We discuss the behavior of the minimal eigenvalue λ of the Dirichlet Laplacian in the domainD1\D2 := D (an annulus) whereD1 is a circular disc andD2 ⊂ D1 is a smaller circular disc. It is conjectured that the minimal eigenvalue λ has a maximum value when D2 is a concentric disc. If h is a displacement of the center of the disc D2 and λ(h) is the corresponding minimal eigenvalue, then dλ(h) dh <...

Utilizing the properties of the smallest singular value of a matrix, we propose a new, efficient and reliable algorithm for solving nonsymmetric matrix inverse eigenvalue problems, and compare it with a known method. We also present numerical experiments which illustrate our results.

This paper modeled a doubly fed induction generator (DFIG) based offshore wind farm integrated through a voltage source converter –based high voltage direct current (VSC-HVDC) transmission system, which is collected with infinite bus for small signal stability analysis. The control system of HVDC system is considered for the stability analysis. The impact of the VSC control parameters on the ne...

Parallel analysis, one of the most promising methods to determine the number of principal components or factors to retain (Velicer, Eaton, & Fava, 2000), has been shown to underestimate the number of components to retain when the first eigenvalue is large (Turner, 1998). In order to further explore the potential problems with parallel analysis, orthogonal and oblique 4-, 8-, and 12-component so...

This paper is devoted to perturbation analysis for the eigenproblem of periodic matrix pairs {(Aj ,Ej )}j=1. We first study perturbation expansions of periodic deflating subspaces and eigenvalue pairs. Then, we derive explicit expressions of condition numbers, perturbation bounds and backward errors for eigenvalue pairs and periodic deflating subspaces. © 2001 Elsevier Science Inc. All rights r...

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/(2N)1/2, where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semi-circle provided c > 1. In this study, using an asymptotic analysis of the secul...

Two methods for model behavioural analysis are implemented on a simple 2 order nonlinear model. The results of applying Ford’s behavioral approach are compared with those obtained using both system-wide and variable-specific loop eigenvalue elasticity analysis. Differences in the division of the time span into analysis intervals are identified as are discrepancies in the outcomes. The effort re...

The branching of un,symmetric equilibrium states from axisymmetric equilibrium states for clamped circular plates subjected to a uniform edge thrust and a uniform lateral pressure is analyzed in this paper. The branching process is called wrinkling and the loads at which branching occurs are called wrinkling loads. The nonlinear von Karman plate theory is employed. The wrinkling loads are deter...

The generalized eigenvalue problem Ax ˆ kBx has special properties when …A;B† is a Hermitian and de®nite pair. Given a general Hermitian pair …A;B† it is of interest to ®nd the nearest de®nite pair having a speci®ed Crawford number d > 0. We solve the problem in terms of the inner numerical radius associated with the ®eld of values of A‡ iB. We show that once the problem has been solved it is t...

We investigate scalar perturbations from inflation in braneworld cosmologies with extra dimensions. For this we calculate scalar metric fluctuations around five dimensional warped geometry with four dimensional de Sitter slices. The background metric is determined self-consistently by the (arbitrary) bulk scalar field potential, supplemented by the boundary conditions at both orbifold branes. A...