Applied Mathematics Commons^™

Modeling Shock Waves Using Exponential Interpolation Functions With The Least-Squares Finite Element Method, Bradford Scott Smith Jr.

Mechanical & Aerospace Engineering Theses & Dissertations

The hypothesis of this research is that exponential interpolation functions will approximate fluid properties at shock waves with less error than polynomial interpolation functions. Exponential interpolation functions are derived for the purpose of modeling sharp gradients. General equations for conservation of mass, momentum, and energy for an inviscid flow of a perfect gas are converted to finite element equations using the least-squares method. Boundary conditions and a mesh adaptation scheme are also presented. An oblique shock reflection problem is used as a benchmark to determine whether or not exponential interpolation provides any advantages over Lagrange polynomial interpolation. Using exponential interpolation …

Cutting Triangles, Nghia Nguyen, Jane Long

Undergraduate Research Conference

The idea of this project began with a question: Draw any triangle on a piece of paper, is it possible to fold the paper so that the triangle can be cut out in one slice?

Diagnosing Autism Spectrum Disorder Through Brain Functional Magnetic Resonance Imaging, Kyle A. Palko

Theses and Dissertations

Autism spectrum disorder (ASD) is a neurodevelopmental condition that can be debilitating to social functioning. Previous functional Magnetic Resonance Imaging (fMRI) classification studies have included only small subject sample sizes (n 50) and have seen high classification accuracy. The recent release of the Autism Brain Imaging Data Exchange (ABIDE) provides fMRI data for over 1,100 subjects. In our research, we derive a subject's functional network connectivity (FNC) from their fMRI data and develop a regularized logistic classifier to determine whether a subject has autism. We obtained up to 65% classification accuracy, similar to other studies using the ABIDE dataset, suggesting …

A Logistic Regression And Markov Chain Model For The Prediction Of Nation-State Violent Conflicts And Transitions, Nicholas Shallcross

Theses and Dissertations

Using open source data, this research formulates and constructs a suite of statistical models that predict future transitions into and out of violent conflict and forecasts the regional and global incidences of violent conflict over a ten-year time horizon. A total of thirty predictor variables are tested and evaluated for inclusion in twelve conditional logistic regression models, which calculate the probability that a nation will transition from its current conflict state, either In Conflict or Not in Conflict, to a new state in the following year. These probabilities are then used to construct a series of nation-specific Markov chain models …

Radial Basis Function Based Quadrature Over Smooth Surfaces, Maloupu L. Watts

Theses and Dissertations

The numerical approximation of denite integrals, or quadrature, often involves the construction of an interpolant of the integrand and subsequent integration of the interpolant. It is natural to rely on polynomial interpolants in the case ofone dimension; however, extension of integration of polynomial interpolants to two or more dimensions can be costly andunstable. A method for computing surface integrals on the sphere is detailed in the literature (Reeger and Fornberg,Studies in Applied Mathematics, 2016). The method uses local radial basis function (RBF) interpolation to reducecomputational complexity when generating quadrature weights for the particular node set. This thesis expands upon thesame …

Asymptotically Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.

Smallest Eigenvalues For A Right Focal Boundary Value Problem, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We establish the existence of smallest eigenvalues for the fractional linear boundary value problems D^α₀₊u+λ₁p(t)u = 0 and D^α₀₊u+λ₂q(t)u = 0, 0

On The Flow Of Non-Axisymmetric Perturbations Of Cylinders Via Surface Diffusion, Jeremy Lecrone, Gieri Simonett

Department of Math & Statistics Faculty Publications

We study the surface diffusion flow acting on a class of general (non--axisymmetric) perturbations of cylinders Cr in IR3. Using tools from parabolic theory on uniformly regular manifolds, and maximal regularity, we establish existence and uniqueness of solutions to surface diffusion flow starting from (spatially--unbounded) surfaces defined over Cr via scalar height functions which are uniformly bounded away from the central cylindrical axis. Additionally, we show that Cr is normally stable with respect to 2π--axially--periodic perturbations if the radius r>1,and unstable if 0

Oscillation Of Solution To Second-Order Half-Linear Delay Dynamic Equations On Time Scales, Hongwu Wu, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

This article concerns the oscillation of solutions to second-order half-linear dynamic equations with a variable delay. By using integral averaging techniques and generalized Riccati transformations, new oscillation criteria are obtained. Our results extend Kamenev-type, Philos-type and Li-type oscillation criteria. Several examples are given to illustrate our results.

Matched Metrics And Channels, Marcelo Firer, Judy L. Walker

Department of Mathematics: Faculty Publications

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this work we study channels and metrics for which those two criteria do and do not coincide for general codes.

