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Minimal Nodal Domains For Strictly Elliptic Partial Differential Equations With Homogeneous Boundary Conditions, Charles E. Miller May 2006

Minimal Nodal Domains For Strictly Elliptic Partial Differential Equations With Homogeneous Boundary Conditions, Charles E. Miller

All Graduate Theses and Dissertations

This work presents a proof of the dependence of the first eigenvalue for uniformly elliptic partial differential equations on the domain in a less abstract setting than that of Ivo Babushka and Rudolf Vyborny in 1965. The proof contained here, under rather mild conditions on the boundary of the domain, �Ω, demonstrates that the first eigenvalue of elliptic partial differential equation

[ �� + �� = 0 �� Ω

[ � = 0 �� �Ω

depends continuously on the domain in the following sense. If a sequence of domains is such that, then the corresponding first eigenvalues satisfy is the first eigenvalue for

[ �� + �� = 0 �� Ω

[ � = 0 �� �Ω

The work also ...


Wavelet Techniques In Time Series Analysis With An Application To Space Physics, Agnieszka Jach May 2006

Wavelet Techniques In Time Series Analysis With An Application To Space Physics, Agnieszka Jach

All Graduate Theses and Dissertations

Several wavelet techniques in the analysis of time series are developed and applied to real data sets.

Methods for long-memory models include wavelet-based confidence intervals for the self-similarity para meter in potentially heavy-tailed observations. Empirical coverage probabilities are used to assess the procedures by applying them to Linear Fractional Stable Motion with many choices of para meters. Asymptotic confidence intervals provide empirical coverage often much lower than nominal and it is recommended to use subsampling confidence intervals. A procedure for monitoring the constancy of the self-similarity parameter is proposed and applied to Ethernet data sets.

A test to distinguish a ...