Zusammenhänge zwischen konvergenten und asymptotischen Entwicklungen bei Lösungen linearer Differentialsysteme vom Range Eins

Ohne Zusammenfassung     

Zusammenhänge zwischen Böschungslinien auf Mittelpunktquadriken und gewissen Affinbewgungen

Ohne ZusammenfassungHerrn Prof. Dr. rer. nat. Friedrich Lösch zum 60. Geburtstag gewidmetMit 2 Textabbildungen     

Über die durch Punktpaarsysteme einerC 3 veranlassten Curven und ihre Zusammenhänge

Ohne Zusammenfassung     

Affine Zusammenhänge auf Mannigfaltigkeiten mit fast-symplektischer Struktur

Ohne Zusammenfassung     

Ein neuer Zusammenhang zwischen einfachen Gruppen und einfachen Singularitäten

Summary We describe a new construction to obtain a simple hypersurface singularity from the corresponding simple complex Lie-groupG. LetX be the closed orbit in the projective space attached to the Lie algebra ofG. Consider a regular nilpotent element and denote byH _{y 0} the hyperplane orthogonal toy ₀ with respect to the Killing form. Then the hyperplane sectionXH _{y 0}, has exactly one singularity which is simple of desired type. By variation of the pointy ₀ we obtain a versal deformation. The construction generalizes with minor modifications to any characteristicp of the basefield. Even in bad characteristic we recover at least the positive part of the semiuniversal deformation. We prove that forp=2 a simple, quasihomogeneous singularity of type A₇ resp. D₈ is adjacent to E₇ resp. E₈ provided its dimension is even. Furthermore A₈ is adjacent to E₈ forp=3.

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Unterstützt durch den Schweizerischen Nationalfonds     

Über Zusammenhänge zwischen der Differentialgeometrie im Großen und im Kleinen

Ohne ZusammenfassungDissertation, Universität Berlin, 1931.     

Die Konstruktion der mittleren Linie bei Oberflächenprofilen und einige Zusammenhänge zwischen den zur Kennzeichnung von Oberflächen benutzten Grössen

Summary Attention is directed first to the analogy between the problem of evaluating collectives and that of finding a numerical expression for an existing surface.For the valueh _RMS /h _AVE , approximations are made using Fourier series of the surface profil based on the center line.h _AVE =center line average (=h _CLA ). Forh _AVE , an upper bound calculated from the Fourier coefficients is stated. With this, and ash _RMS may be determined in a definite form, a lower bound forh _RMS /h _AVE is obtained. Provided that the surface profil is the superimposition of two harmonics, a lower, bound forh _AVE and then an upper bound forh _RMS /h _AVE could be found. In order to get a base line for which the areas embraced by the profile above and below the line are equal and a minimum, a graphical method is constructed.

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Mitteilung aus der Physikalisch-Technischen Bundesanstalt.     

Liesche Gruppen und Affin Zusammenhängende Mannigfaltigkeiten

Ohne Zusammenfassung     

Über die starken maxima und minima bei einfachen Integralen

Ohne Zusammenfassung     

Beachtenswerte Vorgänge bei hochtouriger hydrodynamischer Lagerschmierung

Summary Flow conditions in the lubricating gap of a hydro-dynamically lubricated sleeve bearing at extremely high speed have been investigated theoretically. It is known that hydrodynamic lubrication requires a copious oil supply so as not to interrupt the flow and consequently the generation of pressure. However, it is found that with certain running conditions there may be lack of oil in the lubricating gap despite ample supply of oil in the grooves. This is caused by the fact that the oil discharge may be larger than the amount of oil that can be supplied at the beginning of the gap. The result is a vacuum combined with air evaporation and the formation of bubbles, which endanger the running surfaces locally by denuding them of the protective oil film. The results are explained by an example. This shows that under certain circumstances the region of critical speed can still be attained in practice.      

Wahrscheinlichkeit unstetiger Vorgänge bei kontinuierlich wirkenden Ursachen

Ohne Zusammenfassung     

Kritische Drehzahlen unter Torsion und Druck bei Berücksichtigung des Eigengewichtes

Summary The paper deals with the critical angular velocities of continuously loaded shafts. A method is given for the solution of the problem and an example is presented which shows that the critical angular velocities increase, when, instead of a single concentrated load on the ends, the shaft carries a continuous load of the same magnitude.     

Schrittweise Näherungen bei Integralgleichungen und Eigenwertschranken

Ohne Zusammenfassung     

Stabilität Mehrfach Zusammenhängender Minimalflächen

Multiply connected minimal surfaces of genus 0 with only simple interior branch points, for which the corresponding boundary value problem $$\Delta h - K|x_z |^2 h = 0; h_{|\partial \Omega } = 0$$ (K is the Gauss curvature and x_z is the complex gradient of the surface x) is uniquely solvable and which have the property, that the condition K|x_z|²≠0 holds in the branch points, are always isolated and stable solutions of the Plateau problem, corresponding to their boundary curves. To achieve these results one has to consider the conformal type as a variable. We give a method to perform the variation of the conformal type for holomorphic functions. Using the Weierstrass representation we thus obtain a differentiable structure on the set of multiply connected minimal surfaces. We find interesting connections between the classical Riemann-Hilbert problem and Fredholm properties of a projection operator on this manifold.