Employing Lorentz reciprocity and the Stratton-Chu formalism it is shown that the Poincaré-Steklov or admittance operator can be interpreted as a complex symmetric operator mapping the tangential electric field (instead of the equivalent magnetic current) onto the equivalent electric current. We show that the pertinent block Calderón projectors can be reformulated as operators with a block Hami...

The classical numerical range of a quadratic operator is an elliptical disk. This result is extended to different kinds of generalized numerical ranges. In particular, it is shown that for a given quadratic operator, the rank-k numerical range, the essential numerical range, and the q-numerical range are elliptical disks; the c-numerical range is a sum of elliptical disks, and the Davis-Wieland...

PREFACE 1. CONVERGENT. Does the set of cyclic operators have a non-empty interior?... 2. WEIGHTED. Is every part of a weighted shift similar to a weighted shift?. . . . 3. INVARIANT. If an intransitive operator has an inverse, is its inverse also intransitive? 4. TRIANGULAR. Is every normal operator the sum of a diagonal operator and a compact one? 5. DILATED. Is every subnormal Toeplitz operat...

Suppose that K is a convex polyhedron in the n-dimensional Euclidean space R. Suppose that the extreme points of K are P1, P2, . . . , Pm ( m ≥ n + 1). If P is an arbitrary interior point of K, then there exist vertices Pi1 , Pi2 , . . . , Pin+1 of K and a point Q of R n and a positive number r > 0 for which ||Pik − Q|| = r for 1 ≤ k ≤ n + 1 , ||Pj − Q|| ≤ r for 1 ≤ j ≤ m and P is an interior p...

A two-stage iterative scheme is proposed to handle a central problem of molecular dynamics, the computation of interior eigenvalues of large Hamiltonian matrices. The proposed method involves an initial propagation process for a time-dependent wave operator which is then inserted in an iterative process (R.D.W.A. or S.C.M.) to yield the exact stationary wave operator. The merits of the wave ope...

A complex network of Euler-Bernoulli beams is studied in this paper. As for this network, the boundary vertices are clamped, the displacements of the structure are continuous but the rotations of different beams are not continuous at the interior vertices. The feedback controller are designed at the interior nodes to stabilize the elastic system. The well-posed-ness of the closed loop system is...

We denote the numerical range of the normal operator T by W (T). A characterization is given to the points inW (T) that lie on the boundary. The collection of such boundary points together with the interior of the the convex hull of the spectrum of T will then be the set W (T). Moreover, it is shown that such boundary points reveal a lot of information about the normal operator. For instance, s...