The purpose of this note is to present a criterion for an infinite collection of distinct hyperbolic 3-manifolds to be commensurably infinite. (Here, a collection of hyperbolic 3-manifolds is commensurably infinite if it contains representatives from infinitely many commensurability classes.) Namely, such a collection M is commensurably infinite if there is a uniform upper bound on the volumes ...

In this paper we discuss metric cell complexes satisfying a coarse form of 2-dimensional Poincaré duality. We prove that such spaces are either Gromov-hyperbolic or have polynomial growth. As an application we prove that 2-dimensional Poincaré duality groups over commutative rings are commensurable with surface groups.

An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU -rank. Every definable subgroup is commensurable with an acl(∅)definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU -rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU -rank.

We generalize the conditional symmetry model for an I×I×I contingency table with commensurable ordinal classification variables. The new family of models is constructed in such a way so that possesses the usual desirable properties that appear in the similar generalizations of symmetry and marginal homogeneity models, that is connections between the models above obey a coherent structure.

Wang Bi’s work is often used as evidence for “Confucian” interpretations and translations of the Laozi. Those who argue that explicit rejections Confucian values in chapters 5, 18, 19, 38 should actually be read admonishing hollow imitation mere appearance morality cite Bi. Additionally, this great philosopher normally taken a commentator simply sought to synthesize Daoist ideas. In paper, I wi...