# Research and Publications

Our faculty maintain active research programs and are committed to providing opportunities for students to become involved in undergraduate research in Mathematics. Many students present their research at regional and national conferences, and have won awards for their outstanding work.

## 2020 Joint Mathematics Meeting

*2020*

*2020*

Rand, T. A., Richmond, C. E., & **Dougherty, E. T.**,* Modeling the combined impacts of host plant resistance and biological control on the population dynamics of a major pest of wheat.* *Pest Management Science*, doi: 10.1002/ps.5830

**Dougherty, E. T.**, Turner, J. C., & Vogel, F., *A computational investigation of preconditioning strategies and iterative methods for finite element based neurostimulation simulations.* *Computers & Mathematics with Applications doi: 10.1016/j.camwa.2020.02.021*

*2019*

*2019**Murphy, C, Ryan, C. and Warnapala, Y., Note-Taking Mode and Academic Performance in Two Law School Courses. Journal of Legal Education, Vol. 68, No. 2, pp. 207-229, 2019*

*Small, A. T., & Dougherty, E. T., Mathematical Modeling of Neurostimulation for Post-traumatic Stress Disorder: A Migration Towards Multiscale Modeling to Assess Neural Response to Transcranial Direct Current Stimulation Treatments. 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS), Berlin, Germany, 2019: 2340-2343*

*Lindberg, K. T., Small, A. S., & Dougherty, E. T., A Computation Based Approach for Modeling the Efficacy of Neurostimulation Therapies on Neural Functioning. 2019 9th International IEEE/EMBS Conference on Neural Engineering (NER), San Francisco, CA, USA, 2019: 581-584*

*Lindberg, K. R., & Dougherty, E.T., Location Specificity of Transcranial Electrical Stimulation on Neuronal Electrodynamics: A Mathematical Model of Ion Channel Gating Dynamics and Ionic Flux due to Neurostimulation. Frontiers in Computational Neuroscience, 13(17). doi: 10.3389/fncom.2019.00017*

*2018*

*2018**Halligan, A., Becotte, A., Crane, A., & Dougherty, E., A Mathematical Model for the Effects of Fertilization on Nitrogen Concentrations in Unsaturated Soil on Blueberry Farms in Southern New Jersey. Environ Model Assess, 23: 583-595*

*2017*

*2017***Warnapala, Y. **and Ngo, H., Numerical solutions of the radiosity equation for a spherical quatrefoil on Mars.* African Journal of Mathematics and Computer Science Research, *Vol. 10(4), pp. 24-31, Oct 2017

*Rand, T. A., Richmond, C. and Dougherty, E. T., Using matrix population models to inform biological control management of the wheat stem sawfly, Cephus cinctus. Biological Control,109: 27-36*

**2016 **

**2016****Warnapala, Y**. and Deng, Q., Numerical Solutions of the Radiosity's Equation for Low Reflectivity and Emissivity on Planet Mars. *International Journal of Mathematics Trends and Technology (IJMTT),* V34(1):13-18 June 2016

**Dougherty, E. T. **and Turner, J.C., An Object-Oriented Framework for Versatile Finite Element Based Simulations of Neurostimulation.* Journal of Computational Medicine*, 2016: 9826596

**Dougherty, E. T., **Efficient Implicit Runge-Kutta Methods for Fast-Responding Ligand-Gated Neuroreceptor Kinetic Models. *BIOMATH*, 4(2015): 1512311

**2015**

**2015****Warnapala, Y.**, Dinh, H. and Resh, J., The Modified Galerkin Method for Solving the Helmholtz Equation for Low Frequencies on Planet Mars. *Asian Journal of Fuzzy and Applied Mathematics*, Vol 3 - Issue 4 - August 2015

**2014**

**2014****Warnapala, Y.** and Dinh, H., The Modified Galerkin Method for the Modified Wave Equation for the Shape of Superellipsoid. *British Journal of Mathematics and Computer Science*, 4(18), 2676-2685

