Capstone Projects
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Existence of Solution to an Optimal Control Problem for the Heat Equation
Consider the nonhomogeneous heat equation with Neumann and Robin boundary conditions: (See Poster for the equations (1)(4)). The problem (1)(4) is well posed for sufficiently well behaved data, but what if some of the ... 
Computing the Elementary Symmetric Polynomials of the Multiplier Spectra of z^2 + c
This project investigates a family of polynomials that occur in the field of arithmetic dynamics. These polynomials correspond to quadratic rational maps and are difficult to compute in general. We focused on the subfamily ... 
Applications of Random Matrices to Image Processing for Image Denoising
Random matrices were first introduced in studies related to mathematical statistics by Wishart, Hsu. Later, Dyson recognized that would be required a new type of statistical mechanics to describe the nuclear energy levels ... 
Computer Simulations of FluidStructure Interactions
(i) FlowStructure interactions are everywhere (ii) The problem is difficult to simulate because of the dynamical boundary conditions and coupling (iii) The boundary conditions are complex because of its curved shape, ... 
InitialBoundary Value Problems for Higher Order Linear PDEs with Three Independent Variables
Initialboundary value problems for higher order linear hyperbolic equations with two independent variables were studied in [1] and [2], where necessary and sufficient conditions of solvability and unique solvability of ...