On Bisectors in Minkowski Normed Spaces

We discuss the concept of the bisector of a segment in a Minkowski normed n-space, and prove that if the unit ball K of the space is strictly convex then all bisectors are topological images of a hyperplane of the embedding Euclidean n-space. The converse statement is not true. We give an example in the three-space showing that all bisectors are topological planes, however K contains segments on its boundary. Strict convexity ensures the normality of Dirichlet-Voronoi-type K-subdivision of any point lattice.     

Multiplication groups of topological loops

In this paper, we discuss the question as to which Lie groups can occur as multiplication groups Mult(L) of connected topological loops L, and we describe the correspondence between the structure of the group Mult(L) and the structure of the loop L.     

Quantitative Analysis of aliphatic aldehydes by headspace SPME sampling and ion-trap GC-MS

Summary A fast and simple headspace SPME sampling method has been developed for quantification of volatile aliphatic aldehydes in sunflower oil. Analysis has been performed by gas chromatography, on a 30m×0.25 mm i.d. ×0.25 μm CP-Wax 52CB column, with mass spectrometric detection. Carryover from the SPME fiber could be eliminated by heating the fiber in the injection port between runs. Response factors of all the compounds were linear for concentrations up to 100 ng μL⁻¹. The slopes of the calibration curves decrease with the amount of saturation of the aldehydes. The average responses for unsaturated aldehydes were twice as high as those for the saturated variety. Responses for dienes were approximately one order of magnitude higher than for saturated aldehydes. Depletion of the analyte was examined by repeated extraction from the same vial. SPME was optimized—after 30 min extraction most components were found to have reached equilibration. The detection limit for the compounds studied varied between 0.1 and 1 ng μL⁻¹. Distribution constants were determined for ten different aldehydes and Henry's constants were calculated for unsaturated aldehydes. There was a definite relationship between the response factors and the amount of saturation of the aldehydes. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997     

Linear and cross-linked polymeric solid-state dye lasers based on 8-substituted alkyl analogues of pyrromethene 567

The lasing properties of analogues of the commercial laser dye pyrromethene 567 (PM567) incorporated (dissolved or copolymerized) into polymeric matrices have been studied using both linear and cross-linked methyl methacrylate-based copolymers with different degrees of functionalization. All synthesized dyes have the chromophore core of PM567 but with an ω-acyloxypolymethylene chain at position 8. In general, the new materials exhibited laser emission with higher efficiencies and much higher photostabilities than those containing the commercial dye PM567 under the same experimental conditions. Lasing efficiencies of up to 40% were obtained under transversal pumping at 534 nm. The highest photostabilities, with the laser output remaining stable or dropping by less than 15% after 100 000 pump pulses at the same position of the sample, were reached in cross-linked materials with dyes covalently linked to the polymeric chains. When the polymeric samples were incorporated into a grazing-incidence grating oscillator, narrow-line-width operation with tuning ranges of up to 40 nm was obtained. These results show that efficient and photostable solid-state dye lasers competitive with their liquid counterparts can be developed by adequate chemical modifications in the dye molecules, as well as by the selection of appropriate polymeric formulations.     

Modification of generalized topologies via hereditary classes

The purpose of the paper is to show that the construction leading from a topology and an ideal of sets to another topology remains valid, together with a lot of applications, if topology is replaced by generalized topology and ideal by hereditary class.