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We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under certain assumptions a lower bound on the norm of the (matrix) index of refraction can be obtained from a knowledge of the smallest transmission eigenvalue corresponding to the medium. Numerical examples are given showing the efficaciousness of our estimates. 8. F. Cakoni and H. Haddar, On the existence of transmission eigenvalues in an inhomogenous medium, Applicable Analysis 88, (2009), 475-493. Abstract: We prove the existence of transmission eigenvalues corresponding to the inverse scattering problem for isotropic and anisotropic media for both the scalar problem and Maxwell’s equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Päivärinta and Sylvester to prove the existence of transmission eigenvalues for a larger class of interior transmission problems. Our analysis includes both the case of a medium with positive contrast and of a medium with negative contrast provided that the contrasts are large enough. We prove the existence of transmission eigenvalues corresponding to the inverse scattering problem for isotropic and anisotropic media for both the scalar problem and Maxwell’s equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Päivärinta and Sylvester to prove the existence of transmission eigenvalues for a larger class of interior transmission problems. Our analysis includes both the case of a medium with positive contrast and of a medium with negative contrast provided that the contrasts are large enough. 9. P. Monk and V. Selgas, An inverse fluid-solid interaction problem, Inverse Problems and Imaging 3 (2009), 173-198. Abstract: This paper is devoted to studying the Linear Sampling Method (LSM) applied to the inverse problem for the fluid-solid interaction problem of determining the shape of the solid from far field measurements of the fluid pressure field. We provide a simplified proof of the uniqueness problem in this case, an analysis of the appropriate interior transmission problem, and the existence of a solution to the LSM that can be used as an indicator for the shape of the solid. The analysis of uniqueness rests on a new technical result concerning regularity. Finally we present some numerical results for the method. This paper is devoted to studying the Linear Sampling Method (LSM) applied to the inverse problem for the fluid-solid interaction problem of determining the shape of the solid from far field measurements of the fluid pressure field. We provide a simplified proof of the uniqueness problem in this case, an analysis of the appropriate interior transmission problem, and the existence of a solution to the LSM that can be used as an indicator for the shape of the solid. The analysis of uniqueness rests on a new technical result concerning regularity. Finally we present some numerical results for the method. 10. S. Chandler-Wilde and P. Monk, The PML for rough surface scattering, Applied Num. Math. 59 (2009), 3131-2154.