Einige Ergebnisse über Homotopiegruppen von Sphären

Ohne ZusammenfassungHerrn Professor Dr. G.Köthe anläßlich seines 60. Geburtstags am 25. Dezember 1965 gewidmet     

Anodisch oxydierte Aluminiumoberfläche: Ein neues Adsorbens in der „Dünnfilm-Chromatographie“

The preparation of a very thin chromatographically active Al₂0₃-layer on small aluminium plates or wires by a new anodic oxidation method is described. The excellent suitability of this Al₂O₃-layer for application to separations are demonstrated by the examples of “thin-film Chromatographic” separations of a mixture of dye stuffs, some metal dithizonates and metabolites of the pesticide Endosulfan in the ng and pg range.     

Fuzzy propositional logics

Fuzzy logic $\text{L}$_∞9 considered in connection with fuzzy sets theory, is a special theory, is a special many valued logic with truth-value sets [0, 1], which has been studied already by Lukasiewicz. We consider also his versions $\text{L}$_m for m ? 2 with finite truth-value sets. In all cases we add two further propositional connectives, one conjunction and one disjunction. For these logics we give a list of tautologies, consider relations between their sets of tautologies, prove their compactness, and mention some further results.     

Fuzzy uniqueness of fuzzy mappings

For fuzzy mappings between fuzzy sets of higher level we study a notion of fuzzy uniqueness. i.e. of fuzzy functions, which formalizes the intuition that ‘almost identical’ images under f.Characterizations are given for such fuzzy mappings which are really (i.e. with truth value 1) fuzzy unique or fuzzy biunique, and for those fuzzy sets which can be domains of really fuzzy unique fuzzy mappings.Finally, as an application fuzzy cardinals, their ordering, sum, and product are introduced, and some properties proved.