In this paper, a rigorous convergence and error analysis of a Galerkin boundary element method for the Dirichlet Laplacian eigenvalue problem is presented. The formulation of the eigenvalue problem in terms of a boundary integral equation yields a nonlinear boundary integral operator eigenvalue problem. This nonlinear eigenvalue problem and its Galerkin approximation are analyzed in the framewo...

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.

Concise introduction to a relatively new subject of non-linear algebra: literal extension of textbook linear algebra to the case of non-linear equations and maps. This powerful science is based on the notions of discriminant (hyperdeterminant) and resultant, which today can be effectively studied both analytically and by modern computer facilities. The paper is mostly focused on resultants of n...

This paper studies the behavior under iteration of the maps Tab(x, y) = (Fab(x) − y, x) of the plane R2, in which Fab(x) = ax if x ≥ 0 and bx if x < 0. These maps are area-preserving homeomorphisms of R2 that map rays from the origin into rays from the origin. Orbits of the map correspond to solutions of the nonlinear difference equation xn+2 = 1/2(a − b)|xn+1| + 1/2(a + b)xn+1 − xn. This diffe...

Iterative methods for solving large, sparse, symmetric eigenvalue problems often encounter convergence diiculties because of ill-conditioning. The Generalized Davidson method is a well known technique which uses eigenvalue preconditioning to surmount these diiculties. Preconditioning the eigenvalue problem entails more subtleties than for linear systems. In addition, the use of an accurate conv...

Motivated by the chaos suppression methods based on stabilizing an unstable periodic orbit, we study the stability of synchronized periodic orbits of coupled map systems when the period of the orbit is the same as the delay in the information transmission between coupled units. We show that the stability region of a synchronized periodic orbit is determined by the Floquet multiplier of the peri...

This paper studies the behavior under iteration of the maps Tab(x, y) = (Fab(x) − y, x) of the plane R2, in which Fab(x) = ax if x ≥ 0 and bx if x < 0. These maps are area-preserving homeomorphisms of R2 that map rays from the origin into rays from the origin. Orbits of the map correspond to solutions of the nonlinear difference equation xn+2 = 1/2(a − b)|xn+1| + 1/2(a + b)xn+1 − xn. This diffe...

This paper studies the behavior under iteration of the maps Tab(x, y) = (Fab(x) − y, x) of the plane R2, in which Fab(x) = ax if x ≥ 0 and bx if x < 0. These maps are area-preserving homeomorphisms of R2 that map rays from the origin into rays from the origin. Orbits of the map correspond to solutions of the nonlinear difference equation xn+2 = 1/2(a − b)|xn+1| + 1/2(a + b)xn+1 − xn. This diffe...

We give an optimal upper bound for the first eigenvalue of the untwisted Dirac operator on a compact symmetric space G/H with rkG− rkH ≤ 1 with respect to arbitrary Riemannian metrics. We also prove a rigidity statement. Herzlich gave an optimal upper bound for the lowest eigenvalue of the Dirac operator on spheres with arbitrary Riemannian metrics in [9] using a method developed by Vafa and Wi...

We study the eigenvalues of the biharmonic operators and the buckling eigenvalue on complete, open Riemannian manifolds. We show that the first eigenvalue of the biharmonic operator on a complete, parabolic Riemannian manifold is zero. We give a generalization of the buckling eigenvalue and give applications to studying the stability of minimal Lagrangian submanifolds in Kähler manifolds. MSC 1...