The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON MATHEMATICS
Transactions ID Number: 52-542
Full Name: Pappur Shivakumar
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Age: ON
Sex: Male
Address: Department of Mathematics, University of Manitoba,Winnipeg, Manitoba, R3T2N2
Country: CANADA
Tel: 1 204 474 7477
Tel prefix: 1
Fax:
E-mail address: shivaku@cc.umanitoba.ca
Other E-mails: shivak123@hotmail.com
Title of the Paper: shape of a drum,a constructive approach
Authors as they appear in the Paper: Pappur Shivakumar, Yan Wu
Email addresses of all the authors: shivaku@cc.umanitoba.ca,wuyan1981@gmail.com
Number of paper pages: 11
Abstract: For the classical question, "Can you hear the shape of the drum?",the answer is known to be "yes" for certain convex planar regions with analytic boundaries.The answer is also known to be "no" for some polygons with reentrant corners.A large number of mathematicians over four decades have contributed to the topic from various approaches, theoretical and numerical. In this article, we develop a constructive analytic approach to indicate how a preknowledge of the eigenvalues lead to the determination of the parameters of the boundary. This approach is applied to a general boundary and in particular to a circle, an ellipse, and a square. In the case of a square, we obtain an insight into why the analytical procedure does not, as expected, yield an answer. For the Mathieu equation with a parameter, we demonstrate the determination of the parameter when the eigenvalues are known.
Keywords: Vibrating drum, infinite matrices,Mathieu equations,eigenvalues,Laplacian
EXTENSION of the file: .pdf
Special (Invited) Session: 14th Wseas International Conference on Systems, Latest Trends on Systems II, Corfu Island July 22-24, 2010, pp376-386
Organizer of the Session:
How Did you learn about congress: Helmholtz equation, eigenvalues, infinite matrices, Inverse problem
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