Critical points of discrete potentials in the plane and in space

Trickey, Robert V. (2008) Critical points of discrete potentials in the plane and in space. PhD thesis, University of Nottingham.

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Abstract

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.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Langley, J.K.
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 14362
Depositing User: EP, Services
Date Deposited: 25 Jun 2014 09:21
Last Modified: 14 Sep 2016 09:01
URI: http://eprints.nottingham.ac.uk/id/eprint/14362

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