25 research outputs found
Locating the extremal entries of the Fiedler vector for rose trees
In this note we locate the extremal entries of the Fiedler vector for the class of rose trees, which consists of paths with a star graph attached to it. We derive directly from the eigenvector equation conditions to characterize in which cases the extremal values are located either at the end points of the path or on the pendant vertices of the star graph
A pseudo-resolvent approach to abstract differential-algebraic equations
We study linear abstract differential-algebraic equations (ADAEs), and we
introduce an index concept which is based on polynomial growth of
a~pseudo-resolvent. Our approach to solvability analysis is based on degenerate
semigroups. We apply our results to some examples such as distributed circuit
elements, and a system obtained by heat-wave coupling
Eigenvalues of parametric rank one perturbations of matrix pencils
The behavior of eigenvalues of regular matrix pencils under rank one perturbations which depend on a scalar parameter is studied. In particular we address the change of the algebraic multiplicities, the change of the eigenvalues for small parameter variations as well as the asymptotic eigenvalue behavior as the parameter tends to in nity. Besides that, an interlacing result for rank one perturbations of matrix pencils is obtained. Finally, we apply the result to a redesign problem for electrical circuits
Locally finite extensions and Gesztesy-Šeba realizations for the Dirac operator on a metric graph
On discrete-time dissipative port-Hamiltonian (descriptor) systems
Port-Hamiltonian (pH) systems have been studied extensively for linear
continuous-time dynamical systems. This manuscript presents a discrete-time pH
descriptor formulation for linear, completely causal, scattering passive
dynamical systems based on the system coefficients. The relation of this
formulation to positive and bounded real systems and the characterization via
positive semidefinite solutions of Kalman-Yakubovich-Popov inequalities is also
studied.Comment: 30 pages, 3 figure
On the parametric eigenvalue behavior of matrix pencils under rank one perturbations
We study the eigenvalues of rank one perturbations of regular matrix pencils depending linearly on a complex parameter. We prove properties of the corresponding eigenvalue sets including a convergence result as the parameter tends to infinity and an eigenvalue interlacing property for real valued pencils having real eigenvalues only