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Characterization of a convex obstacle by singularities of the scattering kernel

โœ Scribed by Kazuhiro Yamamoto

Publisher
Elsevier Science
Year
1986
Tongue
English
Weight
553 KB
Volume
64
Category
Article
ISSN
0022-0396

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๐Ÿ“œ SIMILAR VOLUMES

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## Abstract Let __D~j~__,__j__ = 1,2, be two bounded domains (obstacles) in โ„^__n__^, __n__ โ‰ฅ 2, with the boundaries ฮ“~__j__~. Let __A~j~__ be the scattering amplitude corresponding to __D~j~__. The Dirichlet boundary condition is assumed on ฮ“~__j__~. A formula is derived for __A__:= __A__~1~ โˆ’ __A

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We show that if G is a connected graph with the same proper convex subgraphs as (Kn)', the Cartesian product of r copies of Kn, r >t 2, n >t 3, then [V(G)I ~> n" with equality if and only if G is isomorphic to (Kn)'. In this note we consider only connected finite undirected simple graphs. The compl