# UCF Math Dissertations

The Math Department has offered the PhD program since 1993 with a financial mathematics track added in Fall 2017. The program has awarded 71 PhD degrees since 1998.

## 2017

Tyler Gomez (advisor: Jason Swanson)

*Filtering Problems in Stochastic Tomography*

Cheng Cheng (advisors: Xin Li and Qiyu Sun)

*Sampling and Reconstruction of Spatial Signals*

Martin Rolek (advisor: Zixia Song)

*Coloring graphs with forbidden minors*

## 2016

Ashish Bhatt (advisor: Brian Moore)

*Structure-preserving finite difference methods for linearly damped differential equations *

Aritra Dutta (advisor: Xin Li and Qiyu Sun)

*Weighted low-rank approximation of matrices: some analytic and numerical aspects*

Matthew Russo (advisor: Sudipto Choudhury)

*Building Lax Integrable Variable-Coefficient Generalizations to Integrable PDEs and Exact Solutions to Nonlinear PDEs*

Jeff Shape (advisor: Andrew Nevai)

A mathematical model for feral cat ecology with application to disease.

Maria Strawn (advisor: Constance Schober)

*Modeling rogue waves in deep water*

Yi Zhu (advisor: Yuanwei Qi)

*Computational Study of Traveling Wave Solutions and Global Stability of Predator-Prey Models*

### 2015

Lei, Ge (advisor: M. Nashed)

*Calibration of Option Pricing in Reproducing Kernel Hilbert Space*

Siple, Angela (advisor: P. Mikusinski

*Integral Representations of Positive Linear Functionals*

### 2014

Baxter, Mathew (advisor: K. Vajravelu)

*Analytical solutions to nonlinear differential equations arising in physical problems*

Haussermann, John (advisor: D. Dutkay)

*Tiling Properties Of Spectra Of Measures*

Krylov, Roman (advisor: A. Katsevich)

*Inversion of the Broken Ray Transform*

Martinenko, Evgeny (advisor: M. Pensky)

*Functional Data Analysis and its application to cancer data*

Sadiq, Kamran (advisor: A. Tamasan)

*On the range of the Attenuated Radon Transform in strictly convex sets *

Van Gorder, Robert A. *(*advisors: D. Kaup and K. Vajravelu)

*Nonlinear Dispersive Partial Differential Equations of Physical Relevance with Applications to Vortex Dynamics*

Veras, Johann (advisor: A. Tamasan)

*Electrical Conductivity Imaging via Boundary Value Problems for the 1-Laplacian *

### 2013

Benhaddou, Rida (advisor: M. Pensky)

*Nonparametric and Empirical Bayes Estimation Methods*

Losert, Bernd (advisor: G. Richardson)

*Extensions Of S-spaces*

Michalak, Martin (advisor: B. Shivamoggi)

*Dynamical Invariants And The Fluid Impulse In Plasma Models*

Pecora, Keri Ann (advisor: S. Choudhury)

*Partially Integrable Pt-symmetric Hierarchies Of Some Canonical Nonlinear Partial Differential Equations *

Pehlivan, Saliha (advisors: D. Han and R. Mohapatra)

*Spectrally Uniform Frames And Spectrally Optimal Dual Frames*

Pridemore, Kathryn (advisor: M. Pensky)

*Accelerated Life Model with Various Types of Censored Data*

Ramesh Gayatri (advisors: Q. Sun and R. Mohapatra)

*Modified Pal Interpolation And Sampling Bilevel Signals With Finite Rate Of Innovation*

### 2012

Ahmadi Abhari, Seyed Hamed (advisor: J. Brennan)

Quantum Algorithms For: Quantum Phase Estimation, Approximation Of The Tutte Polynomial And Black-box Structures

### 2011

Alrud, Bengt (advisor: D. Dutkay)

*Fractal Spectral Measures in Two Dimensions*

Chen, Teng (advisor: J. Brennan)

*Algebraic Aspects of (Bio) Nano-Chemical Reaction Networks And Bifurcations in Various Dynamical Systems*

Davis, Justin (advisor: M. Pensky)

*Bayesian Model Selection for Classification with Possibly Large Number of Groups*

Riddlesworth, Tonya (advisor: J. Ren)

*Estimation for the Cox Model with Various Types of Censored Data*

Shao, Haimei (advisor: J. Yong)

*Price Discovery In The U.S. Bond Market Trading Strategies And The Cost Of Liquidity*

Smith, Todd Blanton (advisor: S. Choudhury)

*Variational Embedded Solitons, and Traveling Wavetrains Generated by Generalized Hopf Bifurcations, in Some NLPDE Systems*

Galiffa, Daniel J. (advisor: M. Ismail)

*The Sheffer B-type 1 Orthogonal Polynomial Sequences*

Konate, Souleymane (advisor: A. Katsevich)

*Efficient Cone Beam Reconstruction For The Distorted Circle And Line Trajectory*

Lopez, Jerry (advisor: D. Han)

*Optimal Dual Frames For Erasures And Discrete Gabor Frames*

Macon, Lisa Fisher (advisor: Y. Zhao)

*Almost Regular Graphs and Edge-Face Colorings of Plane Graphs*

Shi, Qiling (advisor: Q. Sun)

