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11	Transitions in Line Bitangency Submanifolds for a One-Parameter Family of Immersion Pairs Olsen, William Edward 01 January 2014 (has links) Consider two immersed surfaces M and N. A pair of points (p,q) in M x N is called a line bitangency if there is a common tangent line between them. Furthermore, we define the line bitangency submanifold as the union of all such pairs of points in M x N. In this thesis we investigate the dynamics of the line bitangency submanifold in a one-parameter family of immersion pairs. We do so by translating one of the surfaces and studying the wide range of transitions the submanifold may undertake. We then characterize these transitions by the local geometry of each surface and provide examples of each transition. Thesis University of North Florida UNF Dissertations Dissertations Academic -- UNF -- Mathematics Geometry and Topology Mathematics Physical Sciences and Mathematics
12	Self-Assembly of DNA Graphs and Postman Tours Bakewell, Katie 01 January 2018 (has links) DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and the Windy Postman Problem. Thesis University of North Florida UNF Thickened graphs Boundary components Windy Postman Problem Reporter strands DNA computing Discrete Mathematics and Combinatorics Geometry and Topology Other Mathematics
13	A Study of Nonlinear Dynamics in Mathematical Biology Ferrara, Joseph 01 January 2013 (has links) We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically. Thesis University of North Florida UNF mathematical biology dynamical systems ordinary differential equations ODE ODEs bifurcation analysis tumor growth model nonlinear systems Dynamic Systems

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