …

Evaluation Of Ray-Path Integrals In Geometrical Optics, John A. Adam, Michael Pohrivchak

Mathematics & Statistics Faculty Publications

A brief summary of the physical context to this paper is provided, and the deviation angle undergone by an incident ray after k internal reflections inside a transparent unit sphere is formulated. For radially inhomogeneous spheres (in particular) this angle is related to a ray-path integral; an improper integral for which there are relatively few known exact analytical forms, even for simple refractive index profiles n(r). Thus for a linear profile the integral is a combination of incomplete elliptic integrals of the first and third kinds (though not all are as complicated as this). The ray-path integral is evaluated …

A Study Of The Effect Of Harvesting On A Discrete System With Two Competing Species, Rebecca G. Clark

Theses and Dissertations

This is a study of the effect of harvesting on a system with two competing species. The system is a Ricker-type model that extends the work done by Luis, Elaydi, and Oliveira to include the effect of harvesting on the system. We look at the uniform bound of the system as well as the isoclines and perform a stability analysis of the equilibrium points. We also look at the effects of harvesting on the stability of the system by looking at the bifurcation of the system with respect to harvesting.

Blow-Up Solution And Blow-Up Rate Of Bose-Einstein Condensates With Rotational Term, Nyla Basharat

College of Graduate Studies: Theses & Dissertations

In this thesis, we discuss the Gross Pitaevskii Equation (GPE) with harmonic potential and with an angular momentum rotational term in space R^{^2}, which describes the model for Bose-Einstein Condensation. Local Well-Posedness of the equation and the conservation identities for mass, energy and angular momentum are presented. Using the virial identities, we derive the condition for blow-up solution in finite time. Then a threshold of L^{^2} norm of wave function is obtained for global existence, of GPE in term of ground state solution. This method allows us to obtain our main result ``Sharp sufficient condition for global …

Signal Velocity In Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c+t) in the direction …

Optimal Placement Of Family Planning Centers, Kiera Dobbs

Senior Independent Study Theses

This project investigates and begins to solve the problem of access to family planning services in the United States. We research and implement methods in Operations Research to optimize the location of publicly funded family planning centers in the United States by minimizing travel distance. The solution begins with a designated number of family planning centers for the country. An apportionment integer programming algorithm is then exercised to allocate centers to all the states based on population, percent of population in poverty, and state square mileage. At the state level, we use apportionment again to distribute centers to counties. At …

A Two Host Species Stage-Structured Model Of West Nile Virus Transmission, Taylor A. Beebe

Theses and Dissertations

We develop and evaluate a novel host-vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species and host stage-structure (juvenile and adult stages), with both species-specific and stage-specific biting rates of vectors on hosts. We use this model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates. Our analysis shows that increased exposure of juvenile hosts results in earlier, more intense WNV transmission when compared to the effects of differential host species exposure, regardless of other parameter values. We also find that, in addition …

Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic

Mathematics and Statistics Faculty Publications and Presentations

Coherent state transfer is an important requirement in the construction of quantum computer hardware. The state transfer can be realized by linear next-neighbour-coupled finite chains. Starting from the commensurability of chain eigenvalues as the general condition of periodic dynamics, we find chains that support full periodic state revivals. For short chains, exact solutions are found analytically by solving the inverse eigenvalue problem to obtain the coupling coefficients between chain elements. We apply the solutions to design optical waveguide arrays and perform numerical simulations of light propagation thorough realistic waveguide structures. Applications of the presented method to the realization of a …

A Multivariate Nonlinear Mixed Effects Model For Longitudinal Image Analysis: Application To Amyloid Imaging, Murat Bilgel, Jerry L. Prince, Dean F. Wong, Susan M. Resnick, Bruno M. Jedynak

Mathematics and Statistics Faculty Publications and Presentations

It is important to characterize the temporal trajectories of disease-related biomarkers in order to monitor progression and identify potential points of intervention. These are especially important for neurodegenerative diseases, as therapeutic intervention is most likely to be effective in the preclinical disease stages prior to significant neuronal damage. Neuroimaging allows for the measurement of structural, functional, and metabolic integrity of the brain at the level of voxels, whose volumes are on the order of mm³. These voxelwise measurements provide a rich collection of disease indicators. Longitudinal neuroimaging studies enable the analysis of changes in these voxelwise measures. However, …

Defect-Deferred Correction Method For The Two-Domain Convection-Dominated Convection-Diffusion Problem, Dilek Erkmen

Dissertations, Master's Theses and Master's Reports

We present a method for solving a fluid-fluid interaction problem (two convection-dominated convection-diusion problems adjoined by an interface), which is a simplifed version of the atmosphere ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid-fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied …

Properties Of Polynomial Identity Quantized Weyl Algebras, Jesse S. F. Levitt

LSU Doctoral Dissertations

In this work on Polynomial Identity (PI) quantized Weyl algebras we begin with a brief survey of Poisson geometry and quantum cluster algebras, before using these as tools to classify the possible centers of such algebras in two different ways. In doing so we explicitly calculate the formulas of the discriminants of these algebras in terms of a general class of central polynomial subalgebras. From this we can classify all members of this family of algebras free over their centers while proving that their discriminants have the properties of effectiveness and local domination. Applying these results to the family of …

Cluster Algebras And Maximal Green Sequences For Closed Surfaces, Eric Bucher

LSU Doctoral Dissertations

Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider orientable surfaces of genus n with two interior marked points and no boundary component. We will construct a specific triangulation of this surface which yields a quiver. Then in the sense of work by Keller we will produce a maximal green sequence for this quiver. Since all finite mutation type cluster algebras can be associated to a surface, with some rare exceptions, this work …

Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin

Articles

We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.

