On d=4,5,6 Vacua with 8 Supercharges

We show how all known N=2, d=4,5,6 maximally supersymmetric vacua (Hpp-waves and aDSxS solutions) are related through dimensional reduction/oxidation preserving all the unbroken supersymmetries. In particular we show how the N=2, d=5 family of vacua (which are the near-horizon geometry of supersymmetric rotating black holes) interpolates between aDS_2xS^3 and aDS_3xS^2 in parameter space and how it can be dimensionally reduced to an N=2, d=4 dyonic Robinson-Bertotti solution with geometry aDS_2xS^2 and oxidized to an N=2, d=6 solution with aDS_3xS^3 geometry (which is the near-horizon of the self-dual string).Comment: Latex2e, 19 pages, 1 figure. v2: typos corrected, refs. added. v3: very minor corrections, more refs. added, version to be published in Classical and Quantum Gravit

Distortion maps for genus two curves

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g. In this paper we prove that distortion maps always exist for supersingular curves of genus g>1 and we construct distortion maps in genus 2 (for embedding degrees 4,5,6 and 12).Comment: 16 page

Failure-rate computations based on Mariner Mars 1969 spacecraft data

An analysis of in-flight spacecraft part hours and failure data from the Mariner Mars 1969 Project is given. It contains failure rates computed from this data for all electronic and electromagnetic parts on the Mariners 6 and 7 spacecraft. Also included are failure rates based on combining flight data from Mariners 4,5,6, and 7

Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions II -- Asymptotically AdS Topological Black Holes --

We study asymptotically AdS topological black hole solutions with k=0 (plane symmetric) in the Einstein gravity with Gauss-Bonnet term, the dilaton and a "cosmological constant" in various dimensions. We derive the field equations for suitable ansatz for general D dimensions. We determine the parameter regions including dilaton couplings where such solutions exist and construct black hole solutions of various masses numerically in D=4,5,6 and 10 dimensional spacetime with (D-2)-dimensional hypersurface of zero curvature.Comment: 24 pages, 8 figures, PTPTeX, typos correcte

Double-logarithms in Einstein-Hilbert gravity and supergravity

We study the interplay between graviton reggeization and double-logarithmic in energy contributions to four-graviton scattering in theories with and without supersymmetry. Predictions to all orders in the gravitational coupling are given for these double-logarithms. As the number of supersymmetries grows these terms generate a convergent behaviour for the amplitudes at very high energies. At two-loop level, we find agreement with previous exact results for N=8 supergravity and with those of Boucher-Veronneau and Dixon, who studied the N=4,5,6 supergravities using a conjectured double-copy structure of gravity