# Mathematics PhD Recipients

Modeling the Current-Voltage (I-V) Characteristics of the MOSFET Device with Quantum Mechanical Effects due to Thin Oxide near ‘Si/SiO_{2}’ Interface using Asymptotic Methods

(JDP with CSULB) Advisor: Ellis Cumberbatch

Investigating Castillo-Grone's Mimetic Difference Operators in Development of Geophysical Fluid Dynamics Models Implemented on GPGPUs

(JDP with SDSU) Advisor: Jose Castillo

Finding a Novel Way for Fast Sequence Alignment and Exploiting Information Theory inBacterial Genomes and Complete Phages

(JDP with SDSU) Advisor: Robert Edwards

Adaptive Monte Carlo Algorithms for Continuous and Discrete Transport Problems

Advisor: Jerome Spanier

A Computational Workflow for the Estimation of Environmental Viral Diversity in Metagenomes

(JDP with SDSU) Advisor: Forest Rohwer

Stochastic Properties of Uniformly Optimally Reliable Networks (and their Graphs)

Advisors: Milton Sobel (UC Santa Barbara)

Stochastic Dynamics in Coupled Bistable Systems with Applications to Sensor Devices

(JDP with SDSU) Advisor: Visarath In

Dariouch Herve **Babai**

1995

Models of HIV Mutations and Interaction with the Immune System using Differential Equations: Coupling “Diffusion,” Specific and Global Interaction

Advisor: Kenneth Cooke

Dynamics of Two Components Bose-Einstein Condensates

(JDP with SDSU) Advisor: Ellis Cumberbatch

PDE-Based Image and Structure Enhancement for Electron Tomography of Mitochondria

(JDP with SDSU) Advisor: Peter Blomgren

Performance Feedback and Control of Solar Concentrators using Wave Front Sensing Techniques

(JDP with CSULB) Advisor: Hen-Geul Yeh

Completeness and Reflexivity Properties in Topological Vector Spaces using Standard and Nonstandard Methods

Advisor: Sandy Grabiner

An Integrative Approach to Modeling in Systems Biology

(JDP with KGI) Advisor: Ali Nadim

Susan Anne Elizabeth **Berggren**

2012

Computational and Mathematical Modeling of Coupled Superconducting Quantum Interference Devices

(JDP with SDSU) Advisor: Antonio Palacios

Prediction of High Lift Flows with Separation

(JDP with CSULB) Advisor: Tuncer Cebeci

Structure of Gene Expression Networks Derived from Microarray Time Series Data

Advisor: Greg Dewey

Simulated Associating Polymer Networks

(JDP with SDSU) Advisor: Arlette Baljon

Periodic Boundary Value Problems and the Dancer-Fucik Spectrum Under Conditions of Resonance

Advisor: Adolfo Rumbos

Theodoros Spyridon **Bolis**

1971

Differentiable Nuclear Manifolds

Advisor: Robert James

Linear Phase Orthogonal Filter Bank Constructions with Applications to Image and Geometric Approximations

(JDP with CSULB) Advisor: Nick Panagiotacopulos

Discrete Variable Representation of the Angular Variables in Quantum Three-Body Scattering

(JDP with CSULB) Advisor: Alfonso Rueda

Todd **Cadwallader-Olsker**

2007

Proof Schemes and Proof Writing

Advisor: John Angus

Study of Vortex Ring Dynamics in the Nonlinear Schrodinger Equation Utilizing GPU-Accelerated High-Order Compact Numerical Integrators

(JDP with SDSU) Advisor: Ricardo Carretero

Solid and Fluid Mechanics Case Studies in Advanced Electronic Packaging

(JDP with CSULB) Advisor: Hsien-Yang Yeh

Topological Symmetry Groups of Complete Graphs

Advisor: Erica Flapan

Frombrains to populations: Modeling Animal Interactions with their Environment

(JDP with KGI) Advisor: Animesh Ray

Joint Modeling and Analysis of Recurrent and Terminal Events

Advisor: John Angus

Role of the MicroRNA miR-124 in the Regulatory Network Governing PNS Development in Ciona Intestinalis

