We introduce a new method for computing eigenvalues of the Maxwell operator with boundary finite elements. On bounded domains with piecewise constant material coefficients, the Maxwell solution for fixed wave number can be represented by boundary integrals, which allows to reduce the eigenvalue problem to a nonlinear problem for determining the wave number along with boundary and interface trac...

This paper addresses strong stability, in the sense of Kojima, of stationary solutions of nonlinear programs Pro with a finite number of equality constraints and one abstract convex constraint defined by the closed convex set K. It intends to extend results of our former paper that treated nonlinear programs Pro in a special case that K is the set of nonnegative symmetric matrices S+. Firstly, ...

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteratio...

The system of shallow water waves is one of the classical examples for nonlinear, twodimensional conservation laws. The paper investigates a simple kinetic equation depending on a parameter " which leads for " ! 0 to the system of shallow water waves. The corresponding 'equilibrium' distribution function has a compact support which depends on the eigenvalues of the hyperbolic system. It is show...

below) a sequence of e.0. polynomials [SI S. V. Salehi and E. P. Ryan. “On optimal nonlinear feedback regulation of linear plants,” IEEE Trans. Auiomai. Contr., vol. AC-27, pp. 1260-1264, 1982. [ IO] J . Sandor and D. Williamson. “Design of nonlinear regulators for linear plants,” IEEE Truns. Automar. Conrr.. vol. AC-22. pp. 47-50, 1977. 1111 F. G. Shinsky, Process Control Syslems. 2nd ed. New ...

The nonlinear extension of the balancing procedure requires the case of state dependent quadratic forms for the energy functions, i.e., the nonlinear extensions of the linear Gramians are state dependent matrices. These extensions have some interesting ambiguities that do not occur in the linear case. Namely, the choice of the state dependent matrix in the semi-quadratic form is not unique, and...

In the positive definite case, the extreme generalized eigenvalues can be obtained by solving a suitable nonlinear system of equations. In this work, we adapt and study the use of recently developed low-cost derivative-free residual schemes for nonlinear systems, to solve large-scale generalized eigenvalue problems. We demonstrate the effectiveness of our approach on some standard test problems...

As is well known, the variational equations of nonlinear dynamic systems are linear time-varying (LTV) by nature. In the modal solutions for these LTV equations, the earlier introduced dynamic eigenvalues play a key role. They are closely related to the Lyapunovand Floquet-exponents of the corresponding nonlinear systems. In this contribution, we present some simple examples for which analytic ...

In this paper we present a WKB approximation for sphericallysymmetric solutions of the Schrödinger-Newton equations. These are nonlinear modifications of the ordinary Schrödinger equation involving gravitational selfinteraction of the wavefunction. Applying the WKB procedure leads to two different nonlinear differential equations for the gravitational potential U for positive and negative value...

This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. This new algorithm ca...