The aim of this paper is to study the actions of the groups on lattices and to give some connections between the structure of a group and the structure of its subgroup lattice. Moreover, we shall introduce the concept of direct ∨-sum of G-sublattices and we shall present a generalization of a result about finite nilpotent groups. 1 Preliminaries Let (G, ·, e) be a monoid and L be a G–set (relat...

In a recent paper in Journal of Convex Analysis the authors studied, in non-reflexive Banach spaces, a class of maximal monotone operators, characterized by the existence of a function in Fitzpatrick’s family of the operator which conjugate is above the duality product. This property was used to prove that such operators satisfies a restricted version of Brøndsted-Rockafellar property. In this ...

A family F ⊆ 2[n] saturates the monotone decreasing property P if F satisfies P and one cannot add any set to F such that property P is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the k-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of l-sets and (l + 1)-sets.

A monotone drawing of a graph G is a straight-line drawing of G such that, for every pair of vertices u,w in G, there exists a path Puw in G that is monotone in some direction luw. (Namely, the order of the orthogonal projections of the vertices of Puw on luw is the same as the order they appear in Puw.) The problem of finding monotone drawings for trees has been studied in several recent paper...

In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uni...

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

On-line models assume a player, A (randomized or deterministic), who makes immediate responses to incomming elements of an input sequence s = a 1 : : :a r. In this paper we study the case, when the response for every a i is a single bit, which is interpreted as pick/not-to-pick. The player's objective is to pick as many elements as possible under the condition, that the set of picked elements, ...

We recall and reformulate certain known constructions, in order to make a convenient setting for obtaining generalized monotone-light factorizations in the sense of A. Carboni, G. Janelidze, G. M. Kelly and R. Paré. This setting is used to study the existence of monotone-light factorizations both in categories of simplicial objects and in categories of internal categories. It is shown that ther...

The theory of monotone dynamical systems has been found very useful in the modeling of some gene, protein, and signaling networks. In monotone systems, every net feedback loop is positive. On the other hand, negative feedback loops are important features of many systems, since they are required for adaptation and precision. This paper shows that, provided that these negative loops act at a comp...

Mixed monotone systems form an important class of nonlinear systems that have recently received attention in the 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 systems...