Quantitative Fatou Theorems and Uniform Rectifiability

We show that a suitable quantitative Fatou Theorem characterizes uniform rectifiability in the codimension 1 case.

     

Ein komplexer Neokörper ohne reellen Unterneokörper

Ohne Zusammenfassung     

On a Generalization of the Stone–Weierstrass Theorem

A categorical version of the famous theorem of Stone and Weierstrass is formulated and studied in detail. Several applications and examples are given.     

Compact groups and fixed point sets

Some structure theorems for compact abelian groups are derived and used to show that every closed subset of an infinite compact metrizable group is the fixed point set of an autohomeomorphism. It is also shown that any metrizable product containing a positive-dimensional compact group as a factor has the property that every closed subset is the fixed point set of an autohomeomorphism.

     

First energy and angle differential measurements of e+e−-pairs emitted by internal pair conversion of excited heavy nuclei

We present the first energy and angle resolved measurements of e⁺e⁻-pairs emitted from heavy nuclei (Z≥ 40) at rest by internal pair conversion (IPC) of transitions with energies of less than 2 MeV as well as recent theoretical results using the DWBA method, which takes full account of relativistic effects, magnetic substates and finite size of the nucleus. The 1.76 MeV E0 transition in ⁹⁰Zr (⁹⁰Sr source) and the 1.77 MeV M1 transition in ²⁰⁷Pb (²⁰⁷Bi source) have been investigated experimentally using the essentially improved setup at the double-ORANGE β-spectrometer of GSI. The measurements prove the capability of the setup to cleanly identify the IPC pairs in the presence of five orders of magnitude higher β⁻ and γ background from the same source and to yield essentially background-free sum spectra despite the large background. Using the ability of the ORANGE setup to directly determine the opening angle of the e⁺e⁻–pairs (Θ_e+e−), the angular correlation of the emitted pairs was measured within the range covered experimentally (40°≤Θ_e+e−≤ 180°). In the ⁹⁰Zr case the correlation could be deduced for a wide range of energy differences E _Δ of the pairs (−530 keV ≤E _Δ≤ 530 keV). The ⁹⁰Zr results are in good agreement with recent theory. The angular correlation deduced for the M1 transition in ²⁰⁷Pb is in strong disagreement with theoretical predictions derived within the Born approximation and shows almost isotropic character. This is again in agreement with the new theoretical results. Received: 22 April 1997 / Revised version: 16 December 1997