**2013**

**2013****Warnapala, Y.** and Dinh, H., The Numerical Solution of the Helmholtz's Equation for the Superellipsoid via the Galerkin Mathod for the Dirichlet Problem. *Communications in Numerical Analysis, pp: 1-12 *

**Warnapala, Y.**, The Numerical Solution of the Radiosity's Equation via the Galerkin Method: Dirichlet Problem. *Journal of Numerical Methods and Applications Vol. 10, No. 2, pp: 73-89 *

**Ozer, K. ,** Neubrander F. and Sandmaier T., Rational Approximation of Semigroups without Scaling. *Discrete and Continuous Dynamical Systems*, 33(11/12), pp 5305-5317

**2012**

**2012****Ozer, K.**, Jara, P. and Neubrander F., Rational Inversion of the Laplace Transform. *Journal of Evolution Equations*, 12(2), pp 435-457

**2011**

**2011****Warnapala, Y.**, Pleskunas, J. and Siegel, R., The Numerical Solution of the Exterior Boundary Value Problems for the Helmholtz's Equation for the Pseudosphere. *IAENG International Journal of Applied Mathematics 41(2): 106-111*

**Warnapala, Y**., and Silva, K., Z score demystified: a critical analysis of the Sri Lankan university admission policy. *Journal of Case Studies in Education*, Feb 2011

**2009**

**2009****Burdick, B.**, Mathematical Works Printed in the Americas, 1554-1700. *Johns Hopkins University Press*, Baltimore, January 2009

**Burdick, B.** and Sandifer, E., Fooling with an Euler Series. *International Journal of Mathematics and Computer Science. Vol. 4, No. 1, 2009, pp. 37-42*

**Warnapala, Y.** and Yehiya, Z., Polarization of the Sri Lankan Polity: An Analysis of Presidential Elections (1982-2005). *Proceedings of Intellectbase International Consortium Vol:6*

**2008**

**2008****Warnapala, Y.** and Morgan E., The Numerical Solution of the Exterior Dirichlet Problem for the Helmholtz's Equation via Modified Green's functions approach for the Oval of Cassini. *Far East Journal Of Applied Mathematics, 34:1-20*

*Anderson, D. and Warnapala, Y., Tests of Significance and Effect Size: Meaningful Interpretation of Statistical Data in the Health Sciences. (2008) Essays in Education 23: 142-158 *

**2006**

**2006****Kelly, A**., One-pile misère Nim for three or more players. (2006) *Int. J. Math. and Math. Sci. 2006:1-8*

**2005**

**2005****Kelly, A**., and Kelly, B., eds. The Nature of Mathematics, 2nd ed. (2005) *Pearson Custom Publishing*.

**Warnapala-Yehiya, Y**., The numerical solution of exterior Robin problem for the Helmholtz's equation via modified integral equation approach. (2005) *Far East J. Appl. Math. 21:65-92*

**Warnapala-Yehiya, Y**., and Yehiya, Z., Minority Electoral Politics: A Sri Lankan Case Study. (2005) *J. Asian and African Studies 40:439-462*

**2004**

**2004***Lin, T-C. and Warnapala-Yehiya, Y., The numerical solution of exterior Neumann problem for Helmholtz's equation via modified Green's functions approach. (2004) Computers & Math. w. Applic. 47: 4-5, pp: 593-609 *

**2003**

**2003****Burdick, B**., On the Use of Partial Orders in Uniform Spaces. (2003) *Applied General Topology 4:91-114*

**Kelly, A**., and Kelly, B., On vector-valued Hardy martingales and a generalized Jensen's inequality. (2003) *Int. J. Math. and Math. Sci. 2003:527-532*

**2002**

**2002***Lin, T-C. and Warnapala-Yehiya, Y., The numerical solution of exterior Neumann problem for Helmholtz's equation via modified Green's functions approach. (2004) Computers & Math. w. Applic. 44: 8-9, pp: 1229-1248 *

