The structure of eigenvalues of −y q x y λy, y 0 0, and y 1 ∑m k 1 αky ηk , will be studied, where q ∈ L1 0, 1 ,R , α αk ∈ R, and 0 < η1 < · · · < ηm < 1. Due to the nonsymmetry of the problem, this equation may admit complex eigenvalues. In this paper, a complete structure of all complex eigenvalues of this equation will be obtained. In particular, it is proved that this equation has always a ...

Ostrowski type and Brauer type theorems are derived for the left eigenvalues of quaternionic matrix. We see that the above theorems for the left eigenvalues are also true for the case of right eigenvalues, when the diagonals of quaternionic matrix are real. Some distribution theorems are given in terms of ovals of Cassini that are sharper than the Ostrowski type theorems, respectively, for the ...

It is well known that the main difficulty in solving eigenvalue problems under shape deformation relates to the continuation of multiple eigenvalues of the unperturbed configuration. These eigenvalues may evolve, under shape deformation, as separated, distinct eigenvalues. In this paper, we address the integral equation method in the evaluation of eigenfunctions and the corresponding eigenvalue...

In this paper, on the basis of image processing, plant leaves are respectively extracted 7 HU invariant moment eigenvalues, three shape eigenvalues and eight texture eigenvalues based on gray level co-occurrence matrix. Then the paper adopts BP network, which has been optimized by L-M algorithm to identify the classes of the plant leaves based on 7, 10 and 18 eigenvalues. The experimental resul...

In this paper, we employ transformation operators and Levinson’s density formula to study the distribution of interior transmission eigenvalues for a spherically stratified media. In particular, we show that under smoothness condition on the index of refraction that there exist an infinite number of complex eigenvalues and there exist situations when there are no real eigenvalues. We also consi...