Around random algebra

It is shown that there is a subalgebra of the measure algebra forcing dominating reals. Also results are given about iterated forcing connected with random reals.The first author would like to thank NSF for its partial support under Grant DMS-8701828The second author would like to thank U.S.-Israel BSF for partial supportNote. In the first version of this paper we proved only a weak form of the main result of Sect. 2 (see 2.2). Also, the first version contained a third section, but the main result of that version is a weak form of 2.5     

Friedrich Emich zum 5. September 1930

Ohne Zusammenfassung     

Dünnschichtchromatographie der Dicarbon- und Hydroxycarbonsäuren

Zusammenfassung Dünnschichtchromatographische Trennungen von Dicarbon- und Hydroxycarbonsäuren werden beschrieben. Als Trägersubstanzen dienten Kieselgel, Kieselgel-Kieselgur-Mischungen und Zellulose. Die Untersuchungen ergaben, daß auf Zelluloseschichten unter Verwendung saurer Laufmittel die besten Resultate zu erzielen sind.

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Summary Thin layer chromatographic separations of dicarboxylic and hydroxycarboxylic acids are described. Silica gel, silica gel-kieselguhr mixtures and cellulose were used as carrier substance. The investigations showed that the best results are obtained on cellulose layers with use of an acidic mobile phase.

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Résumé On décrit la séparation par chromatographie en couche mince des acides dicarboxyliques et hydroxycarboxyliques. On prend comme substance support du gel de silice, des mélanges gel de silice-kieselguhr et de la cellulose. Les expériences ont montré que des couches de cellulose et l'emploi d'un éluant acide conduisaient aux meilleurs résultats.

     

Dispersion in retentive pillar array columns

The method of volume averaging is applied to estimate the Taylor–Aris dispersion tensor of solute advected in columns consisting of ordered pillar arrays with wall retention of the type used in chromatographic separation. The appropriate closure equations are derived and solved in a unit cell with periodic boundary conditions to obtain the dispersion tensor (or the reduced plate height) as a function of the Peclet number (reduced velocity); pillar pattern, shape and size; partition coefficient; and resistance to mass transfer. The contributions of the velocity profile, the wall adsorption, and the mass transfer resistance to the dispersion tensor are identified and delineated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns containing ordered pillars. The model is then used to study the effect of pillars’ shape and pattern on the longitudinal dispersion coefficient (plate height).