The Symmetric Tensor Approximation problem (STA) consists of approximating a symmetric tensor or homogeneous polynomial by linear combination rank-1 tensors powers forms low rank. We present two new Riemannian Newton-type methods for rank approximation with complex coefficients. first method uses the parametrization set at most r weights and unit vectors. Exploiting properties apolar product on...

N = (1, 0) supergravity in six dimensions admits AdS3 × S 3 as a vacuum solution. We extend our recent results presented in hep-th/0212323, by obtaining the complete N = 4 Yang-Mills-Chern-Simons supergravity in D = 3, up to quartic fermion terms, by S3 group manifold reduction of the six dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simon...

We calculate the low-lying part of the spectrum of the Z3-symmetrical chiral Potts quantum chain in its self-dual and integrable versions, using numerical diagonalisation of the hamiltonian for N ≤ 12 sites and extrapolation N → ∞. From the sequences of levels crossing we show that the massive phases have oscillatory correlation functions. We calculate the wave vector scaling exponent. In the h...

Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in discrete time, allowing only for single crossovers. While the analogous dynamics in continuous time admits a closed solution (Baake and Baake in Can J Math 55:3-41, 2003), this no longer works for discrete time. A more general model (i.e. without th...