Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Discrete Sparse Fourier Hermite Approximations In High Dimensions, Ashley Prater
Discrete Sparse Fourier Hermite Approximations In High Dimensions, Ashley Prater
Mathematics - Dissertations
In this dissertation, the discrete sparse Fourier Hermite approximation of a function in a specified Hilbert space of arbitrary dimension is defined, and theoretical error bounds of the numerically computed approximation are proven. Computing the Fourier Hermite approximation in high dimensions suffers from the well-known curse of dimensionality. In short, as the ambient dimension increases, the complexity of the problem grows until it is impossible to numerically compute a solution. To circumvent this difficulty, a sparse, hyperbolic cross shaped set, that takes advantage of the natural decaying nature of the Fourier Hermite coefficients, is used to serve as an index …
The Clar Structure Of Fullerenes, Elizabeth Jane Hartung
The Clar Structure Of Fullerenes, Elizabeth Jane Hartung
Mathematics - Dissertations
A fullerene is a 3-regular plane graph consisting only of pentagonal and hexagonal faces. Fullerenes are designed to model carbon molecules. The Clar number and Fries number are two parameters that are related to the stability of carbon molecules. We introduce chain decompositions, a new method to find lower bounds for the Clar and Fries numbers. In Chapter 3, we define the Clar structure for a fullerene, a less general decomposition designed to compute the Clar number for classes of fullerenes. We use these new decompositions to understand the structure of fullerenes and achieve several results. In Chapter 4, …
The Number Of Ways To Write N As A Sum Of ` Regular Figurate Numbers, Seth Jacob Rothschild
The Number Of Ways To Write N As A Sum Of ` Regular Figurate Numbers, Seth Jacob Rothschild
Honors Capstone Projects - All
See Document for Abstract