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- Academic -- UNF -- Master of Arts in Mathematics and Statistics; Dissertations (1)
- Academic -- UNF -- Master of Science in Mathematical Science; Dissertations (1)
- Academic -- UNF -- Mathematic and Statistics; Lie algebras (1)
- Academic -- UNF -- Mathematics; Harmonic Morphisms (1)
- Differential Equations (1)
Articles 1 - 2 of 2
Full-Text Articles in Algebraic Geometry
Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin
Harmonic Morphisms With One-Dimensional Fibres And Milnor Fibrations, Murphy Griffin
UNF Graduate Theses and Dissertations
We study a problem at the intersection of harmonic morphisms and real analytic Milnor fibrations. Baird and Ou establish that a harmonic morphism from G: \mathbb{R}^m \setminus V_G \rightarrow \mathbb{R}^n\setminus \{0\} defined by homogeneous polynomials of order p retracts to a harmonic morphism \psi|: S^{m-1} \setminus K_\epsilon \rightarrow S^{n-1} that induces a Milnor fibration over the sphere. In seeking to relax the homogeneity assumption on the map G, we determine that the only harmonic morphism $\varphi: \mathbb{R}^m \setminus V_G \rightarrow S^{m-1}\K_\epsilon$ that preserves \arg G is radial projection. Due to this limitation, we confirm Baird and Ou's result, yet establish …
On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster
On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster
UNF Graduate Theses and Dissertations
In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .