in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

My lectures at the Minicorsi di Analisi Matematica at Padova in June 2000 are written up in these notes1. They are an updated and extended version of my lectures [37] at Jyväskylä in October 1994. In particular, an account of the exciting recent development of the asymptotic case is included, which is called the ∞-eigenvalue problem. I wish to thank the University of Padova for financial suppor...

Let P, Q be compact selfadjoint operators in a Hilbert space. It is proven that the characteristic and associated vectors of the quadratic eigenvalue problem, x=\Px + (\¡X)Qx, form a Riesz basis for the cartesian product of the closure of the range of P and the closure of the range of Q. 1. Investigations in the theory of hydrodynamic stability (cf. [3, Chapter X] ; [8]) lead to the search for ...

Nonnegative matrices have long been a sorce of interesting and challenging mathematical problems. They are real matrices with all their entries being nonnegative and arise in a num‐ ber of important application areas: communications systems, biological systems, economics, ecology, computer sciences, machine learning, and many other engineering systems. Inverse eigenvalue problems constitute an ...

The Transcendental Meditation program was examined as a possible solution to the difficult problem of inmate rehabilitation. Spielberger's State-Trait Anxiety Inventory was administered to prisoners at the Federal Correctional Institution at Lompoc, California, twice before and twice after they learned the Transcendental Meditation technique. At the final testing they were also administered a S...

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 ...

The rational eigenvalue problem is an emerging class of nonlinear eigenvalue problems arising from a variety of physical applications. In this paper, we propose a linearization-based method to solve the rational eigenvalue problem. The proposed method converts the rational eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploits and preserves the structure and p...