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...

in the present paper, we introduces the notion of integral type contractive mapping with respect to ordered s-metric space and prove some coupled common fixed point results of integral type contractive mapping in ordered s-metric space. moreover, we give an example to support our main result.

The subject is the overview of the use of quasi-entropy in finite dimensional spaces. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone m...

Given a property P of graphs, write Pn for the set of graphs with vertex set [n] having property P. We call |Pn| the speed of P. Recent research has shown that the speed of a monotone or hereditary property P can be a constant, polynomial, or exponential function of n, and the structure of the graphs in P can then be well described. Similarly, |Pn| can be of the form n(1−1/k+o(1))n or 2(1−1/k+o...

A metric space (X, d) is called c-monotone if there is a linear order < on X and c > 0 such that d(x, y) 6 c d(x, z) for all x < y < z in X. A brief account of investigation of monotone spaces including applications is presented. 1 Monotone and σ-Monotone Spaces. In [6] I investigated existence of sets in Euclidean spaces that have large Hausdorff dimension and yet host no continuous finite Bor...

We give a result on existence of periodic orbits for autonomous differential systems with arbitrary finite dimension. It is based on a Poincaré-Bendixson property enjoyed by a new class of monotone systems introduced in L. A. Sanchez, Cones of rank 2 and the PoincaréBendixson property for a new class of monotone systems, Journal of Differential Equations 216 (2009), 1170-1190. A concrete applic...

Monotone Lévy processes with additive increments are defined and studied. It is shown that these processes have natural Markov structure and their Markov transition semigroups are characterized using the monotone Lévy-Khintchine formula. 17 Monotone Lévy processes turn out to be related to classical Lévy processes via Attal's " remarkable transformation. " A monotone analogue of the family of e...