We present some sufficient and necessary conditions under which some linear (or nonlinear) estimators dominate (are better than) others in the sense of PMC. Its applications in linear regressions are also discussed. Furthermore, we obtain results about the eigenvalues of two matrices, which seem to be hard to be proved through pure matrix theory.

General one-parameter families of matrices avoid eigenvalue crossings. It is shown that the matrices associated with the simple waves of nonlinear systems of conservation laws do not obey this rule: a subset of simple waves with nonzero measure has crossing eigenvalues. © 2009 Wiley Periodicals, Inc.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

In [2] Conca et al. stated two inclusion theorems for quadratic eigenvalue problems the proof of which are not complete. In this note we demonstrate by simple examples that the assertions as they stand are false. Taking advantage of an appropriate enumeration for eigenvalues of nonlinear eigenproblems we adjust the results.

In this paper, by applying (p, k)-epi mapping theory, we introduce a new definition of spectrum for nonlinear operators which contains all eigenvalues, as in the linear case. Properties of this spectrum are given and comparison is made with the other definitions of spectra. We also give applications of the new theory.

The spectral problem for an infinite periodic medium perturbed by a compact defect is considered. This may be seen for example as a simplified scalar cross-sectional model of the problem for localised modes in photonic crystal fibers. For a high contrast small size periodicity and a finite size defect we consider the critical (the so called double poros-ity type) scaling. We employ (high contra...

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Appl...

Abstract: In this paper we consider the rational eigenvalue problem governing the relevant energy levels and wave functions of a three dimensional quantum dot. We present iterative projection methods of Arnoldi and of Jacobi–Davidson type for computing a few eigenpairs of this system. Solving the projected nonlinear eigenvalue problems we take advantage of a minmax characterization of the eigen...

So far, various components of image characteristics have been used for steganalysis, including the histogram characteristic function, adjacent colors distribution, and sample pair analysis. However, some certain steganography methods have been proposed that can thwart some analysis approaches through managing the embedding patterns. In this regard, the present paper is intended to introduce a n...