On a Formula for the Kostka Numbers

From Kostant’s multiplicity formula for general linear groups, one can derive a formula for the Kostka numbers. In this note we give a combinatorial proof of this formula. Received January 7, 2005     

Isolement de l'acide 3-amino 12-methyl tetradecanoique et de l'acide 3-amino 12-methyl tridecanoique a partir de l'iturine,antibiotique de Bacillus subtilis

lturin, a peptide antibiotic from Bacillus subtilis, was separated into three iturins: A, B, C by thin-layer chromatography. Iturin A, which has an antifungal activity, contains Asp, Glu, Tyr, Ser, Pro in a molar ratio 3:1:1:1:1 and a lipid moiety AL. The latter was shown to be a mixture of C₁₄ (40%) and C₁₅, (60%) amino-acids. The structure of these was determined by combined gas chromatography-mass spectrometry of the N-acetylmethyl esters. Strong peaks at m/e = 144 and m/e = 102 indicate a β-amino group. Identification of acetone and methylethylketone after chromic acid oxidation indicates an iso and anteiso structure. After comparison of the natural amino-acids with synthetic 3-amino pentadecanoic acid it is concluded that the lipid AL is a mixture of 3-amino 12- methyltetradecanoic acid and 3-amino 12-methyltridecanoic acid.     

Charakterisierung von Kieselsäuresolen mit Röntgenkleinwinkelstreuung,Elektronenmikroskopie und Stickstoff-Adsorption

Zusammenfassung Es werden die mittleren Dimensionen der Teilchen dreier Kieselsäuresole mit derRKWS und demE. M. bestimmt. Entgegen der Angabe anderer Autoren ergibt sich dabei bei Berücksichtigung der Teilchengrößenverteilung nahezu völlige Übereinstimmung beider Methoden.RKWS undE. M. ergeben angenähert auch die gleiche mittlere Schwankung _m der Teilchendurchmesser. Die mit derRKWS bestimmte spezifische Oberfläche ist stets größer als die aus der N₂-Adsorption bestimmte, und zwar nimmt der relative Unterschied mit dem mittleren Teilchendurchmesser zu. Die mit derRKWS bestimmte innere Hydratation liegt bei 0,15–0,26 g H₂O/g SiO₂.

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Characterization of silica sols by means of X-ray small angle scattering, electron microscopy and nitrogen adsorption

X-ray small angle scattering and electron microscopy are used to determine average dimensions of particles in three silica sols. In contradiction to findings of other authors, a nearly complete agreement of both methods is found if the particle size distribution is taken into account. Identical average variations _m of the particle diameters are obtained for both methods. The inner surface determined by means of the X-ray small angle scattering is in all cases larger than that obtained from N₂-adsorption, the difference increasing with average particle diameter. The inner hydration determined by means of the X-ray small angle scattering lies at 0.15–0.26 g H₂O/g SiO₂.

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Mit 8 Abbildungen

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Herrn Professor Dr. Dr. h. c.Otto Kratky zum 70. Geburtstag mit den herzlichsten Glückwünschen gewidmet.     

Crystalline self-assembly into monolayers of folded oligomers at the air-water interface

Insertion of the 1,3-bis(ethynylene)benzene unit as a rigid spacer into a linear alkyl chain, thus separating the two resulting stems by 9 A. induces chain folding at the air-water interface. These folded molecules self-assemble into crystalline monolayers at this interface, with the plane of the folding unit almost perpendicular to the water surface, as determined by synchrotron grazing-incidence X-ray diffraction. Three distinct molecular shapes, of the types U, inverted U, and M, were obtained in the two-dimensional crystalline state, depending upon the number of spacer units, and the number and position of the hydrophilic groups in the molecule. The molecules form ribbons with a higher crystal coherence in the direction of stacking between the molecular ribbons, and a lower coherence along the ribbon direction. A similar molecule, but with a spacer unit that imposes a 5 A separation between alkyl chains, yields the conventional herringbone arrangement.