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Conventional solutions to the strong CP problem all require the existence of global symmetries. However quantum gravity may destroy global symmetries, making it hard to understand why the electric dipole moment of the neutron (EDMN) is so small. We suggest here that CP is actually a discrete gauge symmetry, and is therefore not violated by quantum gravity. We show that four dimensional CP can a...

We present an extension of the “miraculous cancellation” formulas of Alvarez-Gaumé, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. Relations to the Ochanine congruence formula on 8k + 4 dimensional Spinc manifolds are discussed. To cite this article: F. Han, W. Zhang, C. R. Acad. Sci. Paris, Ser. I 336 (2003).  2003 Académie des sciences. Published b...

We report the first likely detections of erupting Dwarf Novae (DN) in an external galaxy: the Large Magellanic Cloud. Six candidates were isolated from approximately a million stars observed every second night over 11 nights with the CTIO 8K × 8K Mosaic2 CCD imager. Artificial dwarf nova and completeness tests suggest that we are seeing only the brightest of the LMC DN, probably SS Cygni-like C...

How will you watch your next TV programme? Will it be on a small phone screen, a head-up display, a tablet, an old CRT TV, a PC monitor, a modern HDTV display, a projector, a 4K or an 8K UHDTV display? And where will the content have come from? A mobile phone video, an old SD TV drama, an HDTV production studio, a digital film master, or a 4K or 8K camera? We rightly expect seamless transfer of...

For all integers $k>0$, we prove that the hypergeometric function \[ \widehat {I}_k(\alpha )=\sum _{j=0}^\infty \frac {\bigl ((8k+4)j\bigr )!j!}{(2j)!\bigl ((2k+1)j\bigr )!^2 \bigl ((4k+1)j\bigr )!} \ \alpha ^j \] is a period of pencil curves genus $3k+1$. We $\widehat {I}_k$ generating Gromov–Witten invariants family anticanonical del Pezzo hypersurfaces $X=X_{8k+4} \subset \mathbb {P}(2,2k+...

Denote by ’ the set of all real symmetric matrices. We use to 8 ‚ 8 K L K ž L a b denote that is positive semidefinite (definite). For or K  L M œ > ß > c d ! 0 Ё_ß > Ó 0 and \ œ P Mß 8 ‚ 8 V \ 8‚8 or ’ _ , denote by the space of all bounded and measurable a b functions from to and by the space of all with M \ P Mß T − P Mß "ß_ _ a b a b \ \ T − P Mß P Mß − P Mß w _ _ _ 8 a b a b a b \ E − V ...

A threshold scheme is a system that protects a secret (key) among a group of participants in such a way that it can only be reconstructed from the joint information held by some predetermined number of these participants. In this paper we extend this problem to one where there is more than one secret that participants can reconstruct using the information that they hold. In particular we consid...