Quantum discord, a measure of genuinely quantum correlations, is generalized to continuous variable systems. For all two-mode Gaussian states, we calculate analytically the quantum discord and a related measure of classical correlations, solving an optimization over all Gaussian measurements. Almost all two-mode Gaussian states are shown to have quantum correlations, while for separable states,...

We construct a smoothly bounded pseudoconvex domain such that every boundary point has a p.s.h. peak function but some boundary point admits no (local) holomorphic peak function.

Type FPs A group Γ is of type FPs if Z, regarded as a ZΓ–module via the trivial action, admits a partial projective resolution Ps → Ps−1 → · · · → P1 → P0 → Z→ 0 by finitely generated ZΓ–modules Pi . Every group is of type FP0 . Type FP1 is equivalent to the property of finite generation. Every finitely-presented group is of type FP2 , but Bestvina–Brady showed the converse does not hold in gen...

Let G be a Lie group and let X be a space. It is believed that G and X are strongly related if there is a proper action of G on X, especially if the orbit space G\X is compact. The paper makes explicit one such relation, namely non-compact dimension. For a field k and a locally compact space X we call nc(X ; k) = inf {/: H'C(X ;k) ^ 0} the non-compact dimension of X (see §2). Let us fix a field...

A classification is given of all spreads in PGð3; qÞ, q 1⁄4 2 , whose associated translation planes admit linear collineation groups of order qðqþ 1Þ.