Star product formula of theta functions

As a noncommutative generalization of the addition formula of theta functions, we construct a class of theta functions which are closed with respect to the Moyal star product of a fixed noncommutative parameter. These theta functions can be regarded as bases of the space of holomorphic homomorphisms between holomorphic line bundles over noncommutative complex tori.Comment: 12 page

Are advanced economies at risk of falling into debt traps?

The gross general government debt-to-GDP ratios in many advanced economies have reached the highest levels in peacetime history and continue to grow, putting into question sovereign solvency in these economies. In case of new adverse shocks, whether economic or political, global or country-specific, which result in the deterioration of growth prospects or higher real interest rates, or both, the situation could easily get out control. Apart from the risk of sovereign default, excessive public debt might also have a negative impact on the stability of financial sector and on economic growth in the medium and long term. Debt sustainability simulations for the group of highly-indebted advanced economies - those in which the general government gross public debt-to-GDP ratio exceeded 80 percent in 2015 - suggest that benefits of the current record-low interest rates and post-crisis growth recovery should be used for fiscal consolidation. The aim of this should be not only to stop further expansion of debt-to-GDP ratios, but also to gradually reduce them. Such corrective measures are needed in six out of seven G7 members (Germany being the exception) and in 10 out of 19 euro-area members. The fiscal situation of Japan, where gross debt has reached 250 percent of GDP, is particularly precarious. In addition, unless there are reforms of public pension, health and long-term care systems, fiscal consolidation in advanced economies must also create room for the higher spending levels in these areas that will result from aging populations

Easy 4G/LTE IMSI Catchers for Non-Programmers

IMSI Catchers are tracking devices that break the privacy of the subscribers of mobile access networks, with disruptive effects to both the communication services and the trust and credibility of mobile network operators. Recently, we verified that IMSI Catcher attacks are really practical for the state-of-the-art 4G/LTE mobile systems too. Our IMSI Catcher device acquires subscription identities (IMSIs) within an area or location within a few seconds of operation and then denies access of subscribers to the commercial network. Moreover, we demonstrate that these attack devices can be easily built and operated using readily available tools and equipment, and without any programming. We describe our experiments and procedures that are based on commercially available hardware and unmodified open source software

Reflected Iron Line From a Source Above a Kerr Black Hole Accretion Disc

In this paper we present a fully relativistic approach to modelling both the continuum emission and the reflected fluorescent iron line from a primary X-ray source near a Kerr black hole. The X-ray source is located above an accretion disc orbiting around the black hole. The source is assumed to be a static point source located on an arbitrary position above the disc, on or off the axis of rotation. We carry out Monte Carlo simulations in order to estimate the iron line spectrum as well as its equivalent width. Because of the gravitational lensing effect, an enhancement of the iron line is expected when the primary source is located close to the central black hole. We find that for a source located on the axis of rotation the enhancement is relatively modest. An observer at inclination 30 degrees would measure an equivalent width of ~300eV in the extreme case of a maximally rotating black hole and a source located at height 1.5 gravitational radius from the centre. This corresponds to an equivalent width enhancement factor of about 2 compared to the classical value where no lensing effect comes into play. However, when allowing the source to be located off the axis of rotation, much stronger enhancement can be obtained. In the extreme case of a maximally rotating black hole and a source located just above the approaching side of the disc, an observer at inclination 30d egrees could measure an equivalent width as high as ~1.5 keV (i.e. ~10 times the classical value). We also find that observers located at high inclination angles observe a stronger line than observers at low inclination angles.Comment: 11 pages, 13 figures. Submitted to Monthly Notices of the Royal Astronomical Society (MNRAS

Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces

We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.Comment: Latex, 10 page

The 3D Spin Geometry of the Quantum Two-Sphere

We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus on the quantum group SU_q(2). We use a frame bundle approach to give an explicit description of the space of forms on S^2_q and its associated spin geometry in terms of a natural spectral triple over S^2_q. We equip this spectral triple with a real structure for which the commutant property and the first order condition are satisfied up to infinitesimals of arbitrary order.Comment: v2: 25 pages; minor change