We study transverse conformal Killing forms on foliations and prove a Gallot-Meyer theorem for foliations. Moreover, we show that on a foliation with C-positive normal curvature, if there is a closed basic 1-form φ such that ∆Bφ = qCφ, then the foliation is transversally isometric to the quotient of a q-sphere.

The aim of this paper is to introduce the concepts of fuzzy strong h-ideals and fuzzy congruences of hemirings. The quotient hemirings via fuzzy strong h-ideals are investigated. The relationships between fuzzy congruences and fuzzy strong h-ideals of hemirings are discussed. Pay attention to an open question on fuzzy congruences. Finally, the normal fuzzy strong h-ideals of hemirings are explo...

Let X be a projective normal toric variety and T0 a rank one subtorus of the defining torus of X. We show that the normalization of the Chow quotient X//T0, in the sense of Kapranov-Sturmfels-Zelevinsky, coarsely represents the moduli space of stable log maps to X with discrete data given by T0 ⊂ X.