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.

Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Impact of differential P450c17 phosphorylation by cAMP stimulation and by starvation conditions on enzyme activities and androgen production in NCI-H295R cells

CYP17A1 plays a pivotal role in the biosynthesis of androgens in the adrenals and the gonads. Although this enzyme catalyzes two different reactions on one single active site, its specific activities are regulated independently. Although the 17alpha-hydroxylase activity is rather constant and regulated by gene expression, the 17,20-lyase activity varies significantly with the amount of cofactors or by protein phosphorylation. cAMP increases CYP17A1 expression, P450c17 phosphorylation, and androgen production. However, the exact mechanism(s) and the specific regulators of CYP17A1 remain unknown. Therefore, we studied the regulation of adrenal androgen biosynthesis in human adrenal H295R cells focusing on CYP17A1. We analyzed androgen production and P450c17 activities in H295R cells grown under normal and serum-free conditions and/or after stimulation with 8-bromoadenosine-cAMP. H295R cells grown in starvation medium produced more androgens and had decreased HSD3B2 expression and activity but increased P450c17-17,20-lyase activity and serine phosphorylation. Although starvation increased serine phosphorylation of P450c17 specifically, cAMP stimulation enhanced threonine phosphorylation exclusively. Time-course experiments revealed that a short cAMP stimulation augmented threonine phosphorylation of P450c17 but did not increase 17,20-lyase activity. By contrast, long cAMP stimulation increased androgen production through increased P450c17 activities by enhancing CYP17A1 gene expression. We conclude that serum withdrawal shifts steroidogenesis of H295R cells towards androgen production, providing a suitable model for detailed studies of androgen regulation. In addition, our study shows that starvation and cAMP stimulation regulate P450c17 phosphorylation differentially and that an increase in P450c17 phosphorylation does not necessarily lead to enhanced enzyme activity and androgen production.