How Much Should You Pay For A Financial Derivative?, Boyan Kostadinov

Publications and Research

We explain some key mathematical ideas behind the no-arbitrage pricing of financial derivatives by replication, starting from a simple coin toss model and ending with the continuous-time limit of a multi-step coin-toss model using a geometric random walk model. In the limit, we obtain the classical Black-Scholes-Merton formula for pricing European call and put options.

A Weak Galerkin Method For Parabolic Equations, Yajie Yu

Theses and Dissertations

Parabolic equations have very broad applications in physics and engineering, such as heat diffusion and ocean acoustic propagation. Here we consider the 2D case with time dependent equations. Many numerical methods have been proposed to solve them, such as discontinuous Galerkin method, hybridized Galerkin method and so on. A weak Galerkin method is introduced by Dr. Wang and Dr. Ye by employing totally discontinuous functions in approximation space and an innovatively defined weak gradient operator which provide desirable flexibilities.In this thesis, we apply this method to solve parabolic equations. This method also has the energy conserva- tion property. Both continuous …

Converting Heterogeneous Statistical Tables On The Web To Searchable Databases, David W. Embley, Mukkai S. Krishnamoorthy, George Nagy, Sharad C. Seth

School of Computing: Faculty Publications

Much of the world’s quantitative data reside in scattered web tables. For a meaningful role in Big Data analytics, the facts reported in these tables must be brought into a uniform framework. Based on a formalization of header-indexed tables, we proffer an algorithmic solution to end-to-end table processing for a large class of human-readable tables. The proposed algorithms transform header-indexed tables to a category table format that maps easily to a variety of industry-standard data stores for query processing. The algorithms segment table regions based on the unique indexing of the data region by header paths, classify table cells, and …

High Contrast Ultrasonic Imaging Of Resin-Rich Regions In Graphite/Epoxy Composites Using Entropy, Michael S. Hughes, John E. Mccarthy, Paul J. Bruillard, Jon N. Marsh, Samuel A. Wickline

Mathematics Faculty Research

This study compares different approaches for imaging a near-surface resin-rich defect in a thin graphite/epoxy plate using backscattered ultrasound. The specimen was created by cutting a circular hole in the second ply; this region filled with excess resin from the graphite/epoxy sheets during the curing process. Backscat-tered waveforms were acquired using a 4 in. focal length, 5MHz center frequency broadband transducer, scanned on a 100 × 100 grid of points that were 0.03 × 0.03 in. apart. The specimen was scanned with the defect side closest to the transducer. Consequently, the reflection from the resin-rich region cannot be gated from …

Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski

Publications

Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in …

Hpcnmf: A High-Performance Toolbox For Non-Negative Matrix Factorization, Karthik Devarajan, Guoli Wang

COBRA Preprint Series

Non-negative matrix factorization (NMF) is a widely used machine learning algorithm for dimension reduction of large-scale data. It has found successful applications in a variety of fields such as computational biology, neuroscience, natural language processing, information retrieval, image processing and speech recognition. In bioinformatics, for example, it has been used to extract patterns and profiles from genomic and text-mining data as well as in protein sequence and structure analysis. While the scientific performance of NMF is very promising in dealing with high dimensional data sets and complex data structures, its computational cost is high and sometimes could be critical for …

Minimizing Differences Of Convex Functions With Applications To Facility Location And Clustering, Mau Nam Nguyen, R. Blake Rector, Daniel J. Giles

Mathematics and Statistics Faculty Publications and Presentations

In this paper we develop algorithms to solve generalized Fermat-Torricelli problems with both positive and negative weights and multifacility location problems involving distances generated by Minkowski gauges. We also introduce a new model of clustering based on squared distances to convex sets. Using the Nesterov smoothing technique and an algorithm for minimizing differences of convex functions called the DCA introduced by Tao and An, we develop effective algorithms for solving these problems. We demonstrate the algorithms with a variety of numerical examples.

Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of single valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets. We apply the concept of single valued neutrosophic sets, an instance of neutrosophic sets, to graphs. We introduce certain types of single valued neutrosophic graphs (SVNG) and investigate some of their properties with proofs and examples.

Supervised Learning-Based Explicit Nonlinear Model Predictive Control And Unknown Input Estimation In Biomedical Systems, Ankush Chakrabarty

Open Access Dissertations

Application of nonlinear control theory to biomedical systems involves tackling some unique and challenging problems. The mathematical models that describe biomedical systems are typically large and nonlinear. In addition, biological systems exhibit dynamics which are not reflected in the model (so-called 'un-modeled dynamics') and hard constraints on the states and control actions, which exacerbate the difficulties in designing model-based controllers or observers.

This thesis investigates the design of scalable fast explicit nonlinear model predictive controllers (ENMPCs). The design involves (i) the estimation of a feasible region using Lyapunov stability methods and support vector machines; and (ii) within the estimated feasible …

Newton's Law Of Cooling, Caleb J. Emmons

Journal of Humanistic Mathematics

A poem reflecting three different viewpoints on Newton's Law of Cooling.