This paper surveys some recent results on the generation of implicitly given hypergraphs and their applications in Boolean and integer programming, data mining, reliability theory, and combinatorics. Given a monotone property π over the subsets of a finite set V , we consider the problem of incrementally generating the family Fπ of all minimal subsets satisfying property π, when π is given by a...

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand 2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok, 10400, Thailand Abstract In this paper, we establish some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings having the mixed monotone property in par...

We extend the recent results of coupled coincidence point theorems of Shatanawi et. al. (2012) by weakening the concept of mixed g-monotone property. We also give an example of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by the results of Shatanawi et. al. but can be applied to our results. The main results extend and unify the results of ...

This paper considers a particular relationship defined over pairs of n-argument monotone Boolean functions. The relationship is of interest since we can show that if ( g, h ) satisfy it then for any n-argument monotone Boolean function f there is a close relationship between the combinational and monotone network complexities of the function (f /\ g) \/ h. We characterise the class of pairs of ...

In this paper, we show the existence of a coupled fixed point theorem of nonlinear contraction mappings in complete metric spaces without the mixed monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled fixed point by using the mixed monotone property. We also study the necessary condition for the uniqueness of a coupled fix...

We prove a lower bound of (n4/3 log1/3 n) on the randomized decision tree complexity of any nontrivial monotone n-vertex graph property, and of any nontrivial monotone bipartite graph property with bipartitions of size n. This improves the previous best bound of(n4/3) due to Hajnal [Haj91]. Our proof works by improving a graph packing lemma used in earlier work, and this improvement in turn s...

We study tent spaces on general measure spaces (Ω, μ). We assume that there exists a semigroup of positive operators on Lp(Ω, μ) satisfying a monotone property but do not assume any geometric/metric structure on Ω. The semigroup plays the same role as integrals on cones and cubes in Euclidean spaces. We then study BMO spaces on general measure spaces and get an analogue of Fefferman’s H1-BMO du...

This paper studies monotonicity and convexity properties of option prices in jump-diffusion models. In such models it is possible for a monotone contract function to give rise to an option price which is non-monotone in the underlying asset. This is connected to the fact that the no-crossing property, which holds for one-dimensional diffusions, may fail in the presence of jumps. We present a si...

As a corollary of the main resu!t of this paper (Theorem i) we show that if ~ i~ not S-dense, then I~[ ~< 1~ s [. This contains as special cases the results of Sauer [4] and Perles and Shelab [5], and of Karpovski and Milman [3]. Before stating Theorem l, we need one more definition; ~ c 3~ is monotone if f ¢ ~ , g e 3 ~ and f ~ g imply g ¢ ~ . Note ~.hat ~ s is monotone and that a monotone fam...