On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov

Articles

We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.

The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov

Articles

A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behavior is examined and compared to that of other known models. The linearised …

Twisted Reflection Positivity, Mostafa Ahmad Hayajneh

LSU Doctoral Dissertations

Reflection positivity has several applications in both mathematics and physics. For example, reflection positivity induces a duality between group representations. In this thesis, we coin a new definition for a new kind of reflection positivity, namely, twisted reflection positive representation on a vector space. We show that all of the non-compactly causal symmetric spaces give rise to twisted reflection positive representations. We discover examples of twisted reflection positive representations on the sphere and on the Grassmannian manifold which are not unitary, namely, the generalized principle series with the Cosine transform as an intertwining operator. We give a direct proof for …

Spectral Properties Of Photonic Crystals: Bloch Waves And Band Gaps, Robert Paul Viator Jr

LSU Doctoral Dissertations

The author of this dissertation studies the spectral properties of high-contrast photonic crystals, i.e. periodic electromagnetic waveguides made of two materials (a connected phase and included phase) whose electromagnetic material properties are in large contrast. A spectral analysis of 2nd-order divergence-form partial differential operators (with a coupling constant k) is provided. A result of this analysis is a uniformly convergent power series representation of Bloch-wave eigenvalues in terms of the coupling constant k in the high-contrast limit k -> infinity. An explicit radius of convergence for this power series is obtained, and can be written explicitly in terms of the …

A Conditioned Gaussian-Poisson Model For Default Phenomena, Tyler Brannan

LSU Doctoral Dissertations

We introduce a new model to study the behavior of a portfolio of defaultable assets. We refer to this model as the Gaussian-Poisson model. It builds upon one-factor Gaussian copula models and Poisson models (specifically Cox processes). Our model utilizes a random variable Y along with probability measures ℙ^• and ℙ^†. The measures ℙ^• and ℙ^† will act as market pricing measures and are obtained via conditioning. The random variable Y will act as a default descriptor.

We provide the distribution of Y under both ℙ^• and ℙ^†. We use a conditional …

Synthesis Of Satellite Microwave Observations For Monitoring Global Land-Atmosphere Co2 Exchange, Lucas Alan Jones

Graduate Student Theses, Dissertations, & Professional Papers

This dissertation describes the estimation, error quantification, and incorporation of land surface information from microwave satellite remote sensing for modeling global ecosystem land-atmosphere net CO₂ exchange. Retrieval algorithms were developed for estimating soil moisture, surface water, surface temperature, and vegetation phenology from microwave imagery timeseries. Soil moisture retrievals were merged with model-based soil moisture estimates and incorporated into a light-use efficiency model for vegetation productivity coupled to a soil decomposition model. Results, including state and uncertainty estimates, were evaluated with a global eddy covariance flux tower network and other independent global model- and remote-sensing based products.

Unique Pseudo-Expectations For C∗-Inclusions, David R. Pitts, Vrej Zarikian

Department of Mathematics: Faculty Publications

Given an inclusion D⊆C of unital C ∗ -algebras (with common unit), a unital completely positive linear map Φ of C into the injective envelope I(D) of D which extends the inclusion of D into I(D) is a pseudo-expectation. Pseudo-expectations are generalizations of conditional expectations, but with the advantage that they always exist. The set PsExp(C,D) of all pseudo-expectations is a convex set, and when D is Abelian, we prove a Krein–Milman type theorem showing that PsExp(C,D) can be recovered from its set of extreme points. In general, PsExp(C,D) is not a singleton. However, there are large and natural classes …

Comparison Theorems And Asymptotic Behavior Of Solutions Of Discrete Fractional Equations, Baoguo Jia, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

Consider the following n-th order nabla and delta fractional difference equations

rn r (a)x(t) = c(t)x(t), t 2 Na+1, x(a) > 0.

and

Va+v-1x(t) = c(t)x(t + v - 1), t 2 Na, x(a + n - 1) > 0

We establish comparison theorems by which we compare the solutions x(t) of (*) and (**) with the solutions of the equations rn r(a)x(t) = bx(t) and Dn a+v-1x(t) = bx(t + v -1), respectively, where b is a constant. We obtain four asymptotic results, one of them extends the recent result [F. M. Atici, P. W. Eloe, Rocky Mountain J. Math. 41(2011), …