Around 1970 Griffiths introduced the moduli of polarized Hodge structures/the period domain D and described a dream to enlarge D to a moduli space of degenerating polarized Hodge structures. Since in general D is not a Hermitian symmetric domain, he asked for the existence of a certain automorphic cohomology theory for D, generalizing the usual notion of automorphic forms on symmetric Hermitian...

We consider ergodic coherent MIMO channels. We characterize the optimal input distribution for various fading matrix distributions. First, we describe how symmetries in the fading matrix distribution are preserved as symmetries in the optimal input covariance and thus yield to specification of the optimal input. We will see that group structures and notion of commutant appear as key elements. S...

A para-Kähler manifold can be defined as a pseudoRiemannian manifold (M, g) with a parallel skew-symmetric paracomplex structures K, i.e. a parallel field of skew-symmetric endomorphisms with K = Id or, equivalently, as a symplectic manifold (M, ω) with a bi-Lagrangian structure L, i.e. two complementary integrable Lagrangian distributions. A homogeneous manifold M = G/H of a semisimple Lie gro...

We introduce the concept of para-Hopf algebroid and define their cyclic cohomology in the spirit of Connes-Moscovici cyclic cohomology for Hopf algebras. Para-Hopf algebroids are closely related to, but different from, Hopf algebroids. Their definition is motivated by attempting to define a cyclic cohomology theory for Hopf algebroids in general. We show that many of Hopf algebraic structures, ...

The title compound, C(72)F(36), is one of four isomers of C(60)(CF(3))(12) for which crystal structures have been obtained. The fullerene mol-ecule has an idealized I(h) C(60) core with the 12 CF(3) groups arranged in an asymmetric fashion on two ribbons of edge-sharing C(6)(CF(3))(2) hexa-gons, a para-meta-para-para-para-meta-para ribbon and a para-meta-para ribbon, giving an overall pmp(3)mp,...