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 Title
 Approximate Isometries as an Eigenvalue Problem and Angular Momentum.
 Creator
 Wilder, Shawn M., Beetle, Christopher, Graduate College
 Date Issued
 20130412
 PURL
 http://purl.flvc.org/fcla/dt/3361373
 Subject Headings
 Black holes (Astronomy), Eigenvalues
 Format
 Document (PDF)
 Title
 Subspace detection and scale evolutionary eigendecomposition.
 Creator
 Kyperountas, Spyros C., Florida Atlantic University, Erdol, Nurgun, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
 Abstract/Description

A measure of the potential of a receiver for detection is detectability. Detectability is a function of the signal and noise, and given any one of them the detectability is fixed. In addition, complete transforms of the signal and noise cannot change detectability. Throughout this work we show that "Subspace methods" as defined here can improve detectability in specific subspaces, resulting in improved Receiver Operating Curves (ROC) and thus better detection in arbitrary noise environments....
Show moreA measure of the potential of a receiver for detection is detectability. Detectability is a function of the signal and noise, and given any one of them the detectability is fixed. In addition, complete transforms of the signal and noise cannot change detectability. Throughout this work we show that "Subspace methods" as defined here can improve detectability in specific subspaces, resulting in improved Receiver Operating Curves (ROC) and thus better detection in arbitrary noise environments. Our method is tested and verified on various signals and noises, both simulated and real. The optimum detection of signals in noise requires the computation of noise eigenvalues and vectors (EVD). This process neither is a trivial one nor is it computationally cheap, especially for nonstationary noise and can result in numerical instabilities when the covariance matrix is large. This work addresses this problem and provides solutions that take advantage of the subspace structure through plane rotations to improve on existing algorithms for EVD by improving their convergence rate and reducing their computational expense for given thresholds.
Show less  Date Issued
 2001
 PURL
 http://purl.flvc.org/fcla/dt/11965
 Subject Headings
 Eigenvalues, Eigenvectors, Wavelets (Mathematics)
 Format
 Document (PDF)
 Title
 Exploring the stability of an eigenvalue problem approximation technique used to define the angular momentum of almost spherical black holes.
 Creator
 Wilder, Shawn M., Beetle, Christopher, Graduate College
 Date Issued
 20110408
 PURL
 http://purl.flvc.org/fcla/dt/3164804
 Subject Headings
 Eigenvalues, Black holes (Astronomy), Deformations (Mechanics)
 Format
 Document (PDF)
 Title
 General relativistic quasilocal angular momentum continuity and the stability of strongly elliptic eigenvalue problems.
 Creator
 Wilder, Shawn M., Beetle, Christopher, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
 Abstract/Description

In general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is welldefined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the...
Show moreIn general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is welldefined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the continuity of an angular momentum definition that employs an approximate Killing field that is an eigenvector of a particular secondorder differential operator. We find that the eigenvector varies continuously in Hilbert space under smooth perturbations of a smooth boundary geometry. Furthermore, we find that not only is the approximate Killing field continuous but that the eigenvalue problem which defines it is stable in the sense that all of its eigenvalues and eigenvectors are continuous in Hilbert space. We conclude that the stability follows because the eigenvalue problem is strongly elliptic. Additionally, we provide a practical introduction to the mathematical theory of strongly elliptic operators and generalize the above stability results for a large class of such operators.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004235
 Subject Headings
 Boundary element methods, Boundary value problems, Differential equations, Elliptic  Numerical solutions, Differential equations, Partial  Numerical solutions, Eigenvalues, Spectral theory (Mathematics)
 Format
 Document (PDF)