Finding ECM-friendly curves through a study of Galois properties

In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM

Phase Diagram of Vertically Shaken Granular Matter

A shallow, vertically shaken granular bed in a quasi 2-D container is studied experimentally yielding a wider variety of phenomena than in any previous study: (1) bouncing bed, (2) undulations, (3) granular Leidenfrost effect, (4) convection rolls, and (5) granular gas. These phenomena and the transitions between them are characterized by dimensionless control parameters and combined in a full experimental phase diagram.Comment: 11 pages, 14 figures, submitted to "Physics of Fluids

The importance of reallocation for productivity growth: Evidence from European and US banking

To what extent has input reallocation contributed to aggregate productivity growth in the banking sectors of Europe and the United States? Interestingly, under-performing banks capture market share, while more productive banks lose market share, in particular in the US. The pattern of reallocation is markedly different between the geographical regions: European productivity has grown by reallocating inputs through the first half of the sample period, at the same time when reallocation diminished growth in the US. The long-run positive effects of creative destruction are especially apparent in the US, where reallocation is an important driver of increases in productivity

Trivariate polynomial approximation on Lissajous curves

We study Lissajous curves in the 3-cube that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications could arise in theframework of Lissajous sampling for MPI (Magnetic Particle Imaging)