On the existence of weak solutions to the equations of non‐stationary motion of heat‐conducting incompressible viscous fluids

This paper is concerned with the equations of non‐stationary motion in 3D of heat‐conducting incompressible viscous fluids with temperature‐dependent viscosity. The conservation of internal energy includes the usual dissipation term. We prove the existence of a ‘weak solution with defect measure’ to the system of PDEs under consideration. Our method of proof is based on a regularization of the equations of conservation of momentum. Copyright © 2006 John Wiley & Sons, Ltd.     

Chlorophyll Breakdown in Maize: On the Structure of Two Nonfluorescent Chlorophyll Catabolites

In extracts of senescent leaves of the maize plant Zea mays, two colorless compounds with UV/Vis-characteristics of nonfluorescent chlorophyll catabolites (NCCs) were detected and tentatively named Zm-NCCs. The constitution of the two polar Zm-NCCs was determined by spectroscopic means, which confirmed both of these tetrapyrroles to have the basic ligand structure typical of the NCCs from (other) senescent higher plants. In the less polar catabolite, named Zm-NCC-2, the core structure was conjugated at the 8²-position with a glucopyranose unit. Zm-NCC-2 had the same constitution as Nr-NCC-2, an NCC from tobacco (Nicotiana rustica). Indeed, the two NCCs were identified (further) based on their HPL-chromatographic and NMR-spectroscopic properties. The more polar NCC from maize, Zm-NCC-1, differed from Zm-NCC-2 by carrying a dihydroxyethyl side chain instead of a vinyl group at the 3-position. In earlier work on polar NCCs, only separate glucopyranosyl- and dihydroxyethyl-functionalities were detected. Zm-NCC-1 thus is a new constitutional variant of the structures of NCCs from senescent higher plants.     

A mathematical model for diffusion and exchange phenomena in ultra napkins

The performance of napkins is nowadays improved substantially by embedding granules of a superabsorbent into the cellulose matrix. In this paper a continuous model for the liquid transport in such an “ultra napkin” is proposed. Its mean feature is a non-linear diffusion equation strongly coupled with an ODE describing a reversible absorption process. An efficient numerical method based on a symmetrical time splitting and a finite difference scheme of ADI-predictor-corrector type has been developed to solve these equations in a three-dimensional setting. Numerical results are presented that can be used to optimize the granule distribution.     

Transfer of galactose to the anomeric position of N-acetyl gentosamine by galactosyltransferase from bovine milk

Galactosyltransferase was found to transfer β-galactose to the β-anomeric position of N-acetyl gentosamine to afford a β,β(1,1)-linked disaccharide. The reaction was generalized supposing an N-acetyl recognition site in the active site.     

Harmonic functions on locally finite networks

Are there nonconstant bounded harmonic functions on an infinite locally finite network under natural transition conditions as continuity at the ramification nodes and classical Kirchhoff conditions at all vertices? We present sufficient criteria for such a network to be a Liouville space, while we show that a large class of infinite trees admit infinitely many linearly independent bounded harmonic functions. Finally, we show that the standard unit cube grid graphs and some of Kepler’s plane tiling graphs are Liouville spaces.