Critical points of discrete potentials in the plane and in space
This thesis looks at various problems relating to the value distribution of certain discrete potentials. Chapter 1 - Background material is introduced, the motivation behind this work is explained, and existing results in the area are presented. Chapter 2 - By using a method based on a result of Car...
| Main Author: | |
|---|---|
| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2008
|
| Online Access: | https://eprints.nottingham.ac.uk/14362/ |
| _version_ | 1848791941697765376 |
|---|---|
| author | Trickey, Robert V. |
| author_facet | Trickey, Robert V. |
| author_sort | Trickey, Robert V. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | This thesis looks at various problems relating to the value distribution of certain discrete potentials.
Chapter 1 - Background material is introduced, the motivation behind this work is explained, and existing results in the area are presented.
Chapter 2 - By using a method based on a result of Cartan, the existence of zeros is shown for potentials in both the complex plane and real space.
Chapter 3 - Using an argument of Hayman, we expand on an established result concerning these potentials in the complex plane. We also look at the consequences of a spacing of the poles.
Chapter 4 - We extend the potentials in the complex plane to a generalised form, and establish some value distribution results.
Chapter 5 - We examine the derivative of the basic potentials, and explore the assumption that it takes the value zero only finitely often.
Chapter 6 - We look at a new potential in real space which has advantages over the previously examined ones. These advantages are explained.
Appendix - The results of computer simulations relating to these problems are presented here, along with the programs used. |
| first_indexed | 2025-11-14T18:36:31Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-14362 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:36:31Z |
| publishDate | 2008 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-143622025-02-28T11:30:21Z https://eprints.nottingham.ac.uk/14362/ Critical points of discrete potentials in the plane and in space Trickey, Robert V. This thesis looks at various problems relating to the value distribution of certain discrete potentials. Chapter 1 - Background material is introduced, the motivation behind this work is explained, and existing results in the area are presented. Chapter 2 - By using a method based on a result of Cartan, the existence of zeros is shown for potentials in both the complex plane and real space. Chapter 3 - Using an argument of Hayman, we expand on an established result concerning these potentials in the complex plane. We also look at the consequences of a spacing of the poles. Chapter 4 - We extend the potentials in the complex plane to a generalised form, and establish some value distribution results. Chapter 5 - We examine the derivative of the basic potentials, and explore the assumption that it takes the value zero only finitely often. Chapter 6 - We look at a new potential in real space which has advantages over the previously examined ones. These advantages are explained. Appendix - The results of computer simulations relating to these problems are presented here, along with the programs used. 2008-07-10 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/14362/1/ThesisMain_Trickey.pdf Trickey, Robert V. (2008) Critical points of discrete potentials in the plane and in space. PhD thesis, University of Nottingham. |
| spellingShingle | Trickey, Robert V. Critical points of discrete potentials in the plane and in space |
| title | Critical points of discrete potentials in the plane and in space |
| title_full | Critical points of discrete potentials in the plane and in space |
| title_fullStr | Critical points of discrete potentials in the plane and in space |
| title_full_unstemmed | Critical points of discrete potentials in the plane and in space |
| title_short | Critical points of discrete potentials in the plane and in space |
| title_sort | critical points of discrete potentials in the plane and in space |
| url | https://eprints.nottingham.ac.uk/14362/ |