ar X iv : m at h / 06 08 26 5 v 1 [ m at h . A G ] 1 0 A ug 2 00 6 COUNTEREXAMPLE TO THE HODGE CONJECTURE

ar X iv : h ep - e x / 00 08 06 5 v 1 2 6 A ug 2 00 0 Search for Large Extra Dimensions in Dielectron and Diphoton Production

ar X iv : m at h / 06 08 37 7 v 1 [ m at h . R T ] 1 5 A ug 2 00 6 ALGEBRAS OF DERIVED DIMENSION ZERO

ar X iv : m at h / 06 08 73 5 v 1 [ m at h . C O ] 2 9 A ug 2 00 6 SUFFICIENT CONDITIONS FOR LABELLED 0 – 1 LAWS

Exponentiating a power series can have the effect of smoothing out the behavior of the coefficients. In this paper we look at conditions on the growth of the coefficients of G(x) = ∑ g(n)x, where g(n) ≥ 0, which ensure that f(n−1)/f(n)→ ∞, where F(x) = e. Useful notation will be f(n) ≺ g(n) for f(n) eventually less than g(n) and f(n) ∈ RT∞ for f(n− 1)/f(n) → ∞; the notation RT stands for the ra...

ar X iv : h ep - p h / 06 08 05 0 v 1 4 A ug 2 00 6 Percolation and high energy cosmic rays above 10 17 eV

ar X iv : m at h / 05 08 06 6 v 1 [ m at h . N T ] 3 A ug 2 00 5 MULTIPLE POLYLOGARITHMS , POLYGONS , TREES AND ALGEBRAIC CYCLES

We construct, for a field F and a natural number n, algebraic cycles in Bloch's cubical cycle group of codimension n cycles in P 1 F \{1} 2n−1 , which correspond to weight n multiple polylogarithms with generic arguments if F ⊂ C. Moreover, we construct out of them a Hopf subalgebra in the Bloch-Kriz cycle Hopf algebra χ cycle. In the process, we are led to other Hopf algebras built from trees ...