Mathematics & Statistics

Recent Recipients of the Ph.D. in Mathematics

2020

Robert D. Freeman

• Dissertation: On the \(p(x)\)-Laplace equation in Carnot groups
• Advisor: T. Bieske

Chi Phan

• Dissertation: Global and Stochastic Dynamics of Diffisive Hindmarsh-Rose Equations in Neurodynamics
• Advisor: Y. You

Vasile Pop

• Dissertation: Restricted Isometric Projections for Differentiable Manifolds and Applications
• Advisors: R. Teodorescu and I. Teodorescu

Emanuele Zappala

• Dissertation: Non-Associative Algebraic Structures in Knot Theory
• Advisors: M. Elhamdadi and M. Saito

2019

Amine Ben Abdeljelil

• Dissertation: Generalized Derivations of Ternary Lie Algebras and \(n\)-BiHom-Lie Algebras
• Advisor: M. Elhamdadi

Maryam Bagherian

• Dissertation: Field Quantization for Radiative Decay of Plasmons in Finite and Infinite Geometries
• Advisor: S. Kouchekian

Daniel A. Cruz

• Dissertation: Hierarchical Self-Assembly and Substitution Rules
• Advisor: N. Jonoska

John Theado

• Dissertation: An Optimal Medium-Strength Regularity Algorithm for 3-uniform Hypergraphs
• Advisor: B. Nagle

2018

Elsayed Ahmed

• Dissertation: Groups Generated by Automata Arising from Transformations of the Boundaries of Rooted Trees
• Advisor: D. Savchuk

Wael Al-Sawai

• Dissertation: Non-equilibrium Phase Transition in Interacting Diffusions
• Advisors: R. Teodorescu and A. Barbos

Matthew J. Green

• Dissertation: Generalizations of Quandles and their Cohomologies
• Advisor: M. Elhamdadi

Xiang Gu

• Dissertation: Hamiltonian Structures and Riemann-Hilbert Problems of Integrable Systems
• Advisor: W. Ma

2017

Gregory Churchill

• Dissertation: On Extending Hansel's Theorem to Hypergraphs
• Advisor: B. Nagle

Indu Rasika U. Churchill

• Dissertation: Contributions to Quandle Theory: A Study of \(f\)-Quandles, Extensions and Cohomology
• Advisors: M. Elhamdadi and A. Makhlouf

Kumar Vijay Garapati

• Dissertation: Structural Analysis of Poloidal and Toroidal Plasmons and Fields of Multilayer Nanorings
• Advisor: S. Kouchekian

Morgan McAnally

• Dissertation: Generalized D-Kaup-Newell integrable sysems and their integrable couplings and Darboux transformations
• Advisor: W. Ma

Yuan Zhou

• Dissertation: Lump, Complexiton and Algebro-Geometric Solutions to Soliton Equations
• Advisor: W. Ma

2016

Matthew C. Fleeman

• Dissertation: Putnam’s Inequality and Analytic Content in the Bergman Space
• Advisor: D. Khavinson

Stephen D. Lappano

• Dissertation: Some Results Concerning Permutation Polynomials over Finite Fields
• Advisor: X. Hou

Solomon Manukure

• Dissertation: Hamiltonian Formulations and Symmetry Constraints of Soliton Hierarchies of \((1+1)\)-Dimensional Nonlinear Evolution Equations
• Advisor: W. Ma

Junyi Tu

• Dissertation: Global Attractors and Random Attractors of Reaction Diffusion Systems
• Advisor: Y. You

Syed Zoalroshd

• Dissertation: On Spectral Properties of Single Layer Potentials
• Advisor: D. Khavinson

2015

Daria Karpenko

• Dissertation: Active Tile Self-assembly and Simulations of Computational Systems
• Advisor: N. Jonoska

2014

Jonathan Burns

• Dissertation: Recursive Methods in Number Theory, Combinatorial Graph Theory, and Probability
• Advisors: A. Grinshpan and N. Jonoska

2013

Teffera Asfaw

• Dissertation: Topological Degree and Variational Inequality Theories for Pseudomonotone Perturbations of Maximal Monotone Operators
• Advisor: A. Kartsatos

Lisa De Castro

• Dissertation: Analytic Functions with Real Boundary Values in Smirnov Classes \(E^p\)
• Advisor: D. Khavinson