*Faculty Problems & Solutions*

*Faculty Problems & Solutions***2013**

**2013****Burdick, B**., Problem 11585, featured in the “Problems and Solutions” column in* The American Mathematical Monthly*, June-July, 2011, p. 558. Solution appeared as “Convolution of Zeta Functions,” *The American Mathematical Monthly*, October, 2013, pp. 757-758. - View problem View solution

**2012**

**2012****Burdick, B**., Problem 11505, featured in the “Problems and Solutions” column in* The American Mathematical Monthly*, May, 2010, p. 458. A composite solution by Roberto Tauraso, Rituraj Nandan, and this author appeared as “Computing Pi from Fibonacci Numbers,” *The American Mathematical Monthly*, April, 2012, pp. 350-351. View problem View solution

**2020**

**Joint Mathematics Meeting (JMM)**

January 15 - 18 Denver, CO

**Joint Mathematics Meeting (JMM)**

January 15 - 18 Denver, COJanuary 15 - 18 Denver, CO

**Matthew D'Amico (Applied Mathematics '20)****"Modified Gakerkin Method for the Wiener-Hopf Integral Equation for a Semi-Inverted Cassini"**

**Emma Dehetre (Engineering/Applied Mathematics '22)****"Social Determinants of Health: Case Study of 10 U.S. States"**

**Lance Dengelegi (Applied Mathematics '20)****"Characterizations of string stability with applications to automobile platoons"**

**Cole Foster **(Engineering/Applied Mathematics '20)**"Detecting Underwater Objects through Scattering Theory; the Wiener-Hopf Integral Equation"**

**Jess Messina (Applied Mathematics '20)****"Developing Stocks Volatility Prediction Model Using Neural Networks"**

**Abigail Small **(Applied Mathematics/Computer Science '20)**"A Mathematical Approach to Assessing tDCS Efficacy for Post-traumatic Stress Disorder"**

**2019**

**International Engineering in Medicine and Biology Society Conference**

July 23 - 27 Berlin, Germany

July 23 - 27 Berlin, Germany

**Abigail Small **(Applied Mathematics/Biology '20)**"Mathematical Modeling of Neurostimulation for PostTraumatic Stress Disorder: A Migration towards Multiscale Modeling to Assess Neural Response to Transcranial Direct Current Stimulation Treatments"**

**Engineering in Medicine and Biology Society Conference on Neural Engineering (NER)**

March 20 - 23, San Francisco, CA

March 20 - 23, San Francisco, CA

** Kaia Lindberg (BS Mathematics '19)****"****A Computer Based Approach for Modeling the Efficacy of Neurostimulation Therapies on Neural Functioning****"**

**Joint Mathematics Meeting (JMM)**

January 18 - 21 Baltimore, MD

**Joint Mathematics Meeting (JMM)**

January 18 - 21 Baltimore, MDJanuary 18 - 21 Baltimore, MD

**Cole Foster **(Engineering/Applied Mathematics '20)

"Wiener-Hopf Integral Equation Model:Uderwater Aplications"

**Elizabeth Gilchrist** (Biology/Applied Mathematics '19)

"A Computational Approach for Constructing an Intracellular Signaling Pathway Mathematical Model with Applications to Parkinson's Disease"

**Kaia Lindberg** (Mathematics '19)

"Investigating Cellular-Level Effects of Neurostimulation Therapies with a Partial Differential Equation Based Mathematical Model"

**Matthew Rose** (Engineering/Applied Mathematics '19)

"Characterizations of string stability of interconnected automobile systems"

**Tyler Simmons** (Applied Mathematics/Marine Biology '19)

"How Healthy is Rhode Island: Life Satisfaction and Risk Prevention Models"

**Abigail Small **(Applied Mathematics/Biology '20)

"A Mathematical Approach for Assessing tDCS Efficacy for Post-Traumatic Stress Disorder"

