Global ETD Search

21	Singular Value Inequalities: New Approaches to Conjectures Chilstrom, Peter 01 January 2013 (has links) Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular value inequalities, and also look at existing conjectures. Thesis University of North Florida UNF math mathematics singular values linear algebra Algebra Analysis
22	Comparing Group Means When Nonresponse Rates Differ Stegmann, Gabriela M 01 January 2015 (has links) Missing data bias results if adjustments are not made accordingly. This thesis addresses this issue by exploring a scenario where data is missing at random depending on a covariate x. Four methods for comparing groups while adjusting for missingness are explored by conducting simulations: independent samples t-test with predicted mean stratification, independent samples t-test with response propensity stratification, independent samples t-test with response propensity weighting, and an analysis of covariance. Results show that independent samples t-test with response propensity weighting and analysis of covariance can appropriately adjust for bias. ANCOVA is the stronger method when the ANCOVA assumptions are met. When the ANCOVA assumptions are not met, a t-test with inverse response propensity score weighting is the superior method. Thesis University of North Florida UNF Dissertations Dissertations Academic -- UNF -- Mathematics Physical Sciences and Mathematics Statistical Methodology Statistics and Probability
23	Matrix Singular Value Decomposition Kwizera, Petero 01 January 2010 (has links) This thesis starts with the fundamentals of matrix theory and ends with applications of the matrix singular value decomposition (SVD). The background matrix theory coverage includes unitary and Hermitian matrices, and matrix norms and how they relate to matrix SVD. The matrix condition number is discussed in relationship to the solution of linear equations. Some inequalities based on the trace of a matrix, polar matrix decomposition, unitaries and partial isometies are discussed. Among the SVD applications discussed are the method of least squares and image compression. Expansion of a matrix as a linear combination of rank one partial isometries is applied to image compression by using reduced rank matrix approximations to represent greyscale images. MATLAB results for approximations of JPEG and .bmp images are presented. The results indicate that images can be represented with reasonable resolution using low rank matrix SVD approximations. Thesis University of North Florida UNF Applied Mathematics Numerical Analysis and Computation
24	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
25	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
26	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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