A signed graph Σ=(G,σ) is a where the function σ assigns either 1 or −1 to each edge of simple G. The adjacency matrix Σ, denoted by A(Σ), defined canonically. In recent paper, Wang et al. extended spectral bounds Hoffman and Cvetković for chromatic number graphs. They proposed an open problem related balanced clique largest eigenvalue graph. We solve strengthened version this problem. As bypro...

A famous result by McKinsey and Tarski ([5] and [6]) provides an interpretation of intuitionistic logic into the modal logic S4. The algebras for S4 are Boolean algebras with an interior operator. One wonders if it is possible to perform a similar construction starting from a logic which is different from classical logic, say a logic extending Full Lambek Calculus FL. The algebraic counterpart ...

70 100 100 100 100 h Discrete: p (n) 1 = 6 12 = 0.5 p (n) 1|1 = 3 3 = 1, p (n) 1|2 = 3 3 = 1, p (n) 1|3 = 0 3 = 0, p (n) 1|4 = 0 3 = 0 Continuous: p (n) 1 = 1 12 (σ(100) + σ(70) + . . .+ σ(−70) + σ(−100)) ≈ 0.5 p (n) 1|1 = 1 3 (σ(100) + σ(70) + σ(100)) ≈ 1 p (n) 1|2 = 1 3 (σ(100) + σ(70) + σ(100)) ≈ 1 p (n) 1|3 = 1 3 (σ(−100) + σ(−70) + σ(−100)) ≈ 0 p (n) 1|4 = 1 3 (σ(−100) + σ(−70) + σ(−100)) ...

Let V be a real vector space of dimension d and V ∗ its dual space. By a cone in V ∗ we will always mean a closed polyhedral cone σ with apex 0 such that σ ∩ −σ = {0}. Let Σ be a fan in V ∗, i.e., a collection of cones such that (1) if σ ∈ Σ then any face of σ belongs to Σ, (2) if σ1, σ2 ∈ Σ then σ1 ∩ σ2 is a face in both. We will assume that Σ is complete, that is ∪Σ = V ∗. The elements of Σ a...