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Dense sets and the projection theorem for acoustic harmonic waves in a homogeneous finite depth ocean
Author(s) -
Gilbert R. P.,
Xu Yongzhi
Publication year - 1990
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670120105
Subject(s) - mathematics , projection (relational algebra) , homogeneous , mathematical analysis , class (philosophy) , harmonic , plane (geometry) , refraction , geometry , acoustics , optics , physics , algorithm , combinatorics , artificial intelligence , computer science
Abstract The scattering of a ‘plane wave’ off a submerged body situated in an ocean of finite depth is investigated. The index of refraction is considered to be depth‐independent. It is shown that the far field is not unique; hence, the problem of determining the shape of an object from its far field is not well‐posed. If solutions are sought among a restricted class of problems the ‘dense set’ property implies that the problem can be made well‐posed.