Unitary implementation of automorphism groups on von Neumann algebras

A necessary and sufficient continuity condition is obtained in order that a topological group of automorphisms of a semi-finite von Neumann algebra in standard form is unitarily implemented. The methods used are extended to the study of unitary implementation for a general von Neumann algebra of those automorphism groups that commute with the one-parameter modular automorphism group.This research was partially supported by the National Science Foundation.     

Axisymmetric buckling of rigidly clamped hemispherical shells

The shell is subjected to a uniform compressive surface load (either a pressure or a centrally directed load). The results of a numerical study are summarized and compared with experiments.     

Ein verallgemeinerter Kettenbruch-Algorithmus zur rationalen Hermite-Interpolation

Summary In this paper we consider rational interpolation for an Hermite Problem, i.e. prescribed values of functionf and its derivatives. The algorithm presented here computes a solutionp/q of the linearized equationsp–fq=0 in form of a generalized continued fraction. Numeratorp and denominatorq of the solution attain minimal degree compatible with the linearized problem. The main advantage of this algorithm lies in the fact that accidental zeros of denominator calculated during the algorithm cannot lead to an unexpected stop of the algorithm. Unattainable points are characterized.

Herrn Prof. Dr. Dr. h.c.mult. L. Collatz zum 70. Geburtstag gewidmet     

Eine Verallgemeinerung der Färbungszahlen

Ohne ZusammenfassungMit 3 Abbildungen     

γ-Sulphenylation of αβ-unsaturated aldehydes,ketones, and esters: the use of O-silylated dienolates

Phenyl sulphenyl chloride is a γ-selective electrophile in its reaction with O-silylated dienolates.     

Periodic solutions of asymptotically linear Hamiltonian systems

We prove existence and multiplicity results for periodic solutions of time dependent and time independent Hamiltonian equations, which are assumed to be asymptotically linear. The periodic solutions are found as critical points of a variational problem in a real Hilbert space. By means of a saddle point reduction this problem is reduced to the problem of finding critical points of a function defined on a finite dimensional subspace. The critical points are then found using generalized Morse theory and minimax arguments.