Delaunay graphs are almost as good as complete graphs

LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$      

On theR-order of coupled sequences arising in single-step type methods

Summary As shown in preceding papers of the authors, the verification of anR-convergence order for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.     

Den Gehalt an leichtem Wasserstoff in schwerem Wasser

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Mikromethode zur quantitativen Chloridbestimmung

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MDGC–MS: A powerful tool for enantioselective flavor analysis

This paper reports the differentiation between the enantiomers of theaspiranes and theaspirones, potent flavor compounds widely used in the flavor industry. Optically pure reference compounds of isomeric theaspiranes were obtained by enantioselective synthesis. Enantiomerically pure reference theaspirones were isolated from quince fruit; their absolute stereochemistry was assigned by CD spectroscopy. For both types of compounds the order of elution was elucidated by using authentic reference compounds. These data enabled the determination of the enantiomeric distribution of both types of compounds in a variety of plant tissues. Because of the complexity of the natural flavor isolates, compounds were identified by mass spectrometry after multidimensional gas chromatography employing a Sichromat 2 double oven chromatograph. After separation of the target compounds on the first, achiral, column (DB-5), they were transferred to a chiral column (C-Dex B) for determination of the enantiomeric distribution. Multiple ion detection (MID) enabled the determination of the enantiomeric distribution even for complex mixtures containing the target compounds at extremely low levels.     

Die spektralphotometrische Bestimmung des Kupfer (II)-Ions

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Nitrat

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