4 problems

Nonvanishing energy integral conjecture. The quantity $\int_{\mathbb{S}^2}\varepsilon|\Phi|^2\,ds$ vanishes if and only if the contrast $\kappa_{\varepsilon}$ coincides with a boun…

Let $G$ and $\hat G$ be the matrix functions in the two vector Riemann–Hilbert problems, and define their indices by … The compatibility conditions relating the solutions of the tw…

The TE spectrum contains dense line segments associated with the material contrast. In the three-dimensional case, the essential-spectrum conjecture. the dense line segments observ…

Let $V$ be a bounded dielectric volume, let $R_V$ be such that $V\subset O(\mathbf 0,R_V)$, and let $\bm E_\mathrm{sc}$ denote the scattered electric field in the exterior region…