Egor Dolzhenko

• Dissertation: Modeling State Transitions With Automata
• Advisor: N. Jonoska

Waththage Neranga Fernando

• Dissertation: A Study of Permutation Polynomials over Finite Fields
• Advisor: X. Hou

Joseph Van Name

• Dissertation: Boolean Partition Algebras
• Advisor: V. Totik

2012

Alrazi Abdeljabbar

• Dissertation: Wronskian, Grammian and Pfaffian solutions to nonlinear partial differential equations
• Advisor: W-X. Ma

Magdy Assad

• Dissertation: Pfaffian and Wronskian solutions to integrable generalized nonlinear partial differential equations
• Advisor: W-X. Ma

Jill Dizona

• Dissertation: On Algorithmic Fractional Packings of Hypergraphs
• Advisor: B. Nagle

Jinghan Meng

• Dissertation: Bi-Integrable and Tri-Integrable Couplings and Their Hamiltonian Structures
• Advisor: W-X. Ma

Tilahun Muche

• Dissertation: Hamiltonian Sets of Polygonal Paths in 4-Valent Spatial Graphs
• Advisor: N. Jonoska

2011

Erik Lundberg

• Dissertation: Problems in Classical Potential Theory with Applications to Mathematical Physics
• Advisor: D. Khavinson

2010

Enver Karadayi

• Dissertation: Topics in Random Knots and R-Matrices from Frobenius Algebras
• Advisor: M. Saito

Kevin P. Wagner

• Dissertation: A Generalized Acceptance Urn Model
• Advisor: S. Suen

2009

Angela Angeleska

• Dissertation: Combinatorial Models for DNA Rearrangements in Ciliates
• Advisors: N. Jonoska and M. Saito

Elliot M. Findley

• Dissertation: Fine Asymptotics of Christoffel Functions and Universality for Szegö Weights in the Complex Plane
• Advisor: V. Totik

2008

Irena Andreevska

• Dissertation: Mathematical Modeling and Analysis of Options With Jump-Diffusion Volatility
• Advisor: Y. You

Rodney M. Taylor

• Dissertation: Lagrange Interpolation on Leja Points
• Advisor: V. Totik

2007

Dhruba R. Adhikari

• Dissertation: Applications of Degree Theories to Nonlinear Operator Equations in Banach Spaces
• Advisor: A. G. Kartsatos

Ibtisam Daqqa

• Dissertation: Subconstituent Algebras of Latin Squares
• Advisor: B. Curtin

John C. Davis, III

• Dissertation: Identification of Parameters When the Density of the Minimum is Given
• Advisor: A. Mukherjea

Daniela Genova

• Dissertation: Forbidding and Enforcing of Formal Languages, Graphs and Partially-Ordered Sets
• Advisor: N. Jonoska

Boubakari Ibrahimou

• Dissertation: The Leray-Schauder Approach for the Topological Degree of Perturbed Maximal Monotone Operators
• Advisor: A. G. Kartsatos

Michiru Shibata

• Dissertation: Pricing Models and Analysis of Corporate Coupon-Bonds and Credit Default Swaptions
• Advisor: Y. You

Ana Staninska

• Dissertation: A Theoretical Model for Self-assembly of Flexible Tiles
• Advisors: N. Jonoska and G. McColm

2006

Kheira Ameur

• Dissertation: Polynomial Quandle Cocycles, Their Knot Invariants and Applications
• Advisor: M. Saito

Edgardo S. Cureg

• Dissertation: Some Problems on Products of Random Matrices
• Advisor: A. Mukherjea

Jemal E. Gishe

• Dissertation: A Finite Family of \(q\)-Orthogonal Polynomials and Resultants of Chebyshev Polynomials
• Advisor: M. E.-H. Ismail

Joseph O. Quarcoo

• Dissertation: Contributions to the Degree Theory for Perturbations of Maximal Monotone Maps
• Advisor: A. G. Kartsatos

Joni B. Pirnot

• Dissertation: Recognizable Languages Defined by Two-Dimensional Shift Spaces
• Advisor: N. Jonoska

2005

Ferenc Tookos

• Dissertation: Hölder Continuity of Green's Functions
• Advisor: V. Totik

Djiby Fall

• Dissertation: Longtime Dynamics of Hyperbolic Evolutionary Equations in Unbounded Domains and Lattice Systems
• Advisor: Y. You

