Maximum‐norm a posteriori error bounds for a collocation method applied to a singularly perturbed reaction–diffusion problem in three dimensions

Collocation with triquadratic C¹‐splines for a singularly perturbed reaction–diffusion problem in three dimension is studied. A posteriori error bound in the maximum norm is derived for the collocation method on arbitrary tensor‐product meshes which is robust in the perturbation parameter. Numerical results are presented that support our theoretical estimate.     

$${\varvec{teaspoon}}$$ : solving the curriculum-based course timetabling problems with answer set programming

Annals of Operations Research - Answer Set Programming (ASP) is an approach to declarative problem solving, combining a rich yet simple modeling language with high performance solving capacities....     

Modulation theory solution for nonlinearly resonant,fifth‐order Korteweg–de Vries,nonclassical, traveling dispersive shock waves

A new class of resonant dispersive shock waves was recently identified as solutions of the Kawahara equation— a Korteweg–de Vries (KdV) type nonlinear wave equation with third‐ and fifth‐order spatial derivatives— in the regime of nonconvex, linear dispersion. Linear resonance resulting from the third‐ and fifth‐order terms in the Kawahara equation was identified as the key ingredient for nonclassical dispersive shock wave solutions. Here, nonlinear wave (Whitham) modulation theory is used to construct approximate nonclassical traveling dispersive shock wave (TDSW) solutions of the fifth‐ order KdV equation without the third derivative term, hence without any linear resonance. A self‐similar, simple wave modulation solution of the fifth order, weakly nonlinear KdV–Whitham equations is obtained that matches a constant to a heteroclinic traveling wave via a partial dispersive shock wave so that the TDSW is interpreted as a nonlinear resonance. The modulation solution is compared with full numerical solutions, exhibiting excellent agreement. The TDSW is shown to be modulationally stable in the presence of sufficiently small third‐order dispersion. The Kawahara–Whitham modulation equations transition from hyperbolic to elliptic type for sufficiently large third‐order dispersion, which provides a possible route for the TDSW to exhibit modulational instability.     

A novel monochromator for experiments with ultrashort X‐ray pulses

Aiming at advancing storage‐ring‐based ultrafast X‐ray science, over the past few years many upgrades have been undertaken to continue improving beamline performance and photon flux at the Femtoslicing facility at BESSY II. In this article the particular design upgrade of one of the key optical components, the zone‐plate monochromator (ZPM) beamline, is reported. The beamline is devoted to optical pump/soft X‐ray probe applications with 100 fs (FWHM) X‐ray pulses in the soft X‐ray range at variable polarization. A novel approach consisting of an array of nine off‐axis reflection zone plates is used for a gapless coverage of the spectral range between 410 and 1333 eV at a designed resolution of E/ΔE = 500 and a pulse elongation of only 30 fs. With the upgrade of the ZPM the following was achieved: a smaller focus, an improved spectral resolution and bandwidth as well as excellent long‐term stability. The beamline will enable a new class of ultrafast applications with variable optical excitation wavelength and variable polarization.     

Gas chromatographic determination of aromatic amines in water samples after solid-phase extraction and derivatization with iodine: I. Derivatization

A new method for the selective determination of aromatic amines is presented, which is based on the solid-phase extraction at pH 9 and subsequent derivatization of the analytes to the corresponding iodobenzenes. These can selectively and sensitively be determined with gas chromatography and electron-capture detection. Separation of at least 30 compounds in a single chromatographic run in 30 min is possible. With this method, 56 aromatic amines were investigated, and only in six cases no derivatives were obtained. Limits of quantitation were between 0.5 and 8 μg l⁻¹, but may still be lowered with higher sample volumes or different injection techniques. The application to water samples revealed the suitability for the investigation of ground, leachate and wastewater.     

Correlation between mechanical and electrical properties on conductive SiC-fibre reinforced composites

Electrical and mechanical properties of ceramic composites are investigated to develop “smart materials” and establish a fracture prediction technique. The “smart materials” are based on silicon carbide fibre-reinforced composites. The SiC-fibres were checked to determine the changes in mechanical and electrical properties during the composites’ production. Samples were produced for the determination of the mechanical strength with in situ detection of the degree of damage by recording the electrical resistance.     

Bis[indanyl]- and bis[indenyl]arylmethanes: New molecular three-bladed propellers

Summary Proton-catalyzed arylmethylation of indan and indene derivatives with 4-methoxybenzaldehyde yield novel triarylmethanes bearing indan or indene substituents. According to Mislow's definition, these molecules belong to the class of molecular three-bladed propellers and exhibit an interesting stereochemistry.

---

Bis[indanyl]- und Bis[indenyl]-aryl-methane: Neue molekulare Dreiblatt-Propeller

Zusammenfassung Die proton-katalysierte Arylmethylierung von Indan- und Inden-Derivaten mit 4-Methoxybenzaldehyd liefert neue Triarylmethane mit Indan- und Inden-Resten. Nach dem Mislowschen Prinzip gehören diese Verbindungen zur Klasse der molekularen Dreiblatt-Propeller.