A graph property G is a collection of graphs closed under isomorphism. G is said to be evasive if, for every possible local search strategy, there is at least one graph for which membership in G cannot be decided until the entire graph has been searched. Most graph properties that one can think of, but not all, turn out to be evasive. A conjecture of Aanderaa, Karp and Rosenberg asserts that ev...

Let (X, d) be a complete partially ordered cone metric space, g : X → X and F : X × X × X → X be two mappings. In this paper, a new concept of F having the mixed comparable property with respect to g is introduced and some tripled coincidence point results of F and g are obtained if F has the mixed comparable property with respect to g and some other natural conditions are satisfied. Moreover, ...

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...

We propose a general model of local property reconstruction. Suppose we have a function f on domain Γ, which is supposed to have a particular property P, but may not have the property. We would like a procedure which produces a function g that has property P and is close to f (according to some suitable metric). The reconstruction procedure, called a filter, has the following form. The procedur...

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...