**2018**

**2018****Joint Mathematics Meeing (JMM)**

January 10 - 13 San Diego, CA

**Joint Mathematics Meeing (JMM)**

January 10 - 13 San Diego, CAJanuary 10 - 13 San Diego, CA

**Kaia Lindberg** (Mathematics '19)

"Computational Simulation of a Partial Differential Equation Based Model of Electrostatic Forces on Neuronal Electrodynamics"

**Kangji Chen** (Biology/Applied Mathematics '18)

"Evolution of microRNA diversity and regulation: Statistical Modeling"

**Andrew DelSanto** (Engineering/Applied Mathematics '18)

"Time-Independent Solution of the Poisson-Nerst-Planck System of Equations for Neurological Applications"

**Madison Guitard** (Engineering/Applied Mathematics '20)

"An Interdisciplinary Approach to Computational Neurostimulation"

**Hien Ngo** (Applied Mathematics/Biology '18)

"Radiosity Equation Model for an Interior Space Illumination Design; Mars Project"

**Abigail Small **(Applied Mathematics/Biology '20)

"Quantifying Electromagnetic Properties of Applied Electric Fields on Neural Tissues"

**2017**

**2017****Northeast Regional IDeA Conference (NERIC) **

August 16 – 18 Burlington, VT

**Northeast Regional IDeA Conference (NERIC)**

August 16 – 18 Burlington, VTAugust 16 – 18 Burlington, VT

**Kaia Lindberg** (Mathematics ‘19) and **Abigail Small** (Applied Mathematics ’20)

“A Mathematical Model of the Effects of Neurostimulation Treatment on Neuronal Electrodynamics”

**Elizabeth Gilchrist **(Biology/Applied Mathematics ’19)

“A Computational Approach to Modeling Dopaminergic Neurons with Application to Parkinson’s Disease”

**Summer Undergraduate Research Fellowship Conference (SURF)**

July 28 – URI, Rhode Island

**Summer Undergraduate Research Fellowship Conference (SURF)**

July 28 – URI, Rhode IslandJuly 28 – URI, Rhode Island

**Kaia Lindberg** (Mathematics ‘19) and **Abigail Small** (Applied Mathematics/Biology ’20)

“A Mathematical Model of the Effects of Neurostimulation Treatment on Neuronal Electrodynamics”

**Elizabeth Gilchrist **(Biology/Applied Mathematics ’19)

“A Computational Approach to Modeling Dopaminergic Neurons with Application to Parkinson’s Disease”

**Biology and Medicine Through Mathematics Conference (BAMM)**

May 18 – 20 VCU, Virginia

**Biology and Medicine Through Mathematics Conference (BAMM)**

May 18 – 20 VCU, VirginiaMay 18 – 20 VCU, Virginia

**Madison Guitard** (Engineering/Applied Mathematics ’20)

“An Interdisciplinary Approach to Computational Neurostimulation”

**Women’s Intellectual Network Research Symposium**

March 4 Brown University, Rhode Island

**Women’s Intellectual Network Research Symposium**

March 4 Brown University, Rhode IslandMarch 4 Brown University, Rhode Island

**Madison Guitard** (Engineering/Applied Mathematics ’20)

“An Interdisciplinary Approach to Computational Neurostimulation”

**Amanda Becotte** (Mathematics ’17), **Ashley Crane **(Mathematics ’17), **Alexandra Halligan **(Mathematics ’17)

“A Mathematical Model for the Effects of Fertilization on Nitrogen Concentrations in Unsaturated Soil on Blueberry Farms”

**Joint Mathematics Meeting (JMM)**

January 4 – 7 Atlanta, Georgia

**Joint Mathematics Meeting (JMM)**

January 4 – 7 Atlanta, GeorgiaJanuary 4 – 7 Atlanta, Georgia

**Hien Ngo** (Applied Mathematics/Biology ’18)

“Numerical Solutions of the Radiosity Equation (Brightness) via the Galerkin Method: Mars Project”

**Qiuyang Deng** (Applied Mathematics ’17)

“Numerical Solutions of the Radiosity Equation by the Galerkin Method for the Spherical Pyramid (Mars Project)”

