On combinatorial optimization problems on matroids with uncertain weights

In this paper the combinatorial optimization problem on weighted matroid is considered. It is assumed that the weights in the problem are ill-known and they are modeled as fuzzy intervals. The optimality of solutions and the optimality of elements are characterized. This characterization is performed in the setting of possibility theory. A method of choosing a solution under uncertainty is also proposed.     

Struktur und reaktivität des koordinativ überladenen komplexes dichloro-η5 -cyclopentadienyl- tris(tetrahydrofuran)ytterbium(III)

The crystal and molecular structure of (η⁵ -C₅H₅)YbCl₂(THF)₃ (1), which crystallizes e.g. from solutions of [(C₅H₅)₂YbCl]₂ in THF, fully corresponds to the structure of the previously examined Er-homologue. In accordance with its rather high SAS-value (0.784), 1 loses spontaneously two THF ligands when exposed to toluene.     

Liouville-type theorems for some complex hypoelliptic operators

It is shown that the natural analogue of Liouville's theorem holds for the well-known hypoelliptic operators _α (for ¦α¦ < n) introduced and studied by Folland and Stein on the Heisenberg group H_n. Since these operators are non-real for α ≠ 0, the usual methods of potential theory fail and are replaced by an explicit use of the fundamental solution.     

Apertureless near field optical microscopy: a contribution to the understanding of the signal detected in the presence of a background field

Apertureless scanning near field optical microscopy techniques have become a common way of studying surface samples. By using a nano-probe that scatters the electromagnetic non-propagative waves emerging from a given sample, this microscopy provides optical images with a resolution beyond the diffraction limit. Despite a great diversity of works covering a wide variety of physical domains, the formation of the images obtained is not yet fully understood. The purpose of this letter is to assess the influence of the tip position and imposed oscillation of the tip in apertureless SNOM when a background field is added to the scattered near field. We propose a simple analytical model which enables us to account for the experimental results and explains how, depending on the experimental conditions, the near field signal can totally disappear or, on the contrary, be greatly enhanced.     

Quality test of a mechanical switching valve for two-dimensional open tubular gas chromatography

A commercially available mechanical micro switching valve has been tested for inertness. The test mixtures used were a modified Grob test and a solution consisting of eight typical aroma compounds, both at the 2-ng level. Cryogenic focusing of the sample after chromatography including one passage through the valve revealed that irreversible interaction of some test substances with valve components was rather small. A composite main peak of a chromatogram from a fruit juice aroma exhibiting a “mixed odor” was selectively transferred (heart-cutting) to a second column and resolved into three peaks. GC-GC/sniffing assigned a minor peak to a substance formerly hidden under the composite peak. Separate heating of the valve during temperature programming of the column was found to be unnecessary.     

Polarity of oligooxyethylene derivatives of alcohols, thio alcohols and alkylamines as measured by gas chromatography

The polarities of oligooxyethylene derivatives of alcohols, thio alcohols and alkylamines were determined by gas chromatography. Relationships between empirical, thermodynamic and dispersive force polarity parameters are discussed. The influence of the structures of the compounds [lengths of oligooxyethylene and hydrocarbon chains, heteroatom linked to the alkyl group(s), distribution of carbon atoms in alkyl chains and the type of the group terminating the molecule] was examined. The average structural increments of the considered parameters for characteristic structural fragments were calculated and used in the prediction of the polarities of compounds from their formulae.