The theory of monotone Riemannian metrics on the state space of a quantum system was established by Dénes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant – monotone – metric can be interpreted as an average statistical uncertainty. The present paper contributes to this subject. It is reasonable to expect that states which are more mixed are less d...

This paper deals with a new family of (A, N)-implications that derived from fuzzy negation and continuous monotone function, and some properties, like the left neutrally, the exchange principle, the ordering property and the laws of contraposition, of the proposed family of (A, N)-implications are studied. Moreover, the T-conditionality and the Modus tollens for the new family of (A, N)-i...

Mixed monotone systems form an important class of nonlinear systems that have recently received attention in abstraction-based control design area. Slightly different definitions exist in the literature, and it remains a challenge to verify mixed monotonicity of a system in general. In this paper, we first clarify the relation between different existing definitions of mixed monotone system, and...

Generator is a concise representation for frequent itemset. And it has the anti-monotone property as the frequent itemset does, which is an important property in real applications. But when itemsets are attached with weights to balance importances between themselves, the anti-monotone property of generator may not hold. Additionally generator with weight may become tough to be dealt with in man...

and Applied Analysis 3 Proposition 2.2 see 2 . Let X,G be a G-metric space and xn a sequence in X. Then, for all x ∈ X, the following statements are equivalent: i xn is G-convergent to x, ii G xn, xn, x → 0 as n → ∞, iii G xn, x, x → 0 as n → ∞, iv G xn, xm, x → 0 as n,m → ∞. Proposition 2.3 see 2 . Let X,G be a G-metric space and xn a sequence in X. Then, the following statements are equivalen...