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The factorization method for cracks in inhomogeneous media

Jun Guo;  Guozheng Yan;  Jing Jin;  Junhao Hu — 2017

Applications of Mathematics

We consider the inverse scattering problem of determining the shape and location of a crack surrounded by a known inhomogeneous media. Both the Dirichlet boundary condition and a mixed type boundary conditions are considered. In order to avoid using the background Green function in the inversion process, a reciprocity relationship between the Green function and the solution of an auxiliary scattering problem is proved. Then we focus on extending the factorization method to our inverse shape reconstruction...

Localic Katětov-Tong insertion theorem and localic Tietze extension theorem

Yong Min Li;  Wang Guo-jun — 1997

Commentationes Mathematicae Universitatis Carolinae

In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.

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