Hausdorff Dimension of Operator Stable Sample Paths

The Hausdorff dimension of the sample paths of a stochastic process with stationary independent operator stable increments is computed. With probability one, every sample path has the same dimension, depending on the real parts of the eigenvalues of the operator stable exponent.     

Exact results for the persistent current in an aharonov-bohm ring with a quantum impurity

We consider the problem of a persistent current in a one-dimensional mesoscopic ring with the electrons coupled by a spin exchange to a magnetic impurity. We show that this problem can be mapped onto an integrable model with a quadratic dispersion (with the latter property allowing for an unambiguous definition of the persistent current). We have solved the model exactly by a Bethe ansatz and found that the current is insensitive to the presence of the impurity. We conjecture that this result holds for any integrable quantum impurity model with an electronic dispersionε(k) that is an even function ofk.     

Generatrices of rational curves

We investigate the one-parametric set of projective subspaces that is generated by a set of rational curves in projective relation. The main theorem connects the algebraic degree of , the number of degenerate subspaces in and the dimension of the variety of all rational curves that can be used to generate . It generalizes classical results and is related to recent investigations on projective motions with trajectories in proper subspaces of the fixed space. Received 9 May 2001.     

Rationale Tschebyscheff-Approximation über unbeschränkten Intervallen

Summary We consider rational best approximations to functions real-valued and continuous on closed unbounded intervals of the extended real numbers. The error of the best approximation is characterized by an alternant, whose length may be different from the well-known number for a bounded interval. Besides some exceptional cases the best approximation is unique.     

Über enolisierte Derivate der Chlorophyllreihe. 132-Desmethoxycarbonyl-173-desoxy-132,173-cyclochlorophyllid a-enol und eine Methode zur Einführung von Magnesium in porphinoide Ligandsysteme unter milden Bedingungen. (Vorläufige Mitteilung)

Enol derivatives in the chlorophyll series. 13²-Desmethoxycarbonyl-17³-desoxy-13²,17³-cyclochlorophyllide a-enol and a method for the introduction of magnesium into porphinoid ligands under mild conditions Magnesium transfer from the iodo-magnesium salt of 3,5-di-t-butyl-4-hydroxy-toluene (BHT) into methyl pheophorbide a is a fast process in methylenechloride/ether solution at ambient temperature. This procedure for the introduction of magnesium into labile chlorin ligands has made possible the preparation of a crystalline 13², 17³-cyclochlorophyllide a-enol. Concomitant use of the lithium salt of BHT facilitates the more critical insertion of magnesium into methyl bacteriopheophorbide a. The preparative success of these magnesium transfers depends crucially upon the solvent system used. Under conditions where the complexation of methyl pheophorbide a with iodo-magnesium-BHT is essentially complete within 2 minutes at 12° in methylenechloride/ether solution, strong inhibition of the magnesium transfer is observed by cosolvents such as pyridine, dimethylacetamide, dioxan or tetrahydrofuran.     

Quality assurance in pesticide residue analysis

Summary During the last few years, the Working Group Pesticide Residues of the Food Chemistry and Forensic Chemistry Division of the Gesellschaft Deutscher Chemiker (German Chemical Society) has organised six laboratory performance tests on the analysis of pesticide residues in which numerous laboratories were involved. In these tests the choice of the analytical methods for the examination of fats or vegetable substrates was free. Organochlorine pesticides in concentrations of over 0.01 mg/kg were mostly readily identified, whereas in the analysis of organophosphorus residues often only the classic compounds (parathion, diazinon, etc.) were reported. Many a false positive result could have been avoided by using more adequate methods for confirmatory analysis. The quantitative results, however, were generally quite reliable and were mostly within the official acceptable dispersion range. It can be concluded that the performance of a residue laboratory is by no means constant, and that it is necessary to assess regularly the quality of the analytical results by participating in such interlaboratory tests.

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Qualitätssicherung bei Rückstandsanalysen von PflanzenschutzmittelnErfahrungen aus Ringversuchen

     

Whole cell matrix-assisted laser desorption/ionization time-of-flight mass spectrometry and in situ structure analysis of streptocidins, a family of tyrocidine-like cyclic peptides

Streptocidins, a family of tyrocidine-like cyclic decapeptides, are an ideal demonstration object for the detection and in situ structure analysis of natural compounds directly in microbial cells using whole cell matrix-assisted laser desorption/ionization time-of-flight-mass spectrometry (MALDI-TOFMS), an emerging technique that can be used for rapid sensitive metabolic profiling of microorganisms. Five main members of the streptocidin family (A-E) were detected in Brevibacillus cells picked from agar plates and identified by in situ structure analysis with post-source decay MALDI-TOFMS. This efficient modern method allows the precise detection of metabolites within minutes without the need to isolate and purify the target compounds. The generated mass spectra are of similar quality to those obtained for the purified peptides. In addition, surface extracts were prepared by treating Brevibacillus cells with 70% acetonitrile in the presence of 0.1% trifluoroacetic acid and fractionated by high-resolution reversed-phase high-performance liquid chromatography (HPLC). In this way ten minor streptocidins were detected demonstrating the full biosynthetic variety of streptocidin production on the cellular level. The streptocidins differ from the well-known tyrocidines essentially in position 3 of the decapeptide chain by replacement of the aromatic amino acid (F/W) found in tyrocidines by L-leucine or L-valine.