Hochschild- and Cyclic-Homology of LCNT-Spaces

We define a class of topological spaces ( LCNT spaces ) which come together with a nuclear Fréchet algebra. Like the algebra of smooth functions on a manifold, this algebra carries the differential structure of the object. We compute the Hochschild homology of this algebra and show that it is isomorphic to the space of differential forms. This is a generalization of a result obtained by Alain Connes in the framework of smooth manifolds.     

Darstellung,Isolierung und Charakterisierung Gemischter Cyanothiocyanatoäthylendiamin-Chrom(III)-Komplexe

Preparation, Isolation and Characterisation of Mixed Cyanothiocyanato-ethylenediamine-Chromium(III) Complexes The complex salts K[Cr(CN)(NCS)₃(en)] and [Cr(CN)(NCS)(en)₂]SCN are prepared for the first time. After the preparative isolation by column chromatography on alumima, they are characterized by the chromium content and the spectra.     

New aspects of the protonation of biliverdins

Biliverdins undergo appreciable self association in acidic solutions especially if solvents like benzene or chloroform are employed. The population of aggregates further depends on the concentration of both the acid and the solute. In chloroform and benzene solutions at high acidity a doubly protonated species is formed. This is concluded from a combinatory evaluation of the CD and electronic absorption spectra of chiral optically active biliverdins (1–6) in benzene, chloroform, and ethanol solutions containing trifluoroacetic acid or hydrochloric acid. The aggregates formed at medium acid concentrations exhibit largeCotton effects in the long-wavelength absorption bands and thus dominate the CD spectra. Similarly, agrregates are the main contributors to theCotton effects of achiral, protonated biliverdins in (S)-(–)-ethyl lactate (SICD) at usual concentrations. The consequence and relevance of these findings with regard to the recent literature is briefly discussed.Dedicated to Prof. Dr.Karl Schlögl on occasion of his 60^th birthday.     

Trigonometric wavelets for Hermite interpolation

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.

     

Austauscher mit cyclischen Polyethern als Ankergruppen—II: Anwendungen

Exchangers with cyclic polyethers as anchor groups have a large range of applications such as separations of cations with a common anion, of anions with a common cation, and of neutral organic compounds, and the determination of water by elution chromatography. Some crown ether monomers, especially 4- and 4,4′-alkyl-substituted benzo-derivatives are suitable for extractions and their adducts with heteropoly acids are used as liquid ion-exchangers. The exchangers are also applied in thin-layer chromatography and thin-layer electrophoresis. Furthermore the exchangers are successfully used in preparative chemistry, e.g., in salt conversions in order to isolate salts which are difficult to prepare by other means, in isolation and purification of organic compounds, and for anion activation in organic reactions.     

Photometrische Sulfitbestimmung mit Trinitrobenzoesäure

SO₃ ^2? can be determined photometrically with trinitrobenzoic acid within 2 min. SO₄ ^2?, S₂O₃ ^2?, S^2? and S_xO₆ ^2? in concentrations up to 1 mMole/100 ml do not interfere. The limit of determination is 0.22 mg SO₃ ^2?/100 ml, the standard deviation for the determination of 7 mg SO₃ ^2? is ± 0.59 Rel.-%.     

O-(2-Hydroxy-5-methyl-phenylazo)benzoes?ure als Reagens zur polarographischen, inversvoltammetrischen und photometrischen Be(II)-Bestimmung

Zusammenfassung o-(2-Hydroxy-5-methyl-phenylazo)-benzoesäure bildet mit Be(II) einen Chelatkomplex, der zu polarographischen, inversvoltammetrischen und photometrischen Bestimmungen verwendet werden kann. In Gegenwart von Al(III), Fe(III), Co(II), Ni(II) und Cu(II) erfolgt die Komplexbildung bevorzugt mit Be(II), wenn die Selektivität des Komplexbildners durch Zugabe von Methanol oder Acetonitril erhöht wird. Für die Polarographie lassen sich die störenden Kationen mit Solochromviolett RS maskieren. So können z. B. bis 10^–9 Mol/ml Be(II) mit einem 3000fachen Al(III)-Überschuß bei einem relativen Fehler von ± 4% simultan bestimmt werden.

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O-(2-Hydroxy-5-methyl-phenylazo)-benzoic acid as reagent for the polarographic, inverse-voltammetric and photometric determination of beryllium(II)

o-(2-Hydroxy-5-methyl-phenylazo)-benzoic acid forms a chelate complex with Be(II) which can be used for polarographic, invers-voltammetric and photometric determinations. In the presence of Al(III), Fe(III), Co(II), Ni(II), and Cu(II) the formation of the Be(II)-complex is selective if methanol or acetonitrile is added. In the polarographic technique interfering cations can be masked with Solochrome Violet RS. 10^–9 mol/ml of Be(II) can be determined simultaneously with a 3000-fold excess of Al(III) with an error ± 4%.

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Zum Teil vorgetragen auf der GDCh-Tagung in Karlsruhe, 13.–18. 9. 1971.     

Papierchromatographische und papierelektrophoretische Untersuchung und Trennung von Anionenverbindungen der Systeme Molybd?n-Wolfram, Niob-Tantal und Silicat-Phosphat

Zusammenfassung Die Untersuchungen erstreckten sich sowohl auf die Trennung der einzelnen Elemente als auch auf die Verfolgung der grundsätzlichen Vorgänge, wobei den Aggregationserscheinungen besondere Beachtung geschenkt wurde.Im einzelnen gelang es, Mo/W in Form ihrer Oxalato-Komplexe mit beiden Methoden gut zu trennen und eine quantitative Bestimmung auszuarbeiten.Während die Oxalato-Komplexe des Nb und Ta auch in Gegenwart von Fe, Ti und V gut papierchromatographisch getrennt werden konnten, erwiesen sich für die Ionophorese die Natriummetallate am geeignetsten. Die Kaliummetallate zeigten verschiedene Aggregationsstufen.Da Silicat in den üblichen Laufmitteln nicht wandert, war eine Abtrennung von Orthophosphat leicht zu erzielen. Mit Hilfe der Ionophorese konnten bei verdünnten wäßrigen Silicatlösungen in Abhängigkeit vom p_H-Wert verschiedene Aggregationsstufen sichtbar gemacht werden.