Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

Root system of singular perturbations of the harmonic oscillator type operators

We analyze perturbations of the harmonic oscillator type operators in a Hilbert space H, i.e. of the self-adjoint operator with simple positive eigenvalues μ k satisfying μ k+1 − μ k ≥ Δ > 0. Perturbations are considered in the sense of quadratic forms. Under a local subordination assumption, the eigenvalues of the perturbed operator become eventually simple and the root system contains a Riesz basis.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

Endocrine disrupting compounds: can they target the immune system of fish?

Endocrine disruption, in particular disruption by estrogen-active compounds, has been identified as an important ecotoxicological hazard in the aquatic environment. Research on the impact of endocrine disrupting compounds (EDCs) on wildlife has focused on disturbances of the reproductive system. However, there is increasing evidence that EDCs affect a variety of physiological systems other than the reproductive system. Here, we discuss if EDCs may be able to affect the immune system of fish, as this would have direct implications for individual fitness and population growth. Evidence suggesting an immunomodulatory role of estrogens in fish comes from the following findings: (a) estrogen receptors are expressed in piscine immune organs, (b) immune gene expression is modulated by estrogen exposure, and (c) pathogen susceptibility of fish increases under estrogen exposure.