Eine genäherte Behandlung des schweren symmetrischen Kreisels in nicht-Eulerschen Koordinaten

Summary The gyroscope has many technical applications as an essential member in a system with several degrees of freedom, the (dynamic) stability of which with respect to a certain equilibrium position may be of particular interest. To investigate the stability of a system by the well-known method of small oscillations, the movements of the different members must be described by convenient coordinates. As to the gyroscope, it is necessary for this purpose to replaceEuler's angles by other coordinates, with which the rigorous equations of its movement are deduced. Assuming only small displacements of the axis of symmetry from its undisturbed equilibrium position, and by making the problem dimensionless, a simple solution can be obtained for the nutation and precession of a heavy gyroscope both as a symmetrical top and as a gyroscopic pendulum. Further, the damping of the gyroscope by its movement around the equilibrium position has also been considered in order to be able to estimate its influence on the stability.     

Paare von gruppenklassen mit der holomorph-eigenschaft

Ohne Zusammenfassung     

Die Orientierungsfunktionen eines affinen Raumes

Ohne Zusammenfassung     

13C-NMR-Untersuchungen zur Azido-Tetrazol-Valenzisomerie. Tetrazolo[1,5-α]pyrimidine

¹³C NMR has been used to study the azido-tetrazolo valence isomerism of three tetrazolo[1,5-α]pyrimidines. Large chemical shift variations of C-4 carbons were found to be useful to distinguish between azido and tetrazolo isomers. Furthermore, the structure of new heterocycles has been proved and the report of LaNoce and Giuliani concerning 9-methyl-s-triazolo[4,3-c]tetrazolo[1,5-α]pyrimidine is shown to be incorrect.     

Fuzzy σ-algebras and fuzzy measurable functions

In this paper we first give an axiomatic definition of a fuzzy σ-algebra which is a generalisation of the family of fuzzy events considered by L.A. Zadeh [13]. The relationship between classical and fuzzy σ-algebras and between topologies and σ-algebras, in both cases, classical and fuzzy, is established in the notation of commutative diagrams. For fuzzy topologies we refer to the work of R. Lowen [8]. After a comparison between classical measurability of functions and fuzzy measurability defined in this paper we finally introduce the product of fuzzy σ-algebras.     

Iterationsverfahren mit Fehlerabschätzung für lineare Operatorgleichungen

Ohne Zusammenfassung Vorgelegt von L. Collatz