Intersections of sequences of ideals generated by polynomials

AbstractWe present a method for determining the reduced Gröbner basis with respect to a given admissible term order of order type ω of the intersection ideal of an infinite sequence of polynomial ideals.As an application we discuss the Lagrange type interpolation on algebraic sets and the “approximation” of the ideal I of an algebraic set by zero dimensional ideals, whose affine Hilbert functions converge towards the affine Hilbert function of I

Elastic Properties and the Band Gap of AlN

Structural and elastic properties of AlNxP1-x, a novel semiconductor alloy, are studied from the first principles in both zinc-blende and wurtzite structures. Performances of the finite difference (FD) method and the density functional perturbation theory (DFPT) are tested and compared. Both of these methods are applied to two different approaches of alloy simulation, a supercell of 16 and 32 atoms (for zinc-blende and wurtzite structures, resp.) and the alchemical mixing (AM) method, where the pseudopotentials are mixed in an appropriate way to form an alloy. All elastic properties, including the elastic tensors, elastic moduli, Poisson’s ratio, B/G, and relaxation coefficient, as well as lattice parameters are calculated using all said methods. Conclusions about the use of the approaches investigated in this paper and about their performance are drawn. In addition, in both crystal structures, the band gap is studied in the whole composition range using the MBJLDA functional. The band gap bowings are unusually high, which confirms earlier reports

FlashCam: A fully digital camera for CTA telescopes

The future Cherenkov Telescope Array (CTA) will consist of several tens of telescopes of different mirror sizes. CTA will provide next generation sensitivity to very high energy photons from few tens of GeV to >100 TeV. Several focal plane instrumentation options are currently being evaluated inside the CTA consortium. In this paper, the current status of the FlashCam prototyping project is described. FlashCam is based on a fully digital camera readout concept and features a clean separation between photon detector plane and signal digitization/triggering electronics.Comment: In Proceedings of the 2012 Heidelberg Symposium on High Energy Gamma-Ray Astronomy. All CTA contributions at arXiv:1211.184