DOI

10.17077/etd.6yf0hhtk

Document Type

Dissertation

Date of Degree

Fall 2009

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Durumeric, Oguz

First Committee Member

Durumeric, Oguz

Second Committee Member

Darcy, Isabel

Third Committee Member

Randell, Richard

Fourth Committee Member

Muhly, Paul

Fifth Committee Member

Vigmostad, Sarah

Abstract

The uniform thickness of knots has been used to investigate knotted polymers and DNA strands. Even though these structures carry great length, it is unusual for them to contain knots. However, when they do, it can cause gene malfunctions. In fact, scientist have demonstrated that knotting may cause a loss of genetic material by blocking DNA replication and also blocking transcription of a gene into its active protein.

Since it is possible for biological structures, such as polymers and DNA strands, to exhibit forces or charges of different strengths the idea of a non uniform thickness of a knot is explored. In his work, O. Durumeric provides a definition for the non uniform thickness. This thesis will provide an alternative characterization for the non uniform thickness of a knot, which is more conducive to computer calculations.

Keywords

Knot, Non-Uniform, Theory, Thickness, Topology

Pages

vii, 58 pages

Bibliography

Includes bibliographical references (page 58).

Copyright

Copyright 2009 Kimberly Jean Huerter

Included in

Mathematics Commons

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