Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse problems for target identification and nondestructive testing. The problem is numerically challenging because it is non-selfadjoint and nonlinear. In this pape...

Let Γ be a co-compact Fuchsian group of isometries on the Poincaré disk D and ∆ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction f of ∆, equivariant by Γ with real eigenvalue λ = −s(1 − s), where s = 1 2 + it, admits an integral representation by a distribution D f,s (the Helgason distribution) which is equivariant by Γ and supported at infinity ∂D = S 1. The geodesic flo...

As an extension of the theory of Dyson’s Brownian motion models for the standard Gaussian random-matrix ensembles, we report a systematic study of hermitian matrix-valued processes and their eigenvalue processes associated with the chiral and nonstandard random-matrix ensembles. In addition to the noncolliding Brownian motions, we introduce a one-parameter family of temporally homogeneous nonco...

The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface Γ. In this paper, following an idea developed by Kleinman and Martin [19] for acoustic scattering problems, we consider methods for solving the dielectric ...

This study investigated an electrocardiogram (ECG) eigenvalue automatic analysis and detection method; ECG eigenvalues were used to reverse the myocardial action potential in order to achieve automatic detection and diagnosis of heart disease. Firstly, the frequency component of the feature signal was extracted based on the wavelet transform, which could be used to locate the signal feature aft...

We present an alternative procedure for solving the eigenvalue problem of replicated transfer matrices describing disordered spin systems with (random) 1D nearest neighbor bonds and/or random fields, possibly in combination with (random) long range bonds. Our method is based on transforming the original eigenvalue problem for a 2 n × 2 n matrix (where n → 0) into an eigenvalue problem for integ...

The concept of orbitaland eigenvalue-dependent exchangeŽ . correlation xc energy functionals is reviewed. We show how such functionals can be derived in a systematic fashion via a perturbation expansion, utilizing the Kohn]Sham system as a noninteracting reference system. We demonstrate that the second-order contribution to this expansion of the xc-energy functional includes the leading term of...

In this paper the inverse eigenvalue problem of recovering the real coefficients in a Sturm–Liouville problem with nonselfadjoint boundary conditions depending on the spectral parameter from the eigenvalues is solved using entire-function theory and the solution of a Marchenko integral equation.

We prove the algebraic eigenvalue conjecture of J.Dodziuk, P.Linnell, V.Mathai, T.Schick and S.Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known, which is not sofic.