The nonlinear Bernstein-Schr\"odinger equation in Economics

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the "nonlinear Bernstein-Schr\"odinger system", which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.Comment: 8 pages, submitted to Lecture Notes in Computer Scienc

The diagnostic value of synovial histopathology in undifferentiated inflammatory arthritis: a prospective study in 154 consecutive patients

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On-line Excited-State Laser Spectroscopy of Trapped Short-Lived Ra+^+ Ions

As an important step towards an atomic parity violation experiment in one single trapped Ra$^+$ ion, laser spectroscopy experiments were performed with on-line produced short-lived $^{212,213,214}$Ra$^+$ ions. The isotope shift of the 6\,^2D$_{3/2}$\,-\,7\,^2P$_{1/2}$ and 6\,^2D$_{3/2}$\,-\,7\,^2P$_{3/2}$ transitions and the hyperfine structure constant of the 7\,^2S$_{1/2}$ and 6\,^2D$_{3/2}$ states in $^{213}$Ra$^+$ were measured. These values provide a benchmark for the required atomic theory. A lower limit of $232(4)$ ms for the lifetime of the metastable 6\,^2D$_{5/2}$ state was measured by optical shelving.Comment: 4.2 pages, 6 figures, 2 tables

Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web

We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, $\alpha$. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of $\alpha$, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution and scale-dependence of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web and yields a promising measure of cosmological parameters. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field.Comment: 42 pages, 14 figure

Isotope Shifts of the 6d\,^2D3/2 _{3/2}\, - 7p\,^2P1/2 _{1/2}\, Transition in Trapped Short-Lived 209−214^{209-214}Ra+^+

Laser spectroscopy of short-lived radium isotopes in a linear Paul trap has been performed. The isotope shifts of the 6d\,^2D$_{3/2}\,$ - 7p\,^2P$_{1/2}\,$ transition in $^{209-214}$Ra$^+$ were measured, which are sensitive to the short range part of the atomic wavefunctions. The results are essential experimental input for improving the precision of atomic structure calculation. This is indispensable for parity violation in Ra$^+$ aiming at the determination of the weak mixing angle.Comment: Accepted for publication in Physical Review A as a Rapid Communicatio

Development of a thermal ionizer as ion catcher

An effective ion catcher is an important part of a radioactive beam facility that is based on in-flight production. The catcher stops fast radioactive products and emits them as singly charged slow ions. Current ion catchers are based on stopping in He and H$_2$ gas. However, with increasing intensity of the secondary beam the amount of ion-electron pairs created eventually prevents the electromagnetic extraction of the radioactive ions from the gas cell. In contrast, such limitations are not present in thermal ionizers used with the ISOL production technique. Therefore, at least for alkaline and alkaline earth elements, a thermal ionizer should then be preferred. An important use of the TRI$\mu$P facility will be for precision measurements using atom traps. Atom trapping is particularly possible for alkaline and alkaline earth isotopes. The facility can produce up to 10$^9$ s$^{-1}$ of various Na isotopes with the in-flight method. Therefore, we have built and tested a thermal ionizer. An overview of the operation, design, construction, and commissioning of the thermal ionizer for TRI$\mu$P will be presented along with first results for $^{20}$Na and $^{21}$Na.Comment: 10 pages, 4 figures, XVth International Conference on Electromagnetic Isotope Separators and Techniques Related to their Applications (EMIS 2007