In this paper, we introduce a new class of monotone operators − (H(·, ·), η)monotone operators, which generalize many existing monotone operators. The resolvent operator associated with an (H(·, ·), η)monotone operator is defined and its Lipschitz continuity is presented. As an application, we also consider a new generalized mixed variational inclusion involving (H(·, ·), η)-monotone operators ...

Given a monotone property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in Pn and the functions |Pn|. We also examine the measure eP (n), the maximum number of edges in a graph of Pn.

Absac A graph property is called elusive (or evasive) if every algorithm for testing this property has to read in the worst case Q) entries of the adjacency matrix of the given graph. Several graph properties have been shown to be elusive, e.g. planarity [2] or fc-colorability [4]. A famous conjecture of Karp [11] says that every non-trivial monotone graph property is elusive. We prove that a n...

Let R be an expansion of a dense linear order (R,<) without endpoints having the intermediate value property, that is, for all a, b ∈ R, every continuous (parametrically) definable function f : [a, b] → R takes on all values in R between f(a) and f(b). Every expansion of the real line (R, <), as well as every o-minimal expansion of (R,<), has the intermediate value property. Conversely, some ni...

Given a set P of n planar points, two axes and a realvalued score function f() on subsets of P , the Optimal Planar Box problem consists in finding a box (i.e. an axis-aligned rectangle) H maximizing f(H ∩ P ). We consider the case where f() is monotone decomposable, i.e. there exists a composition function g() monotone in its two arguments such that f(A) = g(f(A1), f(A2)) for every subset A ⊆ ...

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...

In this paper we study some monotone behavior of the residual (past) entropy of order . We prove that, under some relation between the hazard rates (reversed hazard rates) of two distributions functions F and G, when the residual (past) entropy of order of F is decreasing (increasing) then the residual (past) entropy of G is decreasing (increasing). Using this, several conclusions regarding mo...

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...

Given a graph G, a k-dominating set of G is a subset S of its vertices with the property that every vertex of G is either in S or has at least k neighbors in S. We present a new incremental local algorithm to construct a k-dominating set. The algorithm constructs a monotone family of dominating sets D1 ⊆ D2 . . . ⊆ Di . . . ⊆ Dk such that each Di is an i-dominating set. For unit disk graphs, th...