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Four function space topologies

Creator:

Winter, Lynn Taylor

Abstract:

This paper defines four function space topologies, characterizes two of them in terms of more familiar concepts, and compares the four topologies. Then in the cases of the two less familiar topologies we have considered several common properties of topological spaces and attempted to answer the following question: If the...

Resource Type:

Masters Thesis
Computer techniques yielding automatic and rigorous solutions to linear and nonlinear integral equations

Creator:

Winter, Lynn Taylor

Abstract:

Interval arithmetic is applied to the problem of obtaining rigorous solutions to integral equations on a computer. The integral equations considered are the linear Fredholm equation of the second kind and the nonlinear Urysohn equation. Techniques are presented which enable the computer to find an approximate solution, prove the existence...

Resource Type:

Masters Thesis