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Mathematical and computational modeling of fluid flow with applications in ophthalmology and geoscience
(University of Missouri--Columbia, 2020)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Complex systems in our life can be translated to mathematical models whose solutions can help us to predict the behavior of the system. Disease in eye and internal erosion...
Linear and multilinear spherical maximal functions
(University of Missouri--Columbia, 2020)
In dimensions n [greater than or equal to] 2 we obtain Lp1(Rn) x...x Lpm(Rn) to Lp(Rn) boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples ...
Stochastic forms of functional isoperimetric inequalities
(University of Missouri--Columbia, 2021)
The Brunn-Minkowski and Prekopa-Leindler inequalities admit a variety of proofs that are inspired by convexity. Nevertheless, the former holds for compact sets and the latter for integrable functions, so it seems that ...
Partial connections and contact instantons on contact manifolds
(University of Missouri--Columbia, 2022)
We study partial connections that are defined on a vector bundle E over a contact distribution H of a contact manifold (M2m+1; [zero with middle tilde]) by adapting the Rumin complex of the exterior derivative in a contact ...
Frames with desired angle properties
(University of Missouri--Columbia, 2020)
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The purpose of this dissertation is to study frames with desired angle properties. More precisely, we study the subspace packing problem, harmonic ...
Global bifurcation and stability of solitary waves in two-layer water
(University of Missouri--Columbia, 2022)
The present work concerns two mathematical problems on wave in a stratified body of water governed by the incompressible Euler equations. In the first part, we present a large-amplitude existence theory for two-dimensional solitary waves by means...
A Quiver Invariant theoretic approach to radial isotropy and the Paulsen problem for matrix frames
(University of Missouri--Columbia, 2022)
In this dissertation, we view matrix frames as representations of quivers and study them within the general framework of Quiver Invariant Theory. We are particularly interested in radial isotropic and Parseval matrix frames. ...
Structural features of persistent homology and their algorithmic transformations
(University of Missouri--Columbia, 2021)
We re-examine the theory and orthodox methods that underlie the study of persistent homology, particularly in its calculation of homological cycle representatives that are associated to persistence diagrams. A common ...
Critical perturbations of elliptic operators by lower order terms
(University of Missouri--Columbia, 2021)
suggest a wider range of applications for these techniques. The results contained in this thesis were obtained in collaboration with Simon Bortz, Steve Hofmann, Svitlana Mayboroda, and Bruno Poggi. The resulting publications can be found in [BHL...