(JDP with SDSU) Advisor: Robert Zeller

Quasi-Random Techniques for Monte Carlo Methods

Advisor: Jerome Spanier

Optimization: Nurbs and the Quasi-Newton Method

(JDP with CSULB) Advisor: Ortwin Ohtmer

Cherlyn Lee **Converse**

1992

Lower Bounds for the Maximum Number of Stable Pairings for the General Marriage Problem Based on the Latin Marriage Problem

Advisor: Henry A. Krieger

On the Moments of the Number of Curve Crossings by a Stationary Gaussian Process

Advisor: Jerome Spanier

Mathematical Models in Microfluidics: Capillary Electrophoresis and Sessile Drop Physics

Advisor: Ali Nadim

Development of a Parallel Coupler Library with Minimal Inter-Process Synchronization for Large-scale Computer Simulations

(JDP with SDSU) Advisor: Jose Castillo

Wavelet Feature Extraction of High-Range Resolution Radar Profiles using Generalized Gaussian Distributions for Automatic Target Recognition

Advisor: John Angus

Mohamed Osman **El-Doma**

1986

Analysis of Nonlinear Integra-Differential Equations Arising in Age-Dependent Epidemic Models

Advisor: Stavros Busenberg

Disturbance Decoupling with Stability for Nonlinear Systems using Static/Output Feedback: A Geometric Approach

(JDP with CSULB) Advisor: Fumio Hamano

Claudia Rangel **Escareno**

2003

Modeling Biological Responses Using Gene Expression Profiling and Linear Dynamical Statistical Models

Advisors: John Angus and David Wild (KGI)

Mohammad (Al Ahmad) **Eyadat**

2003

Comparative Performance Evaluation of Practical Digital Watermar Embedded Schemes

(JDP with CSULB) Advisors: Samir Chatterjee, Ali Nadim, Dar -Biau Liu

Identification of Transistor Contact Resistivity

Advisors: Ellis Cumberbatch and Stavros Busenberg

Condensed History Methods for Monte Carlo Solutions of Photon Transport Problems

Advisor: Jerome Spanier

Electrowetting-Based Microfluidics: Modeling and Simulation

Advisor: Ali Nadim

On the Interaction of a Cold Front with a Mountain Ridge

Advisor: Ellis Cumberbatch

Induction of Chromosome Instability by Gene Dosage and Over-Expression in Saccharomyces Cerevisiae

Advisor: Animesh Ray

Mathematical Models of Typhoid Fever

Advisor: Kenneth L. Cooke

Cristina **Garcia-Cardona**

2013

Multiclass Learning on Graphs: Diffuse Interface Models and Beyond

(JDP with SDSU) Advisor: Allon Percus

Cellular Pattern Formation and Noise in O_{(}_{2)} Symmetric Systems

Advisor: Peter Blomgren

Ruben Jeffrey **Glueck**

2013

Pseudo-Spectral and Kronecker Product Methods for Fourth Order Partial Differential Equations

Advisor: Ali Nadim

Cooperative Solution Concepts for Multi-Sided Assignment Games

Advisor: William F. Lucas

Confidence Bounds on Functions of Parameters

Advisor: Janet Myhre

Hamza Abid-ali **Hamza**

1997

Multi-Person Cooperative Games: The Nucleoli Approach Assignment Games

Advisor: William F. Lucas

Perturbation Monte Carlo Methods for the Solution of Inverse Problems

Advisor: Jerome Spanier

Variations on Markov Chain Monte Carlo Methods: Continuous and Discrete Optimization of Scheduling Problems

Advisor: Alpan Raval

Statistical Tests for Stochastic Dominance

Advisor: Henry A. Krieger

Experimental and Numerical Investigations of Steady Turbulent Jets from Round Ribbed Tubes

(JDP with CSULB) Advisor: Hamid Rahai

Statistical and Structural Dynamic Analysis of the Earthman Periometer Measure of Tooth and Implant and Damping Capacity

(JDP with CSULB) Advisors: Ortwin Ohtmer and John Angus

Studies in Differential Equations and Applications

Advisor: Kenneth L. Cooke

Risk Analysis of Software Development using Bayesian Belief Network and Non-Linear Programming Methods

(JDP with CSULB) Advisors: Dar-Biau Liu & Alpan Raval

Lifting Isomorphisms Between l-algebras of f-algebras

Advisor: Melvin Henriksen

t -copula Based Credit Risk Modeling in a Network Economy

Advisor: Henry Schellhorn

Extensions of the Theory of the Fractional Calculus with an Application

Advisor: Jerome Spanier

A New Approach in Blind Equalization of Multipath Wireless Channels

(Joint with CSULB) Advisor: Rajendra Kumar

Some Contributions to the Theory of Random Sets

Advisor: Richard Vitale

Khalil Antoun **Kairouz**

2002

Numerical and Experimental Investigations of a Turbulent Junction Flow with Upstream Ribbed Surface

(JDP with CSULB) Advisor: Hamid R. Rahai

Transport Problems and Monte Carlo Methods

Advisor: Jerome Spanier

Monte Carlo and Quasi-Monte Carlo Methods and their Applications

Advisor: Jerome Spanier

John Patrick **Lambert**

1982

Some Developments in Optimal and Quasi-Monte Carlo Quadrature and a New Outlook on a Classical Chebyshev Problem

Advisor: Jerome Spanier

Convexity Conditions on a Class of Lattice Ordered Rings

Advisor: Melvin Henriksen

Neural Networks for Function Approximation and Control System Design

Advisor: Robert Williamson

A Method to Detect Single and Multiple Delamination Problems using a Combined Neural Network Technique and Genetic Algorithm Optimization

(JDP with CSULB) Advisor: Ellis Cumberbatch

Bayesian Parameter and Order Estimation in Profile Hidden Markov Models

Advisor: Alpan Raval

Quasi-Monte Carlo Methods for Transport Equations

Advisor: Jerome Spanier

A Multilevel Framework for PDEs whose Solution Exhibits Fast Transitions

(JDP with SDSU) Advisor: Ellis Cumberbatch

Trees, Tree-Like Structures, and Extreme Points in Banach Spaces

Advisor: Robert James

A Bond Option Pricing Formula in the Extended CIR Model

Advisor: Henry Schellhorn

A Fire Spread Model Using Levet Set Methods

(JDP with CSULB) Advisor: Burkhard Englert

Nonlinear Dynamics Design and Operation of Advanced Magnetic Sensors

(JDP with SDSU) Advisor: Antonio Palacios

Resonance and Strong Resonance for Semilinear Elliptic Equations in R^{N}

Advisor: Adolfo Rumbos

Curve Estimation and Graduation

Advisor: John Angus

Evaluation Modeling in Performance and Resource Allocation for Residential Broadband Gateways

(JDP with CSULB)

Advisor: John. Angus

Jose Alberto **Luzardo-Flores**

1997

Neural Networks for Approximation and Control of Continuous Time Nonlinear Systems

(JDP with CSULB) Advisor: A. G. Chassiakos

An Approximation Method for Solving Non-Homogeneous Wave Equations and Related Inverse Problems

Advisor: Ellis Cumberbatch

Contributions to the Theory of Error Reduction in Quasi-Monte Carlo Methods

Advisor: Jerome Spanier

Investigation of Progressive Failure Robustness and Alternate Load Paths for Damage Tolerant Structures

(JDP with SDSU) Advisor: Satchi Venkataraman

Quantization of a Low-Density Parity-Check (LDPC) Decoder

(JDP with SDSU) Advisor: Michael E. O’Sullivan

On Some Banach Space Properties Related to the Radon-Nikodým Property

Advisor: Robert James

Jeffrey Louis **Molony**

1997

Studies of the Geometric Theory: Nonlinear Dynamical Systems

Advisor: Courtney Coleman

Watermarking Schemes Robust against Affine Attacks: Applied Mathematics, An Application of Digital Image Processing in Information Technology

Advisor: Hedley Morris

DNA Visualization with Sacks Spiral Method: An Application in Genomic Engineering

