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There and Back Again - An Exploration of the Liouville Transformation and Its Inverse
(m35234)
Authors:
John Vogelgesang
,
Sharmaine Jennings
,
Anthony Austin
Editors:
John Vogelgesang
,
Sharmaine Jennings
,
Anthony Austin
Keywords:
Density
,
Eigenvalue
,
Inverse Problem
,
Mass
,
Potential
,
Rice
,
Spectral Theory
,
String
,
Sturm-Liouville
,
Transformation
,
VIGRE
,
Wave Equation
Summary:
This report summarizes work done as part of the Physics of Strings PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs ... Liouville transformation.
[Expand Summary]
This report summarizes work done as part of the Physics of Strings PFUG under Rice University's VIGRE program. VIGRE is a program of Vertically Integrated Grants for Research and Education in the Mathematical Sciences under the direction of the National Science Foundation. A PFUG is a group of Postdocs, Faculty, Undergraduates and Graduate students formed around the study of a common problem. This module describes a method for recovering the distribution of mass along a one-dimensional non-uniform string from the string's eigenvalues. The eigenvalues are used to construct the string's Sturm-Liouville potential function, and then the mass density is obtained from this potential by means of inverting the Liouville transformation.
[Collapse Summary]
Subject:
Mathematics and Statistics
Language:
English
Popularity:
43.53%
Revised:
2010-11-17
Revisions:
5
Popularity is measured as percentile rank of page views/day over all time
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