This article proves the existence of an infinite number of radial solutions of Δu+K(r)ƒ(u) = 0, one with exactly n zeros for each nonnegative integer n on the exterior of the ball of radius R > 0, Bʀ, centered at the origin in ℝᴺ with u = 0 on ∂Bʀ and limᵣ→∞u(r) = 0 where N > 2, f is odd with ƒ < 0 on (0; β), ƒ > 0 on (β;∞), ƒ(u) ~ uᵖ with 0 < p < 1 for large u and K(r) ~ r-α with 0 < α < 2 for large r.

Article discusses IslandCafe, a proposed method for genomic island detection.

Article describes how the authors plant to deal with orientation preserving homeomorphisms and, more specifically, diffeomorphisms of the unit circle S1. By employing the recurrence method worked out in Pawelec the authors provide effective lower estimates of the proper-dimensional Hausdorff measure of minimal sets of circle homeomorphisms that are not conjugate to any rotation.