منابع مشابه
Transmission Eigenvalues
The scattering of a time-harmonic plane wave in an inhomogeneous medium is modeled by the scattering problem for the Helmholtz equation. A transmission eigenvalue is a wavenumber at which the scattering operator has a non-trivial kernel or cokernel. Because many sampling methods for locating scatterers succeed only at wavenumbers that are not transmission eigenvalues, they have been studied for...
متن کاملNotes on Transmission Eigenvalues
Here k = ω/co is the wave number, ω denotes the frequency of excitation, S2 = {x ∈ R3, |x| = 1} is the unit sphere in R3, and co is such that its real and imaginary parts are respectively <(co)> 0 and =(co)60. The support ofD is assumed to be such that R3 \D is connected, and that ∂D is of Lipschitz type. As a canonical example of the scattering by a penetrable obstacle, consider next the case ...
متن کاملTransmission Eigenvalues for Elliptic Operators
A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient conditions for the existence of transmission eigenvalues and completeness of generalized eigenstates for the transmission eigenvalue problem are derived. In the trac...
متن کاملEigenvalues of Transmission Graph Laplacians
The standard notion of the Laplacian of a graph is generalized to the setting of a graph with the extra structure of a “transmission” system. A transmission system is a mathematical representation of a means of transmitting (multi-parameter) data along directed edges from vertex to vertex. The associated transmission graph Laplacian is shown to have many of the former properties of the classica...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2021
ISSN: ['0002-9920', '1088-9477']
DOI: https://doi.org/10.1090/noti2350