(JDP with CSULB) Advisor: Forouzan Golshani

Ab Initio Nuclear Shell Model Calculations of Some Light Nuclei with a Three-Nucleon Force

(JDP with SDSU) Advisor: Calvin Johnson

Dynamical Properties of Bose-Einstein Condensates

(JDP with SDSU) Advisor: Ricardo Careterro

Numerical Study of the Properties of Compact Stars

(JDP with SDSU) Advisor: Fridolin Weber

An Unified Automated Approach to Surface Approximation via Finite Element and Non Uniform Rational B-spline Methods

(JDP with CSULB) Advisors: Ortwin Ohtmer and Ellis Cumberbatch

Reliability Modeling and Evaluation in Computer Networks and Distributed Systems

(JDP with CSULB) Advisors: John Angus and Dar-Biau Liu

A Hardware Implementation of the Level Set Method for Robotic Path Finding with Multiple Obstacle Avoidance

(JDP with CSULB) Advisor: Ali Nadim

Mathematical Modeling and Digital Signal Processing Techniques for Modern Digital Communication Systems

(JDP with CSULB) Advisor: Hen-Geul Yeh

Meta-Scheduling of Level-Set Methods in a Grid Computing Environment

(JDP with CSULB) Advisors: Dar-Biau Liu & Ali Nadim

Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods

Advisor: Jerome Spanier

Kim Joseph **Olszewski**

1998

Concatenated Reed-Solomon and Reed-Muller Codecs with Blind Adaptation for CDMA Antenna Array Systems

(JDP with CSULB) Advisor: R. Kumar

Contributions to the Theory of Fractional Difference Operators

Advisor: Jerome Spanier

A Service-Oriented Architecture for Thermochemical Computation

(JDP with SDSU) Advisor: Subrata Bhattacharjee

Applications of Cluster Systems

(JDP with CSULB) Advisor: John Angus

The Average Error from the Approximation of Functions and Integrals

Advisor: Robert Williamson

Carlos Orrala **Poveda**

2004

Numerical and Experimental Investigations of Two Side-by-Side Turbulent Jets in a Cross Flow

(JDP with CSULB) Advisor: Hamid R. Rahai

Jerry Emmett **Purcell**

1995

Allpass Filters

(JDP with CSULB) Advisor: Ellis Cumberbatch

Applications of Morse Theory to Semilinear Elliptic Boundary Value Problems

Advisor: Adolfo Rumbos

Diophantine Approximation of Complex Numbers

Advisor: Jerome Spanier

Beltran **Rodriguez-Brito**

2010

A Metagenomic Examination of a Solar Saltern in Southern California

(JDP with SDSU) Advisor: Forest Rohwer

Modeling of Rupture Propagation under Different Friction Laws using High-Order Mimetic Operations

(JDP with SDSU) Advisors: Steven Day & José Castillo

Three-Sided Assignment Games

Advisor: William F. Lucas

On Some Problems in the Theory of Von Neumann Regular Rings

Advisor: Melvin Henriksen

Robert Armin **Schmieder**

2012

A Framework for Identifying Antibiotic Resistance in the Human Microbiome

(JDP with SDSU) Advisor: Robert Edwards

Constructive Neural Networks for Function Approximation and their Application to CFD Shape Optimization

(JDP with CSULB) Advisor: Hamid Hefazi

Banach and Frechet Algebras of Power Series

A Framework for Identifying Antibiotic Resistance in the Human Microbiome

(JDP with SDSU) Advisor: Robert Edwards

Neural Network Predictions of Protein Function

(JDP with SDSU) Advisor: Anca Segall

John** Sepikas**

2011

Enhanced Lattice Methods for High Dimensional Quadrature Applications

Advisor: Jerome Spanier

Predicting Glaucoma Progression Using Random Forests for Correlated Binary Response Based on Longitudinally Collected Standard Automated Perimetry Data

(JDP with SDSU) Advisor: Juanjuan Fan

Autonomous Voice and Motion Controlled Video Camera System for Instructional Technology

