A numerical test of differential equations for one- and two-loop sunrise diagrams using configuration space techniques

We use configuration space methods to write down one-dimensional integral representations for one- and two-loop sunrise diagrams (also called Bessel moments) which we use to numerically check on the correctness of the second order differential equations for one- and two-loop sunrise diagrams that have recently been discussed in the literature.Comment: 11 pages, no figures, published versio

Variations of the high-level Balmer line spectrum of the helium-strong star Sigma Orionis E

Using the high-level Balmer lines and continuum, we trace the density structure of two magnetospheric disk segments of the prototypical Bp star sigma Ori E (B2p) as these segments occult portions of the star during the rotational cycle. High-resolution spectra of the Balmer lines >H9 and Balmer edge were obtained on seven nights in January-February 2007 at an average sampling of 0.01 cycles. We measured equivalent width variations due to the star occultations by two disk segments 0.4 cycles apart and constructed differential spectra of the migrations of the corresponding absorptions across the Balmer line profiles. We first estimated the rotational and magnetic obliquity angles. We then simulated the observed Balmer jump variation using the model atmosphere codes synspec/circus and evaluated the disk geometry and gas thermodynamics. We find that the two occultations are caused by two disk segments. The first of these transits quickly, indicating that the segment resides in a range of distances, perhaps 2.5-6R_star, from the star. The second consists of a more slowly moving segment situated closer to the surface and causing two semi-resolved absorbing maxima. During its transit this segment brushes across the star's "lower" limb. Judging from the line visibility up to H23-H24 during the occultations, both disk segments have mean densities near 10^{12} cm^{-3} and are opaque in the lines and continuum. They have semiheights less than 1/2 of a stellar radius, and their temperatures are near 10500K and 12000K, respectively. In all, the disks of Bp stars have a much more complicated geometry than has been anticipated, as evidenced by their (sometimes) non-coplanarity, de-centerness, and from star to star, differences in disk height.Comment: Accepted by Astron. Astrophys, 13 pages, 4 embedded figure

Numerical evaluation of the general massive 2-loop sunrise self-mass master integrals from differential equations

The system of 4 differential equations in the external invariant satisfied by the 4 master integrals of the general massive 2-loop sunrise self-mass diagram is solved by the Runge-Kutta method in the complex plane. The method, whose features are discussed in details, offers a reliable and robust approach to the direct and precise numerical evaluation of Feynman graph integrals.Comment: 1+21 pages, Latex, 5 ps-figure

Interactive operational decision making:Purchasing situations & mutual liability problems

Three chapters of this dissertation deal with three different types of interactive purchasing situations, in which multiple buying organizations interact with similar (or possibly the same) suppliers for the procurement of the same commodity. Decisions to be made in interactive purchasing concern if and how to cooperate with other buying organizations. If so, one has to tackle the important question of how to allocate possible cost savings. And if not, how to interact with the supplier(s) on an individual strategic level, while taking into account the strategic behavior of the other purchasers