ﻻ يوجد ملخص باللغة العربية
Consider the transmission eigenvalue problem [ (Delta+k^2mathbf{n}^2) w=0, (Delta+k^2)v=0 mbox{in} Omega;quad w=v, partial_ u w=partial_ u v=0 mbox{on} partialOmega. ] It is shown in [12] that there exists a sequence of eigenfunctions $(w_m, v_m)_{minmathbb{N}}$ associated with $k_mrightarrow infty$ such that either ${w_m}_{minmathbb{N}}$ or ${v_m}_{minmathbb{N}}$ are surface-localized, depending on $mathbf{n}>1$ or $0<mathbf{n}<1$. In this paper, we discover a new type of surface-localized transmission eigenmodes by constructing a sequence of transmission eigenfunctions $(w_m, v_m)_{minmathbb{N}}$ associated with $k_mrightarrow infty$ such that both ${w_m}_{minmathbb{N}}$ and ${v_m}_{minmathbb{N}}$ are surface-localized, no matter $mathbf{n}>1$ or $0<mathbf{n}<1$. Though our study is confined within the radial geometry, the construction is subtle and technical.
We present the discovery of a novel and intriguing global geometric structure of the (interior) transmission eigenfunctions associated with the Helmholtz system. It is shown in generic scenarios that there always exists a sequence of transmission eig
We consider a family of spherically symmetric, asymptotically Euclidean manifolds with two trapped sets, one which is unstable and one which is semi-stable. The phase space structure is that of an inflection transmission set. We prove a sharp local s
We prove on the 2D sphere and on the 2D torus the Lieb-Thirring inequalities with improved constants for orthonormal families of scalar and vector functions.
We consider the problem of finding the resonances of the Laplacian on truncated Riemannian cones. In a similar fashion to Cheeger--Taylor, we construct the resolvent and scattering matrix for the Laplacian on cones and truncated cones. Following Stef
We demonstrate the coherent transduction of quantum noise reduction, or squeezed light, by Ag localized surface plasmons (LSPs). Squeezed light, generated through four-wave-mixing in Rb vapor, is coupled to a Ag nanohole array designed to exhibit LSP