Advisor: John Angus

Interaction of the Quantum Vacuum with an Accelerated Object and its Contribution to Inertia Reaction Force

(JDP with CSULB) Advisor: Alpan Raval

The Geographic Mosaic Theory in Relation to Coevolutionary Interactions between Two Species

Advisor: Michael Moody

Allen **Teagle-Hernandez**

2013

Very Efficient Numerical Solutions via the "Mehrstellen" Method in 1D, 2D, and 3D for Complex Differential Equations Demonstrated for Acoustics and Related Fields

(JDP with CSULB) Advisor: Ellis Cumberbatch

Modeling and Simulation of Aeroservoelastic Control with Multiple Control Surfaces Using µ-Method

(JDP with CSULB) Advisor: H. P. Chen

Parallel Implementation of the Curvilinear Ocean and Atmospheric (UCOAM) Model and Supporting Computational Environment

(JDP with SDSU) Advisor: Jose Castillo

Assessment of Functional Activity in Isolated Cardiomyocytes using ComputationalMethods

(JDP with SDSU) Advisor: Paul Paolini

Asymptotic Reliability of the Hypercube and the D-Octahedral Networks

Advisor: William F. Lucas

Multiplications on Banach Spaces

Advisor: Sandy Grabiner

Spectral Conditions for Oscillations and Stabilization of Systems of Differential Equations with Piecewise Constant Arguments

Advisor: Kenneth Cooke

Jorge Xicotencatl **Velasco-Hernandez**

1991

Models of Chagas’ Disease : Stability, Thresholds and Asymptotic Behavior

Advisor: Stavros Busenberg

A Mathematical Description of Diagrammatic Models for Structural Changes in Dendritic Spines

Advisors: Ellis Cumberbatch, Steve Baer (ASU)

Minaya **Villasana de Villagas**

2001

A Delay Differential Equation Model for Tumor Growth

Advisor: Ami Radunskaya

Problems in GPS Accuracy

Advisor: John Angus

Global Asymptotic Stability of a Periodic Solution to an Epidemic Model

Advisor: Kenneth Cooke

A Coupled Vibratory Gyroscope Network with Bi-directional, Uni-directional, And Direct Coupling

(JDP with SDSU) Advisors: Antonio Palacios and Visarath In

Z’ of Gauged Baryon and Lepton Numbers at the Large Hadronic Collider

(JDP with CSULB) Advisor: Subhash Rajpoot

Error Reduction Techniques for Monte Carlo Neutron Transport Calculations

Advisor: Jerome Spanier

Jonathan Louis **Wilson**

2013

Advancements in the Elicitation, Aggregation, and Forecasting of Probability Distributions Under Time Constraints

(JDP with SDSU) Advisor: Kristin Duncan

An Embedding Method for Simulation of Immobilized Enzyme Kinetics and Transport in Sessile Hydrogen Drops

Advisor: Ali Nadim

Integrated Semigroups of Bounded Linear Operations and their Applications to Inverse Problems

Advisor: Stavros Busenberg

Analysis of a Class of Nonlinear Dynamical Systems and Applications to Neural Networks

Advisors: Jerome Spanier and Ellis Cumberbatch

Femvib, An Ab Initio Multi-Dimensional Solver for Probing Vibrational Dynamics in Polyatomic Molecules and Free Radicalsv

(JDP with SDSU) Advisor: Andrew Cooksy

Effects of History and Lift Force on Particle Trajectories in Oscillatory Rotating Fluids

Advisor: Ali Nadim

Stochastic and Deterministic Sets

Advisor: Richard A. Vitale

Globally Accessible Finite Element Based Web Solver for the Vibrational Schrodinger Equation and Application to HC30 and ZnCl2+

(JDP with SDSU) Advisor: Andrew Cooksy

Mathematical Modeling of Cystic Fibrosis

(JDP with SDSU) Advisor: Peter Salamon

A Mathematical Analysis of Vesicle Shapes

(JDP with CSULB) Advisor: Hsien-Yang Yeh

Computational Modeling and Bifurcation Analysis of Bubbling Fluidized Processes

Advisor: Antonio Palacios