Annehmbare Modelle in der linearen Stabilitätstheorie

Zusammenfassung Häufig wird ein System, dessen Stabilität untersucht werden soll (z. B. eine rotierende Welle), durch ein einfacheres Modell ersetzt. Es gibt jedoch Fälle, wo die Stabilitätskarte entscheidend von der Wahl des Modells abhängt. In der vorliegenden Arbeit werden einige Regeln aufgestellt, die man bei der Auswahl eines Modells befolgen muss, damit man dieses als «annehmbar» bezeichnen kann. Die Untersuchungen werden durchgeführt an linearen mechanischen Systemen und linearen passiven elektrischen Netzwerken. Es wird weiterhin gezeigt, dass es Systeme mit unendlichem Freiheitsgrad gibt, die kein annehmbares endliches Modell haben. Die Frage, ob man kleine Einflüsse (Reibungen usw.) in einem Modell vernachlässigen darf oder nicht, wird mit Hilfe einer Störungsrechnung behandelt.

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Summary It is sometimes convenient to replace a system (e.g., a rotating shaft) whose stability is to be investigated by a simplified model. There are cases, however, where the stability pattern obtained decisively depends on the choice of the model. The present paper establishes a few rules for the selection of reliable models, called admissible. The investigations are confined to linear mechanic systems and linear passive electrical networks. Moreover, the author shows that certain systems with an infinite degree of freedom do not have finite admissible models. An important problem is the question as to which small influences (as, e.g. friction) may or must not be neglected in the given situation. This problem is solved by means of a perturbation approach.

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Auszug aus der von der Eidgenössischen Technischen Hochschule genehmigten Promotionsarbeit (Nr. 4837) des Verfassers (Referent: Prof. Dr. H. Ziegler, Korreferent: Prof. Dr. Ch. Wehrli).     

Thermochemistry of fluorine compounds: IV. Rubidium tetrafluoroiodate

From measurement of the heat of hydrolysis, at 25°C , the enthalpy of formation of rubidium tetrafluoroiodate is derived: ΔH°_f [RbIF₄, cryst.]₂₉₈= ?191.12±4.43 kJ mol^?1. Heat capacity measurements for RbIF₄ over the range 273–303 K are also reported.     

Unzerlegbare Darstellungen I

LetK be the structure got by forgetting the composition law of morphisms in a given category. A linear representation ofK is given by a map V associating with any morphism : ae ofK a linear vector space map V(): V(a)V(e). We classify thoseK having only finitely many isomorphy classes of indecomposable linear representations. This classification is related to an old paper by Yoshii [3].

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Unzerlegbare Darstellungen I

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Herrn Professor E. Witt zum 60. Geburtstag     

Spectrophotometric determination of silicate in natural waters by formation of α-molybdosilicic acid and reduction with a tin(IV)-ascorbic acid-oxalic acid mixture

Reaction of dissolved silicate with molybdate at pH 3.8–4.8 in acetate buffer yields only the α-molybdosilicic acid. Treatment of this acid with a solution containing tin(IV) chloride, ascorbic acid and oxalic acid rapidly gives the blue reduced acid without reducing the excess of molybdate reagent. In the recommended procedure, Beer's Law is followed at 740 nm over the range 0–2000 μg Si l^-1 with a coefficient of variation of 0.34% at 400 μg Si l^-1 and 0.52% at 40 μg Si l^-1. The sensitivity of the method is not affected by ionic strength.     

The mass spectra of some naphthoquinones. Lapachol,isolapachol and related compounds

Several alkylhydroxynaphthoquinones and chemically related cyclic compounds were subjected to mass spectrometric investigation. Fragmentation pathways were elucidated by use of metastable ions, relative intensities of normal ions and accurate mass measurement. In these series, differences in the spectra of 1,2- and 1,4-naphthoquinones are slight. Evidence for ring expansion in ions from furans is suggested.