Grid Graphs,Gorenstein Polytopes,and Domino Stackings

We examine domino tilings of rectangular boards, which are in natural bijection with perfect matchings of grid graphs. This leads to the study of their associated perfect matching polytopes, and we present some of their properties, in particular, when these polytopes are Gorenstein. We also introduce the notion of domino stackings and present some results and several open questions. Our techniques use results from graph theory, polyhedral geometry, and enumerative combinatorics.     

Dependence properties and comparison results for Lévy processes

In this paper we investigate dependence properties and comparison results for multidimensional Lévy processes. In particular we address the questions, whether or not dependence properties and orderings of the copulas of the distributions of a Lévy process can be characterized by corresponding properties of the Lévy copula, a concept which has been introduced recently in Cont and Tankov (Financial modelling with jump processes. Chapman & Hall/CRC, Boca Raton, 2004) and Kallsen and Tankov (J Multivariate Anal 97:1551–1572, 2006). It turns out that association, positive orthant dependence and positive supermodular dependence of Lévy processes can be characterized in terms of the Lévy measure as well as in terms of the Lévy copula. As far as comparisons of Lévy processes are concerned we consider the supermodular and the concordance order and characterize them by orders of the Lévy measures and by orders of the Lévy copulas, respectively. An example is given that the Lévy copula does not determine dependence concepts like multivariate total positivity of order 2 or conditionally increasing in sequence. Besides these general results we specialize our findings for subfamilies of Lévy processes. The last section contains some applications in finance and insurance like comparison statements for ruin times, ruin probabilities and option prices which extends the current literature. Anja Blatter was supported by the Deutsche Forschungsgemeinschaft (DFG).     

3D-snapshot flash NMR imaging of the human heart

SNAPSHOT-FLASH is a recently developed, ultrafast imaging technique, based on conventional FLASH imaging. The application of this new variant to 3D imaging allows the acquisition of a 128 x 128 x 32 data set in 12.5 seconds without triggering, or for cardiac imaging with gating within 32 heartbeats. Compared to standard 3D-FLASH this is 128 times faster, because triggering is only required when the 3D phase-encoding gradient is incremented. The method depicts for the first time fast three-dimensional views of the human heart without motional artifacts. The images are spin-density weighted. Using suitable prepulses any desired T1- or T2-contrast may be achieved. The generation of 3D movies is possible without an increase of the total scan time.     

Korrosion von Werkstoffen

Ohne Zusammenfassung