A postscript on distances in convexn-gons

Letg(n) be the largest integerk such that every convex polygon withn vertices and sides has a vertexx such that the nextk vertices clockwise fromx, or the nextk vertices counterclockwise fromx, are successively farther fromx. We prove thatg(n)=[n/3]+1 forn≥4. An example givesg(n)≤[n/3]+1, and an extension of a 1952 construction of Leo Moser for a related planar problem shows thatg(n)≥[n/3]+1.     

Improved high-performance liquid chromatographic method for the determination of 6-N,N,N-trimethyllysine in plasma and urine: biomedical application of chromatographic figures of merit and amine mobile phase modifiers

An internally standardized method for the determination of 6-N,N,N-trimethyllysine in human plasma, human urine, rat plasma, rat urine and hydrolyzed rat urine is described. This methylated amino acid and the procedural internal standard 6-N,N,N-trimethyllysine were isolated from the sample matrices using short ion-exchange columns and detected following high-performance liquid chromatography using a postcolumn reaction (o-phthalic-dicarboxaldehyde-2-mercaptoethanol) and fluorometric detection. The reliable detection limit for 6-N,N,N-trimethyllysine was 0.2 nmol/ml in 200 microliters of human plasma. The chromatographic separation exploits the unique properties of a novel tertiary amine mobile phase modifier, 3-(N,N-dimethylamino)-1,2-propanediol. The capacity factor and "Chromatographic Figures of Merit" (including peak asymmetry and relative system efficiency) were calculated for the chromatographic peak representing 6-N,N,N-trimethyllysine in over 2200 injections made while evaluating 900 biological specimens.     

-complete sequences of integers

An infinite sequence is -complete if every sufficiently large integer is the sum of such that no one divides the other. We investigate -completeness of sets of the form and with nonnegative.

     

Completely distributive CSL algebras with no complements in

Anoussis and Katsoulis have obtained a criterion for the space to have a closed complement in , where is a completely distributive commutative subspace lattice. They show that, for a given , the set of for which this complement exists forms an interval whose endpoints are harmonic conjugates. Also, they establish the existence of a lattice for which has no complement for any . However, they give no specific example. In this note an elementary demonstration of a simple example of this phenomenon is given. From this it follows that for a wide range of lattices , fails to have a complement for any .

     

Ein Mikrodestillations- und Sublimationsapparat

Zusammenfassung Es wird ein Destillations- und Sublimationsapparat mit einem Innenkühler aus Metall beschrieben, der auch für Arbeiten unter vermindertem Druck und für geringe Substanzmengen brauchbar ist.

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Summary A distillation- and sublimation apparatus with a metal internal condenser is described, which is also useful for working under reduced pressure and with small amounts of substance.

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Résumé On décrit un micro-appareil de distillation et de sublimation avec un réfrigérant interne métallique, qui convient aussi pour les travaux sous pression réduite et pour de faibles quantités de substance.

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Mit 2 Abbildungen.     

Ein Verfahren zur Mikro-Schwefelbestimmung

Zusammenfassung Es wird eine Mikromethode für die Bestimmung des Schwefels in organischen Verbindungen beschrieben. Die Einwaagen von 0,5 bis 5 mg werden mit Kaliumpermanganatlösung, Salpetersäure und Salzsäure zerstört, der oxydierte Schwefel mit Benzidinchlorhydratlösung maßanalytisch bestimmt.     

Mikro-Heißluft- und -Gasverdampfer

Ohne ZusammenfassungMit 3 Abbildungen.     

Block Strong M-Bases and Spectral Synthesis

The selection problem for strong M-bases is shown to have anegative solution in Hilbert space. The constructions are usedto demonstrate that spectral synthesis for compact operatorsis not preserved by inflation. The results show that a numberof statements in the literature are incorrect.     

Mikroapparat für Reaktionen in der Dampf- und Gasphase

Ohne ZusammenfassungMit 4 Abbildungen.