Browsing Mathematics electronic theses and dissertations (MU) by Thesis Semester "2021 Spring"
Now showing items 1-4 of 4
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Critical perturbations of elliptic operators by lower order terms
(University of Missouri--Columbia, 2021)In this work we study issues of existence and uniqueness of solutions of certain boundary value problems for elliptic equations in the upper half-space. More specifically we treat the Dirichlet, Neumann, and Regularity ... -
Entropy minimization, convergence, and Gibbs ensembles (local and global)
(University of Missouri--Columbia, 2021)We approach the subject of Statistical Mechanics from two different perspectives. In Part I we adopt the approach of Lanford and Martin-Lof. We examine the minimization of information entropy for measures on the phase space ... -
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 ... -
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 ...