A Newsletter for UMW Faculty and Staff
Professor of Mathematics Leo Lee
Professor of Mathematics Leo Lee saw the recent publication of his paper “A Domain Decomposition Algorithm for Optimal Control Problems Governed by Elliptic PDEs with Random Inputs” in the Journal of the Applied Mathematics and Computation.
Associate Professor of Mathematics Leo Lee
An article in The Free Lance-Star, “Fredericksburg-area health officials say ‘worst is probably still ahead of us’,” mentioned the contributions of Associate Professor of Mathematics Leo Lee, who is working with Dr. Donald Stern, acting director of Rappahannock Area Health District, to develop charts that show “the true number of new cases” locally. Health experts in Virginia have said we still have yet to see the peak and are projecting even higher numbers of diagnoses in the coming weeks. Read more.
A research article “Analytical Solutions of the Susceptible-Infected-Virus (SIV) Model” by Emily MacIndoe (’19) has been published in SIAM Undergraduate Research Online Journal. McIndoe’s research was completed as part of her honors requirement in the spring of 2019, and she was advised by Associate Professor of Mathematics Jangwoon “Leo” Lee. “It is highly unusual for a student to publish a paper in mathematics,” said College of Arts and Sciences Dean Keith Mellinger, who praised MacIndoe’s work and wished her “a hearty congratulations.” McIndoe’s paper is accessible through the following link on the Society for Industrial and Applied Mathematics website: https://www.siam.org/Publications/SIURO/Volume-12.
Abstract: The Susceptible-Infected-Virus (SIV) model is a compartmental model to describe within-host dynamics of a viral infection. We apply the SIV model to the human immunodeficiency virus (HIV); in particular, we present analytical solutions to two versions of the model. The first version includes only terms related to the susceptible cell-virus particle interaction and virus production, while the second includes those terms in addition to the infected cell death rate. An analytical solution, although more challenging and time-consuming than numerical methods, has the advantage of giving exact, rather than approximate, results. These results contribute to our understanding of virus dynamics and could be used to develop better treatment options. The approach used to solve each model involved first isolating one of the dependent variables, that is, deriving an equation that involves only one of the variables and its derivatives. Next, various substitutions were used to bring the equation to a more easily solvable form. For the first model, an exact solution is obtained in the form of an implicit equation. For the second model, we give an analytical solution generated by an iterative method.
Eight members of the Department of Mathematics presented at the annual Joint Mathematics Meetings in Atlanta in January. The JMM is the largest mathematics conference in the country, with registrations this year exceeding 6,000 participants. Highlights of the meeting include:
Associate Professor of Mathematics Leo Lee saw the recent publication of his paper “The h x p Finite Element Method for Optimal Control Problems Constrained by Stochastic Elliptic PDEs” in the Journal of the Korean Society for Industrial and Applied Mathematics. Dr. Lee presented a talk on the results of this article at the Joint Mathematics Meetings in Seattle in January.
During his semester sabbatical leave, Associate Professor of Mathematics Leo Lee has served as visiting professor at Sogang University in Seoul, Korea, teaching courses in computational and applied mathematics for both undergraduate and graduate students. Dr. Lee has also given several research talks on stochastic partial differential equations at Yonsei University and Sogang University and recently published the paper “An Optimization Based Domain Decomposition Method for PDEs with Random Inputs” in the journal Computers & Mathematics with Applications. In addition, Dr. Lee has served as the symposium chair for mathematics and statistics for the US-Korea Conference 2015.
Professor Jangwoon “Leo” Lee presented his latest research at the annual Joint Mathematics Meetings in January, held this year in Baltimore. Dr. Lee’s talk was titled “An Optimization Based Domain Decomposition Method for PDEs with Random Inputs.”
In January three mathematics majors presented their research at the annual AMS-MAA Joint Mathematics Meetings in Baltimore, Md., which is the largest mathematics conference in the world. Kim Hildebrand presented “Using Independent Bernoulli Random Variables to Model Gender Hiring Practices” (advisor: Dr. Debra Hydorn), Casey Howren presented “A Numerical Analysis of the SIR Model for Modeling Epidemics” (advisor: Dr. Leo Lee), and Dane Lawhorne presented “The Fundamental Groups of the Digital Line and Circles” (advisor: Dr. Randall Helmstutler). The students presented as part of the MAA’s undergraduate student poster session, and Dane Lawhorne was given special recognition as an outstanding presenter in the session.
Assistant Professor of Mathematics, Jangwoon “Leo” Lee, recently presented “Domain Decomposition Methods for Solving Stochastic PDEs” at the annual US-Korea Conference (UKC 2013) in New Jersey. In addition to attending many research talks at the conference, Dr. Lee chaired an applied mathematics session.