Volume 20, Issue 4

We prove that a bounded Reinhardt domain of ℂ n +1 with C 2 boundary of constant Levi curvature with rotational symmetry in two complementary sets of variables is a ball. 2000 Mathematics Subject Classification: 53A07, 53O42; 35J70, 35B50, 32T99.

Sharp extensions of Pitt's inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include Hardy-Rellich inequalities. 2000 Mathematics Subject Classification: 58J70, 42B10, 35A15.

If the nilradical 𝔫(𝔤) of the Lie algebra 𝔤 of a pro-Lie group G is finite dimensional modulo the center 𝔷(𝔤), then every identity neighborhood U of G contains a closed normal subgroup N such that G/N is a Lie group and G and N × G/N are locally isomorphic. 2000 Mathematics Subject Classification: 22E65, 17B65, 22A05; 22E15, 22E60, 22E25, 22D05.

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a 2-functor on the groupoid-enriched category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of ( n - 1)-connected ( n + 1)-types for n ≥ 0. 1991 Mathematics Subject Classification: 18D05, 55Q25, 55S45.

We prove the Calderón-Zygmund–type estimates for nonlinear subelliptic systems with quadratic growth, of the type with | A ( z , ξ)| ≈ L (1 + |ξ|), where is the horizontal gradient on Heisenberg group. 2000 Mathematics Subject Classification: 35H20; 35B65.

In this article we study extensions of ℤ 2 -graded L ∞ algebras on a vector space of two even and one odd dimension. In particular, we determine all extensions of a super Lie algebra as an L ∞ algebra. Our convention on the parities is the opposite of the usual one, because we define our structures on the symmetric coalgebra of the parity reversion of a space. 2000 Mathematics Subject Classification: 14D15, 13D10, 14B12, 16S80, 16E40, 17B55, 17B70.

The explicit construction of infinite families of d -regular graphs which are Ramanujan is known only in the case d – 1 is a prime power. In this paper, we consider the case when d – 1 is not a prime power. The main result is that by perturbing known Ramanujan graphs and using results about gaps between consecutive primes, we are able to construct infinite families of “almost” Ramanujan graphs for almost every value of d . More precisely, for any fixed ɛ > 0 and for almost every value of d (in the sense of natural density), there are infinitely many d -regular graphs such that all the non-trivial eigenvalues of the adjacency matrices of these graphs have absolute value less than (2 + ɛ) . 2000 Mathematics Subject Classification: 05C50, 15A18, 11N05, 11F30.

Let F ( t ) be the function field in one variable over the finite field F . We construct a surjective cellular cover γ : 𝒢 → PSL(3, F ( t )), where 𝒢 = G ○ E , G = St(3, F ( t )), E = Ext(ℚ/ℤ K͂ 2 ( F ( t ))) and G ○ E is the commuting product with G ∩ E = K͂ 2 ( F ( t )). Here K͂ 2 ( F ( t )) is the kernel of St(3, F ( t )) ↠ PSL(3, F ( t )). Since 𝒢/[𝒢, 𝒢] ≅ E /K͂ 2 ( F ( t )) is a nontrivial torsion free divisible abelian group, this gives a negative answer to a question raised in the paper “Cellular covers of groups” (J. Pure and Applied Algebra 208 (2007)), by E. Farjoun, R. Göbel and the author. We asked whether a surjective cellular cover of a perfect group is perfect. 2000 Mathematics Subject Classification: 19C09, 55P60.