The concept of informational independence plays a key role in most knowledge-based systems. J. Pearl and his co-researchers have analysed the basic properties of the concept and have formulated an axiomatic system for informational independence. This axiomatic system focuses on independences among mutually disjoint sets of variables. We show that in the context of probabilistic independence a f...

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current understanding are indicated.

We find normal forms for parabolic Monge-Ampère equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation for such integrals; restricted to the analytic case, this equation is shown to have solutions. The other normal forms exhaust the different classes of parabolic Monge-Ampère equations with symmetry p...