Weighted Lp-stability For Localized Infinite Matrices

Sweet, Erik (advisor: K. Vajravelu)

Analytical And Numerical Solutions Of Differentialequations Arising In Fluid Flow And Heat Transfer Problems

### 2008

Boustique, Hatim (advisors: G. Richardson and R. Mohapatra)

Lattice-valued Convergence: Quotient Maps

Bryant, Donald (advisors: X. Li and M. Shah)

*Analysis Of Kolmogorov’s Superposition Theorem And Its Implementation In Applications With Low And High Dimensional Data.*

Khosravi, Mehrdad (advisor: P. Mikusinski)

Pseudoquotients: Construction, Applications, And Their Fourier Transform

Landon, Benjamin (advisor: R. Mohapatra)

*Degree of Approximation of Holder Continuous Functions*

### 2007

Flores, Paul (advisor: R. Mohapatra)

Categorical Properties Of Lattice-valued Convergence Spaces

Holmquist, Sonia (advisor: R. Mohapatra)

*An Examination of the Effectiveness of the Adomian Decomposition Method in Fluid Dynamic Applications*

Mancas, Stefan C. (advisor: S. Choudhury)

*Dissipative Solitons in the Cubic-Quintic Complex Ginzburg-Landau Equation: Bifurcations and Spatiotemporal Structure*

Vogel, Thomas (advisor: D.J. Kaup)

Soliton Solutions Of Nonlinear Partial Differential Equations Using Variational Approximations And Inverse Scattering Techniques

Wlodarczyk, Tomasz (advisor: C. Schober)

Stability And Preservation Properties Of Multisymplectic Integrators

### 2006

Cowan, Doris C. (advisors: L. Andrews and C. Young)

Effects Of Atmospheric Turbulence On The Propagation Of Flattened Gaussian Optical Beams

He, Bin (advisor: J. Ren)

Application Of The Empirical Likelihood Method In Proportional Hazards Model

Jing, Wu (advisor: D. Han)

*Frames in Hilbert C*-Modules*

Singh, Neeta (advisor: D. Rollins)

*Epidemiological Models For Mutating Pathogens With Temporary Immunity*

Vetelino, Frida (advisor: C. Young)

*Fade Statistics for a Lasercom System and the Joint PDF of a Gamma-Gamma Distributed Irradiance and Its Time Derivative*

### 2005

Bradshaw, David (advisor: M. Pensky)

*Decision Theory Classification Of High-dimensional Vectors Based On Small Samples *

Heard, Astrid (advisor: M. Pensky)

*Application Of Statistical Methods In Risk And Reliability *

Salman, Mohamed (advisor: J. Cannon)

*Utilization of Total Mass as a Control in Diffusion Processes*

### 2004

Amezziane, Mohamed (advisor: M. Taylor)

Smoothing Parameter Selection In Nonparametric Functional Estimation

Edwards, Heather (advisor: M. Taylor)

Measures Of Concordance Of Polynomial Type

Masino, Aaron (advisor: C. Young)

*The Wave Structure Function and Frequency Variance of Optical Waves in Moderate to Strong Atmospheric Turbulence With Application to Laser Radar*

### 2003

Boncek, J. (advisor: D. Han)

Studies in tight frames and polar derivatives

Korotkova, Olga (advisor: L.C. Andrews)

*Model for a Partially Coherent Gaussian Beam in Atmospheric Turbulence with Applications for Lasercom and LIDAR Systems*

Muise, R. (advisor: R. Mohapatra)

*Quadratic Filters for Automatic Pattern Recognition*

VanDeCar, Sida (advisor: X. Li )

*Inequalities Involving Complex Rational Functions*

Zamyatin, Alexander (advisor: A. Katsevich)

* Analysis of Cone Beam Reconstruction in Computer Tomography*

### 2001

Boissy, Y. (advisor: G. Richardson)

*Parameter Estimates for Fractional Autoregressive Spatial Processes*

### 2000

Al Habash, Ammar (advisor: L.C. Andrews)

*The Aperture Averaged Scintillation of the Intensity of a Gaussian Laser Beam Propagated Through Strong Optical Turbulence and Reflected By Various Targets*

*ElHor, A. (advisor: M. Pensky) *

*Statistical Estimation of the Locations of Lightning Events*

### 1999

Brown, K. (advisor: S. Choudhury)

*Linear and Nonlinear Kelvin-Helmholtz Instabilities of High Velocity Magnetized Shear Layers With Generalized Polytrope Laws*

### 1998

Kelly, D. (advisor: L.C. Andrews)

*Temporal Propagation Characteristics of Ultrasound Space-Time Gaussian Pulses In A Laser Satellite Communication System*

Minkler, Gary (advisor: G. Richardson)

*Regularity And Compactness in Fuzzy Convergence Spaces*

Minkler, Jing Q. (advisor: G. Richardson)

*On the Regularity of Probabilistic Convergence and Filter Spaces*

Tanriver, U. (advisor: S. Choudhury)

*One And Two Dimensional Coherent Structures Of Nonlinear Partial Differential Equations **Via Painlevé Analysis*

**To add or update information, please e-mail me at qiyu.sun@ucf.edu.**