Intersection-union systems

Set systems with union and intersection constraints

Let 2 ≤ d ≤ k be fixed and n be sufficiently large. Suppose that G is a collection of k-element subsets of an n-element set, and |G| > ( n−1 k−1 ) . Then G contains d sets with union of size at most 2k and empty intersection. This verifies a conjecture of the first author for large n.

Intersection and Union Logic

The intersection and the union of the asynchronous systems

The asynchronous systems f are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input u : R → {0, 1} a set of states x ∈ f(u), where x : R → {0, 1}. The intersection of the systems allows adding supplementary conditions in modeling and the union of the systems allows considering the validity of one of two systems...

Introduction to Intersection-union Tests

The Intersection-Union Test (IUT ) has become increasingly popular, especially through its application in bioequivalence testing. Here we will provide a basic introduction and discuss some properties of the IUT . Since this method is based upon a combination of tests, there may be a concern for the need of a multiplicity adjustment to adequately control the overall type-I error rate. We will ad...

Union-Intersection Multiple Comparison Tests

The union-intersection principle yields a class of multiple comparison tests that include the classical Scheffé tests for analysis of variance, and are easily applied to any likelihood ratio test. Examples are given.