This paper is concerned with the periodic principal eigenvalue kλ(μ) associated with the operator − d 2 dx2 − 2λ d dx − μ(x)− λ, (1) where λ ∈ R and μ is continuous and periodic in x ∈ R. Our main result is that kλ(μ∗) ≤ kλ(μ), where μ∗ is the Schwarz rearrangement of the function μ. From a population dynamics point of view, using reaction-diffusion modeling, this result means that the fragment...

Band structure calculations for photonic crystals require the numerical solution of eigenvalue problems. In this paper, we consider crystals composed of lossy materials with frequency-dependent permittivities. Often, these frequency dependencies are modeled by rational functions, such as the Lorentz model, in which case the eigenvalue problems are rational in the eigenvalue parameter. After spa...

A comprehensive survey of some recent results regarding parameterized inverse eigenvalue problems is given in this paper. Speciic topics include: additive and multiplicative inverse eigenvalue problems, classical inverse eigenvalue problems and generalized inverse eigenvalue problems. Both the theoretic and algorithmic aspects are reviewed. Some open problems are revealed to stimulate further r...

Past work on stability analysis of traveling waves in neuronal media has mostly focused on linearization around perturbations of spike times and has been done in the context of a restricted class of models. In theory, stability of such solutions could be affected by more general forms of perturbations. In the main result of this paper, linearization about more general perturbations is used to d...

Subspace iteration for computing several eigenpairs (i.e. eigenvalues and eigenvectors) of an eigenvalue problem is an alternative to the deflation technique whereby the eigenpairs are computed successively by projecting the problem onto the subspace orthogonal to the already found eigenvectors. The main advantage of the subspace iteration over the deflation is its ‘cluster robustness’: even if...

Let 0: M-,S" be a minimal immersion of a compact surface into a unit sphere. Then, the linear functions of 0 are eigenfunctions for the Laplacian of M corresponding to the eigenvalue 2=2 . The main purpose of this paper is to study those minimal surfaces for which 2 is exactly the first non-zero eigenvalue of its Laplacian. This kind of immersions have a peculiar behaviour among all compact min...

We consider the asymptotic fluctuation behavior of the largest eigenvalue of certain sample covariance matrices in the asymptotic regime where both dimensions of the corresponding data matrix go to infinity. More precisely, let X be an n× p matrix, and let its rows be i.i.d. complex normal vectors with mean 0 and covariance Σp. We show that for a large class of covariance matrices Σp, the large...

In this paper, a novel compensator based on Magnetically Controlled Reactor with Fixed Capacitor banks (FC-MCR) is introduced and then power system stability in presence of this compensator is studied using an intelligent control method. The problem of robust FC-MCR-based damping controller design is formulated as a multi-objective optimization problem. The multi-objective problem is concocted ...

We consider the class of the Orthogonal Projection Methods (OPM) to solve iteratively large and generalised eigenvalue problems. An OPM is a method that projects a large eigenvalue problem on a smaller subspace. In this subspace, an approximation of the eigenvalue spectrum can be computed from a small eigenvalue problem using a direct method. We show that many iterative eigenvalue solvers, such...