On Monday, February 23rd at 3:30 PM in Math 357, Marcus Webb will talk about “The Freshman’s Dream.” Abstract: Let A be an m by n matrix with entries in some finite field – the integers modulo a prime p, for example. What happens to the kernel of A when we raise each entry to the p’th power? In this talk, we will answer this question and consider its generalization to matrices with entries in a commutative ring of prime characteristic. For such rings, every freshman’s dream is true: (a+b)p=ap+bp, and we will explore some of the remarkable consequences of this equality. (flyer in PDF form)
On Monday February 16th at 3:30 in Math 357, Dr. Jonathan Mitchell will be talking about “The Effect of a State-Dependent Delay on a Weakly-Damped Nonlinear Oscillator.” Abstract: We consider a weakly-damped nonlinear oscillator with state-dependent delay which has applications in models for lasers, epidemics, and micro-parasites. We begin by introducing a nonlinear oscillator stemming from the usual predator-prey system and analyzing the evolution of its energy. We will incorporate a constant time lag in the production of the predator population and show that sufficiently large delay can cause oscillations to persist via an Hopf bifurcation. We then consider a variable delay which will depend on the relative size of the prey population. Specifically, we find conditions on the functional form of the delay in which the branch of periodic solutions will be either sub- or super-critical as well as an accurate estimation of the amplitude. (flyer in PDF form)
On Monday, February 9 at 3:30 in Math Building 357, Dylan Poulsen of Baylor University will be talking about “Stability and Control of Dynamic Equations on Time Scales.” Abstract: From cruise-control systems to rocket dynamics, control theory forms a foundation for our modern society. Much of control theory relies on updates to the system occurring at uniform, predictable moments in time. As control systems become distributed over large scales or become controlled by low-speed devices, the uniformity and predictability of the time domain cannot be guaranteed. In this talk, we outline an approach to controlling linear systems on non-uniform and random time domains using a new branch of mathematics called time scales. We will derive a stability theory for this case, and then we will apply the theory in finding the optimal control policy. (Flyer in PDF form)
On Monday November 3rd at 3:30 in Math 357, Dr. Qin Shing from the Department of Mathematics and Center for Astrophysics, Space Physics and Engineering Research at Baylor University will be talking about “Numerical PDEs and the Legacy of ADI and LOD Methods”.
Abstract: Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations. They involve computational methods including the finite difference and finite element, finite volume, spectral, meshless, domain decomposition, multigrid, and in particular, splitting methods. The ADI and LOD approaches are two of them with extraordinary features in structure simplicity, computational efficiency and flexibility in applications. They look similar, but are fundamentally different. Naturally, they lead to different ways of operations, and offer different strategies in computational realizations. This talk will provide an insight into the glorious history of these numerical methods, and discuss some of their latest reinforcements including applications for highly oscillatory waves. (Flyer in PDF form)
About Dr. Qin Sheng: Dr. Sheng received his BS and MS in Mathematics from Nanjing University in 1982, 1985, respectively. Then he acquired his Ph.D. from the University of Cambridge under the supervision of Professor Arieh Iserles. After his postdoctoral research with Professor Frank T. Smith, FRS, in University College London, he joined National University of Singapore in 1990. Since then, Dr. Sheng was on faculty of several major universities till his joining Baylor University, which is one of the research institutions and the second largest private university in the United States. Dr. Sheng has been interested in splitting and adaptive numerical methods for solving linear and nonlinear partial differential equations. He is also known for the Sheng-Suzuki theorem in numerical analysis. He has published over 95 refereed journal articles as well as 6 joint research monographs. He has been an Editor-in-Chief of an SCI journal, International Journal of Computer Mathematics, published by Taylor and Francis in London since 2010. He gives invited presentations, including keynote lectures, in international conferences every year. Dr. Sheng’s projects have been supported by several U.S. research agencies. He currently advises 3 doctoral students and 1 postdoctoral research fellow. He also serves on Panelist Boards for several research agencies including the National Science Foundation, USA.
On Monday October 27th at 3:30 in Math 357, Dr. Tetyana Malysheva from the University of Oklahoma will be talking about “Modeling of Elastic Solids”. The talk will be accessible to undergraduates and grad students. Abstract: In this talk, we will consider a variational approach to the modeling and numerical analysis in linear elasticity and thermoelasticity. The presented method is based on physical principles, geometry of an object, and appropriate approximating assumptions. We will derive strong and weak formulations for the Timoshenko beam model, and discuss a finite element method for numerical solution of forward and inverse problems in linear elasticity. (Flyer in PDF form)
On Monday September 15th at 3:30 in Math 357, Dr. Matt Beauregard will be talking about “Surgical Splitting”. This talk will be interactive and interesting to all levels of students. Students with exposure to differential equations or numerical methods are especially encouraged to attend.
Abstract: Time dependent mathematical models are often written in terms of partial differential equations. The spatial derivatives can then be approximated to develop a system of first order differential equations in time. The solutions can formally be written in terms of an evolution operator. A final approximation can be formulated through approximating the underlying matrix exponential. Approximating the matrix exponential can be time-consuming, especially for high dimension problems. Is it possible to split the problem? If so, how is this influenced by forcing terms, nonlinearities, or geometric considerations? We’ll be investigating these questions with some toy problems. Students with exposure to differential equations are especially encouraged to attend! Come prepared with a few pieces of paper, pen/pencil, and water to stay hydrated as we sweat through this surgical splitting procedure. (flyer in PDF form)
On Monday April 28th at 3:30, Dr. Kalanka Jayalath will be talking about “Geometrical Pattern Identification Using a Bayesian Paradigm.”
Abstract: Identifying spatially distributed point patterns plays an important role in many scientific areas including pattern recognition, computer vision, image processing and some geological applications. Current methods of identifying conic structures depend solely on algebraic or geometric distances and are known as algebraic or geometric fits respectively. This talk focusses on a novel circle and ellipse fitting technique which elicits a Bayesian philosophy on geometric distance. Statistical methods will be discussed to investigate whether the spatial pattern is reasonably attributable to a circular or elliptical pattern. We compare classical and novel circle fitting methods under various error structures. In particular, we focus on their accuracy of estimates when in the presence of noisy data, a topic that is poorly documented in the literature. Finally, our findings will be applied to a pre-historic archeological site to identify the evident geometrical structure. (Flyer in PDF form)