Roy-Steiner equations for piN scattering

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.

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.

A Parallel Solver for the Time-Periodic Navier–Stokes Equations

We investigate parallel algorithms for the solution of the Navier–Stokes equations in space-time. For periodic solutions, the discretized problem can be written as a large non-linear system of equations. This system of equations is solved by a Newton iteration. The Newton correction is computed using a preconditioned GMRES solver. The parallel performance of the algorithm is illustrated.

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

Clinical manifestation of Fuchs uveitis syndrome in childhood

PURPOSE The aim of this study was to describe clinical signs and complications of Fuchs uveitis syndrome (FUS) with onset in childhood. METHODS Ophthalmologic findings and complications in patients with FUS becoming manifest before the age of 16 years were analyzed in a retrospective study at a tertiary referral uveitis center. Inclusion criteria were the presence of pathognomonic FUS findings at any time point and exclusion of any systemic immune-mediated or infectious disease. RESULTS A total of 23 patients (male = 16, female = 7) with juvenile FUS (unilateral n = 20, bilateral n = 3 patients) were included in the study. Mean ages at uveitis and FUS diagnosis were 12.0 ± 4.2 and 22.7 ± 10.7 years, respectively. In six patients, inflammation was noted at age ≤ 7 years. The following inflammatory signs were observed in a total of 26 eyes: ≤ 1+ anterior chamber cell grade (n = 26), vitreous cells (n = 24), fine keratic precipitates (KPs; n = 23), stellate KPs (n = 11), mutton-fat KPs (n = 23), diffuse (n = 24) or inferior (n = 8) distribution of KPs, Koeppe nodules (n = 10), and iris heterochromia (n = 14). A representative subgroup of patients (n = 5) is shown who presented with non-specific clinical signs in the beginning and in whom typical FUS signs became manifest only at a later stage. Secondary complications such as cataract (n = 19), ocular hypertension (n = 3), or glaucomatous disc damage (n = 2) were found after a mean uveitis duration of 11.6, 19.5, and 20.3 years, respectively. CONCLUSION FUS may begin in early childhood, and the characteristic findings may not be present at onset of disease. The diagnosis is often delayed for years, occasionally with the consequence of overtreatment with anti-inflammatory drugs.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.