**2016**

**2016****Joint Mathematics Meeting (JMM)**

January 6 – 9 Seattle, Washington

**Joint Mathematics Meeting (JMM)**

January 6 – 9 Seattle, WashingtonJanuary 6 – 9 Seattle, Washington

**Jill Resh **(Applied Mathematics/Graphic Design Communications ’16)

“The Numerical Solutions of the Helmholtz Equation for the Bloodcell Shape: Mars Project”

*2020*

*2020*

Roger Williams University Provost Fund for Student Research and the *AMS Student Travel Grant****Matthew D'Amico
Emma Dehetre
Lance Dengelegi
Cole Foster
Jess Messina
Abigail Small**

*Joint Mathematics Meeting MAA Outstanding Poster Award in Numerical Analysis****Cole Foster**

*Joint Mathematics Meeting MAA Outstanding Poster Award in Bioinformatics****Abigail Small**

*Joint Mathematics Meeting MAA Honorable Mention Poster Award in Statistics****Emma Dehetre**

*Joint Mathematics Meeting MAA Honorable Mention Poster Award in Applied Mathematics****Lance Dengelegi**

*2019*

*2019*

Roger Williams University Provost Fund for Student Research**Cole Foster****Elizabeth Gilchrist****Kaia Lindberg****Matthew Rose****Tyler Simmons****Abigail Small**

*Joint Mathematics Meeting MAA Outstanding Poster Award in Applied Mathematics****Cole Foster****Matthew Rose**

*Joint Mathematics Meeting MAA Outstanding Poster Award in Biomathematics****Elizabeth Gilchrist****Abigail Small**

**2018**

**2018**

*Joint Mathematics Meeting MAA Outstanding Poster Award in Numerical Analysis****Hien Ngo**

Roger Williams University Provost Fund for Student Research**Kangji Chen****Andrew DelSanto****Madison Guitard****Kaia Lindberg****Hien Ngo****Abigail Small**

*MAA Student Travel Grant****Kangji Chen****Andrew DelSanto****Madison Guitard****Kaia Lindberg****Hien Ngo****Abigail Small**

Jane Pleskunas Fund**Andrew DelSanto**

**2017**

**2017**

**Qiuyang Deng**

Jane Pleskunas Fund

President's Core Value Medallion for the MNS Division

Outstanding Senior Award in Undergraduate Mathematics Research

Outstanding Senior Award in Applied Mathematics

**Hien Ngo **

Mark Gould Memorial Scholarship and Research Fund*STILAS**

**Abigail Small**

Jane Pleskunas Fund

**2016**

**2016**

**Qiuyang Deng**

Roger Williams University Provost Fund for Student Research

**Hien Ngo**

Roger Williams University Provost Fund for Student Research*MAA Student Travel Grant*
NASA Rhode Island Space Grant*
STILAS**

**Jill Resh**

Roger Williams University Provost Fund for Student Research

Outstanding Senior Award in Undergraduate Mathematics Research

Outstanding Senior Award in Applied Mathematics*NASA Rhode Island Space Grant*
MAA Student Travel Grant*
NSF Research Experience for Undergraduates (REU) at UCONN**

**2015**

**2015**

**Hy K. Dinh**

Outstanding Senior Award in Undergraduate Mathematics Research

Outstanding Senior Award in Mathematics

President's Core Value Medallion for the MNS Division*MAA Student Travel Grant**

**Awards in italics are from external organizations.*

**Summer 2018**

**Summer 2018**

**Madison Guitard** (Engineering/Applied Mathematics '20)

Madison is in Hong Kong working for *lululemon*, a growing athletic wear company. She is in the business solutions and costing engineering department.

**Cole Foster** (BS Engineering/Applied Mathematics '20)

Cole is doing mechanical engineering work at NUWC in Newport, RI.

**Hien Ngo** (BS Applied Mathematics/Biology '18)

Hien is a Teaching Artist for Providence CityArts for Youth under AmeriCorps.