Sturm-Liouville operators with indefinite weight functions and eigenvalue depending boundary conditions

We consider a class of boundary value problems for Sturm-Liouville operators with indefinite weight functions. The spectral parameter appears nonlinearly in the boundary condition in the form of a function τ which has the property that λ?λτ(λ) is a generalized Nevanlinna function. We construct linearizations of these boundary value problems and study their spectral properties.     

Minimum-Phase Second-Order Systems and the Spectrum of the Semigroup Generator

Controller design is much easier for minimum-phase systems than for non-minimum phase systems. We show that a wide class of second-order in.nite-dimensional systems with velocity measurements are minimum-phase. The system does not need to be exponentially stable. We show that in general the spectrum can be quite arbitrary in the closed left half plane. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral theory for operator matrices related to models in mechanics

We derive various properties of the operator matrix where A ₀ is a uniformly positive operator and A ₀ ^?1/2 DA ₀ ^?1/2 is a bounded nonnegative operator in a Hilbert space H. Such operator matrices are associated with second-order problems of the form $ \ddot z(t) + A_0 z(t) + D\dot z(t) = 0 $ , which are used as models for transverse motions of thin beams in the presence of damping.     

Applications of the optical trapping technique to analyze chemical reactions in single emulsion particles

The applicability of the single beam gradient force optical trap and the optical levitation technique to investigate dynamic processes in microparticles is examined. The device allows to follow chemical reactions, like the emulsion polymerization and the ester hydrolysis reaction, in single emulsion droplets. Furthermore the usability of optical traps to investigate living cells is demonstrated.     

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. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Invertibility of 2 × 2 operator matrices

Properties of right invertible row operators, i.e., of 1 × 2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2 × 2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated.     

Local spectral theory for normal operators in Krein spaces

Sign type spectra are an important tool in the investigation of spectral properties of selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for normal operators in Krein spaces provide insight in the spectral nature of the operator: If the real part and the imaginary part of a normal operator in a Krein space have real spectra only and if the growth of the resolvent of the imaginary part (close to the real axis) is of finite order, then the normal operator possesses a local spectral function defined for Borel subsets of the spectrum which belong to positive (negative) type spectrum. Moreover, the restriction of the normal operator to the spectral subspace corresponding to such a Borel subset is a normal operator in some Hilbert space. In particular, if the spectrum consists entirely out of positive and negative type spectrum, then the operator is similar to a normal operator in some Hilbert space. We use this result to show the existence of operator roots of a class of quadratic operator polynomials with normal coefficients.     

On Finite Rank Perturbations of Selfadjoint Operators in Krein Spaces and Eigenvalues in Spectral Gaps

It is shown that the finiteness of eigenvalues in a spectral gap of a definitizable or locally definitizable selfadjoint operator in a Krein space is preserved under finite rank perturbations. This results is applied to a class of singular Sturm–Liouville operators with an indefinite weight function.     

Immobilization of an Iridium Pincer Complex in a Microporous Polymer for Application in Room-Temperature Gas Phase Catalysis

An iridium dihydride pincer complex [IrH₂(POCOP)] is immobilized in a hydroxy-functionalized microporous polymer network using the concepts of surface organometallic chemistry. The introduction of this novel, truly innocent support with remote OH-groups enables the formation of isolated active metal sites embedded in a chemically robust and highly inert environment. The catalyst maintained high porosity and without prior activation exhibited efficacy in the gas phase hydrogenation of ethene and propene at room temperature and low pressure. The catalyst can be recycled for at least four times.     

Definitizability of a Class of J-Selfadjoint Operators with Applications

We formulate an abstract result concerning the definitizability of J-selfadjoint operators which, roughly speaking, differ by at most finitely many dimensions from the orthogonal sum of a J-selfadjoint operator with finitely many negative squares and a semibounded selfadjoint operator in a Hilbert space. The general perturbation result is applied to a class of singular Sturm–Liouville operators with indefinite weight functions. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)