In this thesis, we examined some Dirichlet type problems of the form: \begin{eqnarray*} \triangle u & = & 0\ {\rm in\ } \mathbb{R}^n \\ u & = & f\ {\rm on\ } \psi = 0, \end{eqnarray*} and we were particularly ...

Throughout recent years, polymers have been one of the most widely used materials in industry due to their suitability to a vast variety of fields from construction to biomedical and technological utilities. Their extensive ...

Using theoretical models, we undertake the first investigation into the rich behavior that emerges when binary particle mixtures are blended with microphase-separating copolymers. We isolate an example of coupled self-assembly ...

We present results obtained in the context of generative neural models — specifically autoencoders — utilizing standard results from coding theory. The methods are fairly elementary in principle, yet, combined with the ...

High-intensity focused ultrasound is a promising non-invasive medical technology that has been successfully used to ablate tumors, as well as in the treatment of other conditions. Researchers believe high-intensity focused ...

This thesis investigates the problem of enumerating the extensions of certain matroids. A matroid M is an extension of a matroid N if M delete e is equal to N for some element e of M. Similarly, a matroid M is a coextension ...

The character theory of the symmetric group is a powerful method of studying enu- merative questions about factorizations of permutations, which arise in areas including topology, geometry, and mathematical physics. This ...

The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ...

Agricultural production will be challenged in the near future to keep up with the rising nutritional demands of a growing global population. Additionally, climate change, through increased frequency of extreme weather ...