On a variational formula for the H. Weyl curvature invariants
We use the ring of curvature structures, to answer a question of M. Berger about a variational formula for the H. Weyl curvature invariants. Recall that the (2k)-H. Weyl curvature invariant is a polynomial of degree 2k with respect to the Riemannian curvature. In dimension 2k it is just the Gauss-Bonnet integrand, in higher dimensions it appears naturally, as an integrand, in the well known H. Weyl’s tube formula. Mathematics Subject Classification (2000). 58E11, 58C99.
Conformal geometry and fully nonlinear equations
This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.
The MR-TOF-MS isobar separator for the TITAN facility at TRIUMF
At TRIUMF’s Ion Trap for Atomic and Nuclear Science (TITAN) a multiple-reflection time-of-flight mass spectrometer (MR-TOF-MS) will extend TITAN’s capabilities and facilitate mass measurements and in-trap decay spectroscopy of exotic nuclei that so far have not been possible due to strong isobaric contamination. This MR-TOF-MS will also enable mass measurements of very short-lived nuclides (half-life > 1 ms) that are produced in very low quantities (a few detected ions overall). In order to allow the installation of an MR-TOF-MS in the restricted space on the platform, on which the TITAN facility is located, novel mass spectrometric methods have been developed. Transport, cooling and distribution of the ions inside the device is done using a buffer gas-filled RFQ-based ion beam switchyard. Mass selection is achieved using a dynamic retrapping technique after time-of-flight analysis in an electrostatic isochronous reflector system. Only due to the combination of these novel methods the realization of an MR-TOF-MS based isobar separator at TITAN has become possible. The device has been built, commissioned off-line and is currently under installation at TITAN.