David E. Kephart

• Dissertation: Topology, Morphism, and Randomness in the Space of Formal Language
• Advisor: N. Jonoska

Norbert N. Youmbi

• Dissertation: Probability Theory on Semihypergroups
• Advisor: A. Mukherjea

2004

Kalpana Mahalingam

• Dissertation: Involution Codes: with Application to DNA Strand Design
• Advisor: N. Jonoska

Hasan H. Al-Najjar

• Dissertation: Tridiagonal Pairs in Representation Theory
• Advisor: B. Curtin

2003

Ahmed Y. Abdallah

• Dissertation: Global Dynamics of Damped Boussinesq Equations
• Advisor: Y. You

2002

Marina Appiou-Nikiforou

• Dissertation: Extensions of Quandles and Cocycle Knot Invariants
• Advisor: M. Saito

2001

David P. Benko

• Dissertation: Approximation by Weighted Polynomials
• Advisor: V. Totik

Viktor V. Maymeskul

• Dissertation: On Some Problems in Complex and Multivariate Approximation and Interpolation
• Advisor: E. B. Saff

2000

Ming Dai

• Dissertation: Identification of the Parameters of a Multivariate Normal Distribution by the Distribution of the Maximum
• Advisor: A. Mukherjea

Daniel D. Jelsovsky

• Dissertation: Quandle Cohomology and State-Sum Invariants of Knots
• Advisor: M. Saito

1999

Ivan V. Ivanov

• Dissertation: Linear Discrete Operators and Recovery in Uniform Algebras
• Advisors: B. Shekhtman and E. Rakhmanov

1998

Lubomir P. Markov

• Dissertation: An \(L^2\)-Approach to Second Order Functional Evolutions in Banach Spaces
• Advisor: A. G. Kartsatos

1997

Peter D. Dragnev

• Dissertation: Constrained Energy Problems for Logarithmic Potentials
• Advisor: E. B. Saff

Jing Lin

• Dissertation: Homotopy Invariance of Time-Dependent Domains and Perturbation Theory for Nonlinear Operators in Banach Spaces
• Advisor: A. G. Kartsatos

Jifeng Ma

• Dissertation: Spectrum of Some Integral Operators
• Advisor: M. E.-H. Ismail

Plamen C. Simeonov

• Dissertation: Weighted Polynomial and Rational Approximation With Varying Weights
• Advisors: E. B. Saff and V. Totik

1996

Sergey V. Belyi

• Dissertation: Operator-Valued \(R\)-Functions in the Theory of Linear Dynamic Systems
• Advisor: A. G. Kartsatos

Zouhua Ding

• Dissertation: Contributions to the Theory of the Existence of Zeros of Perturbations of Nonlinear \(M\)-Accretive Operators in Banach Spaces
• Advisor: A. G. Kartsatos

Subhankar Dhar

• Dissertation: Probability Measures on Stochastic Matrices
• Advisor: A. Mukherjea

Mohamed A. Elnaggar

• Dissertation: Identification of the Parameters of a Multivariate Normal Distribution by the Distribution of the Minimum
• Advisor: A. Mukherjea

Michael Q. Rieck

• Dissertation: Pseudo-Orthogonal Complementary Subspaces and Hyperbolic Partner Graphs
• Advisor: W. E. Clark

Vladimir F. Veselov

• Dissertation: A Compactification of the Fatou Mapping as a Dynamical System
• Advisors: R. W. Oberste-Vorth and J. H. Hubbard

1995

Guoqui Lu

• Dissertation: Markov Processes With Random Transition Probabilities
• Advisor: A. Mukherjea

Igor E. Pritsker

• Dissertation: Convergence and Zero Distribution of Laurent-Type Rational Functions
• Advisor: E. B. Saff

Margaret A. Yoder

• Dissertation: String Rewriting Applied to Problems in the Braid Groups
• Advisor: J. F. Pedersen

Yanmu Zhou

• Dissertation: Arrangement of Points on the Sphere
• Advisor: E. B. Saff

1992

Tony Y. Chang

• Dissertation: Domination Numbers of Grid Graphs
• Advisor: W. E. Clark