all roots of the equation det(z[alpha](z)I - A) =0 are inside the unit circle if and only if all
eigenvalues of A belong to {z[alpha](z) :[absolute value of z] < 1>.
We note that part of this work was presented at the 24th International Conference on Domain Decomposition Methods and at the same conference an adaptive FETI-DP algorithm with a change of basis formulation was presented by Axel Klawonn, where different generalized
eigenvalue problems are introduced and different tools are used in the analysis of condition numbers.
The operator matrix, L, has real-valued
eigenvalues that are always greater than or equal to 1.
We consider the
eigenvalue problem with [alpha] > 1
It is the purpose of this paper to show the existence of the principal
eigenvalues and determine the sign of the corresponding eigenfunctions for linear periodic
eigenvalue problem
[E.sub.n] and [mu] = [m.sub.1][m.sub.2]/([m.sub.1] + [m.sub.2]) are energy
eigenvalue of nth level and reduced mass of the q[bar.q] system, respectively ([m.sub.1] and [m.sub.2] are quark masses).
(2) [[lambda].sup.-1] is an
eigenvalue of [K.sub.E] with multiplicity m.
Kostic and Voss [9] applied the Sylvester's law of inertia on the definite quadratic
eigenvalue problems.
By m([lambda]) we denote the multiplicity of
eigenvalue [lambda].
If all the adjacent neighbour average sequences [z.sup.(1).sub.i](k) [greater than or equal to] 1 and the chosen sample is the minimal permitted data in grey system, then we conclude that [[summation].sup.n.sub.k=2][([z.sup.(1).sub.i](k)).sup.2] is larger than n - 1, and the maximal
eigenvalue and minimal
eigenvalue are contained in different circles, and the centres of circles are far from each other.
For the
eigenvalue assignment in [A.sup.r.sub.z,2], we encounter singularly perturbed structure so that the two-stage design is applied to the slow and fast subsystems.
In this paper we consider the fractional extension of the Sturm-Liouville
eigenvalue problem
