Phragmen–lindelöf principle for weak subsolutions and cooperative reaction–diffusion systems

One of the principal techniques for treating sustems of reaction–diffusion equations is based on a comparison method using sub and super–solutions. In practice this method is much more effective if non–smooth subsolutions are allowed. In this note we extend the analysis in [2,3] for cooperative systems and prove a comparison principle for a natural and rather general class of weak subsolutions satisfying a Phragmen–Lindelöf condition. An application is then given to a biological model in involving a pair of mutualists.     

A characterization of totally normal structure

In this note it is proved that a subsetA of a locally convex topological vector spaceE has normal structure with respect to every continuous seminorm onE — called totally normal structure — iff every bounded convex subset ofA is precompact. Some consequences are discussed.     

In situ X-ray scattering studies of lyotropic liquid crystalline PBO and PBZT monofilament drawing

The results of a series of novel synchrontron-based in situ x-ray scattering experiments of monofilament fiber drawing from lyotropic solutions of poly(cis-benzoxazole) (PBO) and poly(trans-benzothiazole) (PBZT) are reported. The purpose of the study is to determine orientation and microstructure development in the draw zone as a function of shear rate in the capillary die, and spin draw ratio (SDR). The transition of the extrudate from opaque to the transparent is complete at about a SDR = 3 and f of 0.9. The filament orientation parameter (f) was found to depend strongly on spin draw ratio, but not shear rate. The orientation was found to increase down the extrudate toward completion of the draw down as one proceeds further from the die face up to an extrudate length of 3.8 cm. Coherence lengths on the order of 19 nm (axial), and 4.5 nm (lateral) have been observed. These “microdomain” sizes are consistent with the “crystallite” sizes typically observed in coagulated fiber. The occurrence of these microdomains in the draw zone as a precursor to the microfibrillar structure is believed to be the origin of low filament compressive strength. © 1994 John Wiley & Sons, Inc.     

Complexity models in financial markets

In this approach, the complexity of the self-organizing microstructure of the stock exchange is explicitly taken into consideration: the process of offers and trades as well as the adjustment of individual expectations are modelled with help of a (stochastic) jump process. Its abilities are illustrated by modelling the continuous quotations of asset prices at an auction type stock exchange. The functional form of the transition (hazard) rates is chosen to reflect the individual preferences and expectations as well as the economic environment. The model is described in detail and examples of Monte Carlo simulation results are presented.     

Random Block Copolymers via Segment Interchange Olefin Metathesis

Polycarbonate/polyethylene random block copolymers (RBCs) have been produced using olefin metathesis catalysis in a process termed segment interchange metathesis. An olefin metathesis catalyst tolerant of polar functionality was added to reagent polycarbonate and polyethylene polymers which contained internal unsaturated carbon–carbon bonds. Subsequent metathesis occurred, segmenting the reagent polymers, resulting in RBCs. The block copolymers self-assembled into microphase structures which persisted into the melt state as determined by small angle X-ray scattering (SAXS).

     

Determination of lansoprazole and its metabolites in plasma by high-performance liquid chromatography using a loop column.

A high-performance liquid chromatographic method for the simultaneous determination of lansoprazole, a new proton pump inhibitor, and its metabolites in human plasma is described. Lansoprazole, its metabolites and an internal standard were extracted with tert.-butyl methyl ether. Samples were injected using an automatic injector via a loop column, and separation was obtained using a reversed-phase column under isocratic conditions. The absorbance was monitored at 285 and 303 nm. The quantification limit was 2 ng/ml for lansoprazole and 3 or 5 ng/ml for the metabolites. No endogenous compounds were found to interfere. The mean overall recovery was between 75 and 95% for lansoprazole and its metabolites. This method is suitable for pharmacokinetic studies.     

CEMS-study of the interface in Fe/Cr multilayer systems

The magnetic hyperfine (hf.) fields at the Fe/Cr interface were analyzed in epitaxial Fe/Cr thin film structures of (100)- and (110)-orientation with monolayer resolution by means of in-situ⁵⁷Fe Conversion Electron Mössbauer Spectroscopy (CEMS). The hf. field (300 K) in the 1st Fe-monolayer (ML) at the interface has been found to be strongly reduced to 22.0/20.9 T for (110)-/(100)-orientation, whereas the 2nd and 3rd ML reveal a slightly increased hf. field of 33.7 T as compared with the Fe-bulk value of 33.4 T. The temperature dependence of the hf. field at the interface shows aT ^3/2 spin wave law. The spin wave parameters are enlarged with respect to the bulk value indicating a reduced exchange interaction. A discontinuity in theT ^3/2-dependence is interpreted by the onset of magnetic order (Néel-temperature) of the Cr layers adjoining the⁵⁷Fe probe layer.