Current seminar We have no seminars on Tuesdays when Department meetings are scheduled or during holidays.
All seminars
Shock and rarefaction waves of a subsystem of an Euler system
Speaker: Seunghoon Bang
Date: Wednesday, October 10
Time: 5:00 p.m.
Location: Robinson 419
Abstract: The existence of a solution of the Cauchy problem in a two dimensional compressible Euler system is open. It is difficult to solve the system. Thus, we consider the Rieman Problem in the system. It is also difficult. How can we approach and resolve this difficulty? We study a simpler subsystem of the system and apply the result and methods to the original problem.
According to the initial values in four quadrants, we have 12 main configurations such as interaction of four rarefaction waves, four shocks, four contact discontinuities, two shocks and two rarefaction waves and so on. In this talk, I talk about the some concepts of shock and rerefaction waves from conservation laws, how to solve the one configuration, the interaction of four rarefaction waves.
Prescribing Gauss-Kronecker Curvature
Speaker: Richard Mikula
Date: Wednesday, October 17
Time: 5:00 p.m.
Location: Robinson 419
Abstract: We will examine the problem of prescribing Gauss-Kronecker curvature for convex hypersurfaces in Euclidean space using partial differentiation techniques. In doing this, we will review/introduce the notion of Gauss Curvature and Mean Curvature from differential geometry (using only some ideas from multivariable calculus and linear algebra) as well as the notion of a hypersurface in Euclidean space. We will then discuss some historically relevant problems of prescribing curvature such as the plateau problem. We then examine the modern approaches to this problem which use techniques from Elliptic Partial Differential Equations.
Inverse Problem and Iterative Regularization
Speaker: Muhammad Aslam
Date: Wednesday, October 24
Time: 5:00 p.m.
Location: Robinson 419
Abstract: We present an inverse problem and its solution via iterative regularization in the context of image processing. We will introduce our approach to the problem after some discussion of the recently developed iterative regularization methods for solving this problem. Some of the applications of our method will also be presented especially in image compression and image noise removal.
Finding a Hamilton Circuit
Speaker: Rachael K. Partain
Date: Wednesday, November 14
Time: 5:00 p.m.
Location: Robinson 419
Abstract: There are several algorithms to find the Euler's circuit for a connected graph and the simplest of them is Fleury's Algorithm. Unfortunately, there does not exist a counterpart of Fleury's Algorithm to find the Hamilton Circuit. In this talk, we present an approach to decide whether a given graph has a Hamilton circuit or not and whether the graph has a Hamilton circuit as well as how to find it. Our approach may lead to some interesting counterpart of Fleury's Algorithm for Hamilton circuits.
Functionals on continuous functions (or Different ways to view the integral)
Speaker: Antonia Cardwell (Millersville University of Pennsylvania)
Date: Thursday, November 15
Time: 1:00 p.m.
Location: Robinson 408
Abstract: The scalar-valued linear mappings on the space of continuous functions can be viewed as integrals with respect to different Borel measures. I will give an introduction to the basic ideas of measure of a subset of the real line and integrating with respect to that measure, and also talk about when these integrals can attain their norm (or maximum value on the norm-one functions.) Bishop and Phelps proved (non-constructively) that every functional can be approximated by a norm-attaining functional. I will give an outline of a constructive proof of this result.
