23 5 v 1 2 6 A pr 2 00 0 1 Mathematics for structure functions NIKHEF - 00 - 008

ar X iv : g r - qc / 0 61 10 19 v 2 1 8 D ec 2 00 6 NIKHEF / 2006 - 008 HIGHER DIMENSIONAL V SI SPACETIMES

We present the explicit metric forms for higher dimensional vanishing scalar invariant (V SI) Lorentzian spacetimes. We note that all of the V SI spacetimes belong to the higher dimensional Kundt class. We determine all of the V SI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III....

ar X iv : h ep - t h / 07 03 25 6 v 1 2 8 M ar 2 00 7 NIKHEF / 2007 - 008 VANISHING SCALAR INVARIANT SPACETIMES IN SUPERGRAVITY

We show that the higher-dimensional vanishing scalar invariant (VSI) spacetimes with fluxes and dilaton are solutions of type IIB supergravity, and we argue that they are exact solutions in string theory. We also discuss the supersymmetry properties of VSI spacetimes. [PACS: 04.20.Jb, 04.65.+e]

ar X iv : 0 90 4 . 23 13 v 1 [ m at h . FA ] 1 5 A pr 2 00 9 A DISCRETIZED APPROACH TO W . T . GOWERS ’ GAME

We give an alternative proof of W.T. Gowers' theorem on block bases in Banach spaces by reducing it to a discrete analogue on specific count-able nets.

ar X iv : n uc l - th / 0 50 40 62 v 1 2 1 A pr 2 00 5 1 Structure of 8 B and astrophysical S 17 factor

Preconditioning Legendre Spectral Collocation Approximations to Elliptic Problems

This work deals with the H1 condition numbers and the distribution of the ~ N;Msingular values of the preconditioned operators f~ 1 N;M WN;M ÂN;Mg. ÂN;M is the matrix representation of the Legendre Spectral Collocation discretization of the elliptic operator A de ned by Au := u + a1ux + a2uy + a0u in (the unit square) with boundary conditions: u = 0 on 0; @u @ A = u on 1. ~ N;M is the sti ness ...