Current merging methods for stratified knowledge bases are often based on the commensurability assumption, i.e. all knowledge bases share a common scale. However, this assumption is too strong in practice. In this paper, we propose a family of operators to merge stratified knowledge bases without commensurability assumption. Our merging operators generalize the quota operators, a family of impo...

We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne– Mostow, and fell into 9 commensurability classes. Our groups produce 5 new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for construc...

Miranda and Umbriel have passed through the 3 : 1 mean-motion commensurability if the specific dissipation function (Q) of Uranus is less than about 39,000. There are three second-order inclination resonances associated with this commensurability. Temporary capture into either of the resonances involving the orbital inclination of Miranda can account for the anomalously high (--4*) current incl...