An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove th...

Recent research (Reardon and Firebaugh, 2002, Frankel and Volij, 2009, and Mora and RuizCastillo, 2009a) has shown that two entropy-based segregation indices possess an appealing mixture of basic and subsidiary but useful properties. It would appear that the only fundamental difference between the mutual information, or M index, and the Entropy, Information or H index, is that the second is a n...

We consider the Multilinear set S defined as the set of binary points (x, y) satisfying a collection of multilinear equations of the form yI = ∏ i∈I xi, I ∈ I, where I denotes a family of subsets of {1, . . . , n} of cardinality at least two. Such sets appear in factorable reformulations of many types of nonconvex optimization problems, including binary polynomial optimization. A great simplifi...

For any C-algebra A let A denote the set of all positive elements in A. A state on a unital C-algebra A is a linear functional ω : A → C such that ω(a) ≥ 0 for every a ∈ A and ω(I) = 1 where I is the unit of A. By S(A) we will denote the set of all states on A. For any Hilbert space H we denote by B(H) the set of all bounded linear operators on H . A linear map φ : A → B between C-algebras is c...